ML20245H329
| ML20245H329 | |
| Person / Time | |
|---|---|
| Site: | Yankee Rowe |
| Issue date: | 10/31/1982 |
| From: | Fernandez R, Ghaus J, Sundaram R YANKEE ATOMIC ELECTRIC CO. |
| To: | |
| Shared Package | |
| ML20245H320 | List: |
| References | |
| YAEC-1300A, NUDOCS 8906290460 | |
| Download: ML20245H329 (140) | |
Text
{{#Wiki_filter:- __ YAEC - 1300 A y-) f RELAP5YA A Computer Program For-l Light-Water Reactor System ; Thermal-Hydraulic Analysis l Volume 1: Code Description By R. Thomas'Fernandez . Ramu K. Sundaram Jamal Ghaus { Ausaf Husain # James N.,Loomis TN Liliane Schor Robert C. Harvey I) Roger Habert S l October 1982 i i i Yankee Atomic Electric Company f ('- ) ' Nuclear Services Division - l 1671 Worcester Road 8906290460 890623 fDR ADOCK 05000029 i PDC . . - _ _ _ _ - _ _ - _ _ _ _ - . . )
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e ' 2. Prepared By: .- u . v./ v.. R. Thomas Fernandez, Principal Engineer (Date) Mn . uhelez Ramu K. Suadaram, Senior Engineer ( Dat'e) fY. JamalGhaus,Egneer (/ am 4 0 aatv /A l=2 ?lN-(Date) lh s .wh ,hw Me (2.f T 2.- Ausaf Husain', Manager (Date)
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l ~. .a . .;, s - Roger Habert , Senior Engineer (Pate) Reviewed By: f. 12.f18f82. Ste pheti P. Schulfuii. Mahlger (Date) Nuclear Evaluations and Support Group Reviewed and Approved By: k s Xd ks Ausaf Husain, }Mnager yu w _tl (Date)
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LOCA Analysis Group y, y VI ,. , Approved By: 'a . t /' l. b . 4 It.( b Il'll '[E Bruce C. Slifer, Manager '(Date) Nuclear Engineerlag Department O
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DISCLAIMER OF RESPONSIBILITY
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) This document was prepared by Yankee Atomic Electric Company for its own use and on behalf of Maine Yankee Atomic Power Corporation, Vermont Yankee Nuclear Power Corporation, and the joint owners of the Seabrook Nuclear Power Station. This document is believed to De completely true and accurate to the best of our knowledge and information. It is authorized for use specifically by Yankee Atomic Electric Company, Maine Yankee Atomic Power Corporation, Vermont Yankee Nuclear Power Corporation, and the joint owners of the Seabrook Nuclear Power Station and/or the appropriate subdivisions within the Nuclear Regulatory Commission only.
With regard to any unauthorized use whatsoever, Yankee Atomic Electric Company, Maine Yankee Atomic Power Corporation, Vermont Yankee Nuclear Power Corporation, and the joint owners of the Seabrook Nuclear Power Station and their officers, directors, agents and employees assume no liability nor make any warranty or representation with respect to the contents of this document or to its accuracy or completeness. g]
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ABSTRACT RELAP5YA, a computer program for Light-Water Reactor System thermal-hydraulic analysis, has been adapted by Yankee Atomic Electric Company for Loss-of-Coolant Accident (LOCA) analyses. RELAP5YA provides a consistent, integral analysis capability of the system and core response to LOCA events and other plant transients. YAEC will use this program as a major part of its method to analyze the entire BWR break spectrum and the PWR small break spectrum in a manner that conforms to U.S. Nuclear Regulatory Commission requirements contained in 10CFR50.46 and Appendix X. This program will also be sed for more realistic analyses of LOCA events and other transients. RELAP5YA has been developed from the RELAPS t1001 code that was originally developed by EG and G Idaho, Inc., under USNRC sponsorship. Subriantial modifications have been made to RELAPS M001 in order to a) extend and improve upon the code simulation capabilities, and b) provide options in RELAP5YA that conform to 10CFR50, Appendix K requirements. These include new models for the calculation of interphase drag in two-phase flow, nucleate boiling heat transfer and critical heat flux, rewet/ quench phenomena and radiation heat transfer. New component models have also been added to predict jet pump behavior in BWRs and accumulator response in PWRs. These modifications enhance the ability of the code to perform realistic (Best-Estimate, BE) analyses of reactor systems. To perform licensing (Evaluation flodel, EM) analyses, the Moody model for two-phase critical flow, lockout options when returning to nucleate and/or transition boiling regimes, and extensive fuel rod behavior models have been incorporated. The fuel behavior models can also be used, with minor modifications, to perform BE calculations. A major feature of the RELAPSYA code is the ability to perfonn BE and EM analyses with very few input alterations. The Ett features have been incorporated as options to the user and can be selected individually or in groups to perform sensitivity studies. This document, the first of three volumes, describes the RELAP5YA computer program. Its focus is primarily on modifications by YAEC to the original RELAPS M001 code. The second volume provides a user's manual for RELAP5YA. The third volume presents an extensive assessment of RELAP5YA l -iv-L____
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' .calcu1'ations compared to..many' separate effect'and. integralitesti results. . This:
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, L thermal-hydraul.ic . phenomena encountered in LWR S.vstem analyses of LOCA events
- 'and other transients.
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TABLE OF CONTENTS Page iii DISCLAIMER OF RESPONSIBILITY..................................... ABSTRACT......................................................... iv TABLE OF C0NTENTS................................................ vi LIST OF FIGURES.................................................. viii LIST OF TABLES................................................... ix ACKN0WLEDGEMENTS................................................. xi N O ME N C LATU R E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1
1.0 INTRODUCTION
1.1 Background................................................. 2 O u tl i n e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 2.0 RELAP SY A LWR SYST EMS ANAL YSIS C0D E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1 Hydrodynamic Mode 1......................................... 25 2.2 Hy dro dy nami c C omp o ne n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.3 Process Mode 1s............................................. 52 2.4 P ro g r am S tr uc tu re . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.0 HY D RO D Y N AM I C t 00 E LS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.1 Interphase Drag............................................ 68 3.2 Moody Two -P h a se C ri tic al F10w. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.3 JetPump................................................... 125 3.4 Accumul ator. . . . . . . . . . . . . . . 160 4.0 HEAT TRANSFER MODELS. . . . . . . . . . . . 176 s 3.0, 4.0, and 5.0 are 4.1 Forced Convective Boiling. Proprietary to Yankee Atomic 176 4.2 Cri tical Heat Flux. . . . . . . . Electric Company and therefore 179 were deleted. 187 4.3 Rewet and Quench.......... 4.4 Multiple Surface Radiation 196 4.5 Heat Transf e r Logi c 0pti on. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 5.0 FUEL BEHAVIOR M0DELS............................................. 214 1 5.1 Mo de l D ev el opme n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . 215 5.1.1 Internal Gas Pressure.............................. 215 5.1.2 De fo rma ti on and Ruptu re . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 5.1.3 Ga p He a t Tra n s fe r. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 5.1.4 Zi rc al oy-Wa te r Re ac tio n. . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
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LIST OF FIGURES Number Title Page O 3.1-1 RELAP5YA Flow Regime Map for Vertical Flow (VRT) 105 3.1-2 Variation of Key Parameters in the Bubbly Flow Regime 106 with Void Fraction 3.1-3 Simplified Logic Diagram of FUNCTION FIBUB1 107 3.1-4 Simplified Logic Diagram of FUNCTION FISLG 108 3.1-5 Simplified Logic Diagram of FUNCTION FIANN1 109 3.1-6 Simplified Logic Diagram of FUNCTION FIMIST 110 3.1-7 Variation of Interphase Drag with Void Fraction 111 3.1-8 Variation of Phase Relative Velocity witn Void Fraction 112 3.2-1 Logic for Moody Critical Flow Model 124 3.3-1 Jet Pump Components and Axial Pressure Profile 156 3.3-2 Jet Pump Model 157 3.3-3 Positive Drive; tJormalized Pressure Drop Versus M 158 (Drive Line to Throat) 3.3-4 Flow Chart of Subroutine JETPMP 159 3.4-1 Typical Accumulator 174 3.4-2 Surge Line Idealization 175 4.2-1 Map for the Modified Biasi and Griffith-Zuber Critical 186 Heat Flux Option 4.3-1 Rewetting Correlation of Anderson and Hansen 195 4.4-1 Logic for Radiation Heat Transfer Model 204 4.5-1 Flow Diagram for Heat Transfer Logic Options 213 5.0-1 Use of Fuel Behavior Models in Subroutine HTISST 253 Steady-State Temperature Initialization 5.0-2 Use of Fuel Behavior Models in Subroutine HT1TDP 254 Transient Heat Transfer Calculation l
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TABLE'0F CONTENTS
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Page 233 5.2 Mode 1' Implementation.................- .................... 5.2.1- P rogram Modificati on De scri ption. . . . . . . . . . . . . . . . . . . 233-235
'5.2.2 Input..............................................
5.2.3 I n p u t C h ec k s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238' 5.2.4 U se r Gui del i ne s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239' 5.2.5. 0utput............................................. 239 6.0 COMPLI ANCE WITH 10CFR50 APPENDIX K CRITERI A. . . . . . . . . . . . . . . . . . . . . . .255
' APPENDIX A RELAPS MOD 1 Code Manual, Volume 1: System Models and Numerical Methods APPENDIX B RELAP5 MOD 1 Code Manual, Volume 2: Users Guide and Input Requirements' APPENDIX C RELAP5YA Subroutine Glossary lO 1
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LIST OF TABLES (continued) Number Title Page _ 5.0-5 Slow Ramp Rate Flow Blockage Table 249 5.0-6 Fast Ramp Rate Flow Blockage Table 250 5.0-7 Subroutines Associated with the Fuel Rod Deformation Model 251 5.0-8 Summary of RELAP5YA Fuel Behavior Calculations 252 O l 9
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LIST OF TABLES' f3 Tit 1e- Page L/ Number
.1.1-1 Plant Safety and Licensing Analysis Functions 10 1.1-2 Selection Criteria for LOCA Analysis-Methods 11 1.1-3 Model Development Tasks 17
.2.0 Outline for the RELAP5YA and RELAPS M001 Codes 20 2.1 Allowed Fluid Thermodynamic States 46
'2.4-1 RELAP5YA Program Structure 64 2.4-2 RNEWP Subroutine Structure 65-2.4-3 HTADV Subroutine Structure 66 2.4 HYDR 0 Subroutine Structure 67.
3.3-1 Jet Pump. Nomenclature 152 3.3-2 Jet Pump Conservation Equations 153 3.3-3 . Jet Pump Mechanical Energy Equations 154. 3.3 Definition of Terms Used in Jet Pump Model Development 155-3.4 Nomenclature for Accumulator Model 171 4.2-1 Modified Biasi Critical Heat Flux Correlation 132 4.2-2 Griffith-Zuber Critical Heat Flux Correlation 184 4.2-3 RELAP5YA Critical Heat Flux Logic 185
-4.4-1 Description of Variables in the RELAP5YA Thermal 203 Radiation Model 5.0-1 Summary of RELAP5YA Fuel Behavior Models 243 5.0-2 Assumptions in RELAP5YA Fuel Behavior Models 244 5.0-3 Glossary of Symbols and Corresponding RELAP5YA Variables 245' 5.0-4 Fuel Rod Deformation Model Calculations 248.
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ACK!a0WLEDGEMENTS
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The RELAP5YA code development and assessment effort is the result of support and cooperation from many organizations and individuals. The Vermont Yankee, Yankee (at Rowe), Maine Yankee and Seabrook Nuclear Power Stations provided continued financial support and motivation throughout this project. The RELAPS M001 base computer program, early training-in its use, and occasional advice were extended by staff at EG and G, Idaho, Inc.
! Several of the modifications to the base computer program were achieved through the cooperation and assistance of Intermountain Technologies, Inc.
Several individuals at YAEC have significantly contributed toward this effort. The YAEC management continually provided motivation and support for this effort. William Szymczak and Stephen Schultz provided valuable technical insights and guidance during this project. Dennis Albright provided extensive dssistance with the fuel behavior models. Pat Robertson, Shaig Haq and Rebecca Jones helped with the code assessment calculations and preparation of ~ figures for this document. Finally, the staff of the Word Processing Center,
'd Computer Services Department, and Reproduction Department at YAEC gave invaluable assistance during the many stages of this effort.
We gratefully acknowledge the support of all these individuals and organizations. Nomenclature The nomenclature used within this RELAPSYA document has been selected, where possible, to be identical to that used in the RELAPS MOD 1 document (see Appendix A, pages viii through xiii). For cases where new nomenclature had to be introduced, it is defined in the text of that section. l l 1 1 h w_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ i
1.0 INTRODUCTION
7 RELAP5YA is a computer program for analyzing the dynamic behavior of thermal-hydraulic systems. This program has been developed primarily for analyzing postulated accidents and transients in Light-Water Reactor Systems. These include the following:
- 1. More realistic analyses of Loss-of-Coolant Accidents (LOCAs) in Boiling Water Rea'ctors (BWRs) and Pressurized Water Reactors (PWRs) over the entire break size and location spectra from the initiating event through the recovery phase.
- 2. Evaluation model analyses that comply with 10CFR50, Appendix X, for the entire break spectra in BWRs and for small breaks in PWRs from-the initiating event through the recovery phase.
- 3. Sensitivity studies of LOCA events in LWRs where tne user can select any combination of Appendix X criteria to be applied, except the steam cooling rule at reflooding rates less than one inch per k second.
- 4. Safety analyses for a wide class of LWR plant transients from the initiating event through the recovery phase.
RELAP5YA also contains sufficient generality to simulate many other 1 thermal-hydraulic systems that contain water (steam and/or liquid) as the primary working fluid. In particular, the general formulation of the hydrodynamic components, heat structures, power sources and sinks, trips and control systems allows application of RELAP5YA to simulate a wide variety of thermal-hydraulic facilities as demonstrated by the extensive code assessment results described in Volume III. Section 1.1 of this volume provides background information on the LOCA Methods Development Program at YACC under which the RELAP5YA code development and assessment work was performed. This describes the program objectives, [3- motivation and initial implementation of the work scope. Section 1.2 provides 1 ' Q an outline of the RELAPSYA documentation that contains the Code Description l l C___
(Volume I), User's Manual (Volume II) and Code Assessment (Volume III).
1.1 Background
The LOCA Methods Development Program was initiated at Yankee Atomic Electric Company (YAEC) in 1979. The purpose for this program was to establish improved LOCA analysis methods, qualified against experimental data, to support the Vermont Yankee BWR, Yankee PWR, Maine Yankee PWR, and the two Seabrook PWR plants. This program was motivated by YAEC's commitment to support the safety and licensing analysis functions, identified in Table 1.1-1, for these plants. It was recognized that both Best-Estimate (BE) and licensing Evaluation ;1odel (EM) analyses would be required to carry out these functions (References 1.1-1 and 1.1-2). Two major goals were established for this program. The first was to develop BWR LOCA analysis capability at YAEC to support the Vermont Yankee plant. This capability covers the entire break size and location spectra for LOCA events. The second goal was to improve the PWR small break analysis methods at YAEC to support the Yankee (at Rowe) and Maine Yankee operating plants, and the two Seabrook plants currently under construction. This activity addresses technical concerns about small break LOCA analysis methods identified during critical reviews following the accident at the Three Mile Island - Unit 2 p1rt (References 1.1-3 through 1.1-8). The improved methods are to allow both best-estimate and evaluation model analyses to be performed. Since achieving both goals required major efforts with a strong potential for shared technology, they were combined into one methods development program. Several guidelines for implementing this program were established at the outset. These included:
- 1. Emphasis on realistic analysis methods where possible.
- 2. Utilization of the existing LOCA technology base from domestic and foreign research and development programs developed during the past decade.
- 3. Adaptation of an existing thermal-hydraulic analysis method to meet x the program objectives after a critical review of publicly
) available methods (circa 1979 - 1980).
- 4. Development of improved analytical models, based upon sound physical principles, engineering judgment and experimental data, to extend the simulation capabilities when necessary.
- 5. Assessment of the method by. comparing calculated and experimental results over a wide range of conditions in order to test the veracity of the method and to gain valuable experience in applying the method.
A set of technical and programmatic criteria was established for the analytical capabilities and features required to meet the LOCA Methods Development Program objectives and guidelines. These criteria are listed in Table 1.1-2. Several thermal-hydraulic codes were reviewed and qualitatively assessed against these criteria to select an- appropriate method to adapt for q this program. The computer codes available in late 1979 and 1980 that were (.) reviewed included the following (References 1.1-9 through 1.1-20):
- 1. WREM
- 2. RELAP4 M005, NORC00L and M0XY
- 3. WRAP-BWR
- 4. RETRAN
- 5. RELAP4 M006 and MOD 7
- 6. RELAP5
- 7. TRAC P1A
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Key features sought included the following:
- 1. Potential for both best estimate and evaluation model options.
- 2. Potential for consistent integral accident analyses within a single code.
- 3. Balance between computational accuracy and speed to enhance the variety of LWR cases analyzed at reasonable cost.
- 4. Compatibility with the YAEC computer system. ,
- 5. User convenience features and ease of training new users.
All of the candidate codes satisfied some requirements, but none satisfied all requirements. ilowever, RELAPS was judged to be the most promising analysis method to build upon in order to achieve both near and long-term objectives. RELAPS is a light-water reactor system transient simulation code O daveloped at the Idaho National Engineering Laboratory by EG and G Idaho, Inc., for the United States Nuclear Regulatory Commission. This is a new code based on an advanced two-phase hydrodynamic model and reflects the experience gained from the development and applications of its predecessors, the RELAP4 code versions. The hydrodynamic equations use a two fluid model (7 conservation equations) that allows nonhomogeneity (phasic velocity differences) and thermal non-equilibrium (phasic temperature differences). These equations are formulated such that both single and two-phase conditions can be simulated. The hydrodynamic model is basically one-dimensional with provisions to account for multi-dimensional flow effects such as the merging or partitioning of streams at tees, headers and core-plena interfaces. A key assumption in the formulation is that one of the fluid phases exists at the local saturation state. This assumption is reasonable for most conditions encountered in LWR accident and transient arn -es, and considerably reduces the number of I constitutive equations rauired for mathematical closure of the model. The J , code allows for the presence of a noncondensible gas mixture and nonvolatile solute (boron) within the fluid. The code contains a point reactor kinetics l , i
5 model and fairly extensive heat transfer algorithms to simulate heat sources and sinks within a rystem. Special process models (e.g., critical flow. (/3) pressure losses. associated with abrupt flow path changes), special component models (e.g., centrifugal pumps, valves, separator)- trips and a generalized control system are provided which enhance the code simulation capabilities. The general formulation of the hydrodynamic components, power sources, heated structures, trips and control systems within RELAP5 provides a flexible method for modeling LWR systems. The code architecture, principal solution techniques, and user convenience features are attractive. Early applications of the RELAPS code, that included certain LOFT small break and anticipated transient tests, indicated the code could provide fast and numerically stable solutions. However, our initial code review and preliminary assessment calculations identified several areas that required the addition of new models and modifications to existing models in order to meet the LOCA Methods Development Program objectives. These areas are listed in Table 1.1-3 with an indication of the type of analysis (BE = Best Estimate EM = Evaluation Model) L/ that required these improvements. In addition, the RELAP5 code was relatively new and untested against a wide variety of experiments. Thus, an extensive code assessment effort within YAEC was planned in order to form an independent judgment concerning the code and to gain valuable user experience. The workscope for the LOCA Methods Development Program was carried out under three major tasks: a) Model Development, b) Code Assessment, and c) Documentation. Each task has been completed to meet the objectives for this program. The new version of the code, RELAP5YA, is being applied to plant analyses. Results from these efforts will be documented in future YAEC reports. 1.2 Outline This report documents the RELAP5YA code development and assessment work. Volume I describes the RELAPSYA code, focusing primarily on
, modifications to the RELAPS MOD 1 base program from which RELAP5YA was developed. Section 2.0 summarizes RELAP5YA capabilities and features and L_________._.__ l
1 l l describes the similarities and differences between the RELAP5YA and RELAPS ] MODI code versions. Section 3.0 describes the new hydrodynamic models l incorporated into RELAP5YA. These consist of: ! l
- 1. New interphase drag routines for the vertical flow regime map.
- 2. The Moody two-phase critical flow model for ECCS evaluation model analyses.
- 3. A new jet pump model for BWR analyses.
- 4. A new accumulator model for PWR analyses.
Section 4.0 describes the new heat transfer models and options incorporated into RELAP5YA. These include the following:
- 1. A modification of the forced convective boiling algorithm.
- 2. A new critical heat flux option.
- 3. A new rewet and quench model for reflooding and spray cooling periods.
- 4. A new multiple surface radiation heat transfer model.
- 5. New heat transfer logic options for ECCS evaluation model analyses.
Section 5.0 describes the new fuel rod behavior models, These consist of the following:
- 1. Fuel rod fission gas model.
- 2. Fuel rod deformation and rupture models.
- 3. Gap conductance model.
- 4. Zircaloy-water reaction model.
Section 6.0 describes how the RELAP5YA code will be used for ECCS q evaluation model calculations that comply with 10CFR50, Appendix K, O requirements. Appendices A and B contain reproductions of the two RELAPS M001 documents prepared by EG and G Idaho,. Inc., under USNRC sponsorship. These documents have been included for completeness since they contain information relevant to RELAP5YA. Appendix C provides a glossary for the subroutines contained in RELAPSYA. This glossary briefly describes each subroutine's function and calls made to other subrc-atines. , Volume II provides a User's Manual for RELAP5YA. Scction 1.0 of this volume contains a summary of input differences between RELAP5YA and RELAP5 MOD 1. This table is cseful when converting input decks between the two code versions. .The remaining sections provide detailed input instructions and output descriptions to. assist the user. Volume III presents an extensive assessment of RELAPSYA calculations compared to many separate effect and integral test results. This assessment-v establishes the viability of the RELAP5YA code to predict complex thermal-hydraulic phenomena encountered in LWR system analyses of LOCA events and other transients. I i L______________
h References 1.1-1 Fernandez, R. T., A. Husain, R. Sundaram and J. C. Turnage, "Small Break LOCA Development Activities at Yankee Atomic Electric Company", ANS Specialists Meeting on Small Break Loss-of-Coolant Accident Analyses in LWRs, Conference Sponsored by USNRC and EPRI, Monterey, CA, August 25-27, 1981. 1.1-2 Fernandez, R. T., A. Husain and W. J. Szymczak, "LOCA-ECCS Revisions: One Utility's View", Transactions of the American Nuclear Society, Volume 43, Washington, D.C. , November 14-18, 1982. 1.1-3 Kemeny, J. G., et al ., Report of the President's Commission on the Accident at Three Mile Island, Washington, D.C., October 1979. 1.1-4 op. cit., " Supplemental View by Commissioner Pigford". 1.1-5 Levy, S., "Three Mile Island: A Call for Fundamentals and Real-Time Analyses", Heat Transfer Engineering, Vol .1, No. 4, April-June 1980. 1.1-6 Remarks of Herman Dieckamp, Proceedings of CEO Workshop: Managing for Safety, Institute for Nuclear Power Operations, Atlanta, GA, l May 20-21, 1980. 1.1-7 Generic Evaluation of Feedwater Transients and Small Break Loss-of-Coolant Accidents in Combustion Engineering Designed Operating Plants; NUREG-0635, U.S. Nuclear Regulatory Commission, Washington, D.C. , January 1980. 1.1-8 Powers, D. A., and R. O. Meyers, Cladding Swelling and Rupture Models for LOCA Analysis, NUREG-0630, U.S. Nuclear Regulatory Commission, Washington, D.C. , April 1980. . 1.1-9 "WREM: Water Reactor Evaluation Model (Revision 1)", NUREG-75/056, Division of Technical Review, U.S. Nuclear Regulatory Conunission, Washington, D.C. , May 1975. 1.1-10 Katsma, K. R., et al . , "RELAP4 M005: A Computer Program for Transient Thermal-Hydraulic Analysis of Nuclear Reactors and Related Systems", ANCR-NUREG-1335, Aerojet Nuclear Corporation, Idaho Falls,10, September 1976. 1.1-11 Anderson, J. G. M, et al., "NORC00L: A Model for Analysis of a BWR Under LOCA Conditions", NORHAV-D-32, Research Establishment, Riso, Denmark, December 1976. 1.1-12 Evans, D. R., "M0XY: A Digital Computer Code for Core Heat Transfer Analysis", IN-1392, Idaho Nuclear Corporation, Idaho Falls, ID, August 1970. 1.1-13 Anderson, M. M., " WRAP: A Water Reactor Analysis Package", DPST-NUREG-77-1, Savannah River Laboratory, Aiken, SC, June 1977. I
1.1-14 Buckner, M. R., et al., "The BWR Loss-of-Coolant Accident Capability of the' WRAP-EM System", USNRC Report DPST-NUREG-78-2, Savannah River Laboratory, Aiken, SC,1978.
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1.1-15 Moore, K. V. , et al . .. "RETRAN: A Program for One-Dimensional Transient Thermal-Hydraulic Analysis of Complex Fluid Flow Systems", EPRI CCM-5, Electric Power Research Institute, Palo Alto, CA,. December 1978. 1.1-16 " Assessment of-the RELAP4/M006 Thermal-Hydraulic Transient Code", In1.erim Report No. CAAP-TR-78-035, EG and G Idaho, Inc., Idaho Falls, ID, December 1978. 1.1-17 Private Communications Between A. Husain (YAEC) and S. Behling (EG and G Idaho, Inc ) re RELAP4 MOD 7 Features, February 1930. 1.1-18 Ransom, V. H., et al., "RELAP5/ MOD"0" Code Description", CDAP-TR-057, EG and G Idaho, Inc.,- Idaho Falls, ID, May 1979. 1.1-19 Ransom, V. H., et al ., "RELAP5/M001 Code Manual", EGG-2070 DRAFT, EG and-G Idaho, Inc., Idaho Falls, ID, November 1980. 1.1-20 Safety Code Development Group, " TRAC PIA: An Advanced Best-Estimate
. Computer Program for PWR LOCA Analysis; Volume I: Methods, Models, User Information and Programming Details", Los Alamos Scientific Laboratory, Los Alamos, NM.
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Table 1.1-1 Plant Safety and Licensing Analysis Functions Analysis Type BE EM A. Support Plant Safety Set safe pl ant operating 11mi ts. . . . . . . . . . . . . . . . . . . . . . . . X
- 1. ,
1 Support pl ant personnel trai ning programs. . . . . . . . . . . . . . X 2.
- 3. Assess plant emergency procedures and safeguard systems................................................ X
- 4. Evaluate proposed plant modifications.................. X
- 5. Provide emergency response support and diagnostic aids................................................... X
- 6. Support certain post-incident / accident evaluations..... X
- 7. Address new safety i ssues that may ari se. . . . . . . . . . . . . . . X Quanti fy pl an t sa fety ma rgi ns. . . . . . . . . . . . . . . . . . . . . . . . . . X X 8.
B. Support Plant Licensing
- 1. Assess core reload designs and strategies.. . .. . . ... . . .. X
- 2. Assess proposed pl ant modi fications. . . . . . . . . . . . . . . . . . . . X
- 3. Address licensing i ssues that may ari se. . . . . . . . . . . . . . . . X
- 4. Anticipate potential changes to 10CFR50, Appendix K.... X X C. Support Plant Economics
- 1. Establish operating flexibility based on real safety margins................................................ X X
- 2. Assess plant power uprates............................. X X O!
t
(.- - i Table 1.1-2 is propietary to Yankee Atomic Electric Company and therefore was deleted. O O _ _ _ . _ _ _ . _ _ _ _ _ _ _ _ _ _ . _ . _ . _ . . . . _ _ i
y > Table 1.1-3 Model' Development. Tasks Analysis Requirement A.. Hydrodynamic Models
- 1. Interphase Drag BE, EM
- 2. Moody Two-Phase Critical Flow EM
- 3. Jet Pump BE, EM
- 4. Accumulator BE, EM B. Heat Transfer ~ Models-
- 1. Forced Convective Boiling BE, EM
- 2. Critical Heat Flux: BE, EM
- 3. Rewet and Quench BE, EM
- 4. . Multi-Surface Radiation . BE, EM 5; ' Heat Transfer Logic Options EM I
C. Fuel Behavior Models
- 1. Internal Gas Pressure BE, EM
- 2. Rod Deformation and Rupture BE, EM
~3. Transient Gap Conductance BE, EM
- 4. Zircaloy-Water Reactions EM O
L__________--______---_--_________-____--. - _ _ _ _ _ _ _ - - - _ . - _ - - _ _ _ - _ _ - _ .
}
2.0 RELAPSYA LWR SYSTEMS ANALYSIS CODE The objectives of this section are to provide the following information:
- 1. A brief description of the physical models, numerical methods, and user features contained within the RELAPSYA code.
- 2. Guidelines to other sections within this document that contain more complete descriptions of the models and numerical methods in the RELAD5YA code.
- 3. Identification of similarities and differences between RELAP5YA and its predecessor, RELAP5 MOD 1; this includes clarification and corrections, where necessary, of the RELAPS M001 documents.
- 4. An outline of the RELAP5YA program structure so that users may better understand the flow of information within the program.
RELAP5YA is a computer program for analyzing the transient behavior of thermal-hydraulic systems. The hydrodynamic model is based upon a one-dimensional, two-fluid, non-equilibrium model. This model allows for velocity and temperature differences between the two-fluid phases that frequently occur in transient two-phase flow processes. It allows for the presence of a noncondensible gas component, such as nitrogen or air, mixed with the vapor phase. It also allows for a dissolved, nonvolatile component, such as boron, in the liquid phase. The hydrodynamic model includes necessary thermotvnamic state relations and constitutive equations to complete the physical and mathematical description of two-phase phenomena. These include mass, energy and momentum transfer models and critical flow models. The basic hydrodynamic model is discussed in Section 2.1. ) l Twelve types of hydrodynamic components are available to the user for constructing a simulation model of a thermal-hydraulic system. These components are the vehicle for entering input data, selecting user options, and applying the hydrodynamic model to fluid regions within the system or specifying fluid system boundary conditions. Five components (SNGLVOL, SNGLJUN, PIPE, ANN'JLUS and BRANCH) apply the basic hydrodynamic model to l l I
internal' fluid regions. 'Another five components (SEPARATR, PUMP,-JETPHP,
;.YALVE and ACCUM) modify.the basic hydrodynamic model to account for unique
- s. . ~ hydrodynamic phenomena within separators, centrifugal and jet pumps, valves, and' accumulators. Finally, two components (TMDPVOL and TMDPJUN) allow the user to specify hydrodynamic boundary conditions for a system model. The hydrodynamic components are discussed in Section 2.2.
The RELAP5YA code contains models for simulating other transient processes pertinent to light-water reactors and thermal-hydraulic systems. These include thermal power sources and sinks,. conduction heat transfer within solid materials, fuel rod behavior, control systems and trips. These process models are discussed in Section 2.3. The RELAP5YA program structure is described in Section 2.4. This information is primarily intended to provide the user witn an understanding of the infonnation flow within the program. Appendices A and B contain reproductions of the two RELAPS M001 h documents (Volume 1: System Models and Numerical Methods, and Volume 2: V User's Guide and Input Requirements, respectively) published in March 1982 by EG and G-Idaho, Inc., for the USNRC. These documents have been included for completeness since many models and features are comraon to both the RELAP5YA and the RELAPS MODI code versions. Appendix C provides a glossary for the subroutines contained in RELAP5YA. This glossary briefly describes each subroutine's function, the calls from each subroutine te other subroutines, and supports the discussion of the RELAPSYA program structure contained in Section 2.4. Table 2.0-1 provides a guideline to detailed information within this document that describes the models, numerical methods and features contained in the RELAPSYA and RELAPS MODI codes. This table also identifies those models that are the same and those that are different between these two code vers'i ons. O L=__ - -
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L l L i 2.1 Hydrodynamic Model r% This section briefly describes the formulation of the hydrodynamic model used in RELAP5YA. The governing differential equations, state and .{
' constitutive relations, and numerical solution method are summarized. Table 2.0-1. identifies other sections in this document that contain a more complete ;
description of these topics. 2.1.1 Governing Differential Equations Two-fluid ttydrodynamic models of two-phase flow have generally been derived by performing local spatial and/or temporal averages of the basic Navier-Stokes equations over each separate phase (References 2.1-1 through ' 2.1-6). These derivations yield conservation equations in differential . form that contain averaged values for the dependent variables, and surf ace integrals over phase boundaries that require constitutive equations. These mathematical procedures are complex, reflecting the complex nature of two-phase flow processes, and generally requira further simplifying
,e assumptions in order to achieve tractable, efficient numerical solutions.
( The following principal assumptions are used to derive the differential form of the hydrodynamic model in RELAPSYA and its predecessor, RELAPS M001:
- a. The dependent fluid and field properties are cross-sectional area averaged values. The independent variables are time and one spatial dimension normal to.the cross section.
- b. - Correlation coefficients within the averaged terms are taken to be unity. Thus, the average of a product of several parameters is approximated by the product of the average of the parameters.
- c. The flow field does ilot contain any internal mass sources or sinks; ]
thus ! Ig * -If wnere f is the interfacial mass transfer rate per unit volume.
-2E.
_-__--_____a
- d. The flow field is basically one-dimensional with allowance for gradual area changes. Abrupt area changes and flow branching sections are treated by special process models.
- e. The area averaged pressures for the liquid'and vapor phases are equal for vertically-oriented fluid volumes. For horin ntally-oriented volumes, this assumption is modified to account for buoyancy forces caused by phasic density differences under stratified low flow conditions,
- f. Interphase momenta transfer due to drag and due to mass transfer between the two phases are independently equal.
- g. The interfacial velocity is set equal to the liquid phase velocity for vaporization, and set equal to the vapor phase velocity for condensation- processes. This forces the mass transfer process to always be dissipative and is believed to yield a reasonable approximation for the interphase momentum transfer processes,
- h. Energy dissipation due to wall drag, interphase drag, and mass transfer is included. Dissipation associated with virtual mass acceleration is neglected due to its small value.
- i. The least massive phase of the water component exists at the local saturation state.
J. Any noncondensible component in the gas phase forms a Gibbs-Dalton, homogeneous mixture with steam. The noncondensible gas obeys the ideal gas 1aw.
- k. All properties for the gas phase are represented by mixture properties for the steam-noncondensible mixture when a noncondensible component is present.
- 1. Any nonvolatile dissolved solid present in the liquid phase is sufficiently dilute such that the liquid properties are not altered. The solute remains in the liquid phase and is transported
at the liquid velocity. The inertia of and energy transported by
" the solute is negligible.
The averaging method and assumptions identified above yield a one-dimensional, two-fluid model for simulating transient two-phase flow processes. This formulation allows for two-phase nonhomogeneous (unequal phase velocities) and thermal non-equilibrium (unequal phase temperatures) conditions to occur. The degree of nonhomogeneity and/or non-equilibrium is determined to a large extent by the specific nature of the constitutive models, particularly the interphase drag and mass transfer models, respectively. This model allows for the presence of a noncondensible component in the gas phase and a dilute, nonvolatile solute in the liquid phase. The model also reduces to the appropriate single-phase transient flow equations when either the gas or liquid phase disappears. A key assumption in the formulation is that the least massive phase exists at the local saturation state. This assumption is reasonable for most conditions encountered in LWR accident and transient analyses. As a consequence, one less energy conservation equation is required, and the constitutive information that needs-
'N to be specified is significantly reduced.
(O The basic hydrodynamic model contains eight governing differential equations. These consist of the following:
- a. Four conservation of mass equations; one each for the vapor and liquid phases of water, the noncondensible gas, and the dilute nonvolatile solute.
- b. Two conservation of momentum equations; one each for the gas and liquid phase of the fluid.
- c. One conservation of total energy equation for the gas-liquid mixture.
- d. One equation-of-state relation for the gas-liquid mixture, f3 L)
\ - -- - . - - - - - - - - - - _ - - - - - - - -
}
These equations are recast to obtain a mathematically equivalent set which is more convenient for numerical solution. The mathematical procedures ' to accomplish this are described in detail in Section 2.1.1 of Appendix A. The essential steps in this process are listed below: fi
- a. The conservation of mass equations for the vapor, noncondensible gas, and liquid are summed to yield a mass conservation equation in tems of the gas-liquid mixture density.
- b. The conservation of mass equations for the vapor and noncondensible gas are summed and rearranged to yield a mass conservation equation
'for the total gas mass fraction.
- c. The two momenta equations are added and subtracted to yield a phasic sum and a phasic difference momentum equation.
- d. Conservation of mechanical energy equations are obtained by forming the scalar product of the velocity and momentum equation for each phase. These are summed to yield a mechanical energy conservation equation for the gas-liquid mixture.
- e. The mechanical energy conservation equation for the mixture is subtracted from the total energy conservation equation for the mixture to obtain a thermal energy conservation equation for the gas-liquid mixture.
- f. The equation of state for the mixture is used to express the time derivative of the mixture density as a function of fluid property derivatives and the time derivatives of the pressure, mixture internal energy, total gas mass fraction and noncondensible gas mass fraction.
The eight governing differential equations that result from these mathematical procedures are summarized below: O,
-_ _ - - i
i r
.t !
l
'l The four mass conservation equations.are:
Mixture Density Equation. _ 6 J l ap/at'+ (1/A):[a(aggg o v A + afpfvAf )/ax] = 0 (2.1-1) J Gas idass Fraction Equation' l 1. 1 p(aX/at) + [(1-X)/A][a(aggg . o v A)/ax]'- (X/A)[a(afpfvAf )/ax] - [g (2.1-2) Noncondensible Component Mass Fraction. Equation (2.1-3)
.a(Xn o)/at +-(1/A) [a(ogng o V A)/ax]'= 0 Nonvolatile Solute Mass Equation apB /at.+ (1/A) [a(Cg sfpfvA f )/ax] = 0 (2.1-4).
~ The two momentum conservation equations are:
Phasic Sum Equation 2
- aggo (av g
/at) + afpf(avf /at) + (agg p /2)(av /ax) + (afpf/2)(av 7,x)
= aP/ax + pgg - ggg a p v FWG - afpf fvFWF-r(v g g -v) f (2.1-5)
Phasic. Difference Equation 2 2 av/at-av/at+f(av/ax)-f(av/ax) g f _g
= - (1/p g- 1/pf) (aP/ax - v FWG g + vfFWF - pFI(v g - vf)
+Ig [pV7 - (afpf vg + aggf p v )] / (a gg p afpf) f - . C [p2 /( p gp f)] [a(v g - v f)/at + v f(avg/ax) - v g(avf /ax)] (2.1-6)'
jO
- _ - _ _ _ - _ _ - _ _ - - - _ _ - _ _ _ _ - _ _ _ _ - -. - - _ - A
An additional term is added to the right-hand side of the phasic difference equation for stratified low-flow conditions. This term accounts for bouyancy forces that modify the pressure gradient, and is described in Section 2.1.1.2 h of Appendix A. The mixture therma'l energy conservation equation is: Mixture Thermal Energy Equation a(pV)/at + (1/A) a(agggg o v U A + afpf vUA f f )/ax
= - (P/A) a(a gg v A +vA af f )/ax + Q gg + (a o ) FWG(v g )2
+
(a fpf) FWF(vf)2 (, ,f, ,y) py( ,y f)2 (lrl/2)(v (2.1-7) g - v f)2
+
g The mixture equation of state it.: Mixture Equation of State dp/dt = (ap/aP)U,X,X ,X,X n n
+ (ap/aX)P,U,X (dX/dt) + (ap/aXnP I ,U,X (dXn /dt) (2.1-8) n The following auxiliary relations have been used to obtain the above governing differential equations:
a (2.1-9) g + af = 1
*O *P v (2.1-10)
#g n p = ao (2.1-11) gg + afof X = aggo /o (2.1-12) i<
, :e. ,
j_ Y1 ;
-; 3 ,
- p. , ,
.X n " "g n/p1 (2.1-13)
- n ..
., 7
[ Vy X y
= a o /p gy (2.1-14 ):
P.. P n
+P y =P g =P f (2.1-15)
U XUg + (1-X)'U f (2.1 16)'
-XU g
=XU nn +XU
. yy (2.1-17)
C g = og/[p(1-X)] (3 1-18)' vy .xv +g (1-A)v f (2.1-19) where A'= 0 for vaporization x = 1.for condensation
- j. ,
- The.eight governing differential equations contain two independent variables (spatia 1' coordinate,.x, and time, t) and eight primary dependent variables which are:.
p, X,-X ' n 'B' Vg' #f., U, P To obtain closure for this. equation set, additional thermodynamic state relations, . constitutive relations, and appropriate boundary conditions are required. . Constitutive relations are required for the following parameters: ig Vapor generation rate per unit volume C Virtual mass coefficient FI Interphase drag factor ,' FWF,FWG Wall frictional drag coefficients for the liquid and vespor phases ___ E _ ___ _ _ _ ._ _ . . _
.j
Q Net heating rate to the fluid per unit volume These terms are addressed in the following sections. 2.1.2 Thermodynamic Relations and Allowed States Thermo@namic state relations are used to express the fluid mixture density and all partial properties in terms of the independent state variables, P, U, X, and Xn , with the additional constraint that the least massive phase exists at the local saturation state. This latter condition constrains one of the phasic temperatures to be the saturation temperature ; based upon the vapor partial pressure. The development and use of these state ! relations are described in detail in Section 2.1.2 of Appendix A. ' Table 2.1-1 summarizes the fluid states that are allowed to exist by the hydrodynamic model in RELAPSYA and RELAPS M001. For static qualities in the range, 1/2 < X 5 1.0, the vapor phase will be subcooled, saturated, or superheated when its specific internal energy is less than, equal to, or greater than its corresponding saturated specific internal energy, respectively. Similarly, for static qualities in the range, 0 1 X < 1/2, the liquid phase will be subcooled, saturated, or superheated when its specific internal energy is less than, equal to, or greater tnan its corresponding saturated specific internal energy, respecti ly. Noncondensible gas (when present) and vapor will be in thermal equiliu, N (equal temperatures) since it is assumed that the two form a Gibbs-Dalton mixture. The degree of thermal non-equilibrium between the liquid and gas phases is determined to a large extent by the vapor generation model discussed below. I 2.1.3 Constitutive Relations The hydrodynamic model requires constitutive relations for the following phenomena:
- a. Interphase mass transfer associated with. vaporization and condensation,
- b. Interphase drag. l
)
1 L____--__
~
- c. Wall friction.
n. r
')
- d. Localized mechanical energy losses associated with abrupt changes in flow paths.
- e. Critical flow.
- f. Wall heat transfer.
These relations attempt to describe the macroscopic effect rather than the microscopic details of each phenomena. Thus, algebraic equations rather than differential equations are used. These equations are generally based upon a combination of physical insight, physical principles, and quasi steady-state experimental data. They ultimately relate the phenomena of interest to one or more primary dependent variables as well as geometrical and empirical constants. 2.1.3.1 Interphase Mass Transfer t0 k./ The vaporization and condensation models in RELAP5YA are the same as those in RELAPS MOD 1, and are described in Section 2.1.3.1 of Appendix A. The interphase mass transfer rates for both processes are formulated in terms of the vapor generation rate per unit volume, gf .- Thus, positive values for r gindicate vaporization, and negative values indicate condensation. Each model contains the difference between the equilibrium and actual static quality, (Xe - X), as a factor. This factor represents the driving potential (force) for the interphase mass transfer process. Tne sign of this factor is used to select the vaporization model (positive sign) or the condensation model (negative sign). Hence, each model tends to drive the fluid toward the equilibrium state. The equations for each model programmed in RELAP5YA and RELAPS M001 are restated below since thosa given in Section 2.1.3.1 of Appendix A contain several typographical errors. The vaporization model was derived from the theoretical model proposed by Jones and Saha (Reference 2.1-7) and the empirical correlation proposed by
, Houdayer (Reference 2.1-8):
I v
Vaporization Model (X, - X) > 0.0
~
f=Cg g (Gm # O)o [P(X-X -n X )(Xo ~ e XIIP v where: 1 C - 6.4517175 x 10-3 (see m-2 p,-1/2), empirical constant G = mixture mass flux (Kg m-2 3,c -1) G = 3500.0 (Kg m-2 sec -1), empirical constant o P = pressure (Pa) X = gas phase static quality X, = equilforium static quality X n
= n ncondensible gas st,atic quality X, = 1.0 x 10-5, empirical constant Py = vapor density (Kg m-3)
The proportionality function betweengr and (Xe - X) in Equation 2.1-20 was primarily determined from depressurization experiments. These include Reocreaux's steady-state Moby Dick Experiments that had steep pressure gradients in a converging nozzle, .and the Edwards Pipe Blowdown Experiments that had a rapid depressurization rate. These large pressure changes (spatial and temporal) cause relatively high vaporization rates that are reflected in the empirical constants. A ques' ion arises concerning the applicability of this model to vaporization processes dominated by wall heat transfer and/or i temperature differences between the gas and liquid phases. This question was addressed during the code assessment effort and is discussed in Sections 5.0 and 6.0 in Volume III. In most of the assessment cases, the vaporization rates were calculated reasonably well. The most notable exception occurs during low flow rate, high quality conditions characteristic of nonequilibrium film boiling heat transfer where the vaporization rate appears to be overpredicted. Thus, an improved model in this area is desirable for best-estimate analyses. For licensing analyses, the conservative assumptions imposed by Appendix K yield conservative results as demonstrated in Section j 5.2.3.5 of Volume III. I The condensation model was adapted from the Jones and Saha model, and modified by empirical constants: , I l _ _ _ _ _ _ _ _ _ __ 1
1 Condensation Model (X,- X) < 0.0 q' V I g= K(1 - X + Xc)(X,- X) (2.1-21) . where: K = 1.0 x 105 (ggf, 3-sec), empirical constant i Xc = 1.0 x 10-5, empirical constant From the code assessment, we have inferred that this model tends to overpredict the condensation rate when subcooled ECC is injected into a steam envi ronment. This causes the system pressure to be. low and results in degraded heat transfer in the fuel bundle region as seen in the TLTA and LOFT code assessment cases discus:ad in Section 5.0~ of Volume III. An improved model in this . area is desirable for best-estimate analyses. For licensing analyses, the degraded heat transfer effect and the conservative assumptions irposed by Appendix K yield conservative results. The presence of a noncondensible gas is taken into account in .the vaporization and condensation models described above. However, the vapor l Q generation rate is set to zero for the following two conditions: '
- a. Xn > 0.99
- b. Xn = X, and X > X, Both the RELAP5YA and RELAP5 MODI codes contain nucleation criteria for incipient vaporization in liquid and incipient condensation in steam. These are described in Section 2.1.3.1.3 of Appendix A. However, the liquid superheat value of 2.0 K for incipient vaporization has been changed to 0.0 K in RELAP5YA and RELAP5 MOD 1 Cycle 18.
2.1.3.2 Interphase Drag In the formulation of the hydrodynamic model, the interphase drag was partitioned into two terms: a dynamic drag term due to virtual mass acceleration, and a steady drag term that arises from viscous shear between the phases.
l The dynamic drag tenn is the same in both tne RELAP5YA and RELAP5 MODI codes, and is described in Section 2.1.3.2.3 of Appendix A. The virtual mass _ coefficient, C, that appears in the phasic momentum difference equation (2.1-6) is restated below. For 0 < ag < 1/2: C = [1 + 2ag ]/[2(1 .ag)] (2.1-22) For 1/2 ; og < 1.0: C = [3 - 2ag ]/[2ag ] (2.1-23) The steady drag term depends upon the two-phase flow regime. RELAP5YA and RELAPS M001 use four distinct maps to define the appropriate two-phase flow regime for various hydrodynamic components: i
- a. Vertical Flow Map (VRT) for all vertical and inclined components l except the ANNULUS component.
l }
- b. Horizontal Flow Map (HRT) for all horizontal components.
- c. Annulus Flow Map ( ANN) for all vertical ANNULUS components. i
- d. High Mixing Flow Map (HMF) for PUMP components. l After the appropriate flow regime is selected, the interphase drag factor (FI) contained in the momentum difference equation (2.1-6) and the ;
mixture thermal energy equation (2.1-7) is computed. This factor is generally expressed as: (og af og of)FI = Agf Bgf = Fg (2.1-24) where Agf represents the interfacial area per unit volume, and Bgf represents the momentum transfer coefficient. e!
- 4
The Vertical Flow Map, two-phase flow regimes, and algorithms for r- calculating the interphase drag factor, F y, have been extensively revised in V) RELAPSYA. These revisions are described in Section 3.1 of this volume. The three remaining flow maps and algorithms for Fy have been retained in RELAP5YA and are described in Section 2.1.3.2 of Appendix A. For single-phase conditions, the right-hand side of Equation 2.1-24 is 4 set to the very large value of 1.0 x 10 20 N-sec/m . This forces the j phasic velocities to be equal. Thus, the difference momentum equation becomes negligible and the remaining governing equations reduce to the appropriate set for transient single-phase flow. 2.1.3.3 Wall Friction The wall friction models in RELAP5YA and RELAP5 M001 are the same. The general approach is outlined below to clarify the description contained in Section 2.1.3.3 of Appendix A. ('T The two wall friction drag coefficients are FWF for the liquid phase and FWG for the gas phase. These coefficients appear in the wall friction force terms of the two momenta equations (2.1-5 and 2.1-6), and in the wall friction dissipation terms of the mixture thermal energy equation (2.1-7). We assume that transient frictional effects are negligible, and that the , phase-wetted perimeter on the bounding surface is proportional to the volume Each coefficient is then expressed in fraction (af, ag) for each phase. terms of a Darcy-Weisbach friction factor, x$ , and channel hydraulic j diameter, Dh , as follows: FWF = A fjvj/(20) (2.1-25) f h FWG = A g (2.1-26) lvg l/(20h) For single-phase flow, the appropriate friction factor is selected on the basis of the Reynolds number, Re, and computed by one of the following formulas: L] l l Laminar Flow (1 1 Re 1'2000) A (2.1-27) L = 64/Re l Transttion Flow (2000 1 e1 R 4000) t (2.1-28) A LT = (2 - 4000/Re)(AT-AL I*A L i Turbulent Flow (Re > 4000) i i A T = 1.74 - 2 Log 10[2c/Dh + 18.7/(Ref)] T (2.1-29) The friction factor for laminar flow is derived from the Haegen-Poiseuille solution for laminar flow in pipes. The friction factor for turbulent flow is obtained from the Colebrook correlation (Reference 2.1-9). j For two-phase co-current flow, the HTFS two-phase friction multiplier, 2 0 p, is used to compute tne overall friction pressure gradient in terms of the liquid-alone friction pressure gradient (Reference 2.1-10):
=0 p(h) (2.1-30)
(h) The overall friction pressure gradient is the sum of the phasic friction loss j terms: I v v (2.1-31)
-(h) = FWF af pf p f + FWG a g g g The overall friction pressure gradient is then partitioned by the following procedure. A preliminary estimate is made for each term on the right-hand side of Equation 2.1-31 to determine the smaller of the two terms. These estimates use Equations 2.1-25 through 2.1-29 and the corresponding Reynolds' number for each phase. The wall friction drag coefficient for the smaller term is retained. The wall friction drag coefficient for the larger term is recomputed by solving Equations 2.1-30 and 2.1-31. For example, if
(2.1-32) f > FWG o g og vg v FWF af of k/ then, FWG is retained from Equation 2.1-26, and: (2.1-33) FWF = [-(h) - FWG ag og vg ]/(af af v) f For two-phase countercurrent flow, the HTFS correlation does not apply. For these conditions, the phasic friction factors are computed directly from Equations 2.1-27 through 2.1-29 using the Reyno?ds' number for each phase. 2.1.3.4 Local Pressure Drops and Mechanical Energy Losses Both RELAP5YA and RELAP5 M001 contain models to act ount for local mechanical energy losses in addition to the wall friction losses discussed in the previous section. These losses arise from abrupt changes in flow paths such as sudden enlargements or contractions, orifices, bends, tees, wyes and (3 grid spacers. These terms have r.ot been shown explicitly in either the differential or finite difference forms of the two momenta and the mixture thermal energy equations in Appendix A. 'However, they are included as additional pressure loss terms in the phasic sum and difference equations, and as additional dissipation terms in the mixture thermal energy equation that are solved in both code versions. These terms are restated below and described further in Section 2.2.2 of Appendix A. The local pressure drop due to abrupt changes is formulated in an analogous manner to the wall friction terms. The two terms added to the right-hand side of the phasic sum and the phasic difference momentum equations as local jump conditions are, respectively: Terms for Phasic Sum Equation g + af aPfL [agaP J " ~ EIK v'KAC,9 IIVg II23 "g#gV f
-[(K y +K AC,f IIVl/2]afpff f v (2.1-34)
('
Terms for Phasic Difference Equation [aP /p - APf /pf]L * ~EIK V *K AC,gI !Vg U 2] vg g g
+[(K y +K AC,f I!V!/23V f f (2.1-35) where K
y Are user supplied mechanical energy loss coefficients (constants); one each for forward and reverse flow through junctions, I l Are code calculated mechanical energy loss KAC,f, KAC,9 coefficients when the user selects the Abrupt Area Change Option for junctions. The user supplied loss coefficient for forward flow is used for each phase
'when the junction mass flux is positive. Similarly, the user supplied loss
{ coefficient for reverse flow is used for each phase when the junction mass flux is negative. The assumptions and equations used in the Abrupt Area Change Option to compute those loss coefficients are described in Section 2.2.2 of Appendix A. These dissipative losses are accounted for in the mixture thermal energy equation in an analogous manner to the wall friction losses. l l 2.1.3.5 Critical Flow 1 q The RELAP5 Critical Flow Model described in Sections 2.2.1 and 3.1.6 of j Appendix A are contained in both the RELAP5YA and RELAP5 I4001 codes. This l model provides a realistic estimate of critical flow conditions and rates at fluid system boundaries such as postulated pipe breaks, and at internal locations such as valves and steam line velocity limiters. 1 I In addition, the Moody Two-Phase Critical Flow Model has been i incorporated into the RELAP5YA code as a user option for licensing analyses l that comply with 10CFR50.46. This model and its implementation within RELAPSYA are described in Section 3.2 of this volume.
]
=
T
=
yF~ 'T> "QRL j i
,1
' 2.1.3.6 LWall Heat' Transfer.-
[
. The mixture thermal energy _ equation contains a term, Q, that represents-the net heating rate!per unit . volume of the fluid. This term is composed of twoiparts: convective heat transfer _ from solid boundary surfaces, Q _C, and q direct moderator ' heating, Q D, due to gamma 'and ' neutron interactions with' the -
~c ool a'nt.,
J Q.= Q C OD (2;1-36)- The convective heat" transfer' component is coupled to the transient conduction equation. in.the~ structure,-and is obtained from the thermal boundary condition at the' structure surface: [- k s aTs /ar]B = h ITc S,B-Tp ) + grad (2.1-37)
- QC = (wDHT /Ap ) h c (TS,B-Tp) {2.1-38) where k i Structure thermal conductivity s
b c
= Convective heat transfer coefficient D
HT
= Equivalent heated diameter ^
Ap =. Channel flow area T,T p s
= Fluid and structure temperature y grad = Net radiative heat flux The direct moderator heating component is discussed later in Section 2.3. -
O
1 The RELAP5 M001 code contains an extensive set of algorithms for determining heat transfer modes and coefficients over a broad range of . conditions. These are described in Sections 2.1.3.4 and 3.2.7 of Appendix A ; and Section 4.2 of Appendix B. These algorithms have generally been retained ) in RELAPSYA, except for modifications discussed below. However,-the code l review and preliminary assessment effort indicated that several extensions I were required in order to improve the code simulation's capabilities and to incorporate options for licensing analyses that comply with 10CFR50,46, Appendix K. These changes are identified below and, except for Item a, are described in Section 4.0 of this volume. ll
- a. The static equilibrium quality, X used e
in heat transfer correlations (see Section 2.1.3.4.2 of Appendix A) has been retained for countercurrent flow, but changed to the dynamic quality, X , for co-current flow in order to be more consistent D with the original development of these correlations.
- b. The Forced Convective Boiling algorithm has been changed to improve simulation capabilities in this heat transfer regime. This change is described in Section 4.1.
- c. A new Critical Heat Flux Option to improve CHF predictions has been added, and is described in Section 4.2.
- d. A new Rewet and Quench Model has been added as a user option to better simulate reflooding pnenomena in fuel assemblies for LOCA events. This is described in Section 4.3.
- e. The RELAPS M001 code does not account for the net radiative heat flux term on the right-hand side of Equation 2.1-37. Thus, a new Multiple Surface Radiation Model has been added as a user option j and is described in Section 4.4.
- f. Heat Transfer Logic Options have been added to the RELAP5YA code in order to comply with the return to nucleate and transition boiling lockout criteria contained in 10CFR50.46, Appendix K. These L_ ___ - - - - - - - . - - --
options are intended for licensing analyses, and are described in Section 4.5 of this vclume. ,. v 2.1.4 Numerical Solution Method The' numerical solution method for the hydrodynamic model contained in the RELAP5YA and RELAPS M001 codes are basically the same, and are described in Section 3.1 of Appendix A. These methods are briefly discussed below, and - departures from Section 3.1 of Appendix A are identified. The numerical method is based upon solving a set of finite difference equations for fluid control volumes that represent a thermal-hydraulic system. The finite difference e'quations are obtained by integrating the eight governing differential equations, identified in Section 2.1.1, over control volumes. Specifically, the four continuity equations, the mixture thermal energy equation, and the mixture equation of state are integrated over a generalized fluid control volume. This yields cell centered quantities for the scalar primary dependent variables (p, X, Xn ' PB' u, and P), and flux terms that contain the phasic velocities at the open ends of the cell. The v two momenta equations are integrated over a momentum control voluine, defined between" the centers of adjacent fluid control volume centers, to obtain the phasic velocities at the open ends of the fluid control volume. Scalar quantities required for the boundary flux tenns are either donored or approximated by weighted averages of values from adjacent fluid control. volumes. This forms a staggered system of fluid control volumes and momentum control volumes, where the boundaries of the former coincide with the " center" of the latter and vice versa (see Figure 27 on page 80 of Appendix A). The finite difference equations that result contain time derivative terms and several nonlinear terms. The time derivative terms are approximated by forward finite time differences. The nonlinear terms are approximated by terms that are linear in the dependent variable (forward time level) and coefficients evaluated at the old time level. This yields a new set of semi-implicit, linearized finite difference equations that can be advanced in time directly without costly iterations at each time step. The new set of finite difference equations are rearranged algebraically to yield one equation per fluid control volume that contains the pressure at the new time level and
E . l L old time level values for all other dependent variables. The set of these pressure equations forms an N x N matrix, where N is the total number of control volumes used to simulate the fluid system. This set is solved by a sparse matrix solution method (Reference 2.1-11). Once the pressures are obtained at the new time level for all fluid control volumes, the remaining dependent variables are computed directly from the finite difference equations. l The numerical solution method is described in more detail in Section 3.1. However, the following changes should be noted. First, the finite difference form of the mixture thermal energy equation has been recast into a mathematically equivalent form such that the mixture specific internal energy (u) is obtained directly rather than the product (pu). This modification is used in both the RELAPSYA and RELAP5 M001, Cycle 18 versions of the code.
- ,econd, the finite difference form of the phasic sum and difference equations contain two viscous-like terms identified as VISF and VISG (see pages 83 and 84 of Appendix A). The authors of the RELAPS M001 code have ind cated that these terms have been included to enhance the stability of the code. However, it is recognized that the two-phase numerical model is too bc;1 plex to analytically assure unconditional stability (References 2.1-12 and 2.1-13). Based upon discussions with the, developers of RELAPS M001 and our assessment, we have deleted the leading factor of 0.5 for these two terms contained in the VEXPLT subroutine of RELAPSYA.
G1
)
i - - - - - - - - - - - - - J
l 1 1 1 References i
.n
) 2.1-1 Kocomustafaogullari, G., "Thermo-Fluid Dynamics of Separated Two-Phase
> Flow", Ph.D. Thesis, School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, December 1971.
2.1-2 Drew, D. A., " Averaged Equations for Two-Phase Flows", Studies in Applied Mathematics, L, pp. 205-231, 1971. l 2.1-3 Ishii, M., Thermo-Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, Paris, France, 1975. 2.1-4 Harlow, F. H., and Amsden, A. A., " Flow of Interpenetrating Material Phases", Journal of Computational Physics,18, pp. 440-464,1975. 2.1-5 Hughes, E. D., Lyczkowski, R. W., and McFadden, J. H., "An Evaluation of State-of-the-Art Two-Velocity Two-Phase Flow Models and Their Applicability to Nuclear Reactor Transient Analyses, Volume 2: Theoretical Bases", EPRI NP-143, Electric Power Research Institute, Palo Alto, CA, February 1976. j 2.1-6 Stuhmiller, J. H., "A Review of the Rational Approach to Two-Phase Flow Modeling", EPRI NP-197, Electric Power Research Institute, Palo Alto, CA, July 1976. 2.1-7 Jones, O. C., Jr., and Saha, Pradip, " Volumetric Vapor Generation in Nonequilibrium, Two-Phase Flows", Prepared for Advanced Code Review ' IN Group Meeting of the Water Reactor Safety Research Division, U.S. () Nuclear Regulatory Commission, Washington, D.C., June 2,1977. 2.1-8 Houdayer, G., et al., "Modeling of Two-Phase Flow with Thermal and Mechanical Nonequilibrium", Presented at the Fifth Water Reactor Safety Research Information Meeting, Washington, D.C., November 7-11, 1977. 2.1-9 Schlicting, H., Boundary Layer Theory, Sixth Edition, McGraw-Hill Book Co., New York, p. 584, 1968. 2.1-10 Claxton, K. T. , Collier, J. G. , Ward, A. J. , "H.T.F.S. Correlation for Two-Phase Pressure Drop and Void Fraction in Tubes", AERE-R7162, Atomic Energy Research Establishment, Harwell, Berkshire,1972. 2.1-11 Curtis, A. R. and Reid, J. K., " FORTRAN Subroutines for the Solution of Sparse Sets of Linear Equations", AERE-R6844, Atomic Energy Research Establishment, Harwell, Berkshire,1971. 2.1-12 Ransom, Y. H. , Wagner, R. J. , Trapp, J. A., "The RELAPS Two-Phase Fluid Model and Numerical Solution Scheme for Economic LWR System Simulation", presented at the Advances in Nuclear Systems Thermal Analysis Seminar, Massachusetts Institute of Technology, Cambridge, MA, April 14-16, 1982. [~ 2.1-13 Private communication, Ransom, V. H. (EG and G Idaho, Inc.) and Fernandez, R. T. (YAEC), June 14, 1982. (
l Table 2.1-1 Allowed Fluid Thermodynamic States Fluid All Liquid Two-Phase f41xture All Vapor Static Quality X=0 0<X $ 1/2 1/2 < X < 1 X=1 Vapor State lionexistent Sat Sub, Sat, Sub, Sat, or Sup or Sup Liquid State Sub, Sat, Sub, Sat, Sat flonexistent or Sup or Sup Sub = Subcooled Sat = Saturated Sup = Superheated O
2.2 Hydrodynamic Components q L' The hydrodynamic model described in the previous section is implemented j in the RELAP5YA and RELAPS MODI codes through the selection of hydrodynamic l components. These components serve as building blocks and provide a high l degree of flexibility for the user to simulate a variety of LWR and other thermal-hydraulic systems. Both RELAP5YA and RELAP5 M001 use the~ concept of hydrodynamic volumes (fluid control volumes) and hydrodynamic junctions (momentum control volumes). Hydrodynamic volumes generally contain averaged state properties. These include primary dependent variables (p, X,X'n p g, u , P) and auxiliary variables (af, ag, T f, T ,g X , eand volume averaged phasic velocities). The wall heat transfer rate, vapor generation rate, and mechanical energy dissipation terms are accounted for wi?.hin these volumes. Hydrodynamic junctions generally contain the averaged phasic velocities and properties required for the flux terms at the open ends of hydrodynamic volumes. Fluid inertia, convected momentum, gravitational forces, interphase drag, wall friction, localized pressure losses, and critical flow are accounted for within hydrodynamic junctions. f Twelve types of hydrodynamic components are available in RELAP5YA for constructing a simulation model of a thermal-hydraulic system. These components are the vehicle for entering input data, selecting user options, and applying the hydrodynamic model to fluid regions within the system or specifying fluid system boundary conditions. Five components (SNGLVOL, SNGLJUN, PIPE, ANNULUS and BRANCH) apply the basic hydrodynamic model to internal fluid regions. Another five components (SEPARATR, PUMP, JETPMP, VALVE and ACCUM) modify the basic hydrodynamic model to account for unique hydrodynamic phenomena within separators, centrifugal and jet pumps, valves, and accumulators. The jet pump component, JETPHP, does not exist in RELAP5 M001. The accumulator component, ACCUM, has been extensively modified from that contained in RELAP5 MOD 1. Finally, two components (TMDPVOL and TMDPJUN) allow the user to specify hydrodynamic boundary conditions for a system model. The following sections describe pertinent features and typical applications of these models, and identify sections contained within this document that provide additional information. V l
l 2.2.1 Time-Dependent Volume l O A Time-Dependent Volume, TMDPVOL, must be used at each boundary where fluid can enter or leave the system to provide a fluid source or sink. The user must specify a set of state properties that are constant, a function of time, or a function of a control system parameter. These properties are used for fluid sources, but only the pressure is used for fluid sinks. Time-Dependent Volumes can be used to specify conditions for feedwater and ECC systems, containment volumes, sink volumes at the end of steam lines, and as a pressurizer when establishing the steady state of a system at a known pressure. Further information is contained in Section 3.2.2 of Appendix B and Section 7.4 of Volume II. 2.2.2 Time-Dependent Junction A Time-Dependent Junction, TMDPJUN, is used to specify phasic velocities or mass flow rates as constants, functions of time, or as functions of a control system parameter. Tnis component can connect a .ime-Dependent Volume to an internal system volume, or connect two internal system volumes. The following list provides several examples of how this component can be used:
- a. To specify feedwater or ECCS flow rates as a function of time,
- b. To specify feedwater or ECCS flow rates as a function of downstream pressure or pressure difference using a control system parameter for the independent variable,
- c. To set feedwater mass flow rates equal to steam exit mass flow rates for the steady-state initialization of BWRs or PWR steam generators, and
- d. To set the mass flow rate in a steam separator return line to equal the incoming liquid aass flow rate for BWR steady-state initialization.
O m
)
1 However, the user must use caution when using this component. The boundary
/ j conditions in a system calculation must not be overspecified. The user must 'O apply caution when specifying outflows from a system or when using a time-dependent junction between two active hydrodynamic volumes, since 1.he upstream donored properties may not be known a priori or may not equal junction properties due to area changes. The Time-Dependent Junction is discussed further in Section 3.2.3 of Appendix B and Section 7.6 of Volume II.
2.2.3 Single Volume, Branch, Pipe, and Annulus The SNGLVOL, BRANCH, PIPE, and ANNULUS components are hydrodynamic volumes that can be used to represent general internal fluid regions within a system. At least one junction must be connected to each component. Contrary to statements in Appendix B, multiple junctions can be connected to the inlet and/or outlet ends of all these components. Each of these components may contain heated structures that exchange energy with fluid contained in the volume. p One of the principal differences among these components is the manner U in which input data is entered for each component. The SNGLVOL component allows volume related data to be entered for a single volume only. The BRANCH component allows volume related data to be entered for a single volume and junction related data to be entered for up to nine junctions. The PIPE and ANNULUS components allow volume related data to De entered for "NV" sequential volumes and "NV-1" internal single junctions, where "NV" must be greater than zero and less than 100. Thus, the user may save time preparing an input deck or file by a judicious selection of these components for a system model. The second principal difference is that the ANNULUS component uses, the Annulus Flow Map exclusively for the interphase drag calculation, whereas the other components use either the Vertical or Horizontal Flow Maps. Additional information about these components is contained in Section 3.3.1 of ?.ppendix A and Sections 3.2.4 through 3.2.7 of Appendix B. User input information is provided in Sections 7.3, 7.7 and 7.8 of Volume II. We recommend that the Annulus component not be used in vertical flow geometry. In addition, the Two-Dimensional Branching technique described in Section 3.2.7.2 of Appendix B is not reconnended since it is known that this technique can create g) non-physical recirculation through the adjacent junctions. i
l L 2.2.4 Single Junction , A Single Junction, SNGLJUN, is one junction (momentum control volume) that can be used to represent the flow path between two adjacent system volumes or between a system volume and a Time-Dependent Volume. The junction area is allowed to be different from the flow area in either of the adjoining volumes. The user must be very careful that no elevation change exists between the ends of the two volumes connected by this or any other junction specified by other components such as BRANCH, PUMP, JETPMP, or SEPARATR. Otherwise, nonphysical flows can be introduced because the hydrostatic force is not properly balanced. The junction input data for this component and most other junctions specified in other components allow the user to select several options. These are described in Section 7.5 of Volume II. 2.E.5 Separator The Separator component, SEPARATR, provides a preliminary model to simulate the steam separation process in steam separators or dryers. This component is similar to the BRANCH component except for the following. At least one junction must be describ2d in the input data. The first junction described is assumed to be the exit from the top of the separator. This junction is forced to have one hundred percent static quality for positive outflows. If reverse flow occurs through this junction or if the separator fills with liquid, then the convected quantities revert to those of the upstream volume. The Separator model is described in Section 3.2.8 of Appendix B and Section 7.9 of Volume II. An alternative method was used for modeling the steam separator in the Two-Loop Test Appv3tus to obtain steady-state initialization. This method is described in Section 5.2.3.3 of Volume III, and provided reliable results. 2.2.6 Centrifugal Pumps A centrifugal pump can be simulated by the PUMP component using one of two options: the homologous performance model, or the angular drive velocity model . The homologous performance model determines the pump rotational speed from the angular momentum conservation equation applied to the rotating
, i parts. ' This relates the product'of the pump moment of inertia and angular l n acceleration to the net' torque acting on the pump. The net torque accounts l lkh for the electrical torque from the motor, friction and windage losses' and the hydraulic torque on the impeller. The angular drive velocity mode 1' determines
]
the pump rotational speed from a user supplied table that contains rotational speed as a function of time or as a function of a control system parameter. I This second model is useful when the pump speed' history is known or when a steam turbine-driven pump is to be modeled. Once the pump rotational speed and volumetric flow rate are determined, tne homologous flow to speed ratio is computed. .This quantity and the void fraction in the pump volume are used to estimate the head change across the pump from tabular performance data. The centrifugal pump models are described in Section 2.3.1 of Appendix A and Section 3.2.9 of Appendix 8. User input information is presented in Section 7.11 of Volume II. 2.2.7 Jet Pumps Jet pumps such as those contained in most Boiling Water Reactors can be simulated with RELAP5YA. The throat region is modeled by using the new jet
'l ~
pump component, JETPMP. This component accounts for the momentum mixing effect due to unequal velocities in the drive and suction nozzles in the normal performance region. It also accounts for variable mechanical energy losses within the throat region for all performance regions. The jet pump diffuser and tailpipe sections are modeled using standard hydrodynamic components, such as SNGLVOLs and SNGLJUNs or PIPE, that were described earlier. The new jet pump model is described in Section 3.3 of this volume. Input data is described in Section 7.12 of Volume II. 2.2.8 Valves Five types of valve models are available to simulate a variety of valve actions in a thermal-hydraulic system. These consists of a Trip Valve, Check Valve, Inertial Check Valve, Motor-Operated Valve and a Servo Valve. Each valve model represents a special hydrodynamic junctibn in which the flow area can change when certain conditions occur. These valve models can be classified in two categories. Trip and Check Valves open or close instantaneously. Inertial Check Valves, Motor-Operated Valves and Servo w- - _ _ _
l Yalves open or close gradually. These valves are described in Section 3.3.3 of Appendix A and Section 3.2.10 of Appendix B. 2.2.9 Accumulator The Accumulator component, ACCUM, is a mechanistic, lumped parameter model for simulating the activation and behavior of a PWR accumulator. The model consists of the accumulator tank and the surge line that connects the tank to the Primary Reactor Coolant System. The surge line contains a check valve. The model accounts for the polytropic gas expansion process that forces emergency core coolant from the tank through the surge line into the Reactor Coolant System. Heat transfer from the tank wall and liquid surface to the gas region, and condensation in the gas region are taken into account. The hydrodynamic model for the liquid region accounts for the liquid inertia, wall friction, gravity force and form losses in the tank and surge line. The accumulator nodel in RELAP5YA has bee.. extensively revised from that contained in RELAPS MOD 1, Cycle 14, and is described in Section 3.4 of this volume. User input information is presented in Section 7.13 of Volume II. 2.3 Process Models O The RELAP5YA code contains models for simulating many other transient processes pertinent to light-water reactors and thermal-hydraulic systems. These include thermal power sources and sinks, conduction heat transfer within solid materials, fuel rod behavior, control systems and trips. These models are generally the same as those in the RELAP5 MODI code, except for the fuel rod behavior models which are only contained in RELAPSYA. Each model is briefly discussed below. Sections contained in this document that provide additional information on each model are identified. 2.3.1 Thermal Power Thermal power generated within solid material can be simulated by two options: the point reactor kinetics model, or by user specified power tables. O i 3
-The point reactor kinetics model simulates power generated within a - nuclear core by the fission process, and by actinide and fission product ,
i j decay. This model assumes that the core power can be separated in the product of a spatial and a temporal function. The spatial function does not change with time. The initial condition assumes that the reactor is at a steady-- state condition. Thus, core power history effects must be accounted for in the initial conditions that are entered. The model accounts for the following ' reactivity effects:
- a. moderator density and temperature changes
- b. fuel temperature changes
- c. control and SCRAM rods.
The spatial distribution of core power that is deposited in solid structures is specified on the source data cards for heat structures described in Section 8.1.10 of Volume II. In addition, a small fraction of the core power is directly deposited in the moderator due to gamma and neutron r~') V interactions with the fluid. The direct moderator heating effect, Qd , is not stated explicitly in the RELAP5 M001 documents, but the computation is contained in the point kinetics subroutine, RKIN. The direct moderator heating source is added to the convective heat source in the HTADV subroutine to yield the net heat addition per unit volume for the fluid mixture thermal energy equation given in Section 2.1.1. The differential and finite difference equations for the point reactor kinetics model are given in Sections 2.,3.3 and 3.3.4 of Appendix A. User guidelines for this model are presented in Section 7.0 of Appendix B. The input requirements are contained in Section 11.0 of Volume II. Thermal power sources within solid structures can also be specified by entering a table of power versus time. This power source can be distributed within heated structures by entering distribution factors on the source data cards. This modeling feature is very convenient to use when the power history in a solid material is known a priori. This will exist for LWR cases where the neutronic to thermal-hydraulic coupling is weak such that independent physics calculations can be made and entered as core power history data. This ) l l L x_
l 1 feature is also generally used to simulate the power history in electrically heated fuel rod simulators contained in thermal hydraulic experiments. Thermal power source tables are described in Sections 4.3 and 5.0 of Appendix B. The exothermic oxidation of Zircaloy and steam at high temperature l conditions, such as certain LOCA accidents, creates an additional thermal power source within the core region. This source is accounted for in RELAP5YA, and is described in Section 5.0 of tnis volume. 2.3.2 Conduction Heat Transfer A general one-dimensional transient conduction heat transfer model is contained in RELAP5YA and RELAP5 MOD 1. This model can-be used to simulate thermal conduction within fuel rods, fuel assembly channels, pipe and vessel walls, steam generator tubes, and other pertinent solid structures. The structures can have a rectangular, cylindrical or spherical snape. The heat structure geometry is assumed to be constant in time. The solid structure may be composed of several different materials. Temperature dependent thermal
~
conductivities and volumetric heat capacities (pc) can be supplied for each material or selected from internal thermal property tables for certain materials. At least one surface of each heat structure must be connected to one of the following hydrodynamic volumes: SNGLVOL, BRANCH, PIPE, ANNULUS, PUMP, JETPMP, SEPARATR. Any of several boundary conditions can be selected by the user at the surfaces of the conducting heat structure. These are:
- a. adiabatic surface
- b. user specified temperature versus time
- c. user specified heat flux versus time
- d. user specified heat flux versus surface ter,erature
l J e, internal heat transfer correlations and logic (see Sections 4.1 and _ 4.2) L]
- f. rewet and quench model for reflooding conditions (see Section 4.3)
- g. multiple surface radiation model- (see Section 4.4)
- h. heat transfer logic options (see Section 4.5)
Certain internal heat transfer correlations have been modified in RELAP5YA compared to RELAP5 MOD 1, and are described in Section 4.0 of this volume. In addition, RELAP5 MOD 1 does not contain options f, g, and h identified above. Section 3.2 of Appendix A describes the equations and numerical solution method for the conduction heat transfer model. Section 4.0 of Appendix B provides user guidelines. Section 8.1 of volume describes the input requirements. 2.3.3 Fuel Rod Behavior (n) A set of fuel rod behavior models has been incorporated into RELAP5YA to simulate the thermal-mechanical behavior of fuel rods under transient and accident conditions. The models consist of the following:
- a. internal fission gas pressure
- b. fuel rod deformation and rupture
- c. gap heat transfer
- d. Zircaloy - s,ater reaction.
These models are essentially the same as those contained in the T00DEE2-EM code. However, the internal fission gas model has been simplified, and the deformation and rupture model has been modified to comply with NUREG-0630. The fuel rod behavior models are described in Section 5.0 of this volume. Input requirements are contained in Section 8.2 of Volume II. ; (D V l
2.3.4 Control Systems A generalized control system algorithm is contained in RELAP5YA and O RELAPS MOD 1 that solves simultaneous algebraic and ordinary differential equations. This feature provides the capability to simulate many automatic j control systems used'in Light Water Reactors and thermal-hydraulic systems. Examples include the following:
- a. pressurizer heaters and sprays
- b. feedwater control systems
- c. Variable speed and steam turbine driven pumps
- d. motor-generator sets that drive certain BWR recirculation pumps
- e. water level signals that actuate certain trips.
However, this algorithm can also be used to simulate other actions and phenomena that can be described by algebraic and/or ordinary differential equations such as operator actions that affect the primary system coolant s inventory. In addition, the control system algorithm can De used to define auxiliary computer output (minor edit) quantiti3s. Examples include the following: ) i
- a. differential pressures and temperatures l
- b. internal structural temperatures f
- c. mass inventories in selected regions
- d. collapsed liquid levels
- e. integrated mass and energy outflows.
The control system algorithm is described in Section 8.0 of Appendix B. The input requirements are contained in Section 13.0 of Volume II.
i 1 2.3.5 Trips-r\ : i) A generalized trip algorithm is contained in'RELAP5YA and RELAPS M001.' This capability allows certain actions to be initiated or' terminated wnen user
'specified conditions are satisfied during' a transient. Examples. include the following:
- a. terminating main feedwater and activating auxiliary feedwater pumps from a low steam generator inventory signal'
- b. initiating a SCRAM from a variety of signals such as low inventory
- c. activating an ECC System on a low water signal
- d. activating a BWR Automatic Depressurization System upon a low level signal with a 120 second time' delay e, activating the closure of main steam line isolation valves.
The trip algorithm performs two functions: to det' ermine when a trip-action occurs, and to determine what action is to be taken. Two types of trips are contained within the algorithm: - variable trips, and logical trips. A variable trip compares one variable to a second variable plus a constant which are specified by the user. .The comparison can use one of the following Fortran operations: LT, LE, EQ, GE, GT. If the comparison is true, then a user specified action occurs. A Logical Trip evaluates a statement that relates two user specified quantities using the following logical ~ operations: l AN'D, OR (inclusive). XOR (exclusive). If the statement is true, then a user specified action is taken. Section 6.0 of Appendix B describes the trip algorithm in detail. The input requirements are presented in Section 6.0 of Volume II. L-_______________
l 2.3.6 General Tables A General Table algorithm is contained in both RELAP5YA and RELAP5 MOD 1 9 that allows the user to enter tabular data for models discussed in the previous sections. This algorithm is described in Section 5.0 of Appendix B. The input requirements are contained in Section 10.0 of Volume II. 1 2.4 Program Structure l The RELAP5YA program structure is outlined in this section. This information is primarily intended to provide tne user with an understanding of the information flow and sequence of subroutine calls within the RELAP5YA program. This section is supported by tne RELAP5YA Subroutine Glossary contained in Appendix C. Tne glossary lists all subroutines contained within the main RELAP5YA program in alphabetical order, briefly states their principal functiba, and lists the calls from each subroutine to other subroutines. Subroutines that contain an asterisk indicate new subroutines
' incorporated into RELAP5YA that are not contained in RELAPS M001.
p ' The RELAPSYA program structure is indicated by the diagrams presented in Tables 2.4-1 through 2.4-4. Subroutine names are contained within boxes. Note that the mnemonic names selected for the subroutines suggest their function. The vectors indicate the sequence of calls and information flow. l These should be read from left to right, and then from top to bottom. In general, the tables and glossary show that the RELAP5YA code and its predecessor, RELAP5 M001, use a top-down program structure tnat is very
]
modular. This modularity is based upon subroutine functions and/or physical models. The program architecture facilitates:
)
- a. Understanding the information flow and transient solution sequences.
- b. Error locations and error corrections,
- c. Addition of new subroutines.
- d. Efficient programming.
The RELAP5YA and RELAPS MODI codes contain many comment cards
,]
throughout. These cards define major program variables and parameters, identify subroutine functions, and identify impo-tant solution steps within
- j. subroutines. The efficiency of the two code versions is enhanced by the following:
- a. Careful selection of blank common blocks and equivalence statements to allow dynamic storage of information that tailors computer memory requirements to the current problem size.
- b. Use of packed words that generally contain flags and pointers for program variables and parameters.
RELAP5YA is the main driver routine for the RELAP5YA code as shown in Table 2.4-1. The first subroutine called is INPUT which controls the processing of input data for all problem types. This includes NEW, RESTART, PLOT, REEDIT or STRIP problem types. NRTS library routines are extensively used to facilitate this information processing. The most common proolem type is NEW. The RNEWP subroutine, diagrammed in Table 2.2-2, processes most of ()
\_,/ the information required. This subroutine contains two major sets of subroutines. The R level set, which contain an R as the first character in their name, generally read information from input cards, initialize program variables where possible, and perform many input data checks. The I level set, indicated by an I as the first character of the subroutine names, complete the initialization of program variables and input data checks. After all input data processing is completed, the code returns to the main program, RELAPSYA. If input errors were detected, then the code prints error messages and terminates execution. If no input errors were detected, then the main program calls TRNCTL.
The TRNCTL subroutine controls the solution for the TRANSIENT option (the only option currently implemented) of NEW and RESTART problem types. This subroutine calls TRNSET to set up arrays and indices, and then calls TRAN to perform the transient advancement. From a user's' viewpoint, TRAN and its subroutines embody the heart of the code. This routine calls the following subroutines: (v)
DTSTEP - Controls the hydrodynamic time step. TRIP - Executes the trip algorithm. 9 TSTATE - Calculates state properties for time-dependent volumes and ' junctions. HTADV - Controls the fuel behavior and heat transfer calculations; this subroutine is further described below. 1 HYDRO - Controls the solution of the hydrodynamic model; this subroutine is further described below. RKIN - Eyecutes s the point reactor kinetics calculation. CONVAR - Executes the control system algorithm. ; Finally, the TRNFIN subroutine is called which manipulates computer storage space and files. Upon completion of a transient problem, the code returns to the main program to perform any final actions. These include final actions on a restart-plot file and/or plotting information from tne case executed. If the problem type was specified as PLOT, REEDIT or STRIP, then the code would bypass TRNCTL and proceed to the appropriate subroutine. Table 2.4-3 contains a diagram that illustrates the HTADV subroutine structure. The new radiation heat transfer calculation is contained within this subroutine. The fuel behavior structural option, which contains the PGAPR, DFRMR and HGAPR subroutines, is executed from HTADV when this option is selected. The Zircaloy-water reaction option is executed by QZRWR when this option is selected. Updated material properties for the conduction heat transfer calculation are obtained by the MADATA subroutine. Finally, the conduction heat transfer calculation is performed in' the HTCOND subroutine. This includes application of appropriate heat transfer boundary conditions obtained from the HTRC1 subroutine. HTADV provides the thermal energy source term for the hydrodynamic model.
3 i Table 2.4-4 contains a diagram that illustrates the HYORO subroutine ]
- j. structure. The first level of subroutines, and their functions, that are l ( ,) called by HYDRO are:
1 JPROP - Updates junction properties Dased upon previous time step variables. ] YOLVEL - Computes averaged phasic velocities for hydrodynamic volumes i that are required in certain subsequent routines. MDOT - Estimates a preliminary interphase mass transfer rate at the new time point. I FIORAG - Computes the steady and dynamic coefficients for the interphase drag terms. HZFLOW - Computes the additional body force term in the difference momentum equation for stratified low flow conditions in horizontal components. 73 w] I FWDRAG - Computes wall friction coefficients. l HLOSS - Computes local pressure drop coefficients for junctions that use the abrupt area change option. JETPMP - Computes the momentum-mixing source terms and mechanical energy loss coefficients for the throat region of each jet pump. VEXPLT - Obtains centrifugal pump and accumulator information, initialized certain source terms for the EQFINL subroutine, computes a preliminary estimate of the phasic velocities and velocity derivatives with respect to pressure, and computes the dissipation coefficients for the thermal energy equation. JCH0KE - Checks for critical flow at user-specified junctions, and (~] V recomputes the phasic velocities for those that are choked.
1 i I JPROP - Resets junction properties for choked junctions. i PRESEQ - Computes the elements for the coefficient matrix of the pressure equation. SYSSOL - Obtains new time pressures for all hydrodynamic volumes. YFINL - Computes new time phasic velocities. EQFINL - Computes new time values for p, u , X, X n
, and Ig, and mass flow rates.
4 STATE - Computes new time state properties for all hydrodynamic l volumes, and monitors the mass error parameters. l l Execution of a RELAPSYA problem requires the following information: i
- a. Job Control Cards: Refer to site-specific j computer operating system l l
manual s. l
- b. RELAP5YA Program:
Described in this document.
- c. Input Deck or File: See Volume II for input requirements.
- d. NRTS Environmental Library Routines: References 2.4-1 and 2.4-2.
- e. Water Property Routines: STH2XT file contained in the RELAPS M001 transmittal package.
l The following sections describe the details of new models added to the Dase code, RELAPS M001 Cycle 18, to create RELAPSYA. In general, these modifications have been made in a manner that retains the code architecture , and programming philosophy of RELAPS M001.
C-o ,
,I -
~'
'_)_j' _,
& q
]
' h I References l
.]
1 L D.' 2.4-1 Pfeifer,l C. J., CDC-6600- FORTRAN- Programming - Bettis Environmental 'j' L b. Report, WAPD-TM-668 . January.1967. l; 2.4-2 Wagner, R. J., et al.. INEL Subroutine Package Manual, ' Idaho Nationalf J Engineering Laboratory, December 1972. l r. l 1
,1
, o -
b O _ z_ _ = _ _ __1 _--___ _ _ _ _ _ _ _ _ _ _ . . _ _ _ _ _ _ _ _
Table 2.4-1 PF'.AP?YA Prorram Struerufe l RELAPSYA l
- l GNINT , -! NRTS LIB l lRCARDSl '. NRTS LIB l
- - =( INP2 1
- , INPU T l
'RNEWP l H NRTS LIB l W RPLOT l f NRTS LIB l W RDKLDI l
-- -m=l R ST RI P l : l NRTS LIB l M NRTS LIBj
-*={ TSETSL i -lNRTS LIB}
---mai TRNSETl
-=4 TCNV5L ]
M ISUMRY l rl MIREC
==4 DTSTEPi .]
=*i TRIP l --=4 MOVER l
--+4 TSTATEl H OUTPUT l TRAN l HTADV [ --ma{ PLTREC l
- !TRNCTLl .
f M HYDRO l l PLTRECX { M RKIN ] M REMTIM]
--e={ CONV AR I H RST REC l
- l TRNFIN i -i NRTS LIB l 1]RSTFINl : ' NRTS LIB l
--*4 NRTS LIB l l P M)TMD l :' PLOTIT l H PLOTSX l o
l REEDITi -lNRTS LIB l
! STRIP , - ! NRTS LIB l 9
! 1
-_ b
2
- t' \' Table 2,4-2 RNLVP Subroutine Struct3 4 i RNEWP l
, RESTD 'l ' RCUELT [
RRESTF l , RFIPE l
-- -- o4 RTMDV l W RTSC 1 -----* l RPUMP l W RMIEDT 1, ----ei RBRNCH l' M RPLCrrN l ---o l RCORE l H RTR1P l W RTMDJ l
' RNONCN l W R$NGV l W RCOMPN l RSNGJ 1- l i
------ei RHTCMP l ;' .RVALVE ]
W RMADAT l ----*i RACCUM l H RRADHT l H NRTS LIB l W RRKIN ,'RKINH [ W RGNTBL l ---o4 ISTATE l b' M RCONVR 1 IPIPE l
---e={ ISNGJ l*
% IPLOT l ----*4 POLATL l
----*-{ ITRIP l POLATS l IGNTBL l ---*4 ICMPF l IJ PROP l ICOMPN ; ,
H IHTCMP ; -lHT1SSTl. W INVJT l W IRKIN 1 ----* i IVLVEL l
---*{ IRADHT l l IPUMP l 1CONVR l -- --o 1 1 EDIT l
-----+l IMIEDT l [ NRTS LIB l r
i WRPLID 1 i f
?
\,
)
7 c. j
~
I t Table 2.4-3 G' IITADV Subroutine Structure iHTADV l
' RADHT j l HT1TDP l I
kRTS LIB l 1; POLATS 1 { W PGAPR '
;! RUPTEM i
,DFKMR , M
-lHCAPR l --+4 CTHSTR 1 W FTHEXF l M PLASTIC i ,RUPTEM l H KdROL'T l
-l QZR'dR H M KWRIN l
- ' MADATA l lHTCONDj
'POLATS l
;IHTRCl l
- l DITTUS i
- P REDN B ' ! CHFCAL l
' PSTDNB ' ' NATCIR l
- l CONDEN l 1 NATCIR l
,?OOLDNB , lNATCIRI
_' QUENCH l
, ' TMS FB l i 1
)
l 1 I j
e , a s i t t e
+a i [
V .,e. Table 2.h-4 w }" . . . HYDRO Subroutine Structure. K : (" ( . 1 NYDRO l-l JPROP l' -*{ VALVE I FLOREGA FISUB 1' VOLVEL l FIBUBl. FIANN -
-, MDOT - l, , FICALA- _
~
FIANN1' VRT map FISLC FIMIST FIDIS FLOREGB FISTR FICALB ~- FIBUB
~
!? 10tT esp FIANN FIDIS FIDRAG H FLOREGC FICALC __ FIBUB ANN asp FIANN FIDIS; FICALD FLOREGD
- FIBUB.
RMF map f , FIDIS.
' HZFLOW l FwDRAc ; FRICT F [
RLOSS 1 l JETPHP l. H PUMP l
, VEXPLT ,
' ACCUM l JCHOKE _l ', MOODY l
- JPROP '
[ PRESEQ j-SYS50L l VFINL l
- , EyrinL 1 H F5ATFD ]
l STATE l - STH2X l
\
l l 1 Sections 3.0, 4.0, and 5.0 are proprietary to Yankee Atomic Electric Company, and therefore were deleted. I i [~ t l l 1
6.0 COMPLIANCE WITH 10CFR50 APPEl101X K CRITERIA I V) Appendix K to 10CFR Part 50 delineates required and acceptable features of models for LOCA licensing analyses. Some of the requirements identified in Appendix K are input-related; others are models to be incorporated in the computer programs. All Appendix K requirements are identified in the following subsections. Compliance with requirements related to code models are discussed in detail. Since Yankee intends to use RELAP5YA in the near future to perform Large Break and Small Break LOCA licensing analyses for ; Boiling Water Reactors and only Small Break LOCA licensing' analyses for Pressurized Water Reactors, those requirements which deal with PWR Large Break phenomena are not addressed. Yankee intends to submit two sample problems to the llRC soon after > RELAP5YA has been approved. One will demonstrate the code application to BWR analyses, the other to PWR analyses. Input-related Appendix K requirements ; will be addressed in these reports and the appropriateness and conservatism inherent in these items will then be established.
,a
() 6.1 Required and Acc=ptable Features of the Evaluation riodels 6.1.1 Requirement I.A: Sources of Heat During the LOCA For the heat sources listed in paragraphs 1 to 4 below it shall be assumed that the reactor has been operating continuously at a power level at least 1.02 times the licensed power level (to allow for such uncertainties as instrumentation error), with the maximum peaking factor allowed by the technical specifications. A range of power distribution shapes and peaking factors representing power distributions that may occur over the core lifetime shall be studied and the one selected i. l should be that which results in the most severe calculated consequences, for the spectrum of postulated [ breaks and single failures analyzed. Requirement I.A stated above is an input-related requirement. The power level will be entered as at least 1.02 times the licensed power level. Peaking factors, as well as power distribution shapes selected for the 0) ( licensing analyses, will be justified in the sample problem submittal.
-255-L - ____
t f Requirement I.A.1: The Initial Stored Energy in the Fuel [ The steady-state temperature distribution and stored energy in the fuel before the hypothetical accident shall be calculated for the burnup that yields the highest calculated cladding temperature (or, optionally, the highest calculated stored energy). To accomplish this, the thermal conductivity of the UO2 shall be evaluated as a function of burnup-and temperature, taking into consideration differences in initial density, and the thermal conductance of the gap between the U02 and the cladding shall be evaluated as a function of the burnup, taking into consideration fuel densification and expansion, the composition and pressure of the gases within the fuel rod, the initial cold gap dimension with its tolerances, and cladding creep. Yankee intends to use the FROSSTEY Computer Code (Reference 6.0-1) to calculate gap conductance and stored energy values at the start of the transient. The FROSSTEY code is currently being reviewed by the NRC staff and will meet the requirements of this Section I.A.1, including the effect of uranium pellet densification. From FR0SSTEY calculations, the associated gap conductance parameters including gas composition, internal pressure, and the appropriate fuel and cladding dimensions at the initiation of a LOCA event will be used to determine input to RELAP5YA. These calculations will be used to obtain a match of the fuel stored energy and gas volumes between RELAP5YA and FROSSTEY. For a fixed LOCA limit for the entire plant cycle, the initial stored energy will be calculated for the burnup that will yield the nighest calculated cladding temperatures. However, if a fixed LOCA limit is unacceptable with regard to desired operating margins, burnup-dependent LOCA limits will be established. These calculations will be performed with consistent sets of initial stored energy, initial pressure, and other fuel values calculated by the FROSSTEY code at that particular burnup. Requirement I.A.2: Fission Heat t Fission heat shall De calculated using reactivity and reactor kinetics. Shutdown reactivities resulting from temperatures and voids shall be given their minimum plausible values, including allowance for uncertainties, for the range of power distribution shapes and peaking factors indicated to be studied above. Rod trip and insertion may be assumed if they are calculated to occur.
-256- ;
'The fission. heat calculated by RELAP5YA uses a point reactor kinetics model. Feedback effects from changes in water' density, fuel temperature, and L water temperature, as well as control rod insertion are included. These >
quantities'are supplied as. input to the code. The reactor kinetics model is described in Section 2.3.3 of Appendix A. Control rod insertion rate and the moderator and fuel temperature feedback tables are problem dependent quantities. The selection of these tables will be justified in the sample problem. Requirement I. A.3: Decay of Actinides The heat from the radioactive decay of actinides, including neptunium and plutonium generated during operation, as well as isotopes of uranium, shall be calculated in accordance with fuel cycle calculations and known radioactive properties. The actinide decay heat chosen shall be that appropriate for the time in the fuel cycle that yields the highest calculated fuel temperature during the LOCA.
'^') '
The heat from radioactive decay of actinides is included in RELAP5YA. .
~~ It is described in Section 2.3.3 of Appendix A. The decay heat production assumes infinite operation. The ratio of U-238 atoms consumed per U-235 , atoms fissioned is a user-supplied input and is problem dependent. The selection of this variable will be justified in the sample problem.
Requirement I.A.4: Fission Product Decay The heat generation rates from radioactive decay of fission products shall be assumed to be equal to 1.2 times the values for infinite operating time in the ANS Standard (Proposed American Nuclear Society Standards -
" Decay Energy Release Rates Following Shutdown of Uranium-Fueled Thermal Reactors". Approved by Subcommittee ANS-5. ANS Standards Committee, October 1971). The fraction of the locally generated gamma energy that is deposited in the fuel (including the .
cladding) may be different from 1.0; the value used shall I be justified by a suitable calculation. n
-257-
l The heat generation rates from radioactive decay of fission products have been included in RELAP5YA. The model is described in Section 2.3.3 of Appendix A and is identical to the model used in WREM (Reference 6.0-2). The h decay heat rates obtained by this model were compared with the ANS standard values. It was concluded (Reference 6.0-2) that the ANS standard fission product decay heat data are well represented by this decay heat model. RELAPSYA allows for a fission product yield factor as an input parameter. A yield factor of 1.2 will be used for all licensing analyses. Requirement I.A.5: iletal-Water Reactor Rate The rate of energy release, hydrogen generation, and cladding oxidation from the metal / water reaction shall be calculated using the Baker-Just equation (Baker, L., Just, L.C., " Studies of Metal Water Reactions at High Temperatures, III. Experimental and Theoretical Studies of the Zirconium-Water Reaction", ANL-6548, Page 7 Hay 1962). The reaction shall be assumed not to be steam limited. For rods whose cladding is calculated to rupture during the LOCA, the inside of the cladding shall also be assumed to react ; cer the rupture. The calculation of the reaction rate on the inside of the cladding shall also follow the Baker-Just equation, starting at the time when the cladding is calculated to rupture, and extending around the cladding inner circumference and axially no less than 1.5 inches each ; way from the location of the rupture, with the reaction ! assumed not to be steam limited. The Baker-Just equation has been incorporated in RELAP5YA to calculate the energy release and the cladding oxidation caused by the Zircaloy-water reac tion. The reaction is assumed not to be steam limited. The model is described in Section 5.1.2.6. The metal-water reaction on the inner cladding surface is initiated at the onset of clad rupture. The reaction at the inner surface is calculated I for the entire surface area of the ruptured node. The ruptured node will not be allowed to be less than 3 inches in length for licensing calculations.
-258-
_ _ _ _ - - _ _ _ _ _ 1
t Requirem3nt 'I.A' .6: Reactor Internals Heat Transfer j k' {
/7 Heat. transfer from piping, vessel walls, and non-fuel
()l internal hardware shall be taken into account. j Heat transfer from piping, vessel walls, and other non-fuel internal hardware will be included in Licensing calculations. Heat slabs, with properties. equivalently lumped for the. internal volumes will be specified. The RELAP5YA heat conduction equation along with the heat transfer correlations will be used to calculate the heat transfer rates. Requirement I.A.7: Pressurized Water Reactor Primary.to-Secondary Heat Transfer Heat transferred between primary.and secondary systems through heat exchangers (steam generators) shall be taken into account. (Not applicable to' Boiling Water Reactors.) RELAP5YA possesses this capability. Steam generator tubes are modeled
. as heat slabs with two heat transfer surfaces. Heat transfer coefficients
' appropriate for the . respective fluid conditions on the two sides are
' - calculated. The conduction equation is used to calculate the direction and magnitude of heat transfer.,
6.1.2 Fuel Rod Behavior Requirement I.B: Swelling and Rupture of the Cladding and Fuel Rod Thermal Parameters Each evaluation model shall include a provision for predicting cladding swelling and rupture from consideration of the axial temperature distribution of the cladding and from the difference in pressure between the inside and outside of the cladding, both as functions of time. To be acceptable, the swelling and rupture calculations shall be based on applicable data in such a way that the degree of swelling and incidence of rupture are not underestimated. The degree of swelling and rupture shall be taken into account in calculations of gap conductance, cladding oxidation and embrittlement, g and hydrogen generation. (
-259-l
The calculations of fuel and cladding temperatures as a function of time shall use values for jap conductance and other thermal parameters as functions of temperature and other applicable time-dependent variables. The gap conductance shall be varied in accordance with changes in gap dimensions and any other applicabic variables. RELAP5YA calculates the extent of swelling and the incidence of rupture as a function of the temperature and the differential pressure at the cladding. Cladding swelling and rupture is accommodated in the calculations of gap conductance, hydrogen generation, and flow blockage. The fuel rod behavior models are described in detail in Section 5.0. The fuel rod behavior models are very similar to those used in T00DEE2-EM (Reference 6.0-3). However, the clad rupture correlation and the blockage tables were obtained from NtJREG-0630 (Reference 6.0-4). 6.1.3 Blowdown Phenomena l Requirement I.C.1: Break Characteristics and Flow O'
- a. In analyses of hypothetical loss-of-coolant accidents, a spectrum of poss1 Die pipe DreaKs snalI oe l considered. This spectrum shall include instantaneous double-ended breaks ranging in cross-sectional area up to and including that of the largest pipe in the Primary Coolant System. The analysis shall also include the effects of longitudinal splits in the largest pipes, with the split area equal to the cross-sectional area of the pipe.
This is an input-related requirement primarily for large breaks. Yankee currently intends to use RELAP5YA for the analysis of large break LOCAs for Boiling Water Reactors and for only small break analyses of Pressurized Water Reactors. For BWRs, the break spectrum will include double-ended guilloutine, as well as longitudinal splits in the largest pipe.
- b. Discharge Model. For all times af ter the discharging tiuid has been calculated to be two-phase in composition, the discharge rate shall be calculated by use of the Moody model (F. J. Moody, " Maximum Flow Rate of a Single Component, Two-Phase Mixture", Journal of Heat Transfer, Trans American Society of dechancial Engineers, 87, No.
-260-
1, February,1965). The calculation shall be conducted with at least tnree values of a discharge coefficient applied to the postulated break area, these values 7 3 spanning the range from 0.6 to 1.0. If tne results s 4
) indicate that the maximum clad temperature for the hypothetical accident is to be found at an even lower value of the discharge coefficient, the range of discharge coefficients shall be extended until the maximum clad temperature calculated by this variation has been achieved.
The Moody critical flow model has been incorporated into RELAP5YA. The implementation of the model is described in Section 3.2. The Moody model will be used in all licensing calculations when the discharging fluid is calculated to be two-phase in composition. Analyses with discharge coefficients rangino from 0.6 to 1.0 will oe performed for large breaks in Boiling Water Reactors. However, small break analyses for PWRs, as well as for BWRs, will be performed with a discharge coefficient of 1.0.
- c. End of Blowdown. ( Applies only to Pressurized Water n Reactors.) For postulated cold leg breaks, all emergency (g cooling water injected into the inlet lines or the reactor vessel during the bypass period shall in the calculations be subtracted from the reactor vessel calcu'tated inventory. This may be executed in the calculation during the bypass period, or as an alternative, the amount of emergency core cooling water calculated to be injected during the bypass period may be subtracted later in the calculation from the water remaining in the inlet lines, downcomer, and reactor vessel lower plenum after the bypass period. This bypassing shall end in the calculation at a time designated as the "end-of-bypass", after wnich the expulsion or entrainment mechanisms responsible for the bypassing are calculated not be effective. The end-of-bypass definition used in the calculation shall be justified by a suitable combination of analysis and experimental data. Acceptable methods for defining "end-of-bypass" include, but are not limited to, tne following: (1) prediction of the blowdown calculation of downward flow in the downcomer for the remainder of the blowdown period; (2) prediction of a threshold for droplet entrainment in the upward velocity, using local fluid conditions and a conservative critical Weber number.
O
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3 The above requirement is applicable only to the analysis of large breaks in Pressurized Water Reactors. Yankee currently plans to use RELAP5YA to analyze the entire break spectrum for Boiling Water Reactors and to analyze only small breaks in Pressurized Water Reactors. We, therefore, are not' required to meet the above requirement.
- d. Noding Near the Break and the ECCS Injection Points.
The noding in the vicinity of and including the broken or split sections of pipe and the points of ECCS injection shall be chosen to permit a reliable analysis of the thermodynamic history in these regions during blowdown. The requirement stated above is an input-related item, and will be addressed in the sample problem. However, different noding options near the break were studied in detail. This study, as well as the recorraended nodalization approach, is described in Section 2.2 of Volume III. Requirement I.C.2: Frictional Pressure Drops The frictional losses in pipes and other components including the reactor core shall be calculated using models that include realistic variation of friction factor with Reynolds number, and realistic two-phase friction multipliers that have been adequately verified by comparison with experimental data, or models that-prove at least equally conservative with respect to maximum clad temperature calculated during the hypothetical accident. The modified Baroczy correlation (Baroczy, C. J., "A Systematic Correlation for Two-Pnase Pressure Drop", Chem. Enging. Prog. Symp. Series, No. 64, Vol. 62 1965) or a combination of the Thom Correlation (Thom, J.R.S., " Prediction of Pressure Drop During Forced Circulation Boiling of Water", Int. J. of Heat a Mass Transfer, 7, 709-724, 1964) for pressures equal to or greater than 250 psia and the Martinelli-Nelson correlation (Martinelli, R. C. Nelson, D.B., " Prediction of Pressure Drop During Forced Circulation Boiling of Water", Transactions of ASME, 695-702,1948) for pressures lower than 250 psia is acceptable as a basis for calculating realistic two-phase friction multipliers. Realistic frictional pressure drop models are used in RELAP5YA. The Colebrook correlation is used to calculate friction factors in turbulent flow regimes. The correlation accounts for the wall roughness effects. The HTFS modification of the Baroczy correlation is used to calculate the two-phase
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=
q y 3 e . multipliers. .The models ared' escribed in 'Section 2.1.3.3 of Appendix A. .I y . (}. Requirement,I.C.3: Momentum' Equation
.l I The: following' effects sha11J be' taken into account in the conservation of momentum equation: .(1) temporal change
]-l
' of momentum, (2) momentum convection. -(3) area ' change 1 momentum flux,'(4) mcmentum change,due to compressibility, (5) pressure loss resulting- from wall friction, (6) prNsure loss resulting from area change, and (7) gravitational acceleration.! Any omission of one
- or more of these tenns under stated circumstances shall be justified by comparative analyses or by. experimental data.
RELAP5YA treats the momentum equations for the liquid and the gaseous
. phases separately. All the ' items required for the taomentum equation are included in RELAPSYA. Section 2.1 of Appendix A' describes the hydrodynamic models used. in RELAPSYA.
~
Requirement I.C.4: Critical Heat Flux
\_/
- a. Correlations developed from appropriate steady-state and transient-state experimental data are acceptable for use in predicting the critical heat flux (CHF) during LOCA transients. The computer programs in which these correlations are used shall contain suitable checks to 4 assure that the' physical parameters'are within the range of parameters specified for use of.'the correlations by their respective authors,
- b. Steady-state CHF correlations acceptable for use in LOCA transients include, but are not limited to, the following: ,
(1) W 3. L. S. Tong, " Prediction of Departure from Nucleate Boiling for an Axially Non-uniform Heat Flux Distribution," Journal of Nuclear Energy, Vol. 21, 241-248, 1967. (2) BaW-2. J. S. Gellerstedt, R. A. Lee, W. J. Oberjohn, R. H. Wilson, L. J. Stanek, " Correlation of Critical Heat' Flux in a Bundle Cooled by Pressurized Water," Two-Phase Flow and Heat Transfer in Rod Bundles, i p ASME, New York, 1969.
'l
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L (3) Hench-levy. J. M. Healzer, J. E. Hench, E. Janssen, S. Levy, " Design Basis for Critical Heat Flux Condition in Boiling Water Reactors," APED-5186, GE Company Private ! report, July 1966. (4) Macbeth. R. V. Macbeth, "An Appraisal of Forced Convection Burnout Osta," Proceedings of the Institute of Mechanical Engineers, 1965-1966. (5) Barnett. P. G. Barnett, "A Correlation of Burnout Data for Uniformly Heated Annuli and Its Uses for Predicting Burnout in Uniformly Heated Rod Bundles," AEEW-R 463, 1966. (6) Hughes. E. O. Hughes, "A Correlation of Rod _ Bundle Critical Heat Flux for Water in the Pressure Range 150 to 725 psia," IN-1412, Idaho Nuclear Corporation, July 1970.
- c. Correlations of appropriate transient CHF data may be accepted for use in LOCA transient analyses if comparisons between the data and the correlations are provided to demonstrate that the correlations predict values of CHF which allow for uncertainty in the experimental data throughout the range of parameters for ,
which the correlations are to be used. Where l appropriate, the comparisons shall use statistical I uncertainty analysis of the data to demonstrate the _ conservatism of the transient correlation.
- d. Transient CHF correlations acceptable for use in LOCA transients include, but are not limited to, the following:
(1) GE transient CHF. B. C. Slifer, J. E. Hench,
" Loss-of-Coolant Accident and Emergency Core Cooling Models for General Electric Boiling Water Reactors,"
NED0-10329, General Electric Company, Equation C-32, April 1971. A CHF calculational algorithm has been incorporated in RELAP5YA. This , algorithm utilizes several CHF correlations to cover the range of conditions expected during a LOCA. At high mass flux values, the Biasi correlation is used with a modification to account for bundle geometry. At low-mass flux l values, the Griffith-Zuber correlation is used. At intermediate mass flux ! values, the CHF value is obtained by interpolating between the two corre16tions. The CHF algorithm is described in Section 4.2. The RELAP5YA CHF algorithm has been assessed against steady-state CHF data obtained in fuel rod bundles at Columbia University, GE, and ORNL. The predictions were found to match the data well. Volume III, Section 3.2
1 1
, describes the assessment.
g- 'Tj e. ' After CHFJis first' predicted at an axial fuel rod
. location.during blowdown, the calculation shall not use-nucleate boiling heat transfer correlations et that location subsequently during the. blowdown even if the calculated local fluid and surface conditions,would apparently justify the reestablishment of nucleate boiling. Heat transfer assumptions characteristic of
. return to nucleate boiling (rewetting) shall be permitted when' justified by the calculated local fluid and surface conditions during the reflood portion of a LOCA.
A Return to Nucleate Boiling Lockout algorithm has been incorporated into RELAPSYA as a; user selected option. The logic is described in Section
~ 4 '. 5 .1. When performing EM calculations, the user 'will activate the Return.to Nucleate Boiling Lockout option for all heat structures that represent fuel rods within the core' region. . Once CHF is exceeded at a selected heat '
structure. surface, the Nucleate Boiling Lockout flag, IEM1, is set to 1 ("TRUE"). If the heat transfer logic subsequently returns to nucleate boiling
; mode, the heat transfer coeffici ent is not allowed to be set equal ~ to that
( calculated by the Nucleate Boiling correlation. The resulting heat transfer e X ' coefficient.is, however,' multiplied by a degrading factor of 0.5, thereby
. forcing a degraded heat transfer calculation. The Nucleate Boiling Lockout
. flag will-be deactivated when the log 1e contained in the Rewet and Quench Fron't model (Section 4.3)- calculates that quenching is allowed.
Requirement I.C.5: Post-CHF Heat Transfer Correlations
- a. Correlations of heat transfer from the fuel cladding to the surrounding fluid in the post-CHF regimes of transition and film boiling shall be compared to applicable steady-state and transient-state' data using statistical correlation and uncertainty analyses. Such comparison shall demonstrate that the correlations predict values of heat transfer co-efficient equal to or less than the mean value of the applicable experimental heat transfer data throughout the range of parameters for which the correlations are to be used. The comparisons shall quantify the relation of the correlations to the statistical uncertainty of the applicable data.
- b. The Groeneveld flow film boiling correlation >
.(g (equation 5.7 of D. C. Groeneveld, "An Investi Heat Transfer in the Liquid Deficient Regime,"gation AECL-3281, of a
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revised December 1969), the Dougall-Rohsenow flow film boiling correlation (R. S. Dougall and W. M. Rohsenow,
" Film Boiling on the Inside of Vertical Tubes with tJpward )
Flow of the Fluid at Low Qualities, MIT Report Number 1:
)
9079-26, Cambridge, Massachusetts, September 1963), and the Westinghouse correlation of steady-state transition boiling (" Proprietary Redirect / Rebuttal Testimony of Westinghouse Electric Corporation," USliRC Docket RM-50-1, page 25-1, October 26, 1972) are acceptable for use.in the post-CHF boiling regimes. In addition the transition boiling correlation of McDonough, Milich, and King (J. B. McDonough, W. Milich, E. C. King, " Partial Film Boiling with Water at 2000 psig in a Round Vertical ! Tube,"' MSA Research Corp., Technical Report 62 (llP-6976), (1958) is suitable for use between nucleate and film boiling. Use of all these correlations shall be restricted as follows: 1 (1) The Groeneveld correlation shall not be used in the region near its low-pressure singularity, (2) The first term (nucleate) of the Westinghouse correlation and the entire McDonough, Milich, and King correlation shall not be used during the blowdown af ter the. temperature difference between the clad and the saturated fluid first exceeds 3000F, (3) Transition boiling heat transfer shall not be reapplied for the remainder of the LOCA blowdown, even if the clad super-heat returns below 3000 F, except for the , reflood port.~ $ 1 of the LOCA when justified by the calculated local fluid and surface conditions. A post-CHF algorithm is available in RELAP5YA. The algorithm utilizes several correlations to cover the range of conditions expected during a LOCA. This set of correlations is the same as that used in RELAP5 M001 and is described in Appendix A. t The RELAP5YA heat transfer correlations were assessed against data obtained from THTF, TLTA and LOFT experiments. RELAPSYA wall temperature predictions were compared against data and the code was concluded to be conservatively accurate. The assessment is described in Volume III, Section 5.0. To comply with the item (3) requirement, a Return to Transition Boiling , Lockout algorithm has been introduced into RELAPSYA as a user selected option. The logic is described in Section 4.5.2. While performin; EM
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t g calculations, the user will activate the Return to Transition Boiling Lockout ' g...f f( ) '. option region. Once for aali heatheat selected structures that isrepresent structure surface c'alculated tofuel exceedrods within the c 3000 F wall suosr-heat, the Transition Boiling Lockout flag, IEM2, is set to 1 ("TRUE"). If the heat transfer logic subsequently returns to either the
. transition or nucleate' boiling modes, then the modified logic will extrapolate the film boiling correl'ations. into these' regions to yield a degraded heat transfer coefficient.
Requirement I.C.6: Pump Modeling The characteristics of rotating primary system. pumps (axial flow, turbine, or centrifugal) shall be derived from a dynamic model that includes momentum transfer between the fluid and the rotating member, with variable pump speed as a function of time. The pump model resistance used for analysis should be justified. The pump model for the two-phase region shall be verified by applicable two-phase pump performance data. For BWR's after saturation is calculated at the pump suction, the pump head may be assumed to vary linearly with quality, g.ss going to zero for one percent quality at the pump
- suction, so long as the analysis shows that core flow
.d stops before the quality at pump suction reaches one percent.
A dynamic pump model to simulate' centrifugal pump performance in a nuclear plant is available in RELAPSYA. This model is identical to the RELAPS M001 model . This model is a straightforward conversion of the RELAP4 centrifugal pump model. The model was completely reprogrammed, but ro change was .made to the paysical model. The RELAP4 pump model is-used by YAEC to ) perform EM calculations. This model was found by the NRC staff to meet the Appendix X criteria (Reference 6.0-5). However, use of the pump curves incorporated in the code was to be justified for each application. Requirement I.C.7: Core Flow Distribution Ouring Blowdown. ( Applies only to pressurized water reactors)
- a. The flow rate through the hot region of the core during blowdown'shall be calculated as a function of
(\. time. For the purpose of these calculations the hot (,) region chosen shull not be greater than the size of one fuel assembly. CM' clations of average flow and flow in
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l I the hot region shall take into account cross flow between regions and any flow blockage calculated to occur during blowdown as a result of cladding swelling or rupture. The calculated flow shall be smoothed to eliminate any g calculated rapid oscillations (period less than 0.1 seconds).
- b. A method shall be specified for determining the enthalpy to be used as input data to the hot channel heatup analysis from quantities calculated in the blowdown analysis, consistent with the flow distribution calculations.
The above requirement is applicable only to the analysis of large breaks in Pressurized Water Reactors. During small breaks, the fluid velocity in the core region is expected to be small. Various regions in the core are j expected to communicate with each other and the fluid conditions at various radial locations are not expected to be significantly different at a given elevation. The entire core, therefore, may be represented by an average core for small break calculations. YAEC currently plans to use RELAP5YA to analyze the entire break spectrum in BWRs and only small breaks in PWRs. Therefore, the above requirement does not apply. . 6.1.4 Post-Blowdown Phenomena: Heat Removal by the ECCS Requirement I.D.1: Single Failure Criterion An analysis of possible failure modes of ECCS equipment and of their effects on ECCS performance must be made. In carrying out the accident evaluation the combination i of ECCS subsystems assumed to be operative shall be those available after the most damaging single failure of ECCS equipment has taken place. Vendor analyses are available where possible failure modes of ECCS equipment were analyzed to arrive at the worst single failure criteria for each operating plant. YAEC believes that changes in the analysis methods and minor changes in the HSSS and the fuel will not alter the worst single failure. YAEC, therefore, will use the USSS vendor identified worst single failure in licensing analyses.
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j'. Requirement 1.D.2: Containment Pressure- -l
, (D)
The containment pressure used for evaluating cooling effectiveness during reflood and spray cooling shall not exceed a pressure calculated conservatively for this purpose. The calculation 'shall include the effects of operation of all installed pressure-reducing systems and processes. Calculation of a conservative containment pressure is important for the i analysis of large breaks in PWRs. YAEC currently intends to use RELAP5YA to analyze all size breaks in BWRs and only the small breaks in PWRs. As such, the above requirement is not considered crucial for our current RELAP5YA licensing application. The code, however, is capable of utilizing P-T response generated by an auxiliary code such as CONTEMPT-LT. Containment ; pressure response to be used in licensing analyses will be justified in the l sample problem submittal. Requirement I.D.3: Calculation of Reflood Rate for Pressurized Water Reactors (7 The refilling of the reactor vessel and the time and rate C/ of reflooding of the core shall be calculated by an acceptable model that takes into consideration the thermal and hydraulic characteristics of the core and of the reactor system. The primary system coolant pumps shall be assumed.to have locked impellers if this as.sumption leads to the maximum calculated cladding temperature; otherwise the pump rotor shall be assumed to be running free. The ratio of the total fluid flow at the core exit plane to the tot.a1 liquid flow at t.1e core inlet plane (carryover fraction) shall be ured to determine the core exit flow and shall be determined in accordance with applicable experimental data (for example, " PAR FLECHT (Full Length Emergency Heat Transfer (FLECHT) Group I Test Report," Westinghouse Report WCAP-7435, January 1970; "PWR FLECHT (Full Length Emergency Cooling Heat Transfer) Group II Test Report," Westinghouse Report WCAP-7544, September 1970; "PWR FLECHT Final Report Supplement," Westinghouse Report WCAP-7931, October 1972). i
~
The effects on reflooding rate of the compressed gas in the accumulator which is discharged following accumulator water discharge shall also be taken into account. h (O I l
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t A reflood hee.t transfer method has been incorporated into RELAP5YA as a , user selected option. This method calculates quench front propagation and heat transfer by conduction and convection in the vicinity of quench fronts. j 4 The model is described in Section 4.3. 1 The reflood heat transfer model has been assessed against data obtained l from THTF, TLTA and LOFT experiments. The predictions were found to be acceptable. Volume III, Section 5.0 describes the assessment. Requirement I.D.4: Steam Interaction with Emergency Core Cooling Water in Pressurized Water Reactors The thermal-hydraulic interaction between steam and all emergency core cooling water shall be taken into account in calculating the core reflooding rate. During refill and reflood, the calculated steam flow in unbroken reactor coolant pipes shall be taken to be zero during the time that accumulators are discharging water into those pipes unless experimental evidence is available ! regarding the realistic thennal-hydraulic interaction between the steam and the liquid. In this case, the experimental data may be used to support an alternate assumption. The above requirement is more applicable to the analyses of large breaks in PWRs. As such, this requirement is not crucial for our current ' RELAP5YA, however, is a two Fluid RELAPSYA licensing applications. thermal-hydraulic code and it does have the capability to treat the interaction between liquid and steam. a f Recnfrement I.D.5: Refill and Reflood Heat Transfer for Pressurized Water Reactors For reflood rates of one inch per second or higher, reflood heat transfer coefficients shall be based on applicable experimental data for unblocked cores including FLECHT results ("PWR FLECHi (Full Length Emergency Cooling Heat Transfer) Final Report," Westinghouse Report WCAP-7665, April 1971). The use of a correlation derived from FLECHT data shall be demonstrated to be conservative for the transient to which it is applied; presently available FLECHT heat transfer correlations ("PWR Full Length Emergency Cooling Heat Transfer (FLECHT) Group I Test Report," Westinghouse
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J
'ReportWCI'P-7544,JSeptember1970;."PWRFLECHT. Final Report Supplement,": Westinghouse Report WCAP-7931, e October 1972)~ are not acceptable. ' tiew correlations or modifications to' the FLECHT heat transfer correlations 1 (' ); ,
are acceptable'only after they are demonstrated to be ! conservative, by comparison with FLECHT' data, for. a range of parameters consistent with the transient to which they: are applied..
, During refill and during reflood when reflood rates are less than.one inch per second, heat transfer calculations shall be based on the assumption that cooling is only by -
steam,. and shall take into account any flow blockage calculated to occur as a result of cladding swelling or rupture as such blockage' might affect both local steam flow.and heat transfer. The above requirement is applicable to large break LOCAs in PWRs. As such, it is not needed for our current RELAP5YA licensing applications. However, a reflood heat transfer model has been incorporated into RELAPSYA- as a user selected option. This model calculates quench front propagation and heat transfer by conduction and convection in the vicinity of quench fronts. The model is described in Section 4.3. () Requirement I.D.6: ' Convective Heat Transfer Coefficients for Boiling' Water Reactor Fuel Rods Under Spray Cooling Following the blowdown period, convective heat transfer shall be calcu1ated using coefficients based on appropriate experimental data. For reactors with jet pumps and-having fuel rods in a 7 x 7 fuel assembly array, the following convective coefficients are ecceptable:
- a. During the period following lower plenum flashing but prior. to the core spr.ny reaching rated flow, a convective heat transfer coefficient of zero shall be applied to all fuel rods.
- b. During the period after core -spray reaches rated flow but prior to reflooding, convective heat transfer coeffic:entsofp.0,3.5,1.5,1.5 Stu-hr "-f t-2 F- shall be applied to the fuel rods in the outer corners, outer row, next to outer row, and to those remaining in the interior, respectively, of the assembly.
M'
.(V
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a
j .. L I k' l c. Af ter the two-phase reflooding fluid reaches the level under consideration l coefficient of 25 Btu-hr-I afcgoveqtive t-' F-1 shallheat be transfer ' applied to all fuel rods. l The acceptable model described above will not be used in RELAP5YA calculations. Instead, the RELAP5YA heat transfer algorithm will be used. This algorithm uses several correlations to cover the range of conditions expected during a LOCA. The Multiple Surface Radiation heat transfer option, Return to Nucleate Boiling Lockout cption, Return to Transition Boiling Lockout option and the Rewet and Quench heat transfer options will be utilized for the licensing analyses. The models are described in Appendix A and in Section 4.0 of this volume. The RELAPSYA heat transfer algorithm has been extensively assessed , against data from separate effect and integral tests. The various user options in RELAPSVa (Radiation, Nucleate anti Transition Boiling Lockouts, j Rewet and Quench) have been exercised. These are discussed in Sections 3.0, 4.0 and 5.0 of Volume III. Calculations with and without these options have been carried out and compared to data from the TLTA large break and small break tests. The results have shown that the use of these options will yield conservative calculations suitable for licensing analyses. These are described in Section 5.2 of Volume III. Requirement I.D.7: The Boiling Water Reactor Channel Box under Spray Cooling Following the blowdown period, heat transfer from, and wetting of, the channel box shall be based on appropriate experimental data, For reactors with jet pumps and fuel rods in a 7 x 7 fuel assembly array, the followir,g heat transfer coefficients and wetting time correlatfor, are 4 acceptable.
- a. During the period after lower plenum flashing, but prior to core spray reaching rated flow, a convective coefficient of zero shall be applied to the fuel assembly channel box.
- b. During the period after core spray reaches rated flow, but prior to wetting of the channel, a heat transfer coefficient of 5 Btu-br-1-f t-2, convective F-1 shall be applied to both sides of the channel box.
l
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- c. Wetting of the channel box shall be assumed to occur ,
60 seconds after the time determined using the 1 4 correlation based on the Yamanowhi analysis i f L (" Loss-of-Coolant Accident and Emergency Core-Cooling V Models for General Electric Boiling Water Reactors," General' Electric Company Report NE00-10329, April 1971). ) l The acceptable correlations described above will nct be used in ] s RELAPSYA calculations. Instead, the procedure described for Requirement I.D.6 { will be followed. ) 1 This procedure has been exercised in comparing RELAP5YA calculations against data from large break and small break tests in the TLTA facility. In these calculations, the fuel channel box was modeled explicitly. The results showed that the use of the heat-transfer options in the RELAPSYA heat transfer l algorithm yielded conservative calculations appropriate for licensing analyses. These are described in Section 5.2 of Volume III. 6.2 Required Documentation Requirement II.1.a: Model Description
, q ^ Q.) l A description of each evaluation model shall be furnished. The description shall be sufficiently complete to permit technical review of the analytical i approach including the equations used, their approximations in difference form, the assumptions made, j and the values of all parameters or the procedure for their selection, as for example, in accordance with a I- specified puysical law or eepirical correlation.
A complete and detailed description of models used in RELAP5YA is contait,ed in thia documant which consists of Volume I, Appendices A, 3 and C, Volume II and Volume III. Requirement II.1.b: The description shall be sufficiently detailed and specific to require significant changes in the evaluation model to be specified in amendments of the description. em For this purpose, a significant change is a change that ! i ) would result in a calculated fuel cladding temperature
different by more than 20 0F from the temperature t
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\ -
\
calculated (as a function of time) for a postulated LOCA using the last previously accepted model. The RELAP5YA models contained in this document are described in sufficient detail such' that a modification in the model which gives rise to as , little as 20 F change in calculated clad temperature can be identified. f Model changes leading to 20 F or more difference in clad temperatures will be reported to the NRC staff. Requirement II.1.c: A complete listing of each computer program, in the same , form as used in the evaluation model, shall be furnished to the Nuclear Regulatory Commission. A complete listing of the RELAPSYA computer program will be furnished to the NRC before the code is used for the licensing of any of our operating plants. I Requirement II.2: For each computer program, solution convergence shall be 3 demonstrated by studies of system modeling or noding and I calculational time steps. 1 RELAP5YA has been assessed against a vari oty of Leparate Ef fect and ! Integral System experiments, which are described in Volume III. The results demonstrate the stability of the solution seneme used in RELAPSYA. l 1 1 Requirement II.3: ] Appropriate sensitivity studies shall be performed for i each evaluation model, to evaluate the effect on the l calculated results of variations in noding, phenomena assumed in the calculation to predominate, including pump ! operation or locking, and values of parameters over their l applicable ranges. For items to which results are shown j to be sensitive, the choices made shall be justified. ] l C- _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
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j
RELAPSYA has been assessed. extensively against-data from separate effec.t and integral _ test facilities. The nodalization scheme and the RELAP5YA n.
' options used in modeling each of.these t'ests have been' documented in Volume-
, .Q) _ ~ III.' The influence of nodalization and the use of various RELAP5YA relevant thermal-hydraulic phenomena have been addressed and are described in
' Volume' III.. The experience gained .in this assessment work- will' be' applied in reactor analyses. The sample problem will address the appropriateness and conservatism inherent in the application.
Requirement 11.4: To the extent practicable, predictions of the evaluation model, or portions thereof, shall be compared with applicable experimental information. RELAPSYA calculations have been compared to experimental 1' results from various separate effect and integral test facilities. The various evaluation model options available in RELAP5YA have been assessed singly or in groups against the data. The results have shown that these options perform as intended and yield conservative ' calculations suitable for licensing analyses of reactor systems. Volume III describes this extensive assessment work. Requirement II.5: ' General Standards for Acceptability
. Elements of evaluation models reviewed wil? include technical adequacy of the calculational methods, including compliance with required features of Section I of this Appendix K and provision of a level of safety and margin of conservatism comparable to other acceptable evaluation models, taking into account significant differences in the reactors to which they apply.
The models used in the RELAPSYA computer code have been described in this volume. Appendices A and B of Volume I contain documentation on the i models used 19 the RELAP5 t10D1 code on which RELAP5YA was based. Sections 2.0 through 5.0 ' Volume I describe the additional models in RELAPSYA. The technical adequacy of these models has been addressed in the development of j 1
., these models and has been demonstrated in the code assessment work described
( in Volume III. The required features of Section I of Appendix K to 10CFR50 have been incorporated into RELAP5YA and have been discussed previously in 1
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l l this section. We believe that RELAPSYA contains the required features to conduct BWR analyses over the entire break spectrum and PWR analyses for small breaks. The various evaluation model features have been assessed against data and shown to yield calculations with reasonable margins of conservatism. These calculations are described in Volume III. This assessment has also demonstrated that RELAP5YA contains a sufficient number of input options and features to provide accurate modelir.) of integral test facilities which simulate thermal-hydraulic phenomena relevant for reactor analyses. These input features are described in Volume II and are believed to be adequate for modeling reactor systems with significant differences in geometrical configurations and operational features. O 1 9>
~27s-
_ _ _ _ )
t References y 6. 0 . Schultz, S. P..._and K. E. St. John, " Methods for the Analysis of 0xide Fuel . Rod Steady-State Thermal Effects (FROSSTEY)", YAEC-1249P, April-(" 7. . 1981.1 6.0-2' '"WREM:- Water. Reactor. Evaluation 14odel, Revision 1", Division of -
-- Technical Review, U.S. Nuclear Regulatory Commission, NUREG-75/056,
- May > 1975.-
6.0-3 Lauben,- G.' N., "T000EE2-EM, A Two-Dimensional Time-Dep'endent Fuel Element Thermal Analysis Program", Division of' Technical Review, USNRC, May 1975.
-6.0-4' Powers, D. A., and R. O. Meyers, " Cladding Swelling. and Rupture Models for LOCA Analysi s", NUREG-0630, April 1980.
6.0-5 " Yankee Atomic Electric Company WREM-Based PWR ECCS Evaluation Model" (Version YAEC-053), YAEC-1160, July 1978. O - l 1. O
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I NUREG/CR-1826 - EGG-2070 4 Distribution Category: R4 j O 1 I l l RELAP5/ MOD 1 CODE MANUAL ; VOLUME 1: SYSTEM MODELS AND , 1 NUMERICAL METHODS ,
-I Victor H. Ranson Richard J. Wagner John A. Trapp Kenneth E. Carlson Dennis M. Kiser Han-Hsiung Kuo C,
' J Hueiming Chow Ralph A. Nelson Stephen W. James
'I l
Published March 1932 EG&G Idaho, Inc. Idaho Falls, Idaho 83415 Prepared for the U.S. Nuclear Regulatory Commission l Washington, D.C. 20666 l l
' Under DOE Contract No. DE-AC07-761DOds0 l FIN No. A6038
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r l 9 ABSTRACT The RELAP5/ MODI code is described in three volumes: Volume 1, System Models and Numerical Methods; Volume 2, Users Guide and input Requirements; and Volume 3, Checkout Problems Summary. Volume I contains technical developments of the basic thermal-hydraulic model, constitutive relations, and solution scheme. The adaptations of the basic model for system components such as pumps, valves, accumulators, and branches are discussed with development of the core neutronics and control system models. Volume 2 gives recommendations on code application and detailed input requirements. Volume 3 summarizes the descriptions and results of example checkout problems to which the I RELAP5/ MODI code was applied. The problems range from simple, separate-effects tests to integral , LOFT experiment simulations. Existing. data are compared to code results. O Ol FIN No. A6038 Semiscale Program ii
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SUMMARY
The light water reactor transient analysis code, RELAP5, is being developed at the Idaho ' National Engineering Laboratory (INEL)'under Nuclear Regulatory Commission (NRC) support to provide an advanced best estimate predictive capability for use in a wide spectrum of. applications in support of the .
- regulatory process. Applications of this capability include analytical support for the LOFT and Semiscale' experimental programs; support of the relief valve testing program; and simulation of design basis loss 7of-coolant accidents (DBLOCA), anticipated transients without scram (A'IWS), and operational transients in . ';,
LWR systems for use in regulatory investigations.' RELAPS is a highly generic code that can be used for l
' simulation of a wide variety of hydraulic and thermal transients in both nuclear and nonnuclear systems -
involving steam water-noncondensable fluid mixtures. The RELAP5 code is based on a nonhomogeneous and nonequilibrium model for the two-phase system that is solved by a fast, semi-implicit numerical scheme to permit ' economical calculation of system tran-sients. The objective of the development effort from the outset has been to produce a code that includes < important first-order effects necessary for accurate prediction of system transients, but is sufficiently. simple and cost effective such that parametric or sensitivity studies are possible. The code includes many generic component models from which general systems can be modeled. The : component models include pumps, valves, pipes, heat structures reactor point kinetics,' electric heaters', accumulators, and control system components. In addition, special process models are included for effects ' s*:ch as form losses, flow' at abrupt area change, branches, choked flow. - boron ' tracking, and noncondensable gases. ,4
- The system mathematical models are coupled into an efficient code structure. The code includes exten-ac 'e sive input checking capability to help the user discover input errors and inconsistencies. Also included areJ free format input, internal plot capability, restart, renodalization, and variable output edit features. These user conveniences were developed with recognition that the major cost asociated with the use of a system '
transient code is the engineering labor and time associated with accumulating system data and developing
. the system models. whereas the computer cost associated with generation of the final result is usually small.
The development of RELAP5 has sparned approximately seven years from the early stages of numerical . scheme development to the present. RELAP5 represents a large aggregate accumulative of experience in l
- modeling of two-phase processes and LWR systems in particular. The code development has benefited ,
hotn exttmive appB:utio s and comparison to esperhsents) data fn the loOFT atu! Senuscale programs in , particular.~ Additional experience has been gained through use of the code by many research and develop ment institutions in the U.S. and in several foreign countnes. This manual describes the basic theory ea4 numerict) methods used for the various system models, 1 4 4 includes getaeral guideilnes for apphcation of the code, as well as detailed desc iptions of the input prepara-tion procedure. These subjects are discussed in Volumes I and II. Volume III of the manual includes six sample applications of the code and comparison of calculated results to data. These include three separate effect experiment simulations and three integral system simulations. 1 l III L
l l l l i 1
-l 9
l l 1 1 FOREWORD { l RELAP5/ MODI is the latest code in the series of RELAP codes developed at the Idaho National ) Engineering Laboratory (INEL) for use in Light Water Reactor Safety Analysis. The RELAPS project is i ongoing and it is anticipated that the culmination of this effort will result in the future release of a more advanced version of RELAP5. The RELAP5 project is sponsored by the Nuclear Regulatory Commission 1 and the NRC program manager is Mr. Warren C. Lyon. RELAPS is the product of the INEL Code Development Division, managed by Dr. Felix Aguilar. This report is the product of a cooperative effort ' between the Code Development Division and the Technical Publications Division of the INEL. Mr. Russ Tetley provided technical editing. O, i i l j I 1 l I O: ; l _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ u- 1
1, 5 CONTENTS , i i
- ./ ~'s.
ii - ls f ABSTRACT.......................................................................... 1 4 l
SUMMARY
.......................................................................... iii ! FOREWORD........................................................................ iv i N O M E N C LATU RE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
- 1. INTRO D U CTI O N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 1.1 RELAP5 Project Overview .................................................... I 1.2 RELAPS / MOD I Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Code Design ................................................................ 5 1.4 Numerical Scheme ........................................................... 8 1.5 Development of the Hydrodynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 ,
1
- 2. SYSTEM M O DELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1 Hydrodynamic Model ............ ....................................... .... 9 e 9
( 2.1.1 Field Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . k 2.1.2 State R relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 ; 2.1.3 ' Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 ! l 2.2 SpecialProcess Models ....................................................... 40 2.2.1 Cho ked Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.2.2 Abru p t Area Chan ge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.3 Syrtem Component M occis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . '62~ 2.3.1 ' RELAF5 Pump Model . ... ................ ......... ............... 62 i 2.3.2 Accumulator Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ?! 2.3.3 Reactor Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -75
- 3. NUMERICAL METHODS .... ................. ............................ ... 79 3.1 Hydrod ynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 1
l 3.1.1 Difference Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Volume Average Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.1.2 Implicit Linear Time Step Solution ...................................... 85 3.1.3 Time S t ep Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.1.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.1.5 Implementation of Choked Flow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 p 3.1.6 , Hydrodynamic Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 t ( 3.1.7 m 90 3.2 Heat Tran:fer ...................................... ........................ v l
- _ _ _ _ _ -_ ________________O
3.2.1 Heat Conduction Numerical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.2.2 Mesh Point and Thermal Property Layout ...................... ... ..... 91 3.2.3 Difference Approximation at Internal Mesh Points . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.2.4 Difference Approximation at Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.2.5 Solution of Simultaneous Equations ..................................... 97 3.2.6 Thermal Properties, Boundary Condition Parameters, and Iteration Procedures .................................................. 98 3.2.7 Difference Approximation for Bcundary Conditions ....................... 98 3.3 S ystem Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.3.1 Branching ......................................................... . 99 3.3.2 NumericalScheme Accumulator Model .................................. 101 3.3.3 Valves .............................................................. 103 3.3.4 Reactor Kinetics Numerical Procedures .................................. 105 i
- 4. REFE REN CES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 FIGURES
- 1. Marviken Test 24 mass flows ......................... ....................... .. .. 3
- 2. RELAP5 Wyle small break test mass flow ........... ............................... 4 RELAP5 LOFT L3-7 prediction system pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.
RELAP LOFT L3-7 posttest system pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 4. 14
- 5. Relation of central angle 6 to void fraction og ............................ ......... .
Vertical flow regime map (VRT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 ; 6. Horizontal flow regime map (HRT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 7. Annulus flow regime ma p (ANF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 8. High mixing flow map fMMF) . .................................... ............... 29 9.
....................... .............. . .. .... 31
- 10. Idealized flow field for s* ratified flow 37
- 11. RELAP5 blev'down acat 'Antf er surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
- 12. RELAP5 forced convection boiling curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
- 13. RELAP heat trans fer regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
- 14. Different heat transfer boiling regimes with respect to the quality-wall superheat plane . . . . . . . 39 5?.
- 15. Equilibrium speed of sound as a function of void fraction and virtual mass coefficient ... ..
- 16. Coefficient of relative Mach number for thermal equilibrium flow as a function of 53 void fraction and virtual mass coefficient . ................................. .........
- 17. Subcooled choking process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......... .. 54 Vi t _ --
- 18. Orifice at abrupt area change . . . . . . . . . . . . . . . . . . . . . . . . . . :. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 r
' 19. Schematic flo'w of two-p' ha'se udxture at abrupt area change .................'.............
l 59
- 20. Pump characteristic four-quadrant curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 1
- 21. . Pump h6mologous head curves . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
- 22. Pump homologous torque curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . '65
- 23. Single phase homologous head curves for 1-1/2 loop MOD.1 Semiscale pumps . . . . . . . . . . . . . - 66:
- 24. Fully degraded two-phase homologous head curves for 1-1/2 loop MOD 1 Semiscale pump . . . 67
- 25. Torque versus speed, Type 93 A pump motor (rated voltage) ............................. 71
- 26. ' Typicalaccumulator . . . . . . . . . . . . . . . . .............................................. 72.
- 27. Difference equation nodaliration schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' . . 80
- 28. Typicalbranching junctions . . . . . . . . . . .............................................. 85
- 29. M es h poin t layout . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
- 30. Typical mesh poin ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
- 31. Boundary mes h points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
- 32. Application of branch volume to horizontal tee or plenum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
- 33. Application of branch volume to vertical tee or plenum ................................. 101 TABLES -
RELAP5 Forced Convection Heat Transfer Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 1.
- 2. Standard RELAP5 DNB Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
- 3. Chen's Reyno:ds Number Factor, F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Chen's Suppression Factor, S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.
- 5. Pool Boiling-Natural Circulation Heat Transfer Correlations . . .. . . . . . . . . . . . . . . . . . . . . . . . 48 Semiscale Dimensionless Head Ratio Difference (Single-Phase Minus Two-Phase) Data . . . . . . 68 6.
- 7. Head Multiplier and Void Fraction Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 a
77
- 8. Reactor Kinetics Cons'tants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
yki
1 1 i l NOMENCLATURE g 1 j A Cross sectional area or coefficient matrix ] Al Coefficient in neat conduction equation at boundaries At Surge line cross sectional area At Throat area { a Speed of sound or coefficient in heat conduction equation J B Coefficient matrix or drag coefficient or compressibility Bt Coefficient matrix in heat conduction equation at boundaries b Coefficient in heat conduction equation Bx Body force in x coordinate direction i By Body force in y coordinate direction C Coefficient of virtual mass or general vector function c Coefficient in heat conduction equation CB Boron concentration l Cd Drag coefficient Cs Dimensional constant in correlation for P 8 Cp Specific heat at constant pressure 3 Cy Specific heat at constant volume D Coefficient of relative Mach number, diffusivity, diameter, or heat conduction boundary condition matrix , f Di Coefficient of heat conduction equation at boundaries t d Coefficient in heat conduction equation DISS Energy dissipation function E Total energy (U + v2/2) or term in iterative heat conduction algorithm e Interfacial roughness Eu Euler number F Term in iterative heat conduction algorithm FIF, FIG Interphase drag coeffic.ients, liquid and vapor
t 4 1 FI Interphase drag coefficient FWF, FWG Wall frictional dras coefficients, liquid and vapor - [u
.' (
f Interphase friction factor
- Ghead Pressure drop across valve disk due to gravity G Mass velocity or gradient in heat conduction Gr' Grashof number -
gz,g Acceleration due to gravity H Surge line elevation h Enthalpy, heat transfer coefficient, liquid level, or energy transfer coefficient for I's h3 Mass transfer coefficient hL Dynamic head loss 1 Identity matrix or moment of inertia
-J Junction velocity
.K Energy form loss coefficient f~
()/ k Thermal conductivity , kB Boltzmann constant L ~ Length LL Surge line length M Mach number or mass transfer rate Mn Nitrogen mass Mwall Mass of tank wall N Number of system nodes, number density Nu Nusselt number n Unit vector, order of equation system, nitrogen density, or phase designator 1 PrB Valve closing back-pressure P Pressure or reactor power, or channel perimeter Pp Nitrogen pressure in dome Pr Relates reactor power to heat generation rate in heat structures ix L_--.:.__________-__-________ ___- _ -__ __
1 t l Po Atmospheric pressure p Wetted perimeter i PCV Specified pressure required to close a valve Pr Prandtl number Q Volumetric hat addition Qp Total heat transfer q Heat transfer rate qt Specified time- or space-dependent factor in the source term of heat conduction R Radius Re Reynolds number R ep The particle Reynolds number Rn Universal gas constant S Phasic entropy or source term in heat conduction s Steam T Temperature or vapor temperature in accumulator dome Te Critical temperature
'TR Reduced temperature Tt Specified timedependerJ functioa in heat conduction t Time U Internal energy, vectoc of dependent variaoles V - Volume, specific volume with subscript y
e Choking velocity Vy Volume of nitrogen in dome VISG,VISF Viscous terms in momentum equations W Weight of valve disk Werit Critical Weber number We Weber number Lockhart-Martinelli parameter 8 x .;
.l t 1 v Mixture or phasic velocity, or liquid surge line velocity W Relaxation parameter in the heat conduction equation F -\/ }N :' X Static quality x Spatial coordinate z Elevation change coordinate Symbols a' . Void fraction, subscripted volume fraction or angular acceleration
# Coefficient of isobaric thermal expansion y The right side of heat conduction equation infinite difference form 6 Area ratio or truncation error measure
& Donored property or angle of inclination of valve assembly P Volumetric vapor generation rate A Eigenvalue, interface velocity parameter or friction factor x Coefficient of isothermal compressibility
/
\ p Viscosity p Density E' Depressurization rate a Surface tension or flag used in heat conduction equations to indicate transient or steady state ey Relaxation time in correlation for P or angular position r Kinematic viscosity w Angular velocity AX Increment in spatial variable At increment in time variable APr Dynamic pressure loss Subscripts B Boron or dissolved solid c Vena.contracta or continuous phase xi !
l ___._-___-____-__-_.__-___.-_A
e Thermodynamic equilibrium exp Used to indicate the usage of explicit velocities in choking - F Wall friction f Liquid phase fg Heat of vaporization g Vapor phase HE Homogeneous equilibrium HF Homogeneous frozen I Interface j, j + 1, j-1 Spatial noding index, junctiore K, L Spatial noding index, volumes or laminar m Mixture property n Noncondensiole component of vapor phase o Reference value p Particle number density r Relative Mach number sat Denotes a saturated quantity up Denotes an upstream quantity T Point of mmimum area or turbulent v Mass mean Mach number w Wall or water i Upstream station or multiple junction index 2 Downstream station or multiple junction index Superscripts l b Boundary gradient weight factor in heat conduction I l 1 Imaginary part of complex number I m, m + 1 Time level index in heat conduction finite-difference equation m + 1/2 An average of quantities with superscripts m and m+ 1 1
i , .: ta n, n + 1. Time level index -
"I R Real part of complex number s . Saturation property or space gradient weight factor in heat conduction
~
v Volume gradient weight factor in heat conduction
*- Total derivative of a saturation property with respect to pressure Partial derivative with respect to pressure .
- Vector- .
. Donored quality
- Unit momentum for mass exchange
)
I
a . y t I 1 RELAP5/ MOD 1 CODE MANUAL: -
'VOLUMEL1:t SYSTEMLMODEL.S AND' ig .
NUMERICAL METHODS'
- 1. INTRODUCTION -
3 The RELAP5/ MODI computer code is described in this manual. The RELAP5/ MODI code is a result - i of continued development bei==ia- with the RELAP5/ MODO code which was released to the National Energy Software Center (NESC), May 1979. The objective was to produce a more complete light water '- l - resctor (LWR) transient analysis capability. The MODO versien was a pressurned water reactor (PWR)' blowdown code. The MODI version extended the MODO capability to include models unique to small . break situations and to include added capabilities for modeling accumulators, noncondensible gas,' nucleonics, control systems, separators, and: boron concentrations. The MODI code contains improvements in the flow regime maps, choked flow models, general code running time, and output edit. The RELAPS/ MODI code manual is self-contained and repeats some of % basic development material > presented in the RELAP5/ MODO code manual (Reference 1). The repeated material has been appropri-- ately revised to reflect the content of the MODI code version. The RELAPS/ MODI code manual consists of three volumes: Volume 1, System Models and Numerical .
~
Methods; Volume 2 Users Guide and Input Requirements; and Volume 3, Checkout Problems Summary. Volume 1. discusses the analytical bases for the system models and describes the numerical solution methods employed. Volume 2 gives recommendations for application of models to problems of system. simulations. Detaded descriptions of the required input to the code for each of the models and options are O also included. Volume 3 contains the results for application of the RELAP5/ MODI code to six checkout problems. These problems range from simple separate effects test simulations to LOFT experiment simula-- t ions. Both the input data and results for each problem are presented. Where expenmental results are available the code results are compared to data. These problems serve as examples of recommended applications of the code. 1.1 RELAP5 Project Overview. The RELAP5 project objective is to produce an economic and user-convenient code for best estimate analyses of postulated light water reactor (LWR) loss-of coolant accidents (LOCA) and non-LOCA tran-sients. RELAPS is an advanced, one-dunensional, fast-running system analysis code under development for the U.S. Nuclear Regulatory Comminaion's Division of Reactor Safety Research (USNRC-RSR). It is a completely new code based on a nonhomogeneous, nonequilibrium hydrodynamic model, and features top down s:ructural design, with the significant programming elements coupled in modular fashion. To a great . extent, development .of RELAP5 has been influenced by experience gained through the development and use of the RELAP4 code series. This is evident in the convenience with which both developer and user can interface with the code. The RELAP5 code includes thermal hydraulic and mechanical models used to describe the processes that occur during blowdown of a LWR. The first version of the code, RELAP5/ MODO, was released to the National Energy Software Center (NESC) in May 1979. Development of RELAP5 has continued and a l new version, RELAP5/ MODI, has been completed and is being released to the NESC. The new version 7 includes component process models for pipes, branches, abrupt flow area changes, choked flows, pumps, _O
'L/
check valves, plant trips, control systems, steam separator, heat structures, and nuclear reactor core neutronics; These models have been integrated into a versatile, user-convenient system code framework. 1
1.2 RELAP5/ MOD 1 Capability An assessment of RELAP5/ MODI capabilities is presented herein as a brief review of model O developments since completion of the MODO code, with a summary highlighting some applications of the code. Most applications dier=d are checkout applications of the code and are described in more detailin Volume 3. The RELAP5/ MODO code is a one-dimensional, transient system analysis code designed for analyses of LWR LOCA and non-LOCA transients. Development of this version was terminated at a somewhat ar bitrary point as a result of an NRC decision. Subsequent development of RELAPS continued in support of experimental programs at the INEL. The RELAP5/ MODI code is the product of this continued development. Since the TMI accident, emphasis on LWR safety investigation has shifted frcm the large break LOCA to the small break LOCA. This shift necessitated some change in analysis development plans. Iri particular, reactor kinetics, stratified flows, secondary system components, and control systems now play significant roles in system dynamic behavior and must be modeled. The RELAP5/ MODI development addresses these modeling areas and completes some of the original large LOCA development plans. The new prin-cipal features in RELAPS/ MODI include: a mechanistic accumulator model; a point reacter kinetics model for core neutronics; a flow regime map for horizontal components and a revised flow regime map for vertical components; a generalized control valve model; a feedback control system model; a steam separator model; an Eulerian boron concentration model; and a generalized restart capability. A non-condensible gas field has been added to the hydrodynamic model, and a horizontal stratified flow model has been added to both hydrodynamic and choked flow models. In addition to the new models, several modeling improvements have been added. The more significant of these include: extension of the sub-cooled choked flow model to include nonequilibrium effects; semi-implicit coupling of the choked flow model for faster running; completion of the internal plotting package; and improvement of the major and diagnostic edits. During development of RELAPS/ MODI, the code was used extensively for pre- and posttest predic-tions in the LOFT and Semiscale expenmental programs at the Idaho National Engineering Laboratory. Most of these expenments were small break LOCAs that motivated extension of RELAP5/ MODO model-ing to include mechanistic processes peculiar to small break phenomena. The transient calculations for ; small break experiments span time periods composed of thousands of seconds. Thus, calculational speed l has become increasingly important. The calculational speed and modeling accuracy with RELAP5/ MODI represent significant improvement over those available in past codes. While RELAP5/ MODI is a signifi-cant step toward the goal of a complete LWR system code, there remain several areas that must continue to be developed. These include: thermal-hydraulic and fuel behavior under reflood conditions, even faster running capability, and increased user-conveniences. RELAP5/ MODI overall capability has been successfully applied to a wide range of problems. These applications include many separate-effects tests such as Edwards Pipe Blowdown Experiment, the Moby Dick Tests, the Marviken Experiment, the LOFT Wyle Orifice Calibration Tests, and the General Electric Corporation (GE) Level Swell Tests. The first two of these expenments (documented in the MODO manual) are .' representative of the RELAP5/ MODI capability. Examples of application to the Marviken Test, LOFT Wyle Test, and GE Level Swell Test are given in Volume 3. The code produced results in good agreement with the data in all of the cases listed. Figure 1 is a comparison of predicted and calculated mass discharge rates for Marviken Test 24. This application is a good test of the subcooled choked flow model and the code's ability to model liquid level in a tank. The calculation to 50 s simulated time requires 83 CDC-176 CPU seconds. The LOFT Wyle Orifice Calibration Test requires modeling of stratified flow in a horizontal pipe as well as flow in a vertical vessel component. The predicted mass discharge rate is compared with data shown in Figure 2. This experiment includes periods of subcooled and stratified two-phase choked flow discharge. The simulation to 1500 s required 115 CDC-176 CPU s. 2
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- l ol RELAP5/ MODI was applied in the Ominc=le and LOFT experimental programs at the INEL for-
- W: experiment planning, pietest prediction,'and posttest analyses. Several of these applications were selected
, as checkout problems presented in Volume 3. The best example to illustrate the overall system capability of '
- the code is the e9 plication to LOFT Test L3-7. This is a small break test and pre- and posttest calculations were made with RELAP5. The pretest prediction of the system pressure is compared with the data shown -
' in Figu e 3. The posttest calculation of the system pressure with_ only the steam generator main steam' con-trol valve leakage rate changed to correspond to the actual leak rate is compared with the data in Figure 4 i
The posttest calculations shown in Figure 4 required 24,000 CDC-176 CPU s to simulate 6000 s of system ~ transient. 1.3 . Code Design 1 Convenience, design for future growth, and computer efficiency are the primary considerations in the . RELAP5 system code design. Realization of these goals is facilitated by three factors:
- 1. Development of experience on the RELAP4 code series
- 2. Utilization of a blend of experienced personnelin numerical hydrodynamic analysis and large code design
- 3. The benefit of critical analysis and review of other advanced code development efforts.
Ongoing experience with RELAP4, CONTEMPT, FRAP T, and other large codes has emphasized the importance of convenience in code design. The implications of a simple and clear interface between the code and user go beyond the obvious benefit of efficiency. By reducing sheer bulk, number of options, and ambiguity, the potential for errors is minimized. More significantly, the simplicity of input reduces discre-O . tionary decisions and leads to greater uniformity of results. The predictive capabilities of the code become : more a function of the code and less a function of the user:
~
Significant user-convenience features are included, with respect to both the application of the code and the case with which future modifications can be incorporated. The most visible user-improvements are in the input portions'of the code. A free-format input, convenient for terminal or card input, is ased and an extensive input checking feature has been developed.'All input data are processed regardless of the number' of errors, and a diagnostic printout of the accumulated error messages is provided similar to the . FORTRAN compiler. Thus, most input errors can be found and resolved in a single check run. Although RELAPS is a new code, input similar to that for RELAP4 is maintained, or improved consistent with the philosophy of reducing and simplifying input preparation. Thus, mimmal RELAP4-user retraining is - necessary to make the transition to RELAP5. RELAP5 utilizen mechanistic process models where possible, avoiding the use of optional models to describe the same phenorcena. This leads to less ambiguity in system modeling and provides viable results with fewer trained personnel. The inevitable process of code evolution has been anticipated. A top down structure is laid out with branches provided for future growth. In addition, a modular structure is used in which major code func-tions or models or both, were collected into subroutines. The decision whether to modulanze by model or code function was made to provide the simplest code with the fewest module interconnections. RELAPS is designed to efficiently utilize the capability of modern computers such as the CDC 176. The code features full dynamic storage and word packing so the entire time step solution can be executed without the need to move data between small core memory (SCM) and large core memory (LCM). This
- capability has been demonstrated on problems of up to 260 control volumes. Other efficiency features include restart, postrun reedit, data stripping from output files, and an internal plot package.
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l l l 1.4 Numerical Scheme - 1 The RELAP5 numerical scheme is based on a linear, semi-implicit, finite-difference integration scheme. O The implicitness and use of donor-differencing for convective fluxes is sufficient to ensure stability for all time steps smaller than the material transport limit, and the linearity makes direct time step solution pos-sible. Both of these factors contribute to fast execution. The stability has been tested numerically, applying the code to problems with exact analytical steady state solutions and verifying that the transient calculation converges to the steady state result. The stability was also tested in numerous cases with sudden changes imposed at boundaries. The transient results were calculated without evidence of numericalinstability. i The basic numerical hydrodynamic model was developed in a pilot code where the stability, accuracy, and fast execution capability could be readily evaluated. Once these characteristics were established, the i model was integrated into an efficient, tser-oriented system code structure. L 1.5 Development of the Hydrodynamic Model The hydrodynamic model was selected after careful review of other advanced two-phase model develop-ment efforts. It was concluded 'that the model most consistent with existing knowledge is a five-field equation, two-fluid model. The model consists of the two phasic continuity equations, the two phasic momentum equations, and an overall energy equation. In this model, only two interphase coratitative rela-tions are required; those for interphase drag and interphase mass exchange. An additional specification (that one-phase exists at the local saturation state) eliminates the need to specify energy transfer parti-tioning, either interphase or from the wall. Special process models have been developed for abrupt area changes, branching, choking, pumps, accumulators, core net;tronics, control systems, and valves. The fluid process models are based on the 4 RELAP5 hydrodynamic model for quasi-steady conditions. This approach eliminates the need for local-ized fine nodalization and the attendant computational speed limitations resulting from a greater number of nodes and decreased Courant limit. I Some process and component models were obtained with little or no development work by transforming existing RELAP4 models to International System of Units (SI) and dynamic storage compatible with RELAP5. Examples of models obtained in this manner are those for pumps, valves, trips, neutronics, and certain input features. l l O 8 I 1
j
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2.'. SYSTEM MODELS ~ l 1 2.1. Hydrodynamic Model The hydrodynamic model developed for the RELAPS codel includes the important physics of the two-phase flow process, while incorporating any simplifying assumptions consistent with the end use of the model, that is, light water reactor transient analysis including LOCA. The prmcipal simplification used is the specification that one of the phases be at saturation. Generally, it is sufficient to specify that the least ? mannive phase be at saturation, that is, the phase that is either appearms or disappearms. The specification _ of one-phase temperature greatly reduces the amount of constitutive information that must be provided relative to interphase and overall energy transfer. All interphase energy transfer mechanisms are implicitly
' lumped into the vapor mass generation model. Thus, a single correlation replaces the need for constitutive relations for interphase energy transfer, distribution of external energy transfer between phases, and distribution of energy transfer between sensible heat and heat of vaponzation. In addition, only a single :
overall energy equation is required. The two fluid nonequilibrium hydrodynamic model includes three options for simpler hydrodynamic .. models. These are a quasi-steady flow model, a homogeneous flow model, and a thermal equilibrium model.' The two fluid,1uasi-steady,.or homogeneous flow models can be used with either the none-
' quilibrium or equ 'brium thermal models (that is, six combinations). Most of the development effort was .
. performed using th: two fluid nonequilibrium model. The homogeneous equilibrium option is included to . .
permit the RELAP5 code to be compared with existing homogeneous equilibrium code results for checkout and development. 2.1.1 Field Equations. The differential form of the one-dimensional transient field equations are first t developed assuming a one-component system. The mulifications necessary to consider noncondensibles as a component of the vapor phase and dissolved solids as an additional component of the liquid phase are , discussed separately. For the basic development; the flow structure is assumed uniform or at least symmetric in the plane nor-mal to the spatial direction. The special case of stratified flow in horizontal components is also di=M separately. , 2.r.r.1 vapor /ueowsysamm-The basic field equations for the two fluid nonequilibrium model consist of
> the two phasic continuity equations, the two phasic momentum equatiore, and the mixture total energy . _
equation. The equations are recorded in differential stream-tube form with time and one space dimension as independent variables and in terms of dependent variables that are time and volume-averasc quantities.a The development of such equations for the two-phase process has been recorded in several r'eferences2 ,3. and are not reported herein. The equations are recorded in the basic form with discussion of those terms
. which may differ from other developments. Subsequently, manipulations required to obtain the form of ^
the equations from which the numencal scheme was developed are described. The phasic mass conservation equations are a(agg o )/at + (1/A) a(aggg o v A)/ax = r g (1) . a(afpf)/at + (1/A) a(afofvAf )/ax = rf . (2) l
- a. In all the field equadons recorded herem. the correlation coemeients are assumed unity so the average of a product is equal to the product of the averased variables.
9 i - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ __ -- - _. __ i
l 1 i Generally, the flow does not include mass sources or sinks and overall continuity consideration yields the requirement that the liquid generation term be the negative of the vapor generation; that is, ! i Pf=-T. (3) l The phasic conservation of momentum equations are used, and recorded here, in nonconservative form ] l l for vapor, l 1 f 2 o Al av /ax ' a99 o A(av9 /at) + 7 a 99( 9 ; 1 1
= - a gA(BP/ax) + a ggo B,A - (a ggo A) FWG(v g ) +g r A(v g y-v) g 1
- (a o A) FIG (v - vf ) - Cagf a pA [a(v - vf)/at + v f(av /ax) g l
j
- v g( avf /ax)] (4)
)
for liquid, af ofA ( av f /at) .+ ff aAofav /ax
= - af A(aP/ax) + af ofB ,A - (af ofA ) FWF(v f ) +f T A(vfy-v) f
- (a fof A) FIF(vf - v )g - Caf agoA [a(vf - vg)/at + v g(av f/ax)
)
1
- v f( avg/ ax)]. (5) l The force terms on the right sides of Equations (4) and (5) are: the pressure gradient, the body force, ]
wall friction, momenta due to interphase mass transfer, interphase frictional drag, and force due to virtual l mass. The coefficients, FWG and FWF, are the part of the wall frictional drag, which is linear in velocity l and the product of the friction coefficient, the frictional reference area per unit volume, and the magnitude j of the fluid bulk velocity. The interfacial velocity in the interphase momentum transfer term is the unit I momentum with which phase appearance or disappearance occurs. The coefficients, FIG and FIF, are parts of the interphase frictional drag, which is linear in relative velocity and tre products of the interphase friction coefficients, the frictional reference area per unit volume, and the magnitude of interphase relative velocity. l The virtual mass acceleration terms in Equations (4) and (5) are special cases of objective or frame indif- l ferent formulations proposed by Lahey.4 The coefficient of virtual mass is the same as that used by l Anderson $i n the RISQUE code, where the value for C depends on the flow regime. A value of C > 1/2 ! has' been shown to be appropriate for bubbly or dispersed flows,6,7 while C = 0 may be appropriate for a separated or stratified flow. I _ _ - - - _ - _ _ _ _ _ _ _ - _ - . _ _ __ i
Conservation of interphase momentum requires the sum of the force terms associated with interphase
.x.\ mass and momentum exchange sum to be zero
,I rggv ; - (a ogg) FIG (v g - v f) - Ca gafo [a(v g - vf)/at + vf(av g/ex)
- v g( avf / ax)] + r vf fy - (afof) FIF(vf-v) g a
- Caf ag o [ a(v f - v )/at g + v (av g /ax) f vf (avg /ax)] = 0. (6)
This particular form for interphase momentum balance results from consideration of the momentum equa. tions in conservative form. The force terms associated with virtual mass acceleration in Equation (6) sum to zero identically as a result of the particular form chosen. In addition, it is usually assumed (although not required by any basic conservation principle) that the interphase m.omentum transfer due to friction and due to mass transfer are independently equal, that is, p) vy=vy=vi g f and . o o FIG = aff o FIF = a af o of FI. .(8) 1 These conditions are sufficient to ensure that Equation (6) is satisfied.
~ /
The fifth field equation used as a basis for the RELAPS hydrodynamic model development is the mixture energy equation a(agg o E + a ff o Ej)/at + (1/A) a(a o v EggA + a ffff o v E A)/ax
= - (1/A) a(a vgg PA + af fv PA)/ax + (ago v g + af ofvf)B, + Q. (9)
I The viscous work term due to dilation of the fluid in the flow direction is small and neglected (normal viscous work), and E = U + v2/2. l l The mass, momentum, and energy field equations have been recorded in a basic form to clearly indicate the standard and general nature of these relationships. However, these forms are not the most convenient for development of the numerical model. The following discussion describes the manipulation necessary to obtain the particular forms actually uset. The phasic mass cot- Aion equ4ons are summed directly to obtain the mixture continuity equation ao/at + (1/A) a(aggg o v A + afofvAf )/ax = 0 (10) I
-y(N and differences to obtain o( aX/at) + [(1 - X)/A] [a(aggg o v A)/ax] - (X/A) [a(af ofvfA )/ax] = ra. (11) l 11 e________-_-________.
{ Equation (3) is used to eliminate the l'r term and the relationship between quality and void fraction is j employed; that is, X = ogg o /o. (12) Equations (10) and (11) are the phasic mass conservation field equations used for the numerical scheme development. The momentum equations are also used as a sum and difference. The sum equation is obtained by direct summation of Equations (4) and (5) with the interface conditions (Equations (6), (7), and (8)] substituted where appropriate and the cross-sectional area canceled throughout. The resulting sum equation is 2 oggo ( av g / at) + af fof( av / at) gg +avfg o /axo+ af of avf /ax
= - aP/ax + oB, - a ggg o v FWG - af of fv FWFg- rg(v - vf ). (13)
The difference of the phasic momentum equations is obtained by first dividing the vapor and liquid phasic momentum equations by aSPs and arpr, respectively, and subsequently subtracting. Here again, the interface conditions are used and the common area is divided out. The resulting equation is 2 avg /at - av/at.+fav/ax f g -fav/ax :
= - (1/p -g 1/ of) ( aP/ ax) - v FWG g + v FWF f + rg [ov y
- (aff ov + a o vf )] / (a o affo ) - oFI(v -v) f
. 1 2
-C p /( g f) [a(v g - vf)/at + v f(avg /ax) - v g(avf /ax)]. (14) l t
The total energy equation is transformed into the equivalent thermal energy equation using the momen-tum equations to obtain a mechanical energy equation, which is subsequently subtracted from the total energy equation. The result of this algebraic manipulation is ! i a( oV)/ at + (1/A) a(a goge ,A + af ofvUA f f )/ a x
=
- (P/A) a(a gg v A + afv A)/axf + 0 + (a ogg ) FWG(vg)
+
(of of) FWF(v f )2 +gfg(a a o of) FI(v g
- v f)2 1
+ rg (1/2 - 1) (v g
-v)f + Cagafp(vg - vf ) [a(vg - v f)/at j
+ vf (avg / ax) - vg (avf /ax)] (15) 12
-i q
,+
where the interfacial velocity, vi, is defined as ; 4; a ,L
~
'v y .*'Av :+ (l -A)vf .. (16)'
This definition for vg has the property that if X = 1/2, the interphase momentum transfer process -i associated with mass transfer is reversible. The constant values lead to either an entropy sink or source, !
' depending on the sign of Pe. Howewr, if X is chosen to be 0 forg r positive and + 1 for ranegative (that j '
~ is, a donor formulation), the mass exchange process is always dissipative. The latter model for vg is the ~
most realistic for the momentum exchange process and is used for the numerical scheme development. The thermal energy source term associated'with the virtual mass acceleration term is not necessarily - l
. positive or zero. However, consideration of the second law of thermodynamics dictates that such must be - '(
the case. This contradiction is not resolved at this time, and since the energy dissipation associated with vir- ' taal mass acceleration force is small, this energy source term is presently omitted. The resulting form of the mixture thermal energy equation used in the development of the RELAP5 numerical hydrodynamic model' .
-l is y
a(ou)/at + (1/A) a(agggg o v U A + afof vUAf f )/ax 7
= - (P/A) a(ag v A vA + af f )/ax + Q gg + (a og ) FWG(v )2'
+ (aff o ) FWF(v f
)2 + (a fgfa o o ) FI(v g - vf)2
+ (lr gl/2)'(vg.- v f)2 , {37)
The reason for selecting the thermal energy equation rather than the total energy equation becomes more apparent in the development of the numerical scheme. However, at this point the thernial energy equation does not involve time derivatives of. the. kinetic energy and fewer new time variables appear in the numerical approximation. The field equations that form the basis for the RELAP5 hydrodynamic model are summarized as Equations (10), (11), (13), (14), and (17). The field variables which appear in temporal j i
' derivatives are p X, v ,gvt, and (pU). These are the basic field variables used in the numerical scheme.
f
- 2.f.f.2 Nordeonas/sevenednew-Flow at low velocity in a horizontal passage can be stratified as a result of bouyancy forces caused by density differences between vapor and liquid. When flow is stratified, the area average pressures are affected by nonuniform transverse distribution of the phases. Appropriate modifications to the basic field equations when stranfied flow exists are obtained by considering separate ,
area average pressures for the vapor and liquid phases, and the interfacial pressure between the phases. ! Using this model, the pressure gradient force terms of Equations (4) and (5) become (18)
- a gA(aP/ax) = - agA(aPg /ax) + (Py - P ) A (aag/ax) and (19)
- a fA(aP/ax) = - a fA(aPf /ax) + (P y - Pf)'A (aaf/ax).
i i 13 L
The area average pressure for the entire cross section of the flow is expressed in terms of the phasic area average pressures by P=aP +aP. ff (20) 99 With these definitions the overall or sum of the phasic momentum equations, written in terms of the cross section [ Equation (13)) average pressure remains unchanged. However, the difference of phasic momen-tum equations, contain the following additional terms on the right section (Equation (14)] (21) [o/(agaf og of)] [- a fa(a gg P )/ax + ag a(afP f)/ax + Py (ang /ax)]. The interface and phasic cross-sectional average pressures, Pg, Pg and Pr, can be related to each equation by means of the assumption of a transverse hydrostatic force balance in a round pipe. For a pipe having diameter, D, Py, PE, and Pr, are related by P g =PI-oBDgy sin e/(3nag ) - cose/2 (22) Pf=Py + of B0 y sin e/(3naf) + cose/2 . (23) The angle,6, is defined by the void fraction as illustrated in Figure 5. The algebraic relationship between og and 6 is aw= g (e - sine cose). (24) The additional term in the momentum difference equation [ Equation (21)] can be simplified using Equations (22), (23), and (24) to obtain
-[o/(oof)](of-o)w05/(4 g g sine)(aa/ax) g (25) where e is related to void fraction as given by Equation (24). j l
The additional force term which arises for stratified flow geometry in horizontal pipe is added to the i basic equation when the flow is established to be stratified from flow regime considerations, j
', Vapor area = agA N g Liquid area =a 9 A i Vapor l N i \
f l ) Liquid i t e INEL A 16 788 Figure 5. Relation of central angle 8 to void fraction pg . 14
2.1.1.3 Nancondenstelsein the Gee rhese-The basic, two phase, single-component model discussed above has been extended in RELAP5/ MODI to include a noncondensible component in the gas phase. The non-y, condensible component is assumed to be in thermal and mechanical equilibrium with the vapor phase, so \ l vn"V g (26) T n
=T g (27) where the subscript, n, is used to designate the noncondensible component.
The general approach for inclusion of the noncondensible component consists of assuming that all prop-erties of the gas phase, subscript g, are mixture properties of the steam /noncondensible mixture. The I quality, x, is likewise defined as the mass fraction of the entire gas phase. Thus, the two basic continuity field equations [ Equations (1) and (2)] are unchanged. However, it is now necessary to add the following mass conservation equation for the noncondensible component a(X n p)/at + (1/A) a(o g nVA g )/ax = 0. (28) I where X nis the mass fraction of noncondensible based on the total mixture, and Pn is the density of the nonec~':nsible component at its partial pressure. The remaining field equations for energy and phasic momentum are unchanged, but the vapor field ' properties are now properties for the vapor phase mixture. /~)
- 2.1.1.4 Baron Concentration in the Liquid Field-An Eulerian boron tracking model exists in RELAP5/ MODI that can be used to simulate the transport of a dissolved solid in the liquid phase. The solution is assumed to be sufficiently dilute that the following assumptions are valid:
- 1. Liquid properties are not altered by the presence of the solid
- 2. Solid is transported only in the liquid phase and at the velocity of the liquid phase
- 3. Energy transported by the dissolved solid is negligible
- 4. Inertia of the dissolved solid is negligible.
Under these assumed conditions, an additional field equation for conservation of the solid is required. In differential form, the added equation is apg /at + (1/A) a(C B *f f*f )/ax = 0 D A (29) where the concentration parameter, CB, is defined as C B
- DB /[p(1 - X)] (30) that is C B si the concentration of dissolved solid in mass units per mass unit of liquid phase.
rm 2.1.2 State Relationships. The state relationships are used to express the density of the system and all
) partial properties in terms of the independent state variables, P, X, Xn, and U, with an additional con-straint used to fix the temperature of one of the phases. The approach followed here is to develop the 15 l
i required state relationships for the single-component case, Xn = 0. The required relationships for Xn
- 0 j are discussed as an extension to the basic single-component case. l i
27.2r sing / compen.nr steem/weese syrrem-A determinant system is obtained by means of the state relationship in which the density as well as all of the phasic properties must be expressed as functions of pressure, static quality, and mixture internal energy. However, the state of the system cannot be estab-lished by means of these three independent variables alone, since the phase temperatures are generally different. The indeterminacy results from using only the overall energy equation and is removed by speci-fying that one of the phases exist at prevailing saturation conditions. In RELAP5/ MODI, the least massive phase is assumed to be saturated (that is, that phase which is either appearing or disappearing). This specification is considered an adequate approximation for blowdown, operational, and some reflood LWR transients. However, under conditions of slow reflood this specification must be modified such that superheated steam is produced at relatively low qualities. This modeling is incomplete in the ; RELAP5/ MODI code. j i The necessary state relations are developed for the two cases (vapor saturated or liquid saturated) by first j assuming the vapor to be saturated and then indicating the juxtaposition required to obtain the corres- j ponding relations for the case of the liquid phase saturated. j The state of each phase is established by specification of pressure and phasic internal energy (only the j pressure is needed to specify the state of the saturated phase). For the case of subcooled liquid or i d superheated vapor, those states are established using tabular equilibrium data as a function of pressure and phasic internal energy. For pseudo states of superheated liquid and subcooled steam, the properties are extrapolated along isobars using property derivatives evaluated at the corresponding saturation state. (The procedure for the pseudo states is discussed separately.) , I In addition to nonderivative state properties, derivatives of the mixture density with respect to pressure, ' static quality, and mixture internal energy are required in the numerical solution scheme. These derivatives are described below. The way these derivatives are used is explained in the course of the numerical scheme ' development. { The mixture specific volume is defined in terms of the phasic specific volumes and quality by ; V = XV (P) + (1 - X) V (P,U ). (31) 7 f To express V in terms of the independent state variables, P, X, and U, the phasic internal energy, Uf, must be expressed in terms of P, X, and U. From the definition of the mixture energy U = XV (P) + (1 - X) U (P,X,U) (32) f the phasic energy, Ur, can be solved to obtain U (P,X,U) = U - XU (P) /(1 - X). (33) f With Ur now known as a function of P, X, U, Equations (31) and (33) can be used to express the mixture specific volume in terms of P, X, and U as V = XV (P) + (1 - X) V P, U - XV (P) /(1 - X) . (34) l 16
1 Equation (34) is the desired expression necessary to calculate the derivatives' of the. mixture density,- l
' p = 1/V, with respect to P, X, and U. By a straightforward application of the chain rule to Equation (34), .l '
fN the derivatives of density are
. Lj -
s
- ( ap/aP)X,U = - o X dV /dP ~+' (1_- X) (aV f/aP)X,U (35) .
S
'(ap/aX)P,U = - o V -V f + (1 - X) (aV /aX)P,U f
(36) and (ao/aV)P X = - p [(1 - X) (aVf/au)P,X3 ' I37) The derivatives of the specific volumes must be further expressed in terms of phasic thermodynamic-properties. The derivative of vapor phase specific volume with respect to pressure is obtained as S s (38) . dV/dP=(aV/aP)S+(aV/aT)5(dT/dPf g g . where S 5 dT /dP = T V S -V /(h .h (39) and (aV /aP)s , , yss g r (40). t (aVg /aT)s p
, ysg , , (43)
. The final expression for the vapor specific volume derivative is SS s dVSg /dP = - Vgg c SS+Vs(dT/dP). gg (42)
. The functional form of the liquid specific volume and the associated partial derivatives in Equations (35), (36), and (37) are Vf = V f(P,Uf ) = V f[P,0 f(P,X,U)] (43) k (aVf /aP)X,U = (aVf/aP)g + (aVf /auf )p (au f/aP)X,0 (#I f
17
(aVf /aX)P,U_ = (aV (45) f /au f )p (au f/aX)P,U and (aVf /aV)p = _(aV (46) f /au f )p (auf /au)P,X. The partial derivatives of the liquid phase energy in Equations (44), (45), and (46) are obtained by dif-ferentiation of Equation (33) with respect to P, X, and U (auf /aP)X,U = - [X/(1 - X)] (du /dP) .(47) ( auf /aX)P,U
- f-U /(1 - X) (48) and (49)
(auf /au)P,X = 1/(1 - X). The required derivatives of liquid-specific volume in Equations (44), (45), and (46) are obtained by con-sidering the functional relation V = V (P,Uf ) (50) O f f and application of standard equilibrium, single-phase thermodynamic relations 8 thus ( aV f /aP)U ' * - Y C/~ f *f yf (Cpf - PVf7 8) (51) f and (52) (aVf /auf )p = Vff a /(Cpf - PVf7 8) where 2 (33) C yf =Cpf-TVefff fcy, The derivatives of density required by the numerical scheme, Equations (35), (36), and (37), can now be expressed entirely in terms of known thermodynamic properties. The properties needed in evaluating the derivatives are obtained using water property subroutines. First i the properties at the saturation state are evaluated, which are a, function of pressure only. Jhe saturation properties for vapor include specific volume, V; internal energy, U; tempera-8 ture, T'; specific heat at constant pressure, C ; enthalpy, h isothermal compressibility, x ; and the l isobaric coefficient of thermal expansion, $s. Ab other requirek properties can be derived from these. The thermodynamic properties for evaluating the derivatives of the liquid phase-specific volume are obtained as a function of pressure and liquid phase internal energy. The liquid phase internal energy is obtained l 18 j
- t. 1 E- - _ _ _ .1
} *:
j" ' from Equation (33), where it is assumed that Ur corresponds to a subcooled liquid state. The generaliza-tion for the superheated state is developed later. The properties of the liquid phase are also obtained using a water properties subroutine. The properties required include specific volume, Vr; temperature, Tr; lty)' specific heat at constant pressure,~ C
,V coefficient of thermal expansion, Sr. pr; enthalpy, hr; isothermal compres The corresponding thermodynamic relations where the liquid phase is assumed to be at saturation can be
- obtained by juxtaposition of the f with g subscript and X with (1 - X). The necessary relations for this case are (ao/aP)X,U ' ~ ' ,
aV/aP)X,U+(1-X)(dVf/dP g (54)
+ (55)
(ao/aX)P,U * ~ D ,g (8 g/8X)P U 2 (56) . (ap/au)p,y = 'o X(aVg /au)P,X (57) . dVf/dP=-Vfef+Vfsf(dTf/dPf (58) dTf/dP=Tf(V -Vf)/(h.-hh V (aVg /aP)X,U =-(aVg /aP)U + (aVg/au g)p (au /aP)X,U g g (aVg /aX)P,0 *(8 g/au g)p (au /aX)P,U g (") (61)
' (aVg /au)P,X = (aVg /aug )p (aug/aV)p,y i
(62). { aug /aP)X,U = - [(1 - X)/X] (dUf/dP) (63) (aug /aX)p,g = - (U g -Uf)/X (64) (aug /au)p,y = 1/X (65) g*gCyg/(C pg - PVgg e)
"~
{aVg/aP)U g 19
l 1 l I (avg/au g)P = V e gg/_(C pg - PVgg s) (66) l l ;l I 2 I C vg
=C pg -TVs ggg/c.g (67)
The properties where the vapur is subcooled or the liquid is superheated, are obtained using both proper-ties at saturation and extrapolations at constant pressure. The following properties are evaluated and held fixed at saturation: C p, x, and S. The temperature and specific volume are extrapolated at constant pressure from the values at saturation. The extrapolation is illustrated for the case of the liquid held at saturation and the vapor subcooled. The internal energy of the vapor phase is obtained from the mixture energy relation (Equation (32)] in terms of the liquid phase energy and the mixture energy U g
=
U - (1 - X)U /X. (68) The vapor will be subcooled if S U <U. (59) 9 9 The temperature and specific volume are obtained by a two-term, Taylor series extrapolation from saturation conditions holding pressure constant T g
=T
+ ( aT g / gau )* g(U
-U (70) h and s
=V s + ( aV / au sl (73) g )P \u g - U g)),
V g g g The temperature and specific volume derivatives in Equations (70) and (71) are evaluated at saturation conditions from standard thermodynamic relations 8 S ( aT g / aUgP)s , g j[\C pg - PV g BS g/ SI (72) and (aV /au )s , yss g j/ CS ss (73) g gP g g \ pg - PVgg g )), The derivative of density with respect to pressure, quality, and mixture energy can now be evaluated in the same manner previously described. The case of liquid superheated with the vapor phase at saturation occurs for the condition S (74) Uf>U7 20
g.
- r. t L !
The appropriate extrapolation equations for temperature and specific volume are obtained by juxtaposi- " i
~t ioning X and (1 - X) and the subscripts f and g. In this case, the propr Gs, Cpt, St, and xt, are held fixed i at saturation value.
[ 27.12 #easeadsammes la une ses phase-The vapor phase is assumed to be a Gibbs-Dalton mixture when noncondensibles are present.' The development here consists of the necessary modifications' to the basic state relationships and the temperature constraint. When noncondensibles are present, the system has an added degree of freedom; this is reflected in the need to specify one additionalindependent variable to establish the state of the system. The added variable - used here is the noncondensible quality, Xn, defined as the mass fraction of noncondensible based on the mixture (liquid, vapor, and noncondensible). For a Gibbs-Dalton mixture, the total pressure is the sum of 4 the component partial pressures P=P +P*n (73) Furthermore, the steam and noncondensible occupy the same space (the vapor space), so (76) -
' V X ; = - Vf Xn"vX s3 where ,
X =.X -+ X . (77) ; n .. s , The noncondensible component is assumed to obey the ideal gas law ' ~O P V' = R'T' (78) . nn ng where Rn is the gas constant for the noncondensible (the noncondensible could be a pure component or a - mixture of ideal gases where Rn is the effective gas constant of the mixture).- Substituting Equations (76) and (78) into Equation (75) yields a=P 3 +RXTAV* ( nng 3s The mixture specific internal energy is written as IN
- U U ='(1 - X) Uf + XU g = (1 - X) Uf+XU nn ss where l cT
=U Cy dT.
U + (81) n n o dT g n ( The liquid thermodynamic properties in Equation (80) are functions of total pressure and liquid temperature (for example, Ur = Ur (P, Tr)] while steam thermodynamic properties are functions of steam partial pressure and gas phase temperature. L 21 g
To establish thermodynamic properties of each phase under the general nonequilibrium case in which the phase temperatures are not equal, an additional constraint is necessary. In the single-component case, the least massive phase is assumed to exist at the saturation temperature O defined by the total pressure. An analogous constraint is used for the two-component case where the least massive phase is assumed to exist at the saturation temperature defined by the partial pressure of steam in the gas phase. This assumption is equivalent to assuming that the least ma'sive s phase is in equilibrium at the interface with the surrounding continuous phase (that is, the partial pressure of steam equals the vapor pressure of liquid at the interfacial temperature). In general, this temperature will be different from the continuous phase bulk temperature due to the temperature gradient in the continuous phase. When the gas quality is less than 0.5, the gas phase temperature is specified as the saturation temperature for water at the partial pressure of the steam present in the gas phase, that is, T (82) g =Tsat (Ps ) when the gas phase quality, X, exceeds 0.5, the liquid phase temperature is specified by the vapor pressure / temperature relationship T =T (P ). (83) f With one-phase temperature specified, the state of the system can be found by satisfying Equations (79) and (80) simultaneously with the thermal and caloric equations of state for each phase. An iterative solu- , tion is required because thermodynamic fluid states are at different pressures, and partial pressure of the steam can only be defined through a nonanalytic water property relationship. Once the state of the fluid is obtained, the partial derivatives of the mixture density must be defined for the numerical solution scheme. In particular, the partial derivatives of density, with respect to the flow-independent variables, P, X, Xn, and U, must be calculated. The development here is for the case of the liquid temperature constrained, that is, X > 0.5. The mixture-specific volume can be expressed in terms of the liquid and gas phase-specific volumes ! i I V = (1 - X) V f(P,T f) + XV (P,T g) (84) g { where 1 V 9
= VsnV /(Vs + Vn ). (85) l
)
Equation (84) is now differentiated with respect to, X n , holding P, X, and U fixed to obtain (aV/aXn )P,X,U " (I ~ f 8f(dT f/dP ) (aP /aX s )P,X,U n
+ XV g2 [l/(V P ) - e Vss] (aP /ax )P,X,U nn s n 2
O
+ XV g [1/(Vng T ) - 8 s/V s] (aT g/ax n)P,X,0 . (86) l 22
The partial derivatives of the vapor pressure and temperature in Equation (86) are expressed in terms cf E state properties by partial differentiation of Equations (79) and (80), with respect to Xn. This yields
.0 = Pn ( /X n~+.1/Xs }
- O + *s n).(aP P
/aX s }P,X,U n
+ Pn O/Tg y e )s. (aT /aX )P,X,U (8E g n and 0 = (1 - X) (auf/aTf )p (dTf /dPs ) (aPs /aX n )P,X,U + n (U -U) s
~
+ (
X3 ( au s / aTg )p +XC nV 9 ! n)P,X,U
~ n
+X (aV (aPs /aXn)P,X,U 'I88)
_ 3 /aPs)T 3 g Equations (87) and (88) are solved simultaneously to obtain expressions for the derivatives of vapor pressure and temperature, with respect to Xn, in Equation (86). The liquid temperature is considered the saturation temperature corresponding to Ps. Thus', the liquid temperature derivative is given by the Clausius-Clapeyron relation dTf /dP = fT'(V - fV )/(h s
-h)f (89) evaluated at pressure, Ps-Equations (87), (88), and (89) can now be used to evaluate all derivative terms in Equation (86), so the i
partial derivative of mixture-specific volume can be evaluated in terms of fluid state properties. The above procedure must be repeated for differentiation of the mixture-specific volume with respect to pressure, liquid quality, and mixture internal energy to obtain the derivatives of density needed for the numerical scheme. 2.1.3 Constitudve Relations. One primary feature of the RELAP5 hydrodynamic modelis that only two interphise constitutive relations are required (that is, interphase mass transfer and interphase drag). The specification that one phase exists at local saturation conditions, and use of the mixture energy equa-tion, replaces the need for energy transfer and partitioning functions: both between phases and between each phase and the wall. The only heat transfer correlation required by RELAPS is the overall wall-to fluid correlation which has been the subject of numerous experimentalinvestigations. RELAP5 uses standard correlations developed from the experimental data base. The only additional constitutive relation required for RELAPS is the wall friction. Here, existing two-phase multiplier correlations have been adapted for this purpose. In summary, four constitutive relations are required by the RELAP5 hydrodynamic model; the vapor generation rate, the interphase drag, the wall friction, and the wall heat transfer. These relations are O pnmarily empirical in nature as opposed to the field equations that characterize the dynamic behavior. However, the ability of any numerical hydrodynamic model to accurately agree with or predict physical phenomena depends heavily on the accuracy of the constitutive relations. 23
The approach taken for development of the R4 LAP 5 constitutive models has been to draw on existing information and data. The vapor generation modelis based on data from the Moby Dick Experiment9 and the work of Jones et al.10The interphase drag modelis based on existing flow regime maps and associated ; ' drag correlations, and the wall friction modelis an adaptation of the HTFS modification of the Baroczy two-phase friction multiplier correlation. The wall heat transfer correlations are conversions of the RELAP4/ MOD 6 blowdown heat transfer surface. The RELAPS/ MODI code has constitutive models for modeling LWR blowdown portions of a loss-of-coolant accident. Future versions of the code will require extension of these models for the reflood phase. In this regard, the wall heat transfer correlations will require the greatest modification. The remaining cor-relation development work will extend the range of applicability and scalability of the RELAPS/ MODI correlations. 11.11 Vapor Genereabn Modet-The nonequilibrium character of two-phase flow is governed by the vapor generation rate. The vapor generation rate is the result of several mechanisms such as interphase energy transfer rate, the energy partitioning between phase change and sensible heat, interphase surface area, nucleation site density, and turbulance level. In the RELAP5 hydrodynamic model, all of these separate but interacting mechanisms are modeled by a single correlation for the vapor generation rate. This simplification is a direct result of fixing the appearing or disappearing phase at saturation conditions. This assumption has been demonstrated to be valid by comparison of calculated results with experimental data for widely varying experimental conditions. In particular, the nonequilibrium effects of Reocreaux's Moby Dick Experiment and Edward's Pipe Blowdown Experiments are modeled. The test conditions for these two experiments cover pressures from 2.5 x 10 5 to 7.0 x 106 Pa and range from steady state to highly transient conditions. The model used in RELAP5 was developed by merging the results of two independent and widely v - ing approaches: (a) development of a mechanistic model similar to that developed by Jones and Saha based on interphase energy exchange, and (b) development of an empirical dimensional correlation similar to that developed by Houdayer, et al.,9 from the Moby Dick data. Separate models were developed for vaporization and for condensation. 11.11.1 #EL4P5/ MOD 1 Vaports ewr Modet-The dimensional correlation of Houdayer9 was extended ; and simplified using the work of Jonesto as a guide. The resulting general formula is l
= 96 x(x _ xe ) (90) b o 9
where C'g is a dimensional constant.a i The general correlation given by Equation (90) is adapted for use in RELAP5. The correlation has been extended empirically by defining G = G, + G g 01) where Gm is the mixture mass flux and Go is a constant that characterizes mass transfer at stagnant condi-tions, then Gm = 0. The static quality term, X, in the correlation is replaced by X + Xo, where Xo is a constant that charactenzes nucleation and germination phenomena for the transition from pure liquid to two. phase. The extended correlation for I'g is
- a. Equation (90) can be placed in a dunenssonnens form such that the constant. C'g. becomes a pure constant by the introduction of O
hid properties. The resulting correlation then involves only dimensionless groups (the particular groups are the Weber. Euler, Reynolds Prandt!. and mass transfer Nusselt numbers). 24
F (? Im ,
.C Q(G, + G,M . (92)-
r = -(X+X)-(X'-Xf). g - g o g
%)
[ The constants have been empirically determined as C'g =- 6.4517175 x 10-3 Go. = 3500 Xo = 0.00001. This relation is applied as a vaporization model for 0 m X = 1.0. 27.17.2 asAM/moof condenseensa meets /-A simple relaxation model based on Jones' work was adapted for use as a condensation model. The correlation is given by (93) rg= K [(1 - X) + X ] (X - X )~ 5 where the constants have been empirically established to be K '= - 1.0 x 10 and Xe = 1.0. The selection of either condensation or vaporization is based on the sign of the. quantity, X - X, (vaporization for negative values and condensation for positive values). 2 f.17.3 Needeeman cdsonien- A temperature difference nucleation criterion is used for the ha= inning of ' both vaporization and condensation. The values of 2.0 K and 0.0 K are the criterion for vaporization and p condensation, respectively. Nucleation is also assumed to occur if the static quality exceeds 1.0 x 10-4 for. Q vaporization or is less than 0.9999 for condensation.
- 2 f.12 insurpasse onee-interphase dras consists of two parts: dynamic drag due to virtual. mass accelera-
- ion and steady drag arising from viscous shear between phases. The dynanue drag is included because of its effect on the sound speed, and hence pressure disturbance propagation speed. The dynamic drag is calculated based on the induced mass of a spherical bubble (or droplet) in a mixture of vapor bubbles (or liquid droplets) and liquid (or vapor). The steady drag depends on flow topography. It is formulated on whether the flow is in bubbly, mist, annular, stratified, or churn turbulent flow regimes. The flow regime maps and the calculation of interphase drag are di=~ ad below.
27.22f Mew Aspdsw Asses-RELAP5 employs four flow regime maps to define the flow pattern for various components:
- 1. Vertical flow regime map for vertical pipes i
- 2. Horizontal flow regune map for horizontal pipes
- 3. Annular flow regime map for annulus components such as the downcomer of a pressurized water reactor system
- 4. High nuxing flow map for flow in the pump.
The vertical flow regime map (Figure 6) in RELAP5 is sinular to the one used by TRAC.ll The flow regimes are classified into the following general categories. 25
l l 1 I
- l Transition 1 M g
(CTT) I 8 M 1 1 - 1 I I I I Churn-turbulent ' ! 3000 ---------!.------- --------- assf, gj Transition (TCT) 2000 - - r-- - l- - - - -- - - - - - - r- - - - - { 7 i l I i I i i l l I I I I l 1 1 l l B l T l l l l l
! l R lf 9l A ! Al N IU I .II l h .
) I l Slug lY iS E l Ib l LI QI ^
lRI
~
h ll 0N 1 0 l f4 Y l l l i N l _l lg l^ l IYl I ! I N ~l1 l ~l i 12i i iI i i~i i l J l I I I I l l i I I I I I I I I I I {j 0 0.5 1.0 ) 0 on l INEL-A-16 791 I Figure 6. Vertical flow regime map (VRT). 1
- 1. For mass flux less than 2000 kg/m2.s.
(a) Dispersed flow l (1) Bubbly flow with bubbles dispersed in a continuous liquid (as a 0.10) (2) Mist flow with drops dispersed in a continuous vapor (as a 0.95). , (b) Separated flow l (1) Pure annular flow (0.85 m og 2 0.9). 26
r: L
' < ,(c).. Transitional or mixed flow (1) 0.85),
"' Transitional regions; between bubbly and annular flows (0.10 m ag = low is
,A and between annular, and mist flow (0.9. m ag = 0.95). The slug f treated as transition between bubbly and annulus at present time.
' 2. ' For mass flux greater than 3000 kg/m2 .s. In this region, flow is churn-turbulent in nature.' Dispersed . flow is assumed to be: bubbly for 0.0 m ag = 0.35, mist. for .
4 0.65 m og a 1.0, and a transition region for 0.35 m og = 0.65.
- 3. For mass flux between 2000 and 3000 kg/m2 s, the flow is transitional in nature.
The horizontal flow regime map (Figure 7) is a modification of the vertical map. For mass flux less than : 150 kg/m 2.s, a stratified flow region is added in the map. The elongated bubble or slug is treated as a tran-L - sition region between' bubbly.and mist flow. The annulus flow regime map is shown in Figure 8. An ~ annulus region is defined for void fraction from 0.1 to 0.9 independent of mass flow rate. Low interphase - drag is calculated in this region. The high mixing flow regime map is given in Figure 9. Basically, the flow.-. is assumed bubbly or mist. The abbreviations indicated on the flow map regions shown in Figures 6 and 7 are printed in the RELAP5 output for reference. - The RELAP5 flow regime maps are dimensional maps (that is, the regions depend on mass velocity, G,' which is a dimensional quantity). In this regard, the map is similar to most existing maps where velocity, superficial velocity, or mass velocity are used as coordinates. All are dimensional in nature. The use of . dimensional coordinates for correlation of empirical data casts doubt on the scalability of the results.' This-
- is an area where added constitutive model development is needed for all hydrodynamic codes to establish proper scale dependence.
- i. .
~y 17.112 ssesor orse-Constitutive relations for the steady drag are formulated for separated and dispersed flows. The drag in the transition regimes is calculated by the weighted average of the values of
' the separated or dispersed flow dras coefficients defined at the boundaries of the transition region.
The drag due to relative velocity between vapor and liquid is written as FI
=-aaoof fg FI(v -v)=-A f f
*B (v -v) g f (94) where Ar=g surface area between phase g and f per unit volume Br=
g drag coefficient between phase 3 and f FIg r = force per unit volume due to interfacial steady drag. The surface area per unit volume, Agt, is obtained from the structure of the flow field, and Bgt,is given by B o f (95) gf = c #g ~ #f 9:f where pg = thermodynamic density of the continuous phase fr g
= interphase friction factor.
27
1 I I l I M ei j (CTT) l l Transition y h l ~ j
,G l 1 i
l Churn turbulent l 3000 - - - - - - - L - - - - l- - - - - - - l l l i Mass flux ' (kg/m2.s) Transition (TCT) ; 2000 7 l g T. R lTl l l $ ll IS lN M S l8 l Elongated bubble I I [
- L ol
! or slug (SLG) l~l-0 M i
l$ l N
.)
I ll ei l - ll
- - t 2 t - - - - -- - - -- -- - -- - L4_L _
~
l 200 Transition (TST)
)I 150 - - - - - - - - - - - - - - - - - - - - - - - - f i
Stratified (STR) j i l l l i 1 I I I 0.5 1.0 f 0 J Void fraction INEL A 16 792 Figure 7. Horizontal flow regime map (HRT). The values of Agf and B gr for the dispersed and separa:ed regions are as follows: I l
- 1. Dispersed flow The bubbly or mist flow is considered as dispersed flow. The interphase area per unit volume for dispersed flow is calculated on the assumption that the particles of the dis-persed phase are spherical in shape. The size and number of the particies are obtained for empirical correlations based on a constant critical Weber number. The mean droplet ;
radius, rp, is calculated from the critical Weber number, Werit, defined as 28 _ _ _ _ - _ _ _ _ _ _ _ _ _ - _ __ a
LI
- g. IT 7 l N
! ]E l 'lgl' E l I M fg l p1y
~
ITransitionl M 7, I i 4 E Annulus
- V ; -l (CTT)'
6 y
-[l "l I
5 (ANN) : b 5 Y I _ l (CTM) j l. l h (CTB) IR., L 2 l 1 g 4 lAl ' i r I , i 1 l 0. 0.5 1.0
-1.0 O 0.5 Void fraction Void fraction INEL A.16 799 - INEL A 16 798 Figure 8. Annulus flow regime map (ANF). F gure 9. High mixing flow map (HMF).
=
2r pp c(v g - vf )2 W . cr1t a where a = the surface tension. The values of the critical Weber number are Werit = 13.0 for liquid drops and Werit = 1.24 for vapor bubbles.
-() The surface area between the phases is related to rp and the void fraction by the geometric relations (97)
A gf = 3ag /rpfor bubbly flow and'
,(98)
A f
=.3(1 - og )/rpfor mist flow.
The particle drag coefficient, 8f f , used in RELAP5, is taken from a fit of experiment data.12 The resulting correlation is 0.6 f gf = 1 + 0.15 Re p
+
0.42 {99) 4 1 + 4.25 x 10 Re -1.16 P r where the particle Reynolds number is denned as
.O' L/ v -v 2rpo f
Re = (100) P u c 29 l
where e
= the viscosity for the continuous phase.
- 2. Separated flow The separated flows considered here are annular and stratified. The formulation of the interphase drag for each flow is given below.
(a) Annular flow Only annular flow with liquid on the wall is considered. (The slug region is assumed to be part of the transitional region between annular and bubbly flow regions.) The area per unit volume for annular flow is related to the void fraction by A f= 4alI! (101)
)
I where D is the diameter of the pipe. The friction factor, f gf, is calculated based on the vapor Reynolds number defined as o v -V D g g f g Re = (102) g u , g where Dg = crgl /2 D is the equivalent wetted diameter g = viscosity of the vapor phase. The values of fSf " Re < 500 f = 64/Re 9 9f 9 1500 - Re 500 < Re g < 1500 f gf = 64/Re g 1000 i l Re - 500 -
+ y000 *0.02* 1.0 l
+150(1-a/2 9 .
1.0 + 150 - Re g > 1500: fgf = 0.02 - 1-a/2) .
. (103) j 30 l
_ _ _ = _ _ _ . _ _ _ _ {
7-_--__-. i r 4
.g tb) Stratified flow The idealized stratified flow is shown in Figure 10. The liquid phase is at the bottom M);
( , ~of the pipe with diameter D. The interphase surface area per unit volume for the - stratified flow is l A
#5I"('I2) (104)-
gl = .wD The relation between the void fraction (ag) and angle, 0, is 2w(1 - a9 ) = e - sine. (105)- The friction factor is determined from the Colebrook formula given by
= 1.74 - 2.0 log 2e 18.7
\ (106) 9f gf where 2a wR D = the interface wetted equivalent diameter '
by (sinf+w-e/2)
. %n, '
V ~ V hy'g g f Re . = the Reynold number. 9 At present, the interface roughness (e) is taken to be zero so the liquid vapor interface is assumed hydrodynamically smooth. Vapor phase A
/ \
g T -i
/ N l
\ /
N ~ Liquid phase
~
INEL.A 16 803 Figure 10. Idealized flow field for stratified flow. 31
2 f.222 oraemie ome-The calculation of the drag due to the virtual mass effect is based on objective and symmetric formulation of the relative acceleration.13 The drag force in the momentum equation is written as
/ av av r FA gf = - Cag (1 - ag ) o (v g -v)+v(,g 9 f f
-v g f[ (107) where o = ao 9.9 + (1 - a9)of FA gf = force per unit volume due to dynamic drag. (108)
The factor, Cag (1 - ag)p, is chosen to ensure a smooth transition between og = 0 and og = 1.0. This factor also gives the proper limit, Cagp r, in the thinly dispersed bubbly flow and C (1 - ag)pg, in the dispersed droplet flow. The virtual mass coefficient, C, is given6 as (1 + 2aq ) l C = 1/2 () , for 01a gi 1/2 (109) ! and (3 - 2a9 ) O C = 1/2 , for 1/2 1 og i 1. (110) 9 It may be appropriate to assume that C = 0 should be used for separated or stratified flow. At present, the value of C defined by Equations (109) or (110) is used without regard to the flow regime. 17.2s we// rescuen-In RELAP5, the wall friction force terms only include wall shear effects. Form losses due to abrupt area change are calculated using mechanistic form loss models. Other form losses due to elbows or complicated flow passage geometry are modeled using energy loss coefficients. Wall shear losses in piping systems are usur.ily small compared with form losses, thus a relatively simple approach which yields an accurate steady state frictional pressure drop is acceptable. The HTFS modification of the Baroczy two-phase friction multiplier correlation 4 was used with the l Colebrook correlation for the single-phase friction factor including wall roughness effects. Both laminar and turbulant flow regimes are included. The two-fluid hydrodynam2 model requires the wall friction force be prJtitioned between the liquid and vapor phases. The method is based on void fraction partition-Ing of the wetted area and the phasic dynamic friction components. The phasic friction components are normalized so the sum of the phasic frictional forces agrees with that derived from the two-phase l multiplier approach. 1 In the development of the RELAPS wall friction model, emphasis was placed on obtaining reasonable values for wall friction under all regimes of operation (that is, all range of void fraction from 0 to 1.0, all range of Reynolds number, and countercurrent as well as cocurrent flow). 27.22r rae ovw it ws/r FricWon Pressure Gredient-in the RELAPS momentum equations, the phasic wall friction pressure gradients are expressed as 32 _______ U
r 4 A 'aP)I = FWF(afof A vf) for liquid (111) (af)(p/FWF-
=-
.f g kj and aP
-(aA)(g\j
= FWG(a o Av ) for vapor. (112)-
g gg g The terms, FWF and FWG, can'be expressed in terms of Darcy friction factor as 1 y p f FWF = for the liquid -(113) 8a A
~
and A v p 9 9 9 for vapor. (114) FWG = 3 g,9 Assuming transient frictional effects are negligible, the wall frictional pressure gradient component is calculated using a quasi-steady form of the momentum equations. , Summing Equations (111) and (112) gives the overall pressure gradient V V V V I Af "f0 f f + Ag"g'g g q
-g aP 20 f
20
. (115)-
The phase-wetted perimeter has been assumed proportional to void fraction p =opj ' (116) f p =ap (117) g g where p is the overall channel-wetted perimeter and the hydraulic diameter, D, is defined as l D . (118) The friction factors, A and f A , gcannot be calculated precisely unless the phases are separated. However, the overall pressure drop can be calculated using a two-phase friction multiplier approach. This' overall friction loss (developed in the next section) must still be partitioned between the two phases. Fot .s pur-pose, an e imate of the separate frictional losses .in Equation (115) is necessary. The friction losses in Equation (115) are estimated using standard correlations for the K's based on the Reynold's numbers O of V (4A ) v D R e, = f j f)= of f (119)
"f (P)f "f 33 I.
_._____.i._._________.__________.___________._.__.___..______________________._.__.___________________.__._.__.__.__________1.___
l and j 1 o V (4A o v a 0 q G
= 9 9 0 J Re .
(120) 9 "9 1[-9)= 9/ "9 l respectively, j 2r.zza The Two-phase meson mu/Wes er Approech-The overall friction pressure drop can be expressed a i in terms of the liquid-alone wall fnction pressure drop for which I aP i /aP\ (p 26 =ef 2 g) . (121) I 3 j y is the liquid-alone, two-phase friction multiplier which can be expressed in terms of the HTFS two- ' phase fricuon multiplier correlation.15 The liquid- and vapor-alone friction pressure drops can be calculated in terms of friction factor as api A M M f f f
-(g)f J
=
2D A 2 of for the liquid-alone (122) and
*g "g "g
-(-l aP) ax/g
=
20 A 2 o 9 for yapor (123) where the prime indicates the liquid and vapor alone friction factors, respectively, calculated at the respective Reynold's numbers defined as
, ap pf V f
D ; (124) Ref = "f
, aogg vg D Re = . (125) i 9 u g ,
The liquid and vapor mass flow rates, respectively, are defined as af ofvA M = (126) f f and i M = a o y A. (127) 9 999 34 >
- - _ _ _ _ _ _ _ i
a i 1 The HTFS two-phase friction multiplier correlation is based on Equation (119), for which l
)
D 2
=-I + C + 1 (128, V 6 where, C is a correlation parameter and 5 is the Lockhart-Martinelli parameter defined as j k
3
~
I2=h)f=2 3. (129) { aP
,2
* */ 9 and e is the vapor-alone, two-phase friction multiplier, 1r.2.2.2 .%rudoning the Owen crea Into veuld and vapor preg Terms-Partitioning the overall drag, , into its respective liquid and vapor parts is done by directly calculating the smaller of the component drags in Equation (115) and obtaining the larger component drag by subtracting this smaller -
drag from the overall two-phase pressure drop in Equation (121). This ensures that the component wall drags sum to the overall pressure gradient; (OP/ax)26-a a In particular, assuming At or pglvrlvt As "E PalVgIVs, the calculation uses Agagog lvglv gas the vapor drag component and (" faP 1 l -Aao 999 y v (130) iax/2+ ( 9 9 I as the liquid drag component. If the vapor drag is larger, the roles of the liquid and vapor are interchanged in the above. Equations (128), (129), and (121) include the HTFS two-phase friction correlation parameter, C, which is valid for coeurrent two-phase flow. For countercurrent two-phase flow, the HTFS two-phase friction correlation is invalid. However, for countercurrent two-phase flow, the phases are approximately separated and the friction factors, A tand A g, are used directly with reasonable accuracy. z r.2.2.4 reicwon rector end w s noughnese-.The fluid wall fri<. : ion factors for laminar, transition, and 4 1 turbulent flows are functions of Reynold's number and wall roughness (e) given by 64 xL = g ,1.0 g Re g 2000 for laminar flow (131) and
= 1.74 - 2 log 10 + Re
, 4000 g Re for turbulent flow. (132)
,-e
, Equation (132) is known as the Colebrook equation for transition and turbulent friction factor. Fe i Reynold's number in the range 2000 < Re < 4000, the friction factor is interpolated betwee.
Equations (131) and (132) as a linear function of 1/Re, given by 35
l i f 40001 A L,T*[~Re/IAT,Re ~ AL,Re) * *L,Re II33) where AL ,Re and AT,Re are the laminar and turbulent friction factors, respectively, evaluated at the Reynold's number. Equation (132) is transcendental. In RELAP5, the turbulent friction factor, AT , is computed from a parabolic approximation to Equation (132). 21.14 wa# #mr Trenew-Discussion of the RELAP5/ MODI wall heat transfer is broken into two sec-tions. First is a discussion of the heat transfer surface concept used during the implementation of the cor-relation package to check how the correlations splice together. 'econd is a discussion of the correlations and how they are combined into a package. 27.24.r me nur Trenew surrece rechalgue-The heat transfer surface technique was original 1 developed for RELAP4/ MOD 6 16 and presented at an NRC-sponsored Heat Transfer Workshop!7 Results utilizing this concept have been presented by Nelson,15 Nelson and Sullivan,18,19 and Bjornard and Griffith.20,21 The technique was originally a three-dimensional plot of heat flux that provided a sim-pie visual means of studying parameter trends of individual heat transfer correlations, or groups of cor-relatiotis spliced together. This visualization has proven extremely useful in both problem understanding and solution. The function, z = f(x, y), may be viewed as a surface when z is plotted as a function of x and y. The insight gained from this visual approach can be helpful when a number of functions, zt,22.
- ZN.
must be combined to cover a wide range for the independent variables, x and y. This mathematical concept of a surface has been termed the heat transfer surface when the functions, zt, z2, . . . , zN, are heat transfer correlations and considered as functions of n variables. Thus, the heat flux defined by a number of different correlations is viewed as a function of wall superheat, quality, pressure, mass flux, etc.,: q = q ( aTsat, X, P, G, . . .). (134) Within this discussion, the heat transfer surface represents the total wall heat flux convected into the fluid from a given poi?t on the wall, and the quality is defined on an energy basis. Thus. forced convection to subcooled liquids is represented when the quality is less than zero, or forced convection to superheated vapor for a quality greater than one. Thermodynamic equilibrium is assumed for convenience. Ther-modynamic nonequilibrium could be inciuded; however, it does not change the basic results and adds complexity to the discussion. To plot the heat flux as a three-dimensional surface, the wall superheat and quality are usually picked as the primary independent variables, with the remaining variables assumed constant, as shown in Figure 11. This choice may be changed to study the sensitivity of the surface to other variables. However, when the wall superheat and qurdity are used as primary variables, the definition of a boiling curve arises. A coiling curve shows the dependence of heat flux upon wall superheat with all other variables held constant, as shown in Figure 12. ! l The heat transfer surface shown in Figure 11 is composed of two families of curves. In addi- ) tion to the family of boiling curves, there is the family of constant wall superheat curves, which i view heat flux as a function of quality (termed isothermal curves). Both families assume all f other parameters (independent variables) to be held constant. l l To aid the visualization, Figure 13 denotes different areas on the heat transfer surface in terms of clastical boiling regimes such as single-phase liquid heat transfer, nucleate boiling, transition I 36 i l
r P = Constant G = Constant I ( ( C/ i 5 c E E e a
.. ,, s
, /
0 0.3 MeD 0*O 0 y& Ouai, n9 1.2 b INEL.A-15 652 Figure 11. RELAP5 blowdown heat transfer surface. q . DNB Nucleate l
.V(~~'N, boshng i Transition s y l boikn ,,,,Ml Film F
" l b l
bothng l - P = Constant l- - 84 BA l <0 G = Constant j BT yo BT X = Constant i
- n. w . e. w .
ATCHF ATmin Log ATsat INEL.A 15 658 Figure 12. RELAP5 forced convection boiling cu'rve. boiling, film boiling, and single. phase vapor heat transfer. The slope of the heat transfer surface with respect to wall temperature, aq/aTw, is positive for all boiling regimes, except the transition boiling region. To relate the heat transfer surface approach to the classical boiling curve, as originally proposed by Nukiyama,22 assume that Figure 13 can represent a pool boiling situation. Th'e pool bciling curve can now be shown on the heat transfer surface. For this classical pool boiling curve, the quality u,ed is the average quality at a point on the wall and is changing as the wall temperature changes. In reality, for the pool boil-ing situation, there is a narrow range of qualities, if not just one, for any given wall temperature, so that a
,A full heat transfer surface as just assumed does not exist. Thus, a unique (or nearly unique) classical pool 37 4
Single phase liquid ; Classical pool boiling curve (dashed) ' J Nucleate boiling ) Transition boiling ! I Film boiling and single-phase vapor P = Constant G=Censtant i
\
~
- a
~
s E
- 2 g
' N
- s 0
0.3 ygeD Oh Qu*lity 0.9 0 xb1W 1.2 goMD INEL A.16 777 Figure 13. RELAP heat transfer regimes. boiling curve exists for a given material, pressure wall finish or condition, and geometry. For forced-convective heat transfer, a unique classical boiling curve does not exist as it does for pool boiling. Instead, the heat transfer surface may be transverses in an infinite number of ways as determined by the coupled response of the wall and the hydraulics. 2 r.24.2 We// user Trenster corret c/on Packepe-To discuss the correlations in use and how they inter-relate, the heat transfer surface technique will continue to be employed. Figure 13 denotes some different heat transfer boiling regimes with respect to the heat transfer surface. If the interfacial lines denoting a change from one boiling regime to another (shown in Figure 13) are projected down onto the pality-wall superheat plane and additional regimes that exist are added, Figure 14 is obtained. Figure 14 defines the . different possible boiling regimes with respect to quality and wall superheat. ; Figure 14 provides the fundamentalinforraation necessary to build a heat transfer surface Correlations must be selected to represent each of the boiling regimes shown in Figure 14. If a single correlation cannot be used across all values of the remaining independent variables, several correlations must be spliced together to provide this capability. The RELAP5 wall heat transfer correlation package conshts of a forced-conveedve (flow related) group of correlations and a pool boiling / natural circulation (independent of flow) group of correlations. The forced-convective correlations are an adaption of the RELAP4/ MOD 616 blowdown heat transfer surface. This adaption of the RELAP4/ MOD 6 package eliminated the option to use implicit correlations for the transition and film boiling regimes (shown in Figure 14), and implemented only the explicit correlations 38
*rf r
- ;q._ h ATsat
.?w) .
Film boiling and forced convection to vapor ( 8Tw >0,q>0) Transition boiling 8q AT min ( < 0'q> 0} BT* ATg = 0 ATCHF , Vapor forced convection to wall.
,- Nucleate boiling I ( 89 > 0' q
- 0)
( 0 " > 0,.q < 0) T* I' 8T W _ Forced convection X limit X(quality) to liquid
. . ATsat = 0 (0BT > 0,q > 0) w A T, = 0 Condensation Forced convection X=0 to wall 04
( STw> 0, q<0) 8q
> 0, q < 0) g Indicates boundary between boiling regime INEL A 16 776 Figure 14. Different heat transfer boiling regimes with respect to the quality wall superheat plane, O
39
for those regimes. Condensation correlations replaced the temporary correlations placed in the regime in RELAP4. The pool boiling / natural circulation correlation group was added to provide a lower bound for the low flow /no flow situations which arise. This was achieved by obtaining heat fluxes from both groups i of correlations for mass fluxes below 200 kg/m2 s then using the maximum. 1 2f.14.2.7 Forood ConvecWon Neet Transfer Corrodedons-Figure 14 denotes the heat transfer regimes represented by the forced convection heat transfer correlation group. The correlations for each of these regimes is contained in Table 1. Table 2 contains the standard group of critical heat flux (CHF) correla- l tions used with the forced-convective correlations. Other CHF correlations are available which cams f;om ) RELAP4/ MOD 5; however, these optional CHF correlations are not generally recommended. l l l Detennination of boundaries between different boiling regimes is the single remaining question. For forced convection between a subcooled liquid and wall, the boundary as to whether the wall or liquid receives hat is determined by the loci of points indicating when the wall and liquid are equal in temperatme, ATt = Tw - Tr = 0. A change from forced convection to a subcooled liquid and subcooled ] nucleate boiling is defined by the wall temperature equalling the saturation tempereure, ATr ate 0. All ' other boundaries are self-explanatory except possibly ATCHF and ATMIN. Figure 12 further defines their j meaning where ATCHF enotes d the wall superheat at which CHF occurs. This is obtained by determining j the wall superheat at which the nucleate boiling heat flux is equal to CHF i j (I35I aTCHF = aTsat
- I UNB " QCHF I AT MIN si the minimum wall superheat and represents the wall superheat at the minimum post-CHF heat flux. Within the transition and film boiling regimes modeled in RELAP5, this boundary is not evaluated. l Instead, the post-CHF heat flux is determined by summing the transition boiling and film boiling correlations j I
9 Post-CHF *9TB + "FB' II # Thus while a ATMIN exists and could be evaluated, one is not obtained within the code and the ATMIN boundary is only implied. . 2 f.14.2.2 Pool Bolling / Naturel Circulation Heat Transfer Corraindons- As discussed in Section 2.1.3.4.1, while a heat transfer surface exists for forced-convective heat transfer, only a single boiling curve exists for the pool boiling (no flow) situation. This pool boiling curve does not satisfy the same definition as a forced-convective boiling curve since quality at the point on the boiling area where the curve applies is changing as wall temperature changes. Thus, Figure 12 can conceptually represent the pool boiling curve, { except the mass flux. G, is zero and the quality, X,3 not a constant. Also for this situation, natural cir- j culation can occur for single phase liquid or vapor and must be included. Table 5 lists the current heat j transfer correlations needed to represent the pool boiling curve plus natural circulation. l 2.2 Special Process Models 1 I Special process models are used in RELAP5 to model those processes which have small relaxation times or are so complex in nature that they must be modeled by quasi-steady empirical models. Break flow, inter- ] nal choking, abrupt area change, and branching are examples of processes having short relaxation times j compared with component transport times. The hydrodynamic performance of pumps and valves are i i examples of processes which are too complex to be modeled from first principles and empirical correlations f are used (even single-phase models are based on quasi-steady behavior). 1 L_________ __ __ 1
Tcble 1. RELAP5 forced c:nvecti2n heat transf:r errrolhtirns
;, q Single-Phase Forcad Convection for Wall'to Liouid, Liouid to Wall, or Vapori
(%,) - to Wall: Dittus-Boelter" 0 h = 0.023 D Pr
- Re .8 e
where the physical properties are evaluated at fluid temperature (Tf ) and h = heat tr'ansfer coefficient (W/m2 K) k = thermal conductivity (W/m K) De
= equivalent diameter (m)
Pr = Prandtl number (Cp u/k) Re = Reynolds number (GDe /u) ! Cp = specific heat at constant pressure-(J/kg K) u
= viscosity (kg/m s) ,
G = mass flux (kg/m2 ,3)- r
-f so A
q = h (T -T) f where l heat flux (W/m2 ) q = Tw
= wall temperature (K).
r Saturated Nucleate Boiling: Chen 24 h =.h mic + h, where 0.79 0.45 0.49 f Df f aT0sat
.24 g 0.75 3 l h = 0.00122 0.5 0.29 0.24 0.24 mic ' h o "f fg g 0.4 0.8 h = 0.023 Pr Ref 7
0 mac f 41 l
- - . _ . ._-__________-_________A
L , Table 17 (continued) Satu' rated Nucleate Boiling (continued) F = Reynolds number factor (see Table 3) S = suppression factor (see Table 4) o = density (kg/m3 ) o = surface tension (N/m) h fg =- latent heat of vaporization (J/kg) d ATsat
= Tw -T sat T sat = saturation temperature (K) aP = difference in vapor pressure corresponding to ATsat (N/m2) f = saturated liquid condition (subscript) g = saturated vapor condition (subscript) so q = (b + h, ) aT sat' j
Subcooled Nucleate Boiling: Modified Chen25 q=h aT f}*
~
sat +hmac ( w The modified Chen correlation is obtained by setting F = 1 in hmac and evaluating the properties at Tf. , Hioh Flow Transition Boiling _: Modified Condie-Bengston q = A exp (-0.6708204 faTsat) ATsat TB
~
A = exp 1n I qCHF ~ 9FB + 0.6708 / aTCHF ~ I" ^ CHF AT
- ( CHF/ .
4 8
= high flow film boiling heat flux evaluated at aT CHF High Flow Film Boiling: Condie-Bengston AFB = h aTsat 42
4,. ,
; Tcble 1. . bcntinued)
' - b High Flow Film Boiling (continued)
- k. '
0.4376 s4 k p 2.3070 Re.[0.6004.+ 0.2456 in (1 + eX )] 9 h = 0.081033 De 0.7842 (1 + Xe)2.59028
- 13.89471=eup [.1.4504 (10' ) P Pr ] ,
where, P = pressure (N/m2 ) subscript w. = evaluated.at wall temperature, Tw. Low Flow. Post-CHF Traasition And Film Boiling 9 total
- 911guid + 9 vapor where
=
Qvapor (hc + hr ) (Tw .- Tf ) a , fy hc.
= natural convection' heat transfer coefficient 26 %,.J hp .= radiation heat transfer coefficient I"
1.111 (Gr Prf3),) e h = max 4 c I 0.260 D (Gr Prf $),) Gr = g (De /2) 8 fik (T, - T )f (p/u)2 1m (T +T) f T
- film 2 4
h r
= 1.30548 (10-8) lT,- T / (T,- T f)
B
= thcrmal coefficient of expansion of fluid (1/K)
~ -
1( p /1-Xh A -9f
- I +1 a = void frartion = 1 --
.f\* A e) -
43 i
Table 1. (continued) Low Flow Post-CHF Transition And Film Boiling (continued) 9-(hTB + hFB) ATsat (0.96 - a) if ATSAT > aTHSU 9 11guid h 4CHF if AT SAT 1 aTHSU hTB
= transition boiling heat transfer coefficient 27
= film boiling heat transfer coefficient 28 hFB
~#
h TB
= A exp sat i
A =
) aT
- (0.96 - a) h FB x2.7182L l
HSU > aT
,. HSU_
ATg39 = 1/B ln-in interpolation on pressure where P = 0.413685 MPa B
={B=0.0042222 B = 0.0045556' P = 0.620528 MPa 1
0 3 0.25
/D 3 172 k 0 ( of - o )hf9g 0.620' 3 9 '
h = l FB (Ac/ _ e "g 'I sat _
.0.5
- I'
*c g (of -o)g_
g = acceleration due to gravity (m/s2) . Condensation 25 q = h (Tsat - lw) h = max h from laminar and turbulent correlations. Laminar Flow in Horizontal Section . 0.25 > of ( of - ca ) g hf k f h lh = 0.296 0e uf (Tsat -T) w
3 !- Table 1.- (continued) )
- y. '
b , ' (,-). Condensation (continued) Laminar Flow in'Section at an angle e to vertical. j 3 # of ( of - on ) k cos e .
;h),= 1.766 G 0, uf . l lr Turbulent Flow
~ ~
/ ~2 1/2 Kf jof uf C pf 0.023 og vg ht= 0.065 k uf f f ogD, v q )0.25
. 9 ) .
a Table 2. Standard REL.AP5 DNB correlations
- 1. High Flow Subcooled CHF Correlation: Tong 29 fx
-8 -8 p) q P + 0.1722 - 1.42717 x 10 W-3 (10~ ) = {(2.002 - 6.23952 x 10 CHF x .'exp [(18.177 - 5.98861 x 10~7 P)X3k e X
x {(0.1484-1.596X e. + 0.1729 X e e)[(G/1356.2299)+1.037]} x (1.157 - 0.869 Xe)
.x {0.2664+0.8357exp[-124.05512D3k e x [0.8258 + 3.41359 (10~7) (hf-hin})
x 3.15459 where hin
= inlet specific enthalpy (J/kg).
- 2. High Flow Saturated CHF Correlation: Hsu and Beckner 30 If a (void fraction) < 0.96 4CHF - adry =
/1.76 (0.96 - a) 4W -3 CHF
( X, = 0 h -h g =0 f 45
l l Table 2. (continued) ,
- 2. High Flow Saturated CHF Correlation icontinued) n i
i where
'Dittus-Boelter to vapor 23 if Re > 2000 Qdry l Maximum of Rohsenow-Choi 31 and Free ;
LConvection+RadiationifRe<2000 _ q = Tong's W-3 CHF correlation 29 evaluated at 0 i W-3 quality and 0 subcooling. X e =0-1 l hf-hin=0 If the void fraction > 0.96 then dryout occurs a DNB = 0. j
- 3. Low Flow CHF Correlation: Modified Zuber32 i I#f I 0 qCHF = 0.131 hfg og 0.5 (eg (of -p )] 0.25 .5(0.96 - a) .
- a. See Table 1, O
The use of quasi-steady models for break flow and flow at abrupt area change results in considerable savings in computer time since it is not necessary to use fine nodalization at such points. This results in direct savings since fewer fluid volumes are required and indirect ravings due to the ability to use larger time steps. A decisive advantage for the use of a break flow and choking model results when choking at points of ! abrupt area change occurs, such as at double-ended pipe breaks or at a sudden contraction due to an j orifice. It is not possible to construct one-dimensional grids at such points that will result in meaningful self-choking results, because of the discontinuous variation of flow area with length. 2.2.1 Choked Flow. A choked flow model developed by Ransom and Trapp 33 is included in RELAP5 l primarily for calculation of the mass discharge from the system at a pipe break or a nozzle in scaled I experiments such as Semiscale or LOFT. Generally, the flow at these breaks is choked until the system i pressure nears the containment pressure. The RELAPS choked flow modelis used to ptethct if the flow is j choked at such a point and if it is to establish the discharge bounda.y condition. In addition, the choked I flow model is used to predict existance of and calculate choked flow at internal points in the system. I l \ Choking is defined as the condition wher % the mass flow rate becomes independent of the downstream l conditions (that point at which further totion in the dowratream pressure does not change the mass j flow rate). The fundamental reason that choking occurs is that acoustic signals can no longer propagate j l upstream. This occurs when the fluid velocity equals or exceeds the propagation velocity. The RELAPS l choked flow model is based on a definition that is established by a characteristic analysis using the time-dependent differential equations. ! l 46 I L -
L . , I , i Table 3. Chen's Reynolds number factor, Fa FJ F y-
,x 0.1 1.07 0.2- 1.21 0.3 .1.42 0.4. 1.63-0.6 '2.02 1.0 2.75 2.0 4.30 3.0 5.60 4.0 6.75 6.0- 9.10-10.0- 12.10
-20.0 22.00 50.0 44.70 100.0. 76.00 400.0 200.00
( x, f* * / off*5 fu,* Y* 1-x e 5 .
- a. .See Table 1.
O Table 4. Chen's suppression factor. Sa 1 REf *F .25-103 1,000 104 0.893 2
- 10 44 0.793 3
- 10 0.703 4
- 10 4 0.629 4 0.513 6*{010 0.375 2
- 105 0.213 3
- 105 0.142 4
- 105 0.115 5
6*g0 0.093 , 10 0.083 ! 106 0.000 l
- a. See Table 1.
47 ,
Table 5. Pool boiling-natural circulation heat transfer correlations Natural Circulation for Liouid or Vapor Same as natural circulation correlations for low flow post-CHF transition and film boiling. Pool Nucleate Boiling (Foster-Zuber) Same as hmic in forced convective correlations. Post-CHF (Transition and Film Boiling) Same as low flow post-CHF forced convective heat transfer. Consider a system of n first-order quasi-linear, pardal differential equations of the form A(0) (30/at) + B(0) (a0/ax) + C(0) = 0. (137) The characteristic directions (or characteristic velocities) of the system are defined 34,35 as the roots, Xi (i a n), of the characteristic polynomial (AA - B) = 0. (138) . The real part of any root, Kj, gives the velocity of signal propagation along the corresponding characteristic path in the space / time plane. The imaginary part of any complex root, Xj, gives the rate of gro'vth or decay . of the signal propagating along the respective path. For a hyperbolic system in which all the roots of Equa-tion (138) are real and nonzero, the number of boundary conditions required at any boundary point equals the number of characteristic lines entering the solution region as time increases. If we consider the system [ Equation (137)] for a particular region 0 2 x 2 L, and examine the boundary conditions at x = L, as long as any Xi are less than zero, we must supply some boundary information to obtain the solution. If any Xi are greater than or equal to zero, no boundary conditions are needed at x = L, and the interior solution , is unaffected by conditions beyond this bcundary. l A choked condition exists when no information can propagate into the solution region from the exterior. l Such a condition exists at the boundary point, x = L, when j 1 1 3 g 0 for all j i n. (139) These are the mathematical conditions satisfied by the equations of motion for a flowing fluid when reduction in downstream pressure ceases to result in increased flow rate. It is well known36 that the choked l condition for single-phase flow occurs when the fluid velocity just equals the local sound speed. For this I case, one of the Kj's is just equal to zero. For the two-phase case, it is possible for all Aj 's to be greater than zero under special conditions which can exist during discharge of a subcooled liquid. ! ( During the course of RELAP5 development, extensive investigation was carried out for two-phase l choked flow criterion under two assumed conditions:a (a) thermal equilibrium between phase. and l (b) adiabatic phases without phase change (frozen).37 l l
- a. The RELAPS/ MODI hydrodynamic modelis not based on either of these assumptions; however. the purpose of this analysis is sunply to establish a criterton for a chocked now and thus, there is no conflict with the basic hydrodynamic model.
A l l
,.P The fr ren' assumption was in poor agreement with data, c:mpared to the thermal equilibrium assump--
! tion. Therefore, the thermal equilibrium assumption is used as the basis for the RELAP5 choked flow criterion. In the following subsections, theoretical aspects of choked flow are discussed.
p
' u'
, -4 -
12 r.f cheway cWenden ser mennemosamous seedserAum nw. mass sow- The two-fluid model for the con- -
~ditions of thermal equilibrium (equilibrium interphase mass transfer) is described by the overall mass con- ,
q tinuity equation, two phasic momentum equations, and the mixture energy equation.' This system of equations are a(agg o ;+ mfpf)/atL+ a(aggg o v + mfpfv f)/ax =_0 . (140) . ao[av/st~+v(av/ax)]f+a(aP/ax) p gg g g g g
+ Cagfa o[av g
/at + vf (avg /ax) - avf /at .vg(avf/ax)] = 0_ . (141) a p [avf /at + v f(av f/ax)].+ a (aP/ax)
, ff f
'+Cafap[avp/at+v(av/ax)-_-av/at-v(av/ax)]='0 g g f g f (142)-
a(agog n s + af afsf)/_at + a(agggg o s v :+ af afsv f f)/ax = 0.- (143) . The momentum equations include the interphase force terms due to relative acceleration.38 These force L terms have a significant effect on wave propagation velocity and consequently on the choked flow velocity.- Thc particular form chosen is frame invariant and symmetrical, and the coefficient of virtual mass, Cagarp, is chosen to ensure a smooth transition between pure vapor and pure liquid. For a dispersed flow, the constant, C, has a theoretical value of 0.5, whereas for a separated flow, the value may approach zero. The energy equation is written in terms of mixture entropy, which is constant for adiabatic flow (the energy dissipation associated with interphase mass transfer and relative phase acceleration is' neglected). The nondifferential source terms, C(U), in Equation (137) do not enter into the characteristic analysis or.:. affect the propagation velocities. For this reason, the source terms associated with wall friction, interphase drag, and heat transfer are omitted for brevity in Equations (140) through (143). In the thermal equilibrium case, pg, pf, s ,gand sf are known functions of the pressure only (the vapor
- and liquid values Elong the saturation curve). The derivatives of these variables are designated by an asterisk as follows .
3 dP, o = do 5g/dP
-of.= anf /
(144) g
- s
- s (145) s f = dsf/dP, sg = ds g/dP.
The system of governing equations [ Equations (140) through (143)] can be written in terms of the four dependent variables, ag_, P, v and vf, by application of the chain rule and the property derivatives [Equa-tions (144) and (145)]. Thus,g,he t system of equations can be written in the form of Equation (137) where the A and B are fourth-order square coefficient matrices. 49 j
The characteristic polynomial that results is fourth-order in A and factorization can only be carried out approximately to obtain the roots for X, and establish the choking criterion. The first two roots are
- 1/2 f{afo g
+ oC/2 (oC/2)2 - agafogof fv g \
ag of + oC/2 + (oC/2)2 , ,q,f,q,f 1/2}y )
+
f 1,2 * . (146) (a of g + oC/2) + (ag of + oC/2) These two roots are obtained by neglecting the fourth-order factors relative to the second-order factors in (A - vg) and (A - vr). There are no first- or third order factors. Inspection of Equation (146) shows that the Al,2 h ave values between v gand vt, thus the fourth-order factorss (X - v )g and (X - vy), are small (neglecting these terms is justified). The values for A1 ,2 may be real or complex depending on the sign of the quantity
\(pC/2)2 - agarp gpg}.
The remaining two roots are obtained by dividing out the quadratic factor containing X 1,2, neglecting the remainder, and subsequent factorization of the remaining quadratic terms. [This procedure can be shown to be analogous to neglecting the second- and higher-order terms in the relative velocity, (v g - vr).] The remaining roots are 1 3,4 = v + D(v g
-v)f a (14D where v = (aggg o v + afff o v )/o (148)
- 1/2 2
a=a HE _ Co 2 + p(ag of + afog ) /(Co ,g,f) (349) and 2* 2*- ( ag of - afq o) oa 'f("f f# - "o#a) 2 "("g'aS o + "f# fsf ) 8' "f g * "g f
# 8 2 - %E og of(s -s) p(oof+Co) g g f (150)
The quantity, aHE, is the homogeneous equilibrium speed of sound. The roots, X3 ,4, have only real values. The general nature and significance of these roots is revealed by applying the characteristic considera-tions. The speeds propagated by small disturbances are related to the values of the characteristic roots. In general, the velocity of propagation corresponds to the real part of a root and the growth or attenuation is associated with the complex part of the root. The choked flow condition concerns the velocity while a disturbance propagates from a boundary, thus, the criterion for choking is established from examination j of the real part of a characteristic root. Choking will occur when the signal, which propagates with the j largest velocity relative to the fluid, is just stationary l l 50 )
A = 0 for j < 4 (151) r and V A > 0 for all i / j. (152) The existance of complex roots for Al 2 makes the initial boundary value problem ill-posed. This prob-lem has been discussed by many invest ators5,39 and the addition of any small, second-order viscous effect renders the problem well posed. 40 The whole phenomenon of systems with mixed orders of derivatives and a first order system with the addition of a small, second-order term, has been discussed and analyzed by Whitham.35 He has shown that the second-order viscous terms give infinite characteristic velocities. However, very little information is propagatec' along these characteristic lines and the bulk of the information is propagated along characteristic lines defined by the first-order system. We conclude that the ill posed nature of Fquations (140) through (143) can be removed by the addition of small, second-order viscous term that have little effect upon the propagation of information. Therefore, the choking criterion for the two-phase flow system analyzed here is established frcm Equation (151). The explicit character of the choking criterion for the two-phase flow model defined by Equations (140) through (143) is examined. Since the two roots, Al ,2, are between the phase velocities, vr and vg , the chok-ing criterion is established from the roots, X3 ,4, and Equation (151). The choking c'iterion is y + D(v -v)=1a. (153) g f The choking criterion can be rewritten in terms of the mass mean and relative Mach numbers m M = v/a, M = (v - v )/a (154) iv) v r g f as My + DM r = 1. (155) This relation is similar to the choking criterion for single-phase flow where only the mass average Mach number appears and choking corresponds to a Mach number of unity. The choking criterion [ Equation (155)] is a function of the two parameters, D and a. In Figure 15, a is plotted as a function of the void fraction, ag, for a typical steam / water system at 7.5 MPa with C equal to zero (the stratified equilibrium sound speed), C equal to 0.5 (the typical value for a dispersed flow model), and in the limiting case when C becomes infinite (homogeneous equilibrium sound speed). From Figure 15 it is evident that the virtual mass coefficient has a significant effect upon the choked flow dynamics in two-phase flows.6 F To establish the actual choked flow rate for two-phase flow with slip, the relative velocity term in Equa-tion (155) must also be considered. The relative Mach number coefficient, D, is shown plotted in Figure 16 for values of C equal to 0,0.5 and m. It is evident from these results that the choked flow velocity can dif-fer appreciably from the mass mean velocity when slip occurs. It is significant that the variation of the choked flow criterion from the homogeneous result is entirely due to velocity nonequilibrium, since these results have been obtained under the assumption of thermal equilibrium. The particular values of these parameters used in the RELAPS/ MODI model are further discussed in Section 3.1.6. t n\ V 51 1
I 9 I l ' i
. . e 4
t t . 1
.......................................................................................p...................
i 2 ' 1
. t I i ! l !
l se ! i 4
.....e.j...........
EI. . ... esmummo
- c . o.s (wQ . . . . - . . . .
....4...'...... . . . . . . . . . .
- C = INFINITY .
- e. .
- q. .................;......-..............,......................,.................. , .
E ... ! 2 ! j , *.. e i
- e. .
...............y........................!..........
.....j..........F.....*-
i . 'i /,
--. . . -- z....."
---- ~ i
- i 1 I i e.o e.s o .4 o.s o.s 3. o MPOR FRACTION Figure 15. Equilibrium speed of sound as a function of void fraction and virtual mass coefficient. ;
2.2.1.2 subcooled choking cd: Mon-The previous analysis assumes two. phase conditions exist throughout the break flow process. However, initially and in the early phase of blowdown, the fbw approaching the i break or break nozzle will be subcooled liquid. Under most conditions of interest in LWR systems, the fluid undergoes a phase change at the break. The transition from single- to two-phase flow is accompanied by discontinuous change in the fluid bulk modulus. This is especially true for the liquid-to. liquid / vapor transition. For example, at 600 KPa, the ratio of the single- to two-phase sound speed at the liquid Inund-ary is 339.4. Thus, considerable care must be exercised when analyzing a flow having transitions to o.: from a pure phase (a discontinuity is also present at the vapor boundary, but the ratio is only 1.069). l To understand the physical process that occurs for subcooled upstream conditions, consider the flow through a converging / diverging nozzle connected to an upstream plenum with subcooled water at a high pressure. For a downstream pressure only slightly lower than the upstream pressure, subcooled liquid flow may exist throughout the nozzle. Under these conditions the flow can be analyzed using Bernoulli's equa-tion which predicts a minimum pressure, Pt, at :he throat.a As the downstream pressure is lowered further, a point is reached where the throat pressure equals the local saturation pressure, Ps at. If the downstream pressure is lowered further, vaporization will take place at the throat.b When this happens, the fluid sound speed lowers drastically, but continuity considerations dictate that the veloc;ty, vt, of the two-phase mix-ture (at the point of miniscule void fraction) just equals the velocity of the subcooled water slightly l l a. For all practical cases of choking, the subcooled water can be considered incompressible with infinite sound speed. I
- b. An idealized one-dimensional homogeneous equilibrium model is assumed in the example, j I
l 52
I w . i
;' -o i _
1-
- l t
. i nv j
, y! .. - . - )
n :
. . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . . , , . , . . . . y.
x lg. i .i
. y,,~,-
i ,i 8 ; ,,,*'j i
- g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..........f.,.......9..... ...........j.........................
E
- s
- s
,/. e z
E i
$ T". . . . . . . . . .
... . . (.p.'.'. . . . . . .. . . j . . . . .. . . . .', .. . . .. .. ! . .. . ... .. . . .. ./. .
i
/',,- : '<i !
~~
. " ' i., - -C=0
! 1 p/ ~ ,,
-- C = 0 . 5
- C = INFINITY
.. g !
.T . l . ,
0.0 0.3 0.4 0.8 0.8 1.0 MPOR FRACTION O-Figure 16. Coefficient of relative Mach number for thermal equilibrium flow as a function of void fraction and virtual mass coefficient. upstream of the throat. When this occurs, vt ni the subcooled region is less than the water sound speed, but in the two-phase region, vt can be greater than the two-phase sound speed. Hence, the subcooled water has a Mach number (M) less than one, whereas the two-phase mixture at the throat has a Mach number greater than one. Under these conditions (Mach numbers greater than one in the two-phase region),. downstream pressure effects are not propagated upstream and the flow is choked. In particular, the supersonic two-phase fluid at the throat must increase in velocity and the pressure drop as it expands in the diverging sec-I tion b(transition back to subsonic flow can occur in the nozzle as a result of a shock wave). The choked condition is shown in Figure 17(a). Contrary to the usual single-phase choked flow in a converging / diverging nozzle, there is no point in the flow field where M = 1. This is because the fluid undergoes a discontinuous change in sound speed from single-phase subcooled conditions to two-phase conditions, although the fluid properties are continuous through the transition point. Whe this condition prevails, the flow rate can be established from application of Bernoulli's equation (1/2 p = Pup - Psat). For further decrease in the downstream pressure, no further increase in upstream fluid ve ocity will occur as long as the upstream conditions are maintained constant. Now consider the process where a subcooled choked flow, as described above, initially exists (with a very low downstream pressure) and the upstream pressure is lowered. As the upstream pressure decreases, the pressure at the throat will remain at Psat and Bernoulli's equation will give a smaller subcooled water , s. In a supersonic now. a diversms nozzle implies an increase in velocity. 53
-_.-______mm_____ _ _ _ _ _ _ , _ _ _ _ _ _ _ _
(a) (b) (c)
- J ---em- + ,
g E 4 P up(a) 3 76 s li 2 e p up(b) M 5 I P up(c) P sat M<1 M>1 M>1 M<1 M=1 M>1 M<1 M=1 M>1 vt = up(a) Psat) vt = " Pup (b) Psat = aHE V t = aHE > Pup (c) Psat 2 2- - 2-P P P INEL.A.16 790 I Figure 17. Subcooled choking process. . velocity (vt) at the throat. As P u is lowered further, a point is reached where vt = aHE and M = 1 on the two-phase side of the throat (tSe Mach number in the subcooled portion upstream of the throat is much less than one). This situation is shown schematically in Figure 17(b). As the upstream pressure is lowered further, the point where the pressure reaches Psat must move upstream of the throat [see Figure 17(c)]. The subcooled water velocity at the Psatl ocation is smaller than the two-phase sound speed and the flow is subsonic. In the two-phase region between the point at which P sat is reached and the throat, the Mach number is less than 1, but increases to M = 1 at tne throat, that is the two-phase sonic velocity is reached at the throat, (as in the case of choked flow having a continuous , variation of sound speed with pressure). As P up is lowered still further, the Psat point moves upstream I until the flow becomes completely two-phase The homogeneous assumption applied in the above subcooled choking description is very close to the real situation when vapor is first formed. However, nonequilibrium can result in a superheated liquid state at a throat pressure, Pt , much lower than the saturation pressure Psat. The onset of vaporization occurs at Pt instead of Psat-The pressure undershoot, Psat - Pt, can be described by Alamgir Lienhard-Jones correlation 41,42,43 P -P = max (d, 0) (156) I f with j k 9 = 0.258 e3/2 T R - 1 + 13.25 / (kBcT ) ! (I - V f/Vg) l l 54 l L__-.------- _ _ _ _ )
- 0.07 (A t/A) (i m
'V c 2). -
The first term in AP represents the static depressurization effect and is derived by Alamgir and Lienhard42 based on classical nucleation theory. For a steady flow in a nozzle, the depressurization rate, E', can be shown to be 1 3 \ {= ovg /A (dA/dx)t. (158) Note that in Equation (157) E' is in units of Matm/s; but in Equation (158), E ' is in units of Pa/s. Here, (dA/dx)t si the variation of area with respect to axial length and is to be evaluated at the throat. The second term in AP [ Equation (157)] represents the turbulence effect and is developed by Jones.43 The choking velocity, based upon the process shown in Figure 17(a), can be calculated by applying Bernoulli's equation v = v + 2 (P - Pt)##
! II59) where Pg is to be computed from Equation (156).
For the process shown in Figure 17(b) and 17(c) (160) vc =aE H and the RELAP5 two-phase choking criterion applies. To determine which of the above situations exists, both v e's are calculated and the larger is used as the choking velocity to be imposed at the throat. This velocity is imposed numerically at the throat in exactly the same manner as the choking criterion used for the two-phase condition described previously. The RELAPS/ MOD 1 subcooled choking model is very similar to models proposed by Burnell 44 and Moody;45 however, the criterion for transition from subcooled choking to two-phase choking is now better understood and in agreement with the physics of two-phase flow. The model here is also in agree-ment with cavitating venturi experience (expenmentally confirmed behavior). 2.2.f.2 Nordrenset sevenw choaear sow-Under stratified conditions, the void fraction of flow out of a small break may be quite different from the upstream void fraction. The usual definition of the outlet void fraction as a donored void fraction is no longer applicable. A simple approach based on the height of liquid level and a criterion for the stability of small disturbances to determine the junction void fraction for stratified break flow is described'below. By balancing the upward pressure force due to the Bernoulli effect and the downward gravitational force acting on a small surface perturbation. Taitel and Dukler 46 developed the following criterion for transition from the stratified horizontal flow regime in a round pipe
~
2 ( of - pa) b yA / H v g og dA f/aH f d ~ T{/. (161) q) - -
$5
l t
?
Where Agand A are t the flow areas of vapor and liquid, respectively; the right nide of Equation (161)is the limiting vapor velocity designated by vgt; and e is the central angle formed by a vertical cord and a radius to the liquid vapor interface. The following geometry relations apply as ; Hg = 0 (1 - cose)/2 (162) and Hf = D (1 + cose)/2. (163) We can show that d Ar/d Hfequals D sin 0 and v8L ecomes b
-( of - on ) Byga A 1/2 i v
gL = 1/2 o Osine (1 - cose). (164)
- 9 .
Let D tbe the diameter of the break area. When the liquid level is above the break [that is. Hr > (D + D )/2],t the outlet void fraction, ag,j, which accounts for the pull-through of vapor, is defined ; as a g,3
=a g,k(V g V gL)
(165) where a ,k and v are the void fraction and vapor velocity upstream of the outlet. If the liquid level falls below the break fthat is Hr < (D - D )/2], t liquid entrainment is modeled by defining the outlet liquid fraction, ar,j, as af,) = "f,k(V /VgL) g (166) i where obtain a af,k s the liquid volume fraction upstream of the outlet. The equality, a ,ble out et area
~
(D + Dt fl'j 2 >(or,j), Hr > (Dif ar,3
- Dt (a ],, the
) isvoid known.
fractionWhen theby is obtained liquid level lies interpolation of thewithin two void fractions computed at the boundaries. 2.2.2 Abrupt Area Change. The general reactor system contains piping networks with many sudden 1 area changes and orifices. To apply the RELAP5 hydrodynamic model to such systems, analytical models I for these components have been developed.47 The basic hydrodynamic model is formulated for slowly l varying (continuous) flow area variations; therefore, special models are not required for this case. The abrupt area change model discussed here and developed in detail in Reference 47, is based on the Bourda-Carnot48 formulation for a sudden enlargement and standard pipe flow relations, including vena-contracta effect, for a sudden contraction er an orifice or both. Quasi-steady continuity and momentum balances are employed at points of abrupt area change. The numericalimplementation of these balances is such that hydrodynamic losses are independent of upstream and downstream nodaliration. In effect, the quasi-steady balances are employed as jump conditions that couple fluid components having abrupt change in cross-sectional area. This coupling process is achieved without change to the basic linear semi-implicit numerical time-advancement scheme. 222r Aarupt Arw ch.nce Mod ung Assumpt/ons-The basic assumption used for transient calculation of two-phase flow in flow passages with points of abrupt area change is: the transient flow process can be 36
approximated as a quasi-steady flow process that is instantaneously satisfied by the upstream and downstream conditions (that is, transient inertia, mass, and energy storage at abrupt area change are neglected). However, upstream and downstream flows are treated as fully transient flows. c
) There are several bases for the above assumption. A primary consideration is that available loss correla-tions are based on data taken during steady flow processes; however, transient investigations49 have verified the adequacy of the quasi-steady assumption. The volume of fluid and associated mass, energy, and inertia at j .ints of abrupt area change is generally small compared with the volume of upstream and downstream fluid components. The transient mass, energy, and inertia effects are approximated by lump-ing them into upstream and downstream flow volumes. Finally, the quasi-steady approach is consistent with modeling of other important p' - a in transient codes (that is, heat transfer, pumps, and valves).
212.2 Review of 3/nple Phase Abrupt Aree Change Modeh-The modeling techniques used for dynamic pressure losses associated with abrupt area change in a single-phase flow are reviewed briefly before discussing the extension of these methods to two-phase flows. In a steady incompressible flow, losses at area change are modeled by the inclusion of an appropriate dynamic head loss term, th , in the one-dimensional modified Berneulli equation 2 (v2 /2 + P/p)) = (v /2 + P/p)2 + hl . (167) The particular form of the dynamic head loss is obtained by employing the Bourda-Carnot48 assumption for calculating loss associated with the expansion part of the flow process. Losses associated with the con-tracting part of the flow process are small relative to the expansion losses, and are n,eglected. The most general case of abrupt area change is a contraction with an orifice at the point of contraction. Such a configuration is shown in Figure 18. Three area ratios are used throughout this development. The first is the contraction area ratio at vena-contracta relative to the minimum physical area, ec = Ae/AT - m The second is the ratio of the minimum physical area to the upstream flow area, eT = T A /A 1 . The third is I ) the ratio of the downstream to up-tream flow area, e = A2 /Ag.
> v' The loss associated with the contracting fluid stream from Station 1 to c (the point of vena-contracta) is neglected (measurements indicate that the contracting flow experiences a loss no larger than Mr - 0.05 (1/2 pv 2) e where v isc the velocity at the vena-contracta) whereas the dynamic pressure loss associated with the expansion from the vena-contracta to the downstream section is given by aP f = 1/2 p(1 - A c/A2)2 c. V 068) n A1 AT I
j s[Af Ae 2 17 MN h 2 e o 1 Y INEL A.16 806
/ i 5M Figure 18. Orifice at abrupt area change.
57
The contraction ratio, e c = Ac/A ,Tis an empirical function of eT = A /Ag. T Using the continuity equa-A tions, vc = . T T " VT/'c, and vT "
^"
= k V2, Equation (168) can be written as APf = 1/2 o 1- g v
2 (169) Equation (169) is applicable to all the cases of interest. For a pure expansion, eT = 1. *c " 1, and e > 1; for a contraction, ey = e < 1 and ee < l. Each of these is a special case of Equation (169). The two-phase dynamic pressure loss model is based on an adaptation of the general single-phase head loss given by Equation (169). 2223 Two-phese Abn,pt Ar chenge model-The two-phase flow through abrupt area change is modeled in a manner very similar to that for single-phase flow by defining phasic flow areas. The two phases are coupled through the interphase drag, a common pressure gradient, and the requirement that the phases coexist in the flow passage. The one-dimensional phasic stream-tube momentum equations are given in Section 2. The flow at points of abrupt area change is assumed quasi-steady and incompressible, in addition, the terms in the momen-tum equations due to body force, wall friction, and mass transfer are assumed smallin the region affected by area change. The interphase drag terms are retained since the gradient in relative velocity can be large at points of abrupt area changes.
- i Equations (4) and (5) can be integrated approximately for a steady incompressible, smoothly varying flow to obtain modified Bernoulli-type equations l
2 /FI' (1/2 ofvf+P
=
1 1/2 ofv f2+P 2
+l
( ,f (v7 ) - v g)) L)
)
+ (l70)
(vf2 ~ #g2) L 2 and Iq 1
+P +
(vg ) -v f3) L) l (1/2ov gg =(1/2ov gg2+P
+
FI' (vg2 ~ #f2) L2* (I7l) where FI' = at og pr pg Fl. The interphase drag is divided into two parts associated with the upstream and downstream parts of the flow affected by the area change. 2.2217 Genere/ Model-Consider the application of Equations (170) and (171) to the flow of a two- 9, phase fluid through a passage having a generalized abrupt area change (the flow passage shown in 58
Figure 19a). Here, the area A T si the throat or minimum area associated with an orifice located at the point of abrupt area change. Since each phase is governed by a modified Bernoulli-type equation, it is reasonable to assume that losses associated with changes in the phasic flow area can be modeled by H) separate dynamic pressure loss terms for each of the liquid and gas phases. Hence, we assume that the liquid sustains a loss as if it alone (except for interphase drag) were experiencing an area enange from at , Ag to aft A T to ar2 A 2, and the gas phase experiences a loss as if it alone were flowing through an area change from agl A l to agTAT to a g2 A 2. The area changes for each phase are the phasic area changes (see Figure 19). When the losses for these respective area changes (based en the Bourda-Carnot model and given by Equation (169)] are added to Equations (170) and (171), the following phasic momentum equations are obtained h Liquid phase a 93A 3 "fTAT t af2A 2 aTg AT 0 - N -- "_ a Gas phase 91 A$ a2g A2 l 2 c o . 1 T A INEL A 16 795 Figure 19. Schematic flow of two-phase mixture at abrupt area change. 2 2 v (1/2 ofvf2+P)1 =(1/2off2+P)2 + 1/2 ,fT fc ofT[(1(vf2)
/FI' (vf2~Vg2) '2 (172)
+ (FI'T (v ) - v )) L) +
f g and 2
= 1/2 o99 v 2+P +1/2o!1- 2* \ (V 9) fl/2 o99v 2+P) 2 9{ gT'ge*T) 2
+
(vg ) - v f)) L) + (vg2 ~ Vf2) '2' (I73) V a. In Figure 19, the flow is shown as a separated flow for clarity. The models developed are equally applicable to separa ed and dispersed flow regimes. 59 1
These phasic momentum equations are used ac'oss r an abrupt area change. In Equations (172) and (173),
'fcande aree the same tabular function of area ratio as in the single. phase case except the area ratios used ;
are the asic area ratios cfT " ("fT/ f1) *T (I74) and cg i
- I*gT /*O ) "T (I75) respectively. The area ratios, e = A2 /Ag and eT = A T /A , are 3 the same as for single-phase flow.
The interphase drag effects in Equations (172) and (173) are important. These terms govern the amount of slip induced by an abrupt area change, and if they are omitted, the model will always predict a slip at the area change appropriate to a completely separated flow situation and give erroneous results for a dispersed flow. 22222 Mode / App #cedon- A few remarks concerning tue way Equations (172) and (173) are applied to expansions and contractions, both with and without an orifice, are necessary. In a single-phase steady flow situation, given the upstream conditions, vi and Pg, using of the continuity equation (v1A 1 = v2A2), and Equation (167) one can solve for v2 and P2. Equations (172) and (173) along with the two phasic conti-nuity equations can be used in a similar manner except now the downstream void fraction is an additional unknown which must be determined. 22212.7 Expension-For the purpose of explanation, consider the case of an expansion (aft = art, e > 0, eT " 1. Efc = 'ge = 1, FI'i = 0, L1 = 0) for which Equations (172) and (173) . reduce to 2
= + f2 (1/2 ofvf2+P)1 .
(1/2ofvf2+P)21/2 of 1- fl (vf2) }
/FI'\
+
(vf2~Vg2) '2 (176) 2 and 2
+P (1/2 oggv 2+P + 1/2 o g 1,
=
(1/2 oggv (vg2) (v ~V f2) L2* (I77)
+ (FI'
,9 2 2
These two equations with the incompressible continuity equations i sfj vf)A) = af2 Vf2A2 (178) 60
r -l
'i and l N V A "g1 g1 ).= ag2 g2^2 V (II9) . (V )
J are a system of four equations having four unknowns, af2 (ag2 = 1 - af2). Vf2, Vg2, and P2, in terms of the upstream conditions, afi (agg = 1 - af}), vrt, v gg and P .l (The interphase drag, FI', is a known function of the flow properties.) It is important to note that the downstream value of the liquid fraction i (af2) is an additional unknown compared with the single-phase case and is determined (with the downstream velocities and pressure) by simultaneous solutien of Equations (176), (177), (178), and (179) without additional assumptions. It is reassuring that by taking a proper linear combination of 48 Equations (176) and (177) the usual overall momentum balance obtained using the Bourda-Carnot assumption can be obtained.50,51,52,53 If, as in the cited literature,50,51,52,53 only the overall momentum balance is used at an expansion, there will be an insufficient number of equations to determine all the downstream flow parameters, ar2, vf2 V 2, g and P .2The indeterminacy has been overcome in the cited works by means of several different assumptions concerning the downstream void fraction.a In the model developed here [ Equations (176) and (177)], division of overall loss into liquid and gas, parts respectively, results in sufficient conditions to~ determine all downstream flow variables including af2. In addition, the present model includes force terms . due to interphase drag in Equations (176) and (177), which are necessary to predict the proper amount of . slip and void redistribution that occurs at points of area change. . i 22.2122 coneoccion-Consider the application of Equations (176) and (177) to a contraction. To determine both the downstream conditions and throat conditions from the upstream values of ag1(agl)' vf;, v gl, and P , ian additional consideration needs to be made. To obtain the throat values, apply the momentum equations valid for the contracting section of flow (here, the Lg portion of the interphase force is associated with the contraction) v
/ +
FI'i (1/2 of f2+P)\ =(1/2ofvf2+P)\ v I (v ) - v g)) L) f (180) 1 T ,f /)
= 1/2 ogg v 2+P +
(vg ) - v f)) L) (181) (1/2ov gg 2+P , (182) afj vf)A) = aft VfTAT (183) og)vg)A) = a gT VgTAT. These four equations are solved simultaneously for the values of aft (agT) VfT* V g T, PT at the throat section (minimum physical area). No additional or special assumptions are made concerning the throat conditions since they follow as a direct consequence of the unique head loss models for each phase. After the throat values have been obtained, the conditions at the point of vena-contracta are established assum-ing the void fraction is the same as at the throat. Thus, ere and ege are established using the tabular func-tion in Appendix A of Reference 47 and the throat area ratios, eft and egT, defined by Equations (174) I ? i
- a. J. G. Collier50 mentions three different assumptions that have been used:(i)ag = agi (ii) og s given by a homogeneous model.
and (iii) og is given by the Hughmark void fraction correlation. 61
. _ _ _ __-_-_a
and (175). To determine the downstream values, Equations (172) and (173) can be applied directly from Stations 1 to 2 with the throat values known or the expansion loss equations can be used from the throat section to Station 2. Both approaches produce identical downstream solutions. As in the case of an expan-sion, because the proper upstream and downstream interphase drag is included, this modeling approach establishes the phase slip and resulting void redistribution. An orifice at an abrupt area change is treated j exactly as the contraction explained above (that is, with two separate calculations to establish first the j throat and then the downstream flow variabics). 122121 conneweenwrnew-The preceding development implicitly assumed a coeurrent fiow. For I countercurrent flow, Equations (172) and (173) are applied exactly as in coeurrent flow except the upstream sections for the respective phases are located on different sides of the abrupt area change. The i difference appears in how the throat and downstream voids are determined. To determine the throat prop-erties, equations similar to Equations (180), (181), (182), and (183) are used with the upstream values appropriate for each phase. These four equations are then solved for ag(agT). VfT. gV T, and P T . To determine the downstream values for each phase, only the head loss terms are needed for the downstream l voids (the downstream vt, v a, and P do not appear). For countercurrent flow, these voids are set so the 1 downstream void of each pflase plus the upstream void of the opposite phase add to one (both phases together must fill the flow channel). With the throat and downstream voids now known, Equations (172) and (173) can be used directly to determine the total loss for each phase at the abrupt area change. 2.3 System Component Models 2.3.1 RELAP5 Pump Model. The RELAPS/ MODI pump modelis a straightforward conversion of the ' RELAP4 centrifugal pump model.16 The pump model was completely reprogrammed and converted to the International System of Units (SI), but no change was made to the physical model. The pump head, torque, and rotational speed calculations are identical to RELAP4. The pump is volume-oriented and the head developed by the pump is apportioned equally to the suction and discharge junctions connecting the pump volume to the system. The pump is interfaced to the unequal velocity hydrodynamic model of RELAP5 assuming the head developed by the pump is similar to the body force term in the total momentum equation, but does not affect the difference of momentum equation. Thus, the pump head is partitioned equally between the two junctions adjoining the pump volume. The pump dissipation term for the thermal energy equation used in RELAPS is computed from the total l pump power (given by torque times rotational speed) minus the rate of mechanical energy addition to the fluid. . l 117.1 CanmWpelPump Performance Modet-The pump characteristic curves are empirically developed by pump manufacturers and uniquely define head and torque response of a pump as functions of volumetric flow and pump speed. A typical set of four-quadrant curves is given in Figure 20. The four-quadrant curves can be converted to simpler form by development of homologous curves where head and torque l ratios (actual value to rated value) are input as functions of purnp speed and volumetric flow ratios.54The l developed homologous curves are for single-phase conditions. Typical homologous curves are shown in l Figum L for the head and Figure 22 for torque. i { The pump model allows the user the option of accounting for cavitation or two-phase degradation effects on pump response. The user must supply a separate set of homologous, two-phase curves for head and torque which are in the form of difference curves. Difference curves are used because analysis of l available two-phase pump data, indicated that when the fluid being pumped had a void fraction between O.2 and 0.9, little head was developed by the pump being tested. Outside this range of void fraction, the pump-developed head varied from zero to undegraded single-phase performance. The limited available l 62 ' 1
Pump speed j (rpm)
. bpm
\
100'(o /
-s s
[ s ,
\ N' j
/ \ I
^
'I*
5% [, f
\ 75 %
.I l
% -- M y '
100 %
\ ,/
I l l 26'/.
\A \ 25 % -
/ /
/
/ 4 l / , 25% p ,
/ /
l D 50'/ l f g # d0% 5 f I5% 75'$
) / 100 % / /
/ / / // 100 % . Volumetric j f / p flow
- gpm 100%
j'
- l fl ,
/ 100 % ,
[ ,'/ (gpm) f? I Il\ \ / /
/
/ / /
/ s=0/
j l , j ol 7 r y , ) / / b ( ll ,
!/
I J j / jj/ ,/ Constant head, H j j 7 j / s constant torque, Thy j I l I //
/ /
/ /
/
/ //
t
/ ;
I 100 %
/ k! !
/
/
/ / / / 1ij
/ / // % l
/ / // /\
/# [ INEL A 16 805 rpm I
Figure 20. Pump characteristic four-quadrant curves. I 63
O h/a 2 or h/v 2 hl h/v2 U
- 1.0 yj, q
alv h/a2 : via h/v 2 alv 1.0 v/a or alv 1.0 t / 1 . 4 i 1 a = w/w R(speed ratio) h = H/HR(head ratio) V = Q/Qg(flow ratio) 1.0 l INEL.A-16 784 Figure 21. Pump homologous head curves. e)
- 1
-__ .- --- - _ - - 1
Sla 2 or @lv2 p/v2 - -1.0 1 alv S/a 2 y v/a j pfy2 01, 2 U U a/v v/a 1.0 v/a or alv i ' i ' 1.0 , r' i a= w/w R (speed ratio) p= Thy6 (torque R ratio) v= O/O R (flow ratio)
. 1.0 INEL.A.16 785 Figure 22. Pump homologous torque curvet <,
65
data indicate pump performance in the void fraction range 0.2 to 0.9 is significantly degraded from single-phase behavior. To consider the degraded performance, a set of dimensionless homologous curves was fit to the head data and the fully-degraded, two-phase head was expressed as a function of the standard pump model arguments. To consider the ranges of void fraction where the pump was able to develop head (0 to 0.2 and 0.9 to 1.0), a multiplier as a function of void fraction was used. The multiplier varied from 0 to about 1.0 as the void fraction varied from 0 to 0.2; and the multiplier varied frorn about 1.0 to 0 as the void fraction varied from 0.9 to 1.0. Avnilable pump data from the 1-1/2 Loop Model Semiscale and Westinghouse Canada Limited (WCL) experiments were used in developing the two-phase pump data. Assumptions inherent in the pump model for two-phase flow include:
- 1. The head multiplier, M(a), determined empirically for the normal operating region of the pump, is also valid as an interpolating factor in all other operating regions.
- 2. The relationship of the two-phase to the single-phase behavior of the Semiscale pump is applicable to large reactor pumps. This assumes an independent pump specific speed for the pump model of two-phase flow.
The single. phase pump head (dimensionless) curve for the Semiscale pump is shown in Figure 23 and the two-phase pump head curves are shown in Figure 24. These represent complete pump characteristics for the Semiscale pump operating under two-phase conditions with the average of the void fractions of the pump inlet and outlet mixtures between 0.2 and 0.9. The lines drawn through the data were determined by least square polynomial fits to the data using known constraints. h/v2or h/a 2 1.5- - HAT (1) HVD KHAN 1-- HVT (T/ 0.5- - HVN (2) 0 0!5 0.5 Normal pump ( + O. + a ) (8) a /v or v/ a HVR Energy dissipation (-O, + a )
-0.5 - -
H = H/H R head ratio (- O, - o ) H^ t Normal turbine HV V = O/OR How rati a = W/WR speed ratio Reverse pump (+Q,-a) HAR HVR INEL A.16 796 Figure 23. Single-phase homologous head curves for 1-1/2 loop MOD-1 Semiscale pumps. 66
- _ _ _ _ _ _ _ _ ._. _ 1
I i i 2 2 h/a 0r h/v f y-Qi . -5
.t L/ "
'HAD -4
-3 )
HAT 'l i
-2 -
HVD ' HVT 1 HAN 0.5 M
~
0.5 ~ alv or vla HVN 1
-2 INEL A 16 807 Figure 24. Fully degraded two-phase homologous head curves for 1 1/2 loop MOD-1 Semiscale pump.
(] V A comparison of the two-phase data of Figure 24 with the single phase data in Figure 23 shows that the two-phase dimensionless head ratio (h/v2 or h/a )2 is significantly less than the single-phase dimensionless head ratio for the normal pump operation region (HAN and HVN) For negative ratios of v/a, such as those which occur in the HAD region, the pump flow becomes negative. When the pump flow is negative, the two-phase, dimensionless head ratio is greater than the single-phase dimensionless head ratio. Two-phase flow friction losses are generally greater than single-phase losses, and friction is controlling in this energy dissipation region (HAD). The other regions of two-phase dimensionless head ratio data show similar deviations from single-phase data. Table 6 shows the difference between the single- and two-phase dimensionless head ratio data as a func-tion of v/a and a/v for the various pumping regions shown in Figures 23 and 24. The differences shown in Table 6 are for the eight curve types used for determining pump head. The head multiplier, M(a), and void fraction data shown in Table 7 were obtained in the follotving man-ner. The Semiscale and WCL pump datal6 were converted to dimensionless head ratios of h/a2 or h/v2, Values of the dimensionless head ratios were obtained for pump speeds and volumetric flow rates within 50% of the rated speed and flow rate for the pumps. The difference between the single- and two-phase dimensionless ratios was developed as a function of the average void fractions for the pump inlet and outlet mixtures. The difference between the single and two-phase dimensionless ratios was then normal-ired to a value between 0 and 1.0. The normalized result was tabulated as a function of the void fraction. If the two-phase option is selected, the pump head and torque are calculated from (184) (]~ ' H = H) - Mh (a) (H), - Hg) l 67
I Table 6. Semiscale dimensionless head ratio difference (sirigle-phase minus ' two-phase) data a X = f or lh b Ih \ [h Ib h
)3 h)g l3 )
Curve Type x y Curve Type x y 1 (HAN) 0.00 0.00- 4 (HVD) -1.00 -1.16 0.10 0.83 -0.90 -0.78 0.20 0.09 -0.80 -0.50 0.50 0.02 -0.70 -0.31 0.70 0.01 -0.60 -0.17 0.90 0.94 -0.50 -0.08 1.00 1.00 -0.35 0.00
-0.20 0.05 2 (HVN) 0.00 0.00 -0.10 0.08 0.10 -0.04 0.00 0.1:
0.20 0.00 0.30 0.1G 5 (HAT) 0.00 0.00 0.40 0.21 0.20 -0.34 i 0.80 0.67 0.40 -0.65 0.90 0.80 0.60 -0.93 j 1.00 1.00 0.80 -1.19 1.00 -1.47 3 (HAD) -1.00 -1.16
-0.90 -1.24 6 (HVT) 0.00 0.11
-0.80 -1.77 0.10 0.13
-0.70 -2.36 0.25 0.15
-0.60 -2.79 0.40 0.13
-0.50 -2.91 0.50 0.07
-0.40 -2.67 0.60 -0.04
-0.25 -1.69 0.70 -0.23
-0.10 -0.50 0.80 -0.51 0.00 0.00 0.90 -0.91 1.00 -1.47 7 (HAR) -1.00 0.00 0.00 0.00 8 (HVR) -1.00 0.00 l 0.00 0.00 l
9 l I 68
.j q
l- 1 1 L Table 7. Head multiplier and void fraction data j 7u p .. - v .. a M(a) 0.00- 0.00 0.10 0.00 0.15 0.05 0.24 0.80 0.30 0.96 0.40 0.98
. 0.60 0.97 0.80 0.90 0.90 0.80 0.96 0.50 ,
. 1.00 0.00 .
,D v .
II8#) I = I) - Mt (") (T l4 - T 2+) where le = single-phase value 26 = two-phase, fully degraded value 0.2 < a < 0.9 M = multiplier on difference curve a = average volume void fraction. The differentia pressure change across the pump is dependent on the head value and the average pump volume density (p). Thus, the pressure change is given by ; 6P = pH. (186) 2.3.r.2 cenerseweelrump ortve Modet-The pump torque is used to calculate pump speed after the pump has '. i been shut off by the input trip signal. The speed i:, calculated by the deceleration equation (187) Ih = T 69
l l b f .' l' the solution of which is l
- Tat "t+ at " "t 1 (188) {
l i where l 1 1 T = net torque J I = moment of inertia ' i t = time j at = time step w = angular velocity. ; The rate of energy addition to the pump system is given by wT. l l The total pump torque is calculated by considering the hydraulic torque from th( homologous curves and the pump frictional torque. The net torque with the drive motor shut off is T=T +T fr (I89) where Thy = hydraulic torque Trf = frictional torque. The frictional torque is in the f t,.m of a cubic equation. The value of the frictional torque is also depen-dent on the sign of the pump speed. An option is available to specify whether reverse rotation of the pump ) is allowed. 1 l The RELAP4 pump model has been modified to include the influence of the electric drive motor on the I speed behavior of the pump while the motor remains connected to its power source. The effect of the l motor is incorporated into the pump model by adding the value of motor torque, Tm, to the torque ! summation j l T=-T (190) ! hy -Tfr + Tm where the sign of the n- er torque is the same as that of the hydraulic and frictional torque for steady ' operating conditions, th. ,, zero net torque. Induction motors are used to drive primary coolant pumps. At constant voltage, the motor torque is an explicit function of speed. This torque / speed relationship is normally available from the motor ; manufacturer. Motor torque is supplied to the pump model as 4 tabular function of torque versus speed as defined by the manufacturer's data. A typical torque / speed curve for an induction motor is shown in Figure 25. 70
, . . ~ , 3.
, g, g
4 300 i i i .,_ i i .i. [ ( n _Q
'200 - -
V; ' 3 o (100 , m 3 I-
, 7 0
+
.o.
I
?- -l u, y y.100 -
8 lii n. 200 - - 300 ' ' ' ' ' 40- 60 80 100 120 140 160 180 200 Percent synoronous speed (1200 rpm) INEL A.16 781 . u Figure 25. . Torque versus speed Type 93A pump motor (rated voltage). The capability to simulate a locked rotor condition of the pump is included in the computer program. This option provides for simulation of the pump rotor lockup as a function of input elapsed time, max-: imum forward speed, or maximum reverse speed. At the time the rotor locks (and at all times thereafter), the pump speed is set equal to zero. 2.3.2 Accumulator Model. An accumulator model has been installed in RELAPS/ MODI that features : mechanistic relationships for heat transfer from the tank wall and water surface, condensation in the vapor dome, and vaporization from the water surface to the dome.- The. hydrodynamic model with heat transfer models for the accumulator are described below. The numerical scheme is discussed in a later section. 2.12.7 NyeoWaemte wom- An acct mulator is modeled in RELAP5 as a lumped-parameter component. This model was chosen over a distribt ted model for two reasons; the spatial gradients in the accumulator. are expected to be small, and special tceatment of the equation of state can be utilized. The accumulator model and associated notations are shown in Figure 26. The basic modeling assumptions are
- 1. Heat transfer from the accumulator walls and heat and mass transfer from the liquid are modeled using natural convection correlations assuming similarity between heat and mass transfer from the liquid surface.
a
- 2. The nitrogen is modeled as an ideal gas with constant-specific heat. The steam in the dome exists at a very low partial pressure and is not modeled directly. The energy released as a result of vapor condensation is transferred to the nitrogen.
71
- =_________________. _ _ _ - _ _ _ _ _ _ _
Steam and nitrogen vapor
, O !
l o o o o Vo ume VD TemperatureTo Wall heat QD- + Pressure PD o o o o o _______-______-_____- ----c JL Liquid water Volume V, Temperature Tw h U k A O\
,,r
'JL il Cross sectional area AL H
Lt , v-exhaust II line y velocity
. P system pressure INEL A 16 793 Figure 26. Typical accumulator.
72
v
- 3. . Because of the high heat capacity and large mass of water below the interface, the water is assumed to remain at its initial temperature, gy _ .
- 4. The model for liquid flow includes inertia, wall friction, form loss, and gravity effects.
.tj Using these assumptions, the basic equations governing thermal-hydraulics of the tank and discharge line can be written as
- 1. Conservation of mass (nitrogen)
= constar.t = o n (I9II n D'
- 2. Conservation of energy Nitrogen
< aV aU" M n at
=-P D-at # O. D (192)
Wall aT M Cg)) wan , , 9 (393) wall t )),
- 3. Momentum Equationa
( 2 p,Ag (L g + f'v ) py . .,(p , p D)^L +w g(h + H)A L (I94)
- 4. State Relationships (I")
PYDD=MRTnnD U =C (1%) n vn iD .- Using Equations (191) and (1%), the nitrogen energy equation [ Equation (192)], can be rewritten as aT D II9 I Mn C v at
=-P D vA g +Q*D n
Differentiating Equation (195), and solving for the pressure derivative yields [aTp aV) D l at- t 1 (198) l at 0=PD + { , a_t V/. D
- a. Equation (194) is the combined tank and discharge line momentum equation. The wall drag coefficient. F. is given as M #wf A tv where D -s surge line diameter.
73
w Equations (194), (197), and (198) comprise the system of three differential equations used in the accumulator model. They are used numerically to advance Tp, Vp, and Po in time. J.J.22 #wt Tim &-The heat transfer from the tank wall has been modeled with a lumped-parameter model 0 =A h1 (Tg) - TD)* wall wall (I") The wall convective film coefficient has been defined using a correlation for turbulent natural convection 55 as hj = (k n/L) C (GrPr)I (200) j where the Grashof number is i G r = g s aT L / v2 . (201) In addition to wall heat transfer, convective heat transfer from the accumulator liquid is assumed to be Q jjq =A h2 (T -T) D (202) where h2is defined in the same manner as hg. Liquid is also assumed to evaporate from the water surface due to the temperature difference between the water surface and the nitrogen above. The evaporation rate is assumed to be
- A vap 3, (og)0 ~ (*g) surface
= h3 A, (og )s h e Be(T, - TD) (203) j where the surface variables are at the liquid temperature and B e is the equilibrium compressibility.
The mass transfer film coefficient is determined assuming similarity between heat and mass transfer from the water surface (both are conserved properties modeled by similar equations). h (204) 3 =h2 (d/kn ) (a/d) where d is the diffusivity or water vapor in air 56 defined as P g[T D 12.3
. d = 0.239 (205)
\ 281/
where Po is the standard atmospheric pressure. O l l l 74
1 The mass transfer rate is then .ssi (V M vap = h2 (d/kn ) (a/d)1/3wAg(o ) surface e w B (T -TD ). (206) l The steam in the accumulator dome will condense as the temperature decreases and additional heat of vaporization will be transferred to the nitrogen in the dome. The condensation rate is calcu;ated assuming the steam is saturated at the temperature of the dome M
- cond " vap The heat transfer due to this condensation is s
Q cond vap h (T,) - h (TD) . (208) The net heat transfer to the nitrogen is then calculated as (2M) CD"Owall + Ocond
- Oliq .
2.3.3 Reactor Kinetics. The reactor kinetics capability can be used to compute the power behavior in a nuclear reactor. rhe power is computed using the space-independent or point kinetics approximation which assumes that power can be separated into space and time functions. This approximation is adequate 73 for cases in which the space distribution remains nearly constant. ! ) V The space independent or point reactor kinetics equations are I ! 4 ( t ). = [o(t) - g-8] e(t) + { 1 C44(t) + S (210) i=1 Bf 1 C$ (t) = 3 e(t) - 1 44 C (t) i = 1, 2, . . . , I (211) where l t = time c = reactor fission power Ci = a measure of the number of delayed neutron precursors of group i
$ = effective delayed neutron fraction A = prompt neutron generation time r~s p = reactivity of the system (only the time-dependence has been indicatedt however, the (V) reactivity is dependent on other variables) 75
I fi = fraction of the delayed neutrons of group i Ai = decay constant for group i S = source I =. number of delayed neutron groups. The equation for production and decay of fission products and actinides is i) ' E je - 1 3y) j = 1, 2, . . . , J (2'1 2) where Tj = a measure of the concentration of fission product or actinide group j Ej = yield fraction for group j as shown in Table 8 Aj = decay constant for group j J = number of fission product and actinide groups. i Table 8 lists the delayed neutron, fission product, and actinide constants. The total reactor power is the sum of fission power, fission product, and actinide decay power il P(t) = 6(t) + { 1)y). (213) j=1 Substituting , Sf g r(t) = o(t)
, g
, C4 (t) = W4 (t), y) = ,
(214) i J i the reactor kinetics equations become l l l l I l
+ S.
+(t)=f [r(t) - 1] 6(t) + i=1 {fW $4 (t) (215) i i = 1, 2, . . ., I. (216)
W4 (t) = x$e(t) - A $4 W (t) l O; j = 1, 2, . . ., J. (217) Z3 (t) = 13e(t) - 13j Z (t) 76
r 5 i 9 sc d' Table 8. Reactor kinetics constants ; i I DELAYED NEUTRON C0NSTANTS , f A Group i i ( s-I ') 1 0.038 0.0127. 2 0.213. 0.0317
..4 3 0.188' O.115 4 0.407 0.311 5 0.128 1.40 6 0.026 3.87 RADI0 ACTIVE DEC'AY-CONSTANTS Group j j (s-I) 1 0.00299 1.772 x 10 I 2
0.00825 3 0.01550 5.774 x 10-.2 0.01935 6.743 6.214 xx 10- 10 3-'
% 4-0.01165 4.739 x 10-4 -Ij 5 4.810 x 10 0.00645 6
7 0.00231 5.344 x 10-6 8 0.00164 5.726 x 10 9 0.00085 1.036 x 10-7 10 0.00043 2.959 x 10-8 11 0.00057 7.585 x 10-10 ACTINIDE DECAY CONSTANTS E 1 Group 3 3 (3-1) 1 0.00226 4.91-x 10-4 2 0.00219 3.111 x 10-6 a, Yield fraction for group i.
- i I
77 w _- .-_ - _ _ _ _ _ _ _ _ _ _ _ _ N. _ _ _ - _ _ _ - _ _ _ _ - - _ _ _ - _ _ _ _ _ _ _ _ _ _ - _ _ _
i Initial conditions are derived by assuming steady state operation. This implies that the reactor has been operating an infinite amount of time. That is a reasonable approximation for the delayed neutron calcula-tion, but for many problems, it is not satisfactory for the fission product groups. A later version of : RELAP5 will compute fission product initial conditions from a user-supplied reac;or power history. Set-ting time derivatives to zero and assuming total reactor power and reactivity are input quantities, the initial conditions are P 4(0) = (218) 1 + -[ E j s=, Wi (0) = o(0) i = 1,2,...,I Zj(0) = c(0) j = 1,2, . . . , J B S= y r(0) $(0). (219) Reactivity is computed from
. n- n
- 5
- r(t) = r o +r g + { r,4(t) + { w $,R, -oi ( t )~ +a$ g Ty ,(t)
,j(g)-
i i -
"F
+ WpRp Ty (t) + ap$ T pg(t)f. (220) i The quantity, r o, is an input quantity and the reactivity corresponding to assumed steady state reactor l power at time equal zero. The quantity, rB, is calculated during input processing such that r(0) = ro .
The quantities, rsi, are obtained from input tables defining ns reactivity curves as a function of time. Rp is a table defining reactivity as a function of the ratio of the current density of water gj(t), in hydrodynamic volume, i, to the density in the volume at time zero; W p is the density weighting factor for volume, i; Twi l is the equilibrium temperature of volume, i; aw is the temperature coefficient (not including density ; changes) for volume, i. ngis the number of hydrodynamic volumes in the reactor core. Rp is a table defin-ing reactivity as a function of the average fuel temperature, Tpj, in a heat structure; Wpj and apj are the fuel temperature weighting factor and the fuel temperature coefficient, respectively; and np is the number of heat structures in the reactor core. O 78
I l
- 3. NUMERICAL METHODS q
() 3.1 Hydrodynamics The numerical solution scheme is based on replacing the system of differential equations with a system of finite-difference equations partially implicit in time. The terms evaluated implicitly are identified as the I scheme is developed. in all cases, the implicit terms are formulated to be linear in the dependent variables at new time. This results in a linear time-advanceinent matrix solved by direct inversion using a sparse j matrix routine.57 An additional feature of the' scheme is that implicitness is selected such that the five field I equations can be reduced to a single difference equation per fluid control volume or mesh cell, in terms of the hydrodynamic pressure. Thus, only an N x N system of the difference equations must be solved simultaneously at each time step (N is the total number of control volumes used to simulate the fluid system), j The system of five differential equations that form the basis for the numerical scheme consists of: (a) the overall continuity equation [ Equation (10)]; (b) the difference of the phasic continuity equa-twns in terms of quality [ Equation (11)]; (c) and (a) the sum and difference of the phasic momentum equations [ Equations (13) and (14)]; and (e) the mixture internal energy equation [ Equation (17)]. The following discussion describes the development of the difference or computing equations from these differential equations. It is well known5,39 that the system of differential equations constitute an ill. posed, initial-value prob- i lem. This fact is of little concern physically since the addition of any second-order differential effect (regardless of how small) such as viscosity or surface tension, results in a well posed problem.40 However, the ill-posedness is of some concern numerically since P is necessary that the numerical problem be well-ga posed. The approximations inherent in any numeric:d scheme modify the solution somewhat (truncation error); these effects can be either stabilizing or destabCWng. () A well posed numerical problem is obtained by the method developed here as the result of severai fac-tors. These include the Aective implicit evaluation of spatial gradient terms at c he new time, donor for-mulations for the mass and energy flux terms and use of a donor-like formulation for the momentum flux terms. The term, donor-like, is used because the momentum flux formulation consists of a centered for-mulatioa for the spatial gradient of velocity plus a numerical viscosity term similar to the form obtained when the momentum flux terms are donored with the conservative form of the momentum equations. The well-posedness of the final numerical scheme (as well as its accuracy) has been demonstrated by extensive numerical testing during development. 3.1.1 Difference Equations. The difference equations are based on the concept of a control volume (or mesh cell) in which mass and energy are conserved by equating accumulation to rate of influx through the cell boundaries. This model results in defining mass and energy volume average properties and requiring knowledge of velocities at the volume boundaries. The velocities at boundaries are most conveniently defined through use of momentum control volumes (cells) centered on the mass and energy cell boun- , l daries. This approach results in a numerical scheme having a staggered spatial mesh. The scalar properties ! (pressure, energy, and quality) of the flow are defined at cell centers, and vector quantities (velocities) are defined on the cell boundaries. The resulting one-dimensional spatial noding is illustrated in Figure 27. The term, cell, means an increment in the spatial variable, x, corresponding to the mass and energy control l volume. l The difference equations for each cell were obtained by integrating the mass and energy equations [ Equations (10), (11), and (17)] with respect to the spatial variable, x, from the junction at xj to xj + ;. The
/ momentum equations [ Equations (13) and (14)] were integrated with respect to the spatial variable from l
V] cell center to adjoining cell center (xg to xt). See Figure 27. 79
Mass and energy control Vector node volume or cell orjunction A vgvg Scalar node l N lP,X,U p/ i I I
- 1 - en- v g g o --
o -- Q lK ;L l
+ vg l l 1
- 1
^
j1 j+1 w J Y Momentum control volume or cell INEL A 16 779 Figure 27. Difference equation nodalization schematic. When the mass and energy equations [ Equations (10), (11), and (17)] are integrated with respect to the spatial variable from junction j to j + 1, differential equations in terms of cell-average properties and cell i boundary fluxes are obtained. The resulting equations are
** ' *j + 1 Vap/at + (aggg o v A),3+1 + (af of vAf ), =0 (221)
* *j+1 Vo(aX/at) + (1 - X) (a o v A) j+1 - X(afff o v A)x
= r, A) ggg 3 g
and
" "j+1 UvA V a( ou)/ atgggg +(a o JU v A) ,j+1 + ( af of f f ),J 2 2
= - P(agg v A + afvf A),j+1 + QV + a o vg g g (FWG)V v + a of f (FWF)V
, f J
+aosg oFI(v - v f)2V+(
ff r /2) (g - v f) V (223) where the subscripts and superscripts in parentheses indicate integration limits for the enclosed quantity. The quantities not enclosed in parenthesis are volume averages. The energy source term due to vinual mass effects is omitted. 80
The sum and difference momentum equations [ Equations (13) and (14)] are integrated from cell center-g to-cell center to obtain i >
~# 1 1 2 *L (V/A) [(a o )av /at + (afof)avf /at] + 7 a o v 2)*L+7ao g ff f v
= - (P) L + o 8,(x - x K) ~ I"g g gA V FWG + afof fv FWF) (xt-x) g
- r g(vg -
vf ) (x -x g) (224) and
- - *L *L (V/A) 1 + Co /(ogf o)
[avg /at - avf /at] + v gx K
-f v "K
- , . x . . x 6 2
+
Cvf o /(og of) (vg) - Cvg o /(og of) (vf ) K rs K b
= - (1/p - (v FWG - v fFWF) (xL ~ *K) + r g [ovy 1/of) (P) g g
- (a ff ov -x K) ~ '" ("g ~#
f) (*L ~ *K *
+aov)]/(aoao)f(x gf gff l (225)
Here, the common area term, A, has been factored from most terms. The quantities shown in square brackets with limits are evaluated at the indicated limits while the coefficients are averaged over the cell or integration interval. The indicated derivatives are now derivatives of cell average quantities. Since the integration interval is centered on the junction, these averages are approximated by the jucuion values. In all cases, the correlation coefficients for averaged products are taken as unity so averaged products are replaced directly with products of averages. Several general guidelines were followed in developing numerical approximations for Equations (221), (222), (223), (224), and (225). These guidelines are summarized below.
- 1. Mass and energy inventories are very important quantities in water reactor safety analysis.
The numerical scheme should be consistent and conservative in these quantities (a greater degree of approximation for momentum effects is considered acceptable). Both mass and f) V energy are convected from the same cell and each are evaluated at the same time level (that is, mass density is evaluated at old time level so energy density is also evaluated at old time). 81
- 2. To achieve fast execution speed, implicit evaluation is used only for: those terms necessary for numerical stability, elimination of the wave propagation time step limit, and those phenomena known to have small time constants. Thus, implicit evaluation is used for the velocity in mass and energy transport terms, the pressure gradient in the momen- .
tum equations, and the interphase mass and momentum exchange terms.
- 3. To further increase computing speed, time-level evaluations are selected so the resulting implicit terms are linear in the new time variables. Where it is necessary to retain nonlinearities, Taylor se-ies expansions about old time values are used to obtain a for-mutation linear in the new time variables (higher-order terms are neglected). Linearity results in high computing speed by eliminating the need to iteratively solve systems of nonlinear equations.
- 4. To allow easy degeneration to homogeneous, and single-phase, formulations, the momen-tum equations are used as a sum and a difference equation. The particular difference equation used is obtained by first dividing each of the phasic momentum equations by agog and'arpt for the vapor and liquid phase equations, respectively, and then subtracting.
Using the above guidelines, the fm' ite-difference equations for the mass and energy balances, corre-spondin'; to Equations (221), (222), and (223), are V(o"+I t -o")+{'&"h"g(v)"l)+&"B"(v)][I[A
,g g f p) ]
.n.n gg (v )n+1 ao g) + a.n.n fof (v f)
)n+1 A j at = 0 (226) $
~
I Vo X"+I -X &"g h " (v ) A g - &"5" (vg) A at L
+(1-X g
.n.n n
-X g yf .n.n of (v )n+1f p) Ag - afof (v f3)n+1 at = VL(r gL A )n+1 at (227) and V
g (oL U;,)v1 - (pl g)n u + aoa
.n.n ggg" (v )"p+I g
0"
) + a"fo"f f (v f
)"+I. A p) at
&"b"g g
D "g (vg )
+&"b)Dj(v) f Aj at
= - P" &"g v "g + &"v" A 3 p) l -
&"v"+&yv" A at + O"V tt at + DISS"VL at. (228)
O l l 82
)
i [ The term, DISS[in Equation (228) is the sum of the energy dissipation terms in Equation (223). These terms are evaluated at old time using volume-averaged variables. q () ' The quantities having a dot overscore are donored quantities based on the junction velocities, vg and vr.
. The donored quantities are volume average scalar quantities defined analytically as 1
*= (6g+6)+ L v (*K ~ 'L), v f 0 1229) where e is any of the donored properties and v is the sporopriate velocity (that is, vapor or liquid,. For the degenerate case of v = 0, a simple centered formulation is used i = 1/2 (eg + eg ), v = 0 (230) and where donored values are not used at junctions; linear interpolations between neighboring cell values are used.
A similar approach is used to obtain the fm~ ite-difference form for the phasic' momentum equations. In this case, volume-average properties for the momentum control volume are taken as junction properties (that is, linear interpolations between mass and energy control volume centers). The momentum flux terms are approximated using a donor-like formulation that results in a centered velocity gradient term and viscous-like term. The resulting difference equations are (agg o).v -v ax
+ (afof) v[I -v ax j
- v v v at
("g'g)j L- at + f (af of) f f (aggo) VISG" + (afof)3" VISF" at
= - (PL-P)" g at + p"B,-(ao}}(v) gg g FWG" j (afof)" (vf) FWF]-(r)](v g g -v) f j ax at (231)
-l and 2 n 1,v n n "
y at 1 + Co f(,g,f) y ,y , y f 3,j , ~ V K
+
Cvf o /(og of) (vg )n , (yg)n.at-fVISG]at-f.v
)
83
~ ~ ~" ~
2 2 1
- fv f at -
Cvo/(oof)]"(v)" g g _ f - (v )" f at+gVISF]at
= - [(of - og )/(og of)]" (P L -P) g at -
J hv g -M% 3 f
-rnf n n+1- -a n n n+1 n n n+1
/(a ggff o o o )n' a vg v -o g og vf g f of g _3
+(oFI)](v g -v)f faxj at (232) where the viscous terms are defined as VISG EIVg)j+1(A j+1 /A3 )
3 =1/2fv gL - (v g)3]
- v g g [(vg )3 -(v)j,)(A,)/A)]f g g (233) l l
VISF
=1/2f v f L EIVf)jH(A p)/A3 ) - (vf ))]
1 v f g [(vf)) -(v)3,)(A),)/A)]f. f 3 (234) In Equations (231) and (232), the scalar or thermodynamic variables needed at the junctions are linear interpolations between the neighboring cell values. 3.1.2 Volume-Average Velocities. Volume-average velocities are required for momentum flux calculation and evaluation of frictional forces. On a simple constant area passage, the arithmetic-average between the inlet and outlet is a satisfactory approximation. At branch volumes with multiple inlets or outlets (or both), or for volumes with abrupt area change, use of the arithmetic average results in non-physical behavior. This problem is avoided in RELAP5 by defining momentum-flux weighted, and flow-area normalized, inlet and outlet velocities. The arithmetic as erage of these weighted and normalized velocities result in physically acceptable calculations. A general branched volume having abrupt area changes is shown in Figure 28. The average inlet or outlet velocity is defined such that the inlet or outlet mass flow is preserved when using the average velocities and referenced to the volume cross-sectional area. The arithmetic average of the inlet and outlet velocities satisfies continuity in an average sense and is a well-behaved function numerically. 84
[je- g '*g
-Vj J1
/' /
c-Ajj ' s' p *V (vt)V3-a (. l 3 3 My 4-
.y J2 -*- (V )V3 g 2 'A j2
/
j%., __ i1/ INEL A 16 786 Figure 28. Typical branching junctions. The volume-average velreities for the general case shown in Figure 28 are defined by ("f##f f) j [j (v )n = 1/2
/{[3(a of)3 K
f "A A g 3
-3 inlets
{ ("f f##f) ^j [3 , j
. i (235)
+ 1/2 )[J 1 "A A g
l (' d (afof)3 3 outlets i ( and j j [d ( 9 9 9)j 3 (v )n = 1/2
- 3K A g
gg
'[3 (a o )" J A j
inlets j [ ( 9 9"9)J J -
/[j (a o )" A J (236)
+ 1/2 '
A gg 3 K 3 J outlets where the subscri st, K, is the volume index. The velocities illustrated in Figure 28 are shown in the same direction for clarity; however, Equations (235) and (236) are valid for arbitrary velocity directions.
.( 3.1.3 Implicit Lineer Time Step Solution. The basic five difference equations for mass, momentum, and energy, con;ain terms that involve six variables at the new (n+1) time level. The six variables are
' pressure, P; mixture density, p; static quality, X; mixture energy, U (that appears as the product pU); and 85
T the phase velocities, vs and vr. The additional relationship necessary to render the difference equatiors
~ determinant is provided by the state relationship by which the density can be expressed as a function of pressure, static quality, and mixture energy (an additional constraint is implicit in the state relatiori where j one-phase is assumed at saturation conditions). The state relationship is nonlinear and the basic data are in j tabular form. Thus, to preserve the linearity of the numerical scheme, the density relationship in terms of the other state variables is expressed by a two-term Taylor series expansion about the old time level l W
l p" i 3 p" + (ao/aP)"X,U (P" - P") + (ao/aX)"p,g( [ - [) (ao/aV)" X(U" - U").
+ (237)
The energy variable in the difference equations is the product, pU, which comAins two dependent variables. Application of the chain rule to accomplish a change in independent variaale in the Taylor expansion produces the result o" = o" + ( ao/ aP)X,ou (P" - P") + (ao/ax)P,pu ( -
)
+
[ao/a(pU)]{X [( U)" -(ou)"] (238) where derivatives with respect to P, X, and (pU) are expressed in terms of thermodynamic derivatives ( ao/ aP)X,(ou) = o (ao/3P)X,U I + (so/au)p,y (239
'(ao/aX) o 3 [(ao/au)p,y (2 4
[ g) = o (ap/3X)p,g / and.
. 1 i
[ao/a(pU)] = (ao/au)npy j o n + U"(ap/au)" X . (241) Equation (238) can now be used to eliminate density at the n + 1 time level from the difference equations to obtain a system of five difference equations in terms of the five dependent variables, P, X, (pU), vs, and vg. At this point, the numerical time-advancement (from the nth time level to the n+1 level) could be accomplished by simultarmus solution of the SN x SN system of linear equations that results from applicati on of the five difference equations at each 'f the N nodes (necessary application of appropriate boundary conditions is discussed later). However, the judicious choice of implicit terms in the momentum equations permits the time-advancement problem to be reduced to the solution of an N x N system of J linear equations. This is accomplished by eliminating at a node, all dependent variables except pressure. I I This elimination is possible because the difference equations are linear in the new time variables and the momentum equations only involve the velocities and pressures. The elimination process consists of solving for the phasic velocities in terms of adjoin <,g cell pressures. The velocity equations are then used to , eliminate velocities from the mass and energy equations. Three equations per cell result, which involve 86
energy and quality of only the cell under consideration. Thus, the system of three equations can be reduced to a single linear equation relating cell pressure to the pressure of adjoining cells. This procedure is carried i out for each cell of th'e system so the result is an N x N system of equations for the new time pressures. The i procedure is reversed so the remaining field variables are obtained by back-substitution. LJ After solution for the field variables just described, only the product (pU)is known rather than values of p or U or both. The em gy is required to apply the state relationship and obtain density as well as all other thermodynamic variables. The density energy separation is obtained without iteration using an auxiliary difference equation for the mixture density, p. For this purpose, the mixture continuity equation is used with the momentum equation for velocities described earlier. Thus. density may be solved at each cell in terms of the established pressure field (this solution is accomplished very efficiently in RELAPS, since all convective terms have already been calculated in the pressure field solution). The mixture energy is then calculated from the relation U"d = (oU) /og (242) where Pmn+1 is the mixture mass density calculated from the mixture continuity relation. The state relation is used to calculate the mixture thermodynamic density, p, using the state variables, P, X, and U. 3.1.4 Time Step Control. In general, density obtained from the state relationship is not equal to density calculated from the mixture continuity equation. The difference between these two densities is a measure of the truncation error associated with use of the Taylor expansion [ Equation (2301. This truncation error is sensitive to change in the density derivatives [ Equations (239), (240), and (241)). In a two-phase system, the density derivatives may be highly discontinuous at points of transition between single- and two-phase A regions. Consequently, any numerical scheme will have significant truncation error at such points unless these points are explicitly tracked and appropriate jump conditions applied, or the time step is made suffi-() ciently small for the time step that spans the single- to two-phase transition. This error is controlled by the l latter approach using automatic time step control. 1 The truncation error measure provided by the density difference is used as the basis for the automatic - time step control scheme. This approach has been very successful in controlling mass truncation error, making fast execution possible through use of efficient time step sizes. The error measure is defined by c = max max [ (o$ - og )/pg , i = 1, 2, . . . , N ] , i N I#3' (1/N) { (og - om i)/"i
- l i=1 The time step is selected such that the density error ts maintained between preset limits. If at any time-advancement, .it, the error exceeds the limits, that solution is discarded and the advancement is repeated using a smaller time step. If the error is smaller than a preset limit, the next advancement is made using a larger time step. The actual process includes other considerations besides error bounds and consists of the following four tests.
/ V 87
l l 1. If the Courant limit, expressed analytically by at < max { min [ Ax j/ max ( v g4 vf $.), 1(odd)
= 1, 3, . . . , N - 1 or N],
1 v ),i(even) min [ax$/ max (v$ g f4
= 2, 4, . . . , N - 1 or N] } (244) is not satisfial by the projected time step, the advancement is marked unsuccessful.
- 2. If the extrapolation defining water properties in the metastable states associated with flashing liquid or condensing vapor leads to a negative or zero density, the advancement is marked unsuccessful.
- 3. If the density difference is greater than 2 x 10-3, the advancement is marked unsuccessful.
- 4. If the pressure, static quality, or internal energy correspond to a thermodynamic state out-side the range of water property subroutines, the advancement is marked unsuccessful.
If the advancement is unsuccessful, the time step is halved and compared with the input minimum time , step. If the halved time step is greater than the minimum, the advancement is repeated with the halved time step. If the halved time step is smaller than the minimum, the unsuccessful advancement is accepted unless a water property failure occurs, in which case the transient is terminated. The first advancement is attempted with the user input maximum time step. If this or a subsequent advancement is unsuccessful, the time step is halved. The halving of the time step continues until either a ; successful advancement is made, the advancement is acceepted because of the minimum time step being ! reached, or the advancement is terminated. i 1 When an advancement is successful and the density error (Test 3) < 2 x 10-4, the time step for the next advancement is doubled. ] 3.1.5 Boundary Conditions. A combination of physical considerations and a characteristic ana'ysis usually establishs permissible number / combinations of boundary conditions. However, because the system of differential equations are not totally hyperbolic, it is not possible to use characteristic arguments directly. Therefore, it is necessary to draw on experience with single-phase hydrodynamic models, such as l
. the Navier-Stokes equatio'v, to conclude acceptable combinations of boundary conditions. ]
The first boundary condition to consider is a closed end or null condition. In this case, appropriate boundary conditions are that both the phasic velocities are zero. The more Trum equations at such a junc- I tion are not required and solution of the difference equations is detew < te. l The second case to consider is a constant pressure source or sink. In the case of a sot'rce, all the volume properties are required so that the quality, X, and energy, U, must be specified (this situation exists if either or both phasic velocities cause inflow to the system). Specified pressure is sufficient for a pure sink. A less obvious situation arises in the momentum calculation at either a source or a sink. The momentum i convective terms require velocities at junctions upstream and downstream from the boundary junction, 2 88
.:j
and information is required beyond the source or sink volume. In this case, the boundary conditi:ns are j supplemented by the numerical condition that the derivatives of velocity are zero beyond the last junction (that is, the velocities are constant, permiting evaluation of the momentum convection terms).
'V) The last and most subtle boundary condition is associated with specified nonzero velocities. In this case, '
the boundary volume ptr perties must be specified for the inflow case. If both velocities are specified in addition to pressure, quality, and energy, the problu is overspecified since there are only five field equa-tions. The analogous case for a single-phase flow would be specification of the pressure, energy, and i velocity, which could only be the case if the flow velocity were greater than the sound speed (that is, super- j sonic). The specification of five conditions is only correct for choked or supersonic flow. Generally, the ; flow is less than sonic, so one is forced to conclude that fewer than five specifications is appropriate. It can 1 be shown that only one velocity need be specified and the remaining velocity can be calculated from momentum considerations. However, additional numcical boundary conditions must be employed to calcu'l ate the momentum flux terms discussed previously. This requirement for additional boundary condi-tions is common to most finite-difference schemes and does not seem to cause any significant problem. In conclusion, one can specify both velocities as well as the state properties and generate reasonable results, but caution should be exercised when posing and interpreting results from such problems. 3.1.6 Implemerttation of Choked Flow Model. Ideally," the two-phase choking criterion [ Equation (153)) can h used as a boundary condition for obtaining flow solutions. However, the applicability of Equation (153) has not been fully explored. Instead, an approximate criterion (ag ofvg + af ogfv )/(a of + af o ) = a HE (245) has been applied extensively and produced good code / data comparisons. Equation (245) can be derived from Equation (153) by neglecting the third C term in D and setting C =0 (stratified) on the right side of n Equation (153) and C= co (homogenous) on the left side. Because of extensive experience with this
, approximate model, Equation (245) is currently used in RELAP5/ MODI choked flow calculations.
(O) At each time step and at each flow junction where two-phase cocurrent flow exists, the choking criterion [ Equation (245)) is checked with vr and v g, assuming the explicitly calculated values. When choking occurs, Equation (245) is solved semi-implicitly with the upstream vapor and liquid momentum equations for v gvr and P throat t pressure, at the point of flow choking (upstream u with reference to vgand vr). As P tis not needed in system calculations, we can eliminate BP/Bx for d.e vapor and liquid momentum equations to obtain i
-o avf /at + 1/2 av2/ax og fav g /at + 1/2 av /ax l
l
= o g - ofB, + r g(v y-avfg - agf v )/a fg a
- o gg v FWG + of fv FWF - ofpg(v g - vf ) FI
- C o[a(vg - v f)/at + v favg/ax - v gavf /ax] . (246)
The finite-difference form of this eque. tion is obtained by integrating with respect to the spatial variable from the upstream volume center to the junction. With ayl approximated by [] U 1 89
a =a HE + (aaHE/aP) (P"+I - P") (247) where P is the upstream volume pressure. The finite-difference equations of Equations (245) and (246) can be solved for vj+ 1 and v n+1 in terms of Pn + 1 and old time values. In case of subcooled choking, the choking criterion [ Equation (245)] and the velocity equation l [ Equation (246)] reduce to ! v =v = ,+ vc * ~ I2#8) f ! l 4 Here, v eis determined according to the precedures described in Section 2.2.1.2. The frictional pressure { losses and gravity head, which do not appear in ideal Equation (159), are properly taken into account in i ' the actual calculation. In general, there is a large drop in critical velocity when the fluid changes from a subcooled state to a two-phase state. This sudden change often causes unrealistic velocity oscillations and causes the time step size to be reduced considerably. To provide a smooth transition from subcooled to two-phase, the sub . cooled region is extended to og (upstream volume void fraction) <0.05 and a transition region is defined as 0.01 < as < 0.1, Within the transition region, an underrelaxation scheme, v"+I v" - v") 9- 9 +0.1[\v"*I 9 9/ n+1 n n n O\I v._7 v 7 + 0.1 (v +1 f -v)f (249) is implemented. Experience with this scheme indicates that it works satisfactorily. 3.1.7 Hydrodynamic Options. RELAPS has several, special-purpose hydrodynamic opfbns available to the user that are specified at input. The options are: two velocity or homogenous; transient or pseudo steady state; wall friction or no wall friction; abrupt area change or smooth area change; test for choking, or not test for choking; and equilibrium or nonequilibrium equation of state. Each option can be specified for individual junctions or volumes. 3.2 Heat Transfer j 3.2.1 Heat Conduction Numerical Techniques. Heat structures provided in RELAPS permit calcula-tion of the heat transferred across solid boundaries of hydrodynamic volumes. Modeling capabilities of heat structures are general and include fuel pins or plates with nuclear or electrical heating, heat transfer across steam generator tubes, and heat transfer from p.ipe and vessel walls. Heat structures are assumed to be represented by one-dimensional heat conduction in rectangular, cylindrical, or spherical geometry. Sur-face multipliers are used to convert the unit surface of the one-dimensional calculation to the actual surface of the heat structure. Temperature-dependent thermal conductivities and volumetric heat capacities are , provided in tabular or functional form either from built-in or user-supplied data. Finite differences are used to advance the heat conduction solutions. Each mesh interval may contain different mesh spacing and a different material,' or both. The spatial dependence of the internal heat source may vary over each mesh interval. The time-dependence of the heat source can be obtained from reactor kinetics or one of several tables of power versus time. Symmetry or insulated condition and tables of sur-face temperature versus time, heat transfer rate versus time, and neat transfer coefficient versus time, or _ __ _ _ __ _ _ . _ _ m.
surface temperature are allowed. For heat structure surfaces connected to hydrodynamic volumes, a heat A transfer package containing correlations for convective, nucleate boiling, transition boiling, and film heat ( ) transfer from the wall to water and reverse transfer from water to wall is provided. The following describes the numerical techniques for heat conduction. The integral form of the heat conduction equation is o(T,I)h(I,t)dV= k(T,i)vT(I,t) ds + S(i,t)dV (250) V s ss V where k is the thermal conductivity, s is the surface, S is the internal heat source, t is time, T is temperature, V is volume, x represents the space coordinates, and p is the volumetric heat capacity. The boundary con-ditions applied to each of the two exterior surfaces have the form A(T)T(t) + B(T) a = 0(T). (251) an The n denotes that the direction of the derivative is away from the boundary surface. Thus, if the desired boundary condition is that the heat transferred out of the surface equals a heat transfer coefficient, H, times the difference between the surface temperature and a sink temperature TS
-k aT = H(T - T5 ) (252) n an i,"j the correspondence between the above expression and the parameters of Equation (251) is A = H, B = k, D = HT . (253) s Ir steady state problems, a valid physical problem requires that A be nonzero in at least one of the boun-dary condition equations. If a transient or steady state problem has cylindrical or spherical geometry and a zero radius for the left surface (that is, a solid cylinder or sphere), the left boundary condition is normally BT the symmetry condition, p == 0. Under these conditions if B is nonzero, the numerical techniques used force the symmetry boundary condition, even if it is not specified.
3.lt.2 Mesh Point and Thermal Property Layout. Figure 29 illustrates the placement of mesh points at temperatures to be calculated. The mesh point spacing for a rectangular problem is taken in the positive x direction. For cylindrical and spherical problems, the mesh point spacing is in the positive radial direction. Mesh points are placed on the external boundaries of the problem, at the interfaces between different materials, and at desired intervals between the interfaces, boundaries, or both. Figure 30 represents three typical mesh points. The subscripts are space indexes indicating the mesh point number, and I and r (if present) designate quantities to the left and right, respectively, of the mesh point. The h's indicae mesh point spacings which are not necessarily equal. Between mesh points, the ther-mal properties, k and p, and'the source term, S, are assumed spatially constant, but k nl is not necessarily equal to krn, and similarly for p and S. To obtain the spatial-difference approximation for the nth interior mesh point, Equation (250) is (ov) applied to the volume and surfaces indicated by the dashed line shown in Figure 30. For the spatial-difference approximation at the boundaries, Equations (250) and (251) are used to define the gradient along the exterior surfaces and applied to the volumes and surfaces indicated by the dashed lines shown in 91
1 B
/ oundary77"ns'$*c'es -sooneary '
. ..... . . . . . . .......... .Menh 12 3 4 etc. .---Mesh point numbering INEL A-16 800 Figure 29. Mesh point layout.
k k rn fn ; Aln Arn k Sn i S rn ) f~h" t h ! F2
-- ;"--I>
- i
- = h rn hfn
~
l n-1 n n+1 j l i INEL.A 16 787 Figure 30. Typical mesh points. Figure 31. If the coefficient of the gradient in the boundary equation is zero, the surface temperature is given directly from Equation (251). Since the code is one-dimensional, the dimensions of the volume for other than the x or r coordinate are set to one. For rectangular geometry, the volume is a rectangular solid. For cylindrical geometry, the volume is a cylindrical annulus, and for spherical geometry, the volume is a spherical shell. The spatial finite-difference approximations use exact expressions for the space and volume factors and simple differences for the gradient terms. To condense the expressions def~ ming the numerical appror.imations and to avoid writing expressions unique to each geometry, the following quantities are defined. For sk ? geometry 5 = I h s , 1 h En h g rn h rn h V
=
h" h V
=
h rn (254) in 2 rn 2 hb n
= 1. (255)
_- 7 r--- 01 8 2 - N1 , _ _ _ _ON e __ a
, hr1 - =- -hfN ~ INEL-A 16 808 Figure 31. Boundary mesh points.
w .___ - - _-_ I
if'$i Jy( j r- -c.,
. For cylindrical geometry
, 1
,; y .; ..
g 9 A F 0
<t v ..
h in Y ' h'n i h j v
'h rn j I' hrnI 1-
-h.
in
=.2w 2 ;(*n ' 4/ h rn. = Zw 2.(n*4)~ ,
I. 'h I / h# ") 5 5 *l x + h.= ' "l x- - I h -= ' In. h rn
,.7 an (n 2. )_ -
hrn.(#' -
/-
hbn= 2wx n* , (256) , For spherNat geometry. 3 , <{ h-in Y ( h' Y V i x + -x x h*rn' = #3'
~h in = 7w ;n A ,n 2)L ,
j n 2) n h ""
/ 5 4" tn h
5 =
+
- h =
rn' in
- h tn 3 n~ : 2/ h rn (xn 2~ j .
hD = 4,x , (257) n , For all geometries (258) Gn " ' "in in * #rn rn. b The superscripts, y and s, refer to volume and surface-gradient weights. The h"is a surface weight used at exterior boundaries and in heat transfer rate equations. 3.2.3; Difference Approximation at internal Mesh Points. Using a forward difference for the time t' derivative, the first term of Equation (250) for the volume of Figure 30 is approximated by-o(T,i)'h(i,t)dVm ( -( . (259) 1it , The superscript m refers to time; thus, TSindicates the temperature at mesh point n at time tm, and Tm+1 indicates the temperature at mesh point n at time tm + 1 '= tm + At. The second term of
- Equation (250) for the surfaces of Figure 30 is approximated by 93
.r
,il
k(T,I)a T(i,t) ds = ('in Tn) k tn h tn + (Tn +1 - Tn ) k rn hfn. (260) 3 Note that the above expression includes the standard interface conditions of continuity of temperature and heat flow. The surface lategral of Equation (250) is usually evaluated by integrating only along the exterior j surfaces of the volume it:dicated by the dashed line in Figure 30. If, however, the voltime is divided into two subvolumes by the in'erface line and the surface integrals of these subvolumes are added, the surface i integrals along the cormnon interface cancel due to the continuity of heat flow. The continuity of temperature is implied by use of a single valued temperature at the interface. A contact resistance interface condition cannot be specified directly sir:e the temperature, instead of being continuous rt the interface, is given by q = H AT e where q is the heat transfer rate across the inter-face H is e the contact conductivity, and AT is the temperature change across the interface. This condition can oc specified by defining a small mesh interval with thermal properties of k = He h and p = 0. The size of the mesh interval, h, is arbitrary except in cylindrical or spherical geometry, the surface and volume weights are dependent on the radius. This mesh interval is usually chosen very small with respect to the dimensions of the problem. The space- and time-dependence of the source term in Equation (250) are assumed to bg separable l functions i S(x,t) = P fP(t)Q(x) (261) where Pr is the facts which relt.tes the reactor power (or power from a table) to the heat generation rate for a particular heat structure, P(t) the reactor power (or power from a table), and Q(x) is the space-dependent function. Q(x) is assumed constant over a mesh interval, but each interval can have a different value. The third term of Equation (250) is then approximated as S(I,t)dV=(Q tn h tn +O rn h rn)PP(t). f (262) Gathering the approximations of terms in Equation (250), the basic difference equation for the nth mesh point is (T**I" - T*
" G h s
k h 5 g " = - (Tn -Tn-1) k 1 in + (Tn +1 -T) n rn rn
+ 0 in h
in
+O rn hrn Pf P(t). (263) i Using the symbol,6 n, to represent the right side, Equation (263) can be written as 4
i T**I
" -T*)G"
=6 I I at n' I
Thus far, the time superscripts for Gn and i have n been omitted and the procedure for approximating the temperature-dependence of the thermal properties has not been mentioned. The procedures for I I 1
temperature-dependent thermal properties are discussed later. However, superscripts for thermal pr per-
' ties are written here even though their significance is not explained until later. For steady state, the
- difference approximation becomes )
'N 0 = 'a n (265) .. and no time superscripts are needed. For the time-dependent case, an equation of the type z . T**I
-T*IG"' "
at-
=w6 + (1 - w) 6* (266) is an explicit formula if w is zero and is an implicit formula when w is nonzero. RELAP5 uses the implicit formulation with w = 1/2.
Writing Equation (266) in full, the difference approximation for the nth interior mesh point for transient and steady state cases is a* n T*+I n-1 + b* n nT**I + c*nn T*+ 1n = d s K* h at
,m , , in in n 2 b*n = oG*- a*n -c n A
n n c*n * - e dn =aa ,) + o ( + o G[+a[+c ( - o c[ ( )
+ atP 7 P** + oP* Q in h in +O rn hrn (267) and o is I for transient cases and 0 for steady state cases.
3.2.4 Diffeience Approximation at Boundaries. To obtain the difference approximations for the mesh points at the boundaries. Equation (250) is applied to the volumes of Figure 31 with Equation (251) used to define the gradient at the surface. The second term of Equation (250) at x = xii s approximated by k 5 k(T,i) vT(i,t)
- ds ::: - (A)T)-D))hk+kr1 (T2 - T)) hg. (268) 95
The complete bacic expression for the left boundary mesh point becomes
~ k v b h g=
at r1 B)N (A)T) - D)) h) e v
+k g (1 2 - T)) hg + Og h g Pf P(t). (269)
If B in the boundary condition equation is zero, the above equation is not used since the boundary condi-tion determines the temperature. Also in that case, a divide by zero would be indicated if Equation (269) were used. Approximations for the boundary at x = xn are derived in a similar fashion. These equations for the boundary mesh points are converted to the implicit formulas in the same manner as for the interior mesti points. Thus, for the left boundary b* [ + c* T[ I = d) A* h at m m v 1 b*= cog hg+ m - c) 2B) 5 h at m k*1 r r1 C)=- 2
! k"I A* h at\
d) = - oc* T* + ei p*) hg + c* ( r -
- 28) /] I I
h D* At D at
+
ok") + k*) h 2B* 2B* V hg at
+P f (cP* + P**I)2 O rl - (270) l
}
For the right boundary, I a T + b* Tf = dy i l l l 96 l -_ _- i
prg , 7
+ ,
q p q i at t
' ,m . , l LN htN 2
]ll.
b
- k*LN A*N h at' q V
b*N = op EN h 3LN + N ',3 m 2B"
" 1 s
J l h b~.at\ mm ,.y , k*tN A*N tN . gg + .aN h dN .='- a TN-1 **l
~
8 N m
\ 2B g
[ m- b m m b m ok h D at: k_tN . hgDg *at
+- LN N N +
5 ' 28* 28 V at
+P f (eP*+ P**I) O LN.h tN . (271) ,
2 t 3.2.5 Solution of Simultaneous Equations. The difference approximations for the mesh points [ Equations (267), (270), and (271)] lead to a tri-diagonal met of N equations. The coefficient matrix is sym-metric unless the boundary condition specifies the surface temperature. In that case, the elements, c3 and aN, are 0, and destroy the symmetry. The solution to the above equations is obtained by c) ' d) (272)
- 1. ' Form E) = p and F) =p 1 1
~
- 2. Form E j =
c 3 and F d 3-a3 F3 ,) b.-a j E j j-1 j=bj-aj J-1 E for j = 2, 3, . . ., N-1 (273)
' +I N FN-1 (274)
- 3. =
Form T*N by-ay Ey ,3 o.
- 4. Form T =-E 3_ ( ) + F3 for j = N-1, N-2 , . . ., 3, 2, 1. .(275) 97 q
These procedures can be derived by applying the rules fo- Gaussian elimination. This method of solution introduces little roundoff error if the off-diagonal elements are negative and the diagonal is greater than the sum of the magnitudes of the off-diagonal elements. From the form of the difference equations, these conditions are satisfied for any values of the mesh point spacing, time step, and thermal properties.
?.2.6 Thermal Properties, Boundary Condition Parameters, and Iteration Procedures. The ther.
mal conductivity, k, and the volumetric heat capacity, p, are considered functions of temperature and space. These thermal properties are obtained for each half interval and averaged for thermal properties over the entire ir.terval. Using k(Tln and k(Tr,n) for the thertaal conductivity for half intervals to the left
- and right, respectively, of the mesh ) point, n, k * =k r,n-1 (276) in 2
+T t,n+1 \
r,n k rn = k( T 2 / I=k 1,n+1 - (277) The program uses k(TI ,n) = k(Tr,n) wherever the same material is placed in the half intervals adjacent to the mesh point. The quantity, p, is treated in the same manner. The boundary condition parameters, A, B, and D, are considered functions of temperature and time. In steady state problems, no superscripts would be required for the thermal parameters, k, p, A, B, and D. Accordingly in Equations (267), (270), and (271), those quantities written with superscripts m or m + 1/2 are ignored since they are multiplied by a = 0, and only quantities with superscript m+1 are used. If these quantities are not temperature-
~
dependent, the solution of Equations (267), (270), and (271) would immediately give steady state temperatures. When these parameters are temperature-dependent, iterations are used to resolve the dif-ficulty of obtaining thermal parameters as a function of temperature when the temperatures are unknown. In transient problems, the thermal properties, k p, A, B, and D, with superscript m are evaluated as a function of the temperatures, Tm, at the begin' ting of a time step. Since these are either initial temperatures or results of the last time-advancemetu, the corresponding thermal parameters can be deter-mined. Those thermal parameters with superscript m + 1 are evaluated as a function of the temperatures, Tm + 1, at the end of the time step. Since these temperatures are not available, the initial estimate of the I thermal parameters is obtained using km+1 = km and similarly for p, A, B, and D. The superscript m + 1/2 indicates an average of the quantities with superscript m and m+ 1, or m m+i/2 om+1 + o o . (278) 2 If thermal parameters and boundary conditions are constant, or do not vary greatly during a time step, the temperatures obtained from the solution of Equations (267), (270), and (271) with km+ 1 = km, etc., are satisfactory. This is presently assumed in RELAP5. However, the coding includes an iterative procedure that can be used to more accurately determine km+1. The iteration consists of obtaining thermal parameters with superscripts m+1 from the temperatures obtained from the initial solution for the first iteration or the previous iteration for subsequent iterations, and again solving Equations (267), (270), and (271). The iterations continue until convergence is obtained or the iteration limit is reached. 3.2.7 Difference Approximation for Boundary Conditions. The development of the difference equa-
- l. tions uses a general form for the boundary conditions, but RELAPS uses only the followiig conditions, aT O
-k g = 0 (279) j
-li 98
~aT.
-k g m qT(t) (280)
H Y) aT
-k g = H(T - TB ) (281)
T = TT (t) (282) where qT and TTare tabular functions of time. For the first three conditions, the heat transfer rate is given directly by the boundary conditions once the surface temperature has been calculated. For the temperature boundary condition, an expression for the heat transfer rate is obtained from the difference equation. The ' l expression for the right boundary is m+1 b m m+1h s m m m s N * ~ 'QN hb+km+i / m+1 h g QN h N tN N-1 ~ N fh g + ok g TN TN m+1/2 V
+ Pf (eP* + P#I) Q LN h V
g- T - T* h g. (283) 3.3 System Components
/ O 3.3.1 Branching. In order to model flow in interconnected piping networks, it is necessary to model the -Q two-phase fluid process at tees, wyes, and plenums. A general description of the two-phase flow process is complicated by the possibility of phase separation effects that can occur at a tee where flow division occurs 50. However, there are many situations where wye or plenum branching is adequate for both flow merging and division. Typical situations where such models are adequate are parallel flow paths through s the reactor core, and any branch from a vessel of la:ge cross section (in this case since the fluid momentum is small, it is permissible to neglect the momentum convective terms). For branching situations where phase separetion effects due to momentum or body fo:ce effects, or both are important, a branching algorithm :
has been developed for RELAPS in whis 'he parallel or wye branching modelis used to map the two-dimensional situation onto the one-dimensional space of the fluid model. 127.7 one-vimenesens/ arenching -The one-dimensional branching model consists of a single control volume with multiple junctions (two or more) at its inlet and outlet (see Figure 28). An additional distinc-tion is made wherein junctions are identified as inlet or outlet junctions on a volume. Junctions Ji and J2 (shown in Figure 28) are inlet junctions whereas Junction3J is an outlet junction relative to Volume V3 . The modeling is relatively simple. Ideal mixing is assumed in Volume V3 in the sense that inlet flows merge to form single vapor and liquid velocities. The volume velocities,(vr)V 3 and(vg)V3, associated with the inlet junctions of cell V are 3 obtained using the volume average velocity definitions developed in Sec-tion 2.2.1.2. These volume velocities are then used to evaluate the momentum flux terms (1/2 pv2) in the momentum equationsa for allinlet junctions connected to Volume V3 . l N' a. This type of formulation satisfies the momentum equations for each stream, but does not satisfy global momentum for the mixed 7 flow. Momentum interchange occurs due to mixing and the magnitude is proportional to the pressure and velocity differences I ( between the mixing streams. For this reason. the branching model will not accurately describe the momentrn exchange in a jet pump. The missms momentum terms are planned for addition to futur- code versions.
The losses associated with inlet or outlet junctions are calculated using the assumption that the fraction of the volume area, AV3, seen by a typical junction connected to Volume V3 , is in direct proportion to the volumetric flow rate. We assume that each junction flow expands or contracts from the area of the junc-tion, Aj, to the apportioned area in Volume V 3(see Figure 28). The flow area of Volume V 3is assumed to be apportioned according to a volumetric flow fraction defined as
+
(af) ] (v f)'jA j (a)"(v)]A3 g q Ag (Ak )j = h . (284)
"A +
(af )" (v f)3 3 (a)](v)]A3 g g With the apporuoned areas defined, the RELAP5 abrupt area change model is applied at all junctions connected to Volume V3 . . I The branching algorithm just described and shown in Figure 28 is used in RELAP5 for all one-dimensional branching su:h as at parallel channels, low angle wyes, and plenums. 11u moerme 7 Modet-The physical process occurring at a 90-degree horizontal tee is mapped onto the one-dimensional calculational space by an algorithm that approximates the two-dimensional momen-tum effects that occur at a physical tee. The myping utilizes the fact that each volume has an orientation and inlet / outlet designation. The orientation or the branch volumes used in the mapping and interconnect-tions are shown on Figure 32. The arrows in each volume indicate the one-dimensional sense of ucction and are drawn by definition from the inlet to the outlet junctions. The junction areas for the inlet and outlet legs of the tee are the same as the pipe cross section. The areas of the junctions associated with the branched leg of the tee are each equal to one-half of the area of the branch leg. This mapping has the effect l that half of the momentum at Junction J associated 2 with Volume Vg is opposite to the corresponding momentum at J3associated with Volume 2. On the other hand, half the momentum at J2associated with Volume V is in the same direction as the corresponding half at Junction J 3. Thus, the momentum treat-3 ment approximates the two-dimensional situation at the tee wherein the branch leg sees a closed passage and the flow must turn to enter through the flow passage. As in the one-dimensional branch, losses are calculated at all junctions by the RELAP5 abrupt area change model, except that now the fractional area associated with each junction differs according to the sizes of J3 and J2-J3 t V3 -
- V 3 __
=l ,.:
J2 J3 i j INEL A 16 789 Figure 32. Application of branch volume to horizontal tee or plenum. ____m _ _ N !
l
)
'l as.f.s ower assem ere ree-In branching situations whete the velocity through the tee is low relative to o ~ the branch leg velocities, body force effects may be significant. In such cases it is possible to orient the Jm branch volume 'such that its orientation is in _the same one-dimensional direction as the branch leg. The
(
)' junction connections follow a similar pattern to the tee if the through flow passage is treated like the ,
branch, and vise versa. This ' mapping is shown in Figure 33. A gravity head is included in the branch ~ j Volume V 3and V and 4 results in a corresponding separation effect due to buoyancy. The prescription for - j partitioning the junction area is the same as for the 90-degree tee. This mapping has been used to model the - i inlet annulus with connections to the cold legs and the downcomer. In this case, the downcomer is the branch leg. The results of application to the Semiscale problem showed that this model exhibited flow bypass and downcomer dumping; both of which are characteristic of the actual data. V2 V1 J3 V3 J2 l ~ b J3 h J4 N J 5 0 Q v4 i l INEL.A 16 797 Figure 33. Application of branch volume to vertical tee or plenum. 3.3.2 Numerical Scheme Accumulator Model. The numerical scheme used for the accumulator model includes special features for coupling the solution scheme to the main code in such a way that it is time step independent. This scheme, as in RELAPS, is semi impucit, however, special considerations for the nitrogen energy and mass balances are employed to reduce truncation error. The numercial scheme uses finite-difference techniques to solve the differential equations used in the hydrodynamic model. The time-advancement variable, Pp , and the sur8e line velocity, v (a RELAP5 time. advancement variable), are both centered in time [that is, Pp = 1/2 (Ph+I + PS) a v = 1/2 (v +n 1 + v )] nn the energy equation. TMs, the energy equation [ Equation (197)]. becomes r P" P" / n+1 n Mn C V n 2 2 Y*Y where the heat transfer rate [ Equation (209)] is then integrated and coupled explic. .f to the system.
) The continuity equation [ Equation (198)] and the momentum equation [ Equation 194)] are written as l' ( difference equations. Equation (285) is linearized and substituted to eliminate Tg+ and the following equations are obtained. They are 101
nt y Mn /PD + 1/2 VAL at/T DV C n D
~
g
~
+ 1/2 Ag at on + P g/T D C y $ " (v - v") = B) (286) n)_
and (-AL) P* U D
-P D E
+ E'wA g(Lg /at + 1/2 v) + F] (v"+ -
v") = 0 2 (287) where n B)
= -
A o + P D/TDv ~ OD/TDyC at n n_ and B 2 E*w4 L + h) A ]" - [(P - PD ) #L ]" - 1/2p vA - (Fv)" . I These two equations can be solved simultaneously for P and vn+ 1 in terms of the RELAPS system I pressure. Pn + 1. The equation for P is solved implicitly with the RELAPS system pressure equation at each time step. n After the pressure solution, Tg+1 may be solved by back substitution with Pn+1 and v +1 in Equation (285). The goal of this model is to be time step independent and for nitrogen mass to be iden-tically preserved. This is accomplished by rewriting the nitrogen energy equation (Equation (138)] in differential form F aT MRT aV MC *- +O D (288) nv n at V D at which can be solved dire:tly by integrating between Tgand Tg+1, and V6 and V6+I, which gives R n n OD at 00 ^t TDn +1 " ' D
'C V T D~ n
+
n (289) R -V D R Yn+1D / n _ V8+I - V" *n n [/n+1 D "n n where l n+1
- V D
Y D + [\v"*I) +Ltv"\ A o 2 A 102 u_________.___ _ _ _ _ - . _ _ _ - - - . -. - i
This solution results in an exponential decay of temperature with volume reduction and heat addition. Once Tg+ 1 is found, the pressure is reset by using Equation (195). At small time steps, the pressure from e ~; Equation (195) and the pressure from the matrix solution in the program are identical. At larger time steps ( ,1 or sharp transients, the reset pressure gives an exact solution while the RELAPS matrix solution can be quite different. 3.3.3 Valves. Valves are quasi-steady models that are used either to specify an option in a system model or to simulate control mechanisms in a LWR. The valves can be classified into two categories (a) valves that open or close instantly and (b) valves that open or close gradually. Either type can be operated with the control system or by flow dynamics. Valves in the first catagory do not include the physics of valve opera-tion, while valves of the second category are more physicalin operation. The valves in the first category are the trip valve and check valve. The valves in the second category are the inertial swing check valve, the motor valve, and the servo valve. The inertial valve assembly movement is calculated using Newton's second law of motion (angular version). The abrupt area change model con-trols losses through the valve as the cross-sectional flow area varies with valve assembly movement. The motor and servo valve use differential equations to control salve movement. The abrupt area change model is used to calculate losses across the valve. These two valves also include an option allowing use of flow coefficients (Cv) instead of the abrupt area change model. The Cy's are converted to energy loss coefficients, K. Several types of valves may be modeled by RELAPS at a junction. The types of valves are defined , below. 3.3.3.7 Trip ve/ve- A trip valve is solely dependent on the trip selected. With an appropriate trip, an 7 l ! abrupt (not time-smoothed) opening or closing of the valve including latching open or closed is modeled. L) 3.J.J.2 Check Ve/ve- A check valve can be specified 10 operate by static pressure differential or on flow dependent pressure differential. The types of check valves available are described below. The valve will open or close based on static pressure differential across the juncuon according to dg - PCV > 0, valve open (290) P g L+#L 5,0, valve closed where Pg,PL = thermodynamic presst.res l APgg ,APL g = static pressure change due to gravity between volume center and valve PCV = pressure required to close valve (user input). f The valve will close based on dynamic pressure differential and open based on static pressure differential Q] across the junction by 103 1 L_m_.__
i Pg - @g - - PCV > 0, opens valve from closed position PL + AP _ g 1/2 G G /p - PCV s 0, closes valve from open position (291) { i where ! l n l G c " I"f f f}j 8V + ("g'g g)nj V (292) l p
=(afof}}+(ao). gg (293)
Equation (291)is checked only for Oc < 0 with the valve open; Equation (290)is checked only if the valve is closed. For hysteresis, the inequality in Equation (291) is changed to strictly greater than. 4 1 All check valves may be initialized either open or closed. Leakage is not allowed with any check valve. The abrupt area change model is used to model the valve area as an orifice. 123.3 ineerder vehe-This valve models the tnotion of the valve disk assembly (flapper) in an inertial type check valve.58 The abrupt area change model is used to calculate losses for the flapper as an orifice that changes area in time as a function of the physical properties of the inertial valve. The motion of the flapper about the rocker shaft axis is given by Newton's second law (angular version) O as [T=Ia (294) where the external torques acting on the valve disk are given by T-= I
- W L sin (e + 6) - A L(aP D + PBP
- bhead}
and AP is the pressure drop across valveaand a is the angu'.ar acceleration. Substituting Equation (295) into Equation (294) gives I I I a = - W L s i n e - w R L ( aP + PBF + Ghead)
.where o has been dropped by assuming the valve is a horizontal pipe. Equation (2%) is then written in finite-difference form I l
2 a"=h-WLsine"-wR L(aP" + Pgp + Ghead) (297) 91
- a. The inertial valve assumes an orientation such that it will open for flow from the K volume to the L volume and will close for flow from the L volume to the K volume.
__ _-_ _- _ .- - _ . 8%
where the s6 script, r., indicates the time level, t + n At. Integrating Equati:n (297) with respect 13 time yields the angular velocity , n+1 n
=mn + a at . (298)
K) ( w Similary integrating Equation (298) gives the angular acceleration 1 e" = e" + wnH at. (299) The normalized throat flow area for the valve is set by thi following function 59,60 A throat
= w ane for e < 26. d 2
= wR for e > 25.565 . (300)
Several options are allowed with the use of this valve, minimum and maximum valve positions as a func-tion of angular position, latch or no latch options, and leakage. 1114 motor veke-This valve has the capability of controlling the junction flow area between two con-trol volumes. The operation of the valve is controlled by two trips; one for opening the valve, and a second for closing the valve. A rate parameter controls the velocity of valve movement, which is the same for opening or closing. The motor control valve can be used in conjunction with a general table. When the general table is specified, the rate parameter controls the valve stem position and the general table relates the stem position to the flow area. When the general table is not specified, both the stem position and flow p area rse cumrolicd by the rate parameter, k The abrupt area change model is used to implement the flow area in the transient calculation. If the nor-malized valve flow area has a value less than 1.0E-10, the valve is asstuned closed. A second option allowed for this valve is the specification of energy loss coefficients. This is specified by the addition of table entries (with the valve component) of Cy versus normalized stem position. The con-- version of Cy to the energy loss coefficient, K, is 2A 2 "" " (301) K=2 C 8 v 0 where po =: density of water at 288.71 K. Provisions exist for multipliers on stem position and Cy. The area of the valve may be varied in the same two ways as in the motor valve without the Cy table. However, the abrupt area change option must be specified as smooth. The stem moves linearly in time, as specified by the rate parameter. 1115 servo veNe-The servo valve operation is similar to that of the motor valve; however, the stem position is moved by the control systems rather than by a specified rate parameter. The servo valve has the
/m same options as the motor valve, that is, Cy table or abrupt area change specified losses, and general table entries for flo'w area versus stem position or the flow area varies directly with stem position.
3.3.4 Reactor Kinetics Numerical Procedures. The reactor kinetics equations are advanced in time using the modified Runge-Kutta method of Cohen.61 A first-order differential equation is written as 105
n(t) = a n(t) + R(n,t) (302) h where a is constant over the time step, and R(n,t) contains the remaining terms of the differential equation, including the nonconstant portion of any coefficient of n(t). If the coefficient of n(t) is #(n,t), a ';.ould be 4[n(0),0], and R(n,t) would contain a term of the torm, IS[n(t), t]- al n(t). Multiplying Equation (302) by an integraths factor and integrating gives i t n'(t) = n(0) eat + fe(t-A)R(n,A)dA. (303) do Since n(0) e*t = n(0) + an(0) ea (t-A)dx, do n(t) = n(0) + [an(0) + R(n,A)]e*( ~*)dl. (304) J Letting A = ut, then dA = tdu, and O 1 n(t) = n(0) + t [an(0) + R(n,u)]e " du. (305)
)o The numerical technique for advancing the solution over the time step consists of making approximations to the behavior of R(n,u) over the time step. For convenience in the following expressions, the following function is defined 1
*-I cm(x) = u e *II-")au. (306)
O stage 1: Assume R(n,X) = R [n(0),0] = oR . and write n(0) aso n ; then compute n h n) =n(h)=ng +h(ang +R)C)(ah). g (307) stage 2: 1 Assume straight line variation of R(n,A) between Ro and Rg, and compute n
= R(ng, , j
a R(n,1) = R g
'+ '2(R) - R-)A. (308) h p
bu R(n,u) = Rg + (R) - Rg )'u- (using1=uf (309) n2*" " "I + (Rj-R)C(a g 2
. (310)
Stege 3: Assume straight-line variation of R(n A) between Ro and R 2=Rfn2, , and compute n(h), R (.n,1) = R g + 2(R2-R)xg (3II) n R(n,u) = R (using A a uh) g + 2(R2-R) (312) g n (313) 3 = n(h) = ng + h(ang +R)C) g (ah) + 2h(R2 - R g) C 2(ah). , stage 4: Assume quadratic through points R o , R2 , and R3 = R(n3, h); then compute n(h), 3 ) u + (- 3Rg+ 4R 2-R)u+R R(n,u) = (2R (314) g - 4R2.+ 2R 3 g. n (315) 4 = n(h) = n3 + h (Rg - 2R 2 + R3 ) [2C3 (ah) - C2 (ah)]. Suge 5: Assume quadratic throughpoints R o , R2 , and R4 = R(n4 h); then comrute n(h), n (316) - 5 = n(h)-= n4 + h (R 4 - R3 ) [2C3 (oh) - C2(ah)]. The third , fourth , and fifth-order approximations are obtained by terminating the process at the end of the third, fourth, and fifth stages, respectively. By direct integration, the function, Cg(x), is given by
~
(317) C)(x) = , 107 J_:_=_____-_-_____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Using integration by parts, a recursion relation for Cm(x) is mC (x) - 1 OI8) Cm +1(*) " x During machine calculations of the Cm(x) functions for x s 1, excessive loss of significance occurs. For this range, C3(x) is computed from its MacClaurin series expansion , l r x x 2 x 3 x 4 x 5 x 6 x 71 C3 (x) = 2 y+g+g+g+g+g+g+y. 1 j M C2and Cg are evaluated by selvmg Equation (318) for Cm(x). During the advancement in time of the solution, the time increment is automatically increased or decreased to maintain a specified degree of ace'tracy. After the calculations for a reactor kinetics time-advancement, an empirical formula is used to estimate the error if the error is excessive, the time incre-ment is halved, and the advancement calculation is redone. If the error is sufficiently small, the time interval is doubled for the next time step. If the estimated error is between limits, the same intervalis used for the next time-advancement. These procedures for time step control, taken from the AIREK62 code, are as follows
= evaluated from Equation (215) w) 0 e(h) (320) *3 = e(h)*
h G is defined from e(h) = 6(0)e I h C2(ah) 0.= i c](,n) (lw)-2;+"3). (321) The a in Equation (321) is that of the power equation. The quantity, 6, is defined as the maximum (taken
. over all differential equations) of the quantity,- The .
"I(" QL and Qg appearing below are 0.0001 and 0.001, respectively.
- 1. If 6 < 2-15 and Q m QL, the program continues with the same time step.
- 2. If 6 < 2-15 and Q < QL, the program doubles the time step for the next advancement.
- 3. If 6 a 2-15 and (a) Q < QL, the time step is doubled for the next advancement (b) Q s QH, the same time step is used for the next advancement (c) Q > QH, the time advancement is recalculated with half the time step.
108 ;
.____________________-______a
h
,- 4. The time advancement is also recomputed with the time step halved if ~4 ; j (a) ah of any equation > 88.0 v
(b) minus or zero power is computed. If the coefficient of the power in Equation (215) is negative, a subtraction is involved in determination of the derivative of power, and a loss of significant figuies can occur.lf this coefficient is negative, a check is made of the number of bits lost in the subtraction. If more than nine bits are lost, the value o. nower com-puted by the current stage of the advancement procedure is discarded; instead, power is determined from the expression obtained by setting the power derivative to zero .
'l SA
{f $ Wj (t) 7 i=1 4(t)
- r(t) - 1 . (322)
The transfer of information between the reactor kinetics calculation and the other RELAPS calculations is explicit. Hydrodynamic and heat conduction / transfer calculations piecede reactor kinetics, and the con-trol system calculation follows reactor kinetics. The reactor power used in hydrodynamics and heat con-duction is the value at the beginning of the time step. The reactivity used as an end-of time step value in the kinetics advancement uses end-of-time step values from hydrodynamics and heat conduction and beginning-of-time step values from the control system. The reactor kinetics equations are advanced at the same time step rate as the hydrodynamics. The max-imum time step for the reactor kinetics is the hydrodynamic time step. That time step is reduced (if
.[p] - necessary) as described above.
l k I r\ k
- 4. REFERENCES
- 1. V. H. Ransom et al., RELAPS/ MODO Code Description, CDAP-TR-057, Idaho National Engineering Laboratory, May 1979.
- 2. M. Ishii, Thermo-Fluid Dynamic Theory of Two-Phase Flow, Direction des Etudes et Recherches d' Electricity de France,1975.
- 3. F. H. Harlow and A. A. Amsden, " Flow of Interpenetrating Matenal Phases," Journal of Computational Physics, 18,1975, pp. 440-464.
- 4. R. T. Lahey, Jr., "RPI Two-Phase Flow Modeling Program," Presented at the Fifth Water Reactor Safety Research Information Meeting, Washington, D.C., November 7-11, 1977.
- 5. P. S. Andersen, P. Astrup, L. Eget, O. Rathman, " Numerical Experience with the Two-Fluid Model RISQUE." Presented at ANS Water Reactor Safety Meeting, July 31-August 4,1977.
- 6. N. Zuber, "On the Dispersed Two-Phase Flow in the Laminar Flow Regime," A merican Institute of Chemical Engineers, 19,1964, pp. 897-917.
- 7. L. Van Wijngaarden " Hydrodynamic Interaction between Gas and Bubbles in Liquid," Journal of Fluid Mechanics, 77, .Part 1,1976, pp. 27-44.
- 8. P. W. Bridgmen, The Thermodynamics ofElectricalPhenomenon in Metaland a Condensed Collec-tion of Thermodynamic Ecemulas, New York: Dover Publications, Inc.,1961.
- 9. G. Houdayer et al., "Modeling of Two-Phase Flow with Thermal and Mechanical Nonequilibrium,"
Presented at the Fifth Water Reactor Safety Research Information Meeting, Washington, D.C., November 7-11, 1977.
- 10. O. C. Jones, Jr. and Pradip Saha, " Volumetric Vapor Generation in Nonequilibrium, Two-Phase Flows," Preparedfor Advanced Code Review Group Meeting of the Water Reactor Safety Research Division, U.S. Nuclear Regulatory Commission, Washington, D.C., June 2,1977.
I1. Thermal Reactor Safety Group, TRAC-P1: An Advanced Best-Estimate Computer Program for < PWR LOCA Analysis. Los Alamos Scientific Laboratory (undated).
- 12. F. E. Marble, "Some Gasdynamic Problems in the Flow of Condensing Vapors," Astronautics Acta,14,1969, pp. 585 593.
- 13. D. Drew, L. Cheng, R. T. Lahey, Jr., "The Analysis of Virtual Mass Effects in Two-Phase Flow,"
International Journal of Multiphase Flow, 5, pp. 233 242.
. i $. K. T. Claxton, J. G. Collier, A.1. Ward, H. T. F. S. Correlationfor Two-Phase Pressure Drop and Void Fraction in Tubes, AERE-R7162,1972. \
- 15. R. A. Nelson, " Forced Convection Post-CHF Heat Transfer and Quenching," ASME 1980 Wimer Annual Meeting, Chicago, Illinois, November 1980, 80-WA/HT-69.
- 16. EG&G Idaho, Inc., RELAP4/ MOD 6: A Computer Program for Transient Thermal-Hydraulic Analysis of Nuclear Reactors and Related Systems, User's Manual, CDAP-TR-003, EG&G Idaho, Inc., Idaho Falls, Idaho, May 1978 (available from the U.S. Nuclear Regulatory Commission Public Document Room in Washington, D.C.).
110
m m 5 ' 1.1
~
[ .17. - R. A. Nelson, "The' Hett Transfer Surface Technique," LOCA Hert Transfer Workshop, Idaho - I T" Falls, Idaho, July 21-22,1975, sponsored by the U.S. Nuclear Regulatory Commission. 'fT 18. R. A. Nelson: and L. H. Sullivan, "RELAP4/ MOD 6 Reflood Heat Transfer and Data V Comparison," CSNI Specialists Meeting on Transient Two-Phase Flow, Paris, France, June 1978.
' 19.- R. A, Nelson and L H. Sullivan, " Blowdown Heat Transfer Surface in RELAP4/ MOD 6 and Data Comparison," ENS /ANS International TopicalMeeting on Nuclear Power Reactor Safety, Brussels, Belgium, October 2,1978, pp.1719-1728.
- 20. T. A. Bjornard, Blowdown Heat Transfer in a Pressurized Water Reactor, Ph.D. Thesis, M.I.T.,
August 1977.
- 21. .T. A. Bjornard and P. Griffith, "PWR Blowdown Heat Transfer," ASME Symposium on the Thermal and Hydraulic Aspects ofNuclear Safety, November 27-December 2,1977,1, pp.17-39.'
- 22. I. Nukiyama, " Maximum and Minimum Values of Heat Transmitted from a Metal to Boiling Water Under Atmospheric Pressure," Journal of the Society of MechanicalEngineers, Japan, 37,'1934.
- 23. F. W. Dittus and L. M. K. Boelter, " Heat Transfer in Automobile Radiators of the Tubular Type,"
Publications in Engineering, Universit) of California, Berkeley, 2,1930 pp. 443-461.
- 24. J. Chen, "A Correlation for Boiling deat Transfer to Saturated Fluids in Convective Flow," Process Design Development, 5,1966 pp. 312-327.
- 25. J. G. Collier, Convection Boiling and Condensation, London: McGraw-Hill Book Company, Inc., .
1972.
- 26. F. Kreith, Principles of Heat Transfer, 3rd edition, Scranton, PA: International Textbook Company,1968.
- 27. Y. Y. Hsu, "A Tentative Correlation for the Regime of Transition Boiling and Film Boiling During Reilood," presented at 3rd Water Reactor Safety Research Information Meeting (USNRC), October -
1973.
- 28. M. L. Pomeranz, " Film Boiling on a Horizontal Tube in Increased Gravity Fields," Journal of Heat Transfer, 86,1964, pp. 213-219.
- 29. L. S. Tong, " Prediction of Departure frem Nucleate Boiling for an Axially Non-Uniform Heat Flux Distribution," Journal of Nuclear Energy, 21,1%7, pp. 241-248.
- 30. Y. Y. Hsu and W. D. Beckner, "A Correlation for the Onset of Transient CHF," cited in L. S. Tong and G. L. Bennett, "NRC Water Reactor Safety Research Program," Nuclear Safety,1B,1, January / February 1977.
- 31. W. M. Rohsenow and H. Choi, Heat, Mass and Momentum Transfer, Englewood Cliffs, NJ:
Prentice-Hall Book Company,1%1.
- 32. R. A. Smith and P. Griffith, "A Simple Model for Estimating Time to CHF in a PWR LOCA,"
Transactions of American Society of Mechanical Engineers, Paper No.16-HT-9 (1976).
- 33. V. H. Ransom and J. A. Trapp, "The RELAP5 Choked Flow Model and Application to a Large L
Scale Flow Test," Proceedings of the ANS/ASME/NRC International Topical Meeting on Nuclear Reactor Thermal-Hydraulics, Saratoga Springs, New York October S-8,1980 pp.199-819. l 111
1
- 34. P. R. Garabedian, Partial Differential Equations, New York: John Wiley and Sons,1964.
- 35. G. B. Whitham, Linear and Nonlinear Waves, New York: John Wiley and Sons,1974.
- 36. ; A. H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow, H, New York: Ronald,1954,
- 37. _ V. H. Ransom and J. A. Trapp, RELAPS Progress Summary Analytic Choking Criterionfor Two.
Phase Flow, COAP-TR-013. EG&G Idaho, Inc.,1978. l 38. R. T. Lahey, Jr., "RPI Two-Phase Flow Modeling Program," Presented at the Fyth Water Reactor Safety Research information Meeting, Washington, D.C., November 7-11, 1977.
- 39. D. Gidaspow (Chairman), "Modeling of Two. Phase Flow," Proceedings ofRound Table Discussion RT-12 at the Fifth International Heat Transfer Conference, Tokyo, Japan, September 3-7,1974, also in ASME Journal of Heat Transfer, 3,1974.
- 40. J. D. Ramshaw and J. A. Trapp, Characteristics, Stability and Short Wave Length Phenomena in Two-Phase Flow Equation Systems. ANCR-1272, Aerojet Nuclear Company,1976.
- 41. N. Abuaf, O. C.1ones, Jr., B. J. C. Wu, Critical Flashing Flow in Noz:les with Subcooled Inlet Conditions, BNL Informal Report, BNL-NUREG-27512,1980.
- 42. M. D. Alamgir and J. H. Lienhard, " Correlation of Pressure Undershoot During Hot Water Depressurization " Preprint Submitted to ASME Journal of Heat Transfer.
- 43. O. C. Jones, Jr., " Flashing Inception in Flowing Liquids," ASME Journal of Heat Transfer 102, O 1980, pp. 439-444,
- 44. J. W. Burnell, " Flow of Boiling Water through Nozzles, Orifices, and Pipes." Engineenng, December 1947, pp. 572-576.
- 45. F. J. Moody, " Maximum Flow Rate of a Single Component, Two-Phase Mixture," Transactions of the the American Society of Mechanical Engineers, February 1963, pp.136-143.
- 46. Y. Taitel and A. E. Dukler, "A Model for Predicting Flow Regime Transactions a Horizontal and Near Horizontal Gas-Liquid Flow," American Institute of Chemical Enginecrs,1976, pp. 47 55.
- 47. J. A. Trapp and V. H. Ransom, RELAPS HydrodynamicModelProgress Summary - Abrupt Area Changer and Paralle/ Branching, PG-R-77-92, EG&G Idaho, Inc., November 1977.
- 48. J. K. Vennard Elementary fluid Mechanics,4th Edition, New York: John Wiley and Sons,1965.
- 49. J. Weismam, T. Ake, R. Knott, "Two-Phase Pressure Drop Across Abrupt Area Changes in Oscillatory Flow," Nuclear Science & Engineering, 61,1976, pp. 297-309.
- 50. J. G. Collier " Advanced Study Institute on Two-Phase Flows and Heat Transfer," Afi Proceedings,1stanbul-Turkey, August 1976.
- 51. M. M. El-Wakil, Nuclear Heat Transport, International Textbook Company,1971.
- 52. B. Harshc, A. Hussain, J. Weisman, Two-Phase Pressure Drop Across Restrictions and Other Abrupt Area Changes, NUREG-0062, University of Cincinnati, April 1976.
__ ___-____ __ - _ _ _ m.
' '.j L.
g , l 3 .J I .53. P. A. Lottes, " Expansion Losses in Two-Phase Flows," Nuclear Science and Energy, 9,1961, 1 pp. 26 31. I V )
'i .
- 54. V. L. Streeter and E. B. Wylie. Hydraulic Transients, New York: McGraw-Hill Book Company Inc.,1%7. 1
- 55. J. P. Holman, Heat Transfer,4th edition New York: McGraw-Hill Book Company, Inc.,1976, g pp. 244-245, 280. i
- 56. R. J. Hanks, "1958 Water Vapor Transfer in Dry Soil," Proceedings of the Soil Science Society, 1958, pp. 22:372 374 e
- 57. ' A. R. Curtis and 3. K. Reid, FORTRAN Subroutinesfor the Solution of Sparse Sets ofLinear Equa-tions, AERE R6844, Atomic Energy Research Establishment,1971.
- 58. R. A. Berry, An Analysis Toolfor Predicting Transient Hydrodynamics in Nuclear Piping Systems Containing Swing Check Valves, RE-A-78-261, Rev. 2, EG&G Idaho, Inc.,1978.
- 59. ; R. S. Sa'mra, " Impact Energy Calculations for a Steam Check Valve following a Posttilated Pipe Rupture," ASME Winter AnnualMeeting, December 1976,76-WA/FE-8.
- 60. - V. K. Chexal and 1. S. Horowitz, Analysis Report: Maximum Energy of Disc impact, Main Steam Check and Isolation Valvesfor Kewanuee Unit, Nuclear Services Corporation Report, PIO-02-03, September 1973.
~
- 61. E. R. Cohen, Some Topics in Reacter Kinetics,15 A/ CONF,1958, p. 629.
- 62. A. Schwartz, Generalized Reactor Kinetics Code AIREK H, NAA-SR-Memo.4980,' 1960.
O 113
NURE3/CR 1826 EGG 2070 Distribution Category: R4 RELAP5/ MOD 1 CODE MANUAL VOLUME 2: USERS GUIDE AND INPUT REQUIREMENTS Richard J. Wagner Kenneth E. Carlson Dennis M. Kiser Victor H. Ransom
/ Han-Hsiung Kuo Hueiming Chow John A. Trapp Stephen W. James Douglas G. Hall Published March 1982 l
EG&G Idaho, Inc. I idaho Falls, Idaho 83415
~
Prepared for the U.S. Nuclear Regulatory Commission O Washington, D.C. 20555 Under DOE Contract No. DE-AC07-761001570 l
1 1 l 1 CONTENTS
]\
- 1. INTRODU CTIO N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 1.1 Contents................................................................. I 1.2 User Training ............... ............................ ..... ........ . I 1
1.3 Differences Between MODO and MODI Versions ... ............................. 2 l i'
- 2. RELATIONSHIP TO PREVIOUS RELAP CODES . ................................. 3
- 3. HYDRODYNAMIC MODELING . . . . . .......... ...... ........................... 5 l
l I 3.1 Concepts of Volumes and J unctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 3.2 Components ............................... ............ ...... ............ 6 ; i 3.2.1 Common Features of Components .... ................ .............. 7 3.2.2 Time-Dependent Volume Component ......... .... . ... . .. ... ..... 11 ; 3.2.3 Time-Dependent Junction Component ............. . . . ... ..... 12
]
3.2.4 Single Volume Component ........ .. .. . ..... . ......... ....... 13 3.2.5 Single-Junction Component ......... ................ . .............. 13 3.2.6 Pipe and Annulus Components .. ........... ..... . .. ... .... ..... 13 3.2.7 Branch Component .............. .... ... ............. ....... . .. 13 3.2.8 Separator Component .... . .. ....... ..... .. ................. 15 3.2.9 Pump Component .. .. . . . ... .... ... ......... . ..... 16 3.2.10 Valve Component . ... . ... . . .... .. . ..... . .. ... 19 3.2.11 Accumulator Component .. . .......... ....... ... ....... . ... 20 3.3 Hydrodynamic Output . .. ... .. .. .. ....... ............. .. . .. . 21
- 4. HEAT STRUCTURE MODELINO . .. . ... ...... . . ... ... .... ... . 28 4.1 Heat St ucture Geometry . . . . . . . .. ...... . .. . .. .. ..... . . 28 4.2 Heat Structure Boundary Conditions .. ... . .... ... . . ..... . ..... .. . 29 4.3 Heat Structure Sources . . . . .. .... . .... . .. ... ... . 32 4.4 Heat Structure Output .. .. ..... . .. .. .. ... . ... ..... . . . 32
- 5. GENERAL TABLES . . . .. . . . . .. .. .. .. . .. .. 33
- 6. TRIPS . .. .. . ... . . .. .. . .. . . .. .. . . . .. . . . 34 6.1 Variable Trips . . . . . . .. . . . 34 6.2 Logical Trips . . . .. . . .. . . . 35 6.3 Trip Execution ... . . . . . . ... ... . 36 6.4 Trip Logic Example . ., . . . . . . 36 ii
F'
, ): ?
. 6.5 Trip Output ................................................................. 38
. . . 7. REACTO R KINETI CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 39 C- e
- f b..,
V :- 8. CONTROL SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . u . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
- 9. P RO BLEM EDITI NO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 9.1- Printed Output .............................................................. 46-9.1.1 Input Editing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ' 46 9.1.2 - M aj or Edi ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 9.1.3 Mino r Edits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 9.1.4 Diagnostic Printout ................................................... 47 9.1.5 FinalTermination .................................................... 47 9.2 Plotted Ou tput . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
- 10. TIME STEP CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
- 11. ' TRANSIENT TERMINATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57.
- 12. PROBLEM TYPES AND OPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
- 13. PROBLEM CHANGES AT RESTART . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
- 14. RELAPS FILE USt.GE ........................................................... 61 14.1 I nput File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ 61 14.2 Output File ................................................................. 61 14.3 RSTINFile ...................... .......................................... 61 14.4 RSTP LT File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 14.4.1 RSTPLT File Written by NEW. RESTART Problems . . . . . . . . . . . . . . . . . . . . . . . 62 14.4.2 RSTPLT File Written by STRIP Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 14.5 PLFILEFile ................................................................ 64 14.6 P LOTFL File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 64 14.7 STH2XT File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 64
- 15. RELAPS CONTROL CARD REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 l
- 16. RELAPS/ MODI TRANSMITTAL INFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 16.1 Selectios of Compile Time Options ............................................. 68 16.2 Transmittal Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 16.3 Installing RELAPS Using the Transmittal Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 1
1 iii w-_____. - _ _ _ _ _ _ _ _ _ -
- 17. RE FE RE N CES . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 APPENDIX A-RELAP5 INPUT DATA REQUIREMENTS ......... ..... ............... 75 APPENDIX B-INPUT DATA REQUIREMENTS FOR PLOTTING . . . . . . . . . . . . . . . . . . . . . . . 161 FIGURES
- 1. Sketch of three volumes and two junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
- 2. Juncion connection example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
- 3. Typical branching junctions ........................................................ 14
- 4. Application of branch volume to horizontal TEE .. ..... ........................... 15
- 5. Application of branch volume to vertical TEE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
- 6. Major edit from Edwards Pipe Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
- 7. Mesh point layout ........... ..... ......... . ..... .................. . . ... 28
- 8. Listing of default reactor kinetics constants ..... . .. . ...... ............ ... ... 40
- 9. Minor edit from Edwards Pipe Problem ..... .. ... ... ....... . . ...... ........ 48
- 10. Pressure plot. Edwards Pipe Problem, gauge Station i . .. ....... ..... .... ....... 49
- 11. Pressure plot, Edwards Pipe Problem, gauge Station 2 . .. .. .. . ... .. .. .. 49
- 12. Pressure plot, Edwards Pipe Problem, gauge Station 3 ... .......... . .. . ..... 50
- 13. Pressure plot, Edwards Pipe Problem. gauge Station 4 . . ... .... ... .. . . ...... 50
- 14. Pressure plot, Edwards Pipe Problem, gauge Station 5 . .. .. ........ .... ,. 51
- 15. Void fraction plot, Edwards Pipe Problem, gauge Station 5 . .. . .. .. .. . .... 51
- 16. Temperature plot, Edwards Pipe Problem, gauge Station 5 .......... .. ..... . .. .. 52
- 17. Pressure plot Edwards Pipe Problem, gauge Station 6 . . . . . . . . . . . . . . .. 52 1
- 18. Pressure plot, Edwards Pipe Problem, gauge Station 7 ... ......... . ... .. . . 53
- 19. CPU time plot, Edwards pipe .... . .. . ......... . ... .. .. . 53
- 20. Vapor generation rate plot, Edwards pipe, Volume 3200000 . .. ..... . 54
- 21. RELAPS control cards for execution of a new problem .. .. . 65
- 22. RELAP5 control cards for execution of a restart problem . . 65 ;
- 23. RELAP5 control cards for program modification / execution . . . . . 66 iv
- 24. . Control cards to build disk files for RELAPS use from transmittal t pe . . . . . . . . . . . . . . . . . . . . 71-TABLES
'~
l : ,.
- 1. Pump Homologous Curve Definitions ..........-....................................... 17
- 2. Logical Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . 35
- 3. Truth Table Examples . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 t.
- 4. Boolean AlgebraIdentities .......................................................... 37 o
V
RELAP5/ MOD 1 CODE MANUAL VOLUME 2: USERS GUIDE AND INPUT REQUIREMENTS g a
- 1. INTRODUCTION !
The purpose of Volume 2 of the RELAP5 docutaentation is to provide sufficient information to allow application of RELAP5 to thermal-hydraulic systems. This volume assumes that the user has some famdiarity with the RELAP5 models described in Volume 1. 1.1 Contents This volume has two principal parts. The first describes the RELAP5 program from the users viewpoint. Each model or feature is di-swi with emphasis on how the user uses the feature to represent a physical 1 system. Input data requirements, user options, and descriptions of available output are included. A description of the programming features of RELAPS has not been prepared, so this volume includes some information regarding required files and use of the program transmittal tape. The second part is a detailed description of the input data requirements and format. This information is maintained as a file of 72 character records and a copy of this file is included on the transmittal tape. This information is formatted by TEXTJAB to I a report form that can be printed on a Cyber printer with an upper / lower case print train. The detailed input description is presented in Appendix A. 1.2 User Training In applying RELAPS to a hydrodynamic system, the components of the system suggest major noding boundaries. System components such as pumps and valves have equivalent RELAP5 components. Upper and lower plenums, inlet annulus, and ECC injection points are modeled by the branch capability. Steam i separators and dryers can be modeled by a separator component. The modeling flexibility of pipe com-ponents and the completely general attachment of heat structure 10 h~drodynamic components allow pipes to model such diverse components as reactor core, d;wncomer, pressurizer, parts of steam generators, and of course interconnecting piping. The question of how many nodes should be used to represent various portions of the system is much more difficult and few definitive guidelines can be stated. For a given system and simulation time span, as the number of volumes and time steps increases, the finite difference approximations approach the original differential equations. An adequate nodahzation is dependent on the system to be modeled and even the particular transicnt to be simulated. As a general rule, volumes should be defined to be approximately the same length. The same idea, expressed negatively, is that a large volume should not be adjacent to a small volume. If a hydrodynamic system is expected to have some parts to experience sluggish behavior and other parts to experience rapid changes, large and small volumes can be used appropriately, but there should be a gradual transition in volume sizes between these parts of the system. l l A users manual can describe the mechanics of using the program. But unfortunately, user experience seems to be the best guide for making effective use of the code. Simulation experience with RELAP4 and RELAPS has shown that detailed study of an experiment is necessary to model it properly. That study, followed by comparisons of simulated results with measured data has led to greater understanding of both the computer program operation and the experimental phenomena. In several instances, increased con-fidence in REL APS has been gained when more accurate modeling of an experiment has led to better (b' agreement with the experiment. 1
Some user experience can be gained by study of sample problems, especially those compared to data. Volume 3 of the RELAP5 documentation describes the application of RELAP5 to several experimental facilities. Application of RELAPS to a new system or even a previously modeled system under significantly different conditions may require a space nodalization study. 1.3 Differences Between MODO and MOD 1 Versions ) i The MODO version had significant and very general modeling capabilities for one-dimensional hydrodynamics and associated one-dimensional heat conduction and heat transfer. Additions and improvements to these capabilities incorporated in MODI include: accumulator, steam separator, and annulus components, noncondensible gas (air), boron tracking, improved vertical flow maps with addi-tional horizontal flow maps, horizontal stratified flow, horizontal break flow, improved break tiow model with semi-implicit numerics, and additional heat transfer correlations for condensing heat transfer, natural circulation, and pool boiling. Motor operated valves and general servo controlled valves have been added to allow trip logic or a control system to control flow rates. Nondimensional(point) reactor kinetics that include gamma decay heat have been added. Power from the reactor kinetics can be used as internal heat sources for fuel pins and direct moderator heating. Reac-tivity feedback from hydrodynamics and heat conduction is provided but the effects of boron on reactivity has not been included. The MODI version has added the first phase implementation of a control system. The control system allows a user to define control variables that are the results of addition, subtraction, multiplication, divi-sion, exponentiation, differentiation, and integration on any of the variables advanced in time, including control variables. The control system design allows simultaneous, nonlinear, algebraic and differential equations to be defined and advanced in time. However, the currently implemented numeric advancement technique limits the full use of this capability. O 2
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- 2. RELATIONSHIP TO PREVIOUS RELAP CODES l I
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As the name implies, RELAPS is the fifth in a series of computer codes designed primarily to simulate the phenomena in a light water reactor loss-of-coolant accident. Each succeeding code has incorporated l the knowledge gained from the extensive research in water reactor safety. Each reflects the increased i knowledge and new simulation requirements from both large and small scale experiments, theoretical l research in two-phase flow, numerical solution techniques, computer programming advances, and the j increasing size and speed of computers. RELAP5 follows the tradition of past RELAP codes; the odd { numbered series are complete rewrites of the program while the even series have extensive model changes 1 but utilize the program structure of the previous code. i The principal feature of RELAPS is the use of a two-fluid, five equation hydrodynamic model for two- ) phase flow. The five equations are a mass conservation equation for each phase, a momentum conserva-tion equation for each phase, and an overall energy conservation equation. The one energy equation is supplemented by the assumption that one of the pheses is at the saturated state. These equations allow a full two-velocity treatment and an adequate treatment of unequal temperature effects. Metastable states are allowed during vaporization and condensation. This advanced model replaces the one-fluid model, : l with slip used in RELAP4. The new model also replaces RELAP4 submodels such as the bubble rise and enthalpy transport models. The new structure of RELAPS has allowed several improvements over RELAP4. Although systems oriented programs such as RELAP require large amounts of input data, considerable reduction of input is achieved through the use of component oriented data. The elimination of the need for strictly consecutive ; numbering of volumes, junctions, and heat slabs has simplified input preparation, expecially when modi- ! fying existing models. The restructuring has allowed subroutine modularity and top down organization so that the coding is easier to follow and extensions to the MODI version can be easily implemented. Dynamic (~~ storage is used for all problem dependent variables and excess memory space is returned during problem V] execution to reduce computer costs. 1 Most of the experience gained with RELAP4 is applicable to RELAPS because both codes use the con- l cepts of volumes and junctions; the pump models are identical; heat conduction equations are identical although the input is different; RELAPS heat transfer is heavily based on RELAP4/ MOD 6 blowdown cor- : relations; and RELAP5 has similar, but increased trip logic capability compared to RELAP4. However, the new hydrodynamic model and the philosophy of its implementation in RELAPS dictate several changes in approach when modeling systems with RELAPS compared to RELAP4. The RELAP3 and RELAP4 codes were originally written for computers with relatively small memories compared to current computers and were restricted in the number of volumes and junctions that could be used. To overcome the inaccuracies resulting from representing a system with a small number of rather large volumes, models such as bubble rise and enthalpy transport were superimposed on the basic hydrodynamic model. In contrast, RELAP5 relies exclusively on the two-fluid model with the possibility of using specialized constitutive relations in different parts of the system. RELAP5 is designed to be primarily a one-dimensional program and at present has only onedimensional volumes. The finite difference approxirua-tions to the conservation equations assume that fluid enters or leaves a one-dimensional volume only at its ends. Thus, when following a mixture level is important or when a large spatial enthalpy gradient occurs such as in the reactor core, a larger number of volumes should be used with RELAPS than with RELAP4. Given a large vertically oriented vessel with several pipes leaving at various elevations, RELAP4 might model such a configuration, with one volume having junctions connected at the different elevation levels. When the vessel contains two-phare fluid with the liquid settling towards the bottom due to gravity, the [d 1 RELAP4 bubble rise model would determine the varying mixtures of liquid and vapor entering the junc-tions. With RELAP5, separate volumes are defined such that the pipes leave at volume ends. The two-velocity model which allus countercurrent flow of liquid and vapor determines mixtures entering the { junctions. 3
r . _ . _ - _ - - - _ _ There are several reasons for the RELAP5 approach. First, the larger memories of current co nputers allow this approach to be implemented. Secondly, the superimposed models, especially the bubble rise model, are not compatible with the two-fluid equations that permit dynamic slip. The enthalpy' transport model is easily rationalized when the reactor is close to its normal operating mode but is less easily ' defended during flow reversals. Finally, the superimposed models are differential equations, and when combined with the basic hydrodynamic equations and the logic to merge them, the RELAP4 hydro-dynamic modelis more complex than the RELAPS model. Careful consideration to storage requirements and coding practices have made it possible for RELAPS with its larger number of volumes and junctions but simpler logic to be more cost effective than RELAP4. i Test problems have demonstrated the superiority of the RELAP5 approach. Tests with vertical pipes ; have shown the capability of the program to compute a sharp liquid / vapor ir.terface to within one volume. Excellent agreements have been achieved with several experiments. In the limited cases where there are comparable RELAP4 and RELAP5 simulations, RELAP5 has required less computer time. The computer time to advance one hydrodynamic volume one time step is very fast, approximately 1.0 ms. A time step control algorithm, based on an estimate of the mass truncation error, selects the time step. A feature in RELAP5, not available in RELAP4, allows a time-advancement with excessive error to be discarded, and the advancement to be redone with smaller time steps. It was stated above that the volumes currently allowed in RELAPS are one-dimensional and flow was assumed to enter or leave a volume only at the ends. A branching capability provides for the merging and splitting of flow paths. Any hydrodynamic system that can be modeled by RELAP4 can also be modeled by RELAPS. Several components of hydrodynamic systems such as tees have multidimensional phenomena. An application technique of the branching capability b presented that allows modeling of these components. O O 4
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- 3. HYDRODYNAMIC MODELING I i
Q v 3.1 Concepts of Volumes and Junctions i When applying RELAPS to a hydrodynamic system, the system must be examined to identify those por- i tions of the systert that must be simulated and the boundaries, if any, of the system beyond which simula- I tion is not needed and at which sufficient information is available to define a properly posed problem (that is, the proper boundary conditions). Some systems (for example a simple closed loop) have no such boun-daries and thus do not require boundary conditions. A closed end of a pipe has the boundary conditions that the phasic velocities are zero at the closed end. In the case of a blowdown into fixed conditions such as i the atmosphere, the backpressure from the atmosphere must be furnished as a boundary condition. For a i fill boundary condition, the pressure, density, and internal energy of the incoming fluid must be furnished as boundary conditions so that the incoming energy and work terms are available. If the fill rate depends on the pressure difference, the pressure from the boundary is needed to compute the flow. If the fill is pumped through a constant displacement pump, an additional boundary condition of specified velocities is needed. RELAPS is organized such that a volume end without any connecting junctions is treated as a closed end. Thus, no special boundary conditions are needed for closed ends of pipes or vessels. This also means that boundary volumes are needed only where fluid can enter or leave the simulated portion of the system. At each of these boundaries, a time-dependent volume must be used to furnish the thermodynamic proper-ties of the fluid at the boundary. Constant or nontime varying conditions are just a special case of time-dependent conditions. When flow is out of the system into the time-dependent volume, only pressure from the time-dependent volume is used, and, in the event of choked flow, not even the pressure is used. For flow from the time-dependent volume into the system, pressure, density, and internal energy are used to compute the convected internal energy and work terms. The phasic velocities of the fluid in the time-(3 dependent volume are needed for spatial acceleration terms and are calculated using the connecting V junction velocities multiplied by the ratio of the junction flow area to the volume flow area. Stagnation boundary conditions are often desired, and these conditions can be approximated by specifying a time-dependent volume with a very large volume flow area relative to the downstream volume flow area. Velocity boundary conditions are defined by time-dependent junctions. These time-dependent junctions are usually used in conjunction with a time-dependent volume to describe a time specified inflow to the system. Even if the time-dependent junction specifies outflow and no information is needed from the downstream conditions, a time-dependent volume is still required because all junctions must connect two volumes. Time-dependent junctions may also connect two system volumes (defined below) to model a situation in which some external control system is forcing a prescribed flow. Caution should be used implementing junction boundary conditions in RELAP5/ MODI. With time-dependent junctions, it is pos-sible to specify a flow between two volumes against the pressure difference. Pump work is implicitly required to maintain such a flow and this work is not included in the calculation. The terminology time-dependent volumes and time-dependent junctions imply that these boundary volumes and junctions are a function of time only. However, fluid conditions at each boundary volume and velocities at each junction can be specified as a function of time or any of the other time-advanced quantities. 4 The physical space over which the hydrodynamic behavior is simulated is divided into system volumes. A system junction is the connection of one volume to another. The word system in system volume and system junction was introduced to distinguish them from time-dependent volumes and tune-dependent junctions used for boundary conditions. In the remainder of this report, system volumes and system junctions are often simply written as volumes and junctions. A staggered spatial mesh is used in deriving the finite-difference approximations to the hydrodynamic equations. Continuity and energy difference equations are finite-difference approximations to the volume a 5
and surface integral terms of these equations over each volume. Momentum difference equations are associated with junctions and are approximated by finite-difference approximations to the line integral of the stream tube form of the momentum equations. The line integral extends over the adjacent halves of the connected volumes. The scalar quantities pressure, static quality, and energy that are the dependent variables of the continuity equations and energy equation are defined at volume centers. That is, they are volume average quantities. Density is a scalar quantity that is derived from the pressure, static quality, and energy through the equation of state and is thus also defined at the cell center. The vector quantities, liquid and vapor velocities that are the dependent variables for the momentum equations, are defined at cell boundaries (that is, junctions). The volume oriented difference equations require the convected scalar quantities mass and internal energy to be defined at the junctions. The current upstream (donor cell) volume quantities are used for these junction quantities. Likewise, liquid and vapor velocities need to be defined at volume centers. These vector quantities are calculated from averaged junction velocities. (Detailed descriptions of the two-fluid hydrodynamic equations and their finite-difference approximations are given in Volume 1.) In one-dimensional components, only the algebraic sign is needed to indicate the direction of vector quantities. Each volume and junction has an assigned coordinate direction to which the vector quantities are related. The volume input specifies both the coordinate direction and the volume orientation; that is, vertical, horizontal, or slanted. The ends of one-dimensional volumes are designated as inlet (i) and outlet (o), consistent with the coordinate direction. The junction specifications include both the volumes being connected and which ends are being joined. A sketch of three volumes and the two junctions connecting them are shown in Figure 1. The arrows on the top and bottom of the volumes show volume coordinate directions. The arrows at the volume inter-faces show junction coordinate directions. The user will normally align volume and junction coordinate directions in a systematic manner to facilitate input preparation and output interpretation. Usually adja-cent volumes and connecting junctions will be aligned, but as shown in Figure 1, that is not necessary and in some realistic situations, uniform alignment is impossible. The different results obtained by changing one end specification at a junction are shown in Figure 2. The two volumes in each part of Figure 2 are vertically oriented volumes. Part a of Figure 2 shows the two volumes unconnected. Part b shows the result when the outlet of Volume 1 is joined to the inlet of Volume 2. Part c shows the result when the inlet of Volume 1 is connected to the inlet of Volume 2. The program design and coding have been tested to ensure that if coordinate directions are reversed, but the physical problem remains unchanged, the only differences in results are reversals in signs of the vector quantities associated with the changed coordinates. 3,2 Components The basic two-fluid model is applied in a uniform manner to all volumes and junctions. Thus, the pro-gramming design of the hydrodynamic calculation is primarily organized on volumes and junctions. Components are organized collections of volumes and junctions and, to a lesser extent, the program is organized on components. Components are designed for either inpu'. convenience or to specify additional i = ? e 4 i ? O eT I Figure 1. Sketch of three volumes and two junctions. 6
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b b b h 2 1 1 2
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a b c Figure 2. Jimetion connection example, j specialized processing. A pipe component is an example of a component designed for input convenience, ) since by taking advantage of typical features of a pipe, several volumes and junctions can be described with { little more data than for one volume. Pump and valve components are examples of components requiring l additional processing. A pump component includes data defining pump head and torque characteristics for single-phase and two-phase conditions as a function of pump angular velocity. A pump component requires additional processing to advance the differential equation defining pump angular velocity. A valve component requires additional data defining its characteristics and additional processing to calculate the junction flow area as a function of valve position. Components are numbered with a three-digit number,001-999. Components need not be in strictly con-secutive order so that changes to a model of a hydrodynamic system requiring addition or deletion of com-ponents are easily made. Volumes and junctions within a component are numbered by appending a six (Q/ digit number to the component number, cecxxyyzz. The ccc is the component number. The xxyyzz format is used to permit a geometric structure to volume and junction numbering of multidimensional com- i ponents if these are added to RELAPS in some future version. At present, yyzz are zeros and xx is numbered consecutively starting at 01 for the volumes and junctions in the one-dimensional components presently defined. 3.2.1 Common Features of Components. Each volume flow area, length, and volume must be sup-plied as input. As noted previously, each one-dimensional volume has a coordinate direction along which fluid flows in a positive or negative direction. The volume flow area is the volume cross-sectional area perpendicular to the coordinate direction. The volume length is the length along the coordinate direction. The hydrodynamic numerical techniques require that the volume be equal to the volume flow area times the length. This requirement is easily satisfied for constant area volumes, but poses difficulties for irregularly shaped volumes. It is very important that a systems code such as RELAP5 conserves mass and energy, with momentum being an important but lesser consideration, it is recommended that an accurate volume be used; that the volume flow area be the cross sectional area averaged over the actual length of the volume; and the volume length be the quotient of the volume and the flow area. The component input routines permit the volume, flow area, and length of each vc'ume to be entered as three nonzero positive numbers or two nonzero positive numbers and a zero. If three nonzero quantities are entered, the volume must equal the flow area times length within a relative error of 0.000001. If one quantity is zero, that quantity is computed from the other two. The volume horizontal angle specifies the orientation of the volume in the horizontal plane. The code numerics have no requirement for this quantity and it was entered so a graphics package could be i developed to show isometric views of the system as an aid in model checking. Such a graphics package is not included in the MODI version. The horizontal angle is checked to verify that its absolute value is less ( V) than or equal to 360 degrees, but no further use is made of the quantity. 7 l L
J l l l The volume vertical angle specifies the vertical orientation of the volume. This quantity would also be ; used in the graphics package and in addition specifies the vertical orientation of the volume coordinate I direction. The vertical angle must be within the range 90 to -90 degrees. The angle 0 degrees means the ver- . tical coordinate direction is in the horizontal plane; a positive angle is directed upward; and a negative angle is directed downward. Slanted vertical orientation, such as an angle equal to 45 degrees, is permitted. The coordinate direction implies the position of the inlet and outlet ends of the volurae. The terms inlet and outlet are convenient mnemonics relative to the coordinate direction, but do not riecessarily have any relation to the fluid flow. The direction of fluid flow is indicated by the sign of the velocity relative to the l coordinate direction. For input convenience or ease in output interpretation, the coorceate direction should be an easily remembered direction such as the normal flow direction as opposed to the Gows in an accident situation. As noted in the discussion of Figure 2, and described further bebw, a junction connects a specified end of one volume to the specified end of another volume. This,in turn, establishes relative positioning of the j volumes. Because of gravity heads, the relative position is important to any volume with a nonzero vertical component of the volume coordinate direction (vertical angle is nonzero). If the coordinate direction in a volume with a vertical component is reversed but no other changes are made, the inlet and outlet ends of the volume are also reversed. The physical problem is changed since the relative vertical positions of the volumes are changed. If appropriate changes are made to junctions connecting the reversed volume, such that the physical problem remains unchanged, the only change in the problem results would be a reversal in , sign of the vector quantities associated with the volume. Furthermore, given a stack of vertically oriented l volumes, the proper gravity head is computed whether the direction coordinates are all upward, all j downward, or any random distribution. This assumes that junction connections are such that a vertical stack is specified. As shown on Figure 2, a change in junction specification can change the relative position of two volumes frun two, verticall*f-stacked volumes to a U-tube configuration. Input for a volume includes the elevation change in a volume. For a straight pipe, the elevation change (f) is related to the volume length (t) and the vertical angle (a) by ! C=1 sin a. (1) 1 Note that the elevation change has the same sign as the vertical angle. To allow for irregularly shaped and j curved volumes, the input elevation change is used for gravity head calculations. Input checks are limited to: the magnitude of the elevation change must be equal to or less than the volume length; the elevation change must be zero if the vertical angle is zero; and the elevation change must be nonzero and have the I same sign as the vertical angle if the vertical angle is nonzero. The volume input does not need the elevation l height of a volume relative to an arbitrary base. The elevation change data performs the same function in j determining gravity heads. j If the hydrodynamic system has one or more loops, the user must insure that the sum of the elevation , i changes of the volumes in each loop is zero. A loop is any hydrodynamic flow path starting at a volume, passing through one or more other volumes, and returning to the starting volume. The elevation for any ) volume in which the loop flow path enters and leaves the same end should not be included in the sum. If the net elevation change in a loop is not zero, an incorrect gravity head exists; this is comparable to having an l i l undesired pump in the loop. This error is not checked by the program; detection of this error may be added l in a later version. The horizontal flow regime map is used rather than the vertical flow regime map when the angle deter-
.nined from the ratio of r/t is less than 15 degrees. Horizontal flow calculations include a horizontal stratified flow capability and a horizontal break flow model.
'Vall friction effects are computed from pipe roughness and hydraulic diameter data entered for each volume. If the input hydraulic diameter (DH) is zero, it is computed from the volume flow area (Ayh 8
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A y=3Df/4. (2) j q j -V A check is made that the pipe roughness is less than half the hydraulic diameter. l t Most volumes allow two control flags. One flag determines whether wall friction from the volume is to be included or neglected. The other flag controls whether a nonequilibrium (two phases permitted to have s unequal temperature) or an equilibrium (two phases forced to have equal temperatures) equation of state is used. Generally it is recommended that wall friction be computed and that the nonequilibrium equation of state be used. System volumes require initial thermodynamic state conditions, and time-dependent volumes require state condition as a function of time or a time-advanced quantity. Seven options, numbered 0 through 6, are available to specify state conditions. Options 3 through 3 specify water-only conditions and do not allow a noncondensible ga.s. Option 0 requires pressure, internal energy, and static quality, and the none-quilibrium or equilibrium equation of state is used depending on the volume flags. If equilibrium condi-tions are used, the static quality is set equal to the equilibrium quality determined from the pressure and internal energy; thus, any valid number (such as 0) may be ettered for the static quality. Options I and 2 always specify saturation conditions; Option I requires saturation temperature and equilibrium quality; Option 2 requires saturation pressure and equilibrium quality. Two phases are present if the quality is neither 0 nor 1. Option 3 always specifies single-phase conditions and reouires pressure and temperature. Options 1 through 3 can only specify equilibrium conditions even if the nonequilibrium equation of state is requested. The next three options can specify the presence of a noncondensible gas. Option 4 requires pressure, temperature, and void fraction. Equilibrium conditions are assumed and the vapor consists of air and water vapor at 100% hum:dity. If the temperature is greater than the saturation temperature, it is reset to the saturation temperature and the air fraction is set to zero. This option with a zero air fraction is g similar to Option 2, except a void f: action is specified instead of quality. Option 5 requires pressure, vapor (N temperature, void fraction, and liquid temperature. Nonequilibrium conditions are assumed. The liquid temperature must be less than the vapor temperature and the calculated quality of the water must be less than 0.5. Option 6 requires pressure, vapor temperature, void fraction, and air pressure. Nonequilibrium conditions are assumed. The calculated quality of the water must be greater than 0.5. If the air pressure is entered as zero, the vapor temperature is ignored and sa:urated conditions are calculated. For Options 0 through 6, the boron concentration is assumed to be zero. If 10 is added to the above option numbers, a boron concentration is required. Boron is assumed to be only present in and to be con-vected by liquid water. If a volume with liquid and boron has the liquid water removed by convection, the boron is also removed. If the liquid water is evaporated, the boron remains. This is analogous to boron ! precipitating out as water is evaporated. Infinite solubility of boron in water is tasumed and boron remains in solution regardless of its concentration until all of the liquid water dhappears. Boron is instantly redissolved the instant the quality becomes less than 1. Boron concentrations are computed using only a boron continuity equation for each volume. Boron is { I assumed to have no momentum, no internal energy, and to have no effect on the equation of state. Junctions connect two volumes by specifying a connection code for each volume. The connection code specifies both the volume and a specific face of the volume. With the one-dimensional components now svailable, the connection code is simply ccmm00, where ecc is the component number and xx is 00 for the inlet end of a component and 01 for the outlet end. Except for a pipe component, current components have only one volume and a component reference is essentially a volume reference. The nature of a pipe is such that connections can be made only to the inlet of the first volume and the outlet of the last volume. The pipe connection code permits the number of volumes in a pipe to be changed without changing the connec-(s tion codes in junction references to the pipe. The connection codes for each component type are described ( in the beginning of the input description for that component. 9
The junction coordinate direction is from one volume end to another volume end and the input descrip-tions use the words, FROM and TO, to identify the connections. If a junction is reversed, the sign of the vector quantities associated with the junction are reversed. To maintain the same physical problem, no fur- - ther changes are needed in other components. The initial velocities in reversed system junctions or time-dependent velocities in time-dependent junctions should also be reversed. A volume end without connecting junctions is considered a closed end. Except for branch components, l only one junction may connect to a volume end. This restriction is not required by program logic, but is i imposed to detect unintended connections. Two quantities, the junction area, and the junction area ratio, are defined from the user-supplied junc-tion area. Junctions can connect two volumes with possibly different volume flow areas and the junction can also ha"e a different flow area. Two options are provided for calculating area change effects as the fluid flows through the upstream volume flow area, the junction flow area, and the downstream volume flow area. The smooth area change option uses only the stream tube form of the momentum equation that includes j spatial acceleration and wall friction terms. This option should be used when there are no area changes or 1 when the area changes are smooth such as in a venturi. There are no restrictions on the user-supplied junc. l tion area for smooth area changes and the junction area may be smaller than, larger than, or between the adjacent volume flow areas. The junction flow area is set to the user-supplied flow area and the junction area ratio is set to 1.0. The abrupt area change option provides for additionallosses due to abrupt expansions, abrupt contrac-tions, orifices, and vena-contracta effects. The user-supplied junction area must be equal to or less than the minimum of the adjacent volume areas for an abrupt area change. The junction area is set to the minimu.n of the adjacent volume flow areas and the junction area ratio is set to the ratio of the user-supplied junc-tion area to the minimum of the adjacent volume flow areas. When the user-supplied flow area equals the minimum of the volume flow areas, the junction area ratio is 1.0 and the junction is a contraction / expansion. Program logic tests flow direction and an expansion with flow in one direction is treated as a j contraction when flow reverses, and vice versa. If the user-supplied junction area is less than the minimum i volume area, an orifice is indicated and the junction area ratio is less than one. Specifying the abrupt area change option when there is no area change gives the same result as specifying the smooth area change option but slightly more computer time is required. Valve junctions using either area change option vary the junction area ratio as the valve opens and closes. Junction velocities are in relation to the junction flow area. Thus, the flow rate of a phase is the product of the appropriate junction void fraction, the junction density (donored quantities), the junction velocity, and the junction flow area. For orifices and valves, the actual flow velocity is higher at the minimum area ; which is the junction area multiplied by the junction area ratio. The junction area ratio is used to compute j the velocity at the minimum area when needed, such as in the choked flow model. For user convenience, if the user-supplied junction area is zero, it is set to the minimum of the adjacent volume areas regardless of the area change option. This is the proper default value for most junctions and only smooth area changes (where there is an area change) and orifices need nonzero user supplied junction areas. Junction loss coefficients can be entered when additionallosses above the wall friction and area change , losses are needed. These losses could arise from pipe bends, irregularly shaped volumes, entrance or exit j losses, or internal obstructions. Two coefficients are entered, one for forward (positive) flow, the other for l reverse (negative) flow. The coefficients are applied to the junction dynamic pressure. Zero coefficients l mean no additional losses are computed. l 1 I 10 l J
l Four control flags are associated with junctions. The first controls application of the choking model. It 1 is recommended that the choking model be applied to all system junctions. This would include internal junctions (those between system volumes) and external junctions (those connecting to a time-dependent f} G, volume). The hydrodynamic equations have the inherent capability to model the choking phenomena but quite detailed noding compared to that needed for the other hydrodynamic behavior is required to accurately compute the choking conditions. Some computing time can be saved if the choking calculation is bypassed for junctions that are judged never to have choked flow based on the geometry of the problem ) or other considerations. { i I The second flag is for the area change option which has already been MM The third flag controls the type of momentum treatmcht, two velocity, drift flux, or one velocity models. I The two velocity model is recommended and most program testing has been done with that model. The other two options were included to allow comparisons to codes only having those models, and to assess the model changes as' the more advanced two-phase treatments are applied. The drift flux option was never j tested in MODO and has not been maintained in MODI. Input processing still permits selection of this ; option but its use can lead to unpredictable results. j i The fourth flag controls whether the inertia terms are to be used or a pseudo steady state approximation is to be used. The pseudo steady state option sets the time derivative term of the momentum equation to zero. In the development of the numerical approximations to the momentum equations, after the space derivatives have been replaced by finite differences but before the time derivatives have been replaced, the inertia form is a differential equation and the pseudo steady state form is an algebraic equation. The same linearized time-advancement scheme is used for both equations. For the algebraic equations, the advance-ment is similar to one iteration of a Newton Raphson technique for nonlinear equations. For an acceptable advancement of algebraic equations, the initial conditions must satisfy the algebraic equations. During the time advancement, the time step control algorithm should lead to small enough variations that the one (q') iteration can maintain acceptable solutions. The pseudo steady state option has had little testing and the inertia form is recommended. The pseudo steady state option might be used where a few junctions have much faster time constants than the remaining system or when a transient is being run to obtain steady state values. System junctions require initial velocities and time-dependent junctions require velocities as a function of time. Two options are available to specify the velocities. One option requires the velocities; the other requires mass flow rates from which the velocities are computed. If the flow is single-phase, the velocity of the missing phase is set to that of the flowing phase. This matches the transient calculation that computes equal phasic velocities when one phase is missing. The velocity conditions also require an interface velo-city. This input is for future capability involving moving volume interfaces. For now, the interface velocity must be set to zero. 3.2.2 Time-Dependent Volume Component. A time-dependent volume must be used wherever fluid can enter or leave the system being simulated. The geometry data required is similar to system volumes but during input processing, the volume's length, elevation change, and volume are set to zero. With the stag-gered mesh, the pressure boundary would be applied in the center of the time-dependent volume. Setting these quantities to zero moves the boundary to the edge of the system volume. The state conditions as a function of time or some time advanced quantity are entered as a table, with time or the time-advanced quantity as the independent or search variable. The table must be ordered in increasing values of the search varisble and each succeeding value of the search variable must be equal to or greater than the preceding value. Linear interpolation is used if the search argument lies between search variable entries. End point values an ased if the search argument lies outside the search variable entries. If constant state values are desired, only one set of data consisting of any search value and the associated con-O stant data need be entered. The program recognizes when only one set of data is entered and computer time is saved, since the equation of state is evaluated only once rather than every time-advancement. Step changes can be accommodated by entering two adjacent sets of data with the same time or an extremely small time difference. 11
i The default search argument is time. If no trip number is entered, or if the trip number is zero, the cur- i rent advancement time is used as the search argument. When a nonzero trip number is entered, a unit step , function based on the time the trip was last set is applied. If the trip is false, the search argument is 1.0. ) Wh;n the trip is true, the search argument is the current advancement time minus the last time the trip was set. Thus, the search argument is always -1.0 when the trip is false and can range between zero and the problem time when the trip is true. A time-dependent volume could have some constant condition when the trip is false, then when the trip is true, follow a prescribed function of time where the time origin is the time of the trip not the start of the transient. Through an input option, nearly any time-advanced quantity can be specified as the search argument. The allowed quantities are listed in the input description. The search variables in the table are assumed to have the same units as the search argument and table lookup, interpolation, and treatment of out of range arguments are identical to that described for the default time argument. However, handling of trips is dif- ; ferent. If the trip number is zero, the current value of the specified time-advanced variable is used. If the trip number is nonzero, the time delay cannot be applied as for the default time case, since the search argu-ment may not be time. Thus, if the trip is false, the search argument is -1.0E99; if the trip is true, the cur-rent value of tiie specified variable is the search argument. When time is the search argument, the current value is the value at the end of.the time step; for any other variable, the current value is the value at the beginning of the time step. Time is the default search argu-ment, but time can also be specified as the search argument thrcugh the input option of naming a time-advanced variable. These two uses of time as the search argument are different if a trip is used, since the default method can apply a time delay and the other cannot. 3.2.3 Time-Dependent Junction Component. Time-dependent junctions can be used whenever the phasic velocities or phasic mass flow rates are known as a function of time or other time-advanced quan-tity. Time-dependent junctions en connect any two system volumes or a system volume and a time-dependent volume. Phasic mass fk v rates are converted to phasic velocities using the upstream phasic densities. Examples of their use would be to model a constant displacement pump in a fill system, a pump or a valve or both, with an associated control system, or measured experimental data. Time-dependent junctions are also used frequently in test problems to check code operation. The phasic velocities or mass flows in the time-dependent junction as a function of time or the time-advanced quantity are entered as a table, with time or the time-advanced quantity as the independent or search variable. The requirements, interpolation, and trip logic are identical to that for time-dependent volumes. The capability of using time-advanced quantities as search arguments can be used to model pressure-dependent water injection systems. If the injection flow is a function of the pressure at the injection point, the volume pressure at that point is used as the search argument. A trip is defined to be true when the injec-tion system is actuated. One entry of table data with a negative pressure and zero flows causes the flow to be zero when the trip is false. The remaining table entries define the injection flow as a function of positive pressures. The source of injection water is a time-dependent volume. The pressure of the water supplied by the time-dependent volume could also be a function of the pressure at the injection volume to represent the work of pumping the water into the system. If the injection flow is a function of a pressure difference, the pressure difference can be defined by a control system variable, and that control variable is then defined as the search argument. Some uses of time-dependent junctions can cause modeling difficulties. When using a time-dependent < I junction to specify flow from a time-dependent volume into the system, the incoming phasic densities, void fractions, phasic velocitics, phasic mass flow, and energy input can be specified. But when using a time-dependent junction to specify flow out of a system, the densities, void fractions, and energy of the fluid leeving the system are not known in advance. Thus, use of time-dependent junctions to control outflow is not recommended. The following is one example of a modeling problem. The user anticipates that a i l l
1
. v lume will c:ntain enly vapor and accordingly sets a time-dependent junction to a ntnzers vapor flow l and zero liquid flow. If he anticipated incorrectly and liquid condenses or is carried into the volume, the :
liquid will accumulate unrealistically since it cannot leave the system. l In a simple pipe modeling application, a time-dependent volume and junction can be used to specify the inlet flow. Likewise, a time-dependent volume and junction can model the feedwater flow into a reactor steam generator. Controlling the fluid flow out of the pipe or controlling the water / steam flow out of the steam generator through a time-dependent junction is not recommended. If a system junction (flows com-puted by the simulation rather than specified as boundary conditions) connected to a time-dependent volume is not sufficient, perhaps a servo valve can provide the required simulation. 3.2.4 Single. Volume Component. A single-volume component is simply one system volume. A single volume can also be described as a pipe component containing only one volume. This single volume compo-nent uses fewer input cards and fewer data items than a pipe component. However, if the single volume might be divided into several volumes for nodahntion studies, the pipe component is suggested, since such changes are quite easy for pipes (especially with interactive termmals and a text editor). 3.2.5 Single-Junction Component. A single-junction component is simply one system junction. It is used to connect other components sut as two pipes. Initial junction conditions can be phasic velocities or phasic mass flow rates. 3.2.6 Pipe and Annulus Components. A pipe or an annulus corponent is a series of volumes and interior junctions, the number of junctions being one less than the number of volumes, and the junctions connect the outlet of one volume to the inlet of the next volume. An annulus is identical to a pipe compo-nent except the annulus component uses a modified flow regime map more appropriate for an annular flow passage (=h as the downcomer in a reactor). Pipe components can be used for those portions of the system without branches. Pipe components offer input conveniences, since most characteristics of the p) 1 volumes and junctions in a pipe are similar or change infrequently along the pipe, and input data requirements can be. reduced accordingly. Because of the sequential connection of the volumes, junctions - l are generated automatically rather than being individually described. Although the input is designed to assume considerable similarity in volume and junction characteristics, any of the volume and junction features (such as flow area, orientation, pipe roughness, or control flags) can be changed at each volume or junction. 3.2.7 Branch Component. Branch components are provided to modelinterconnected piping networks. The branching modelis based on one-dimensional fluid flow which is adequate for most cases of branching and merging flow. Such situations include wyes, parallel flow paths from upper and lower plenums, jet - pump mixing sections, and any branch from a vessel of large cross section. For branching situations where phase separation effects due to momentum or gravity are important, an approximate mapping technique can be used to map the two-dunensional rituation onto the one-dimensional space of the fluid model. A branch component consists of one system volume and zero to nine junctions. The limit of nine junc-tions is due to a card numbering constraint. Junctions from other components, such as single junction, pump, other branch, or even time-dependent junction components, may be connected to the branch com-ponent. The results are identical whether junctions are attached to the branch volume as part of the branch component or in other componcats. Use of junctions connected to the branch but defined in other com-ponents is required in the case of pump and valve components and may also be used to attach more than the maxunum of nine junctions that can be described in the branch component input. 127.7 oneolmwwone/ armacung-Figure 3 shows a typical one-dimensional branch. The figure is only one example and implies merging flow. Additional junctions could be attached to both ends and any of the volume and junction coordinate directions can be changed. The actual flows may be in any direction, and f thus, flow out of V3 through J3 and into V 3through J 2is permitted. t 13
J l
,_ g ,
% 3 A ~
e > j l ,V 3 % 1
~ '
~
f bIf V1
-[._: - -, . .
da y g 3 V 3 - a4
- d i l x(Vg)V3 A
j2,V3 , e
% /
, _ {,"
Figure 3. Typical branching junctions. The volume velocities are the arithmetic average of the volumetric flux weighted and junction flow area normalized inlet and outlet velocities. The volume velocity for V3 is used to evaluate the momentum flux terms for all junctions connected to V 3. The losses associated with inlet and outlet junctions are calculated using the assumption that the fraction of the branch volume flow area that is associated with a junction is in direct proportion to the volumetric flow at the particular junction. It is assumed that each junction flow expands or contracts from the junction flow area to the apportioned volume flow area. Using the junction flow area, the adjacent volume flow areas, and the apportioned branch volume flow area, the stream tube form of the momentum equation is applied to each junction. Abrupt area or smooth area change options may be specified at each junction. The present branching model does not include momentum exchange terms associated with mixing. These terms can be significant when streams having either large pressure or velocity differences or both are merged such as in a jet pump. These terms are being developed and their inclusion is planned for future versions of the code. The processing described above is applied to all volumes and junctions. The processing for a nonbranch volume with at most one junction at each end is just a special case of the above processing. n.n Two-oimension / srenching- The physical process occurring at a 90 degree tee is mapped onto the one-dimensional space by an application technique which approximates the two-dimensional momentum effects in the tee. The term, application technique, is stressed because there is no special flagging of a branch component as a tee and the desired two-dimensional effects are obtained using the same algorithms used for one-dimensional branches. The orientation of the volumes used in the mapping and their intercon-nections are shown in Figure 4 for a tee in which the flow in the through direction, that is , V i o t V3 is more important or predominate over the branch flow, iV to V 2 or V3to V .2 Any of the volume and junc. tion coordinates may be reversed. In the case of a tee where the through volumes have the same cross sec-tions, the volumes Vi and V 3and the junction Jg have the same flow area. The branch junctions, J2 and J3should have a flow area equal to one-half the flow area of V 2. This mapping has the effect that the momentum associated wM volume V 2 si divided between volumes Vg and V3 but with opposite signs. Thus, the momenLm treatment approximates the two dimensional situation at the tee wherein the branch leg sees a closed passage and the flow must turn to enter the through-flow passage. As in the one-dimensional branch, either the smooth or abrupt area change option can be selected at any or all of the junctions. This modeling technique also provides the two-dimensional effect which occurs when a body force acts in the direction of volumes V i and V3 . If the tee is rotated so that volume V i or V3is below the horizontal plane through volume V 2, a gravity head is present and the liquio has a tendency to drain from the tee. The technique in Figure 4 has been used in reactor simulations for the connection of the pressurizer surge pipe and the ECC injection pipes to the coolant piping. 14 L__- __-__--_ _
r V3 J V3
,3 p .
p d J2~ J3
~ ~ ~ '
Through path V2 1 Branch path INEL A.16 780 Figure 4. Application of branch volume to horizontal TEE. In tee situations where the predominant flow is in the branch direction, the configuration shown in Figure 5 can he used. Here the coordinate directions of the branch volumes 2V and V4 are aligned with the branch flow d ection and two junctions are connected to the opposite branch volumes and to each of the volumes along the through path (V2and V h3 This usapping has been used to model the inlet annulus and the connections to the cold legs and the downcomer in a reactor syrtem. In this case, the downcomer is the branch leg. To allow tee modeling, an exception to the input restriction that only branch volumes may have more than one junction connection to an end is allowed. Two junctions may attach to a volume end if the two junctions connect to the opposite ends of a branch component. The two-dimensional branching technique should be used with caution because it has been found that t under two-phase conditions, a strong recirculation can be calculated to exist and this has a significant effect on the results. The effect is nonphysical and is believed to be caused by the omission of the momen-tum mixing terms at branch points. The two-dimensional mapping technique should only be used whe;e one-dimensional branching is not a reasonable and consistent approximation. 3.2.8 Separator Component. A separator component implements a very prelimmary model of steam separator / dryers. The model is simply that the junction representing the steam exit from the separator V2 1 r V1 J{l2 V3 co 4 - C J3---- J 4 J 5 co path I V4 , 7 l I 0 Branch path INEL.A 16 778 { Firtre 5. Application of branch volume to vertice' TEE. 15
volume is restricted to passing only steam unless the separator volume is completely flooded with liquid. The steam-only restriction is imposed only for fiow out of the separator. For flow in the steam exit line into the separator, the convected quantities are those of the current upstream volume. The input requirements for a separator are identical to a branch component except that at least one junc-tion must be described by the component. The first junction of the separator component is assumed to be the steam exit. The volume coordinate direction should be vertical and directed upwards. In typical use, two other junctions are attached to the separator volume. One represents the fluid entering the separator; the other is the fluid rejected by the separator. No special treatment is given these other junctions. This model is preliminary in that 100% separation of steam is assumed. However, the model allows reverse and positive normal flow in all junctions and steam can be carried out with the liquid rejected from the separator. 3.2.9 Pump Component. A pump volume consists of one volume and two associated junctions. The coordinate directions of the junctions are aligned with the coordinate direction of the volume. One junc-tion is connected to the inlet and is called the suction junction; the other junction is attached to the outlet and is called the discharge junction. The pump head, torque, and angular velocity are computed from volume-oriented quantities. The head developed by the pump is divided equally to the suction and discharge junctions and is treated like a body force in the momentum equations for each junction. The interaction of the pump and fluid is described by empirically developed curv s relating the head and torque response of the pump to the volumetric flow and pump angular velocity. Pump characteristic curves, frequently referred to as four quadrant curves, present the information in terms of actual head, torque, volumetric flow, and angular velocity. This data is generally available from pump manufacturers. The four quadrant curves can be couverted to a more condensed form called homologous curves which use dimensionless quantities. The dimensionless quantities involve the angular velocity ratio, volumetric flow ratio, head ratio, and torque ratio, where the ratios are actual values to rated values. The rated values are required pump component input. A pump component uses the homologous form of pump characteristics. The curves are entered in tabular form and the dependent variable is obtained as a function of the indepen-dent variable by table search and linear interpolation. Table ! Iists the definition of the homologous curves. There are 16 curves, eight each for head and torque. The independent variable is either the ratio of the angular velocity ratio to the volumetric flow ratio or its reciprocal such that the magnitude of the independent variable is less than or equal to one. The definition of the dependent variable is related to that of the independent variable, that is, the denominator of the independent variable appears in the denominator of the dependent variable. There are twc curves for each of the four quadrants. The quadrants are named under tne regime mode heading. T he two curs es for each quadrant relate to the form of the dependent variable. The curve identification i; HXY, where X is set equal to A or V depending whether the angular velocity rat ~, alpha, or the volumetric flow is the numerator of the independent variable, and Y is defined by the underlined letter in the regime mode name. The regime number is required as part of homologous curve input data to indicate the regime. Not all the regimes need be described by the input, but a problem is terminated if an empty table is referenced. The homologous curves are ceveloped for single-phase conditions. In two-phase conditions, the single-phase tables are evaluated using the two-phase conditions. To better model cavitation or two-phase degradation effects on pump response, two additional sets of data may optionally be entered. One set of data are homologous curves of two-phase difference data. The independent quantities are the same as for the single-phase homologous curves, but the dependent data are the fully degraded two-phase value minus l the single-phase value. The second set of data are difference multipliers as a function of pump volume void ! fraction. The head ant' torque values are given by the single phase homologous value minus the product of the difference multiplier r.d the two-phase difference homologous value. ; The sign conventions of various pump quantities are as follows: a pump operating in the normal pump regime has a positive angular velocity; the volumetric flow is positive if in the same direction as the volume's coordinate direction; the head is positive if it would accelerate the flow in the volume coordinate 16
i- ,4 i Toble 1. Pump homologous curve definitions Dependent [ Variable Regime. Regime Mode Independent
'a v/s Variable Torque f
Number ID Name v Head-E 1 HAN Normal >0 20 il v/= h/m2 gf,2-2 HVN Pump >0 - 20 >l a/v h/v2 gfy2' 3 HAD Energy >0 <0 2 -1 v/s h/,2 ala2 4 HVD- D_issipation >0 <0 < -1 a/v h/v2 gjy2 5 HAT Normal 10 <D _ 11 v/a h/m2 gf,2 6- HVT Turbine 10 10 >l a/v h/v2 g/y2~ 7 HAR 50 >0 2 -1 v/m h/m2 gf,2 R_everse 8 HVR Pump '50 >0 < -1 a/v h/v2. s/v2 a = Rotationa, velocity ratio. O v = voie etric rie < t4o. h - Head ratio. a = Torque ratio, direction; and the torque is that exerted by the fluid on the pump and is negative when it tends to decelerate the pump. In normal pump regimes and in steady state, this torque is negative and is balanced by the torque from the pump motor. The pump computation for a time step begins by computing pump head and torque from the homologous data using pump angular velocity and volume conditions at the beginning of the time step. The head is used in the momentum equations. The remaining pump calculation determines the pump angular velocity at the end of the time step. The logic for computing pump angular velocity is somewhat complex since stop logic, friction, an initializing calculation, the presence or absence of two tables, and two trips are involved. A pump stop card containing limits on problem time, forward pump angular velocity, and reverse angular velocity may optionally be entered. The pump angular velocity is set to zero and remains zero for the remainder of the problem if any of the limits are exceeded. Selected tests can effectively be disabled by entering a very large number for the test. A time-dependent pump velocity table and an associated trip number may be entered. If the table is entered and the trip number is zero, the pump angular velocity is always detennined from this table. If the trip number is nonzero, the table is used only when the trip is true. The default search variable for the time-dependent pump velocity table is time, but time-advanced quantities can be specified as the search variable. 17
~
l l l When time is the search variable by default, the search argument is time minus the time of the trip. When a I time-advanced variable is specified as the search variable even if it is time, the search argument is just the specified variable. The following is a possible example of the use of a time. advanced variable as the search argument in the l pump velocity table. The turbine driving a feedwater pump is modeled using the control system and one of I the control variables is the rotational velocity of the turbine. The feedwater pump is modeled as a i hydrodynamic pump component. The torque exerted by the water on the turbine would be one: of the input variables to the pump model. Turbine velocity is supplied to the pump component by specifying the turbine velocity as the search argument of the time-dependent pump velocity table. The table would relate the tur- i I bine rotational velocity to the pump rotatior.al velocity. If the turbine and pump were directly coupled, the scarch variables and dependent variables woind be the same. (The cumbersome use of a table when the pump velocity is equal to a control system variable will be eliminated in a future version.) Whenever the time-dependent pump angular velocity table is not being used, the pump angular velocity is determined by the advancement in time of the differential equation relating pump moment of inertia, angular acceleration, and net torque. The net torque is the pump motor torque minus the homologous torque value and the frictional torque. If the pump trip is false, electric power is being supplied to the pump motort if the trip is true, electric power is disconnected from the purnp motor and the pump motor torque is zero. If a table of pump motor torque as a function of pump angular velocity is entered, the pump motor torque is obtained by table lookup and interpolation when needed. If the table is missing, the pump motor torque is assumed to be such that the net torque is zero. This is implemented in the program by simply setting the pump angular velocity at the end of the time step equal to that at the beginning of the time step. This latter option is usually used when the problem starts with the pump at its normal steady state velocity. the pump is assumed to remain at this velocity until the pump trip, and the trip once true remains true for the rest of the problem.
' The frictional torque can be described as a cubic function of pump angular velocity, TF < TF0 + TFl*S + TF2*S2 + W 3*S3 43) where TF is the frictional torque. TFO, TF1, TF2, and TF3 are input quantities, and S is the pump angular velocity.
Two examples are discussed to illustrate pump operation. Consider a pump in a closed loop filled with liquid water. At the start of the transient, all the water in the loop is at zero velocity but the pump is rotating in the positive direction. No pump motor torque table is used, the pump trip is initially false, and thus the pump angular velocity is constant at the initial value until the pump trip becomes true. With the pump rotating at a constant angular velocity but the water at rest, the head is high and the water is accelerated. As the velocity of the water increases, wall fricticn and area change losses increase because of the dependence of these losses on water velocity. At the nme time, the pump head obtained from the homologous data will decrease as the volumetric flow increases. A steady state wn! be reached when the pump head and the loss effects ba'ance. If no wall friction options are selected and no area losses are present, the water will accelerate until the pump head is zero. If when steady state is reached the pump trip is set true, the pump will begin to decelerate becsuse the pump frictional torque and the torque that is exerted by the water on the pump are no longer balanced by the pump motor torque. The water also begins to decelerate due to loss effects. The interaction between water and pump depends on the relative inertias and friction losses between the two. If the water tends to decelerate more rapidly than the pump, the pump will use its rotational kinetic energy to tend to maintain water velocity. If the pump tends to decelerate l rsore rapidly than the water, the pump, depending on its design (as reflected in the homologous data) may continue to act as a pump or the kinetic energy of the water may tend to maintain pump angular velocity. The second example is similar to the first example except the initial pump angular rotational velocity is zero and a pump motor torque curve for an induction motor is used. The motor torque curve tvpically is
!8
positive at zero angular velocity, increases slowly up to a velocity slightly below the synchronous speed, then decreases sharply to aero torque at the synchronous speed, and contin ~ues to negative torque. At the
. initial conditions, the net torque is positive, the pump angular velocity increases, and the water.is accelerated. If the pump torque is sufficiently high, the pump velocity increases to slightly below the syn.
% chronous speed where the developed torque matches the frictional torque and the torque imposed by the water. As the water accelerates, the angular velocity decreases'slightly to meet the increased torque requirements. The angular velocity decrease is very small due to the steep slope of the torque versus angular velocity near the synchronous speed. Thus, once the pump approaches synchronous speed, the transient behavior of the second example is'sunilar to the first example.
The program contains built-in, single-phase homologous data for a Ringham Pump Company pump with a specific speed of 4200 and a Westinghouse Electric Corporation pump with a specific speed of $200. Two-phase difference homologous data are also associated with these pumps, but the data curves are iden- . ; tical and were obtained from two phase test of the Semiscale pump. (The data curves are stored as data ! statements in subroutine RPUMP.) No built-in, two-phase multiplier tables are entered. Specification of built-in, single-phase homologous data does not require specification of the built-in, two phase difference homologous data or vice versa. If multiple pump components are used and some tables are common to more than one component, user effort and computer storage can be saved by entering the data for only one component and specifying other components to use that data. This holds true for built-in data, since built-in data are treated as input data and stored in the pump component data when requested. There are no component ordering restric-tions when one pump component references tables in another pump component. Thus, a pump component may reference a pump component numbered higher or lower than itself. Also, a pump component may reference a pump component that references another pump component, as long as a pump component with data entered is eventually reached. 3.2.10 Valve Component. A valve component is a single junction with additional logic to move the valve to the closed, partially open, or fully open position. A completely closed valve is treated as a time-dependent junction with velocities set to zero. A valve with a nonzero junction area ratio is treated as a system junctiora and smooth or abrupt area change, are used as specified with the current valve junction area ratios. Choked flow calculations are based on the current flow areas. The five types of valves are trip, check, inertia, motor, and servo valves. Valve geometry and initial conditions are similar to a single-junction component. Additional input is required for each type valve. A trip valve is open or closed as the associated trip is true or false. The trip valve is assumed to open or close instantly. Check valves may be pressure or flow operated. Pressure-operated check valves are opened or closed based on static pressure. A flow-operated check valve opens from a closed position based on a static pressure test and closes from an open position based on a flow test. A flow operated check valve without hysteresis opens when the static pressure equals or exceeds the input defined backpressure. The valve with hysteresis opens only when the static pressure exceeds the backpressure. Check valves open or close instantly. A leak ratio is entered to define the fraction of junction area for leakage when the valve is nommally closed. An inertial valve junction area ratio is computed by advancing the second-order differential ec:uation ! l relating the angular acceleration of a valve flapper, its moment of inertia, and the torque exerted by the fluid. Reference 2 contains a more complete description of this model. Motor and servo valves h'a ve identical hydrodynamic features but differ in the matter of controling the valve stem position. A motor valve assumes the valve stem is moved in either the open or close direction by a constant speed motor. Two trips control the motor. The valve moves in the open direction when the open
.O trip is true and closes when the close trip is true. The valve stem is stationary when both inps are false and a terminating error exists if both trips are true. The servo valve stem position is set equal to a specified control system variable.
19
The valve stem position is converted to a normahzed or dimensionless quantity by dividing the stem posi-tion by the allowed stem travel. The dimensionless stem position is zero for a closed valve and is one for a fully open valve. The motor valve imposes these limits; the control system must similarly limit the control variable specified as a stem position to these limits. The effect of the valve on the hydrodynamics is computed from the change of valve flow area and energy loss coefficients as a function of time. If the flow area is a linear function of : tem position, the flow area ratio is equal to the normalized stem position. Otherwise, a table of Dow area ratios as a function of nor-malized stem position is entered. The table allows for a nonlinear variation of flow area with stem position and also allows for stem overruns. For example, if the stem can move 5% after the valve area is fully closed or open, the table would have zero flow area between stem positions 0 through 0.5 and flow area of 1.0 for stem positions 0.95 through 1.0. If the abrupt area option is specified, pressure losses through the valve are computed assuming the cur- i rent flow area is an orifice. If the smooth area change option is selected, the pressure losses are computed i from tables of forward and reverse energy loss coefficients as a function of stem position. The energy loss coefficients are not input directly; rather they are computed from tables of forward and reverse flow rates as a function of stem position. This information is commonly supplied by valve manufacturers or must be determined experimentally. 3.2.11 Accumulator Component. The accumulator component consists of a single volume and a single outlet junction that has its own special hydrodynamic model described in Volume 1. The component con-tains an internal valve that opens on static pressure drop, and closes on reverse flow. The surge line volume is lumped into the liquid volume; however, the momentum equation is formulated to include inertial and wall friction effects in the line. The coefficient of friction in the wall friction model is 0.03. Most accumulator data include measureo line losses. This loss can be modeled in two ways: (a) if the loss is specified as an energy loss coefficient, this may be input directly on the junction geometry card for user-specified energy losses, (b) if the loss is specified as a frictional loss (that is, fL/D), the surge line can be lengthened to add the additional loss. In the first case, the wall friction option on the volume geometry card should be set for wall friction calculation. In the second case, energy loss coefficients should not be specified on the junction geometry card. There are two special features of this component. First, the model contains its own heat transfer package ; and second, once all the liquid is expelled from the accumulator, this component converts to a normal l volume filled with nitrogen. The heat transfer model uses standard correlations for natural convection for ; vertical flat plates (tank wall) and horizontal flat plates (water surface and tank top). In addition, there is a i provision to model the evaporation of the liquid and then to model the heat given up by the vapor as it con-denses. Modeling this effect helps to give the polytropic response typical of accumul tors. The conversion of the accumulator volume to a normal volume filled with nitrogen is performed using the following assumptions: (a) the equation of state assumes thermal equilibrium; (b) the air component in the code is initialized with nitrogen; (c) the normal RELAP5 momentum, continuity, and energy equations are used; (d) heat transfer from the tank wall to the nitrogen is calculated by the accumulator model; (e) starge line losses, if frictional, are converted to an energy loss coefficient and applied at the junction; and (f) the accumulator valve remains in effect. The numerical scheme in the accumulator is formulated in such a m."ner that there is no truncation l error (that is, nitrogen mass is conserved). However, this can create protnems if the user chooses to model an accumulator next to a time-dependent volume. Truncation error is not measured either in the accumulator or in the time-dependent volume, so at large time steps (1.0 second or larger) an oscillation may occur which causes the accumulator liquid to be expelled early. This problem is prevented if a system volume is always included downstream of the accumulator. Future modification to the accumulator component will include a time step controller so the above problem will not occur. Other modifications will include options for isothermal and isentropic expansion of the nitrogen gas and an option to close off the accumulator after the liquid has been expelled so that no nitrogen injection will occur. a 20
w 13.3L Hydrodynamic Output At major edit prints, hydrodynamic dats is printed in a volume-oriented block and a junction-oriented
. block, each block having two sections. These blocks contain the information for the current time step for all volumes and junctions in the system. Editing during input processing includes a hydrodynamic edit -
similar to the major edit. Figure 6 shows one major edit from a sample problem representative of the l Edwards Pipe Esp-at. The first section of the volume edit prints the pressure; internal energy; static quality; mass fraction of noncondensible gases; equilibrium quality; void fraction; liquid, vapor, and equilibrium temperatures; and the volume flag for each volume. The pressure, internal energy, and static quality are d==dat variables advanced in time by the hydrodynamic advancement algorithm. The static quality is the fraction of. water that is vapor, but if two. phase, only one of the phases need be at saturation conditions. The equilibrium goality is obtained from the equation of state using pressure and in*stnal energy as input and assuming equilibrium conditions. The difference between the static and equilibrium qualities is an important factor . in flashing or condensing. Void fraction is based on nonequilibrium conditions. Liquid and vapor temperatures are based on nonequilibrium conditions and these temperatures are equal r Jingle-phase con-
' ditions. Equilibrium temperature is based on equilibrium conditions. This section ixmdes pump angular velocity, head, and torque for pump volumes.
The second section of the volume edit prints thermodynamic densitier for the mixture and each phase, internal energy of each phase, volume, sonic velocity, heat input from heat structures, and vapor genera-tion rate. In two-phase, the isentropic sonic velocity is printed. This section can be suppressed by an input option. The first section of the junction edit prints the velocities of each phase, total mass flow, junction area,
.- X throat area ratio, junction flag, choke flag, and a choking summary for each junction. In single phase, the
(' ) velocities are equal. A choke flag equal to 1 means the flow through the junction was determined by '.he choking model. The choking ' summaries indicate for how many time steps the choking model was applied:
- the heading EDIT, lists the number rince the last major edit, the bending TOTAL, lists the number for the entire problem.
The second section of the junction edit prints the densities and internal energies fer each p' hase, void . fraction entering the junction, void fractions at the throat, and void fraction downstream of the throat for each junction. The latter two void fractions are listed as zero for junctions with smooth area changes. This second junction section can be suppressed by an input option. i 1 O 21 _ _ - - _ - _ _ _ _ - _ _ - _ _ - - _ _ _ _ _ _ _ _ _ _ . _ - _ _ = - ___ _ - - _ _ -
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- 4. HEAT STRUCTURE MODELING Heat structures represent the solid portions of the thermal-hydrodynamic system. Beir.5 solid, there is no flow, but the total system response is dependent on heat transferred between the structures and the fluid, and the temperature distributions in the structures are often an important requirement of the simulation.
System components simulated by heat structures include fuel pins, pipe walls, core barrel, pressure vessel, and heat exchanger tubing. Temperatures and heat transfer rates are computed from the one-dimensional form of the transient heat conduction equation. A heat structure is identified by a number, cccgOnn. The subfield cce, is the heat structure number and is analogous to the hydrodynamic component number. Since heat structures are usually closely associated with a hydrodynamic component, it is suggested that hydrodynamic components and attached heat struc-tures be given the same number. Since different heat structures can be attached to the same hydrodynamic component, such as fuel pins and a core barrel attached to a core volume, the subfield, g, is used to dif-ferentiate different geometries within a heat structure number. Input data is organized about the heat structure geometry combination. Up to 99 individual heat structures may be defined using the geometry described for the heat structure geometry number. The individual heat structures are numbered con. secutively starting at 01; this number is the subfield, nn, of the heat structure number. The heat structure input requirements are divided into input common to all heat structures with the heat structure geometry number and input needed to uniquely define each heat structure. 4.1 Heat Structure Geometry The temperature distributions in heat structures are assumed to be represented adequately by a one-dimensional form of the transient heat conduction equation in rectangular, cylindrical, or spherical coor-dinates. The spatial dimension of the calculation is along any one of the rectangular coordinates and is along the radial coordinate in cylindrical or spherical coordinates. The one-dimensional form assumes no temperature variations along the other coordinates. Figure 7 illustrates placement of mesh points at which temperatures are computed. The mesh point spacing is taken in the positive direction from left to right. A composition is a material with associated thermal conductivity and volumetric heat capacity. Mesh points must be placed such that they lie on the two external boundaries and at any interfaces between different compositions. Additional mesh points may be placed at desired intervals between the interfaces or boun-daries. There is no requirenient for equal mesh intervals between interfaces, and compositions may vary at any mesh point. The heat structure input processing provides convenient means to enter the mesh point spacing and com-position placement. Compositions are assigned a three-digit, nonzero number, which need not be con-secutive. For each composition specified, corresponding thermal property data must be entered to define the thermal conductivity and volumetric heat capacity as a function of temperature. The temperature Composition as-- Boundary 4 Interfaces e---- Boundary o . . .... .............. . .. ...... =*---- Mesh Points: 4- Mesh Point! 1 2 3 4 etc. Numoering {
~
Figure 7. Mesh point layout. O 28
i I dependence can be described by tabular data or by a set of functions. Defining therme property data fcr compositions not specified in any beat structure is not considered an error but does waste storage space. ' g Thermal property data for aluminum, carbon steel, stainless steel, uranium dioxide, and zirconium are
- ) stored within the program. The data were entered to demonstrate the capability of doing so andshould not V ~ be considered recommended valuer. Input editing includes the thermal properties and a listing of the built in data can be obtained by assigning the built in materials to unused composition numbers in any input / check run. The thermal property data must span the expected temperature range of the problem.
Problem advancement is termmated if temperatures are computed outside the range of data. Heat structures can have an internal volumetric beat source which can be used to represent nuclear, ) samma, or electrical heating. The source S (x,t) is assumed to be a separable function of space and time, j S(x,t) - P s(x) P(t) (4) f where Pr is a scahng factor, s(x) is a space distribution function, and P(t)is power. The space function is assumed constant over a mesh interval but may vary from mesh interval to mesh interval. Only the relative distribution is important and any scahng factor can be used. For example, given a heat structure with two zones, the first zone having twice the internal heat generation of the second, the space distribution factors for the two zones could be 2.0 and 1.0,200.0 and 100.0, or any numbers with the 2 to I ratio. Zeros can be entered for the space distribution if there is no internal heat source. ! The mesh point spacings, composition placement, and source space distribution are common to all the heat structures defined with the heat structure geometry number, and only one copy of this information is stored. If a heat structure geometry has this data in common with another heat structure, input preparation and storage space can be saved by referencing the data in the other component. There are no ordering restrictions as to which heat structure geometry may reference another, and one heat structure geometry may reference another which in turn references a third, etc., as long as a defined heat structure is fm' ally f s reached, An initial temperature distribution is associated with each heat structure geometry. This initial distribu-tion is common to all heat structures defined with the same heat structure geometry number, but storage space for temperatures are assigned to each heat structure. Referencing initial temperature distributions in other heat structure geometries is allowed. The input temperature distributions can be used as the initial temperature distribution or as an option, initial temperatures can be obtained from a steady state heat conduction calculation using initial hydrodynamic conditions and zero-time power values. The input temperature distribution is used as the initial temperature guess for iterations on temperature-dependent thermal properties and boundary condi-tions. If a good temperature guess is not known, setting the temperature of any surface connected to a hydrodynamic volume equal to the volume temperature assists the convergence of the boundary conditions. 4.2 Heat Structure Boundary Conditions Boundary condition input specifies the type of boundary condition, the possible attachment of a heat structure surface to a hydrodynamic volume, and the relating of the one-dimensional heat conduction solu-tion to the actual three-dimensional nature of the structure. Each of the two surfaces of a heat structure may use any of the boundary conditions and may be connected to any hydrodynamic volume. Any number of heat structure surfaces may be connected to a hydrodynamic volume but only one hydrodynamic volume may connect to a heat structure surface. When a heat structure is connected to a hydrodynamic volume, heat transferred from or to the heat structure is added to or subtracted from the internal energy content of the volume. For both left and right surfaces, a positive heat transfer rate is heat transferred out of the surface. 29
A symmetry or insulated boundary condition specifies no heat transfer at the surface, that is, a zero
- emperature gradient at the surface. This condition should be used in cylindrical or spherical coordinates ,
when the radius of the leftmost mesh point is zero, although the numerical techniques impose the condition ! regardless of the boundary condition specified. In a rectangular geometry structure with both surfaces ! attached to the same hydrodynamic volume with the same boundary conditions, and having symmetry l about the structure midpoint, storage space and computer time can be saved by describing only half the structure. The symmetry boundary condition is used at one of the surfaces and the heat surface area is doubled. This boundary condition can also be used when a surface is very well insulated. When a heat transfer surface is connected to a hydrodynamic volume, a set of heat transfer correlations can be used as boundary conditions. The correlations cover the various modes of heat transfer from a sur- ) face to water and the reverse heat transfer from water to the surface. The heat transfer modes are listed j below with the mode number used in the printed output:
- l. Forced convection of subcooled liquid
- 2. Subcooled nucleate boiling
- 3. Saturated nucleate boiling
- 4. Subcooled or saturated transition boiling at low now
- 5. Subcooled or saturated transition boiling at medium flowa using low flow correlation
- 6. Subcooled or saturated transition boiling at medium flowa using high flow correlation
- 7. Subcooled or saturated transition boiling at high flow
- 8. Subcooled or saturated film boiling at low now, CHF exceeded O
- 9. Subcooled or saturated film boiling at medium flowa using low flow correlation, CHF I' exceeded
- 10. Subcooled or raturated film boiling at medium flow a using high flow correlation, CHF exceeded
- 11. Subcooled or saturated film boiling at high flow
- 12. Saturated film boiling at low flow for dryout conditions l '
l
- 13. Saturated film boiling at medium flowa for dryout conditions, usmg low flow comlation
- 14. Saturated film boiling at medium flowa for dryout conditions, using high flow correlation
- 15. Saturated film boiling at high flow for dryout conditions i
- 16. Forced convection of superheated vapor at low flow l
l
- 17. Force convection of supetheated vapor at medium flow a using low flow correlation l
- 18. Forced convection of superheated vapor at medium flowa using high flow correlation
- a. For medium flow ranges (modes 5,6. 9.10.13.14.17, and 18). the maximum of the high and low flow correlations is being O
chosen. 30
s
.f 19. Forced convecdon cf superheated vrpor ct high flow
-20. ' Forced convection from subcooled liquid to the ~ wall j
. W: -i
'h 21. Forced convection from saturated two-phase mixture to the wall
- 22. Forced. convection from superheated vapor to the wall
- 23. Im=inar natural convection of subcooled liquid
- 24. . Turbulent natural convection of subcooled liquid
- 25. Iaminar natural convection of two phase mixture
- 26. Turbulent natural conyc: tion of two-phase mixture
- 27. ' Laminar natural convection of superheated vapor
- 28. Turbulent natural convection of superheated vapor
- 29. Pool nuclante boiling
- 30. T ==iaar condensation within a horizontal tube
- 31. 12minar condensation within a vertical or angle tube
- 32. Turbulent condensation widnin a horizontal or vertical tube.
O The heat tramfer correlations are applied in the form,
- V
/ #1 \
-k =
q
+h T -T*j W where the left side of the equation is an expression for the heat flux q at the surface of the wall, k is t se
!- thermal conductivity, T is the wall surface temperature, and the superscripts m and m + 1 indicate old and new time values, respectively. The quantity printed in major and minor edits under the label, heat trans! er coefficient, is the derivative of the heat transfer rate with respect to surface temperature. In this veesior. of RELAP5, the derivative is usually assumed to equal the heat transfer coefficient. A notable exception is transition boiling where the derivative is a negative quantity. Other boundary condition options that can be selected are: setting the surface temperature to a hydrodynamic volume temperature, obtainmg the surface temperature from a temperature versus time table, obtaining the heat flux from a time table, and obtaining heat transfer coefficients from either a time-or temperature-dependent table. For the last option the sink temperature can be a hydrodynamic volume temperature or can be obtained from a temperature versus time table. These options are generally used to support various efforts to analyze expenmental data. A factor must be entered to relate the one dimensional heat conduction representation to the actual heat structure. Two options are provided; a heat transfer surface is entered, or, a geometry-dependent factor is entered. For rectangular geometry, the factor is the surface area and there is no difference in the options. In cylindrical geometry, the heat structure is assumed to be a cylinder or a cylindrical shell sud the factor is the cylinder length. For a circular pipe where a hydrodynamic volume represents the flowing part of the O pipe and a heat structure represents the pipe walls, the factor equals the hydrodynamic volume length. For 31 _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ . _ )
a hydrodynamic volume representing a core volume with fuel pins or a heat exchanger solume with tubes, the factor is the product of the hydrodynamic volume length and the number of pins or tubes. In spherical geometry, the heat structure is assumed to be a sphere or a spherical shell and the factor is the fraction of the sphere or shell. For a hemisphere, the factor would be 0.5. Except for solid cylinders or spheres where the inner surface area is zero, one surface area can be implied from the other and the mesh point spacing information. Nevertheless, both surface areas must be entered and an input error will exist if the surfaces are not consistent. This requirement is easily met with the second option of entering a geometry-dependent factor since the factor is the same for the left and right boundary. . l 4.3 Heat Structure Sources I l Volumetric heat sources for heat structures have previously been described as consisting of the product of a scaling factor, a space-dependent function, and a time function. The space-dependent distribution has I already been discussed. The time function may be total reactor power, fission power, fission product decay power from the reactor kinetics calculation, or may be obtained from a table of power versus time. The input specifies which power is to be used and provides for three multipliers. The first multiplier is applied 4 to the power to indicate the internal heat source generated in the structure. This means that in steady state, heat equJ to the multiplier times the power table value would be generated in the heat structure and transferred out its left and right surfaces. Within the program, this multiplier is divided by the integral of ; the space-dependent distribution to allow for the arbitrary scaling of that function. The other two i multipliers provide for the direct heating of the fluid in the hydrodynamic volumes attached to the sur- l faces. Heat equal to the factor times the power value is added to the internal energy of ihe fluid in the j hydrodynamic volume. Zeros are entered where no heat source or hydrodynamic volumes exist. ' 4.4 Heat Structure Output Two sections of heat structure output are printed at major edits. Figure 6 includes a heat structure edit. O The first section prints the mesh point temperatures for each heat structure. This section can be suppressed ; by an input option. l 1 The second section prints one line of heat transfer information for each surface of each heat structure. The information on each line is: the heat structure number; a left or right surface indicator; the connected hydrodynamic volume or if none, zero; the heat transfer area; the heat transfer rate; the critical heat flux; the mode of heat transfer; and the derivative of heat transfer rate with respect to surface temperature ] (although it is labeled as heat transfer coefficient). The first line for each heat structure also includes the
- heat input to the structure, the heat transferred out both surfaces, and the net loss from the structure.
l 1 i l 1 i
)
l O 32 I > 4
- 5. GENERAL TABLES b
' . [] , The general table input provides for the following tables: power versus time, temperature versus time, - (j heat transfer rate versus time, heat transfer coefficient versus time, heat transfer coefficient versus temperature, reactivity versus time, and normahzed valve area versus nornWized stem position. An input I item identifies each table so that proper units conversion and input checking can be done. For example, specifying a temperature table when a power table is required is detected as an error. Because these tables are often experimental data, or scaling is often needed for parameter studies, the input provides for con-version or scaling factors or both for these tables. Input editing of these tables include both the original and scaled data. (- C I l 1 33
6 TRIPS Extensive trip logic has been implemented in RELAP5. Each trip statement is a single logical statement, but because logical trip statements can refer to other trip statements, complex logical statements can be constructed. There are two aspects to trip capability: (a) to determine when a trip has occurred, and (b) to determine , what tc, do when a trip occurs. In the modular design of RELAP5, these two aspects have been separated. The term, trip logic, refers only to the first aspect and includes the input processing of the trip statements and the transient testing to set trip status. The action to be taken when a trip occurs is considered to be part 1 of a particular model and that aspect of trip coding is associated with the coding for the model. Examples of the second aspect of trips are the effects of trips on pump models and check valves. Trip capability provides for variable and logical trips. Both trips are logical statements with a false or ! true result. A trip is false off (that is off, not set, or has not occurred)if the result is false. A trip is true on 1 (that is on, is set, or has occurred) if the result is true. Trips can be latched or unlatched. A latched trip, once true (set), remains true (set) for the remainder of the problem execution, even if conditions change such that the logical statement is no longer true. An unlatched trip is tested each time step and can switch i states at any step. All trips are initialized false at the start of a problem. j Up to 99 variable trips and up to 99 logical trips can be defined. Each trip has a number which is the l card number of the card describing the trip. Trip numbers need not be consecutive. Trip numbers 501-599 define variable trips; trip numbers 601-699 define logical trips. l Several options are available on restart. If no trip data is entered, trips are as defined at restart and with the values at restart. It is possible to delete all trip definitions and enter completely new definitions. Individual trips can be deleted or redefined and new trips can be inserted. Individual trips can be reset to false. All new or redefined trips are initialized to false. At restart, a latched trip can be reset. 6.1 Variable Trips A variable trip evaluates a comparison statement comparing two variables and a constant using one of the operations, equal (EQ), not equal (NE), and greater than or squal (GE), greater than (GT), less than or equal (LE), or less than (LT). The variables currently allowed are listed in the input description. Most variables advanced in time are allowed and any variable that is permanently stored can be added to the list. The only restriction on the two variables is that they have the same units. Thus, a hydrodynamic volume temperature can be compared to a heat structure temperature, but a pressure cannot be compared to a velocity. The variable trip statement is NUM VAR 1 OP VAR 2 + CONSTANT (6) where NUM is the trip (and card) number; VAR 1 and VAR 2 are each two words to identify a variable, the first word is alphanumeric for the variable type, the second word is a number for the particular variable; OP is the comparison operation; CONSTANT is a signed number to be added to VAR 2 before the com-parison; and either L or N is used to indicate a latched or unlatched trip. A special form NULL,0 is used to indicate no variable is to be used. VAR 2 must be NULL,0 if VARI is to be compared only to the constant. Either VAR 1 or VAR 2 may also be TIMEOF, trip number. TIMEOF is a variable containing the time the trip was last set true and the trip number may refer to either a variable or logical trip. This quantity is always -1.0 for a trip with the value false. When a trip is switched to true, the time at which it switches replaces the -1.0 value in TIME ~ For a latched trip, this quantity once set to other than -1.0 always retains that value. An unlatched trip may have several TIMEOF values other than -1.0, Whenever an unlatched trip switches to false TIMEOF becomes -1.0; when true again, the new time of switching to true is placed in TIMEOF. Three examples of variable trips are, 34
L
'501 P,3010000 LT- NULL,0 .1.5 + 5 N n
502 P,5010000. GT- P,3010000 2.0 + 5 N. w 510, TIME,0. GE NULL.O 100.0 .L l(] ' Trip 501. is: the pressure in volume 3010000 less than 1.5 bar (1 bar equals 105 Pa).' Trip 502 is: the pressure difference between volumes 5010000 and 3710000 greater than 2.0 bar. Trip 510 is: the current advancement time greater than or equal to 100 s. Use of the equal (EQ) or not equal (NE) operator should be avoided because fractions expressed exactly in demal notation may not be exact in bmary notation. As an example, assume a time step of 0.01. After ten advancements, the time should be 0.10, but an equality test of time equal to 0.10 would probably fail. An analagous situation is dividing I by 3 on a three digit decunal calculation, obtaining 0.333. Addag 1/3 . l three times should give 1.000, but 0.999 is obtained.
. 8.2 Logical Trips =
' A logical trip evaluates a logical statement relating two trip quantities with the operations AND, OR (inclusive), or XOR (exclusive). Table 2 defines the logical operations where 0 indicates false, I indicates tnae. Each trip quantity may be the origi.ral value or its complement. (Complement means reversing the true and false values; that is,' the complement of true is false.)
Table 2. Logical operations AND OR XOR 0011 0011 0011 0101 0101 0101 0001 0111 0110 The logical trip statement is L NUM
- TRIP 1 OP
- TRIP 2 (7)
N
.where NUM is the trip number, TRIPl and TRIP 2 are either variable or logical trip numbers, OP is the logical operator, and L or N are for latched or unistched trips. A positive trip number means the' original trip value; a negative number means the complement value. Examples of logical trips are, .
601 501 OR 502 N 602 601 AND 510 N
- 620 -510 OR -510 N O
35
Trip 602 involves a previous logical trip and illustrates the construction of complex logical statements. Using parentheses to indicate the order of logical evaluation, Trip 602 is equivalent to: ( (Pressure 3010000 less than 1.5 bar) OR (Pressure 5010000 greater than (Pressure 3010000
+ 2.0 bar) ) ) AND (Time greater than or equal to 100 s). Trip 620 is the complement of Trip 510 and the AND operation in place of the OR operation would also give the same result.
6.3 Trip Execution All trips are initialized to false for a new problem and the trip printout at time equal to O s will show all trips false. On restarted problems, the trip printout at the restart time may be different from the corres-ponding time on the original problem because trip changes can be made during restart input processing. Trip computations are the first calculation of a time step. Thus, trip computations use the initial values for the first time step and the results of the previous advancement for all other advancements. Because trips use old values, they are not affected by repeat of the hydrodynamic and heat structure advancements. Trips are evaluated in order of trip numbers, thus variable trips first, then logical trips. Results of variable trips involving the TIMEOF quantity and logical trips isvolving other trips can vary depending on their position relative to other trips. As an example, consider 6XX -650 OR -650 N which just complements Trip 650. Also assume Trip 650 switches to true this time step, and thus 650 was false and 6XX was true previous to trip evaluation. At the end of trip evaluation,6XX is true if 6XX is less than 650 and false if 6XX is greater than 650. If Trip 650 remains true for the following time step, Trip 6XX with 6XX less than 650 becomes false one time step late. Similarly, TIMEOF quantities can be one time interval off. This can be minimized by ordering TIMEOF tests last and defining logical trips ahead of using them in logical statements. 6.4. Trip Logic Example Techniques from Boolean algebra can assist in formulating the logical trip statements. Consider a l motor-operated valve which operates such that if the valve stem is stationary, it remains stationary until a specified pressure exceeds 12 bar or drops below S bar. The valve starts opening when the pressure exceeds 12 bar and continues opening until the pressure drops below 11 bar. The valve starts closing when the pressure drops below 8 bar and continues closing until the pressure exceeds 9 bar. The motor valve requires two trips, one to be true when the valve should be opening, the other to be true when the valve should be closing. The following procedure is used to derive the open trip logic. A Boolean variable has one of two possible values, f alse (0) or true (1). Define as Boolean variables: V o which is to be true when the valve should be opening, P iis true when the pressure is greater than 11 bar, and P 2 si true when the pressure is greater than 12 bar. Table 3, is a truth table that has been constructed by listing all possible combinations of the three input variables, Vo, P2, and P i, and the desired output, V o. The number in the rightmost column is the number resulting from assuming the input values form a binary number, which is used to ensure that all combinations are listed. From the truth table, the following expression can be written, Vg = (V g@ P 2 Py ) + (V g@ P 2 P1 ) + (Vg@ P2 @ P1 ). (8) where@ indicates AND, O indicates OR, and the bar indicates the complement.'Th: exp ession is derived by combining with OR operations terms from each line having a true value in the output column. Each term consists of the combining of each input variable with AND operations, using the direct variable if the l 36
h
- Table 3. Truth table examples O
. V.
Output Input V P P g V, 2 1 Num 0 0 0 0 0 0 0 0 1 1 impossible 0 1 0 2 < 1 0 1 1 3 0 1 0 0 4 1 1 0 1 5 impossible 1 1 0 6 1 1 1 1 7 value is true and die complement if the value is false. The table shows that two of the combinations are impossible. This is because if P2is true, P must 1 also be true; that is if the pressure is greater than 12 bar, it is also greater than 11 bar. Because of the relationship between 2P and P1 , Pg @P1-P2 P2 @P y-P. g (9). Using the Boolean identities from Table 4, the logical expression can be reduced ( V0 " IYO P2 ) + EY 0 P 1 (P 2 P2 )3
- IVO 2) + (YO P1 ). (10)
The following trip input implements the logic. Trips 601 through 603 implement the rightmost expression above. Trip 603 would be specified as the open trip in a motor value. Table 4. Booleon algebra identities A@A=A A@A=A A@0=0 A@0-A A@X=0 A@A=1 A@l-A A@l=1 A@B=B@A A@B=B@A A@(B@C)=(A@B)+(A@C) l A@(B@C)=(A@B)*(A@C) t NOTE: @denotesAND,@denotesOR,-denotescomplement 37
4 501 P,1010000 GT NULL,0 11.0 + 5 N (PI) 502 P,1010000 GT NULL,0 12.0 + 5 N (P2) . 601 403 AND 502 N (FIRST TERM OF EQ) 602 603 AND 501 N (SECOND TERM OF EQ) 603 601 OR 602 N (OPEN TRIP) The close trip logic can be written similarly. 6.5 Trip Output At major edits, each defined trip number and the current TIMEOF quantity is printed. The TIMEOF quantity is -I .0 when the trip is false, and when greater than or equal to zero indicates the trip is true and is the time the trip last switched to true. Figure 6 includes an example of a trip edit.
'I O
I Ol ; l l l 38
- _ _ _ - _ _ _ _ _ _ _ . }
- 7. -REACTOR' KINETICS
, The reactor kinetics capabdity can be used to compute the power behavior in a nuclear reactor. The power is computed using the space inopendent or point kinetics' approximation, which assumes that power can be separated into the product of space and time functions. This approxunation is adequate for those cases in which the space distribution rammina nearly. constant.
. Data for the six generally accepted delayed neutron groups are built into the code. Optionally, yield ratios and decay constants for up to 50 groups may be entered.
The total reactor power is the sum of fission power and fission product / actinide decay power. The fis-sion power is computed by the reactor kinetics equations. The power resulting from the decay of fission products and medah are computed from differential equations advanced in time with the reactor kinetics equations. The user can specify three options for computing reactor power: fission power only; fission and fission product decay power; or fission, fission product decay, and actinide decay power. The com-putations for fission product and actinide decay are identical, but separate input of yield fractions and decay constants is provided. Data for 11 fission product groups and two actinide groups are built into the program or alternately up to 50 groups each may be entered for fission products and for actinides. Separate factors can be applied to the yield fractions for fission products and actmides. For fission pro. ducts, the factor is usually 1.0 for best estimate e=M= dons and 1.2 is often used for conservative calcula- - tions. For actinides, the factor is usually the ratio of U238 atoms consumed per U235 atoms fissioned, but additional factors may also be included for conservative calculations. The built-in data are recommended values an[i are listed in the edit of input data when used as shown in Figure 8. Reactivity is computed from: O e s-p [p4(t)) r(t) = r o +r g
+{r i(t).{
i=1 s i=1 W R,' k / n f
+a T (t) + Wp Rp Tp (t) + ap Tp (t) (11) i=1 where ns is the number of reactivity curves, npis the number of hydrodynamic volumesin the reactor core, and af si the number of heat structures in the reactor core. Note that the sign of the feedback terms are positive. Negative quantities must be entered where negative feedback is desired.
The quantity t is o an input quantity and is the reactivity corresponding to assumed steady state reactor power at time equrl zero. This quantity must be less than or equal to zero. A nonzero quantity indicates a neutron service is present. For most applications, to qual e to zero is acceptable. The quantity rB si calculated during input processing such that r(0) = ro. The quantities r can have ans kd associa,. trip number.are If theobtained trip number isfrom not entered general or zero, tables time is thedefining reactivity as search argument. O If the trip number is nonzero, the search argument is -1.0 if the trip is false and the time minus the time at which the trip last turned true if time. These tables can be used to describe reactivity changes from rod motion. 39 _ _ _ . -_ _ ___a
e e N 0*
- 4 O
e S 4 O U W med
% Q 4
0 4
% E M K W O 4 O O
>= op= to 2 OZ Z Q 4 e4 4 >=
>== N e=e>= iwf*S to 4 MO v1 0000 OM O W Z 4 2 8888 CZ $ 3 > >
c ua Q WWWW Oc W Q >=== >=a= W ==C OO veu ==O O O O O Ov e==Q **vt aaMOO pew UQ me refWWWW e wo a DE *
.>E G O
> $ U wr= > 0f*af G 4aO* see k i O N **4 M4GO M Wr**e# E4 Wr* *=6e=eNen 4 L>e P= >=.J t=.JOO WWe=etel e QWWen Nef*@ WWe Q U.J W-40O e4 M
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- GEwo Kw l t; W w C:
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>= a4 >= ee a=e s. W O Q Q O(
Z GE U Z >= 4 4 D= 4 w Q m Z w
& U **
g *] WM W Z 4 W w W 4% QW QL Q >= to dD Q E W yl Q w =J 4 3 QM . 2 80 UZ >= t= 3 Q 4 >= v4 o
>= /. 4 4 46= >= >= 4- Q 4 ee E m=* W v1 E w >= Z t== Z 4 Z Das e4 QC EL.J $
WJ= Q 4= W had 44 ese 4 Q 4 >= *=e W EQ 00 M=ad W Z >= 2 Q Que N 4 W MO 3 4 (M t= N # @f*C C0 00,=e >=
#= # U vt O 4 A WQe e*
E >=wCOO [ MM & 3 0 > >Z l w >=Z 8064l J Z l oc > > W Q4 W 4 4Q W W .stQ WWWWW 3 Q W w O >=== >=== >= AW Q 4 (E W WQa==O OO Q Qu===O O W Q Q Q 4 ev-=O M ==M O aeMO Z O W =ad W peO OO MNOOOOG w >= *=eo a McLO DEO Q E ud a* + > Q Q> l Os)O > >> g P= m ost o n W 47$Q 4.s e= 40 meg o 2 QL QM WQ 4 WP* we# 4 44 Uf* 4 m# me Q Qagu M E >= .J O >= d 0 4 Q a= 4 W O Q Q U gaNamee W WWue ef=f* mon W WQn w se u.J e v.J e p. UrD U O Z Z Z W yl e e=* W Wud .M eoeee > >WMe >= 99 ud4 Q W eg GO A v 4 4 O Q 4 4 C ==W Q QQ a=r 4 4 0*'8F* 4 4 Q *=** E -d WQ N .J WQ N
- QC 4
==J E A O =4 WW Z ud ED eC==* $ cD QC=== Q Q w C00 QL W M C >= Q Q Q Q WW Q em 4 aus e= 000
.a o u .J .J Z Z Q Q me E >= >= v >= 000 m e 4 W WZ 4 4Z Z >= c 4 Z C00 Q ad QC me meQ Q Q QQ 4 Z > > w 0 er)C e aC u. >>== Q C>e Z Z>=e aC >= se me NnN (L >= N .J =b= MNNm## 4 4 t= m W us og > me OW eee w a Z Z ZU C W WW C0000Q u o & .J >>= >W Z J OW Q Q C4 I w w4 88l 144 Q G4 l Q muJ ww ME w we h QC QE QL EE W > >QC and Wuewusua .J .4K
,4 >= M e= 3 >=
*nme=e ud >= >= >= 4 000 w C00000 W uaw O ua = uZ v >= 00 Z M4 3 3 3 3 000 > > 000000 Ww O a= 4W *E 4 OO O O Q W W WC O cDtO 4 4Q C00000 > >Q O ** > WQ W aC 00 **
QM 0, Z Z Z .J CON U UJ 0* c es=eOO .J 4 Z e= c5 e ac W ee W e C00 Ee W ED e=e=4 ua una Ob ergwmef== ud WW N ** ** E & OO 3 Q C00
*=m c .J Q Q O e=e e ee O Q*=e oeoeoe Q Q,e e W > p eg gig CQ Z pov neC 4 ud nad W> m > N e=6MN ED en ==e be > N Z e=8 >= Q e Waad g me W COO A4 w > > > 4 4 Z Z *e ,= ** Z O -J p== E .J MNm aE .S >= 4 4 4 E E ** ** OM & 3 Q C00
.J Q me =J .J .J K E >= >= og 4 Z A .J > mmm tesud Z W W us 4 4 O U Q uJ W G Q COO QC == Q Q Q OO 4 4 e QC Q Q > 000 1
4 40 l
The functi:n R, is a table defining reactivity as a functi:n cf the r'tio cf the current density pj(t) in
- hydrodynamic volume I to the density in the volume at time zero p(0). One table of R p is used for all volumes. W p3i s the density weighting factor.for volume i. Tw is the equilibrium temperature in volume i i and aw is the temperature coefficient (should not include de,nsity changes)p for volume 1. W
.} y]s need be; entered only for those hydrodynamic volumes representing the reactor core.
Reactivity feedback from heat structures is treated similarly to that for hydrodynamic volumes. The function Rp is a table defining reactivity as a function of the average fuel temperature Tpg in the ith heat structure. Wp and ap; are the fuel temperature weighting factor and the fuel temperature coefficient, respectively. gUsually only one of the quantities, Wp; and ap;, is nonzero. Tp; shou average temperature of only the fuel region of a heat structure (fuel pin or plate). The heat structure input provides a means of specifying which portions of a heat structure are to be included in the averaging com-putation. Wp; and ap; need be entered only for those heat structures representing fuel in the reactor core. The reactor kinetics output lists total reactor power, fission power, decay power, reactivity, and reciprocal period. Either the total power, fission power, or decay power can be specified as the time varying part of the heat source in heat structures. O e I l O , 41 l y
l
. 8. CONTROL SYSTEM -
I The control system provides the capability to evaluate simultaneous algebraic and ordinary differential O' equations. The capability is primarily intended to simulate control systems typically used in hydrodynamic systems but it can also model other phenomena described by algebraic and ordinary differential equations. Another use is to define auxiliary output quantities such as differential pressures so they can be printed in major and minor edits and be plotted. The control system consists of several types of control components, each type of component defining a control variable as a specific function of time-advanced quantities. The time advanced quantities include: hydrodynamic volume, junction, pump, valve, heat structure, reactor kinetics, and trip quantities and the control variables themselves including the control variable being defined. Permitting control variables to be input to control components allows complex expressions to be developed from components that perform simple, basic operations. The control components are addition-subtraction y - S (A0 *Al1*AV22 + . . .) (12a) multiplication y-SVY 12... (12b) division y = 5/V 1 or S V 2/Y 1 (12c) h integer power I y = SV y (12d) real power y = SV (12e) 1 variable power 2 y - SV y (12f) differentiation dV y y= (12g) integration t y= Vy dt (12h) 42 i _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ a
I functional I y = SF(V$ )' [b 'N unit trip (12i) l y = SU(Tr ) (12j) l i trip delay 4 I l y - S T p(Tr) (12k) l where S is an input scaling factor; the A[s are input constants; the V[s are time-advanced variables; I is an integer input quantity: R is a real input quantity; F can be absolute value, square root, exponential, natural logarithm, sine, cosine, tangent, arctangent, or a tabular function defined by a general table; U is zero or one as the trip Tr is false or true; and Tpis -1.0 if the trip, Tr is false and is the trip time if the trip is true. The integral is evaluated numerically by y"+1 = y* + S (V* + V**1) f (13) where the superscripts m and m + 1 iridicate the values at the beginning and end of a time step and At is the time interval. r3 Two options are available for differentiation. One is the direct inverse of the integration formula ano (,) can only be used if an, exact initial value of the derivative is known. The other is a simple difference formula ym+1 ,3 ([ [) (34) that is less accurate but does not need an initial value. As a general rule, differentiation should be avoided if possible and differentiation of the control variables should seldom be required. As shown in an example below, advancement of a high-order differential equation is possible without using a differentiation component. Each control component generales an equation and together the components generate a system of nonlinear simultaneous equations. Ultimately the system of equations will be solved using sparse matrix techniques and iterations will be used if the equations are nonlinear. Additional components and the ability to specify upper and lower limits are also planned. MODI contains only a preliminary implementation of the control system. The solution of the simultaneous equations is approximated by simply evaluating the equation for each component in order of increasing component numbers and using the then available information. For time-advanced variables other than control variables, both the old (Vm) and new (Vm + 1) quantities are available. If a control variable is defined (by appearing on the left side of an equa- , tion) before it appears on the right side, both the correct old and new variables are the correct quantities. If I a control variable appears on the right side before it is defined, or if it appears in the defining equation, the new and old values are off 6y a time step. That is, Vm + 1 uses Vm, and Vm uses Vm-1. For good results, the user should try to define a control variable before using it. This is not always possible as shown in the second example below. . 1 The control system input provides for an initial value and a flag to indicate that the initis' value is to be i computed during the initialization phase of input processing. The initialization of neativ all other systems l 43
I l l l l such as hydrodynamics, heat structures, and reactor kinetics precedes that for control systems. If one of those systems needs an initial value of a control system variable, the input value is used. The initial values I et the start of a transient are those computed during control system initialization. . RELAP5 treats control system variables as dimensionless quantcies. No units conversion of the input l waling factors or multiplier constants is done when British input units are specified and no units conver-sion is done on output when British output units are specified. All dimensioned variables are stored within the program in SI units and the units for variables that can be used in control components are stated in the input description. The user may assume any desired units for each control variable. It is the user's respon-I sibility to enter appropriate scale factors and multiplier constants to achieve the desired units and to maintain unit consistency. Two examples of control system use are given. The first is to compute the total flow ratio in a volume from W = aggg o v A + a7pfvAf . (15) where a is void fraction, p is density, v is velocity, A is flow area, the subscript f denotes liquid, and the subscript g denotes vapor. Two multiplication and one addition-subtraction components are used. The time-advanced quantities a, p, and v, are specified as V1 , V2, and V 3respectively in the two multiplication components, one for each phase. The area A would be entered as the scaling factor. An addition-subtraction component adds the results from the multiplication components with A0 = 0, A1=A2 = S = 1.0, and Vi and V2being the control variables defined by the multiplication components. For the present numerical scheme, the products should be defined first. The second example is to solve A 2
+A y i+A 10 *A 0
X+B Xdt = C. (16) Assignment of control variables, Yj, are made to derivative, integral, and product terms as listed below. In addition, each line shows equivalent expressions derived from algebraic manipulation, definition of an integral, and the assignments. I Yy = XX = Y Y34 (17a) 1 Y2=X =p2 C-AYy3-A 10Y y - A04- Y 5 (17b) Y 3=A= Y dt = Y2 dt (17c) Y4=X= i dt = Y dt 3 (17d) Y Xdt = Y4 dt (17e) 5= M \
The control components are defined by the rightmost expression. Thus, the third-order, nonlinear equa-tion is defined by a multiplication, an addition-subtraction, and three integration components. Note that-- i jq the above expressions cannot be rearranged so that all control variables are defined on the left before being "Q used as operands on the right. The above order is recommended for the current numerical scheme. Control variables are printed in major edits, can be specified for minor edits, and can be plotted. a l 1 i l l l l i
)
1 l
) .C
( 45 J
l l 1
- 9. PROBLEM EDITING Printed output is always generated and plotted output is optionally produced. Frequency of output is I user-specified and discussed under time step control.
l l 9.1 Printed Output l i A program version identification and page number is printed at the top of every page. (The program installed in computers not at INEL may not have this feature.)
)
1 l i 9.1.1 Input Editing. Printed output for a problem begms with a list of card images, one per lin:, pre-l ceded by a sequence number. The sequence number is different from the card number on data cards. I I Notification messages are listed when data card replacement or deletion occurs. Punctuation errors such as ! an alphabetic character in number fields, multiple signs, periods, etc., are noted by an error message and a i
$ is printed under the card image indicating the column position of the error. 5 input processing consists of three phases. The first phase simply reads and stores all the input data for a problem such that the data can later be retrieved by card number. Error checking is limited to punctuation checking and erroneous data flagged during this phase nearly always causes additional diagnostics in later .
phases. The second phase does the initial processing of data. Input data are moved and expanded into dynamic arrays sized for the problem being solved and default options are applied. Processing and error checking is local to the data being processed. That is, when processing a single-junction component, no checking whether the connected volumes exist is performed. Similarly, hydrodynamic volumes connected to heat structure surfaces are not checked during processing of heat structure boundary data. At the end of this phase, all data cards should have been used. Unused cards are considered errors and are listed. ; I Asterisks following the card number indicate that the card nurnber was bad, an error was noted in the card I image listing, and that the number is the sequence number rather than the card number. The third phase i completes input processing and performs requested initialization. Upon completion of the second phase, data specifying linkages between various blocks of data can be processed and checked. Examples of error checking during this phase are junction connections made to nonexisting volumes, illegal multiple connec- j tions, heat structure surfaces connected to nonexisting hydrodynamic volumes, and specified thermal i properties and power data not entered. Solution of steady state heat conduction for initial temperature distribution in heat structures is an example of initialization. t l Depending on type of data, input is edited in only one of the last two edits or in both of them. Error I l diagnostics can be issued during either phase, even if no editing for the erroneous data is done in a phase. 1 When an error is detected, possible corrective actions are: disregarding the data, which usually leads to other diagnostics; inserting benign data; or marking data as being entered but useless for further proces- ) sing. These actions are taken so that (other than errors on problem type and options) input processing con-tinues despite severe errors. Regardless of errors, all data are given preliminary checking. Severe errors can limit cross checking. Correcting input errors diagnosed in a submittal may lead to other diapostics in a l subsequent submittal as elimination of errors allow more detailed checking. Except for exceeding i requested computer time and printed output limits, any abnormal termination is considered a program-ming error and even exceeding computer time limits is prevented during transient execution. The final message of input processing indicates successful input processing or that the problem is being terminated due to input errors. 9.1.2 Major Edits. Major edits are a complete editing of the quantities being advanced in time. Output includes a time step summary, trip information, reactor kinetics data, two sections of hydrodynamic volume data, time step controlinformation for each volume, two sections of junction data, heat structure temperatures, heat structure heat transfer information, and control variable results. Major edits are quite lengthy and care should be ssed in selecting print frequencies. Some sections of major edits can be bypassed through input data on time step control cards. One complete major edit is as shown in Figure 6. 46
9.1.3 ' Minor Edits. Minor edits are edits cf user specified quantities. Frequency cf minor edits 'are user o , specified and may be different from maja edits. Figure 9 shows one page of minor edits. Selected quan-tities are held until50 time values are stored. The minor edit information is then printed,50 time values on a page, nine of the selected quantities per page, with time printed in the left column on each page. Minor edits can print selected quantities at frequent intervals using much less paper than major edits. -l 1y :1 9.1.4. Diagnostic Printout. During transient advancement, if difficulties arise that force ternunation of .
.the problem and these difficulties are of the type caused by programming errors, the advancement is- 1 repeated producing tables of variables that are used in and computed by each subrmatine. This output is normally used only by the development staff to correct the program.
8.1.5 Final Termination. The last line indicates the reason'for problem termination. 9.2 Plotted Output . The RELAP5/ MODI computer code includes an improved plot package in which input data is of the same format and is processed with other RELAP5 input data. Input for the MODI plot package is described in Appendix A. In addition the RELAP5/ MODO plot package has been retamed and may be accessed by entering a special card. Input data for the MODO plot package is described in Appendix B.
' Both plot packages utilize the DISSPLA3integrated software system.
The RELAP5/ MODI plot package is designed to provide maximum user convenience in that only one-plot request card is required for each plot desired. All other leput cards are optional. Each plot request card may specify that up to nine curves of RELAP5 results will be drawn per plot. Up to ten curves per plot of input data may be specified by entering plot companson data table cards. The plot comparison data tables we also input and processed wi'h the standard RELAPf input data. Optional input cards for the plot package are provided so that users can specify special units, special character styles, headings, titles, logarithmic axes, grids, c 2rve line styles and symbols, and curve labels. The options can be specified for all of the plots or individual plots. This extensive set of options has been - provided so that high quality plots can be produced for presentations, reports, or publications. Examples - of the graphs produced by the plot package are shown in Figures 10 through 20 and in Volume 3. Two additional plot packages MAGNUM and QKPLOT that are extended to RELAP5 are also 4 available. These plot packages are part of the ISDMS Experimental Data Processing System and can generate graphs of RELAP5 results compared to expenmental results using either batch or interactive processing. Fummples of graphs produced using MAGNUM are presented in Volume 3. 47
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4-a- O 0.0 d.1 d.2 6.3 d. < i.s T!MC (SCC) Filmre 13 Pressure p!ct, Edwards Pipe Problem, gauge Station 4. 50
E RELRP5/M001/001 RCACTOR LOSS Or COOLANT ANALYSIS PROGRAM,
- m. CDWARD'S P!PC PROBLEM BASE CRSC WITH CXTRAS 11/06/80 g.
I e d" o---e CDWARDS P-GS-S 3 P 3080000 E_ a. e e-O n 5 c.o d. I d.2 d.3 d.4 d.s TIME ISCCI Figure 14. Pressure plot. Edwards Pipe Problem, gauge Station 5..
- ' RELRPS/M001/001 REACTOR LOSS Or COOLRNT ANALYS]S PROGRAM CDWARD'S PIPC PROBLEM BASC CRfC WITH EXTRAS 11/06/80 o
8 8* . o - cCDWARDS v01DG-GS-S.
- VOIDG 3080000 si-
=
- o. p o. i o.2 o. 3 c. < o. 5
[ TIMC ISCC) k Figure 15. Void fraction plot, Edwards Pipe Problem, gauge Station 5. 51
RCLAPS/M001/001 RCACTOR LOSS Or C008. ANT ANALYSIS PROGRAM-COWARO'S P1PC PROBLCM BASC CASC WITH CXTRAS 11/06/80 I-3" N _
. . , ~ .
_ l-5 3' o - cEDWARDS TEMPr-GS-5 TEMPr 3080000 3" a b , , , . 0.0 0.1 0. 2 0. 3 0. 4 0. 5 TIME ISE01 Figure 16. Temperature plot, Edwards Pipe Problem, gauge Station 5. RCLAP5/M001/001 RCACTOR LOSS Or COOLANT ANALYSIS PROGRAM O COWARO'S PfPC PROBLCM BASC CASC WITH CXTRAS 11/06/80 DE =$. a ei - t a 4- 3 -cCOWARDS P-GS-6 _ P 3050000 E_ L a 4~ l h- - a d'
, a C
I 0.0 d.1 d.2 d. 3 d. 4 d.5 1 TIMC ISCC) ' Figure 17. Pressure plot, Edwards Pipe Problem, gauge Station 6. 52
)
E__
RELAP5/M001/001 RCACTOR LOSS Or COOLANT ANA YSIS L PROGRAM
,-~s GOWARO'S PlPC PROBLEM BASE CASC WITH CXTRAS 11/06/80 l ) ~J y, O
s* ll o"
# o--e CDwAROS P-GS-7 )
P 3010000 f
\
(L y : :
~,
c. O - c.c d. I d.: d.3 c'. 4 d.5 TIME ISCCI Figure 18. Pressure plot. Edwards Pipe Problem, gauge Station 7 p-g I
'~
RELAPS/M001/001 RCACTOR LOSS Or COOLANT ANRLTSIS PROGRAM COWARO'S PIPC PROBLCn BASC CASC WITH EXTRAS 11/06/00
=
O E5" 3. U M
~#
p 2" bo s' 0 O, O
- 0. O d. I d.2 d,3 d,4 g,s i
! (.%; TIMC (SCCI
\. '/
Figure 19. CPU time plot, Edwards pipe. 53
O RELAPS/M001/001 REACTOR LOSS Or COOL.*NT ANALYSIS PROC, RAM COWARD 5 PrPC RROBLCM SASC CASC wf Th.PTRAS t I/06/80 e o i
~
a H g i m Fa $" Z h
"o O
30 d.1 0'2 U'* 3 N.4 3'. 5 IIMC ISCC) ] Figure 20. Vapor generation rate plot. Edwards pipe, Volume 3200000. 4 i ll 1 l l l l 9' 54
. 1 10.l TIME STEP C' ONTROL '. Input data for time step control' consist of one or more cards containing a time limit, minimum time step, requested (maximum) time step, control option, and minor edit, major edit, and restart frequencies.
The time limit must increase with increasing card number. The information on the first card is used until problem time exceeds the card limit, then the next card is used, etc. In restart probletas, these cards may remain or may be totally. replaced. Cards are skipped if necessary until the problem time at restart is
. properly positioned with regard to the time limit values.
Three time step control options are available. Transfer of information between the hydrodynamic and ' heat conduction advan=nents is explicit and the advancement routines are coded so that each advance-ment can use a different time step. Although not now used, each heat structure can also use its own time step. Option 0 attempts to advance both the hydrodynarnic'and heat conduction advancements at the
- requested time step. However, the hydrodynamic time step will be reduced such that the Courant limit is satisfied. If out of range water property conditions are encountered, the advancement will be retried with reduced time steps. The problem will be terminated if the time step must be reduced beyond the mimmum :
time step. Each time step reduction halves the previously attempted time step. At the beganing of an advacement for a requested time step, a step counter is set to one. Whenever a reduction occurs, the step counter is doubled. When a successful advancement occurs, the step counter is reduced by one. When the' ' step counter is decremented to zero, the problem has been advanced over one requested time step. Doubl-ing of the time step is allowed only when the step counter is even, and the step counter is halved when the time step is doubled. With Option 0, the time step is doubled whenever possible. At the completion of advancements over a requested time step, the next requested advancement is obtained and may be different from the previous requested time step if data from the next time step control card is used. If necessary, the new requested time step is reduced by halving until the new actual time step is less than 1.5 times the last successful time step. Option 1 includes the features of Option 0 and in addition uses the halving and doubling procedure to maintain an estimate of hydrodynamic truncation error within program defm' ed limits. If an acceptable error is not reached and the next reduction would lead to a time step below the minimum time step, the advancement is accepted. The first 100 such occurrences are noted in the output. Optien 2 includes the heat conduction advancement in the above procedures. Only the hydrodynamic error is monitored but t$e heat conduction advancement is advanced at the same time step as the hydrodynamic advancement and both advancements are repeated when a time step reduction occurs. Option 0 is not recommended except for special program testing situations. If Option 1 is selected, care must be taken in selection of the requested time step. Individually, the hydrodynamic and heat conduction advancements are stablet the hydrodynamic time step is controlled to assure stability, the heat conduction solution with constant thermal properties is stable for all time steps, and the change of thermal properties with temperature has not been a problem. The explicit coupling of the hydrodynamic volumes and heat structures through heat structure boundary conditions can be unstable and excessive truncation error with large time steps can occur. This has been observed in test problems. Future versions of the code should include an automatic time step control for each heat structure, but user care is required in the present ver-sion. Option 2 usually eliminates the problem, but often with unnecessary calculations. Judicious use of this option during dryout and initial rewetting may be cost effective. Most LOFT and h=ble simulations have used Option 2 for the entire problem. The minor edit, major edit, and rcstart frequencies are based on the requested time step size. A fre-quency n means that the action is taken when a period of time equal to n requested time steps has elapsed. The edits and restart are taken at time zero, and at the specified frequencies up to the time limit on the time step control card. The maximum time step is reduced if needed and the edits and restart are forced at the time limit value. Actions at the possibly new specified frequencies begin with the first advancement with a new time step control card. A restart forces a major and minor edit, and a inajor edit forces a minor edit. l
l 1 Plot information is written to the internal plot and restart-plot files whenever a minor edit is taken. Note l that minor edits are produced only if minor edit requests are entered; a plot file is written only if plot requests are entered; and plot and restart data are written on the restart-plot file only if the file is l i requested, j An option used for program testing can force a plot print, minor edit, major edit, or combinations of these at each advancement. Care should be used since considerable output can be generated. . As shown in Figure 6, the first section of a major edit prints t!'e problem time and statistics concerning time step control. REPEATED ADV. is the number of advancements that were not accepted and were retried with a halved time step. SUCCESSFUL ADV. is the number of accepted advancements and ATp!MPTED ADV. is the sum of the number of successful and repeated advancements. REQUESTED ADV. is the number of advancements with the specified requested time step. These are presented in two columns. The TOT. column is over the entire problem; the EDIT column contains the number since the previous major edit. MIN. DT, MAX. DT, and AVG. DT ar e the minimum, maximum, and average time step used since the last major edit. REQ. DT is the requested time step used since the last major edit. This quantity may not be the requested time step entered on the card if the major edit is for the final time value on the card. LAST DT. is the time step used in the last advancement. CRNT. DT is the time step limit imposed by the Courant stability criterion. ERR. EST is the estimate of the truncation error at the advancement. Time step control Options 1 and 2 reduce or double the time step to keep this quantity between the limits 2.010-5 and 2.010-3. CPU is the CPU time for the entire problem up to the time of the major edit. TOT. MS is the total mass currently contained in the hydrodynamic system and MS. ERR is an estimate of the error in the total mass due to tmncation error. M.RATO is the ratio of the mass error to the total mass at the start of the transient; M.RATN is the ratio of the mass error to the current total mass. The output lists the ratio with the largest denominator, thus the smaller of the two ratios. Major edits forced by the program testing option or the last major edit of the problem terminated by approach to the job CPU limit may not coincide with the requested time step. When this occurs, a warning message that not all quantities are advanced to same time points is printed. Major edits contain optional time step statistics for each volume. Figure 6 includes an example of this section. The numbers under LRGST. MASS ERR are the number of times a volume had the largest mass error. The numbers under MIN. COURANT are the number of times a volume had the smallest time step based on the Courant stability limit. One volume under each of the headings is incremented by one each successful advancement. The columns under REDUCE indicate volumes that have caused time step reduc-tions. The MASS and PROPTY columns are for reductions due to mass error and out of range ther-modynamic properties. The QUALITY column is for reductions due to static quality being advanced te a value less than -0.01 or greater than 1.01. The EXTRAP column is for reduc? ions when extrapolation into a metastable thermodynamic state leads to a negative density. Columns under the REDUCE headings are incremented only after a successf ul advancement following one or more successive reductions. Quantities are incremented only for those volumes that caused the last reduction. More than one column and row quantity can be incremented in a time step. The control option is a packed word containing the time step control option, a major edit select option, and a debug output option. The major edit select option allows sections of major edits for the hydrodynamic volumes and junctions, hest structures, and statistics to be skipped. The debug output cption forces any combination of plot, minor edits, or major edit output at each successful advancement rather than at just the completion of advancement over a requested time step. All options can change with each time step control card. O 56
l
- 11. TRANSIENT TERMINATION
"\
(d The transient advancement should not abort (terminate by operating system intervention) except for exceeding ph line limits. (Program aborts are indications of programming errors.) The user may optionally specify one or two trips to terminate a problem. Normal termination is from one of these trips or the advancement reaching the final time on the last time step control card. Minor and major edits are printed and a restart record is written at termination. Since trips can be redefined and new time step cards can be entered at restart, the problem can be restarted and continued. Transient termination can also occur based on two tests on the CPU time remaining for the job. One test terminates if the remaming CPU time at the completion of a requested time step is less than an input quan-tity. The second test is similar but the comparison is to a second input quantity and is made aftcr every time-advancement. The input quantity for the first test is larger than for the second test because the pre-ferred tennination is at the completion of a requested time step. In either case, the termination can be restarted. Failure terminations can occur from several sourcer, including hydrodynamic solution outside of range of water property subroutines, heat structure temperatures outside of thermal property tables or functions, and attempting to access an omitted pump curve. Attempting to restart at point of failere or at an earlier time without some change in the problem input will only cause another failure. The problem changes allowed at restart in the MODI version may allow the problem to be successfully restarted. Requested plots are generated after a failure termination. O
!]
lO 57 i 4
. _ - _ _ _ _ . _ _ . i
- 12. PROBLEM TYPES AND OPTIONS RELAP5 provides for five problem types, NEW, RESTART, PLOT, REEDIT, and STRIP. The first two are concerned with simulating hydrodynamic systems; NEW starts a simulation from input data describing the entire system; RESTART restarts a previously run NEW or RESTART problem. PLOT, REEDIT, and STRIP are output type runs using the restart-plot file written by NEW or RESTART problems. NEW and RESTART problems require an additional option to be selected, STDY-ST, STDY-TRN, or TRANSNT. TRANSNT is the only option fully implemented in MODI and specifies the solution of a transient problem.
A steady state problem can be solved by specifying boundary conditions suitable for a steady state problem, entering constant power, and running a transient problem until a close approximation to steady state is reached. In reactor type problems, the steam dome of the pressurizer should be replaced with a liquid-filled, time-dependent volume at the prescribed pressure. Rather than guess at pressure and velocity distributions, specifying all pressures equal to the pressurizer pressure and zero velocities might be more effective and is easier to set up. Changes are needed to initiate the transient. Unless this can be c.ccom-plished by trip logic, a manual transfer of steady state results to the transient model is required. When transferring results to the volume initial conditions, the option requiring pressure, internal energy, and static quality should be used. This option uses the same water property calculations during input proc-essing as used during transient advancement. Other initial condition options can introduce slight perturbations. A RESTART problem may restart from any restart record. A nr se indicating the restart number and record number is printed at the end of the major edit whenever a restart record is written. The restart number is equal to the number of attempted advancements and is the number to be used on Card 103 to identify the desired restart record. The record rmmber is simply a count of the number of restart records written, with the restart record at tinte equal zero naving record number zero. PLOT, REEDIT, and STRIP are output type runs. PLOT generates plots from data stored on the restart plot file. Any of the quantities that can be plotted in a NEW or RESTART problem except interior heat structure temperatures can be plotted in a PLOT run. REEDIT will generate minor edits from a restart-plot file but this capability is not available in the MODI version. STRIP write: selected information from a restart plot file onto a new file. The new file consists of records containing time and the user-selected records in the order selected by the user. 1 l l l i 1 l l O
$8 l l
_ _ _ _ _ _ _ _ _ . _ _ l
- 13. ' PROBLEM CHANGES AT RESTART >
The most common use of the restart option is simply to continue a problem after a normal termination. O- If the problem terminated due to approaching the CPU time limit, the problem can be restarted with no changes to information obtamed from the restart file. If the problem stopped due to advancement time reaching the time end on the last time tlep card, new time cards must be entered. If the problem was ter-minated by a trip, the trip causing the termination must be redefined to allcw the problem to continue.
. Thus, the code must provide for some input changes for even a basic restart capability.
The ability to modify the simulated system at restart is a desirable feature. The prunary need for this feature is to provide for a transition from a steady state condition to a transient condition. In many cases, simple trips can activate valves that initiate the transient. Where trips are not suitable, the capability to ,
- redefine the problem at restart can save effort in manually transcribing quantities from the output of one simulation to the input of another. One example of a problem change between steady state is the use of a liquid-filled, time-d==dat volume in place of the vapor region of a pressurizer during steady state. The time-dependent volume provides the pressurizer pressure and supplies or absorbs water from the primary system as needed. The time-dependent volume is replaced by the vapor volumes at initiation of the tran-
- sient. This technique avoids modeling the control system that maintains liquid level and temperature dur-ing steady state calculations when they are not needed in the transient.
Another reason for problem change capability is to reduce the cost of simulating different courses of action at some point in the transient. An example is a need to determine the different system responses when a safety system continues to operate or fails late in the simulation. One solution is to run two com-plete problems. An alternative is to run one problem normally, and restart that problem at the appropriate time with a problem change for the second case. The problem cha ,e capability could also be usef . tenodalize a problem for a certain phase of a tran-sient. This has not been necessary or desirable for eroblems run at INEL. For this reason, techniques to
\ automate the redistribution of mass, energy, and niomentum when the number of volumes changes have not been provided.
The current status of allowed problem changes at restart in RELAP5/ MODI are summanzed below. In all instances, the problem definition is that obtained from the restart tape unless input data is entered for deletions, modifications or additions. The problem defined after input changes must meet the same requirements as a new problem. Time step control can be changed at restart. If time step cards are entered at restart, all previous time step cards are deleted. New cards need only define time step options from the point of restart to the end of transient. Minor edit and plot input data cards can be changed at restart. If any of the minor edit cards are entered, all previous cards are deleted. New cards must define all desired minor edit quantities. The plot request data cards are handled in the same manner. Trip cards can be entered at restart. The user can specify that all previous trips be deleted and can then define new trips. Alternately, the user can specify that the previously defm' ed trips remain, but that specific trips be deleted, be reset to false, or be redefined, or that new trips be added, i Existing hydrodynamic enmponents can be deleted, changed, and new components can be added. An especially useful feature is that the tables in time-dependent volumes and junctions can be changed. Control system components can be deleted, changed, or added. 59
Heat structures, general tables, and material properties cannot be changed. The inability to change heat structures limits the ability to change hydrodynamic volumes that are attached through boundary condi. tions. A hydrodynamic volume that is connected to a heat structure cannot be deleted since the boundary I condition would then be in error. Reactor kinetics can be defined only at the beginning of a problem and cannot be changed at restart. O 1 l l l l l O r
- 14. RELAP5 FILE USAGE '
[) k/ The following descriptions assume standard CDC operating s stems. A NOS-BE system is assumed to be a Cyber-176 or -173 type machine operating under the NOS-BE system. A SCOPE-2 system is assumed to be CDC 7600 operating under the SCOPE-26 system. Default file structures are used. The program cards for RELAP5 are: NOS-BE PROGRAM RELAP5 (INPUT. OUTPUT,RSTIN,RSTPLT, TAPE 5 = INPUT, j TAPE 6= OUTPUT,
- DEBUG = OUTPUT,PLOTFL,STH2XT) !
SCOPE 2 PROGRAM RELAP5 (INPUT, OUTPUT,RSTIN,RSTPLT. TAPE 5 = INPUT, TAPE 6= OUTPUT,
- DEBUG = OUTPUT PLFILE,PLOTFL).
14.1 Input File , The input data uses the standard 80 column card or its equivalent. However, to accommodate card maintenance programs such as UPDATE7 and interactive text editors such as EDITOR8, RELAPS reads and echos to the output up to 90 columns of information. Only the first 80 columns are used for program input; the other 10 columns are for assistance in external manipulating of card data. If UPDATE is used, the D option to specify 80 columns of data should be specified. If EDITOR is used to create program input, the file should be saved without line numbers or the command F.CH =80 should be used to define /7 80 columns of information if line numbers are desired. Detailed input requirements are given in b Appendix A. The older of the two currently installed plotting options uses a different input philosophy than the main part of RELAP5. If this plotting option is used, only 80 columns of information must be presented to the program. For UPDATE, the D,8 option must be used; for EDITOR, the edit numbers must not be included. This plot input is described in Appendix B. 14.2 Output File The output file is a standard output file. The default line limits are used and if a large amount of printed output is expeted, PL = n, where n is somewhat more than the expected number of lines, should be added to the RELAP5 execute card. 14.3 RSTIN File This file is required for all problem types except NEW. This file is the RSTPLT file written in a previous RELAP5 execution. The file may be a tape or disk file. If a tape file, a REQUEST (RSTIN,...) control card for NOS-BE or a STAGE (RSTIN, PRE,...) control card for SCOPE-2 must be used. A disk file may be a local file created in a previous step or an attached permanent file. On SCOPE-2 systems, the input to the program can attach and return a permanent file, freeing the user from entering control cards. 14.4 RSTPLT File 4 m ; This file is optionally written in NEW and RESTART type problems and is always written in STRIP l] \ problems. If a tape file is desired, a REQUEST (RSTPLT ...) control card for NOS-BE or a STAGE 61
(RSTPLT, POST) control card for SCOPE-2 is required prior to the RELAPS execution card. If a perma-nent disk file is desired, the user can use a REQUEST (RSTPLT,*PF) card ahead of the RELAP5 execu-tion card and a CATALOG (RSTPLT,...) after the execution card. On SCOPE-2 systems, the user may also request RELAP5 to create the permanent file or stage the tape eliminating the need for the contro! cards. 14.4.1 RSTPLT File Written by NEW-RESTART Problems. This file can be subsequently read as RSTIN file. It can also be read by other programs (such as plotting programs) tlut generate comparison plots with experimental data. The file is written by BUFFER OUT (RSTPLT,1) statements. The letters A I, and R indicate alphanumeric, integer, or real type variables. 14.4.r.r asmT RecoM-This record is the first record. Words 1 - 2(A) Program identification identical to the first 10 columns at the top of every printed page. At tic of writing this document, the words contain RELAP5/MODl/001. Words 3 - 4(A) These words contain RESTART-PLOT FILE. Word 5(I) This word currently contains 0. It can be incremented whenever program changes make previously written RSTPLT files incompatible for restart with a newer version. The plot record philosophy should be immune to these changes. Word 6(A) This word contains the date the file was written. 14.4.r.2 PLOTINF, PLOTALF, PLOTNUM. and PLOTREC Records-These records are used to store simulation results and to provide for subsequent use of these results in the PLOT, REEDIT, and STRIP options of RELAP5. These records can also be used to pass simulation results to other computer programs although the STRIP file is recommended because it is easier to use. Simulation quantities written to tape are time j and hydrodynamic component, volume, junction, heat structure, reactor kinetics, and control system I results. The amount of data is problem-dependent and can change at restart if the problem is changed. The PLOTINF record is a three-word record containing PLOTINF in the first word and zero in the third word. The second word contains the length of the following PLOTALF, PLOTNUM, and PLOTREC records. PLOTALF and PLOTNUM records always immediately follow a PLOTINF record. The PLOTALF, PLOTNUM, and PLOTREC records are of equal length and the words in the PLOTALF and PLOTNUM records are the identification for the quantities stcred in the corresponding words of the PLOTREC records. The identification is the same as.the request codes for plotting and minor edits. Word I of the PLOTALF contains PLOTALF; the remaining words contain the alphanumeric por-tion of the variable request code for the corresponding word in PLOTREC records. W>rd 1 of the l PLOTNUM record contains PLOTNUM; the remaining words contain the numerical fortion of the i variable request code. The number of PLOTREC records depends on minor edit frequenues on the time i step control cards. Word 1 of the PLOTREC record contains PLOTREC. Word 2 rantains time; the l remaining words contain simulation quantities corresponding to the time value. PLOTINF, PLOTALF, and PLOTNUM records are always written as the second, third, and fourth record of a RSTPLT file. These records define the length of the PLOTREC records and the position of the simulation results in the records. Whenever a problem changes at restart, the length or content of the PLOTREC records changes. PLOTINF, PLOTALF, and PLOTNUM records are written to define the new length and position of results. 62
_m L i l> J A ud.f.3 AfsTANT Assoms-Whenever the printed output indicates a restart record is' written, in reality a d block of records is written, and the number or records and their length is. problem d==d-t. These i
. . ' records are of use only to RELAP5 during a restart. For use outside of RELAP5, any record not having j t.
PLOTINF, PLOTALF, PLOTNUM, or PLOTREC as the first word should be skipped.
\_ /
M4.r.4 #essunt ene asrMrme-The following procedure is suggested for extracting information from - the plot records of the RSTPLT file. Identification quantities to be extracted are' read from an input file.< These should be the variable request code for each quantity consisting of an alphanumeric and a numeric e - word. These request codes relate directly to the quantities used in the RELAP5 run that generated the file. The first record of the RSTPLT file is read and checked to verify that it is a RSTPLT rde from RELAP5. propriate combinations of the This BUFFER IN statement and status checks made using the UNIT function. using yThe9 LENOTH subroutine and all other reads of the RSTPLT file should be made be used to determine the actual length. Good programming practice is to attempt to read one more word - l than expected and check that only the expected number of words were actually read. Using the record .
- length from the PLOTINF record, two buffers are established and the PLOTALF and PLOTNUM records are read.
l For each variable request, a search is made of the information in the PLOTALF-PLOTNUM records for a match. Failure to obtain a match is not necessarily an input error. The desired quantity may not be present at the begmning of a RSTPLT file, but due to a problem change at a restart, may appear later in the file. Similarly, deletion of a desired quantity may occur at a restart. The program reading the file must provide for entering default data or terminating when there are missing quantities. If a match is found, the - position of the match (index in the buffers) is saved for future retrieval of information from PLOTREC records. After all the input requests are processed, PLOTREC records can be read into the buffers previously containing the PLOTALF and PLOTNUM records using a double buffering technique if desired. If the first word of a record is not PLOTREC or PLOTINF, the record is ignored, since it h a record from the restart information. When a PLOTREC record is read, the desired information can be extracted from the positions of the data determined previously. If a PLOTINF record is read, the buffer lengths are adjusted for the new record length given in the PLOTINF record and the process of reading PLOTALF and PLOTNUM records, attempting to match requests, and reading PLOTREC records is repeated. An end of file return from the IF (UNIT...) test - indicates the end of the RSTPLT file. The above procedures allow programs processing a RSTPLT file to be used even when additional variables are added to the RSTPLT file. 14.4.2 RSTPLT File Written by STRIP Problem. For convenience, the RSTPLT file written by a STRIP type problem will be called the STRIP file and the RSTPLT file written by a NEW or RESTART problem will be called a RSTPLT file. The STRIP file is simdar in structure to the RSTPLT file, but readmg the STRIP file is much simpler than reading the RSTPLT file, since only information requested by the user is written and written in the order requested. No restart records are written on a STRIP file.
. x4.2.7 srmP Ascent-This record is the first record. This record is identical to the RSTPLT (first) record of the RSTPLT file except Words 3-4 contain STRIP FILE, and Word 5 is always zero.
24.2.2 Mormr, MotAtr, Morwuar, omtMor#tc Asseds-These records for the STRIP file are identical in structure and positioned the same as for the RSTPLT file. Word 2 of the PLOTREC records is time; the remaining words are quantities requested by the user in the order requested. The alphanumeric and ' l numeric quantities in PLOTALF and PLOTNUM will be identical to user-supplied request codes. Since the input requests do not vary during a STRIP problem, the PLOTALF and PLOTNUM records never change. Thus, the PLOTINF, PLOTALF, and PLOTNUM records are written only once as the second, third, and fourth records. Whenever a requested variable is not present on the RSTIN file being processed, O a negative indefinite quantity (60000000000000000000B) is written in place of the missing variable. A pro-gram reading the STRIP file can test for missing variables by an integer test for the indefinite value or through the LEGVAR9 function. 1
)
63
14.4.2.3 Reed /ng the STRIFFne-The STRIP tape may be read using the same procedures as for reading the RSTPLE file. However, shortcuts can be taken since the order of information is controlled by the user. Consider a case where an analysis program needs a particular volume pressure and density from a RELAPS simulation. One job step could be a STRIP type RELAP5 problem extracting the desired pressure and density (and in that order). The STRIP file is rewound and the analysis program executed. The analysis program skips the first four records (STRIP, PLOTINF, PLOTALF, and PLOTNUM records). Then, as needed, subsequent records are read and Words 2-4 of each record contain time, pressure, and density. . 14.5 PLFILE File The plotting capability uses the DISSPLA3 package and plotting commands are written on PLFILE. The commands are in a generalized form and an auxiliary DISSPLA program is needed to transform them to a particular plotting device. Because of the differences in DISSPLA between the two systems, this file appears on the PROGRAM card for SCOPE 2 systems, but not for NOS BE systems. The NOS-BE ver-sion of RELAPS is compiled with the STATIC9 option. The DISSPLA subroutine writing the PLFILE may need modification to operate in the static modt. 14.6 PLOTFL File PLOTFL is a scratch file on which information is written during problem advancement for plotting after transient termination. 14.7 STH2XT File This file name is on the PROL AAM card for the NOS-BE version but not on the SCOPE-2 version. This file is a water property table file consisting of two records read by FORTRAN unformatted reads. The file is required only for NEW and RESTART problems. This file can be generated by the STH2OO10 progrs.m. O 64
)
i
- 15. RELAP6 CONTROL CARD REQUIREMENTS .i i
q Control card sequences used to execute RELAP5 on a Cyber 176 using the NOS-BE operating system
-Q are shown in Figures 21 through 23. The control cards are described in the NOS BE reference t..anual.5 1 The user normally would not use these control cards since very general procedures that perform the same functions with only a few control cards are described in the input decription. These examples show required control cards without the added complexity of conditional Cyber control language statements. ,
ij 880Htihit!!!!!ihBIiP-R (Flor) 4 Ai aCH(R$ LAP 50eIS=4JW) (IP AT E ( P= E E L AP 5 0, C, C )
- p"UP N ( REi A14 3 ) i A 7 ACH( R E L A P5 Xt IC wA JW )
A1'T ACH(STh2X SIC =PJW) R EQUE T (RITP Ts PEsE 8s RINGsSVsNs VSM=0) FTLEL eT ss F=WO) FMLFd ST T , B F = N f;) F LECPLC 8F=MC) RFL(CM 2 a sEC=2M) RELAP5X( E LEsPL=20000) 7-8-9 CA C Gk *E"P ,
- COMP 1 E tub 7RM J Figure 21. RELAP5 control cards for execution of a new problem.
i#8{6Util>ifffi5!88:8 iip-O RFha C=0) AT ACH(RELAP5X ID=RJW) AT"A4h(stb 2XT D=RJW) RF3bEST fRSTIN Es'8sNORINGsEsVSN=??????) t R EGl.E ST LRS1 PL , PE s E Es RINGsS ksNs VSN=0) FILE (RS"!NsSB =MO) F L E(Ra"7 LTsSBF=MC) F LE(FLOT6LsS6F=Nrl R L(CM=270f0SsEC=2M ) R ELaP 5 X (P L = 20000 ) 7-6-9 CARC CR *EP' -RESTART 1-
=EDWAdD'S FIPE FRC8LEP 8ASE CASA WITH EXTRAS 1&3 Sol 204 0.600 1.0-7 0.001 1 10 50 loi
. END CARC Figure 22. RELAP5 control cards for execution of a restart problem.
The following files are assumed stored as permanent files: RELAP5S RELAP5 source in UPDATE OLDPL format RELAP5L RELAP5 object decks in library form (created by EDITLIB) RELAP5X RELAP5 absolute binary SELECTX Program to select compile time options ENVRLl76S INEL Environmental Library L STH2XT Water Property File 65 (
1
$ $2)
UP c RE LEN(PELai53) ATT*Cb(SeLECIXsID=RJW) , SFLFoix(OCMrILEsCOMP) RETbRN(SELECTX) R5kINDLC3f'F) i F Ttt ( I =C RtTbnN(gdF,400n0,'TATICsOPT=2sR=3,AsT) QMF) A77 ACH(RE L A P58 s 10 =R Jw ) ! AF faCH(E4VkL,fMVRLl76S,ID=RJm) A" TACH (01;SPLA, hew 0ISSDLASTATIC) RFL(EC=1) SEGLUA0(T=CCMPTLEsb=RSLAF5X) ! LLI EI(L 4 S skcl AP 5 L /ENb RL / DI5 SP L asp RiSET= NGINDEFs ERR = N0hd ) LwAC(LGC) L ABLO AL (EhVEks $HCR =$) NCGC. a 6TbaW( d'L AP5 6 s FN vt L,0T ?a rL As COMP ILes LGO)
=RJW)
ATTACH (5 H4xTpIgJ=RJW) ATTALH(kELAP50s-UFOATE(L,P=RELAP!Cs0) REfDRH(RsLAP50) FIL E ( Rs Tin, ad e =NO ) r 1Lc ( RS TP Lis s 38 =NC) F15F(PLGTFL,SBF=NO) R rt (C M= 27C000, cC = 200) RELAP5X(CtePILE,8L=20000) 4EJUGE. RFLLEC=0) R ETunn (RE L A P5 X s STH2X TsC OnP ILes P LJTF L ) 8EGP4(Fh80P;P) 7-6-9 CAAL OA *EJE
*IDFbT RJ Axx
*LJ'dPILE LECINEsf5GDIR l
*I AtLAP5.3 C JL;T ANY CA#D TO SH0w UPDATING Of THE PRwGRAM.
7-8-9 CAAL CR
- EOR
*L3PPALE EONEWPL Figure 23. ,RELAP5 control cards for program modification / execution.
RELAP5D Various input decks for RELAPS stored in UPDATE OLDPL i format. i These files can be obtained from the RELAP5 transmittal tape. The cards needed for execution of a NEW problem are shown in Figure 21. The REQUEST card causer the RSTPLT file to be saved on tape. This can be omitted if the file is not to be saved on tape or the file could be saved on disk using REQUEST-CATALOG control cards. The program is executed from the absolute binary. The RFL card defines the maximum amounts of SCM and LCM memoty to be used dur-ing the execution. If a diagnostic message indicating insufficient memory is available, the appropriate requested size should be increased. The sizes in the example, SCM = 270K, LCM = 200K, were used for all problems discussed in Volume 3. If the older plot package is used, the LCM size required is 400K. During certain phases of program execution such as transient advancements, the field lengths are reduced to the minimum needed in order to reduce computer costs. The reduced sizes are problem-dependent and are listed under FLS and FLL in the printout immediately preceding the first major edit. The FLS and FLL numbers could be used to judge whether smaller sizes could be used in the RFL request. The UPDATE card selects the problem labeled EDHTRK from a file containing input for several problems. The control cards needed for execution of a RESTART problem are shown in Figure 22. The first . REQUEST card indicates that the RSTFIN file containing the restart information is a tape file. The second REQUEST card indicates that the RSTPLT file is to be stored on tape. Appropriate ATTACH and 66
-___----__-__--___a
REQUEST-CATALOG cards can be used for disk files. Tape files are illustrated here since the size of fdes j_ - for any but trivial problems may be large. The input data is for RELAP5 and defines the restart point. Modification of the RELAP5 main program source, loading of the changed with the unchanged object decks, and execution of a problem is shown in Figure 23. The first UPDATE modifies the main program; in this case only a comment card is inserted. Whenever source decks are written on the COMPILE file, a
' COMPILE DEFINE is required to force the DEFINE deck containing cards defining the compile time options to be written at the beginning of the COMPILE file. The ' COMPILE SEGDIR card forces the directives to the segment loaderll onto the compile file. A 'CWEOR card preceding the directives separates the modified program source from the directives. SELECTX impleinents the compile time options. More information on the compile time options and the selection process is given in the next sec-tion. SELECTX writes the source decks to be compiled on COMP and leaves the COMPILE file posi-tioned at the loader directives. SEGLOAD initiates the load process. The modif".ed object decks are loaded from LOO and the unmodified decks are obtained from RELAP5L which is a library of object decks cor.
responding to the source file. Environmental library subroutines are obtained from ENVRL and plotting subroutines are obtained from DISSP! A. The resultant absolute binary is executed with a problem obtained through UPDATE from the set of samp3e problems. This problem generates plots and BEGIN (FR80 POP) calls an INEL procedure which converts generalized DISSPLA commands to microfilm plot-ter commands. The resulting graphs are shown in Figures 10 through 20. O ! l 67
- 16. RELAP5/ MOD 1 TRANSMITTAL INFORMATION RELAP5/ MODI is operational at INEL on a Cyber-176 running under the NOS-BE operating system.
A previous version of RELAP5 operated on a Cyber-76 running under SCOPE-2. An attempt has been made to maintain SCOPE-2 capability on this version but no testing under SCOPE-2 has been done. h Coding has also been included to allow operation on Cyber-175 type computers (no LCM memory) but very little testing has been performed with this option. Coding unique to the three different versions is selected by compile time options. Two other options are also selected at compile time. Coding to measure the execution time of the various phases of transient i- advancement can be included. A slight amount of computer time can be saved if the timing is omitted, l since the timing subroutine involves calls to the operating N*em. Another option determines whether vec-tor subroutines should replace equivalent FORTRAN codin s. The vector subroutines execute operations on vectors two to three times faster than OPT =2 FORTRAN by taking advantage of the instruction stack and the segmented, parallel operating functional units. Here, a vector is a series of numbers stored at fixed memory intervals. At present, vector subroutines are used in RELAP5 only to move vectors. . I 16.1 Selection of Compile Time Options UPDATE 7 allows compile time selection of options through *lF and *ENDIF statements. 'IF statements are written as *IF DEF VAR,N. VAR represents one of several variables that may be defined or undefined. If VAR is defined, the next N statements are included in the COMPILE file; if VAR is unde-fined, the next N statements are omitted. If N is missing, statements up to the terminating *ENDIF card are included or omitted. If a minus Sign precedes DEF, the logic for including or omitting cards is reversed. VAR is defined if it appears in a
- DEFINE VAR statement, otherwise it is undefined. Nesting of 'IF with different VAR is permitted. Complete omission of statements leads to inconveniences when making changes unique to different versions. Since the FORTRAN listing shows only one version, other listings showing alternate versions or a listing of active cards from UPDATE must be used.
The SELECTX program provides a more convenient compile time selection of options even though the selection process is very similar to UPDATE. To use SELECTX, SIF and SENDIF cards are placed in the - source in exactly the same fashion as the
- equivalent cards. However, with the 5 in place of the *, the 5 cards are treated as statements, not UPDATE cards, and thus are written to the COMPILE file. In addi-tion, the first deck written to the COMPILE file contains none, one, or more $ DEFINE VAR cards.
SELECTX reads the SDEFINE VAR cards if any are present to set which variables are defined. SELECTX then reads the remaining COMPILE file and writes file COMP with the options implemented. SELECTX processes SIF and $ENDIF cards in the same manner as UPDATE processes the
- equivalents except cards, instead of being omitted, are written with an
- in column 1. The SIF and $ENDIF are also converted to *lF and *ENDIF. Since an
- in column 1 is a comment card to FORTRAN, the $ control cards and omitted cards are listed but have no effect on compilation.
In the RELAP5 source file, the first deck is named DEFINE and contains the following pair of cards for each compile time option.
*IF DEF, VAR,1 SDEFINE VAR Thus, for each variable defined by
- DEFINE VAR, a corresponding SDEFINE VAR card is written to the COMPILE file. A
- COMPILE DEFINE card must be used in the UPDATE input to force the DEFINE deck onto the COMPILE file. No *IF or *ENDIF statements appear in the remaining decks of the RELAP5 source, but they do appear in the loader directives.
The environmental library source does not use SELECTX and uses only UPDATE logic to select options. 68
l
-i Both the RELAP5 source and the environmental library source use the following four ' DEFINE variables to select various options: {
(~% ! V SCOPEO. No LCM use SCOPEI NOS BE SCOPE 2 SCOPE-2 SCOPE 3 Use LCM. The RELAP5 source uses two additional
- DEFINE variables:
TIMED Include transient timing calls VECTOR Use vector subroutines. The CDC transmittal tape contains the source decks set up for a Cyber 176 operating under NOS-BE. For this computer and system, SCOPEl, SCOPE 3, TIMED, and VECTOR are defined and SCOPE 0 and SCOPE 2 are undefined. For a Cyber-76 with SCOPE 2, SCOPE 2 and SCOPE 3 should be defined; SCOPE 0 and SCOPEI should be undefined. For a Cyber l75 type machine (no LCM), SCOPE 0 and SCOPEI should be defined, SCOPE 2 and SCOPE 3 should be undefined. To remove the ' DEFINE cards use:
*D RJWDEF.4 for SCOPEI (RELAPS)
'D RJWDEF.3 for SCOPE 3 (RELAPS)
*D RJWDEF.2 for TIMED (RELAP5)
*D RJWDEF.1 for VECTOR (RELAP5)
'D RJWDEF.2 for SCOPE! (environmental)
*D RJWDEF.! for SCOPE 3 (environmental).
The non-CDC tape does not contain any
- DEFINE cards but does contain all the other logic selection cards. Applying the options for a Cyber-175 machine would be an appropriate start for converting to most non CDC machines.
16.2 Transmittal Package The following discussion pertains to the RELAPS transmittal package prepared at INEL. Other sources such as the National Energy Software Center may choose other formats. The transmittal package contains the following:
- 1. RELAP5/ MODI documentation (three volumes)
- 2. Environmental library manual
- 3. Transmittal tape
- 4. Dayfile showing writing of transmittal tape
- 5. Cards used at INE to test transmittal tape (CDC transmittal only)
- 6. Microfiche containing printed output from a test of a CDC transmittal tape.
p The transmittal tape contains six partitions. (A partition is equivalent to a file on many other computer g systems.) 69 a-_______- - - - - - - - _ _ _ - _ _ _
Partition 1. RELAP5 source. In UPDATE OLDPL form for CDC transmittal; in UPDATE SOURCE form for non-CDC transmittal .j i Partition 2. Environmental source in same format as Partition 1. l Partition 3. RELAPS input data in same format as Partition 1. l Partition 4. Cyber controllanguage procedures for executing RELAP5. i l Partition 5. Editor form of RELAP5 input description. Used as input to j TEXTJAB Ito generate input description in Appendix A. Partition 6. Output file from a test of a transmittal file. Microfiche contains printout of this partition. I As nned above, transmittal tapes are prepared differently for CDC and non-CDC transmittals. The CDC tape is written using standard file defaults for the NOS-BE system. Thus, the first three files are RT=S; the fourth and fifth files are RT=Z, MRL=80; the last file is RT=Z, MRL=137. Unless , specifically requested otherwise. the CDC tape is an unlabeled, nine track,1600 bpi, phase encoded tape j with EBCDIC character labels. The REQUEST card is REQUEST,RELAP5T,PE EB,N, RING,VSN =0. The first five partitions of the non-CDC transmittal tape contains 80 columns EBCDIC coded card images in fixed block format. The last partition contains EBCDIC coded print lines of 140 characters in fixed block format. Unless requested otherwise, the non-CDC tape is an unlabeled, nine-tre-k,1600 bpi, i phase encoded tape with EBCDIC coded characters. The REQUEST card is I REQUEST,RELAP5T,PE,EB, RING,SV,S,VSN = 0. The FILE card for the first five partitions is FILE (RELAP5T,RT = F,BT = K RB = 20,FL = 80,CM = YES), and for the last partition is FILE (RELAP5T,RT = F,BT = K,RB = 20,FL = 140,CM = YES). The IBM OS equivalents are ' DCB = (RECFM = FB,LRECL = 80,BLKSIZE = 1600) DCB = (RECFM = FB,LRECL = 140,BLKSIZE = 2800). 16.3 Installing RELAP5 Using the Transmittal Package A listing of a job deck used to test a CDC transmittal tape is shown in Figure 24. Slight modification of this deck (included in the transmittal package) should allow installation of RELAP5 on CDC computers. The sixth partition of the transmittal tape and the microfiche contain the printed output from a job using these cards. The first group of cards mount the transmittal tape, copy the first five partitions to disk, catalog them as permanent files, and return the tape drive. The second group of control cards and associated input data builds the environmental library file. The input data to UPDATE selects decks to be compiled, omitting plotting subroutines which are not needed in RELAP5 although the resulting library still contains several subroutines not needed by RELAP5. One 70
l t\ [~' R4.;1.T27T,92,'~200,3E1,STANY. as;Juait?*J0.'Il#A24)D.3121
- L - COMMjNT.-RETURN LCM SPACE IN C ASE JOB CAWO EC FIELD ASS IGNED IT.
I R FL (c C = 0) l C C * *. E N T . RE4 JEST TaANSMITTat TAPE TU SE M0JNTED. R E30E S T ( A cL AP5T,D E. E3,N04INu, E, VSN= A424e* l CCa*ENT. CONVERT SEOUEN TI AL ULDPL OF RELAPS SOURCF ON T APE AND C ATALOG CCM*ENT. REQUc3T(RELA AS RAND 9F C 355,**F)LDPL 04 0154. UP3&TE(A,N=REL&P35,0=RELAp3T,R) l CQPYsF(dELAP5T, NULL) l RcTUJh(NULL) CATALOG (RELA 355,ID=RJWTEST,xR=RJWTEST,RP=Q99) COMMjNT. CONVC37 SEQUENTIAL ULOPL OF ENVIRONMEN T AL LISR AR Y SOURCE JN COM?cNT. Tape AND C AT AL 3G AS 4 ANDOM OL3PL JN JISK. RE30EST(iNVRS,*PC) J PO A T RELAP5T, CC3V3r j (( A o N= ENULL) N VR S , P= D $( A o 5 T, D ) RETUEN(NJLLI CATALOG (ENVRS,ID=RJ4 TEST,(R=RJWTEST,RP=4441 CJMPENT. CONVcRT SE0JENTIAL OLJPL OF RE L APS S AMPLE PR0dLEMS ON C J a *E 1T . T APE. AND C AT AL3G A5 R ANDOM OL0PL ON DISA. REJUEST(RELA *53,*P: 1 UPDATE (A,N=4ELAP50,P=RELAP5T,R) . C09Y3F(RELAP5T, NULL) R E T UR N( NJ LL ) CATALOG (4ELA750,ID=RJWTEST,XR=RJdTEST,RP=999) RETv4N(RELAPS)) COMMENT. COPY REL AP 5 PR OCE3URES FROM T APE AND C AT AL OG ON DIS K. RE2UEST(PROCS,*PF) C07Y6F(RELAP5T,P20CS1 C AT ALOG( P ROCS ,R EL AP 5940CS ,ID=RJ WTES T, xR =RJ W TES T ,RP= 9991 COMMENT. CUPY TEXT INPUT TO TEXTJAB 0F RELAP5 INPUT DESCRIPTION FROM C OM ME NT . TAPE AND CATAL0u ON DISK. RE3UEST(TEXT,*PF) i CUPY9F(RELAP5T,TEXTl ( CATALOG (TEXT,RELAP5 INPUT,ID=RJWTEST,xR=RJWTEST,RP=999) 360= RETURN (TEXT RETURN (TixT) COMPENT. YOU COULD *RINT TH E NE XT FILE, BUT IT SHOULD BE VERY MUCH T4E CD1 MENT. SAME AS THE DUTPUT FROM THIS JCB, THAT IS, INSTALLING AND C0 AMENT. EXECUTING RELAP5 FROM THE TRANSMITTAL TAPE. COMMENT. THEREFORE, RETURN THE TRANSMITTAL TAPE. RETURN (RELAP5T) COMMENT. USE UPDATE TO SELECT SUBROUTINES FROM ENVIRONMEN T AL LIBR AR Y COMMENT. SOURCE (PLOTTING D ECKS EXCLUDEDI, COMP ILE/ ASSEMBLE BUILD COMMENT. LIBRARY, AND C AT ALOG ON DISK. S= ON FTN NEEDED F0k SYMBOLIC CCMPENT. SUBROUTINES, FIRST COMPASS GENERATES A TEXT, SECOND USES TEXT CD#. MENT. TO ASSEMBLE MODIFIED FORTRAN OUTPUT SUBROUTINE. UPDATE (0,P=ENVRS) F TN (I = COMP ILE ROUND,0PT=2,S T ATJ C C OM P ASS (5 = 0,0 =INE L T X T ,I = C OMPIL e i, R = 3, A, T, S= SYS T E X Ts S =PF MTE X T C OM P A S S ( 5 = FCL TE X T, S = I OTE X T,5= S Y ST E X T,G= INEL TX T,1 = COMP IL E) R ETURN( INEL TX T) REQUEST (ENVRL,*PF) EDITLIB(L=0) CATALOG (ENVRL,ENVRL1765,ID=RJWTEST,xR=RJWTEST,RP=999) COMPENT. USE UPDATE TO EXTR ACT SELECT PROGR AM, COMPILE, LOAD, AND COMMENT. CATALOG CN DISK. UPDAfElQ,P=ENVRSI kb ,0PT=2,R=3,A,T) RE: UEST(SELECTX,*PF) L3 SET (LI3=ENVRL) LOAD (LGO) NOG 0(SELECTxt C AT AL OG(S EL ECTX,ID= RJWTESie xR =RJW TES T,R P = 9991 COMMENT. USE UPDATE TO EXTR ACT WATER PROPERTY GENERATION PROGRAM, COMMENT. COMpILF AND LDAD. SEGLOAD DIREC TIVES ALSO DBT AINED FROM 4 COMMENT. ENVR$ OLDPL. f N/ Figure 24. Control cards to build disk files for REAPS use from transrattal tape. 71
l U D ) A T :( 0, d = E'lV? S ) 9
*E=IN3(L30)
F TN t I .JP T =2,40VNO,4 = E,IT A TIC , A, T ) 25L(:C=Il L3 Jf > i ',:[.A( 0L .$j == C O
- J I L E ,4 = S TH 2 X G )
c1V2L) L71 tL3C)
$NT. .3 E U23 ATE TO GE T. D AT A FROM ENVR$ CLJPL FOR DATED PRCPERTY C'**E:4T. GENERATION PdGGRAM, EXECUTE, AND CATALOG =ATER PROPERTY FILE.
Uc3 ATE (0 2=ENVRS,0,3) 4 ;- T J R N ( E M V R S ) RrL(130030) iCl)EST(STH2(T,*3F) 3TM24GtC1 molle,,STH2XT)
*E)U EFL(;j. :.=0)
CATALO3(STn2XT,ID=RJ TEST,XR=RJwfEST,47=949)
<ET;4N(3TH2xT)
C**ENT. USE UDOATE TO GET PEL AP5 S OURC E FR OM OLD9L. UPJATE(P=RELAPSS,F,I= NULL) d E T JR N ( R E L A P 5 5,1ULL )
".C*'ENT. USE SELECT TO IMDL EMENT COMPIL E TIME JoTIONS FOR RELAP5.
3ELECTt(;U" PILE.CC"P)
<tTVRN(5:LECTX)
DEviN0(C3FP,L30) C'9*CMT. COMPILE 2c' F TN ( I = C OM a , R 0uN D , c31.1 D 5.2 STarIC,R=3,A,T> RETURN (CJMP) C0==ENT. SUILO LIB 2iRY OF RELAPS OdJECT ]ECKS. 2d:UEST(RELAP5L,*PF) EDITLI3(L= NULL) RETURN (L30,NULLI C A T AL OG(REL A*5L,ID=RJWTESTe XR=RJWTES T,R P=999) COMMENT. LO AO REL APS USING SEGLOAD DIRECTIVES DBT AINED FROM REL AP5 CCM"ENT. OLCPL, CATALOG ABS OLU TE SINAR Y. L;" MENT. IF DISS PL A NOT AVAILABLE, GM IT FOLLOWI NG C ARD, UNSATISFIE0 CC" MENT. RESULT 30T R EL AP S WILL EXECUTE 04 IF NO PL JTTING IS T R I E O . -- YTT AC H( DI SS PL A, NEWOIS SP( AS T ATIC ,MR = L) RE;UEST(RELAP5X,*PF) DFL(EC=1) SE3 LOA 0(I=COMPILC,B.RELAP5X) LD5 ET (LIB =R EL AP 5L /ENVRL /DISSPL A,PR ESE T= NGINDEF, ERR = NONE ) LISLOA0(ENVRLe& HOR =1) NpS0. Rc TJRN( REL AP5L, ENVRL, COMPIL E,0ISS PL A) CATA 3G(GELAP5X,ID=RJWTEST,xR=RJWTEST,RP=999) RETJ(N(RELAP5<> C09M3NT. USE DRrc TO EYECUTE RELAP3, S A MPLE INDUT D AT A IS OBTAINED C09"!NT. FROM 4.8LAP 53 OLOPL. S E GIN ,R L 2 5 x, PR OC s , r ID =R Jd TE S T,0 PF N,0I D = R J W T E S T ,0U PF .4.
"3**: NT N:R A TC 9ICROFILM PLOTS FROM GENERALIZED PLOT COMMANDS EG9"$NT.. Ge G{NERAT@D BY RELAPT3.
dEGIN(FR90700) .
- EOR l ASTCM.GET
*CJMP
- COMPILE IL{ NF.lER OUT
- COMPILE TNEL TX T,0U TC = ;
- EOR l LIB R AR Y(E NVRL,NEW)
REWIN 0(LGO) A00(*,LGO) FINISH. j ENDRUN.
*E02
*CO MP ILE SELECT '
*ECR
*CDMPILE STH2XG,STH2XS
- EOR Figure 24 (conunued).
72 j
1.
*COMPIL6 STH2005
- EOR LIBRARY (RELAPSL,NEW) d,q REWIND (L501' A00(*,LG0)
FINISH. E ND RU N.
- EOR
*COMPfLE EDHTRK Figure 24. (continued).
FTN and two COMPASS calls are needed. The STATIC option is needed on NOS-BE systems. The COMPASS calls assemble a modified version of the CDC subroutine OUTC= that processes formatted WRITE statements. The modifications add entry points HEADER and LINES which are used in RELAP5. HEADER defines title lines which are automatically printed at the top of each page and LINES returns the number of lines remaming on a page (see description of subroutine HEADER in the INEL environmental library manual). The modified OUTC= may not operate on SCOPE-2. If this is the case, remove the two COMPASS cards and replace the ' COMPILE INELTEXT,0UTC= with ' COMPILE HEADERX. The result is that a dummy subroutine and function are compiled. These satisfy the HEADER and LINE entry points and issue a printer command to not print over paper folds. Program and problem titles will not appear at the top of each page. The next group of control cards and associated input builds the SELECTX program which is used to select compile time options for RELAP5. ( The next group of control cards and associated input generates the water property file needed in (^ RELAPS execution. A larger table that allows increased accuracy of the water property subroutines can be generated by replacing the
- COMPILE STH20DS with
- COMPILE STH20DL. Most problems at INEL have been run with the smaller table. The table is stored in LCM if it is available. Little impact on max-imum problem size or execution costs results if the larger table is used on machines with LCM.
The next group of control cards and associated data builds a library of RELAPS object decks and an executable file. If a DISSPLA library is not available, unresolved external references will exist, but the program executes as long as no plots are requested. The final control cards use a procedure to execute a problem obtained from an UPDATE file containing several RELAP5 sample problems. l l 1 73
- 17. REFERENCES
- 1. R. R. Ragan, TEXTJAB Reference Manual, Control Data Corporation Revision 04, 17316600, February 5,1976.
- 2. R. A. Berry, An Analysis Toolfor Predicting Transient Hydrodynamics in Nuclear Piping Systems Containing Swing Check Valves, VE-A-18-261, March 1979.
- 3. DISSPLA: Display Integrated Software System and P,'otting Language, Volumes 1, 2, and 3, Integrated Software Systems Corporation, February 1976.
- 4. K. D. Russell and H. R. Bruestle, ISDMS 1.0-A Scientific Data Management System, ISD-SCD-80-4, April 1980.
- 5. NOS-BE Reference Manual, ControlData Corporation, Revision F,60493800, October 13, 1978.
- 6. Cyber 70/Model 76 Computer System, 7600 Computer System, SCOPE 2.1 Reference Manual, Control Data Corporation, Revision L, 60342600, January 1977.
- 7. UPDA TE] Reference Manual, Control Data Corporation, Revision B,60449900, March 31,1978.
- 8. INTERCOM Version 4 Reference Manual, Control Data Corporation, Revision B, 60494600, July 16,1976, pp.11-21 through 112-27.
- 9. FORTRAN Extended, Version 4, Reference Manual, Control Data Corporation, Revision D, 60497800, March 31,1078, pp. 5 20, 8-23, 8-25, 8 15,10-8.
- 10. RELAP4/ MOD 5: A Computer Code Program for Transient Thermal-Hydraulic Analysis of Nuclear Reactors and Related Systems, Users Manual, Volume 2, Program Implementation,"
ANCR-NUREG-1335, September 1976, pp. 265-275. 11., Cyber Loader Version / Reference Manual, Control Data Corporation, Revision G, 60429800, June 15,1979, pp. 7-1 through 711. 9 l 74 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
O ; l i APPENDIX A RELAP5 INPUT DATA REQUIREMENTS O 1 O 75
1 APPENDIX A i [~'t
'w/
RELAP5 INPUT DATA REQUIREMENTS This description of the input data requirements for RELAPS has been developed and maintained through EDITOR A-3 as a file of 72 character records. The file is formatted to the report form by the TEXTJAB -2 A program and printed on the Cyber-176 printer with an upper-lower case print train. The '
]
EDITOR based file is included on the RELAP5 transmittal file. j While the body of the text of Volumes I and 2 corresponds to RELAPS/ MODI Cycle 1, this appendix has been updated to correspond to RELAPS/ MODI Cycle 14. l - O 77
RELAP5 Input Da ta Re qui renents 08/07/81 C0NTE NTS h 00 INTR] DUCTION . . . . . . . . . . . . . . . . . . . . . . 1 0 1 OATA DECK ORGANIZATION . . . . . . . . . . . . . . . . 1 0.2 TITLE CARD . . . . . . . . . . . . . . . . . . . . . . 1 0.3 COMMENT CARDS . . . . . . . . . . . . . . . . . . . . 2 0.4 DATA CARDS . . . . . . . . . . . . . . . . . . . . . . 2 0.5 CONTINUATION CARDS . . . . . . . . . . . . . . . . . . 3 0.6 TERMINATOR CARD . . . . . . . . . . . . . . . . . . . 4 0.7 SEQUENTIAL EXPANSION FORMAT . . . . . . . . . . . . . 4 3.6 QATA CARD REQUIREMENTS . . . . . . . . . . . . . . . . 5 1.0 CARD 100, PROBLEM TYPE AND OPTION . . . . . . . . . . . 5 2.0 CARD 101, INPUT CHECK OR RUN OPTION . . . . . . . . . . 5 3 0 C ARD 102, UNITS SELECTION . . . . . . . . . . . . . . . 6 4 0 RESTART CONTROL CARDS . . . . . . . . . . . . . . . . . 6 4.1 CARD 103, RESTART INPUT FILE CONTROL CARD . . . . . . 6 4.2 CARG 104, RESTART-PLOT FILE CONTROL CAR) . . . . . . . 6 5 0 CARD 105, CPU TIME REMAINING CARD . . . . . . . . . . . 7 0.0 CARD 110, NONCONDENSIBLE GAS TYPE . . . . . . . . . . . 8 7.0 CARDS 201-299, TIME STE P CONTROL C ARDS . . . . . . . . . 8 < d.0 CARDS 301-399, MINOR EDIT REQUESTS . . . . . . . . . . . 9 8 1 GENERAL QUANTITIES . . . . . . . . . . . . . . . . . . 10 8.2 COMPONENT REL ATED CJ ANTITIES . . . . . . . . . . . . . 10 8.3 VOLUME REL ATED QU ANTITIES . . . . . . . . . . . . . . 10 11 8.4 JUNCT ION RE L A TED QUANTI TI ES . . . . . . . . . . . . . 8.5 HEAT STRUCTURE RELATED QUANTITIES . . . . . . . . . . 11 8.6 REACTOR KINETIC QUANTITIES . . . .. . . . . . . . . . 12 8.7 CONTROL SYSTEM QUANTITIES . . . . . . . . . . . . . . 12 10.0 CARDS 500-699, TRIP INPUT DATA . . . . . . . . . . . . 12 10.1 CARD 500, TRIPS CANCELLATION CARD . . . . . . . . . . 12 10.2 CARDS 501-599, VARIABLE TRIP CARDS . . . . . . . . . 13 10.3 CAROS 601-699, LOGICAL TRIP CARDS . . . . . . . . . . 14 10.4 CARD o00, TRIP S T OP ADVANCEMENT CAR) . . . . . . . . 14 11.0 CAR 3S CCCXXNN, HYDRODYNAMIC COMPONENTS . . . . . . . . 15 11.1 CARD CCC0000 COMPONENT NAME AND TYPE . . . . . . . . 15 11 2 SINGLE /0LUME COMPONENT , . . . . . . . . . . . . . . le
- 11. 3 TIM E DEPEN DENT VOLUME C0hPONENT . . . . . . . . . . . 16 11 4 SINGLE JUNCTION COMPONENT . . ,. . . . . . . . . . . . 19 11.5 TIME DEPENDENT JUNC TION C DetPONENT . . . . . . . . . . 21 ,
11 6 PIPE AND ANNULUS COMPONENTS . . . . . . . . . . . . . 22 - 11 7. BRANCH OR SE P AR4.TCR COMPONEN T . . . . . . . . . . . . 27 ! 11.8 V ALVE JUNCTION COMPONENT . . . . . . . . . . . . . . 29 I 11.9 PJMP COMPONENT . . . . . . . . . . . . . . . . . . . 33 I 11.10 ACCUMUL AT OR C OMPONENT . . . . . . . . . . . . . . . 40 12 0 CARDS 1CCCGXNN, HEAT STRUCTURE INPUT . . . . . . . . . 42 13.0 CARDS 20lMMMNN, HEAT STRUCTURE THERMAL PROPERTY DATA . 48 ,' 13 1 CARD 201MMM00, COMPOSITION TYPE AND DATA FORMAT . . . 48 13.2 CARDS 201 MMM 01-20 lM M M 4 9, THE RM AL CON 00C TIVITY DATA . 49 Appendix A i l 78
RELAP5 Input Data Requirements- ) 08/07/81 () ~13.3 CARDS 201MMM51-201MMM99, VOL UME TRIC HE A T C A P ACITY DATA .. . . . . . . . .. . . .. . . , . .. . . . . . . . . 50
.14.0 CARDS 202TTINNs GENERAL TABLE DATA . . .. . . . . . . 51 14.1 CARD-202TTT00, TABLE TYPE AND MULTIPLIER DATA 51 q
14 21 CARDS 202TTT01-202TTT99, GENERAL TABLE DATA . . . .. 52 15.0 CARDS.30000000-30099999, SPACE INDEPENDENT RE ACTOR KINETICS.. . .. . . . . . . . . . .: .. .. . . . . - . . . . 52
-15.1 CARC 30000000, REAC TOR KINETICS TYPE C ARD . . . . . '.- 53 i 15.2 CARD 30000001, REACTOR KINETICS INFORMATION CARD . .: 53 15.3 CARDS 30000101-30000199, DELAYED NEJTRON CONSTANTS . 53 15 41 CARDS 30000201-30000299s FISSION PRODUCT DECAY CONSTANTS . . . . . . . . . . . . . . . . . . . . - . . . . 54 15.5 CARDS 30000301-30000399, ACTINIDE DEC AY CONST ANTS . . 54' 15.6 CARDS 30000401-30000499, PREVIOUS POWER HISTORY DATA 54 15.7 CARDS'30000011-30000020, REACTIVITY-CURVE NUMBERS . . 55 15.8 CARDS 30000501-30000599, DENSITY REACTIVITY TABLE . .- 55 15.9 CARDS 30000601-30000699, DOPPLER REAC TIVITY TABLE . . 56 15 10 CARDS 30000701-30000799, VOLUME WEIGHTING FACTORS . 56 15.11 CARDS 30000801-30000899p HE AT STRUCTURE WE IGHTING FACTOR . . . . . . . . . . . . . . . . . .. . . . . . . . . 56 16.0 CARDS 20300000-20399999, PLOT REQUEST INPUT DATA . . . '57 16.1 CARD 203000KK, 2D PLDT GENERAL HEADING AND SPECIFICATIONS . . . . . . . . . .. . . . . ... . . . . . 57 15 2 C ARDS 20300000-20330009, GENERAL 2D PLOT'4EADER CARDS . . . .. . . . . . .. . . . . . .. . . .. . . . . . 57
- 16. 3 C ARD S 20300010-19s GENERAL PLOT OPTIONS KEYWORDS . . 58 16 4 CARD 20300020, GENERAL PLOT SIZE DIMENSIONS . . . . . 59 16 5 CARDS 203NNNKK 2D PLDT REQUESTS AND SPECIFICATIONS . 60 10.6 CadDS 204MMMLL 20 PLOT COMPARISJN D AT4 T&3L ES . . . . 65 l'7. 0 CARDS 20bMNN00-20$NNN999, CONTROL SYSTEM INPUT DATA . . 69 17 1 CARD 205NNN00, CONTROL COMPONENT TYPE C ARD . . . . . 69 17 2 CARDS 20$NNN01-205NNN99, CONTROL COMPONENT DATA
' CARDS . . . . . . . . . . . . . . . . .. . .. . . . . . 70 18.0 CAR 05 1001-1999, STRIP REQUEST DATA . . . .. . . . . . 74 19.0 RELAP5 OPERATING PROCEDURES . . . .. . . . . . . . . . 75 19.1 11PUT DESCRIPT ION PROCEDURE . . .. . . . . . . . . . 76 19.2 RELAP5 EXECUTION PROCEDURES . . . . .. . . . . . . . 76 O Appendix A il I 79
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d i RELAP5 IhPUT OATA R E JUI R EM EN T 3 03/07/dl J.0 13IiOLJCLICU Co90lete oescripticns of cata deck organization anc cat a carc reqair ements f or all praclem types now allowoo in RELAP5 ar e gi ven. 3.1 JATA J i;A ORGANIZATION A 4tLAp5 problem input consists of at least one title cara, optional comment cards, cata cards, and a terminator c ar o. A listing of cne cards is printed at tne oeginnin; of each RELAPS proolem. The orcer of t he title, data, and comment cards is not critical except that 0!y tne last ti tl e caro anc the l as t cata carc naving a cuplicate cata card numoer is used. It is recosmencec that for a base deck, the ti tle carc be first followed oy data cards in card number o r d er . Comment carc ; shoJid be used freely to document the input. For parameter s tudi es and change cases, a new title cara, tne in se r tion, modification, ano deletion data cards, and comment caras should De pl aceo just ahead of tn e terminating cara. In this manner, a base cecx is maintained yet enanges ar e easily made. Wnen a card format error is detected, a line containing a , collar sign ( 5) located un d e r the char acter causing the error and a sessage giving the card column of the erro* are printed. An ar ror fl ag is set such that input processing continues, but the RELAP5 prootem is terminated at tne end of input processing. ilsua l l y another error comment is produced dur ing input processi19 when the program atteno ts to pro cess the erroneous data. 0.2 TITLE CARD A ti tl e car d must be enterec for each RELAP5 proolem, A title car d is icentified by an equal sign (=1 as the first non bl an k character. The titl e ( r em ai nd er of the title card) is printed as the second line of every page. If more than one title caro is enterec, the l ast one enterec is usec. Appencix A 1 l l 1 80 ,
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RELAP5 Input Data Requirements 0.3 COMMENT CARDS An asterisk (*) or a dollar sign ($) ap p e ar i n g as the f irst nonbl ank ch ar acter identifies the card as a comment. card. Blank c ar ds ar e tr eateo as comment cards. .The only pr oce s s ing .of comment cards is ~ the printing of their contents. Comment cards may De- placeo anywhere in the input deck except before conti nuation cards. 3.4 DATA CARDS Data cards ' cont ain varying number of fields which may be integer, real (floating p o i n t), or alpnanuseric. Blanks preceeding and following fields are ignored. The first field on a data card is a card number which must De an unsigned integer. If the first field has an. err or or is not.an integer, an error flag is set. ConseaJently, data on the carc are not used and the card .ill be identified by the card s eq u e n c e number in the list of unused dat a car ds. After each c ar d numDer and the accompanying data are read, the card nuscer as compared to previously entered car d numbers. If a matching card nJaber is found, the data entered on the previous card ar e replaced by data on the current card. If the card being pr oc e s se d contains only a car d number, the card number and data from a previous car d with that card number are deleted. Deleting a nonexistent car o is not considered an error. If a card causes replacement or deletion of data, a statement is printed i n d i c at i n g that the card is a replacement card. Cemment information may follow the data fields on any cata card b/ initiating the comment alth an asterisk or doll ar sign. A number fielc is star ted by either a digit (O through 9), a sign (+ or -), or e cecimal point (.). A comma or Diank (with one exception subsequently noted) terminates the number fielo. The number ficio has a number part and optionally an exponent p ar t . A number field w i tho u t a decimal point or an exponent is an integer fielo; a number with either a decimal point, an exponent, or both is a real field. A real number without a decimal point is assumec to have a decimal point immedi ately in front of'the first digit. The exponent part denotes the power of ten to be applied to the number part of the field. The exponent p art has an E or D, a sign (+ or -), or both followed by a number giving the p ow er of ten. These rules for real numbers are identical to those for ent er ing data in Fortran E or F fields except that no blanks (with one exception) are allowea Appendix A 2 i []
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l 81
RELAP5 Input Data Requirements 08/07/81 Detween char acters. Real data punched by Fortr an programs can oe read. To permit this, a blank following an E or D cenoting an exponent is treated as a plus sign. Acceptable ways of entering real numberss all containing the quantity 12.45, are illustrated by the f ol l o wi n g six fieldst 12.45,+12.45 1245+2 1 245+1,1 245E 1 1.245E+1 Alpnanuseri c fi elos have three forms. The most common alpnanumeri c field is a field starting with a letter and is ter mi na te d with a blanks a commas or the end of the card. Af t er the fi rs t l ett er char acter s all characters except commes and olanns are allowed. The second form is a seri es of characters dell 34ted by quotes (") or apostroones (8). Either a quote or an apostrophe initiates the fi el d ano the same character terainates the field. Tne del i mi t ers ar e not par t of the alphanumeric c word. If the delimiter char act er is a desired char a ct er within the f ie ld s two adjacent delimiting ch ar ac te r s are tr eated as a character in the field. The third alphanumeric type has the forms nHz, where n is the number of characters in the fields ano the field starts at z and extends for n ' columns. With the exception of the delimiters and even these can be ent er ed if entered in pairsa the last two alphanumeric type fielos can enter any desired characters. The nueber of char acter s that can be stor ed in a word is ten. If the number of characters is less than tens the wora is lef t justi fied and padded to the r ight wi th b l anks. If more tnan ten characters are entereas the fiela generates as many words as needed to store the f i el ds ten characters per words and the.last word is padded with blanks as needed. Regardless of the alphanumeric types at least one blank or comma must separate the field from the next field. 05 CONF INJ ATION C ARDS A continuat ion cards indicated by a plus sign as the first non-blank character on a cards may follow a data card or another contiriuation card. Fields on each card must be completes that i s, a field say not start on one card and be c on t i n ure d on the next card. The data card and each continuation card may have a comment field starting with an ' asterisk or doll ar si gn. Ne card nuss e r field is ent er e d on the continuation card since continuation cards mer ely extend the amount of information that can be enter ed under one card nunoer. Deleting a card deletes the data card and any as so c i a te d continuation cards. Appendix A 3 82 -____ mum ___-._.-_m_
- = - _ _ _ _ - _ - _ - __ ___ _ _ _ _ ___ - - - - - - - - - - - _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
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.1 RELAP5 ' Input Data RequireeAnts l' 08/07/81 j
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O.6 TERMINATOR CARO f ine inpui data for each RELAP5 probles.is. terminated by a slasa . o r a ' period car o. Tne slash and period cards have a slash (/) .ano a period. (. ) r es pective ly. as tne first nonblank~ character. Comments any follow the slash and period Lon these c ar d s. when's sl ash car d is used as the terminator, .the list- of card nunners and associated data used in a problem is passed to the next problem. Cards entered for the next problem are moded to the passac list or act as replacement cards depending on the cara number. The resulting input is the same as if all prevlous slash cards- were 'r e mo ve d from the input data up to the last perloc caro or the beginning of the input data. khan a perioc card is used as terminators all previous input ~ is erased before the input to the next problem is processe0. The soliity to process multiple problems 11s of little .use in proouction runs of large, time consuming problems. Futnermore, m a gn et i c tape considerations, especially . when wanting to use the file wr itten in' one prooles as the input file to the nexts limit ability to use multiple problems. In' the 1 [\- tape c as e, multiple c on t r o l cards for RELAP5 execution can be useo. The multiple prooles capability is useful for small ~ test probl ems or for input checking of sever al prob 4ess. 07 SEQJENTIAL EXPANSION FORMAT Several different typts of input are specified in sequential expansion format. This format consists of sets of datae each set containing one or more data items followed by. an , integer. The cata items are the parameters to be e xp an ded and the integer is the termination point for the expansion. The expansion begins at one more than the termination point of the previous- set and continues to the termination point of the l current set. For the first sets the expansion begins at one. The termination points are 7.nerally volume, Junction, or sash polit numbers, and always form a strictly increasing sequence. The input description will indicate the number of words per set (always-at least two) and the last terminating point. The t er mi na t i ng point of the last expansion set must equel the last t er mi n a ti ng point. Two examples ar e given. For the vol ume flow ar eas' in a pipe components the f ormat is two words per set in sequential expansion format for NV sets. Using the number of Appendix A 4 83
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'RELAPS Input Data Requirements 08/07/81 vol um es in the pipe (NV) as 10, tne volume flow areas could be ent er ad as, 0010101 0 01,10 In this case. the yolume flow areas for volumes 1 thr ough 10 have tne value 0.01. The pipe volume friction cata format is l three wor ds per set for NV se ts. Possible data might be 3310001 1.0-6,0,8 10-3,0,9 0010802 1.0-6,0,10 Heren volumes 1 through e and 10 nave the same values and volume 9 has a different value.
l 0.8 DATA C ARD REQUIREMENTS In the following description of the data cards, the car d nusoer is given with a descr ipti ve title of tne data cont ainea on tne card. Next, an explanation is given of any variable data which are incluoed in the car d numDer. Then, the order of the data, the typee and the description of the data item ar e g i ven. The t yp e is inoicated by A for alphanumeric, I for integer, and R'rar real. 1.0 CARQ.AQQt_ERQhCE1_11EE_AdQ_DEIID8 Tnis carc i s al ways r equi r ed. u1(A) PROBL EM TYPE. Enter one of the following: 1 ewe RESTART, PLOT, ! REEDIT, or STRIP. REEDIT type is not currently implemented. W2(A) PROBLEM JPTION. This word is needed only if wl is NEW or RESTART. I f needed, enter one of tne followings STDY-ST, STDY-TR1, or TRANSNT. Only TRANSNT is now implemented. 20 CARQ_12Lt_1HEul_CusCE_RE_EuB_QE11QH This car c 'is optional for all types. allA) OPTION. enter either INP-CHK o r R'J N ; if card i s om i t ted, RUN is assumed. If INP-CHK i s ent er e d, pr oblem stops a t end of input processing; if RUN is entered, problem is executed if no input err crs ar e de tected. 1 Appendix A 5 84
RELAPS Input usta Requirements 08/07/81 [\_)D 3.0 CAR 2.10Zt ud11S_1ELECLlad This card is optional for all problem typer. If card is omitteo, SI units are assumec for both input and output. If car o is used, enter either SI or BRITISH for each word. W1(A) INPUT UNITS. W2(A) DUTPUT UNITS. If this word is missing, SI units are assumed f or output. 4.0 RE1L&EL_CONIBDL_ CARDS 4.1 CARD 103, RESTART INPUT FILE CONTROL CARD This caro is required for all problem typas (W1 of Card 100) except NEW and is not allowed for type NEW. Attaching of p er ma ne nt files within RELAPS is n'o t ayallable under N05-8E s ys te ms, so a n_ag t_antst_i nis t n a ti n o _ini a _ d g tdi_1_thtaugh_h_g a 303:1f.1x11:a1 . l g-] W1(I) RESTART NUMBER. Must be r number printed in one of the r es t ar t (' ,) print messages and whose associated restart information is stored in the RSTPLT file. W2( A) ID. Id for attach of permanent file. d3-W6(A) PERM ANE NT FILE NAME. Words 2 through 6 ar e us ed if the r e s ta r t file is to oe obtained f rom a permanent file. These words are not ent er e d if the file is already a local file or will be stageo. 4.2 CARD 104, RESTART-PLOT FILE CONTROL CARD This carc can be ent er ed for NEWS RESTART, and STRIP options. For the stri p option, this card controls the strip file anc the NONE option is not allowed. If this carc is omitteds the Gefault action on the Re s tart-Pl o t file is the same as the NOACTION option. To prevent the Restart-Plot file from being written, a car d with NONE must be entered. Wl(A) ACTION OR 10 FIELD. This word may not be olank. If NONE, no Restart-plot is written. If N3 ACTION, tne file is r ewound at the end of the problem but no further action is taken and the user should provide system control cards (REQUEST, STAGE, [ } Appendix A 6 G/ 85
RELAPS Input Data Requirements 08/07/81 C AT AL OG, etc.) to dispose of file. If STAGE (SCOPE-2 only) is entered, the file will be staged to tape when a RETURN (RSTPLT) control statement or end of job is reached. If STAGE-RTN (SCJPE-2 only) is entered, the action is the same as for STAGE e xcep t that the file is immediately returned by RELAP5 at the coupl etion o f the problem. If REQUEST (NDS-BE only) is entered, . the file will De written on a nine track labeled tape and saveo ' when returned or at the end of the job. If REQUESTRTN ( NO S-B E only) is entered, the ac ti on is the s ame as for REQUEST except that the file is r e t ur n e d by RE L AP5 at the completion of the problem. If not blank and none of the above, this word is assumed to be an ID for cataloguing the Res t ar t-P l o t f il e as a p er m anent file. Only nine characters ar e allowed and the next wora aust be nonblank. The permanent file and tape options ar e not available in this RELAP5 version on NOS-sE, so da_nal__taltL infatmalian inta_targs_Z_1btausb_2_muto_no_321=aE_sritzas. W2-W5(A) PERMANENT FILE NAME. These words are entered only if the Restart-Plot file is to be catalogued as a permanent file. The persanent file name can be up to forty characters. A prior Restart-Plot file is always returned at the beginning of a problem th at writes a Rest ar t-Plo t f i l e an d this can limit the options in multiple case input. b.0 CA8Q_121t_;EU IldE_EEUAlblBG_CAdQ CPU time allocated for a job i s speci f ed on the JOB card. At the end of each time step, the CPU time remainin; for the Job is deter mined. If the remaining CPU time is less than Word 1, the translent i s immedi ately t er minated. The advancement may not be at tne eno of a' requesteo time step due to time step r e du c t i on, the hydrodynamic, heat co n du ct i on, and reactor kinetics may not ce advanced to the same point, or the ad v an c emen t may not be suc ce ss f ul and the advancement is se ne d ul ed to be repeated wi th reduced' time step. Major edits, minor edits, plot edits, and a restart recoro ar e f or ced. The tr ansi ent c an De r es t ar te d from this point as if the problem had not been interrupted. The transient is also terminated after success f J i adv ancement over a requested time step and th e C P U time is less than Word 2. Word 2 should be larger than Word 1. Tne default values for Words 1 and 2 are 1.0 and 2.0 sec.. The default values ar e used if the c ar a is not supplied or the entered numbers are less tnan defaait values. Word 2 is also f or ced to be 1.0 sec l arger than word 1. W1(R) FIR 5T TIME VALUE. Tested every time step. Appendix A 7 i 86
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I 1 i dELAPS ~ Input Data Requirements ' e~N 08/07/81 W2(R) SECOND TIME VALUE. Te s ted after successful advancement over r equ es t ed ti me step. o.O C AE U. l L Q t. M auCQhEEN11 ELE _E A1_11EE 1 This card is op tion al . If card is omitted, air is l assumed as the nonconcensible gas. i W1(A) NONC3NDE1SIBLE GAS TYPE. Enter one of. the following noncondensible gas t yp es : AIR, ARGON, HELIUM, H Y D R OGE N, NITROGEN, or OXYGEN. It is r ecommended that NITROGEN be input if tne accumulator mocal is used. 7.0 CARQ1_EQl:122t.Ilds.SIEE.tQNIRQL_C&EQ1 i At least one card of this series is required for NEW problems. If this series is entered for RESTART problems, it replaces the series from the problem being restarted. This series is not used f or other type problems. Car d numbers need not De consecutive. O W1(R) TIME END FOR THIS SET i nc r e as i ng carc number. (sec). This quantity must increase wi th W2(R) MINIMUN TIME STEP (sec). This quantity should be a positive numDe r less than 1 0E-6. If a larger number is entered, it is reset to 1.0E-6. W3(R) MAXIMUM TIME SYEP (sec). This quantity is also called reque sted t ime step. W4(1) TIME STEP CONTROL OPTION. If ssdOO is entered, no error esta s ate t i ee step control is useo and the maximum time step (W3) is attempted for botn h ydr o dyn ami c sno heat s tr uc ture advancement. However the hydrodynamic time step will be reduced to the mater ial transport limit and further to the minimum time step for causes such as water property failures. If ssdO1 is ent er ed, heat transfer uses maximum time step and the hydr odynami c s, in addi ti on to the time step control describec f or ssdOO, uses a mass error analysis to control the time step between the minimum and maximum time step. If ssdO2 i s ent ered, the t ime st ep contr o l is identical to that for ssdO1, the heat s tr uc tur e time step is the same as the hydrodynamic time step, and the neat conduction advancement is repeated whenever the h yd r o d yn ami c time step is re pea te d. The ssdO1 option is recommended if the maximum time step is kept sufficiently small Appendix A 8 87
f l f RELAP5 Input Data Requirements 08/07/81 to assure that the explici t connection between the hyd rod yn ams es ano neat conduction / heat transfer calculations remains st abl e. If there is any doubt, us e the 'ss dO2 option. The letter, de which represents a number from 0 through 7 can De used to obtain ! extra output at every hydrodynamic time step. This number is l treated as a three bit number consisting of a four bit, a two l bit, and a one bit. If no bits ar e se t, i.e., the number i s 0, the standard output at the maximum time step is obtained. If the lumber i s nonz er o, output is ootained at each time step, and the bi ts indi cate which ou t p u t is ootainec. If the one bit is one major edits are obtained every time step, if the two oit is o n, asnor edits are obtasned, and if the four. bit is one pl o t i recoros ar e written e ve r y time step. Tnese ootions should be useo carefuity since consi der able output can be generated. Tne di~gsts ss which represents a number f rom 0 thr ough 15 is useo to control the printed content of major eoits. The number is i treated as a four bi t number. If the numoer,is zero, all the { s t an d ar d major printed output is given. If the 8 bit is sets l the statistics block is omitted; if the 4 bit is set, the second por t i on of tne volume block is omitted; if tne 2 bit is set, the secono por ti on of the Junction block is omi tted; and if the 1 oit is set, heat structure temperatures are ositted. d5(I) M113R EDIT AND PLOT FRE QLE NC Y. Number of maximum or r equest ed l time aav an c es per minor edit and write of plot information. Hust be l ess than or equal to 4096. d6(I) MAJGR EDIT FREQUENCY. N um b e r of requested time aovances per major ecit. Must be less than or equal to 4396. 47(I) RESTART FREQUENCY. Numoer of reques ted time advances per write of r estar t inf orma tion. Must be less tnan or equal tn 4096. 8.0 C&d11_12L:122t.51Eua L211_lE9UE1II. < These cards are optional for NEW and RESTART problems, ar e required for a REEDIT problem, and are not allowed for PLOT ana STRIP prooiens. If not pr es e nt, no minor edi ts ar e pr inted. If present, sinor edi ts ar e gener ated and the order o f the printec quantitles is given by the card number of tne request card. 3ne request is entered per card and the card numoers need not be consecutive. d1(A) VARIABLE CODE. d2(I) PARAMkTER. The quantitle s that can De edited and the required input Appendix A 9 9, 88 l
RELAP5 Input Data requirements (~N, 08/07/81 d are listed below. For convenience, quanti tl es th at can be usea in plotting requests, in trip specifications, as s e ar c h var i a bl es in taoles, and operands in control statements are listaa. Jnits for the quanti ties are also given. Quantities comparea in variable trips must have the same units-and input to tables s p eci fi ed by var ia ble request coces must have the specifleo units. 8.1 JENE 4 AL QUANTITIES tast Quantitz TIME Time (sec). The p ar amet er . is C. This specification cannot be used for minor edit requests. TIMEDF Time of trip occurring (sect. Parameter is trip number. This specification is allowed only on trip cards. CPUTIME The current CPU time for tnis problem (sec). Par ana ter i s zer o. MULL Speci fies null field; allowed only on trip carcs. P ar ame te r is 0. () 8.2 COMPONENT 4 ELATED QUANTITIES The quantities li st ed below are unique to certain components; thus a pump velocity can only De requested for a pump component. P ar amet er is component numoer. Cean Sun 1LLL1 PMPVEL Pump velocity in pump component (rad /sec, rev/ min). PMPHEAD Pump need in pump component (Pa, Ibf/in2). PNPTRQ Pump tor que i n pump component (N-me ibf-ft). VLV ARE A Valve ar ea ratio in valve component. 8.3 VOLUME RELATED QUANTITIES For the following var l aol e codes, the parameter is the velJae numbef . Cast Quan111x RHO Total density (kg/m3, Ib/ft3). R40F L i ,qu i d density (kg/m3, Ib/ft3). RHOG V ap o r density (kg/m3, Iu/ft3). U Specific internal ener gy (J/kg, B tu/ l b ) . Appendix A 10 89
1 . l l 4ELAP5 Input Data Requirements I JF Specific liquio internal e,n e r g y (J/kg, Stu/lb). ; JG Specific vapor internal energy (J/kg, Btu /lb). j VOI]F Liquid void f raction. V010G Vapor void fr action. l 1 VELF Volume oriented liquid velocity (m/sec, ft/sec). , VELG Volume oriented vapor velocity (m/sec, ft/sec). l P Volume pressure (Pa, ibf/in2). J QUALS Volume static quality. QUALA Air mass f r acti on. Q"UALE Volume equili br ium quality. O Volume heat source (watt, Btu /sec). TtMPF Volume liquid temperature (K, degF). 4 l TEMPG Volume v apor temperature (K, degF). l TEMP Volume equilibrium temperature (K, degF). S3UN0d Volume sonic veloci ty (m/sec, ft/sec). f
~
VAPGEN Volume vapor generation rate (kg/sec, Ib/sec). 8.4 JUNCTION REL ATED QUANTITIES j i For \ the following vari abl e request cooes, the parameter is the junction number. j Casa Ruta 111x VELFJ Junction l i qu i d vel oci ty (m/sec, ft/sec). VELGJ Junction v apor velocity (m/sec, f t/ sec) . VELJ Inter f ace veloci ty (m/sec, ft/sec). V3IDFJ Junction liquid void f rac tion. v010GJ Junction vapor v oi d f r ac ti on. i RHOFJ Junction liquid density (kg/m3, ib/ft3). RHOGJ Junction vapor density (Kg/m3, 11/ft3). JFJ Junction liquid in tern al en er gy (J/kg, Btu /lb). JGJ Junction vapor internal onergy (J/kg, Stu/lb). MFLOWJ Combined liquid and vapor flow rate ( k g/ s e c, 10/ sec). 85 h HEAT STRUCTURE REL ATE D QUANTI TIE S i for tne request co d e, H T P O W, the parameter is the heat ! s tr uc tur e-g eome t r y n um b er . For the remaining codes, the I parameter as the s t r uc tur e-g e ome tr y number with a two di gi t code appel ded. For codes other than HTTEMP, the code is 00 for the l left coundary anc 01 for tne right boundary. For HTTEMP, the ! code is the mesh point number. Only the surface t emp er atur e s are written in plot recor ds on the RSTPLT file and thus plot requests in plot type problems and strip requests ar e limitto to those temperatures.
I AELAPS Input Data Requireaants (~'>) 08/07/61
\
"ada Ruan111x l HTP0h Power input (watt, Btu /s ec ). 1 HTR1R Heat transf er r ate (watt /m2, Btu /sec-ft2). I HTCHF Critical heat flux (watt /m2s Stu/sec-ft2). l HTHIC Derivitive of heat tr ansf er rate with respect to surface temperature (watt /m2-K, Btu /sec- ,
ft2-cegF). HTTEMP Mesh Point temperature (K, degF). ! 86 KE ACT OR KINE TIC QUANTITIES The parameter is zero for reactor ninetic quantitles. Cada 9Wa01112 RKTPO. Total reactor power i.e.,' sum of fission and fission product decay power (watt). (<FIPJW Reactor power from fission (watt). 4(GAP 3d Reactor power f r om fissi on prod uc t decay (watt). R(REAC Reactsvity (co l l ar s). o.7 CONTROL SYSTEM QUANTITIES O The parameter is the contr ol component number. Cada Quan111x CNTRLVAR Control component number. T5ese quantitles are assumed dimensionless. 10.0 CidQ1.222-h22t_I&lE_lhEul_Q&la These cards are op tional for NEW and RESTART type problems and are not used for other type proolems. 10c1 CARD 500, T RIPS C ANCE LLATION C ARD ini s c ard is allowed only f or restart problems. This caro causes all trips in the problem being restarted to be deleted. Any d es i r ed trips must be reentered and all reentered tr ips are ini ti al 6 zed to false. Appendix A 12 91 __ ___o
l RELAP5 Input Data Requirements 08/07/81
- d1(A) DISCAR0. Any other entry is an error.
10.2 CARDS 501-599, VARIABLE TRIP CARDS Each c ar d defines a logical statement or trip condition concerned with the quantities Deing advanced in time. A trip is false or not set if the tr i p condition i s not met ano true if it is iet. The trip number is tne same as its card number and trip numbers neea no t be consecutive. On restart, new trips can be introcuced, old trips can be deleted, and a new trip with the same number as an old trip repl aces the olo tr ip. Tr ips f or new probl ems or tr i ps introduced on restart are initialized to false. t The variable codes and p ar aset er s are tne saae as describec f or minor edits, Section 8.0. NULL is allowed for the right side when only a comparison to the constant is desired. The var i a bl e code TIMEOF with the parameter set to tne trip nuster indicates the time at which tne tr i p was last set. d1(A) VARIABLE CODE. On r es t ar t problems, this word can also contain DISCARO or RESET. DISCARD deletes the trip; RESET sets the trip to false. If DISCARD or RtSET are entered, no further words are entered on the card. d2(I) PARAMETER. d3(A) RE L AT IONS HI P. May be ei ther EQ, NEs GT, GE, L T, or LE, where , the symbols have the standard Fortran meaning. Note that ) contr ary to Fortran, do not use the pericos, i.e., use G E, not
.GE.
i d4(A) VARIABLE CODE. i d5(I) PARANETER. d6(R) ADDIT IVE CONST ANT. v7(A) LATCH INDICATOR. I t' L, the trip once set true, r emains true even if the ccndition later is not met. If N, toe tr i p is testeo each time sa v a nc e me n t . The lostcal statement is Dons the quantity given by Werds 1 and 2 have the relationship given oy word 3 with the quan ti ty given oy Words 4 and 5 plus mora 64 If the r el ationship is false, the trip is false or not set. If tne r e l at i onshi p is true, tne trip is true or set. The TIMEOF variable is -1.0 if the trip is false. If the trip is tr ue, thes variable is the Appendtx A 13 92
1 lL i , l NELAP5 Input Data Requirements l 08/07/81 time tne trip was last set true. 4' latched. trip is'never resets- l so the trip time never changes once it changes from -1.0. For l the nontatched tr a ps, the trip time when se t remains constant until the trip concition becomes false and then the trip time is. l -1.0 again. If the trip condition cecomes true again, tne process is repeated. For trips sucn as a time tests L should be used to eliminate repeated testing although no error or difference in'results will occur if~N is used. 10.3 CARDS 601-699, LOGICAL TRIP CARDS If these cards are enter ed, at least one of. the varible trip cards sust have been entered. Each card defines a logical relationship with the tr ips def ined on these cards or Car ds 501-
$99. .
i W1(I) TRIP NUMBE R. The absolute value of tnis number must be one of i the trip nusoers defined by the 501-599 or 601-699 cards. A minus trip nu m b er indicates that tne complement of the trip is to be used in the test. W2(A) OPdRaidR. May be AND, OR, or XOR. For restart problems,- th i s quantity may also contain DISCARD or RESET. DISC ARD delete s the j'
. [~s trip and RESET sets the trip to false. If DISCARD or RESET are T- entered, no f ur ther words ar e entered on the card and W1 may De Zero.
W3(I) TRIP NUMBhR. S imil ar to 41. w4(A) LA>TCH INDICATOR. I f L, the trip when set remains set. If N, the trip is testeo each time advancement. Tne trip condition is given by the result of the logical ; expressions CONDITION OF TRIP IN W1 UPERATOR CONDITION OF TRIP IN W3. 10 4 CARD 600, TRIP STOP ADVANCEMENT CARD Tnis card can be entered in new anc restart problems. One or two trip numbers m&y De enttred. If either of the i nd i c t, t e d trips are true, the probics advancement is termina ted.
/1(I) fRIP NUM3ER.
Appendix A 14 O 93
RELAPS Input Data Requirements 08/07/81 W2(I) TRIP NdMBER. A second trip number need not ce entered. 11 0 CA8Q1.CCC11bdA_dlD8DDldAf1C_CddEQMEMll These cards are requi reo for NEW type problems and may be ent er ed for RESTART problems. A hydrodynamic system is descrioed in a NEk problem. In a RESTART problem, the hydr o dynami c system may be modi fi ed by deletings addings. replacings or moolfying components. The r esultant problem must descrime at least tw o volumes and one Junction. The hydrodynamic card numbers are civided into fields where CCC is the component number an d the component numbers need not be c ons e cu ti v e , XX is the car d type, and NN is the card number L within type. When a r ange is indicated, the numbers need not be consecutive. 11 1 CARD CCC0000 COMPONENT NAME AND TYPE inis caro is required for each component. wl(A) COMPONENT NAME. Use name descriptive of component's use in system. n2(A) CLMPONENT TYPE. Enter one of tne f ollowing component typess ! SN3LVOL, TM0pVOL, SNGLJUN, TMDPJUN, PIPES ANNULUS, PUMPS B R ANC 4, WALVEs SEPARATR, or ACCUM, or toe commands DELETE. ] The command, 1 DELETE, i s alloweo only in RESTART prnblems and the component l nusoer must be an existing component at the time of r es t ar t. { The DELETE command deletes the component. W3(A) FLAG COMMAND. The cosmand FLAGS say be ent er ed in RESTART proolens only l and the component nusber aust be for L component ! existing at the time of restart. Tne component type on th i s j c ar d and the exis tinc component must be the same. If FLAGS is 1 enter eds enly the ccrds containing tne vonuse and Junctions flag d at a may be en te re d and only voluse of Junction flag data are changed. 3tner data on tne cards centaining the fl ag data s hou t a De enterto property nith respect to in teger er real char acter is tic s, but no at n er cr.ec k i ng is done (zeros are 1 acceptaaie.) For time dependent volunes and junctions, the time Jepencent data may also be changed with FLAGS j specified. When , FLAGS is ositted on a new or replacement component, the normal l initialization i t. performed. When FLAGS is entered, oniy the flag indicators ar e changed. 12.DQ1_M14.Jti.31QGA.11.11_201X { EALLl1111.1221AQAQ120 Appendix A 15 l l 94 1
1
.f . RELAP5 Input Data Requirements
( 08/07/81 ine remaining cards for each component ar e cependent on the 3 type of component. ! ! l 11.2 SINGL E VOLUME COMPONENT A single volume component is indicted by $NGLVCL on card CCC0000. In Junction references, . the inlet code for this component i s' CCL000000 ano tr.e outl e t code is CCC010000. Except for connections to a bran:h components only one junction may De co nn e c t e d to the inlet and only one junction may be connected to { the outlet. If a junc ti on is not speci fi ed for an ends that and I is consicer ad a closed end. 11.2.1 Catat_;CCQ101=CCCQlaga_11nalt_Laluss_Ganaatcx_Cacd1 inis card (or cards) is required for a single volume component. Tne nine wor ds can be entered on one or more c ar ds ano the card numbers need not be consecutive. W1(R) VOLU1h FLOW AREA (m2, ft2). W2(R) LENGTH OF VOLUME (m, ft). - W3(R) VOLJME OF VOLUME ( m 3, ft3). Tne progr am requires that the volume equals the volume flow area times l en gt h (W3=Wi*W2). At i, least two of the three qu an t i t i e s, W 1s W2, d3s must be nonzero. If one of the quanti ties is zero, li will be computed from the other two. If none of the words ar e zero, tney must satisfy the volume equals area times length within a relative error of 0.000001. W9tR) AN3LE FOR HORIZONTAL ORIENTA1 ION (deg). The absolute value of this angle must be less than or equal to 360 deg. This quanti ty is not used in the cal cul ation but is specified f or possible automated drawing of noding di agr ams. Wi(R) ANGLE FOR VERTICAL ORIENTATION (deg). The ab so l ute value of this angle must be less than or equal to 90 deg. The angle 0 ce; is horizontal and positive angles ' nave an upward d i r ect ion. W6(R) ELEVATION CHANGE (mi ft). A positive value is an increase in elev a tion. The absolute value of tnis quantity must ne less , than or equal to the volume length. If the vertical angle orientation is zeros this quantity must be z er o. If the v er t i ca l angle is nonzeros this quantity must also be nonzero and h av e the s ame s ign. () Appendix A 16 95
--_______-____-___-_ A
RELAPS Input Data Requirements 08/07/81 u?(R) PIPE ROUGHNESS (as ft).
uB(R) H1DRAULIC DIAhETER (ms ft). If zeros the hyd r aul i c cl amet er is computed from 2.0*(VOLUME AREA /PII**0.5. A eneck is made that tne pipe roughness !s less tnan nalf the nydraulic diameter.
09(I) VOLJME CONTROL FLAG. E n.te r fe where f is zero if wall friction effects ar e to te computed for the volume, f is 1 if wall friction is not to be computeds e is O for n on-e qu i l i b r i um )
(unequal t emper a tur e ) and 1 for equilibrium ( eqJ a i t emp er a tur e )
calculation.
11.2.2 Cats _CCCQgQQ_lingin tatutt_laitial_Cansitina This card is required for a single volume.
u1(I) CONTROL WORD. Control wor ds o through 3 specify only water.
Control words 4 thr ou gn 6 allow the specification of waters ai r s or wa ter-ai r mi xtur es.
If Os the next three woros are i n te rpr e ted as pressure (Pas Ibf/
in2), internal energy (J/kgs 8tu/lDJs and static quality; these quantities will be i nt er pr e ted as non-equilibrium or equi!!brium condi tions depending on volume control flag. If equilibrium, the s tatic quality is checkeo out only the pressure and i n t e rn a l energy ar e used to define the thermodynamic state.
If is the next two woros are interpreted as temperature (Ks 1 degF), and quality in equili orium condition. j l
If 2s the next two words are interpreted as pressure ( P as Ibf/
in2) and quality in equili br ium condi tion.
If 3s the next two norcs are interpre ten as pressure (Pas Ibf/
in2) and temperature (x, degF) iri etullibrium condition.
i If 4s the next three woros ar e i n te rpr e te d as pressure (Pas IDf/
I in21, tesp er atur e (As degF)s and ocncondensible quality. The non c ond en s i b a e qu a l i a.y mus t De g re a te r than or equal to zer o and less tnan or equal to Jn e.
If 5, the next three w o r d ro are interpreted as temperature (
Appendix A 17 l
REL4P 5 Input Data Requirements
.g g 08/07/81
' 6, tne next four wor ds ar e inte r pr e teo as pressure (Pas Ibf/
If in28, internal ener gy (J/kg, B t u/ l b ), static quality, anc i noncondensible quality. The limits for equilibrium quality and ) nonconetnsible quality are tne same as for type 5. The nusbers, O through 6, specify zero Doron concentration. If 10 is added to tne above numcers, a boron concentration (parts of boron per par ts of liquid water) is ent er ed after the other i reqJired i nf or mat ion. W2-W6(Ri QU AN T IT IE S AS DESCRIBED UNDER W1. Dependsng on the control wor ce two thrcush five quantities may be r equi r ed. Tne minimum number must be entered; quantities not required may be omitted i but if entered must be zero. 11.3 TIME DEPENDENT, VOLUME COMPONENT This component is i na i c a *.e d by TMDPVOL on car d CCC 0000. In J un c t i o n r ef er ences, the connection code for this component is CCC000000 and no distinction is made between inlet and outlet. Only one junction may be connected to this component.
~'T 11 3.1 Catss_GC;Q191-CCC0102t_Ilac_Raasagent_1 alums _2snatitz (G
This carc'(or cards) is required for time dependent volumes and the :ard format is i dent i ca l to tne card (si for a single vol uee (11.2.1). 11.3.2 C at a _ CC C Q Z Q Qt _Il g s _ Q s E AD 920 t _ in lutt.Q S.it_C11L L Ll_ M a t e This eard is r equired for time dependent volume components. W1(I) CONTROL dORD FOR TIME DEPENDENT DAfA DN CCCO2NN CARDS. Tnis number is the same as the control word descrioed in 11.2.2. W2(I) TABLE TRIP dbMBER. This war d is optional. If missing er zero and W or d 3 (s missir.g, no trip ir used and the time argument is the advancement time. If non ero and Word 3 is missing, thi s number is the trir number and the time argumen t i s -1 0 if the trip is fasse and the advancement time minus the trip time if the trip is true. Appencix A 18 97 l
RELaPS 11put bata Requirements 06/07/81 d3(Al ALPHANUMERIC PART OF VARIAdLE REQJEST CODE. This quantity is optional. If presents tnis wor d and the next are a variaDie ! request code that specifies the search ar gumen t for the taDie lookup and i n te r p o l a ti on . If the trip number is zeros the specified argumen t i s used. If the trip number is nonzeros
-1 0E99 is useo if the trip is f alse and the specified argument is used if tne trip is true. TIME can be selecteas but note that the trip loge c is dif f er ent than if thi s. word were omitted.
d4(I) NUMERIC P ART OF V ARI ABLE REGUEST 000E. Assumed zero if missing. 11.3.3 CRE21.CCCQLQl-CCCQ1221.1152 22EtQdtQ1 lalu11.DALA.CJEd1 Thes e caras are required for time dependent volume components. The card numbers need not be cons ecutives but the falue of the sear cn vari abl e in a succeedi ng set must be equal to or gr eat er than the val ue in the previous set. One or more sets of data up to 100 sets are allowed. A set of data is made up of th e search variable followed by the r e q'u i r ed data indicated by the control word in CCCO200. L-i n e a r interpolation is used if the search argument lies between the search variaDie entries. End point values are used if the argument lies outside the taole values. Only one set is needeo if constant values are des i r eo and computer ti me is reduced when only one set is entered. Step ch an g e s c an be accommodated by entering the two adjacent sets with the same s e ar ch variable values or an extremely small difference between tnem. Given two identical argument valuess the set selected will be the closest to the previcus er gu men t value. Sets may be enter ed one or more per car o and may be s pl i t across card s. The total number of words nust be a multiple of the set size. 11.4 LINGLE JUNCTION COMPONENT A ringle Junction component is . indicted by SNGLJUN on card CC;0000. 11 4.1 CAEg_CCC23Gl-CCCClSit. lid 212..JJDGliDQ.Gt9ECAT2 C2EE inis card is required for singic Junction components. al(I) FROM CDNNdCTILN CODE TO A C O M P G N E;4 T . Appendix A 19 l 98 I
RELAP5 Input Data Requirements
\ 08/07/81 W2(I) TO QNNECTION CODE TO A COMPONENT.
W3(M) JUN; TION AREA (m2, ft2). If zero, ar ea is set to minimum volume area of the adjoining volumes. For acr upt area changes, the JunctiJn area must De equal to or smaller than the minimum of tne adjoining volume ar eas. For smooth area changes, t her e are no restrictions. W4(R) FORWARD FLOW ENERGY LOSS COEFFICIENT. w 5(R ) RE/ E RS 6 FLOW dNERGY LCSS COEFFICIENT. W6(I) JUNCTION FLAGS. A four digit number, cahs, is entered where c=0 means tnat the choking model is to be applied, c=1 means that the choking model is not to be applied, a=0 means either a smooth ar ea change or no area change, a=1 means an abrupt area change, h=0 means two velocities, h=1 means drift flux approximation, h=2 means one velocity, s=0 means full inertia treatment, s=1 means pseudo-steady state approximation. Drift flux has Deen disabled in this version, so dQ.nat_ Mat _h=1 W7(R) SOSCJULEO DISCHARGE COEFFICIENT. This quantity is applied only to suDcooled chokeo flow calculations. The quantity must be greater than zero and less than 2.0. If missing or zero, it is set to 1.0. ( W8(R) IWO PHASE DISCHARGE COEFFICIENT. This quantity is applied only to two phase choked flow calculations. The quantity must be great er than zer o and less than 2 0. If missing or zero, it is set to 1 0. 11.4.2 Cat s . C G C 2221t_310 q1g_ dynglign _laitial_C a n g it i S D S This card is requires for single junction components. W1(I) CONTROL WORD. If 0, next two wordt are velocities, if 1, next i twc words are flows. d2(R) INITIAL LIQUID VELOCITY. This quantity is either velocity (m/ sec, ft/sec) or flow (kg/s ec, ib/sec) depending on the control wor 3. W 'J t R ) INITIAL '/ A P O R VELOCITY. This quanti t y is either velocity (m/ sec, ft/sec) or flow (ka/sec, Ib/sec) oepending on the c on tr o l word. - Appendix A 20 n 1 l w_ -_ _ -- -__ - _ - _ A
RELAP5 Input Data Requirements 08/07/81 d4(R) INTEkFACE VELOCITY ( m/s ecs ft/sec). Enter ze ro. 11.5 TIME DEPENDENT JUNCTION COMPONENT This component is indicated oy TMDPJJN on C ar d CCC0000. 11.5 1 Gatg_gCCQ1Q1_Ilgg_utR1Ddtat_duGE112Q.112E11L2 This caro is requireo for time dependent junction components. This card should not be entered if FLAGS is specified on Card CCC0000. d1(I) FROM CONNECTION CODE TO A COMPONENT. d2(I) TO CONNECTION CODE TO A CO MP O NE N T. d3(R) JUNCTIJN ARE A (m2, ft2). If zer os area is set to the minimum q area o f the adJoini ng vol ume s. There are no Junction area j restr ic tions for time cependent Junctions. ? 11.5.2 Cata_CCCQZQQt_Ilme_Qtannstat_duantlan_Canttal.dsta This caro is optional. If this car 6 is missings the second ; and third words of the tise dependent data are assumed to oe I v e l o c i t i e s., d1(I) CONTROL n0RD. If Os second and third words of time dependent i data are velocities. I f 1, second and taird words of time i dependent data ar e flows. u2(I) TA8LE TRIP NUMBER. This wor d is optional. If missing or zero and dord 3 is missing, no trip is used and the ti m e argument is the advancement time. If nonzero and Word 3 i s ra i s s i ngs this nutoer is the trip number and tne time argusent is -1.0 if tne l i trio is f alse and the advancement time minus the trip time if the trip in true. c3(A) ALPHAhvMEP.IC Pt.RT OF VARIABLE REQUEST CODE. This quantity is , optional. If pr ese n ts tnis word and the next are a variable ! r ee.u es t cooe that specifies the saarcn ar gume nt for th e table
- lookap anc i n ter p o l a t i on . If the tr i p numsar is zero, the i
specified argument is always used. If the trip number is i nonzeros -1.0E99 is used if the trip is false anc the speci fi ed argument is usen if the trip is true. TIME can be selected, out Appendlx A 21 100 _____J
I i RELAP5. Input Data Requirements
.[wJsl C 6 /07 /61 1
! note that the trip logic is different than if this word is ) omitted. t d4(1) NUMERIC PART OF VARIABLE REQUEST CDDE. Assumed zero if missing. 11.5.3 Catgg Cs;Qggi-CCggg33t_11gt.QtE1Qdant_JunctigD.2411 Tnese cards are required for time dependent Jun c ti o n components. The card numb er s need not be consecutive but the value of the search variable in a succeeding set must be equal to or greater than the value in tie previous set. One or mor e sets of data up to 100 sets may be entered. Each set consists of tne search variables li qui d velocity (m/ secs ft/sec) or flow (kg/ secs ib/sec)s vapor velocity (m/sec, ft/sec) or flow (Hg/ sec, ib/sec), and inter f ace velocity (m/sec, ft/sec). Enter zero for interface velocity. The choice of velocity or-flow depends on the control w or d (11.5 2). The interpolation and card formats for the time dependent data ar e identical to that in 11.3.3. 11.6 PIPE AND ANNULUS COMPONENTS ( U A pipe component is indicated oy PIPE and an ennulus component is indicated by ANNULUS os Card CCC0000. The remaining input for both components is identical an o the only difference in processing is that an annulus uses a flow r egime map appropriate for downcoser representations. In junction connections, the code fcr corponent inlet is CCC000000 and the code for ccaponent outle t is CCC010000. Except for connections to a br anch components only one Junction may be connected to the inlet and only one junction may De connected to the outlet. An and without a connecting Junction i s consi cer ed a closed eno. 11.6.1 CAL d . C C C2 Q Ql A..ElRR _1D CAIR& tlE D.C &Ld , This caro is required for pipe components. d1(1) NUM8ER OF VOLUMES, NV. NV must be greatar than 0 anc less than 100. The number of associetco Junctions inter nal t.o the pdpm is H V- 1. The outer junctions ar e uescribed cy otner components. () Appendix A 22 101
RELAPD Input Data Requirements 08/07/01 - 11.6.2 Cacgg.CC;21Q1 CCCQ133t.E12a talume.Eins.Atta The format is two words per set in sequantial expansion f or ma t for NV sets. These cards ar e required and the carc numoers need not be consecutive. The words for one set are W1(R) VOLU4E FLOW AREA (a2, ft2). W2(I) VOLUME NUMBER. 11.6.3 Catat.CCCgEQL:LLCQE135.Elat.dunElina. Elan.Attas These cards are op t i o n a l and if entereo the card numbers neea not be consecutive. The format is two words per set in sequential expansion format for NV-1 sets. W1(R) INTERNAL JUNCTION FLOW ARE A (m2s ft2). If cards are missing or a word is zero, Junction flow area is set to the minimum area of the aoJoining volumes. For abrupt area enanges, the junction area must be equal to or less than the minimum of the adjacent volume areas. There is no r estriction f or smooth area changes. W2(I) JUNLTIGN NUMdER. 11.6.4 Catat_CCCQ101 CCCQ122t_Elag.1glust.Langtus This card is required for pipe components. The format is two worcs per set in se quen ti al expension format for NV sets. C ar c namber s neec not be consecutive. ol(R) PIPE VOLUME LENGTH (m, f.t ) . W2(I) VOLUME NUMBED. 11.6.5 Cat 21.CCCQi21:CCEQifft.21Et.Y21MEL.12Lk511 1 The format is two words per se t in sequen t i al format for NV sets. Car d numbers need not or consecutive. i d1(R) 10LJM6 (m3, ft3). If car ds are missing, volymes equal to Zero l are assaieo. The pr ogr am requi res th at each volume equal tne l flow area times length. For an y volume, at least two of the three quantities, areas lengtn, or volume, sus t ce nonzero. If Appendix A 23 102
RELAp$ Input Data Requirteents j ' C/l;_') l 08/07/81 one of the quantities is zero, it will De computed from the otner two. If none of the quantities are zero, the volume must equal the area times the length wi thin a rel ati ve err or of 0.000001. W2(I) VOLJME NJMBER. 1166 Cat 2L_CCCQ191=CCC2222t_E1Et_Eniust daLL2Rotal_AQsla These caras are op t ion al and if not entered, horizontal angles are set to 0. The hori zont al. angles are not used in the calculation Dut are entered for possible automated nocing graphics. The format is two wor ds per set in sequential expansion format for NV s ets and c ar d numbers need not be consecutive. dl(R) HORIZONTAL ANGLE ( deg). The absolute value of the angle sust De less than or equal to 360 deg. W2(I) VOLJME NUMBER. (-] 11.6.7 Catst_CCCQhD1:CCCQA11t_Elat_Enisat_ittlical.0LLantatino LJ These cards are re qui red for pipe components. The f o rm at is two worcs per set in sequential expansion forest for NV sets and car d numDers neeo not oc consecutive. wi(R) VERTICAL ANGLE (degl. The absolute value of the angle must De less thsn or equal te 90 deg. The angle o ces is horizontal, and a positive angle has an uovard di r ec ti en. W2(1) VOLUME NUMBER. 11 6.8 Cara_C0C2IQ1:CCC9Z22t Elst_Yn.lume.Eitxation.Chansa These cards are optional. If cards ate elssitg, elevation change is computed from tr ol ume length times sino of ver t6 cal an gl e. The c2ro f orma t is two norcs per set in sa que n ti a l espansion f or mat up to NV sets and card nueotrr. need not be consecutive. d1(R) ELEVATION CHANGE (m, ft). Positive value is increast in eieration. Magnitude must be equal to or less than volume lengtn. If the vertical angle orientation is zero, this [- ') Appenois A 24 103 _ _ _ _ _ _ _ _ _ _ - _ - _ _ _ _ _ _ - _ _ _ . _ _. A
l \ l l 4ELAP5 I1put Data Requirements l 06/07/81 quantity must ta zero. If the vertical angle is nonzero, this ! quantity must also be nonzero and n av e the s ame s a gn. j i d2(I) VOLJME NJMBER. 1 l l 11 6.9 Catgi_CCCQaQl:CCCQa22A_Elat_Yalust_EtiLilac_2ata l These cards are r equi r e d for pipe components. The car d f or ma t is tnree words per s et for NV sets and card numbers neea not De consecutive. l 41(R) PIPE ROUGHNESS (m, ft). 02(R) HYDR AULIC ul AMETER ( m, ft). If 0, nyoraulic clameter is computed from 2.0*(VOLUME AREA /PI)**0.5. A check is made tnat the roughness is less than nalf t1e .1ydr auli c di amet er. 03(I) VOLJME NJMBER. 11.o.10 CatgE_CCCD201-CCCQ222A_Eint_duaaliaa_La11_CQtifin12D1E These cards are optional and if missing, energy loss coef f ic ients are set to zero. The card format is three worcs per s e t in se quen t i al expansion format for 1V-1 sets and cara numbers need not De cons ecuti ve. dl(R) FORWARD FLOW EhtRGY LGSS COEFFICIENT. d2(R) RhiERSd FLOW ENERGY LOSS COEFFICIENT. 03(I) JUNCTIQU NUMBER. 11.6.11 C at al_CCCl 221:CCCl222t_Elat_Y aluag_Cantc al_ El as These cards are required for pipe volumes. The card format is two wor ds per set in se quen ti al expansion format for NV sets and c ar a numoers need not De consecutiv e. 01(I) CONTROL FLAG. Enter te wher e f =0 mesns tnat wall friction is computed for the volbme, f=1 means that wall friction is not computed, e=0 means that a non-equilibrium (unequal t e mp e r a t ur e ) equation of state is useca e=1 means that an equilibrium (equal temperature! equation of state is used. App en di x A 2b 104
t
,7-~g RELAP5 Input Data Requir enents l i
) 08/07/81 1
%~- ;
W2(I) VOLJMt NJMdtR. 11 6.12 Caldt CCC11Dl:CCC1122t Eitt duantina Canttel Elass i These caros are required f or pipe components. The car d f or ma t is two words per set in sequential expansion format for NV-1 sets and car c numbers need not be consecutive. W1(I) CONTROL FLAGS. A four diWit number cans is entered where c=0 i means that the choking model is to os applied, c=1 means that the cnosing mocal is not to be applied, a=0 means a smooth ar e a chtnge or no area change, a=1 means abrupt area change, h=0 means two velocities; h=1 means drift flux appr oximation, h=2 seant one velocity; s=0 means full inertis treatment; s=1 means pseudo-steady state appr oxi mation. The orift flux option has caen oisabled in this version, so da. ant ust.bala W2(I) JUN; TION NUMBER. 11.6.13 Calgt.CCC1LQ1=CCC1C22s.Elag.ggiutt IQ11La1.Coodi1Lans
,~
These cards ar e ritquir e d for pipe. components. The car d format is six woros per set in sequential expansion format for NV sets and card numbers need not be consecuti ve. W1(I) CONTROL WORD. S ee s ect i on 11 2.2 for description of control word and required quantities in Words 2 through 5. If a control word gr est er than 9 indicating Doron is present, Cards CCC2001-CCO2099 must be entered to define the initial boron concentrations. Boron concentrations are not entereo in Words 2 througn 5 of these cards, but si x numbers must be entered per s et and zer os should De entered for unused quantitles. W2-W5(R) QUANTITIES AS INDICATED BY THE CONTROL WOR 3. W6(I) VOLUME NUMBER. 11.6.14 Cntts CCCLQQ1:CCCCQ22L.$DLLlki 09LQQ.CQDLLG1LEl{2OL Tnese cards ar e required only if one of the control wor d s in Cards CCC1201-CCC1299 is gr eater than 9. The card format is two words per set in sequential expansion format for NV sats. Boron concentrations mus t be entered for each volume and zero shoul d be entered for those volumes whose associated control () Appendix A 26 105
RELAPS Input Data Requirements l l dero cid not specify boron. wi(R) 80431 CONCENTRATION (parts of Doron per parts of liquid water ). 1 d2(I) VOLUME NUMBER. 11.6.15 Cacg.CCCll221.ELEL.duaS11SD C200111201_CaaIc2L_tacs l Inis c ar d is optional and if missing, velocities are l ass J me d on C a r ds CCC1301-CCC13 99. dl(I) CONTROL W0RD. If 0, firs t and secono wor d of each set on cards CCC1301-CCC13 99 a re vel ocs ti es. If 1, fir st and second word of each set on Cards CCC1301-CCC1399 are flows. Llek.Lb Catas CCCL1RL-CCC11SSL.Etan duacLLao LDL5LaL C11GLLLean W1(R) INITIAL LIQUID VE LOC ITY (velocity in m/s'ec, ft/sec or flow in Kg/sec, 10/sec). W2(R) INITIAL VAPOR VELOCITY (velocity in m/sec, ft/sec or flow in
<g/sec, 10/sec).
w3(R) INTERFACE VELOCITY (m/sec, f t/ sec) . Enter zero. W4(I) JUNCTION NUMBER. 11.7 BRANCH UR SEPARATOR COMPONENT A branch component is indicated by BRANCH and a steam s ep ar at or is indicated by SEP AR ATR on C ar d CCC 0000. In Junction ref er ences, the code for component inlet is CCC000000 and the code for component outlet is CCC010000. More than one junction may be connected to the inlet and outlet. If an end has no Junctions, tnat end is considered a closed end. In order to represent tees, two Junctions from opposite ends of a br anch component may connect to the same end of a singig volumes pipe, or annulus. Multiple connections to one end of these components is lorially not allowed. A sep ar ator component is sitilar to a br anch component except that the first entered Junction is assumed to be tne steam exit. The FROM junction code of the first junction must refer to this component. At l east o ft e J u r.c t i o n must ce descriDeo by a separator component. 106 l l L__________________--___
I I f- AEL AP b Input Data Requirements (g) I 08/07/81 11.7.1 Cact CCC2221.8L30Sb.1012tB11190 CELA This c ar o is r equired for branch components. W1(I) duMSER OF JUNCTIONS, NJ. NJ is the number of junc t ions descrioed in the input data for this component and must be equal to or greater than zero and less than ten.- Not all the junctions c onnec ti ng to the br anch need be descr ibed with this component input and NJ is not necessarily the total number of Junctions connecting to the br anch. Junc tions described in single junc tions, time dependent junctions, and other b r an ch es can De connectea to this Or anch. W2(I) INITIAL CONDITION C ONTROL. Inis word is optional and if missing, the Junction initial velocities in the first and second woros on Carcs CCCN201 are assumed to be velocities. If zer o, velocities ar e assumedi if nonzero, flows are as s u m e o. 11.7.2 01LGE.CCCQ101:CCCQ102A.Stacch.Xnluta.Etantitz.Cacd1 Thes e caras ar e laentical to C ar ds CCC0101-CCC0109 for Single Volumes, S e c t i on 11.2.1.
)
11.7.3 SC ADG b.X21uat.1Q111Al Candl19.01 inis card is identical to Card CCCO200 f or Single Volumes, Sec t i on 11.2.2. 11.7.4 Catal CCCulDit.QCADGD.JMDal100 Gta111tX Catd Thes e car as ar e requi red if NJ is greater than zero. Cards witn N equal to 1 through 9 are entered, one for each Junction. N need not be consecutive, but NJ cards must ce entered. Tne card format other than N instead of 0 for the f ourth digit is identical to Card CCC0101 of Single Junction Geometry C ar d, Section 11.4 1, except that Words 7 and 8 are not allowed. 11.7.5 Catgs.CCCMZQlt. attach.dunallan.lnitla1.CEDdi112D1 These caras ar e required depending on the value of NJ as descr io eo f or C ar ds CCCN101. () Appendix A 28 1(n
RELAP5 Input Data Re quirenen ts 08/07/61 cl(R) INITIAL LIQUID VELGCITY (velocity in m/sec, ft/sec or flow in Mg/ secs lo/sec). dE(R) INITIAL VAPOR VELOCITY (velocity in m/sec, ft/sec or flow in ng/seca lo/sec). d3(R) INTERFACE VELOCITY (m/ secs ft/sec). Enter zero. 11.8 VALVE JUNCTION COMPONENT A valve Junction component is indicated Dy VALVE on Caro CCC0000. 11 8.1 Cacg.GCCQ1Q1-CCCQ12gt_yg11g.dMatitaa.EagagCty.13td
'This card is requirea f or v al v e Junctio n c omponen ts.
d1(I) FROM CJNNEC TION CODE TO A COMPONENT. e2(I) TO CONNECTION CDDE TO A COMPONENT. Eltner the TO or the FROM connection code mus t r e f er to this component. a3(R) JUNCTI3N AREA (32, ft2). Inis quantity is tne full open ar e a of the value. If zeros the ar ea is set to the minimum area of adjoining yolumes. If nohzeros this area is used. When an abrupt area change mooel i s s pec if ied, this area must be less tnan or equal to the minssum of the ajoining vol um e ar eas. d4(R) FORD ARD FLOW ENERGY LOSS C0hPFICIENT. f d5(R) REWERSE FLOW ENERGY LOSS COEFFICIENT. I u6(I) JUNCTION FLAGS. A four di g i t F.u m b e r s cahst is entered where c=0 l means that the choking model is to be appli eds c=1 me ans that l the choking model is not to De app l i ed, a=0 means smo o th or 43 ar ea change, a=1 means abrupt ar e a enange, h=0 means two velocities, n=1 means drift flux approximation, h=2 means one 1 , velocity, s=0 means full inertial treatments s=1 means pseuco- l ( steady state approximation. If a motor or servo y alv e is I specified, the flag, as mast be 1 if no CSUBV table is entered or nust se oif a CSUBV taDie is entered. Drift flux h as been disaoled so 42.221.Mit.b21 d7(R) SUSC00 LED DISCHARGE COEFFICIENT. Th i s quantity is applied only to succooled choked flow :al c ul a ti ans . The quantity must be greater than zero and less tnan 2.0. If missing or 2er ce it is Appendix A 29 1 l 108 I
RELAPS Input usta' Requirements 08/07/81 set t o 1.0.
'd8 (R ) TWO P HASE 01SCHARGE COEFFICIE NT. This quantity is applied only to two phase choked flow calculations. The quantity must be greater than zero or less than 2.0. If missing or zeros it is i
set to 1.0. 11.a.2 Cata_CCCQ101t_Valts_Juos11oo_In111al_Canditinas This card is requireo for valve junction components. dl(I)- C ONT R OL WORD. If Os next two words are velocitiess if 1s the next'two words are flows. w2(R) INITIAL LIQUID VELOCITY. Tnis' quantity is eitner velocity (m/ sacs ft/sec)s or flow (kg/ secs ID/sec) depending on the control word. W3(R) INITIAL VAPOR VELOCITY. This quantity is either velocity (m/ secs ft/sec), or flow (kg/ secs Ib/sec) depending on the control woro.
- h4(R) INTERFACE VEL'0 CITY ( m/s ec s ft/sec). Ente r ze ro.
11 8.3 Cact CCCD1QQt_yalrs_Iyas_Cate This carc is required to specify the valve type. dl(a) VALVE TYPE. This word must contain one of the f ollowings CHXVLV for check valves TRPVLV for trip valve, INRVLV for inertial valves NTRVLV for motor valves or SRVVLV for servo valve. 11.d.4 Catd_CCCQaQ1:CCCS122t_Ealta_Qata_Ang_In111al_ Canal 11ans These cards are requir ed for valve junction components. Five cifferent types of valves are al l owe c. The following words may De placed on one or more cards and the card numbers need not os consecutive. The card format of these caros depends on the v al v e t yp e. 11.8.4.1 CSECd.XALVES Appendix A 30 (" ( 109
l REL AP 5 Input Data Requirements k al(I) CHEC( VALVE TYPE. Is -1 for flow operated check valve with nysterisis, is O for flow operated cneck valve without nysterisis, as1 for pr essure dif f erential cnecn v al v e. 42(I) CHECK WALVE POSTION. Valve is initially open i f Os closed if 1. d3(R) CLOSING B ACK PRESSURE (Pa, Ibf/in2). d4(R) LEAK RATIO. Fraction of junc ti on area for leakage when valve is nomi n a l ly closec. 11.8.4.2 IBIE.2& LYE 41(1) TRIP NUMBER. Must De a valic trip number. If trip is off, valve is closed; if tr ip i s on, valve is open. 11 8.4 3 18Ehll&L_1&LtE al(I) LATCH GPTION. Valve can open ano close repeatedly if latch option is 3, valve either opens or closes only once if latch option is 1. d2(I) VALVE INITIAL CONDITION. Valve is initially open if 0, ini ti ally closed if 1. d3(R) CLO5ING BACK PRESSURE. ( Pa , IDf/in2). d4(R) LEAKAGE FRACTION. Fraction o f junction area for leakage when valve is nominally closeo. d5(R) INITIAL FLAPPEk ANGLE (deg). F l app er angle must be wi thin the minimum and maximum angles sp eci fi e d in W6 and W7. d6(R) MINIMUM ANGLE (deg). e7(4) 3AX1101 ANG LE (ceg). W8(R) MOMENT OF INERTIA 0F VALVE FL APPER (kg-s2, to-ft2). d9(R) INITIAL ANGULAR VELOCITY (rad /sec). W10( R) MGMENT LENGTH OF FLAPPER (m, ft). d il( R) RADIUS OF FLAPPER (m, ft). d12(R) MA53 OF FLAPPER (kg, 10). 11.8.4.4 5DIQ3_i&Lyg 1 Appendix A 31 Oi l l 110 1
i l i l RELAPS Iaput Data Requirements j Wl(I) UPEN TRIP NUMBER d2(I) CLOSE TRIP NUMBER Both tne open and cl ose trip numbers must De l valia trips. When both trips are' false, the valve remains at 1 its current position. When one o f the trips is'true, the valve opens or closes depending on which trip is tr ue. The transient will ' be ter minated if b o th trips are true at the same time. d3(R) VALVE CHANGE RATE (sec-1). If W5 is not entered, this quantity is the rate of change of the normalizeo valve area as the valve opens or closes. If W5 is entereo, this' quantity is the rate of change of the normalized valve stem position. This word must be greater than zero. d4(I) INITIAL POSITION. This number is the initial normalized valve area or the initial normalized stem position depending on W5. This quanti ty must be between 0.0 and 1.0. d5(I) VALVE TABLE NUMBER. If this word is not entered, or entered as zers, the v alve' ar ea is determined directly by the valve change r at e an d the tr ips. If tn i s word t s entered as nonzero, the v al ve stem position is determined by the valve change rate and the trips, and the val ve area is detere8 .ed from a general table containing nor mal ize d valve area versus normalized stem postion. 11.8.4.5 EgatQ gALgE W1(I) CONTROL VARIABLE NUMBER. The value of the indicated control v ar i a l.l e is either the normalized valve area or the normalized stem position depending on whether Word '2 is entered. The contr ol variable is also the saaren argument for the CSUBV table if it is entered. W2(I) VALVE TABLE NUMBER. If this word is not entered, the control vari ant e v a lu e is the normalized flow area. If it is entered, the control v ar i able value is the normalized stem position and the gen er a l table inoicated by thi s word contains a table of nortalized area versus normalized stem position. 11.8.5 Catst.CC;QiQQ:CCCQi22_CSuht.Lahls The C SUBV table contains forwaro and reverse fl o w c oe f f ic ie nt s as a function of normalizeo stem position. These cards ar e r equi reo if the junction flag, as for a motor or servo valve specifies a smooth area change (a=0). Appenoix A 32 til
r7-~- - l RELAP5 Input Data Requirements l' 08/07/81 11.8.5.1 C&gq1_;C;Qigg.gACIQg$ inis card i s opti on al. The factors apply to the stem and the flow coefficients entries in the CSSUBV taole. dl(R) NORMALIZED STEM POSITION F AC T OR. j i d2(R) FLOn COEFFICIENT FACTOR. j l 11.8.5.2 CAgu1_CCCQi21:CCCQi22_IARLE_Eb1ELES I The table is enter ed by using tnree word sets. W1 is the stes position and must be normalized. The factor W1 on card CCC0400 can De useo to normalize tne stem posi tion. h2 and W3 J are tne forwar o and reverse flow coefficients. Code internally l converts flow coef f icients to energ y loss coef ficients by K = 2* AJ * *2/ ( RHO *C SUBV* *2) where RHO is density of water at 60 cegF (268.71 K) and AJ is the full open valve ares, and CSUBV is the flow coefficient. W2 on cara CCC0400 may De used to modify the l def s nition of CSU6V. Smooth ar ea change mus t be spe ci fi ed in d6 j on C ar o CCC0101 to use the CSJBV table. CSUdv is entered in Britesn units only. dl(R) NORMALIZED STEM POSITION. d2(R) FORWARD CSUBV (gal /ain-(Ibf/in2)**0 5). Tne CSUBV is input in dr i t i sn units onlys and as converteo to 51 units using 7.5980555-7 as the conversion factor. W3(R) REVERSE CSJBV (gal / min-(Ibflin2)**0.5).
'11.9 PUMP COMPONENT
& pump c om p one n t is indicated by PUMP on Card CCC0000. A pump consists of one vol ume and two junctionss one attachec to each and of the volume.
11 9 1 Cacaa_CCCQ121:CCCQ12It_fusa_talust_2tastitx_ Cards Tnis cara (or c ar ds ) is required for a pump component. The seven words can De ent er e o on one or more car cs and the card nusoers ated not be consecutive. d1(R) VOLJME FLOW AREA (m**2s ft**2). Appendix A 33 112
,_ RELAP5 Input Data Requirements
} 08/07/81 d2(R1 LEN3TH OF VOLunE (me ft).
W3(R) VOLUME OF VOLUME (m3, ft3). The pr ogr am requires that the volume equals the volume flow area - times the length tw3=W1*W2). At least two of the three quantities, die W2s W3s must be nonzero. If one of the quantities is zero, i t will be computea from the other two. If none of tne words ar e zer os they must satisfy the volume equals area times length wi th i n a relative error of 0.000001. W4(R) ANGLE F OR HORIZONTAL ORIENTATION (deg). The absolute value of this angle must be less than or equal to 360 deg. This qu:ntity is not usea in the calcula tion but is sp e ci fi ca for pos s ib l e automated crawing of n od in g diagrams. W5(R) ANGLE FOR VERTICAL GRIE NT ATION (deg). The absolute value o f this angle must be less than or equ al to 90 aeg. The angle O deg is h or iz on tal and Positive angles have an uphar d di rect ion. W6(R) ELE V A TIOM CHANGE (m, ft). A positive value is an increase in e le va ti on. The absolute value of tnis quantity must be equal to or less than the volume length, If the vertical angle orientation is zero, this quantity must be zero. If the vertical an gl e is nonzeros this quantity must al s o be nonzer o and h av e the same sign. 47(I) VOLUME CONTROL FLAG. Enter o for non-equilibrium:(unequal temp e r atur e ) and 1 f or equillDrium (equal t emp er a t ur e ) ther modynamic calculation. No wall friction flag is all owed and no wall fr i ct i on is computed for a pump since it is included in the homologous pump data. The printed output volume fl ags will I show the no friction flag set to 1. 11.9.2 C a t s . C C C Q 10ar_Eu a a_la tt1_ilu s tin ul.J u n s t l a n_ C a cd W1(I) VOLUME CODE OF CONNECTING VOLUME ON INLET SIDE. W2(R) JUNCTION ARE A (m2, ft2). If zero, area is set to minimum of volume ar e as of adjacent vol use s. If an acrJpt ar ea Changer area must be equal to or less than minimum of soJacent volume areas. If a smooth ar es changes no restrictions exist. W3(R) FORWARD FLOW ENERGY LOSS COEFFICIENT. W4(R) REVERSE FLOW ENERGY LOSS C0 EFFICIENT. W5(I) JUNCTION FLAGS. A four algit num0ere cahs, is entered where c=0 means that the choking model is to be applieo, c=1 means that the choking model is not to be applied, a=0 means a smooth or no () Appendix A 34 113
4hLAP5 Input Data Requirements 08/07/81 area enange, a=1 me ans an abr upt area change, h=0 means two velocities, h=1 means or if t flux approximation, h=2 means one velscity, s=0 means full inertial treatment, s=1 means pseudo-state approximation. The drift flux approximation has been disaoleo in this version so an_nat_uta h=1 11.9.3 Cata_CCC21Q2t_Eume_Qu11al_1Qianhatas1_dunstino_Cata This cara is requireo for a pump componen t. The format for this carc is icentical to Card CCC0108 except data are for the outi e t Junction 11.9.4 Catt_CCCQEQQt_EuRR_121 Mat _lQillal_C2Qdl11SQ1 Cara This card is re' quired for a pump component. d1(I) CONTROL WORD. This numoer is tne same as the contr ol word d es cr i D ed in 11.2 3. d2-W4(R) QUANTITIES AS REQUIRED BY THE CONTROL WORD IN WORD 1. 11.9.5 Cato_CaCQggit_Euan_init1_Auac11an_laitial_Candilian Catd O This card is required for a pump component. d1(I) CONTROL d]RD. I f 0, the next two words are ve l oc i ti es ; i f 1, the next two words ar e flow rates. U2(R) INITIAL LIQUID VELOCITY. This quantity is either velocity (m/ sec, ft/sec) or flow ( kg/s ec, Ib/sec). d3(R) INITIAL VAPOR VELOCITY. This quan ti ty is ei ther velocity (m/ sec, f t/s ec) or flow (kg/sec, ID/sec). 44(R) INITIAL INTERFACE VELOCITY (m/sec, ft/sec). Enter zero. 11.9.6 Catg_G;CQ222t_Egag_Qu11al.1gactiga_ initial.;nogltinn_Cata l inis card is simil ar to C ar c OC0 0201 excep t dat a ar e for the outlet Junction. Appendix A 35 114 j
1 so i 4 4 ELAPS Input Dat a' Requir ements 11.9.7 Catt.GGGQ1Q1t_gggg.IngaX kDd.QE11RD.Catt This caro is required for a pump component. d1(I) PUMP TAdLE DATA IN DI C AT OR. If 0, single phase tables are enter ed with this component. A postive nonzero number indicates , that the single phase tables are to be obtained from the pump ' component wi th thi s number. I f ,-1, u se buil t in data for. the 6ingham pump. If -2, use built in data for the Westinghouse Pump. w2(I) TW3 P HASE INDEX. E n t er -1 if two phase option is not to be used. Use o if two phase option is desired ano two phase i mul ti plier tables ar e enter ed with thi s component. Use nonzero if two ph as e option is desired and two phase multiplier table i data are to be obtained f r om the pump component with the nu mber entered. There ar e no built-in data for the two phase mul ti plier tabl e. d3(I) TWO PHASE DIFFERENCE TABLE INDEX. Enter -3 if two phase di f f er ence table is not needed (i.e., if W2 is -1). Use 0 if table is entered with this component. Enter a positive nonze r o number if table is to be ootained from pump component with this number. Enter -1 f or buil t-in data for the Bingham pump. Enter s -2 for built-in data for the westinghouse pump. , d4(I) PUMP MOTOR TORGbE TABLE INDEX. If -1, no table is used. I f 0, tacle is enterec for this component. If noizero, use the t ab l e from component with this numDer. W5(1) TIME DEPEdDENT PUMP VELOCITY INDEX. If -1, no table is used and pump velocity is always deter mined by torque-inertia equation. If 3, taDie is entered with this component. If nonzero, table from pump component wi th this nunper is used. W6(1) PUNP 1AIP NUMBER. When trip is offe electrical p owe r is supplied to the pump motor; when trip is on, electrical power is disconnected f rom the pump motor. The pump velocity depends on the pump velocity table and asso ci ated tr i p, the pump motor I tor que data, and thi s trip. If the pump velocity table is being useo, the pump velocity is always computed from that table. If the pump velocity table is not being used, the pump velocity j cepends on the pump motor torque data ano this trip. If the I trip is off and no pump motor torque data is present, the pump , velocity is the same as for the previous time step. This will De tne in i tial pump v el oci t y if the pump trip has never been set. Usually the pump tr i p is a latched trip but that is not necessary. If the trip is of f and a pump mo tor torque t able is present, the pump velocity is given from the torque-inertia Appendix A 36
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RELAP5 Inpu t Data Re qui reients 08/07/81 equation where the net torque is given from the pump motor t or qu e data ano the homol ogous tor que data. If the trip is on, the t or que-inerti a equation is used ano the pump motor torque is set to zer o. If the pump trip numoer is zero, no trip i s tested and t he pump trip is assumed to be always off. 07(I) REVERSE INDICATOR. If 0, no reverse is allowed; if 1, r ev er s e is allowed. 4 11 9.8 Cata_CCCQAQ2-02t_Euse_Dasst12112n_Cata This card is required for a pump component. 41(I) RATED PUMP VELOCITY ( rad / sec, r ev / mi n ). d2(R) RATIU OF INITIAL PUMP VELOCITY TO RATED PUNP VELOCITY. d3(R) RATED FLOW (m3/sec, gal /iin). do(R) AATED HEAD (m, ft). 09(R) RATED TORQUE (N-me I b f- f t ) . d6(R) MOMENT OF INERTIA ( k g-m 2, lo-ft2). ()' 07(R) RATED DENS ITY (kg/m3, ib/ft3). If zero, initial censity is used. 08(R) R ATED PUMP MOTOR TORQUE (N-m, Ibf-ft). If thi s wor d is zero, tne rated pump motor torque ' i s' computed from initial pump velocity and pump torque which is computeo from the initial puso velocity, initial vol ume condi tions,- and the homologous curves. This quantity must be nonzero if relative pump motor torque taole is entered. d9(R) TF2, FRICTION TORQUE COEFFICIENT (N-me ibf-ft). d10(R) TF0, FRICTION TORQUE C OE FF IC IE NT (N-a, Ibf-ft). 011(R) TF1, FRICTION TORQUE COEFFICIENT (N-me Ibf-ft). I dl2(R) TF3e FdICT I ON TORQUE COEFFICIENT (N-a, ibf-ft). l l 1 1A.9.9 Cata_CCC0310t_ fuse.StsE_Qata_CaLa If t hi s card is omitted, the pump will not be stopped oy Appenoix A 37 116 i I
I REL APb Input Data Requirements j 08/07/81 73 N.,) the program. 1 i I W1(R) ELAPSED PROBLEM TIME FOR PUMP STOP (sec). W2(R) MAXIMUM FORW ARD VELOCITY FOR PUMP STOP (rad /sec, rev/ min). W3(R) MAXIMUM REVERSE VELOCITY FOR PUMP STOP ( r ad/s ec, r ev/ min) . 4 Note tnat r everse velocity is a negative nuecer, 11 9.10 Catst_CCCKKQ2:CCCXX224_Sinala_Ehast_datalanaus_Cutxas These cards are needed only if W1 of Card CCCO301 i s 0. Ther e are sixteen possible sets of homologous curve dat a to completely describe the single phase pump operation, th at i s, a curve for each nead and torque f or each of the eight possible curve types or regimes of oper at i on. En ter ing all sixteen curves is not necessary, Dut a error will occur from an at t emp t to reference one that has not been entered. Card numbering is CCC1100-CCC1199 for the first curve, CCC1200-CCC1299 for the second cur ve througn CCC2600-CCC2699 for the sixteenth curve. Data for each Indivioual curve are input on up to 99 carcs which need not De numbered consecutively. W1(I) CURVE TYPE. Enter i f or a head curve) enter 2 for a torque curve. W2(I) CURVE REGIME. aes RELAPS users manual for furtner information. W3(R) IN3cPENDENT VARIABLE. V al ues for each curve range from -1.0 to 0.0 or f r om 0.0 to 1.0 inclusive. W4(R) DEPENDENT VARIABLE. Additional pairs as 1eeded ar e entered on this or f ollowing cards up to a limit of 100 pair s. 1 11.9.11 Catas_CCCEL2Q:CCC1122t_Ima_Ebass_5ultla11st_lakles These cards ar e neede d only i f d2 o f Car d CCC0301 is 0. XX is 30 and 31 for the pump head mul tipli er table and the pump torque mu ltiplier tab l e re spect i vel y. W1(1) EXTRAPOLATION INDICATOR. Not usede enter 0. Appendix A 38 f" ( 117 L _-_- -_ _ -
1 i l l l l I RELAPD Inpu t' Data Requi remen t s 08/07/81 W2(R) VOID FR AC TI ON. I W3(R) HEAD Ud TORQUE MULTIPLIER DEPENDING ON TABLE TYPE. Additional pairs of data as needed ar e enter ed on th i s or additional c ar as as needed up to a limi t o f 100 p air s. Void fractions must te in increasing order.
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11.9.12 Catst_CCC1&QQ:CCCIESSt_Iza_Euata_QLIIntenst lables 1 Tnese cards are requi red only if W3 of Card CCC0301 is 0. The two phase di f f erence t aoles ar e homologous curves entered in ; a similar manner to the single p h as e homologous data. Card i numbering is C C C410 0-C CC 4199 for the first curves CCC4200- ) CCC4299 for the second cur v e through CCC5600-CCC5699 for the ! si x te en tn curve. D ata ar e the same as the cata for the single l pnase data excep t the dependent variable is single phase minus two phase data. 11.9.13 CAE21.CCCa2DL-CCChQ2St_Etiatila_Eu1E_dalEL_12C2Ws_Q212 These cards are requi r eo onl y if W4 of Card CCCs301 is 0. If the pump velocity table is not being used and these cards are presents tne torque-inertia equation is used. When the electrical power is suppli ed to the puma motor (the pump trip is off), the net torque is computed from tne rated pump motor t or qu e tises the relative pump motor torque from tnis table ano the t or que from the homo lo gous data. If the electrical power is disconnected f r o m t h e pu mp ( the pump trip is onis pump motor torque is zero. Wl(R) . PUMP VELOCITY (rad / secs rev/ min). W2(R) REL AT IVE PUNP MOTOR TORQUE. Addi t i onal pairs as needed are added on this or additional car ds up to a maximum of 100 pairs. 11.9.14 Catst CCChlQQt_Ilgt_QtStaggat_Eutg_is1SGitX C201L21_Catn inis card is required only if W5 of Card CCC0301 is 0. The vel oc ity taole if present has priority in setting the pump velocaty over the pump trips the pump motor torque datas and the torque-liertia e qu at i on. Ap p en ci x A 39 118
RELAPD Input Data Requirements (,,) 08/07/81 41(I) TRIP NdMBER. If trip number is zeros the pump velocity is-always computed from this table using time as the search ar gu m en t. If the trip number is nonzeros the trip de te rm ine s wh et h er taole is to be used. If trip is offs the pump velocity is set from the trips the pump motor torque Jatas and the tor qu e-iner tial equation. If trip is ons the pump velocity is compu te d from this t abl e. If Word 3 is alssings the s ear ch v ar i a b l e in the table is time and the searen argument is time minus the trip time. W2(A) ALPHANUMERIC PART OF VARI A6LE REQUE ST CODE. Thi s quanti ty is optional. If presents t hi s wor d and the next are a v ar i ab l e request code t h at specifies the search argument for the table loo <up and interpolation. TIME can be selected, but the trip time is not subtracted from tne time. I W 3(I) NUMERIC P ART OF VARI ABLE REQUEST CODE. Assumed zero i f miss ing. 1142s11.Catut_.CCChlQl:CCChl22t Ilas..Qsaandant..Euaa..Xains11x Caros These caros are requi r ed only if W5 of Card CCCO301 is 0. () W1(R) SEARCH VARIABLE. search vari abl e. Units depend on the quantity selected for the W 2(R) PUMP VELOCITY (rad / secs rev/ mini. Additional pairs as needed are added on this or additional caras up to a maximum of 100 pairs. Tise values must be in incr e as i n g or der . 11.10 ACCUMULATOR COMPONENT An accumulator component is indi cated by ACCUM on Card CCC0000. An ac c umul a to r consists of one volume and one ; Junction. 11.10 1 Catd.CCC21Q1t.Enlust.G12BalLX d1(A) VOLUME FLOW AREA (m2, ft2). Flow area of tank. W2(R) LENGTH OF VOLUME (ms ft). Lengtn of tank. Appendix A 40
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I RELAPb Input Data kequirenents - 08/07/81 ' j I W3(R) VOLvME OF VOLUM6 (m3, ft3). The pr o gr am requires that the volume e qual s the volume flow ar ea times length (W3=Wl*W2). At ]! least two of the tn ree quan ti t e es, dl, W 2, n3 must be no n zer o. If one of the qu an t i t i es is zero, it will De computed from tne otner two. If none o f the worcs are Zoro, they sust s atisf y the volume equ al s ar e a times length within a relative err or 0.000001. d4(R) ANGLE FUR HORIZLNTAL ORIENTATION (deg). The absolute value of j this angle must be less than or equal to 363 deg. This quantity J is not usec in the calculation out is specifico for pos s ib l e automated drawing of nod in g diagraas. d5(R) ANGLE FOR VERTICAL ORIENTATION (deg). The absolute value of tnis an gl e must be l e ss th an or equal to 90 deg. The angle o is norizontal and positive angles have an upwar c dir ection. W6(R) ElsVATION CHANGE (mr ft). A posstive value is an increase in elevation. The aDsolute value of this quantity must be less than or equal to the volume length. If the vertical angle orientation is zero, thi s quantity must De zero. If the 4 non ze r o , this quantity must also be nonzero l v er t i ca l angle is and nave tne same sign. 07(R) PIPE ROUGHNESS (m, ft). W8(R) HYDRAULIC OIAMETER (m, ft). If zero, the hydraulic diameter cosputea from 2. 0 * ( VOL LM E A RE A / P I ) *
- 0. 5. A check is made that the pipe roughness is less than hai f the hydr au lic c l ame ter.
W9(1) VOLJME CONTROL FLAG. En te r fe where f is zero if wall friction effects ar e to De computed for the surge line, f is 1 if wall friction is not to De computed. The flag, es must be 1 to specify an equilibrium (equal temperature) calculation. l 11.10.2 Cata_CCCQE22_ AccugulataI_Iant_ initial _^ nnaltinas W1(R) PRESSURE (Pas I b f/ i n2 ) . W2(R) T EMP E R AT J RE ( K, degF). 11.10 3 CAL 2_CCCllDit AEEusula12I_duna11aa_Gt2111L2 Wl(I) TO ;GNNE; TION CODE TO A COMPONENT. Fros c o n n e c t .t o n is not enter ed since it is a l wa ys from the accumulator. AppendlX A 41 120
RELAPS Input Data Requirements 08/07/81 d2(R) J UN C T ION AREA (m2, ft). Surge line flow area. W3(R) FOdwARD FLOW ENERGY LOSS COEFFICIENT. W4(R) REVERSE FLOW ENERGY LOSS 0 0EFFICIEN T. W5(I) JdNCTION FLAGS. Must be zero. 11 10.4 Catg_CCCEEQQt_Assusu111AI_ lank _laitiaL_CandillaDE W1(R) LIQJID VOLUME IN TANK (m3, ft3). The volume of water contained in tne surge line must be included with the water in the tank. W2(R) LIQUID LEVEL IN TANK (m, ft). Either W1 or W2 must ce ' specified. _ W3(R) SURGE LINE LENGTH (ms ft). k4(R) SURGE LINE ELEVATION (as ft). Inis is the elevation change from tne tank bottom to the injection point. W5(R) TAN ( WALL T HIC KNE S S ( m, ft). Not al l o wed to be zero. W6(Il HEAT TRANSFER FLAG. If zer o, heat transfer will be calculated. () W7(R) If on e, no heat tr ansf er calculated. TANK DENSITY (Kg/m3, Ib/ft3). If zero, will default to density o f car oon s teel. W8(R) TANK VOLUMETRIC HEAT CAPACITY (J/kg-K, Stu/lb-degF). If zero will default to heat c ap aci ty of car 00n steel. i W9(R) THERMAL CONDUCTIVITY OF NITROGEN (watts /m-4, 8tu/sec-ft-degF). If zero will default to t he t her,ma l c onduc t i v i ty of nitrogen at atmospheric pressure and temper atur e of 300 K. 12.0 CARQ1_lCCCE1 Nut _dEAI_11&UCIUEE_INEUI inese car ds ar e used only in NEW type problems and are required only if heat str uc tur e s are des cri bed. The heat structure car d numbers are di vided leto fielos where 8 i CCC is a heat structure nuaber. The heat s tr u c tu r e I numbers need not be consecutive. It is suggested but not required that wher e heat s t r uc tur es and hydrodynamic vo l um es ar e related, th e y be given the same numoer. G i s a geometr y number. The combination CCCG is a heat j Appendix A 42 121
RELAP5 Input Data Requirements 08/07/81 s t r u ctur e-geomet r y combination that i s r ef er enced ih neat structure input cata. X is the cara type. NN is the car d numoer within a cara type.
- 12. 1 Cacg_1;c;100Qt_Gacetal_htat 11ructuts_Qata This card is required for heat structures.
c1(I) NUMBER OF HEAT STRUCTURES WITH THIS GEOMETRY, NH. This number must be greater than 0 and l ess t nan 100. W2(I) NuinER OF MESH PGINTS FOR THIS GE0 METRY, NP. This number must ce gr eater tnan 1 anc less than 100. W3(I) GEOMETRY TYPd. Enter 1 for r ectangul ar, 2 f or cylindrical, and 3 far spherical. d4(I) STEADY STATE INITIALIZATION FLAG. Use 0 i f no steady state ini ti ali zati on is desired, i.e., use the initi al conditions entered on input cards; use 1 if steady state calculation for ini ti al conoitions is desired. d5(R) LEFT B0uiOARY COORDINATE (m, f t ). 12.2 Cac2.lCCCG100&_dtat.lttustuts dt10.Ela21 , This card is requirea for heat structure input. al(I) MESH L3 CATION FLAG. If zero, geometry data i ncludi ng mesh interval data, composition data, and source distribution data are entered with this' heat structure input. If nonzero, tha t information is taken fr om the geometry data from the heat structure-geometry (CCCG) number in thi s wor d. If this word is nonzero, the r e ma i n i ng geometry information des cr ibe d in Sections 12.2 through 12.5 is not entered. d2(I) MESH FORMAT FLAG. This word is needed only if W1 is zero al t ho u g h no error o c c ur s if it is present when W1 is nonzero. The mesh interval data is given as a sequence of p ai r s of numoers an one of two f or m at s. If this wor d i s 1, the pairs af numbers c ontain the number of mesr, intervals in this sp ace and the riant b oun d ar y co or ai nate. For the first pair, the left cooroinate of the space is the left boundary coordinate en t er ed in d5 of Caro ICCCG000; f or succeecing pairs, the lef t coorcinate is the r i ght coor d i na te of tne previous pair. If Appendix A 43 122
RELAPS Input Data. Requiremen ts 08/07/81 (t~) . is sequential expansion of me sh \ s' this' w ar d is 2, the format intervals. 12.3 Catst_lC;CE1Q1:lCCCE21L_dtat_11tuGLutt_ Bath _l01stX11_Q111 l These cards are required if W1 of Card ICCCG100 is zero. In format 1, the sum of the numbers of intervals must be NP-1. In format 2s the sequential expansion must be for NP-1 intervals. The car d numbers need not be sequential. Entaat_1 W1(1) NUMBER OP INTERVALS. W2(R) RIG 4T COORDINATE (m, ft). EQcasL_2 d1(R) MESH INTERVAL (as ft). W2(I) MESH NUMBER. 12.4 Catg1_1CCCEZQ1:1CCCEE22s_dsat_11cuctutt_Casans111an_Qata. r-ss O Tnese cards ar e r equired if W1 of Card ICCCG100 is zero and must not be entered otherwise. The card format is two numbers per set in sequential expansion format for NP-1 intervals. The cara numbers need not be in sequential order. W1(I) COMPOSITION NUMBER. The absolute value of this quantity is the composition number. The sign indicates whether the space over which this composition is applied i s to be included or excluded from the volume averaged temperature computation. If plus, the space is included; if minus, the sp ace is not included. W2(1) INTERVAL NUMBER. 12.5 Catas_1CCCE1Q1:1CCCS122t_dsat_Sttuntuta_alticiantian_ Data These cards ar e requireo if W1 of Card ICCCG100 is zero and , must not be entered othe r wi se . The car d format is two numbers ! per set in sequential expansion format for NP-1 intervals. The cara number s need not be in sequential order. I Appendix A 44 r 123
dELAPb Input Data Requirements 08/07/81 VALUE. These are r el ative values only ano can be scaleo k d1(A) SOURCh by any factor without ch an g i n g results. 22(I) MESH INT ERV AL NUMBE R. 12.6 Cacd_1CCCGiD0t_ Initial.Issaccatutt_ Elan This ' car d is opt ional and i f mi ssi ng, W1 is assumed zero. W1(I) INITIAL TEMPERATURE FLAG. If this word is zer o or -1, in i ti al temper atur es ar e entered with the input data for this heat structure-geometry data. If greater than zero, initial temperatures for this heat structure-geometry are taken from the neat structure-geometry number in tnis word. 12.7 Catas_1CCCGiD1:1CCCgi22t_1011Lal_Itm2cLalWC1_Qata l These cards ar e r equired if W1 of card 1CCCG400 is zero or
-1. If di is zero, one temperature distribution is entered and the s ase distribution is applied to all the Ni heat structures.
The card format is two number s per set in sequential e xpansi on format for NP mesh points. el(R) TEMPERATURE (K, degF). d2(I) ME34 POINT NLMBER. De If W1 is -1, a separate temper atur e distribution must ent er ed for each of the NH heat structures. The distribution f or the f ir st heat s tructur e is ent er e d on Card ICCCG401, the d is tr iouti on for the second heat s tr uctur e is entered on Card ICCCG402, and the r emai ni ng distributions ar e entered on c on se c u ti v e car a numbers. Continuation cards can be used if the c at a cannot fit on one car d. W1-hN(R) TEMPERATURE ( K, cegF). Enter the NP sesh poi nt t emper atur es in order fros left to right. I 12 8 Catas_1CCCG501:lCCCG222A Lati anundatx_Cancitian_Qata The coundary condition d at a for the heat s tr uc tures wi th slightly modified form of this geometry are entered in a a sequential e xpansion using six quantities per set for the number ] of heat s tr uc ture s wi th this geometry (NH sets). Appendix A 45 g ei 124 , l l 1 I I
s I RELAP5 Input Data Requirements gs () 08/07/81 wl(I) SOUNDARY V O LJME . This wor d specif ies the hydr odynamic volume or general table associated with the left surface of this heat s tr uc tur e. If zero, no volume or general taole is associated witn the left surface of this heat structure and a temperature of Zero is used for a surface temperature or a sink temperature in boundar y conditions. A boundary volume. is entered as a positive nunper. A general table is entered as a negative number (-1 through -999). W2(I) IN;REMENT. This word and W1 are tr eated di f f erently from tne standar d sequential expansion. W1 of the first set applies to the first heat structure of the heat struc ture-geometry set. The increment is applied to W1, and that applies to the s e co n d heat s tr uc tur e. The in cr ement is app 0ied up to the limit in W6 of a set. W1 of the next set applies to the next heat s tr uc ture, and incr ements ar e applied as for tne first set. The increment say be zero or nonzero, plus or minus. W3(Il 80JND ARY CONDITION TYPE. If, 0 a symmetry or insulated coundary condi ti on i s used. The coundary volume must De O. 1 a convective b ound a r y condition where the heat tran sf er coef ficient is obtained froa heat tr ansf er package 1 is used. The sink temper atur e is the temperature of the (j (ms e boundary volume. W1 must sp eci f y a boundary this bouncary condition type. volume with 1003 tne temperature of the boundar y volume or the temperatu're from tne gener al t ab l e (as specified in W1) is used as the left surface temperature. If W1 is zero, the surface teape r atur e is set to zer o. lxxx the temperature in general taole xxx is used as the left sur f ace temper atur e. 2xxx the neat transf er rate f rom table xxx is used as the left boundary conoitton. 3xxx a convective boundary condition is used where the heat transfer coef f icient as a function of time is obtained from gener a l table xxx. The sink temperature is tne temperature of the boundary volume. 4xxx a convective boundary condition is used where the heat transf er coef fi ci ent as a function of surface The sink temper atur e temperature is obtained from gen er al table xxx. is the temper ature o f the boundary volume. W4(1) SURFACE AREA CODE. If 0+ WS is the left surface area. If 1, W5 is the surface area in rectangular ge ome tr y, is the cylinder heignt or equivalent in cylindrical geometry, or is the fraction of a sphere (0.5 is a hemi spher e) in spherical geometry. () Appendix A ~46 125
RELAPS Input Data Requirements 08/07/81 l l d5(R) SURFACE AAEA OR FACTOR. As indicateo in w4, this word contains the surface area (m2s ft2) or a geometry dependent multiplier ( (m2s ft2 for rectangular; ms ft for cylindrical; or I dimensionle ss f or spnerical geometries). co(I) HEAT STRUCTURE NUMBER. 12.9 Catas 1CCCEhQl:lCCCEC22t_11Ebl.aQuadat1 CaaditL20_CacA1 inese cards are the same as Cards 1CCC3 501-1CCCG599 but f or f the rignt bouncary. The left and right surf ace areas must be j compatible with the geometry. ) i i 12.10 Catst_lC;C12Q1:1CCCGZS2t_1gutag_Qata.Catgs These cards are r equi r ed for heat struc ture data. The car d f orma t is sequenti al f or ma ts five words per sets descr ibing NH neat structures. al(I) SOURCE TYPE. I f 0, no s our ce is used. If a positive number less than 1000, power f r om the general table wi th this number is used as the source. If 1000 th r o u r gn 1002, the source is taken 3 from the reactor k ine tic s calculation; 1000 s peci f i es tota l i reactor power, 1001 specifies fission product decay powers and 1002 specifies fiss ion power. I f 2 001 though 2999, the source is tn e contr ol variable unose number is this quantity minus H 2000. ; d2(R) INTERNAL SOURCE MULTIPLIER. d3(R) JIREC T HEATING FOR LE FT BOUNDARY VOL UME. W4(R) DIREC T HEATING FOR RIGHT BOUNDARY VOLUME. c5(I) HEAT STRUCTURE NUMBER. 12.11 Car d s _ l CC C EaQ1:1CCCG R22t_ A d ditin n al_ L a f1_a nu n d atr _C a tai Thes e caras ar e required whenever any of the left boundary conditions use heat transf er package 1. The c ar d format is sequential f or mats five words par sets describing NH heat s tr ucture s. l Appendix A 47 h 126 l 1
.: .s RELAP5 Input Data Requirements ( . 08/07/81 j l
-W1(I) CHF AND HE AT TR ANSFER C ORREL A TION FL AGS. Enter zero.
W2(R) HYDR AULIC DI AMETER (m, ft). If zero, hydraulic di amet er from Doundary volume is used. If the heat structure does not represent the pipe walls, the default probably s hou ld not be t ak en . w3(R) HEATED EQUIVALENT DIAMETER tu, ft). If zero, hy dr aul i c diameter is used. w4(R) CHANNEL LtNGTH (m, ft). W5(I) HEAT STRUCTURE NUMBER. 12.12 C at s s _1 C; CE2Ql-lCCL2222A.A d di t12041. B in D 1. & 2 W adat r_C EI11 These cards are the s ame as Cards 1CCCG801-1CCCG899 but for the r iant cound ar y. . 13.0 CAEQ1 ZEldddhht.dEAI_1IELCluRE_IdE&d&L_EEQEEEL1_QAIA These car as ar e used only in NEW problems. These cards are r eqsi reo i f Caras 1CCCGXNN, Heat S tr uctur e Input Cards are ent er ed. These data if present are processed and stored even if no Cards ICCCGXNN ar e ente red. The subt,ield MMM is the composition number and the c ar ds with tnis subfield describe the tneraal pr oper ti e s of composition MMM. The composition number entereo on C ar ds l 1CCCG201-1CCCG299 correspond to this subtleid. A set o f C ar ds 201MMMNN sust ce entered for each composition number used, but MMM need not be consecutive. 13 1 CARD 201MMM00, COMPOSITION TYPE AND DATA FORMAT This card is requireo. wl(A) M ATE RI AL TY PE. Ther ma l proper ties f or five materi als ar e stored within the pr og r am s al us i n um (AL), car bo n steel (C-STEEL), stainless steel (S-STEEL), uranium dioxide (UO2), ano zirconium (ZR). Thes e proper ties are sel ected by enter ing the name in p ar en t hes es in this woro. If a user supplied table or function is to be used, enter TBL/FCTN in this word. At present, the data is primarily to demonstr ate capabili ty. The user should , , Appendlx A 48 127
i I I RELAP5 Input Data Requir ements 08/07/d1 chec< whetner the cata is satisfactory. Tne next to woros are requirec only if IbL /FC TN was j entered in kl. c2(I) THERMAL C GNDUC TIVIT Y FURMA T FL AG. Enter 1 it a table containing t emper atur e and thermal conductivity as to be entereo; enter 2 , af functions are to be entereo. J e3(I) VGLUMcTRIC HEAT CAPACITY FLAG. Enter 1 if a table containing temperature and vol umetric neat cap aci t y is to be entered; enter
-1 if a taole containing oniy volumetric neat capacities are to be entered ano the temperature values are i de n ti c a l to the ther ea l conductivity table; enter 2 if functions are to be entereo. 3 13.2 CARDS 201MMM01-201MMM49, THERMAL LON00CTIVITY DATA l Inese cards ar e r equired if .1 of Card 201MMM00 cantainea fBL/FCTN. Tne car o nu toer s need no t be consecutive.
13.2.1 11Q13.E2t331 If only one word is enter ed, tnat wor d conta ins the thermal condJctivty which is assumed constant. Otherwise pasrs of numbers are entered. The nusoer of pair s is limi ted to 100. The temperatures must De in increasing order. The end poi n t temperatures must bracket tne expected temperatures during the transient. el(R) TEMPERATURE (K, degF). d2(R) THERMAL CONDUCTIVITY ( wa t t/ m-K, Stu/sec-ft-degF). 13 2 2 Eunstianal_Entsat In the functional forsat, sets of nine quantities are entereo, each set containing one function and its range of application. The function is k = A0 + al*TX + A2*TX**2 + A3*TX**3 + A4*TX**4 + A5
- T x ** (-1 ) where TX = T-C and T i s the temperature argument. E ach f unction has a lower and upp er limit of a ppl ica tion. The first function entered must be for the l owe s t temperature range. The lower ll sit af a following f unct ion aust equal the upper bound of tne previous f un ct i on.
Appendix A 49 128
RELAP) inpu t D ata hequir ements t.
/\ 08/07/81
- N)
L Wl(R) LOWit Llili TE1P ER ATUR E (K, cegF). W2(R) JPPER LIMIT TEMPERATURE- (K,'cegF). W3(R) AO (watt /m-K, B t u/ se c-f t-de g F ) . W4 (R ) A1 (watt /m-K2, B tu/ se c-f t-d e gF2 ). - W5(R) A2 (watt /m-K3, Btu /sec-ft-degf3). W6(R) A3 (watt /m-K4, Bt u / s ec-f t-ce gF 4) . W 71 R ) A4 (Natt/m-KS, S t u / s ec-f t-de gF S) . W8(R) A5 (watt /s, Stu/sec-ft). W9(R) C (K, ce gf ). 13.3 C ARDS 201 MM M51-201 M MM99, VOLUMETRIC HE AT C AP AC ITY DATA These caros are requireo if W1 of Car d 210MMM00 contains TBL/FCTN. The cara numoer s need not be consecutive. O V 13.3 1 Iagig_Entmal If only one war a is enter e d, that word contains the volumetric' heat capacity which is assumed constant. Pairs of temperatures and volunietric heat capacities are entered if- the temperatures ar e offferent from the tneraal conductivity table or functions wer e usec for the re al conductivity. If the tempe r a tur e values are, identical, only the volumetric heat capacities need be entered. The nunper of pairs or single entries is limited to 100. The t emper at ur es must be in i ncr e as i ng orcer. The end point temperatures must bracket the expected temperatures during the tr ansi ent. dl(R) TEMPERATURE (K, cegF). If only volumetric heat capaci ties are bei ng entereo, this word is not entered. W2(R) VOLUMETRIC HEAT CAPACITY (J/m3-K, Stu/ft3-degF) 13.3.2 EMDE11 Raat.Entaat in the functional format, sets of nine quantities are [' Appendix A 50 129
i l RELAP5 Input Cata kequirenents 06/07/81 enterec, each set c on ta i n i n g one function and its range of app l i ca t i on . The function is e = + 40 Al*TX + A2*TX**2 + A 3* T X ** 3 + A4*TX**4 + AS*TK**(-1) where TX = T-C and T is the temperature argument. Each function has a lower and upper limit ; of application. The first f ul: ti on eitered sust be for the i l owe s t temperature range. The lower limit of a following ' function must equ al the upper couna of the previous function. Ultd) LDmc4 LIMIT TEMPERATURE ( K, degF). 02(R) JPPI4 LIMIT TEMPERATURE (<, cegF). d3(R) AO (J/m3-K, Btu /ft3-cegF). d4(R) A1 (J/m3-K2, Btu /ft3-degF2). d5(R) A2 (J/m3-K3, Btu /ft3-cegF3). aD(R) A3 ( J/ m3- A4, S tu/ f t3-de gF 4 ). d7(R) A4 (J/m3-45, Stu/ft3-degF5). ad(R) A5 (J/m3, 6tu/ft3). d9(R) C (<, degF). ' 14.0 Cadkl ZQEIIIbut.GEUEBAL IAhtE.2 AIL 1 i inese carcs are used only in NEW t yp e pr ob le ms. These { caras ar e r equirec if any input references general tables. TTT 4 as the taole numoer, and taole r ef erences such a s f o r p o we r , neat transfer coefficients, or temper atur es refer to tn i s nusoer. Data must De entered for each table that is referencea, out TTT need not De consecutive. Tables entered but not r ef er enced are stored ano tni s is not considered an error. 14.1 CARD 232TTT00, TAbtE TYPE AND MULTIPLIER DATA 'd l ( A ) TABLE TYPE. Enter POWER for power vs. time; enter HTRNRATE for neat tr ans f er rate vs. ti me ; enter HTC-I for heat tr ans f er j coefficient vs. time; enter HT;-TEMP 'for heat transfer coefficient vs. t e mp er a tu r e ; enter TEMP for t emper atur e vs. tiie; enter REAC-T for reactivity vs. time; ent er NORMAREA for lor sali zea ar ea vs. normalized length. Tne following two, threes or four wo r ds are optional and allod trips anc factors or unit changes to be applied to the Appendix A 51 f 130
I l I l
,_s REL APs ' Input Data Requirements l \ 08/07/81 L) table entr ies. If the factorseare omitted, the data are usec as entered. One multiplier is used f or times power, heat tr ansf er rates heat transfer coefficient, normalized length, and normalizeo area; a multiplier ano addstive constant are used for tempe a tur e as T = M*TX + :s where M is the multiplier, C is the addi ti v e constant, anc TX is the temperature entered. The first one or twa factors apply to the argument v ari abl es time or tesser atJr e; one factor is applied if the ar gument is time, two f actors ar e us ec if the ar gument is temperature.- The remaining one or two factors are used for the function, two f actors ceing useo if temperature is the function.
d2(1) TABLE TRIP NUMBER. This number is optional unless factors are ent er ed. If missing or zeros no trip is used and the time ar gum en t is the savancement time. If nonzer or the numbe r i s the trip number and the time argument is -1 0 if the trip is false ano the advancement time sinus the trip time if the trip is true. This fielo may De omitted if no f actors are entered. This nunoer must be zero or blann f or tables that are not a function of time.
'w3 w5(R) FACTORS. As describec abover enter factors such that when appli ed to toe table values enterede the r e s ul t ant values have the appropriate units. For the NORMAREA tables the resultant values for both the normalizec lengtn and area must be greater y than or equal to zero anc less than or equal to 1 0.
14.2 CARDS 202TTT01-202TTT99s GENERAL T ABLE DATA The card number s need not be consecutive. The units given are the uni ts reaci red a f t er the factors on Card 202TTT00 have been appliea. Pairs of numbers are entereo; the limi t on the number of pairs is 200. Wl(R) ARGUMLNT VALUE (sec if time; (, degF if t emp er a tur e ; dimensionless if normalized length). d2(R) FUN CT IGN VALUE (watte Mw if power; K, degF i f t emper atur ep watt /m2, 8tu/sec-ft2 i f he at tr ansf er rate; watt /m2-K, Btu /sec-ft2-oegF if heat tr ansf er coef fi ci ent; collars i f r eactivity; dimensioiless if nor ma l ize d area). 15.0 CAEQ1.30Q00000-30922222t.1EACE_lSDEEENQESI EE& CIDE.ElHEILES These cards are r equi r ed only if a space independent (point) reactor k i n e t i cs calculation is desired. These car ds () Ap p e r.d i x A 52 131
l RELAPb Input Data Requirements 08/07/81 aay se en t er ed in a new proolem or any restart. If no reactor ninetics as present in a re start proolem, it will be added; if r eact or minetics is alreacy present, it is celeted anc replaced ; oy tne new data. A c ompl e te set of reactor kinetics data must ' always be ent er eo. Initial conditions are computea the same for new or restart proolems; tne ini ti al concitions can be obtainea from as s J mi n g infinite operating time at the i np: t power or from an input power history. 13.1 CARO 30000000, RE ACTOR KINETICS TYPE CARD d1(A) TYPE. Enter POINT for the only r eactor ninetics option now availaole. enter DELE TE in a restart problem if reactor Minetics is to be deletec. No other cata is neeceo if reactor ninetics is being deletc3. L5 2 CARD 30000001, RE AC TOR KINETICS INFORMATION CARD d1(A) FIS$ 10N PRODUC T DEC AY TYPE. Enter NO-GAMM4 for no fission procact aecay calculations, GAMMA for stancard fission product decay calculations, or GAMMA-AC for fi ssion product decay plus act i n i ce decay c a l c u l a t i on s. d2(R) TOTAL REACTOR POWER (WATTS). Sum of fission power and fission product and actinide dec ay power. a3(R) INI TI AL RE AC TIVITY (DOLLARS). Must ce less tnan or equal to zero. u4(R) DELAYED NEUTRON FRACTION OVER NEUTRJN GENERATION TIME. (sec-1) e5(R) FISSION PRODUCT YIELD FACTOR. This usually is 1.0 for best e sti m ate pr oDi ems, 1.2 for conservative mode p r o .b l e m s . The factor, 1.0, is assumeo if tnis word is not en t er e c. d6(R) ACTI110E YIELD FACTOR. This usually is tne ratio of U-238 atoms cons J eec per U-235 atoms fissioned. The factor, 'I . 0, is assumed i f this war a is not entered. 15.3 CARD 5 30000101-30000199, DEL AYED NEJTRON CONST ANTS if tnese caros ar e mi ssi n g, constants for the six g ene r al l y accep ted de & ayeo neutron groups ar e supplied. Otherwise, two numbers f:r each decay group ar e entered, one or more p airs per card. Cara numbers neeo not De consecutive. Ihe number of p air s 01 thes e car ds define the nusoer of decay groups. Up to J Ap p en ci x A 53 m3
RELAPS Input Data Requirenants (~'g 08/07/81 (s/ . 20 delay gr osps may be entered. Wl(Ri OELAYEJ NEUTRON PRECUR50k YIELD RATIO. W2tR) 'O EL AY EG NhuTRON DECAY C ONS T A N T (sec-1). 15.4 CARDS 30000201-30000299, FISSION PRODUCT OtCAY CONSTANTS These cards are not needed if W1 of Caro 30000001 is NO-GAMMA. If tnis word is GAMMA or GAMMA-AC, data from these cards or default data are used to define fission product decay. If j the cards are missing, data for eleven fission product decay I group s ar e supp li ed. Op to 30 fission product j groups may be entereJ. Data are entered on cards similar ly to Caras 30000101-30000179. Tae f actor in w5 of Card 30000001 is applied to th e yield fractions. W1(R) FISSION PRODUCT YIELD FRACTION. W2(R) FISSION PRODUCT DECAY C0hSTANT (sec-1).
. 15 5 CARDS 30000301-30000399, ACTINIDE GECAY CONSTANTS iness caros are not needed unless W1 of Caro 30000001 is GAMMA-AC. If GAMMA-AC is entered, data from these cards or def ault cat a is used to cefine actinice cecay. If the cards are missing, data f or two groups ar e supplied. Up to 50 actinice groups say be entered. Data are entered similarly to Cards 30000101-30000199. The factor in W6 of Caro 30000001 is applied l to the yield fractions.
l W1(R) YIcLD FR AC TION. W2(Ri DECAY CONSTANT (sec-1). 15.6 CAR)5 30000401-30000499, PREVIOUS POWER HISTORY DATA If these cards are not present, initial conoitions for fission product and act ini de gr oups are for steady state oper a ti on at the power given in WE of Card 30000001 This is equivalent to oper ation at tnat power for an infinite ti m e. If these cards gr e pr esent, the power history consisting of power and time duration is useo to determine the fission product and actinide initial conditions. The power from gamma and actinide Appendix A 54 133
l l RELAP5 Input Data requirements 08/07/61 occay is assumed zero at tne ceginning of the first time dur a t i on. Data are entered i n thr ee wor o se ts, one or more sets per caro. Card number: neco not ce consecutive.
#1(R) REA; TOR POWEA (watts). This quantity is total reactor power, that is the sum of fission power and decay power and must ce greater than or equ a l to zer o. If a decay power obtained from the power nistory exceeds this quan ti ty, tne fission power is issuned zero.
a2(4) T11E DJRATION. Units ar e as gi ven in ne xt word. This quantity must ce gr eater than or equal to zero. 43(R) TIMc DJRATION UNITh. Must ce SEC, MIN, HR, DAYS, or kK. 15.7 CAR)5 30000011-30000020, REACTIVITY ldRVE NUMBERS Re ac ti vi ty (or scram) curve numDers from the general t abl es (Carcs 202nnnxx) to define reactivity due to rod motion are defined on these car ds. These cards are not used if there are no r eferences to reactivity curves. Curves referenced must be defineo in the gen er al tables. No error is indicated if reactivity curves ar e defi ned but not referenced on this c ar d, out memor y sp ace i s wasted. Curve numbers, which are the NNN of the general t abl e car d number, are entereo one or more per car d. Care numbers need not ce :ensecutive. ultI) REACTIVITY CUkVE NUMBER FROM GENERAL TABL6. Up to 20 numcers m ay be entered. 15.8 CARDS 30300501-30000599, DENSITY REACTIVITY TABLE One or more pairs of numbers are entereo to define densi ty reactivity as a f unc tion of normalized water censity. This table is required oniy i f Car ds 30003701-30300799 are entered. Data are enterec one or more pairs per card and card nuaters neen not ce consecutive. Up to 100 pairs may oe entered. d1(4) NORhALIZd o w ATER DENS IT Y. u2(4) 4c AC T I/IT Y (dollars). Appendix A 55 134 1
l l { WELAPb Input Data Requirements 1 08/07/81 l [G} 15.9 CARDS 30300601-30000699, DOPPLER REACTIVITf TABLE One or more r. airs of nummers are entered to define DoPpl er rea:tivity as & function of vol ume averaged fuel t emp er atur e, This table is required only if cards 30000801-30000899 are entered. Data are enter ed one or more pairs per. card and car d numbers neeo not be cons e cu t i ve. Up to 100 pairs may be entered. d1(R) TEMPE R ATURE 8K or degF). w2(R) REA;TIVITY (collars). 15.10 CARJS 30000701-30000799, VOLUME WEIG4 TING FACTORS Each card contains the input for reactivity feedback due to conditions in one or more hydrodynamic volumes. Words 1 .and 2 are a volume number and an increment. Words 3 an d 4 ar e the reactivity dat a f or the volume defined by Word 1, Woros 5 ano 6 are tne r eactivity oa ta for the volume defined by Word 1 plus dor a 2, doras 7 ano 8 contai n data for the volume defined by
,s doro 1 plus two times Word 2, etc. Each card must contai n at I least four worcs. Volumes must be defined by hydrodynamic component cat a car ds and any voluta reactivity data must be defined only once on these cards. Car d numbers neec not be consecutive.
d1(I) HYDRODYNAMIC VOLUME NUMBER. W2ill IN;4EMENT. W3(R) WEIGHTING F ACTOR FOR DENSITY FEEDSAC<. d4(R) DATER TEMPERATURE COEFFICIENT ( do l l ar s / K, dollars /degF). 15.11 CARDS 30000801-30000899, HEAT STRUCTURE WEIGHTING FACTOR Each car a cont ains the input f or reactivi ty feedback due to conoi ti ons in one or more nea t structures representing fueled Porti ons of the reactor. Data is entered in a manner slall ar to Cards 30300701-30000799. For each neat structure specified si these cards, input in the heat s tructur e data C arcs ICCCG2XX, must define the fueled region as the space over which the volume aver age temperature is computed.
/ Appendix A '56
( 135
AELAPS 19put Dat a Requir ements 08/07/81 Usually either Wora 3 or 4 is zero.
ul(I) HEAF STRUCTURE NUMcER.
c2(I) INCREMENT.
d3(R) d E I54 T I NG FACTGR FOR DOPPLER FEEDBACK.
d4(R) FUEL TEMPERATURE COEFFICIENT (dollars /K, collars /degF).
16.0 CAEQ1 ZD309999-ZD12222St ELQL BE92 Ell _1SEWI Q&IA The plot input data permits extensive user control over the plots and graphs suitable for report use can be generatea.
However if time plots of selectec quan ti tie s using default options are Gesireds only the caras descrioed in 16.5.1 need be entered. The RELAP5/M000 Plot pacsage can be accessec if the woro GLDPLOTS is snpet on Caro 20330000. Further input for the 3000 pacxage is aes cr ibed in Appendix 3. If the M000 Plot pacnage is accessed none of tne 23300000-20399999 or 204MMMLL cards can De input or an error will result.
16.1 CARD 203000KK, 2D PLOT GENERAL HEADING AND S PECIFIC ATIONS G, These cards are optional and may De input to define the gener a l 20 Plot Headings plot options and plot size specifications if the user desires to specify these parameters.
The number Jroup KK des i gn at es either data group or chrd sequence numoers as notec in the following.
16.2 CARDS 20300000-20300009s GENExAL 2D PLOT HEADER CARDS Each car d defines a line of tne general heacing for the 20 plots. This general heaoing will De written at the top of eacn plot. JP to three lines of neading may by inputs in which case eacn line of the heading will De wrstten at the top of the 20 Plots in tne ascencing order of the card sequence number < Input Data Requir ements 08/07/81 is entered. Howevers if tne card is omitted the independent var i aDi e code defaults to TIME. fne independent variable or variaoles to be plotted are definea oy the combination of the i ndep enden t v ar i ab l e code and eacn p ar amet er term input on its cor r esponai sig plot r e que s t caros (cards 203NNN00-09). The r es s i ti ng plot will then De compos ed of a set of curves with each curve defined by tne dependent var i so l e code-perameter versus the i nce pe nd en t v ar i ab l e cod e-p ar ame ter .
16.5.3 C a t s s _ Z Q a d d haq:12_ Elg1_C21En t i& Q Q _ Q al a _I a D i t _ E ti t Lina t
)
These caras define the table number f or plo t comparison input data to oe plottea on the same gr aph as RELAP5 results for visual comparison. Up to 10 taole numbers can be input. Each taDie nusber en t er ed is cefined by the 204MMM00 card. where the nusber MMM0J is the plot comparison data t able numcer. Each number enttred must refer to a plot comparison data taDie that nas been input or an error will result. 16.5.4 Catus_2Qludd3Q:222_Eini Iltic_and Atas Ilties
/
These three cards are optional and input tne plot title and the x and the y axes ti tles r especti vely. The format for each h of the te tie cards i s identical to that for the header cards (Cards 23300000-09). Any or all of tne cards may be omitted. However wnen input the car d sequence nuaDer KK des i gnat es the type of ti tl e ent er ed. The plot ti tl e is input on 203NNN20 cara and is written on the pl ot as the last line o f the header. If the plot ti t le car d is omi tted it def aul ts to a b l ank char act er s tr i n g and is ignored. The x-axas title is input on the 203NNN21 car o ano wr i tten on the plot en parallel with the encependent v ar i ab l e axis (x-axis). If the x-axis title card is omittea it defaults to tne inaependen t v ari aol e code, parameter and units encodea togetner. The y-axis title is input on the 203NNN22 card ano is written on the plot in parallel with the dependent variable axi s ( y-axi s ). If the y-axis title card is omi t t ed it defaults to the cependent variaole code, parameter and uni ts encodea together. I 13 5.5 catas_zQauassQ:ilt_to_Eint_ axes _sassittaa11aos Tnese caros input the specifications for dr awing the 20 i plot andepenoent and dependent variable axes respectively. The c ar ds ar e optional and may be omitted in wnien case cefaults are j set dhicn will pr oduce optimal and attractive axes. Appencix A 61 i 140 - - - - - - _ _ _ _ _ _ _ _ - - _ _ _- l
rw R EL APS Input Data Requirements
- ) 08/07/81 x,j None of the input terms will absolutely define an axes specification except the keyword LIN E AR unless the following plot design criteria are satisfied. The plot axes are designed with respect to RELAPS computational results. In order to achieve maximum visual effect the phtted curve of R EL AP5 results must span as much of the independent variable axis as possible and the dependent variable axis must span all of the data plotted. The axes must also be subdivided into intervals rounded to the first significant figure for simple labeling.
The terms input by each card are described as follows. 16.5.5.1 C A R D 203N N N40,IN DEPE N DE N T V ARIABLE A XIS SPE CIFIC ATIO N This card inputs the independent variable axis (x-axis) specification. The card is optional and may be omitted. Up to five words of data may be input in the following form at. Wl(R) SPE CIFIE D X-A XIS MINIM U M. (X MIN SP). Def aults to -1.0E+99 so that the minimum R EL AP5 results will be selected. W 2(R) SPE CIFIE D X-A XIS M A XIM U M (X M A XSP). Defaults to +1.0E+99. So that the maximum R EL AP5 result will be selected. W 4(I) SPECIFIE D N UM BER OF G RID SUBIN TERV ALS (IX GRID). IX GRID is the (-] number of grid subintervals per labelled interval. IX GRID is ignored if (' '/ N 0 G RID is specified in the plot options. If IX GRID is omitted it defaults to 1 if a grid is specified in the plot options. W5(A) X-A XIS T Y PE K E Y W 0R DS LIN E AR 0R LOG. Defaults to Linear. The L O G option has temporarily been disabled. X MINSP specifies the independent variable minimum only if it is greater than or equal to the actual minimum of the data. If X MINSP is less than the data minimum it is ignored. Similarly X M A XSP specifies the independent variable maximum only if it is,less than or equal to the actual maximum of the data. IF X M A XSP is greater than the data maximum it is ignored. If X MIN SP and X M A XSP satisfy these conditions then the curve will be plotted beginning at X MINSP and ending at X M AXSP. H ow ever, the axis extremities must still be adjusted to the N DIV X and IX GRID specification. The terms N DIVX and IX G RID specify the number of subintervals into which the axis is divided. The design criteria specify that these subintervals must be rounded to the first significant digit and that the axis must be spanned by as Appendix A 62
,.,_s y
141
l R EL A PS Input Data Requirements 08/07/81 much of the data as possible. Therefore the axis extremities not only m ay be expanded but the number of labeled intervals specified by N DIV X may be reduced or increased to give an optimum axis. The axis type keywords LIN E AR or L0 G specify that the axis is to be drawn as a linearly scaled or as a logarithmic (base 10) scaled axis respectively. If the keyword is omitted the default is to LIN E A R. If the keyword LOG has' been specified and during the course of processing a plot data point is found to be zero an error message will be printed, the axis type will be reset to LIN E A R and the plot will be completed. 16.5.5.2 C A R 0 203 N N N 41, D E PE N D E N T V A RI AB L E A XIS SP E CIFIC A T10 N This card inputs the dependent variable axis (y-axis) specification. The card is optional and may be omitted. Up to five words of data may be input in the following form at. W1(R) SPE CIFIE D Y-A XIS MINIM U M, (Y MI N S P). .0E+99 so that the minimum R EL AP5 result will be selected)(Defaults to W 2(R) SP E CIFIE D Y-A XIS M A XIM U M. (Y M A XSP). (Defaults t .0E+99 so that the maximum R EL A P5 result will be selected). W 3(I) SPE CIFIE D N U M B ER OF Y- A XIS IN TER V ALS. (N DIV Y). (Def aults to S). W 4(I) SPECIFIED N U M BER OF GRID SUBIN TER V ALS (IY GRID) IY GRID is the number of grid subintervals per labelled interval. IY GRID is ignored if N 0 G RID is specified in the plot options. If IY G RID is omitted and a grid is specified in the plot options then IY G RID defaults to 1.
. W5(A) Y-A XIS T Y PE K E Y W O R DS, LIN E AR O R LO G. Defaults to LIN E A R.. The LO G option has temporarily been disabled.
The rules that apply to the use of the dependent variable axis' specifications are the same as those for the independent variable axis except for the terms Y MINSP and Y M A XSP. To achieve the plot design criteria all of the dependent variable data plotted must be included within the y-axis extremities. Therefore Y MIN SP specifies the dependent variable minimum only if it is less than or eoual to the actual minimum of the data within the interval X MIN SP, X M A XSP. If Y MINSP is greater than the data minimum it is ignored. Similarly, Y M A XSP specifies the dependent variable maximum only if it is greater than or equal to the actual m aximum of the data within the interval X MINSP, X M A XSP. If Y M A XSP is less than the data m aximum it is ignored. Appendix A 63 l 9l 142 j
i 1 i RELAPD Input-Data Requirements . i 06/07/81 16 5.6 Caca.ZQaddd2Q-12a.Gutzg_Qtaming.11 21f1S411201 Tnese cards input the . speci fi cations for dr awing e achL c ur ve r eq J es t ed =in- a pl ot' request (C ar ds 203NNN00-09) . The saquence number of the card refers to . the seqJence number of.'the Jplot ; request for which the curve drawing specification is input. 'For' ! examples'203NNN50 refers to the first plot requests' 203NNN53 ! ref er s to -the f our th plot requests etc. If a curve drawing s pec i fi cati on . r ef er s to an undef ined pl o t request -an err or will result. Any or all o f the car ds may be omi tted in which case appropr ia te def aul ts will be selecteo. The data entered on the: caros specify a curve legeno label, the type of line drawn f or the cur ver the type of symDol drahn for,the curves =the. number 1of: data points skipped between symbols and a 5PLINE option which will draw a smoothed curve using- a- spline Interpolation technique. .If on ly' one cur ve is to De dr awn the legend -label' is i gnor ed and no legend is written on tne plot. The data is, input in the following format.
'wl-W2(A) L63END LA8EL. Defines the legend label and Is composed of two alpnanJeer ic worcs enclose d D y quotation symbols (defaults to t he -variaDie coce,- parameter words . described for. the plot reque st Ca rds 203NNN00-09). If the legend' lapel is ent er e d it.
must be composed of sufficient characters'for 2 words. O W3(A) CURVE LINE following. TYPE KEYWORD. Must be entered as one of the 10LINE No line will De dr awn connecting the data points. This automatically requires that a plot symbol is to be drawn at each data point. To define the plot symbol refer to word W4. L I Nd A continuous line will De drawn connecting the data points. 00T3 A dotted line will be drawn connecting the points. DASMES A dashed ilne will be dr awn connecting the points.
- DOTS A chain dotted line will be drawn connecting' the points. (The chain pattern is composed of a long dash followed by a space, a dot and a space) l CDASHES A chain dashed line will be drawn connecting' the points. (The pattern is composed of a long das h followed by a spaces a short dash and a space) ;
W4(I) SYMBOL INDEX. Defines the plot symDol to De drawn at intervals of a specified nuncer of' data points. If W6 is omitted or input as 3 a symbol will not be drawn. However, if the line type neyword input for word w3 is NOLINE a default symbol will be selected. Tne symbol inoex is checked for each curve to De drawn. If a redundant symDol has been input an error message will De printed and the input symbol will be r eset to the ne x t Appendix A 64 143
i AELAP5 Input Data Requirements ! 08/07/81 ava il ao le symDol. j i d > (I )- NUM3Ex 0F DATA POINT INTERVALS. Defines the num0er of data j point intervals between plot symbols. The plot symbol cerineo j sy word d4 *ill be drawn at intervals of WD cata points. If e5 { is onitted it will default to 5. However, if the line type ' Keywofo input for worc W3 is NOLINE then h5 is set to 1 uncon ci t s on al l y. Ub(Al SPLINE INTERPOLATION KEYWGAD. Tne Keyworos wnich may be enter ea are SPLANE and NOSPLINE. If W6 is omitted it will cefault to NOSPLINE and the curve will De dr awn wi th straight line segetents connecting each cata point. If 46 is entered as the keyaoro SPLINE the curve will De drawn as a smooth continuous curve oy means of spline interpolation between data points. If d6 is enter eo as any woro other than SPLINE or NJSPLINE an error will result. _ 10.U.7 Cat 21.ZQldMhh2-22_Ela1.DE110Q_dDAQatis,. Tnese car as oefine changes to any or all of the general plot options input by caras 20300010-19. These changes will be in efrect for only the NNN00 Plot and the gener al plot options will r emai n in effect for all other plots. The input f orma t f or tnese c ar os is identical to that for tne 20300010-19 cards. 15.o.8 1Acc.2233312Q.ElSt llat Liit011aQ.CDAQ941 Tnis card defines changes to tne general plot si ze dimenssons input by card 20300020. Tne enanges will be in effect only for the NNN00 Plot anc tne general plot size cimensions will remain in effect for all other plots. The input f or ma t for tnis car d is identical to that for the 20300020 car o. 16 6 CARDS 204MMMLL 20 PLOT COMPARISON DATA TABLIS ines e car os i n pu t taoles of data whicn ar e to be plotted on the same gr aphs as RELAPS results for visual comparison. Eacn set of car ds define th e table dependent and independent v ar e a bl es anc the format by which the data are input. The plot curve speci f ica tions f or e acn table ar e also defined. Appendix A $5 144 I
r_ . i
; dELAPs input Data Requirements 08/07/01 j)% \~ >
1661 C ALQ.2Qid55Qd.lQ.2121.CRER AL1100.Q &la.11 alt.d t 2W R11s.. Tnis caro inputs the varisole code naming the 2D plot 3 consarison dat a table dependent v ar i aDi es its corresponding i units Keyword ano the two keywords defining the tsble data input format. Tne card is required in order to define a 20 Plot 1 i comparison data table. If the car d is omitted an o t ani e sp eci fi ca t i ons or data is entered an error will result. The data input Dy the card is entered i n the f ollowing format. W1(Al TAdLE OEPENDENT VARIABLE CODE (YNAME) YNAME is requireo and may not De omittsc. The variacie code is definea similarly to that for c ar ds 300-399 ano 203NNN00-09. Tne variaDie code YNAME for a 20 Plot comparison cata table must ce identical to the var iable code PARNAM for a 2D plot request ref erencing the table or an error will result. W2tA) DEPENDENT VARIABLE UNI TS (EYWQ40. RELAPS calcu lati ons are preformed in SI units throughout the code. Therefore 20 Plot comp ari son data must be converteo upon input to SI units for use oy the coce even though th e uni ts in whi ch a plot is to be made may not De SI units. The unsts keyworos allowed are descriced as f o llows. If omitted, the default is $1. 51 (Default) The depencent variaale data is input in 73 SI units. 4
)
' BRITISH The dependent variaole data is input in British units. The coce will automatically correct the input to SI units for storage.
SPECIAL The dependent v ar i aD ie data is input in special units. For this card the coefficient for a units equation mus t De input on C ar ds 234MMM01-08 or an error will re sul t. a3( A) TABLE FORM AT S PECIF IC A TION KEYh0RD. Enter one of the two table f or ma t spec if ic a tion keydords PAIRS or SETS. If PAIRS is enter ed the table cata must De input as pairs of independent-depencent variables or (vice versa). If SETS is entered the t abl e dat a must be input in comple te sets of independent and then dependent variables (or vice ver s a ) . Refer to the 204NNN20-99 caros for addi ti onal explanation. If k3 is omitted it cefaults to PAlds. w(A) TA8LE FORMAT SPECIFICATION KEYWORD. Enter one of the two t ab l e f or ma t specification k eywor ds INDEPFIRST or DEPFIRST. If INDEPFIRST is entered the taole cata must be input with the independent v ar i able occur ing first. If DEPFIRST is entered the taDie data must be input wi th the dependent variable occuring f ir st. Refer to the 204NNN20-99 cards for additional explanation. If W4 is omitted it defaults to INDEPFIRST.
/h Ap p en di x A 66 V
145 } l
i dELAPD Input Data Requirements 08/07/81 lb.b.! Catag.E2hdddQl-Qh.lt21Da101.4101Aalt.4Qiti.EQQ11t11SQ These caras are required i f SPECI AL is entered as W2 on car d 2041NN00. Each card inputs a uni ts conversion coe f fi cient a(k) wnere the coefficient index k is implied by the card number 2041NN0K, where K can De equal to or between 1 and 8. The unsts conversion equation iss Y(51) = a(8)*Ca(1) + Y*Ca(2) + Y*Ca(3) + Y*a(4)33 + a(2)*Y*a(6) + a( 7)
- AL OG( Y )]
Any of the car ds may be omitted in wnich case the omitted coef ficient will cefault. However, at least one card must be snput or an error will result. The coe f fi ci ents default to the followitg values. a(1) =0 0 a(2)=1.0 a(3) tnrough a(5)=0.0 a(6)=1.0 a(7)=0.0 a(8)=1 0 Any value may be entered for a c oef f ic ient providing the following conditions are s atisi f ed. At least one of the coefficients a(1) through a(5) or a(7) must be nonzero. A(6) may not De entered as zero. Y may not ce entered as zero if a( 7) is nonzero. A (6 ) may not De entered as zero. If any of 1 tnese conditions is not satisfied an error will result. 16.6.3 CAC2.lQiddB10_I2 bit inutREQacQ1.1LLIAalt { l i .. i s cara inputs tne variable code naming the 20 Plot comparison data taDie independent v ari able and its corresponding ] tacle units keyword. The card may be omitted in which case the j v ar i abl e co de will default to TIME and the units keyword will I cerauit to SI. The fo ri at for the data must be entered as l follows.
)
l 01(A) VARI ABLE CODE FOR THE TAdLE INDEPENDENT VARIABLE. (XNAME). ) XNAME is the vari abl e coce for the taole independent v ar i abl e. The variaole code is definea similarly to tn a t for Cards 300-399 and 203NNN10. The v ar i able coce XNAME must ce icentical to the variable code XARNAM for a 20 Plot request r ef erencing the table or an error will result. (XNAME defaults to the var iable code j f1ME). , I d2( A) TABLE INDEPENDENT VARIABLE UNITS (EYsORD. E nt er a units keyword uefining tne units of the taole independent variable input cata. The 5 eywor cs ano the rules for entering them are e xpl a ined s i mi l ar l y to those for word n2 o f C ar o 20 4MMM00. If the keyword Appendix A 67 ei 146
y dELAPS Input Data Requirements 08/07/81 entered i s SPECI AL' then the appr opr iate units coe f fici ent car ds 204MMM11-18 sust be enter ea as described for cards 204MMM01-08. 16 6.4 Caggt.lgk35311:11.lDaaRaDEaQt.taIlakia.dnitt.;kD1aL& lad These caros are required if SPECIAL.is entered-as. word W2 on Cara '204MMM10. Each card inputs a unit conversion coefficient b(k) where the coe f fici ent index is implied- by the car d number 204MMM1Ks wnere K can be equal to or between 1 and
- 6. . The Jnits conversion equation ist X(SI) = b(6)*Cb(1) + X*Cb(2) + X*Cb(3) o X*b(4)33 + b(5)*X*b(6) + b(7)*ALOG(X))
The rules applying to the b and X terms are sisitar to those explained for'the a and Y terms for cards 204MMM01-08. 16.6.o Cata EQiaEE115 data.tutxa.Saas111aatina inis caro is optional and the data entered ar e identical to. that.explasned for the 203NNN40 car d. O Data ins 16e. Cates _ZQiB55ZQ:22.lQ.Elat..lamaatitan..Qata..lakia _Inaut inese cards contain the 2D Plot Comparison data and ar e required if a 204MMM00 card is input. Storage h as been allocated for up to 4000 data points. The same number of independent and dependent variable data points must tHe ent er e d or an error will r esul t. The order of the ' card numbering sequence determines the or der in unich the independent variables are plotted. However, the c ar d s. need not be numberee successively ano need not be input in order as the code will sort thee. If more than one independent v ari able is entered per carde the independent variaDies must be enter ed in the order they are to be plotten. The dependent v ari able data points must ce entered in a one- to-o n e cor r es pondenc e order with the independent varisDie data. If sore than 80 caros are required to input the datas continuation car ds may be used. The f ormat for entering the data on the cards is defined ey wor ds W3 and W4 on the 204hMM00 car d. For example if word W3 is PAIRS and word W4 is INDEPFIAST then the data must be entereo as an independent-dependent variable pair followed by the next independent-dependent v ar i abl e pairs etc. If word W3 is SETS and wora W4 is DEPFIRST then the da ta must be entered as the Appendix A 68 147 1 ___ _a
RELAP5 Input Dat'a Requirements ll entir e set of' dependent vari aDi e cata followea Dy the en ti re set of independent variaDies. If tne numoer of cependent variaDies ent er ed is not e qual to tne numoer of independent variaDies, an error will result. L7.0 tagas_222118da-101HME122t_C0dIdQL_SIsIEd_13EUL_DALA Tnese caras ar e used in New and REST ART problems if a control system is oesired. This input can also be useo to generate additional quantities from tne normally computea quantities ano the additional quantities can De output in major and minor ecits and plots. NNN is the control variable number whoch may have a number from 1 througn 999. C on tr o l variable nuscars neea not be consecutive. 17 1 CARD 205NNN00, CGNTROL COMPONENT TYPE CARD cl(A) ALPHANUMERIC NAME. Ente r a name descriptive of tne component. This name will appear in printec ou tput along with the component number, d2(A) CONT 4UL COMPONENT TYPE. Enter one of the component namess SUM, ' dVLT, JIV, DIFFRENIs DIFF RE NO, IN TEGR AL, FUNCTION, STOFNCIN, TRIPUNIT, TRIPDLAY, P0hERI, POWERR, or POWEdx, or the commana, DELETE. If CELETE is enterec, enter any al ph anum er i c word in word 1 ana zeros i n the r ema ining words. No other cards are needed unen deleting a componen t. W3(R) SCALING FACTOR. W4(R) INITIAL VALUE. dS(I) INITIAL VALUE FLAG. O means no initial cond i ti on c al cul a tion and d4 is used as the initial condi ti on; I means compute initial l conaition. d6(I) LIMITER CONTROL. En ter ze ro or omit this and the following worcs if no limits on the control varisole are to De imposed. Entar 1 if only a sinimum limit is to De snposed, 2 if only a maximum limit is to be imposed, and enter 3 if both minimum and maxinus limits are to be i mposed. u?(R) MINIMUM OR MAXIMUM VALUE. This word is the minezum or maximum valJe if on8 7 one Iimit is to De imposed or is the minimum value if botn li~ are to be imposed. Appendix A $9 148 L
i j 1 lT d6 LAP 5 Input Data Requirements I (m/ 08/07/b1 l l W8(R) MAXIMUM VALUE. Thes word is used if noth Ismits are to be imposed. ) i 17.2 CARDS 205NNN01-205NNN99, CONTROL 00MPONENT 0ATA CARDS The format of these cards depend on the control component type. A1 equation is used to descrioe tne processing by each consonent. The symbol, Y, is the control y ari able def ined Dy the component. The symbol, AN, N = 1, 2, . . ., is a c ons tan t defsned by control component input cata. Var i ab l es, VN, N = 1, 2, . . ., are one of the varisoles listed in the minor eoit inpat description. Be si de s hydr odynami c component data, heat s tr uc t u r e datas reacto r ki neti c dat a, etc., any of the control v ar i a bl es including tne. vari acl e being cefined may be specified. The symbol, 5, is the scale factor on C ar o 205NNN00. 17.2.1 Sys:giftetgDC&_CREESQtD1 inis component is inoicatea oy SUM in wor d 2 of Car c. 20$t4N00. The sum-di f f ere nce c omponen t is defined by j f = S*[A0 + Al*V1 + A2*V2 +. . . J wl(R) CONSTANT AO. W2(R) CONSTANT A1.. d3(A) AlphanJmer i c par t of variable request code for V1. w4(1) Numer ic par t of vari able r equest code for V1. At least four words which define a constant and one product term must be entered. Add i t i on al sets of three words c o r r e sp ondi n g to Words 2-4 can be en ter ed for additional product terms up to twenty pr od uc t te rm s. One or more cards may be useo as desired. Card numbers need not be strictly consecutive. The si gn of AN determines addi tion or subtr action of the product terms. 17.2.2 duttialist_Coussosat This component is indica ted by MJLT in word 2 of Card 205NNN00. The multiplier component is defined by Y= S*Vl*V2* . . . 1 \,/ ( Appendix A 70 149 l
RELAPS Input Data Requirements 08/07/61 ' wl(A) Alphanumeric part of variable request code for V1. W2(A) Integer par t of vari able request code for V1. At least two wor ds defining one factor must be entered. Additional pairs of words can De antered on this or additional c ar os tJ define additional f8Ctors. Card numbers neeC not be stri ct l y consecutive. 17 2.3 Qigids C2ESaDsD1 Tnis component i s indicated by DIV in Word 2 of Caro 20tNNN00. The divide component is defined oy Y= S/V1 or Y = S*V2/V1. Two words on the card indi cate the first form and,four words on the card indi cate tne second f or m. W1(A) A lpnanumer ic part o f v ariable r equest code for V1. W2(A) Integer p ar t o f v ari aDie r equest code for V1. a3(A) Alpnanumeri c part of v ar iable request code for V2. d4(Il Int e g er p ar t of variable request code for V2. 17 2.4 QLLLstsaLLALLaa.Cannsata11 inese componen ts are indi cated by DIFFRENI or DIFFREND in Wor d 2 of Card 2 0 5 NN N3 0. The di f f er entia ting component i s defined of Y = S*DIFF(VI) where DIFF is the total derivitive with respect to time operator. Tnis is ev aluat ed by
=
Y S*L2(V1 - Vlo)/DTJ - Yo (DIFFRENI)
=
Y S*(V1 - Vlo)/DT (DIFFREND) where DT is the time step, and Vlo and Yo are values at the beginning of the time step. The numerical approximations for the 01FFRENI and INTEGRAL components are exact enverses of each otner. Ho w ev er , an exact initial v al ue is required to use the DIFFRENI component and erroncous results are obtained if an exact initial value is not furnished. The DIFFREND component uses a simple difference approximation wnich is less accurate, is not consistent with the integr ati on appr ?xi ma ti ons but does not require an initial v al u e. dince oi f f er enti ation, especially n um e r i c a l differentiations can introduce " noise" into the calculations it Appendix A 71 150
l RELAP5 Input Data Requirements 08 t'0 7 / B l ' sho; .i d be avoided if possiple. When using control components to solve olfferential equations, the equations can be arranged sucn that INTEGRAL components can handle all indicated derevitives except possibly those involving non-control variables. Wl(A) Alphanumer ic par t of variable request' code for V1. d2(1) Integer part of variable request code f or V1. 17.2.5 initatalina_CaRREQ2n1 This component is indicated D) INTEERAL in doro 2 of Card 205NNN00. The integr ating c ompone n t i s defined by Y= S* INT (VII where 11T is the integral with respect to time operator. This is evtluateo Dy Y= Yo + S*( V1 + Vlo)*0T/2 dner e DT is the time step and Yo ana V10 ar e values at the oeginning of the time step. wi(A) Alphanumer ic par t of variable request code f or V1. () W2(I) Integer part of variable request code for V1. 17.2.6 Eunctianal_Casannant This component is indicated by FUNCTIO 1 in Word 2 of Card 205N1N00. The component is defined by Y= S eFUNC TI ON( V1) where FJNCTION is def ined by a general taole. This allows the use of any function which is c' conveniently defined by a table lookJp and inter pola tion procedure. The function component can also be useo to set limiting values. wl(A) Alphanu mer ic par t of variable request code f or V1. 62(1) Integer part of variable request co de f or V1. d3(I) Gener al table number of function. 17.2.7 llandatd_EMDEllEE.ERREADSQL Tnis component is indicated Dy STOFNCTN in Word 2 of Card 20$NNN00. The component is defined by Appendix A 72 151 ;
1 RELAP5 Input Data Requirements 08/07/81 Y= S*FNCTN(VI) l wner e FNCTN is A85 (absolute yclue), SQRT (square root), EXP (e r ai s e d to power), ALOG (natural logaritnm), SIN (sine), CDS (cosine), TAN (tangent), or ATAN (arctangent). dl(A) FNCTN. d2(A) Alpianumeri c part of v ariable request code for VI. 33(I) Integer p ar t of y ar iable r equest code for VI. 17 2.8 JQlt_ILLE_snaESDAD1 This component is indicated by TRIPUNIT i n wor d 2 of Card 205NNN00. The component i s definea by Y= S*UFNCTN(TI) wher e UFNCTN is 0.0 if the trip, 71, is false and is 10 i f the trip is true. el(I) Trip numoer, T1. 17.2.9 1t12.01111 12RE2nA01 ll Tnis component is indicated by fRIPDLAf in word 2 of Card 205NNN00. The component is defined cy Y = S *TR P TIM ( T1) wnere TRPTIM is the time the trip l as t turned true. If the t r .i p is false, the value is a negative nonzero number; if the trip is true, tne value is zero or a positive number. dl(I) Trip numo e r , T1. 17.2.10 Inicast E2 Mat CSEEEQEQ1 This component is indicated by POWERI in Word 2 of Carc 205NNN00. The component is defined oy Y = S*Vl**II. wl(A) Alpaanumeri c p ar t of v ar s sole request code for V1. a2(I) Integer part of v ar i able r equest code for V1. Appenoix A 73 152
ry RELAP5 Input Data kequireaents 08/07/61 W3(1) 11. 17 2 11 daal_Egutt_Cannantal This component is indicated by POWERR in Word 2 of Carc 205NNN00. The component is defined oy y = S*Vl**kl. Wl(A) Alpn anumer i c par t of var iaDie request code for V1. d2(I) Integer par t of variable request code for VI. W3(R) RI. i 17.2.12 Matlabit_E2ktL_CERERQEQ1 This component is indicated by POWERx in Word 2 of Car d 205NNN00. The component is defined oy Y = S*Vl**V2
.'~N Wl(A) Alpnanumeri c par t of variable request code for V1.
W2(I) Integer a ar t of var iable request code for VI. W3(A) Alpn anumer i c p ar t of var iable request code for V2. W4(I) Integer p ar t of variable request code for V2. 18 0 CA821_L221:1212t_11&lE_REEuE11_QAIA inese cards are requi r ed only in STRIP type problems. One or acre caras ar e entered, each card containing one var iable request. Cara numbers need not be consecutive. Variables are ordered on the RSTPLT (strip) file in tne order of i n cr e as i ng car o nJeber s. W1(A) Aspnanumeri c part of var iable request code. W2(1) Int eger p ar t of var iable request code. Appendix A 74 153 I
RELaPS Input Data Re quirenents 08/07/81 19.3 SEL&E2 DEEEAL18E.EEQCEMUEES Op er ati ng procacures have Deen written using CDC Cyber l Control L an gu a ge to simplify tne execution of RELAPS on the ca s o J t er . The following procedures reflect the operating philosopny at INEL. Other install ations iay choose to define comparable procacures. Two series of RELAPS are typically maintained. The first i s er i es, called the RELAP5 series, contains puolically rel e as ed ! v er s i o ns , modified versions of the publically released version j containing only error corrections and no model additions, and i recently developed versions consi der ed sufficiently reli able for 4 production use. The second series is calleo the KELAP5 seri es and contains versions under development. Each series may have one or more cycles. For the RELAP5 series, the higher cycle is } cne more reliable version and lower nusoered c ycl es are r etainea 1 only to permit completi on of parameter studi es that require a l fixed v er si on. Because of the developmental n atur e of the ! XELAP5 series, the higher cycle versions gener ally have more modeling capaDility but are not always more reliable. Production wor k with the XELAPS series should only be done with close contact with the development staff. UPDATE Each cycle has three files
- RELAPSS, OL3PL format; the source RELAP5L, oDject accus in library format; file in O
anc RELAPSX, an absolute Dinary. S ev er a l input data decks are maintained in a fi l e RELA P50. The cycle number of RELAP50 does not maten the other fi l es since tne data are changed infrequently. The XELAPS series has s im il ar f il e s, XEL AP5S, XEL AP'5L, xELAP5X, and XELAP50. inree procedures are proviaed. 3ne produces a copy of the input description. The other two execute RELAP5, one from an absolute oinary, the other after updating, compiling, and loading the pro gr am. The executing procedur es issue a sessage oloc4, stating the availability and status of v ar i ous v er s ions of RELAPS. Before t tl e first use of a procedure, the file containing the orocedures must be attacned by ATTACH 4PROCS,RELAP5PROCS,ID=RJW) nach procedure is called by BEGIN, pr oc,PRGCS,p ar am et er s. where proc i s the procedur e name and par ame te r s indicate that Appenaix A 75 15s
L
<( t RELAP5' Input Data Requirements s 08/07/81 one or more par ameters'separa ted oy commas and terminated by a p eri o o ar e enter ed to specify the options.
19.1 INPUT ' DESCRIPTION PROC EDUR E Execution of the procedure, RLP51NP, generates a computer printeo listing of this RE LAPS input description. SANNER=name.. This parameter must be enter ed and the a l ph anum er i c quantity entered for'name becomes the banner on the first page of the computer printout. The first three characters should be the assigned USERID. FC, FC=nus, or not entered , If'tnis parameter is not entered, the output is printed on 11x14.in. paper. If FC is specified, the output is on 8-1/2x11 ' paper. If FC=num where num i s a two digit nueber, num spec;lfies the forms code f or. tne paper. The smaller . size paper is recoamencea f or code users. TEXT = pf n or not entered ID=idname or not entered
\ CY=cynum or not entered '
These parameters define the file generated oy the .TEXTJAS progr am that is to be printed. If TEXT is not entered, the def ault file maintained by the REL4P5 development staff is used. If specified, pfn is the p er manent file name of the file. If the 10 parameter is missing, the default ID is .used. If entereo, idname is the ID. If the CY parameter is missing, the largest av ail abl e cycle is used. Entering the p ar a met er specifies the cy c l e nu mbe r . . It may De entered With either the default file or the user specified file. 19.2 RELAP5 EXhCUTIDH PROCEDURES The pr ocedur e, RLP5X executes from an absolute binary file and the procedure, RLP5;LX, updates, compiles, loads, and executes fr om the g e n e r a te d absolute Dinary file. Many of the p ar am eter s are common to both procedures; those uni que to a crocecure are so indicated. No options are provided for tne ASTIN, RSTPLT, ano PLFILE files. Approprf9te REQUEST, CATALOG, and RETURN statements should be placed before and after the procecure call (BEGIN) statement as required. All other files are attached and returned as needed. f F Appendix A 76 155
RELAPS Input Data Requirements 06/07/61 1 NOMESSG or not enterea If not ent er ed, inf ormation descr ibing status of availaole RELAP5 versions i s p r in te a. I f en t er to, the status inf ormation is not pr in ted. X or not entered E i tn e r use r sp eci fi ed or default files, RELAPSS, RE L APS L, R EL A P DX, RELAP50, XE LAP 55, etc., can De selected. If a def ault file is selected, x not en t er ed means tnat a RELAP5 file is used and entering X means t hat a XELAPS file is useo. SPFN=sfile or not' entered SID=sname or not entered SCf=snum or not entered These p ar ame ter s are used for ALP 5CLX only and specify the source fi l e. If SPFN is not entered, the default source file is useo. If SPFN-is entered, sfile is the permanent file name of the suurce file and sname is the 10. If SCf is missing, tne nighest cycle is used; if entered, cycle snum is useo. NOF TN or not entered This parameter is used for RLP5CLX only and if entered, specifies tnat tne UPDATE di d not generate any Fo r tr an s ta t e me nts to be compiled. The procedure assumes that the update issues the segioad directives. ' SUPFN=ufile or not en t er ed SUID=unate or not ent er ed SUC Y = un ua or not entered Tnese parameters are used only in RLPSCLX. If SUPFN is not entered, the input f i le for the upd ate i s t he file INPUT. If SUPFN is entered, ufile is tne periaient file name ano SUID is the ID of a permanent file containing the update input. If SUCY is not ent er ed, the hignest cycle is used; if entered, unum is the cycle numoer. FLIST, FLIST=5R=25, or not entered inis par ame te r is used for ALP 5CLX only ano secifies the For tr an listing options. If not entered, L=0 is useo; if FLIST is e nter ed, R=1 is used. As snown, a speci fication can be entered and .'. r must be enc l os ed in "5". LPFN, LPFN= l fi l e, or not entered - LID =iname or not ent er ed LCY=inus or not entered These parameters are used for RLP5CLX oniy and specify the object deck library f il e. If LPFN is not entereo, no objec t libr ar y file is used. If LPFN i s ent er ed, tne default library file as used. If LPFN=lfile is entered, Ifile is the p e r ma ne n t file name and iname is the ID of the object library file. If Appendix A 77 l 156 1
RELAP5 Input Data Requironents D8/D7/81
'~' LCY..is not entered, the highest cycle is used; if entered, cycle Inus is used.
LMAP, LMAP=SBEX, or not en t er e d This par ameter specifies the load map- options. If not entered the map o p t i o ns are the standard, SB; if LMAP is entered, no load map is gener a ted. As shown, other map options can be specified. EPF1=efile, or not entered , ECY=inum or not entered EID=Iname or not entered These parame ters are used for RLP5CLX only and specify the env i r onme nta l library. The default is ENVRS1765, ID=RJW and the highest cycle. XPF N, XP F N= xf il e or no t, en te r ed XID=uname or not entered XCY= x num or not entered These p ar amet er s are used in .the RLP5X and RL P5C LX pro:ecures and specify the absolute binary file. The use is somewhat di f f er ent in the two procedures. For RLP5X If not ent er e c, the default file is useo. If entered, the absolute binary file i s- the permanent file with permanent file name xfile and ID xid. If XCY is not enteredf .(). the hi ghes t cycle is used; if entered, xnum is the cycle number. For RLP5CLX If not entered, the absolute binary file created.during the lead is not catalogued. If entered, the absolute oinary file is catalogued using the XPFN and XID par ameter s f or the permanent fi l e n am e and 10. If XCY is not enter ed, .the next higher cycle number is used or the cycle number is 1 if no cycles exist. DPFN, DPFN=dfile, or not entered DID=dname or not entered DCY=dnum or not entered These parameters specif y the input data file. If DPFN is not entered, the input data to RELAP5 is on the file INPUT and the DUPFN p ar ameter is not tested. If DPFN is ent er ed, the default fi le REL AP5D or XEL APSD which is in UPDATE form is used as the input file. If DPFN=dfile is entered, dfile is the permanent fi l e name, and dname is the ID of a permanent file to be us ed as a input file. It is treated as di r ec t input to RELAP5 or en update f or m a t file depending on the DUPFN entry. If DCY is no t entered, the highest cycle is used; if entered, dnum is the cycle number. DUPFN,'DUPFN=cufile, or no t enter ed DUID= duname, or no t entered DUCY=cunum, or not entered
)
Appendix A 78 l 157 l
REL AP 5 Input Data Requirements 08/07/81 DD or not enterec. O Tnese p ar amet er s specify tne update input to extract the RELAP5 input from an update flee. Tney are effective only if some entry for DPFN is made. If DUPFN is not entered, the fi l e DPFN is not in UPDATE format and contains input for RELAP5. If DUPFN is entered, DPFN is in update format and the file INPUT contains input to UPDATE to gen er ate tne input file. If GUPFN=0ufile is enterec, dufile is the permanent file name and duid is the ID of a permanent fil e containing input for the UFDATE to generate the input data for RELAP5. If DUCY is not enter eo, the highest cycle is used if entered, dunum si s the cycle nunoer. If DD is not entered, the input consists of 90 column reco rds, the first 80 columns containing the RELAPS input, the last 10 co lumns conta ining the update line number. fhe s tand ar d RELAP5 input processing reads and edits 90 columns out processes only 80 columns. If OD is entered, the input consi sts only o f the 80 columns of KELAPS input. Specifying 00 is n ecess ar y when using the plot p ack age that ooes not use st an d ar c RE L AP S input. WPPFM=wpfil e or not entered JPID=wpname or not entered d PCY= wpnum or not entered These parameters specify the w at er pr oper ty file. If not enter ed the def aul t file of STH2XT,ID=RJW, highest cycle number is used. If entered, the permanent file with permanent fil e name wpfile anc 10 wpname i s us ed. If WPCY is not entered, the nighest cycle is used; if entered, wpnum is the cycle number. PL=plimit or not entered This p arameter sets the RELAP5 execution print line l i mi t. If not entered, the default limit is 20000 lines. If entered, plizi t is the line limit. SCM=nnnnnn LCM = mas Tnese p ar ame ter s spec if y the taximum tesor y to be used. If not en t er e d, the def aul t values of SCM=273300 and LCM =200 are aseo. DMPl=5L1,L25 0MP2=sL1,L25 OMP3=5L1,L25 Enter these parameters if up to three different parts of memory are to be dumped after an anormal termination. Use OMP1 if only one part of memory is to De dumped, use DNP1 and DMP2 If two parts are to De dumped, etc. Suostitute the first and last words of memory to be dumpea f or L1 anc L2. Tne control statements to execute the nignest cycle of tne Appencix A 79 158
RELAPb Input D at a Require:ents 08/07/61 l) 's> ' procuction series of REL AP 5 from input dats entered with the job is BEGINsRLP5XsPROCS.
- EOR REl, APS input data The control statements to execute the highest cycle of the e xpe r isen tal series of RELAP5 from input dat a stored as permanent file MYDATA, ID=RJW is BE GIN, RLP5X, PROC Ss DPF N= MYD ATA,0ID=RJW.
The control statements to modify the highest cycle of the experimental series of RELAP5 with updates from permanent file XELAP50150s 10=RJW and execute the EDHTRK probles from the st an d ar d input cata file is BEGIN,RLP5CLX,PROCSsXsSUPFN=XELAP5U150,5UID=RJW,LPFNs DPFN,0UPFN.
- EOR
- COMPILE EDHTRK O
O Appendix A 80 159
l REFERENCES l A-1. [HTERCOM Version 4 Reference Manual, Control Data Corporative:, Revision B, 60494600, July 16,1976, pp.11-21 through 11-2 27. A-2. R. R. Ragan, TEXTJAB Reference Manual Control Data Corporation, Revision 04, 17316600* February 5,1976. i O' O
O , , APPENDlX B INPUT DATA REQUIREMENTS FOR PLOTTING O O 161
l APPENDIX B INPUT DATA REQUIREMENTS FOR PLOTTING This appendix contains the first part of a letter which describes a plotting capability for ; code used to develop RELAPS numerical procedures. If RELAP5 generated plots are desired, input data described in this appendix is placed immediately after the slash on period termination card on the standard RELAPS input. The EDHTPL deck in the sample problems partition of the transmittal file contains the input data used to generate the plots in Figures 12-20. O O 163
l4
/v EERS Idaho i
~
INTEROFFICE CORRESPONDENCE ..
. September 20, 1977
- i. V. H. Ranso
,, D. M. Kiser
.. RELAP-PILOT CODE INPUT DATA DESCRIPTION FOR PLOTTING - DMK-2-77 i
Three-dimensional and two-dimensional plot routines have been developed for the RELAPS-PILOT code. The plot routines consist of four subroutines which are PLOT 3D, which performs the 3D plots; PLTCOM, which performs the 2D plots; AXISDV, which divides the axes into labeling intervals; and j RONOFF, which rounds numbers to the next highest nth significant figure. j The subroutine PLOTS which already existed in the RELAPS-PILOT code was '
, modified to call the developed routines and to input the data required for the plots. The purpose of this letter is to provide the user with an input data description for plotting and an example of the input cards i and plots.
Data for the plots is input by disk in list directed input form and by cards in both formatted for:n and list directed form. The data input by disk consists of the results stored during the execution of the h RELAPS-PILOT code. The data input by cards consists of the plot control parameters, titles and data for comparison with the calculated results. Three plot control parameters are input in subroutine INPUT and are described in D. M. Kiser Ltr to V. H. Ransom, "RELAPS-PILOT Code Input Data Description", DMK-1-77 dated July 22, 1977. These control parareten are PINC, IPLOTS and NPLOTS. If IPLOTS = 0 then plots will not be made and no further input data is required. If IPLOTS = 1 then plots will be made and the input data required is described as follows. A plot heading must be input which consists of from one to three cards witn each card containing a line of the heading. Each line of the heading is composed of up to 60 characters. The last character of each line must ta followed by a $ symbol. The first heading card must be input with the number of heading lines. LINSHD, punched in columns 1-5 (right justified ). l followed by the first line of the heading punched in columns 6-66 (left justified). The maximum number of heading lines is three (i.e.; 1 LINSHg3). 1 If LINSHD>l then (LINSHD-1) cards must be input with the heading punched in columns 6-66 (left justified). The entire heading will be printed at the I top of each plot as part of the plot title. The last line of the plot titi defines the plot and is predefined or is input as described in the fc110 wing. If NPLOTS = 1 or 0 nine three-dimensional (30) plots of the RELAP4-PILOT code results will be made. Input of data by cards is not required for the 3D plots. The last line of the plot title for each of the 3D plots is predef9 in the plot routines as " VOLUME DATA" for the volume cell parameters phttu < m.o.,,,and as " JUNCTION DATA" for the junction cell parameters plotted. The J j
- om plots are made in an X, Y, Z cartesian coordinate system. For the vo,. w '
_ _ _ _ _ _ - - - - - - - _ . - - - - - 1
f V. H. iansom September. 20, ' 1977 DMX-2-77: Page 2 cell data plotted, the X-axis. represents the axial distance from the center of volume cell number 1 (i.e., volume cell index 2) to the center of each successive volume. cell number 2 through NVOL. The center of the volume cell number .1 is defined as X 5 0.0. For the junction cell data pictted i the X-axis represents the axial distance from the center of junction cell number 1-(i.e., junction cell index 2) to the center of each successive. junction cell number 2 through NJUN. The center of junction cell number 1 is defined as X = 0.0. The Y-axis represents the' problem time where each time interval plotted is At = TIMEMX/PINC. The Z-axis represents the va've of the plot parameter. Table I gives the nine plot parameters and Z-uis labels for the 3D plots. If NPLOTS i 0 or -1 two-dimensional (2D) plots are made which require card data input. Any number of 2D plots can be made. Each 2D plot requires-the input of two' or more cards. The 2D plots are made in the order of the card input. Each 20. plot is made in the X,Y cartesian coordinate system. . The X-axis represents the problem time in seconds where'each time interval plotted ;is At = TIMEMX/PINC. The Y-axis represents the parameter, in SI units, to be plotted. The first card input for each plot contains the name of the parameter to be plotted, punched in columns 1-6 (lef t justified); the axial distance from junction number 1 in meters at which the plot parameter is calculated, punched in columns 8-16 (either fixed or floating point);'the number of curves, NCURVS, which are to be plotted, punched in
~
columns 18-19 (right justified);-and the last line of the plot title, x punched in columns 21-80. The last character of the plot title must be followed by a $ symbol. Table II gives the list of plot parameter names and their explanation. The second card input for each plot contains a plot parameter scale factor, YSFACT, punched in columns 1-9; the Y-axis minimum, YMINSP, if it is to be specFied, punched in columns 11-19; the Y-axis maximum, YMAXSP, if. it is to be specified, punched in columns 21-29;
. and the Y-axis label punched in columns 31 through 80. The plot parameter is divided by YSFACT for scaled plotting. The last character of the Y-axis label must be a $ symbol. If NCURVS=1 then only the RELAPS-PILOT code results are plotted and no further input is~ required for the plot. If NCURVS=2 then the RELAPS-PILOT code results and card input data are plotted.
The card input data is input in list directed input form. The cards are punched with the number of data pairs NPTSD punched first, followed by a comma or one or more' blank spaces, followed by a time conversion factor, XDFACT, followed by a comma or one or more blanks followed by a plot para-meter conversion factor, YDFACT, followed by a comma or one or more blanks, followed by the list of data pairs, XDAT(n), YDAT(n). Each XDAT YDAT must be separated by a coma or one or more blank spaces and each data pair must be separated by a cma or one or more blanks. Time is represented by XDAT and the plot parameter is represented by YDAT. XDAT is divided by XDFACT for conversion to seconds. YDAT is divided by YDFACT for con-version to SI units and then divided by YSFACT for scaling. After the cards are input for a 2D plot the plot is generated and the cards for the next plot are input. To teminate the 2D plots, a blank card must be input as the first card for a plot. 165
V. H. Ransom September 20, 1977 DMK-2-77 Page 3 0! Table III summarizes the input data cards for plotting. The attached example illustrates the data cards which must be input for plotting. Figure 1 represents the problem input data and the plot inp'it data for the example problem described in D. M. Kiser Ltr to V. H. Ransom.
"RELAPS-PILOT Code Input Data Description", DMX-1-77 dated July 22, 1977, except that the input parameters IPLOTS and NPLOTS are changed to IPLOTS=;
and NPLOTS=0. The resulting plots are shown in Figures 2 through 13. ma Attachments: As stated cc: K. E. Carlson H. H. Kuo L. H. Sullivan J. A. Trapp R. J. Wagner Central File D. M. Kiser File O i i i I J O 166 - _ _ _ _ _ _ _ i
L V.~H. Ran:!om September 20 1977~ DMK-2-77. - Page.4 l TABLE I- ! LIST OF PARAMETERS PLOTTED VS. AXIAL POSITION AND TIME l FOR THE RELAP5-PILOT CODE THREE DIMENSIONAL ~ PLOTS l l Parameter Description- Z-Axis Label Volume Pressure PRESSURE (N/SQM). Volume Static Quality STATIC QUALITY-Volume Internal Energy ENERGY (J/KG). Volume Liquid Fraction LIQUID FRACTION
. Volume Phase TEMPG-TEMPL(K)
Temperature Difference Volume Static and QUALITY DIFF XS-XE Os Equilibrium Quality Difference Junction Liquid Velocity LIQUIDVELOCITY(M/SEC) Junction Vapor Velocity VAPOR VELOCITY (M/SEC) Junction Phase VELOCITY DIFF VG-VL (it/SEC) Velocity Difference O 167 ______. __.____m_ _ _ _ . _ _ _ _ _ _ _ _ _ _ . _ _ _ _ .
V. H. Ransom l S:ptember 20, 1977 DMK-2-77 ~ Page 5 l l TABLE II NAMES OF PARAMETERS WHICH CAN BE PLOTTED VS. TIME FOR THE RELAPS-PILOT CODE TWO-DIMENSIONAL PLOTS l Parameter Name. Parameter Name Explanation i P Volume Pressure QUALS Volume Static Quality QUALE Volume Equilibrium Quality ; VOIDG Volume Vapor Fraction (i.e., Void Fraction) TEMPF Volume Liq'Jid Temperature TEMPG Volume Vapor Temperature U Volume Internal Energy RHO Volume Mixture Density VELFJ Junction Liquid Velocity VELGJ Junction Vapor Velocity WP ' Junction Mixture Mass Flow DPJ Junction Pressure Differential QUALSF Volume Liquid Static Mass Fraction (i.e.,1-Static Quality) QUALEF Volume Liquid Equilibrium Mass Fraction (i.e.,1-Equ. Quali:yi VOIDF Volume Liquid Fraction (i.e.,1-Vapor Fraction) DTGTF Volume Phase Temperature Difference (i.e. , Vapor-Liquic' Temperature) DXSXE Volume Static and Equilibrium Quality Difference , i DVGVF Junction Phase Velocity Difference I 91I l 168
F V. H. Ransom September 20, 1977 DMK-2-77 Page 6 l TABLE III
SUMMARY
OF INPUT DATA CARDS FOR PLOTTING Plot Control Card (Namelist; reference D. M. Kiser Ltr to V. H. Rannm, "RELAPS-PILOT Code Input Data Description", DMK-1-77 dated July 22, 1977) Columns Quantity Parameter Punched Punched Explanation (Namelist Name) 208 $PLTDAT Columns 1 and 9 must be blank spaces
. IPLOTS Free IPLOTS=1 For generating plots, punch anywhere after Column 9 Default The default value is IPLOTS=0 and if Blank no plots swill be generated NPLOTS Free NPLOTS=1 Generates only 3D plots NPLOTS-1 Generated only 2D plots Default The default value is NPLOTS=0 for
() if Blank which both 3D and 2D plots will be V generated (Terminator) Free $ The namelist must be terminated by punching a $ symbol First Plot Feading Card (Not Required if IPLOTS=0) Columns Quantity Parameter Punched Punched Explanation LINSHD 1-5 1 (Default) Number of heading lines, lgINSHD13. (RT, 2 or 3 If punched as blank or zero, the Justified) default is LINSHD=1 (HeadingLine) 6-66 Alpha- From 1 to 60 characters, the last numeric character punched must be a $ (Ending symbol with a $) l O 169
i V. t!. Ransom September 20, 1977 DMK-2-77 - 'Page 7 TABLE III (contd.) i
SUMMARY
OF INPUT DATA CARDS FOR PLOTTING l
\
Second and Third Heading Card (Not Required if IPLOTS=0 or if LINSHD=1) l Columns Quantity Parameter Punched Punched Explanation (HeadingLine) 6-66 Alpha- From 1 to 60 characters. The last Numeric character punched must be a $ (Ending symbol j with a $) l Two-Dimensional Plot Title Card (Not Required if IPLOTS=0 or if NPLOTS=1) Columns Quantity * { Parameter Punched Punched Explanation (PlotParameter) 1-6 Alpha- The list of plot parameter names is Name) (Left Numeric given in Table II
- Justified)
Blank = If columns 1-6 are punched as Plot blank spacas the plots are terminated Terminator l INDX 8-12 Integer Volume or junction sequence number. If INDX is positive, the x-axis is time. If INDX is negative, the x-axis is axial position. , (Axial Distance 14-22 Fixed or The axial distance punched must be q from Junction #1) Floating in SI units (not used in RELAPS) ! PT NCURVS 24-25 1 (Default ) if NCURVS=1 then only the RELAP5-(RT PILOT code results are plotted. ; Justified) or 2 if NCURVS=2 then both the RELAPS- l PILOT code results and data input ' from cards are plotted. if punched as blank or 0 NCURVS defaults to 1. if punched as greater than 2 NCURVS defaults to 2. . i ei l 170 _ _ _ _ _ - _ _ i
V. H. Ransom l September 20. 1977 DMK-2-77 Page 8 LJ TABLEIII(contd.)
SUMMARY
OF INPUT DATA CARDS FOR PLOTTING (PlotTitleLine) 27-76 Alpha- From.1 -to 50 characters. The last Numeric characterpunchedmustbea$ symbol (Ending with a $) 4 Two-Dimensional Y-Axis Label Card (Not Required if IPLOTS=0 or if NP!.0TS=1) Columns Quantity Parameter Punched Punched Explanation YSFACT 1-9 Fixed or Y'-Axisscalefactor(i.e.,exceptfor Floating temperature the parameter plotted is PT dividedbyiSFACT. For temperature if:) YSFACT g,2.0 Deg. Rankine is plotted; YSFACT ,,1.0 Deg. Kelvin is plotted; YSFACT = -1.0. Deg. Celsius is plotted; YSFACT f, -2.0 Deg. Farenheit is plotted. If YSFACT is punched as blank or zero, it defaults to 1.0. YMINSP 11-19 Fixed or Specified Y-Axis minimum. YMINSP Floating is ignored if: PT (1) Both YMINSP and YMAXSP are zero (2) YMINSP is greater than the minimum of the data plotted YMAXSP 21-29 Fixed or Specified Y-Axis maximum. YMAXSP is Floating ignored if: PT (1) Both YMINSP and YMAXSP are zero (2) YMAXSP is less than the maximum of the data plotted (Y-AxisLabel) 31-80 Alpha- From 1 to 50 characters. The last Numeric character punched must be a $ symbol (Ending ' with a $) 171
- l. H. Ransom
. September 20, 1977 DMK-2-77 Page 9 TABLE III (contd.)
SUMMARY
OF INP(IT DATA CARDS FOR PLOTTING l Card Data Pairs for Plotting' (Not Required if IPLOTS=0, NPLOTS=1 or if NCURVS=1) I l Columns Quantity i Parameter Punched Punched Explanation I NPTSD Free Integer The number of data pairs following (Coma and/or any Free Separator between NPTSD and the I number of blanks following j XDFACT Free 1.0 The XDAT(I) terms following are (default) divided by XDFACT for conversion to l or free seconds. If XDFACT is punched as blank or zero, it defaults to 1.0. (Comma and/or any Free Separator between XDFACT and the number of blanks) following YDFACT Free 1.0 The YDAT(I) terms following are (default) divided by YDFACT for conversion to or free SI units and YSFACT for scaling. If ! YDFACT is punched as blank or zero ; it defaults to 1.0. The rules ex-plained for YSFACT also apoly to YDFACT. O 172 _ s
'?
1
. ,m i k-V a
APPENDIX Cs RELAP5YA SUBROUTINE GLOSSARY PROGRAM RELAP5 RELAPS IS THE MAIN ROUTINE OF'RELAP5YA. CALLS THE FOLLOWING ROUTINES: INPUT PLOTHD REEDIT RSTFIN STRIP STSTAT TRNCTL TRNSIS SUBROUTINE ACCUM CALCULATES THE HYDRODYNAMICS AND HEAT TRANSFEB 0F THE ACCUMULATOR COMPONENT AND SURGE LINE.
- lV SUBROUTINE AXISDV DIVIDES A PLOTTING AXIS OVER THE INTERVAL XMAX - XMIN INTO NDIV OR (NDIV + 1) INTERVALS OF LENGTH XINTVL.
THE DATA END POINTS ARE INCLUDED. CALLS THE FOLLOWING ROUTINES: RONOFF FUNCTION CELMOD(T)* Ts CLAD TEMPERATURE (DEG K) l CELMOD s CLAD ELASTIC MODULUS (N/M2) SUBROUTINE CHFCAL !
.... .......... l CALCULATES CRITICAL HEAT FLUX.
CALLS THE FOLLOWING ROUTINES: TABEND STH2X3 THCON VISCOG
- New routines added in RELAP5YA C-1 L_________-______-
O' SUBROUTINE CONDEN CONDENSATION HEAT TRANSFER CORRELATIONS SUBROUTINE CONVAR ' ADVANCES THE CONTROL VARIABLES OVER A TIME STEP. CALLS THE FOLLOWING ROUTINES: FABEND POLATS FUNCTION CTHSTR(T2,T1,NT)* FUNCTION CCMPUTES TOTAL TMEPMAL STRAIN CF 'IRCALOY CLAD WHEN HEATED FROM TEMPERATURE T1 TO T2 IN DEC K SUBROUTINE DFRMB
- FUEL PIN DEFORMATION MCCEL CALLS THE FOLLOWING ROUTINES:
CELMOD CTHSTO FTHEXP PLASTIC SUBROUTINE DITTUS DITTUS.BOELTER FCRCED CONVECTION HEAT TRANSFER CCREELATION SUBROUTINE DOLEND j SUBROUTINE TO LEFT JUST!FY A CHARACTER STRING AND TO TERMINATE THE CHARACTER STRING WITH A $ SYMBOL. j l SUBROUTINE DTSTEP HYDRODYNAMIC TIME STEP CONTROL. CALLS ROUTINES TO PhINT EDITS AND WRITE PLOT RECOROS. CALLO THE FOLLOWING AOUTINES: 1 i MIREC MOVER OUTPUT PLTREC PLTRECX PLTWRT REMTIM RSTREC TIMEL TIMER O1 l l New routines added in RELAP5YA l C-2 _ _ _ _ _ __ J
.'1(f 4 SUBROUTINE EDSET
- PROTECTS AND CHECKS CODING FOR REEDIT OPTION, LOAD REQUIRED FILES FROM DISK, COMPUTES INDEXES OF ACTUAL LOCATIONS FOR COMPONENT AND JUNCTION BLOCKS AND CALLS SUBROUTINE TO RELEASE EXCESS SPACE.
CALLS.TNE FOLLOWING ROUTINES: DELETE DMPLST FTBRDC FTBRSV FTBSFT ISUMRY LCONTG NEXTID TCNVSL TSETSL SUBROUTINE ECTINL
- EQFINL LOOPS OVER ALL JUNCTIONS AND COMPUTES SOURCE TERMS (MASS,' ENERGY AND QUALITY CONTRIBUTIONS) TO CELL K FROM
. JUNCTION I FOR FORWARD FLOW OR FROM CELL L FROM JUNCTION I FOR REVERSE FLOW.
LOOPS OVER ALL VOLUMES AND COMPUTES FINAL MIXTURE DENSITY, AVERACE INTERNAL ENERGY, NON.CONDENSIBLE QUALITY, STATIC QUALITY AND MASS TRANSFER RATE.
,s CALLS THE FOLLOWING ROUTINES:
( HELPTR FUNCTION FIANN COMPUTES FIJ IN ANNULAR FLOW FOR HRT, ANN AND HMF MAPS FUNCTION FIANN1e COMPUTES FIJ IN ANNULAR FLOW FOR VRT MAP AT MASS FLUXES BELOW 2000 KG/Mee2.SEC. FUNCTION FIBUB COMPUTES FIJ IN BUBBLY FLOW FOR HRT, ANN AND HMF MAPS. ALSO USED IN VRT MAP AT MASS FLUXES ABOVE 2000 KG/M**2-SEC. FUNCTION FIBUB1* 1 I COMPUTES FTJ IN BUBBLY FLOW FOR VRT MAP AT MASS FLUXES BELOW 2000 KG/M**2.SEC. (
- New routines added in REIAPSYA
%./
l C-3
O SUBROUTINE FICALA COMPUTES FIJ IN ALL FLOW REGIMES FOR VRT MAP. CALLS THE FOLLOWING ROUTINES: FIANN FIANN1 FIBUB FIBUB1 FIDIS FIMIST FISLG FLQREGA SUBROUTINE FICALB COMPUTES FIJ IN ALL FLOW REGIMES FOR HRT MAP.. CALLS THE FOLLOWING ROUTINES: FIANN FIBUB FIDIS FISTR FLOREGB SUBROUTINE FICALC COMPUTES FIJ IN ALL FLOW RECIMES FOR ANN MAP. CALLS THE FOLLOWINC, ROUTINES: FIANN FIBUB FIDIS FLORECC SUBROUTINE FICALD COMPUTES FIJ IN ALL FLOW REGIMES FOR HMF MAP. CALLS THE FOLLOWING ROUTINES: FIBUB FIDIS FLOREGD FUNCTION FIDIS COMPUTES FIJ IN MIST FLOW FOR HRT, ANN AND HMF MAPS. ALSO USED FOR VRT MAP AT MASS FLUXES BELOW 2000 KG/M'*2-SEC. SUBROUTINE FIDRAG CALCULATES INTERFACIAL SHEAR AND VIRTUAL MASS COEFFICIENTS FOR ALL JUNCTIONS INCLUDING VALVE JUNCTIONS. WHERE MOODY CHOKING MODEL IS USED, FIJ IS SET TO A VERY LARGE VALUE TO INSURE NO SLIP AT MOODY CHOKED JUNCTIONS. CALLS THE FOLLOWING ROUTINES: FICALA FICALB FICALC FICALD VALVE O I C-4 j l
a
+
,.;g-
' FUNCTION FIMIST
- CA'LCULATES FIJ IN MIST FLOW FOR VET MAP AT MASS FLUXES BELOW 2000 KG/M**2.SEC.
FUNCTION FISLG *' CALCULATES FIJ IN SLUG FLOW FOR VRT MAP AT MASS FLUXES BELOW 2000 KG/M'*2-SEC. FUNCTION FISTR , CALCULATES'FIJ IN STRATIFIED FLOW FOR HRT MAP. CALLS THE FOLLOWING ROUTINES: FRICTF INTEGER FUNCTION FLOREG FLOW REGIME MAP'FOR FIJ CALCULATION INTEGER FUNCTION FLOREGA FLOW REGIME MAP (VRT) FOR FIJ CALCULATION INTEGER FUNCTION FLOREGB FLOW REGIME MAP (HRT) COMPATIBLE WITH FICALB INTEGER FUNC'i10N FLOREGC FLOW REGIME HAP (AND) COMPATIBLE WITH FICALC INTEGER FUNCTION FLOREGD FLOW REGIME MAP (HMF) COMPATIBLE WITH FICALD
- New routines added in RELAP5YA l
l-C-5
1 O FUNCTION FRICTF DETERMINES THE LAMINAR, TRANSITION OR TURBULENT FRICTION FACTOR FOR PIPES. THE TURBULENT FRICTION FACTOR IS CALCULATED FROM THE COLEBROOK CORRELATION. FUNCTION FTHEXPe FTHEXP CALCULATES FUEL LINEAR THERMAL EXPANSION FOR SOLID AND LIQUID PHASES AS A FUNCTION OF TEMPERATURE AND LIQUID FRACTION. SUBROUTINE FWDRAG CALCULATES THE WALL DRAG TERMS DOES NOT INCLUDE PHASE CHANGE EFFECTS ASSUMES BOTH PHASES ARE INCOMPRESSIBLE CALLS THE FOLLOWING ROUTINES: FPICTF HEADLN HELPHD SUBROUTINE GNINIT SUBROUTINE PERFORMS ONCE ONLY CALCULATIONS AND GENERAL INITIALIZATION INCLUDING SETTING COMMON BLOCK LENGTH AND CLEARING THEM. CALLS THE FOLLOWING ROUTINES: DELETE FTBMEM FTBRSV HEADER INITAL ISFDES NEXTID SYSTEMC TIMSET SUEROUTINE HELPHD WRITES TdE DIAGNOSTIC PAGE HEADER j i New routines added in RELAPSYA C-6 l I L - - -._ -__- .-
i A 5Vl. SUBROUTINE HELPTR SUBROUTINE TO PERFORM DIAGNOSTIC PRINTOUTS FOR SUBROUTINES CALLS THE FOLLOWING ROUTINES: HEADLN HELPHD STRACE SUBROUTINE HGAPR
- CALCULATES GAP HEAT TRANSFER COEFFICIENT AND VOLUMETRIC HEA*
CAPACITY CALLS THE FOLLOWING ROUTINES: POLATE2 STMCON SUBROUTINE HLOSS
' CALCULATES VOID FRACTIONS AT THROAT AND DOWNSTREAM OF AN ABRUPT AREA CHANGE AND ASSOCIATED HEAD LOSS TERMS ~\
SUBROUTINE HSUAB - ' CALCULATES CONSTANTS (A,B) FOR HSU'S TRANSITION BOILING l CORRELA* ION. SUBROUTINE HTADV HTADV CALLS RADHT FOR RADIATIVE HEAT TRANSFER. BOUNDARY CONDITIONS. HTADV CALLS HT1TDP FOR HEAT STRUCTURE CALCULATIONS INCLUDING FUEL BEHAVIOR, METAL. WATER REACTION, MATERIAL PROPERTIES, HEAT TRANSFER BOUNDARY CONDITIONS AND CONDUCTION SOLUTION. CALLS THE FOLLOWING. ROUTINES: HT1TDP RADHT SUBROUTINE HTCOND RETURNS LEFT AND RIGHT BOUNDARY CONDITIONS FOR A HEAT STRUCTURE. CALLS THE FOLLOWING ROUTINES: HTRC1 POLATS
-p% .
- New routines added in RELAPSYA g
)
i C-7 i I
l O\ SUBROUTINE ETRC1 i
................ ),
I COMPUTES HEAT TRANSFER COEFFICIENT FROM CORRELATIONS. PACKS HEAT TRANSFER FLAGS AND MODE NUMBERS INTO HTINCO.
)
CALLS QUENCH ROUTINE. i CALLS THE FOLLOWING ROUTINES:
}
CONDEN DITTUS NATCIR POOLNB PREDNB PSTDNB QUENCH THCON VISCOG VISCOL SUBROUTINE HT11NP' SUBROUTINE HT1INP PROCESSES INPUT FOR THE HEAT 1 SUBCODE. CALLS THE FOLLOWING ROUTINES: INP10 INP2 INP5 LINES LINK SUBROUTINE HT1SST (HINDEX,INDEX,PROBID,ERRSW) SUBROUTINE HT1SST SOLVES THE 1-D STEADY-STATE HEAT PROBLFM. CALLS THE FOLLOWING ROUTINES: DFRMR HCAPR HTCOND MADATA MOVE PGAPR POLATS SUBROUTINE HT1TDP HT1TDP PERFORM HEAT STRUCTURE CALCULATIONS INCLUDING FUEL BEHAVIOR, METAL.WA*ER REACTION. MATERI AL PROPERTIES, HEAT TRANSFER BOUNDARY CONDITIONS AND 1.D CONDUCTION SOLUTION. CALLS THE FOLLOWING ROUTINES: DFRMR HCAPR HTCOND MADATA PGAPR POLATS QVMOV QVSUBR CZRWR TIKEL SUBROUTINE HYDRO CALLS VARIOUS ROUTINES TO BUILD AND SOLVE THE I THERMAL. HYDRAULIC EQUATIONS. HYDRO YIELDS NEW TIME PRESSURE, PHASE VELOCITIES AND STATE PROPERTIES. PUMP (CENTRIFUGAL) AND ACCUMULATOR SUBROUTINES ARE CALLED IN SUBROUTINE VEIPLT. CALLS THE FOLLOWING ROUTINESs ECFINL FIDRAG FWDRAG HLOSS HZTLOW JCHOKE JETPMP JPROP MDOT PRESEQ STATE SISSOL TIMEL VEIPLT VOLVEL vrInt . i i e C-8 l - _ _ _ - - _
i f-~s l s, i I: SUBROUTINE HZFLOW CALCULATES COEFFICIENT OF VIRTUAL MASS FOR HORIZONTAL FLOW. CALCULATES AN ADDITIONAL FORCE TERM WHICH ARISES FROM I STRATIFIED HORIZONTAL FLOW AND ADDS THE TERM TO THE i MOMENTUM EQUATION. SUBROUTINE ICMPF j FINDS INDEX FOR COMPONENT. CHECKS IF CCMPONENT HAS BEEN ENTERED. SUBROUTINE ICOMPN CONTROLS CROSS CHECKING OF COMPONENT INPUT AND COMPLETION OF COMPONENT INITIALIZATION. CALLS THE FOLLOWINO ROUTINES: DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV FTBSFT ICMPF IEDIT IJPROP INVJT IPIPE IPUMP ISFDES ISTATE ITRSCN IVLVEL LCONTG NEXTID POLAT SCNREC STH2XI { SUBROUTINE 7 COMPT CHECKS AND INITIALIZED THE 2D PLOT COMPARISON DATA TABLES CALLS THE FOLLOWING ROUTINES: DOLEND SUBROUTINE ICONVR CHECK CONTROL SYSTEM VARIABLE REQUESTS, COMPUTE INITIAL VALUES. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV ITRSCN LCONTG POLATS SUBROUTINE ICRLT PREPARES TABLES AND VARIABLES FOR LATER USE BY HEAT TRANSFER CORRELATION FUNCTIONS AND SUBROUTINES. C-9
O SUBROUTINE IEDIT EDIT FINAL RESULTS OF INPUT INITIALIZATION. SUBROUTINE IGNTBL CROSS CHECKS AND ESTABLISHES LINKAGES FOR GENERAL TABLES AND TRIPS. CALLS THE FOLLOWING ROUTINES: ! DELETE FTBCHK FTBIN FTBOUT FTBRSV ITRSCN LCONTG SUBROUTINE IHTCMP L CHECKS AND PERFORMS REFERRALS ON GEOMETRY, COMPOSITIONS, SOURCE DISTRIBUTIONS, AND INITIAL TEMPERATURES BETWEEN HEAT STRUCTURES, CHECKS COMPOSITION NUMBERS, CHECKS HEAT TRANSFER TYPES, AND CALLS SUBROUTINE FOR STEADY STATE INITIALIZATION OF SPECIFIED HEAT STRUCTURES. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV HT1SST ICRLT ISFDES LCONTG LINES MOVE NEXTID , SUBROUTINE IJPROP COMPUTES JUNCTION PROPERTIES AS PART OF INPUT INITIALIZATION. SUBROUTINE IMIEDT USES VINOR EDIT REQUEST FILE WRITTEN IN RMIEDT TO PREPARE MINOR EDIT CONTROL FILE. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV LCONTG NEXTID SCNREQ l SUBROUTINE INPUT CONTROLS ALL INPUT DATA PROCESSING. IF AN ERROR IS FOUND, l EDITING FOR THE CASE IS COMPLETED. CASES THAT FOLLOW ONLY I HAVE THEIR INPUT LISTED. 1 CALLS THE FOLLOUING ROUTINES: GNINIT INP2 IPLOT RCARDS RDREDT RNEWP RPESTF RPLOT RPLOTN RSTRIP
\
C-10 l. L
( i k j :
%.J' I
l l SUBROUTINE INVJT PREPARES INVERTED JUNCTION TABLE AND CHECKS FOR PROPER NUMBER OF JUNCTIONS PER VOLUME. INVERTED TABLE CONTAINS FOR EACH VOLUME THE NUMBER OF INLET JUNCTIONS WHICH MAY BE ZERO FOLLOWED BY THE JUNCTION NUMBERS THEN THE NUMBER OF OUTLET JUNCTIONS. AND THE OUTLET JUNCTION NUMBERS. JUNCTION NUMBERS HAVE THE SIGN BIT SET IF THE~
- JUNCTION DIRECTION IS OPPOSITE OF THE VOLUME DIRECTION.
CALLS THE FOLLOWING ROUTINES: DELETE FTBRSV FTBSFT ICMPF ISFDES LCONTG NEXTID SUBROUTINE IPIPE-SETS TO.FROM POINTERS AND INITIAL CONDITIONS TOR A PIPE COMPONENT. SUBROUTINE IPLOT CHECKS,' INITIALIZED AND CROSS REFERENCES THE PLOT DATA CALLS THE FOLLOWINC ROUTINES: DELETE DOLEND FTBCHK FTBIN FTBORG FTBOUT FTBRSV ICOMPT IPLT2D IPLT3D ISFDES LCONTG NEXTID SUBROUTINE IPLTSI THIS ROUTINE CONVERTS COMPARISION DATA TO SI AND SCALES X VALUES BY CON 1
'SUBRDUTINE IPLT2D CHECKS AND INITIALIZED THE 2D PLOT REQUESTS'AND SPECIFICATIONS CALLS THE FOLLOWING ROUTINES:
DOLEND SCNREQ SORPTR SUBROUTINE IPLT3D IPLT3D CHECKS AND INITIALIZED THE 3D PLOT REQUESTS AND SPECIFICATIONS. O 1 I l C-11 j
l 1 i 9! SUBROUTINE IPUMP ! RESOLVES TABLE POINTERS AND COMPUTES FRICTIONAL TORQUE IF REQUESTED IN PUMP INPUT. CALLS THE FOLLOWING ROUTINES: POLATS PUMP 2 SUBROUTINE IRADHT* CHECK THE RADIATION HTX INPUT FOR ERRORS AND INITIALIZE VARIABLES CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV LCONTG SIMUL SUBROUTINE IREDMI*
.USES MINOR EDIT REQUEST FILE WRITTEN IN RMIEDT TO PREPARE MINOR EDIT CONTROL FILE.
' CALLS THE FOLLOWING ROUTINES:
DELETE FTBCHK FTBIN FTBOUT FTERSV LCONTG NEXTID SCNREQ SUBROUTINE IRKIN COMPLETE CHECKING OF REACTOR KINETIC INPUT, SET POINTERS, AND COMPUTE BIAS REACTIVITY. CALLS THE FOLLOWING ROUTINES: 3 i' DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV LCONTG POLATS SUBROUTINE ISNGJ CHECKS AND SETS TO.FROM POINTERS AND INITIAL CONDITIONS FOR SINGLE l JUNCTIONS, TIME DEPENDENT JUNCTIONS, PUMPS, BRANCHES, AND TEES. CALLS THE FOLLOWING ROUTINES: l ICMPF POLATS j l
- New routines added in RELAP5YA l
4 I C-12 l - - - - _ _ _ _ - _ i
.: n L
SUBROUTINE ISTATE 1i COMPUTES VARIOUS THERMODYNAMIC PROPERTIES FROM INITIAL CONDITIONS FOR NORMAL VOLUMES AND FOR TIME DEPENDENT VOLUMES AFTER INTERPOLATION FOR TIME : 0.0. CALLS THE FOLLOWING ROUTINES: FABEND POLATS PSATPD STH2XB STH2XF STH2XO STH2X1 STH2X2 STH2X3 STH2X6 SURTEN VISCOG VISCOL SUBROUTINE .ISUMRY
- PRINTS
SUMMARY
OF OP'! IONS BEING USED CALLS THE FOLLOWING ROUTINES: MADATA POLATS SUBROUTINE ITRIP COMPLETE CHECKING AND PROCESSING OF TRIP DATA AND SET INITIAL ( VALUES OF TRIP. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBOUT FTBRSV ITRSCN LCONTG SCNREQ SUBROUTINE ITRSCN CHECK THAT NUM IS VALID TRIP NUMBER IN TRIP AND RETURN PACKED CODE. SUBROUTINE IVLVEL CALCULATES AVERAGE VOLUME VELOCITIES BY AVERAGING THE AVERAGE JUNCTION VELOCITIES IN AND OUT OF THE VOLUME CALLED DURING HYDRODYNAMIC COMPONENT INITIALIZATION. SUBROUTINE JCHOKE COMPUTATION OF CHOKING THEORY CALLS THE FOLLOWING ROUTINES: HEADLN HELPHD MOODY PSATPD PSTAG STH2X0 STH2X1 STH2X2 STH2X3
~
STH2X6 O
- New routines added in RELAP5YA C-13
l 9 SUBROUTINE JETPMPa CALCULATES EQUIVALENT LOSS COEFFICIENTS AND MOMENTUM MIXING TERMS FOR A JETPMP COMPONENT. SUBROUTINE JPROP JPROP PROVIDES JUNCTION FLUID PROPERTIES. SUBROUTINE MADATA THIS SUBCODE CCMPUTES THE THERMAL CONDUCTIVITY AND VOLUMETRIC HEAT CAPACITY FOR EACH MESH ELEMENT EVALUATED AT THE AVERAGE TEMPERATURE OF THE ELEMENT. SUBROUTINE MDOT COMPUTE MASS TRANSFER BETWEEN LICUID AND VAPOR. i CALLS THE FOLLOWINC ROU*INES: HELPTh BLOCK DATA MDYTBL
- MOODY CRITICAL FLOW TABLES (BLOCK DATA) l l
SUBROUTINE MIREC TRANSFERS RESULTS OF TIME STEP TO SAVE AREA FOR MINOR EDITS AND EDITS THE INFORMATION IF SAVE AREA IS FULL. CALLS THE FOLLOWING ROUTINES: POLATX
- New routines added in RELAP5YA C-14
- =- _ ._ - - _ _ _ - -- _
_;___-__ _ _ . --. j
'I lm L) l I
.i SUBROUTINE MOODY
- l
................. j PERFORMS TABLE LOOKUP FOR MOODY CRITICAL MASS FLUX, !
GIVEN-PRESSURE AND ENTHALPY. IT ALLOWS EXTRAPOLATION l IF PRESSURE OR ENTHALPY ARE OUTSIDE RANGE OF TABLES. il PRINTS AN ERROR MESSAGE THE FIRST TEN TIMES' i EXTRAPOLATION OCCURS. ! CALLS THE FOLLOWING ROUTINES: POLATX
)
l SUBROUTINE MOVER
................ 1 i
RESETS NEW VARIABLES TO OLD VARIABLES FOR NEXT TIME STEP CALCULATION CALLS THE FOLLOWING ROUTINES: CVMOV QVSUBR STATE TIMEL' SUBROUTINE MWROUT *
.( .................
1THIS SUBROUTINE COMPUTES METAL WATER REACTION HEAT PRODUCTION RATE AND THE DISTANCE THE REACTION HAS PENETRATED THE CLADDING FROM THE OUTSIDE TO THE INSIDE. SUBROUTINE MWRIN* THIS SUBROUTINE COMPUTES METAL WATER REACTION HEAT PRODUCTION RATE AND THE DISTANCE THE REACTION HAS PENETRATED THE CLADDING FROM THE INSIDE TO THE OUTSIDE. SUBROUTINE NATCIR NATURAL CIRCULATION HEAT TRANSFER CORRELATIONS CALLS THE FOLLOWING ROUTINES: STH2X3 THCON VISCOG VISCOL SUBROUTINE OUTPUT PRINTS MAJOR OUTPUTS f
'I
- New routines added in RELAP5YA C-15
l l l l O SUBROUTINE PGAPR
- CALCULATES FUEL RCD CAS PRESSURE CALLS THE FOLLOWING ROUTINES:
*0 LATE 0 POLATS RUPTEM SUBROUTINE PLASTIC *
.......c..........
THIS FUNCTION CALCULATES PLASTIC STRAIN ACCORDING TO FORMULATION BY F. COFFMAN USING HARDY'S DATA CALLS THE FULLOWING ROUTINES: POLATE2 POLATS RUPTEM SUBROUTINE PLOTIT DRAWS 3D PLOTS CALLS THE FOLLOWING ROUTINES: BCNPL DONEPL ENDPL ECF FABEND HEIGHT PLOT 3D PLTCOM TITLE UNIPLOT SUBROUTINE PLOTMD CONTROLS PLOTTING USING DATA GENERATED IN THIS CASE OR OBTAINED FROM A RESTART / PLOT FILE. CALLS THE FOLLOWING ROUTINES: DELETE FTBORG FTBRSV ISFDES LCONTG NEXTID PLOTIT PLOTSX SUBROUTINE PLOTSX* SORTS PLOT INFORMATION AND CALLS THE 2D AND 3D PLOT ROUTINES ROUTINES CALLS THE FOLLOWING ROUTIN23: BCNPL DMPLST DONEPL ENDPL FABEND FTBCHK FTBIN FTBRSV HEIGHT LCONTG LENGTH MCVE NEXTID PLOT 2 TITLE UNIPLOT UNIT
- New routines added in RELAP5YA O
C-16
7 N [
. b. .
30 SUBROUTINE PLOT 2D DRAWS 2D PLOTS WITH NCURVS CURVES DRAVN ON EA NOTE... PLOT 2D CALLS THE DISSPLA SOFTWARE SY CALLS THE FOLLOWING ROUTINES: GRID HEAD MESSAG MRSCOD NOBRDR YLOG XMESS GRAF RESET SUBROUTINE PLOT 3D PLOT 3D ... PLOTS 3-D SURFACES USING THE DISSPLA. SYSTEM CALLS THE FOLLOWING ROUTINES: AXES 3D TITL3D VUABSAXISDV BGNPL BOX 3D CURV3D ENDPL GRAF3D HEADIN NOBRDR SUBROUTINE PLTCOM PLTCOM . .. MAKES NOPLTS PLOTS WITH NCURVS CURVES DRAWN ON EACH PLOT FOR COMPARISON. NOTE ... PLTCOM USES THE DISSPLA SYSTEM' CALLS 1THE FOLLOWING ROUTINES: AXISDV BGNPL BLNK1 COMPLX CURVE DOT DUPLX ENDPL FRAME GRAF GRID HEADIN HEIGHT MARKER MESSAG SUBROUTINE PLTFND THIS SUBROUTINE DETERMINES THE LOCATION IN PLTREC DATA RECORDS OF THE INPUT PLOT REQUEST IALPHA,1NUM CALLS THE FOLLOWING ROUTINES: PLTFND ZEROUT
/
N. C-17 _ _ - _ - - _ _ - _ - _ - _ - - _ _ - _ _ _ _ _ _ = _ - _ _ _ - -- - - _ _ _
~
till SUBROUTINE PLTPAK*
?HIS SUBROUTINE WRITES THE PLOTFL FILE DURING STAND.ALONE
- LOT JOBS WHICH READ A PREVIOUSLY GENERATED RESTART. PLOT
'ILE. .
CALLS THE FOLLOWING ROUTINES: UNIT SUBROUTINE PLTREC THIS ROUTINE STORES DESIRED VARIABLES ON DISC FOR PLOTTING IF DESIRED. .THIS ROUTINE CAN BE GENERALIZED. l CALLS THE FOLLOWING ROUTINES: UNIT SUBROUTINE PLTRECR THIS ROUTINE STORES DESIRED VARIABLES CN DISC FOR PLOTTING IF CESIRED. USED IN COPYING PLOT RECORDS ON RESTART. PLOT TO INTERNAL PLOT FILE DURING RESTART. THIS ROUTINE CAN BE GENERALIZED. CALLS THE FOLLOWING ROUTINES: UNIT l SUBROUTINE PLTWRTR MOVE DATA FROM PLOT RECORD INTO STORAGE. USED IN RESTART WITH PLTRECR TO WRITE INTERNAL PLOT FILE UP TO FOINT OF RESTART. EviROUTINE POLATL 1 PERFORP.S LINEAR INTERPOLATION ON DATA IN TBLE USING ARG AS SEARCH ARGUMENT. INTERPOLATED VALUES RETURNED IN VAL. FIRST WORD OF TBLE CONTAINS FOUR 15 BIT QUANTITIES T'.i" TABLE TYPE, THE NUMBER OF ITEMS PER SET THE TOTAL NUMBER OF ITEMS, AND THE LAST USED SUBSCRIPT. REMAINING VALUES OF TELE CONTAIN THE TABLE. THE FIRST WORD OF EACH ENTRY IS THE SEARCH VARIABLE. LCM VERSION
- New routines added in RELAP5YA l C-18
j
.)
I -
; ,f i
~t .
SUBROUTINE POLATS
.................. J PERFORMS LINEAR INTERPOLATION ON DATA IN TELE USING ARG AS SEARCH i ARGUMENT. INTERPOLATED VALUES RETURNED IN VAL. FIRST WORD OF TBLE CONTAINS FOUR 15 BIT QUANTITIES. THE TABLE TYPE, THE. NUMBER OF ITEMS PER SET, THE TOTAL NUMBER OF ITEMS, AND = THE LAST USED SUBSCRIPT. REMAINING VALUES OF TBLE CONTAIN THE TABLE. THE FIRST WORD OF EACH ENTRY IS THE SEARCH VARIABLE.
SCM VERSION FUNCTION POLATXe THIS ROUTINE IS CALLED BY ROUTINE MOODY FOR ENTHALPY INTERPOLATION DOES EXTRAPOLATION IF REQUIRED AND PRINTS WARNING MESSACE. SUBROUTINE POLATE2
- THIS SUBROUTINE INTERPOLATES X FOR Y t, SUBROUTINE P00LNB(IEM1)
POOL NUCULATE BOILING HEAT TRANSFER CORRELATIONS CALLS.THE FOLLOWING ROUTINES: NATCIR STH2X0 SUBROUTINE PREDNB PRE-DNB FORCED CONVECTION HEAT TRANSFER CORRELATIONS CALLS THE FOLLOWING ROUTINES: CHFCAL REYFAC STH2XO SUFFAC SUBROUTINE PRESEQ THE PRESSURE EOUATION IS OBTAINED BY SUBSTITUTING THE MOMENTUM AND ENERGY EQUATIONS INTO THE MASS EOUATION AND USING STATE PROPERTIES. THE PRESSURE EOUATION HAS THE FOLLOWING FORM COEFP(I,J)eP(J) SOURCP(I)
;
- New routines added in RELAP5YA C-19
O SUBROUTINE PSATPD
........u........
CALCULATE SATURATION PRESSURE. PRESS, AND DPDT FOR A GIVEN TEMPERATURE OR SATURATION TEMPERATURE AND DPDT FOR A GIVEN PRESSURE. SUBROUTINE PSET PSET SETS ARRAY ELEMENTS AS REQUIRED BY PMINVR SUBROUTINE PSTAG
- ROUTINE TO FIND PRESSURE CO'ZISTENT WITH INPUT ENTHALPY AND ENTROPY !
USING A MARCHING METHOD. CALLS THE FOLLOWING ROUTINES: STH2x5 SUBROUTINE PSTDNB - POST.DNB FORCED CONVECTION HEAT TRANSFER CORRELATIONS CALLS THE FOLLOWING ROUTINES: FABEND HSUAB NATCIR STH2x3 THCON VISCOG SUBROUTINE PUMP CALCULATES NEW PUMP SPEEDS OR RESTORES OLD VALUES CALLS THE FOLLOWING ROUTINES: FOLATS PUMP 2 SUBROUTINE PUMP 2 INTERPOLATE PUMP HCMOLOGOUS CURVES. CALLS THE FOLLOWING ROUTINES: POLATS
- New routines added in RELAP5YA C-20
' SUBROUTINE QUENCH
- CALCULATES THE QUENCH FRONT POSITION FOR BOTTOM.UP AND/OR TCP-DOWN CUENCHING AND CALCULATES ENHANCED HEAT TRANSFER AT QUENCH FRONT LOCATION.
CALLS THE FOLLOWING ROUTINES: FABEND STH2X3 THCON TMSFB VISC00 SUBROUTINE QIRWR* DRIVER SUBROUTINE FOR METAL. WATER REACTION CALCULATION. SAVES PREVIOUL CALCULATION. CALLS THE FOLLOWING ROUTINES: MWRIN MWROUT SUBROUTINE RACCUM PROCESS ACCUMULATOR COMPONENT DATA. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV FTBSFT INP10 INP2 LCNTCS LCONTG LINES LINK MOVE SETNDF SUPROUTINE RADHT* CALCULATES THE RADIOSITIES AND NET RADIATIVE HEAT FLUXES AT RADIATING SUFACES SUBROUTINE RBRNCH PROCESS BRANCH, SEPARATOR, OR JET PUMP COMPONENT INPUT DATA CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV FTBSFT INP10 INP2 LCNTGS LCONTG LINES LINK MOVE NEXTID SETNDF
- New routines added in RELAP5YA C-21
I SUBROUTINE RCARDS SUBROUTINE READS INPUT DATA FOR THE NEXT CASE, WRITES DATA ON DISK IF NOT LAST CASE. CALLS THE'FOLLOWING ROUTINES: DELE *E FTBCHK FTBIN FTBORG FTBOUT FTBRSV FTBSFT INP INXGET LCONTG NFSIZE IABS SUBROUTINE RCDELT DELETES AN EXISTING COMPCNENT. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBOUT FTBRSV FTBSFT LCONTG LINES MOVE MASK SHIFT SUBROUTINE RCOMPN PROCESSES HYDRODYNAMIC COMPONENT DATA CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBCRG FTBOUT FTBRSV FTBSFT INP10 INP2 INP9 iSFDES LCNTCS LCCN*G LINK NEXTID RACCUM RBRNCH RCDELT RCORE RPIPE RPUMP RSNGJ RSK3V RTEE RTMDJ RTMDV RVALVE SUBROUTINE RCCMPT SUBROUTINE To READ THE PLOT COMPARISON DATA TABLES AND CURVE SPECIFICATIONS CALLS THE FOLLOWING ROUTINES: INP2 LINK RCRVSP RPUNIT SUB, ROUTINE RCONVR PROCESSES CONTROL CCMPONENT INPUT DATA. I CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK F* BIN F*BOPG FTBOU* F*BRSV FTBSFT INP10 INP2 INP9 ISFDES LCONTG LINK MOVE NEXIID O C-22 l l'
7____--_-__- (r SUBROUTINE RCORE , RCORE IS A DUMMY ROUTINE' SUBROUTINE RCRVSP SUBROUTINE TO READ PLOT CURVE DRAWING SPECIFICATIONS AND LABELING. (THE CURVE DRAWING SPECIFICATIONS ARE PACKED INTO THE LAST WORD ~0F KURVSP.) CALLS THE FOLLOWING ROUTINES: IN' 2 oDBROUTINE RDREDT p .............a... k-- PROCESSES INPUT DATA FOR REEDITING FROM A RESTART. PLOT FILE. CALLS THE FOLLOWING ROUTINES: DATE DELETE FTBCHK FTBORG FTBOUT FTERSV HEADER INP2 INPB IREDMI NEXTID REDMI REDRST SUBROUTINE REDMAP
- 4 THIS SUBROUTINE MAPS THE EDIT REQUEST PARAMETERS TO THE DATA IN PLTREC DATA RECORDS FOR REEDIT OPTION L CALLS THE FOLLOWING ROUTINES: ,
PLTFND ZEROUT l SUBROUTINE REDMI* PROCESSES MINOR EDIT CARDS CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBOUT FTBRSV FTBSFT INP10 INP2 INP9 ISFDES LCONTG LINK NEXTID
- New routines added in RELAPSYA C-23
O SUBROUTINE REDRST* READS RESTART INPUT FILE, INPUT DATA FOR OUTPUT RESTART FILE, AND COPIES INPUT.TO OUTPUT FILE. CALLS THE FOLLOWING ROUTINES: DELETE FABEND FAPFIM FTBCHK 'FTBEXP FTBOUT FTBRDC FTBRSV FTBSFT FTNREQ INP2 LCNTCS LCONTG LENGTH .%CVE NEXTID UNIT IABS LOCF KASK SHIFT SUBROUTINE REEDIT THIS SUBROUTINE DRIVES THE RE-EDIT PROCESSING OPTION i CALLS THE FOLLOWING ROUTINES: DELETE EDSET FABEND FTBCHK FTEEXP FTBIN FTBORG FTBRDC FTBRSV FTBSFT LCNICS LCONTG LENGTH MIRED MOVE NEXIID OUTPUT RE MAP UNIT FUNCTION REYFAC CALCULATE REYNOLDS NUMBER FACTOR F USED IN CORRELATION OF MACRO HEAT TRANSFER COEFFICIENT IN CHEN'S CORRELATION. SUBROUTINE ICRLT MUST BE CALLED FOR INITIALIZATION PEFORE THIS SUBROUTINE CAN BE USED. CALLS THE FOLLOWING ROUTINES: POLATS SUBROUTINE RCNTBL PROCESSES GENERAL TABLE INPUT DATA. CALLS THE FOLLOWING ROUTINES: DELETE FABEND FTBCHK FTBORG FTBOUT FTBRSV FTBSFT INP10 INP2 INP9 LCNTGS LCONTG LINK NEXTID SUBROUTINE RHTCHP PROCESSES INPUT DATA AND SETS STORACE FOR HEAT STRUCTURES. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBORG FTBOUT FTBRSV FTBSFT HT1INP INP10 INP2 INP5 INP9 ISFDES LCNTCS LCONTG LINK NEXTID ABS IABS MASK
- New routines added in RELAPSYA C-24
'5, ff n
(BLANK PAGE) e r C-25
l O SUBR5UTINE RKIN ADVANCES THE SPACE INDEPENDENT REACTOR KINETICS. CALLS THE FOLLOWING ROUTINES: POLATS SUBROUTINE RMADAT PROCESSES THERMAL PROPERTY COMPOSITION CATA. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBORG FTBOUT FTERSV FTBSFT INP10 INP2 INP9 LONTCS LCONTG LINK MOVE NEXTID SUBROUTINE RMIEDT PROCESSES MINOR EDIT CARDS CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBOUT FTERSV FTBSFT INP10 INP2 INP9 ISFDAS LOCNTG LINK NEXTID SUBROUTINE RNEWP PROCESSES INPUT DATA FOR NEW PRCBLEM AS OPPOSED TO RESTART, PLOT, REEDIT, OR STRIP PROBLEMS. CALLS THE FOLLOWING ROUTINES: DELETE FTBORG ICOMPN ICONVR IGNTBL IHTCMP IMIEDT INP2 INP8 IPLOT IRADHT IRKIN ITRIP RCOMPN RCONVR RGNTBL RHTCMP RMADAT RMIEDT RNONCN RPLOTN RRADHT RRESTF RRKIN RRSTD RTRIP RTSC WRPLID FUNCTION RONOFF J
............... 1 j
RONOFF ... ROUNDS VALUE TO THE NFIG SIGNIFICANT FIGURE i l 1 C-26 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -)
1
~
3 j)/ SUBROUTINE RNONCN. PROCESSES INPUT DATA FOR CONSTANTS NEEDED IN NONCONDENSIBLES CALCULATION CALLS .HE FOLLOWING ROUTINES: INP2-SUBROUTINE RPESTF READS RESTART. PLOT INPUT-FILE'AND WRITE INTERNAL PLOT FILE. CALLS THE FOLLOWING ROUTINES: DELETE FAPFIM FTBCHK FTBIN FTBORG FTBOUT FTBRSV FTBSF* INP2 ISFDES.LCONTG LENGTH MOVE NEXTID PLTMAP PLTPAK UNIT
.- ~ SUBROUTINE RPIPE
{ . . . . . . . . . . . . . . . . . PROCESSES PIPE COMPONENT INPUT DATA
, CALLS THE FOLLOWING ROUTINES:
DELETE FTBCHK FTBIN-FTBORG FTBOUT FTBRSV FTBSFT INP10 INP2 INP5 LCNTGS LCONTG LINES MOVE SETNDF SUBROUTINE RPLOPS SUBROUTINE TO READ THE PLOT OPTION CARDS AND PACK THE OPTIONS INTO ONE WORD CALLS THE FOLLOWING ROUTINES: INP2 RPUNIT SUBROUTINE RPLOT PROCESSES INPUT DATA FOR PLOTTING FROM A RESTART-PLOT FILE. CALLS THE FOLLOWING ROUTINES: DELETE FTBORG INP2 INP8 RPESTF G C-27 i L - _ - ____________-_ __ -.
I 1 O SUBROUTINE RPLOTN i
.........__.__... I i
SUBROUTINE TO READ THE PLOT HEADER CARDS. CALLS i SUBROUTINE INP. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBORG FT30UT FTBRSV FTBSFT INP2 INP9 ISFDES LCONTG NEXTID RCOMPT RPLOPS RPLT2D RPLT3D RSIZPL MASK SUBROUTINE RPLT2D SUBROUTINE TO READ THE PLOT REQUEST AND SPECIFICATION CARDS FOR EACH PLOT. CALLS THE FOLLOWING ROUTINES: INP2 LINK RCRVSP RPLCPS RSIZPL SUBROUTINE RPLT3C SUBROUTINE TO READ THE 3D PLOT TITLE CARD SUBROUTINE RPMPDC READS PUMP INPUT DATA (E.G. HEAD AND TORQUE TABLE) CALLS THE FOLLOWING ROUTINES: INP2 SUBROUTINE RPMPMD READS PUMP TWO. PHASE MULTIPLIER INPUT CALLS 'THE FOLLOWING ROUTINES: FTBBFT INP2 LCNTCS MOD SHIFT O C-28
L SUBROUTINE RPHPVNJ PROCESSES VOLUME AND JUNCTION DATA FOR PUMP COMPONENT. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBOUT FTBRSV FTBSFT INP2 LCONTG LINES MOVE SETNDF SUBROUTINE RPUMP PROCESSES PUMP' INPUT DATA CALLS THE FOLLOWING ROUTINES: FTBORG FTBSFT SUBROUTINE RRADHT
- READ RADIATION HEAT TRANSFER MODEL INPUT
- g- CALLS THE FOLLOWING ROUTINES:
\s,/ ' DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV INP2 INP5 NEXTID SUBROUTINE RPUNIT SUBROUTINE TO CHECK THE PLOT DATA UNITS KEYWORD AND TO INPUT UNITS CONVERSION COEFFICIENTS
. CALLS THE FOLLOWING ROUTINES:
.INP2 SUBROUTINE RRESTF READS RESTART INPUT FILE, INPUT DATA FOR OUTPUT RESTART FILE, AND COPIES INPUT TO OUTPUT FILE.
CALLS 'THE FOLLOWING ROUTINES: DELETE FABEND FAPFIM FTBCHK FTBORG FTBOUT FTBRSV FTBSFT FTNREQ INP2 LCNTGS LCONTG LENGTH MOVE NEXTID PLTRECR PLTWRTR UNIT
- New routines added in RELAP5YA i
e C-29 l: . G-_ _ _ - - _ _ - . _ - _
O SUBROUTINE RRKIN PROCESSES REACTOR KINETICS INPUT DATA. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBORG FTBOUT FTBRSV FTBSFT INP10 INP2 SUBROUTINE RRKINH COMPUTE INITIAL CONDITIONS OF FISSION PRODUCT DECAY GROUPS FROM INPUT POWER HISTORY. SUBROUTINE RRSTD READ DATA FOR RESTART FILE. CALLS THE FOLLOWG ROUTINES: FAFFIM FTBCHK FTBORG FTBOUT FTBRSV FTNREQ INP2 NEXTID UNIT SUBROUTINE RSIZPL SUBROUTINE TO INPUT THE PLOT SIZE SPE,CIFICATIONS CALLS THE FOLLOWING ROUTINES: INP2 SUBROUTINE RSNGJ PROCESSES SINGLE JUNCTION INPUT DATA CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV FTBSFT INP10 INP2 LCNTGS LCONTG LINES MOVE SETNDF SUBROUTINE RSNGV
................ 1 PROCESSES SINGLE VOLUHE INPUT DATA CALLS THE FOLLOWING ROUTINES:
DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV FTBSFT INP10 INP2 LCNTGS LCONTG LINES MOVE SETNDF C-30
4
% .,?N r
l/Q i i V SUBROUTINE.RSTFIN. D0' FINAL ACTIONS ON RESTART. PLOT FILE.
. CALLS THE FOLLOWING ROUTINES:
~*
FAPFIM FTR.CHK FTBIN FTBORG UNIT SUBROUTINE RSTREC' WRITES RESTART RECORDS ON FILE RSTPLT. CALLS THE FOLLOWING ROUTINES: FTBCHK FTBIN UNIT SUBROUTINE RSTRIP
. PROCESSES INPUT DATA FOR STRIP OPTION.
CALLS THE FOLLOWING ROUTINES: DELETE FTBORG FTBRSV FTBSFT INP2 INP8 ISFDES LCONTG LINK. NEXTID
, SRESTF UNIT
- SUBROUTINE.RTEE RTEE IS A DUMMY ROUTINE SUBROUTINE RTMDJ PROCESSES TIME DEPENDENT JUNCTION INPUT DATA CALLS THE FOLLOWING ROUTINES:
DELETE FTBCHK FTBIN FTBORG FTBOUT FTBRSV FTBSFT INP10 INP2 LCNTGS LCONTG LINES MOVE- SCNREQ SETNDF SU,BROUTINE RTMDV PROCESSES TIME DEPENDENT VOLUME INPUT DATA CALLS THE FOLLOWING ROUTINES: DELETE FTBCHE FTBIN FTBORG FTBOUT FTBRSV FTBSFT INP10 INP2 LCNTGS LCONTG LINES MOVE SCNREQ SETNDF C-31
O SUBROUTINE RTRIP PROCESSES TRIP CARDS. USED IN NEW AND RESTART PROBLEMS. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTBOUT FTBRSV FTBSFT INP10 INP2 INP9 ISFDES LCONTG LINK MOVE NEXTID SUBROUTINE RTSC PROCESSES TIME STEP CONTROL CARDS. IF RESTART TYPE AND IF NEW DATA IS READ, CURTCL IS SET NONZERO TO INDICATE RESTART AND POINTER IN CURCTL IS ADVANCED TO PROPER POSITION. CALLS THE FOLLOWING ROUTINES: DELETE FTPCHK FTBORG FTBOUT FTBRSV FTBSFT INP10 INP2 INP9 ISFDES LCONTG NE)?ID SUBROUTINE RUPTEM
- CALCULATES CLAD RUPTURE TEMPERATURE SUBROUTINE RVALVE PROCESSES VALVE INPUT DATA. A VALVL HAS THE SAME INPUT AS A SINGLE JUNCTION IN ADDITION TO ALVE DATA.
THREE TYPES ARE PROCESSED, TRIP VALVE, CHECK VALVE, AND INERTIAL VALVE. CALLS THE FOLLOWING ROUTINES: DELETE FTBCHK FTBIN FTSORG FTBOUT FTBRSV FTBSFT INP10 INP2 LCNTGS LCONTG LINES MOVE SETNDF SUBROUTINE SCNREQ PROCESSES VARIABLE REQUESTS USED IN MINOR EDIT RECUESTS, PLOTTING RECUESTS, AND TRIP SPECIFICATIONS.
- New routines added in RELAP5YA C-32
_ _ _ _ - _ _ . - R
1 O, ,
.[]
Y,) FUNCTION SIMUL TAKEN FROM THE TEXT BY CARNAHAN, LUTHER,AND WILKES BY R.T.~JENSEN ON MARCH 26,1977..... ( AND. RECHECKED BY-DEL MECHAM DEC. 1980)
-WHEN INDIC IS-NEGATIVE, SIMUL COMPUTES THE INVERSE OF THE N BY N MATRIX A IN PLACE. WHEN INDIC IS ZERO, SIMUL COMPUTES-THE N SOLUTIONS X(1)...X(N) CORRESPONDING TO THE SET OF LINEAR
;CUATIONS WITH AUCMENTED MATRIX OF COEFFICIENTS IN THE N BY N+1 ARRAY A AND IN ADDITION COMPUTES THE INVERSE OF THE
- COEFFICIENT MATRIX IN PLACE AS ABOVE. IF INDIC IS POSITIVE, THE SET OF LINEAR EQUATIONS IS SOLVED BUT THE INVERSE IS NOT COMPUTED IN PLACE. THE GAUSS. JORDAN COMPLE*E ELIMINATION KETHOD IS EMPLOYED WITH THE MAXIMUM PIVOT STRA*EGY.
! SUBROUTINE SORPTR SUBROUTINE TO SORT AND COLLECT PLOT VARIABLE POINTERS...FILID(19) i SUBROUTINE SRESTF j' '
READS RESTART INPUT FILE, INPUT DATA FOR STRIP FILE, AND PLOTALF AND-1 PLOTNUM RECORDS.- CALLS THE FOLLOWING ROUTINES: FAPFIM FTBCHK FTBOUT FTBRSV FTNREQ INP2 LENGTH NEXTID UNIT SUBROUTINE SSTAT CONTROLS SOLUTION OF STEADY STATE THERMAL-HYDRAULIC PROBLEM. SUBROUTINE STATE COMPUTES EDUATION OF STATE FOR BOTH TIME DEPENDENT VOLUMES AND TIME ADVANCED VOLUMES. INCLUDES MASS ERROR COMPUTATIONS. CALLS THE FOLLOWING ROUTINES: HELPTR PSATPD STH2XB STH2XF STH2XO STH2Xi STH2X2 STH2X3 STH2X4 STH2X6 VISCOG VISCOL FUNCTION STMCON
- THIS SUBROUTINE COMPUTES TRANSPORT PROPERTIES FOR STEAM, AND WAS TAKEN FROM 700DEE/EM b
t.g
- New routines added in RELAPSYA C-33
i i O SUBROUTINE STRFIN DO FINAL ACTIONS ON STRIP FILE. CALLS THE FOLLOWING ROUTINES: FAPTIM FTBCHK FTBIN UNIT - SUBROUTINE STRIP WRITE STRIP FILE BY COPYING INFORMATION FROM RESTART-PLOT FILE. CALLS THE FOLLOWING ROUTINES: FTBEXP FTBORG FTBRDC FTBRSV FTBSFT LCNTGS LCONTG LENGTH NEXTID STRFIN UNIT SUBROUTINE STSET PROTECTS AND CHECKS CCDING FOR STEADY STATE ITERATIONS, LOAD REQUIRED FILES FROM DISK, COMPUTES INDEXES OF ACTUAL LOCATIONS FOR COMPCNENT AND JUNCTION BLOCKS, CALLS SUBROUTINES TO ACQUIRE MATRIX SOLUTION SPACE AND CCNTROLS FOR LOADING MATRIX, AND CALLS SUBROUTINE TO RELEASE EXCESS SPACE. SUBROUTINE STSTAT CALLS STSET TO SET UP ARRAYS AND INDEIES AND CALLS SSTAT TO DO THE ADVANCEMENT / ITERATIONS FOR STEADY FTATE. CALLS THE FOLLOWING ROUTINES: FTBEXP SSTAT STSET FUNCTION SUFFAC CALCULATES THE SUPPRESSION FACTOR S IN THE CALCULATION OF THE MICR0 CONVECTIVE HEAT TRANSFER COEFFICIENT IN CHEN'S CORRELATION. SUBROUTINE ICRLT MUST BE CALLED TO INITIALIZE THIS SUBROUTINE BEFORE IT IS USED. CALLS THE FOLLOWING ROUTINES: POLATS REYFCC l till C-34 u__. __
ec. .
.3 p * , .
l i 'p- ' - u 1 1 FUNCTION SURTEN 1 1 1
, COMPUTES SURFACE TENSION OIVEN-TEMPERATURE. FORMULA'FROM SCHMIDT.
PROPERTIES OF WATER AND STEAM IN SI UNITS, 1969.. SUBROUTINE SYSITR-THIS ROUTINE NOT USED. SUBROUTINE SYSSOL-SOLVES THE MATRIX EOUATION FOR CHANOE IN PRESSURES.- SUBROUTINE TCNVSL SETIINDEXES.FOR ADVANCEMENT OF CONTROL VARIABLES. r /\'j FUNCTION THCON
.{ ..............
~
COMPUTES THERMAL. CONDUCTIVITY OF SATURATED LIQUID AND SATURATED AND SUPERHEATED VAPOR, 1967 ASME. TABLES. CALLS THE FOLLOWING ROUTINES: POLATS SUBROUTINE TMSFB
- CALCULATES THE MINIMUM STABLE FILM BOILINO TEMPERATURE SUBROUTINE TRAN TRAN CONTROLS THE TIME. STEP ADVANCEMENT OF THE THERMAL-HYDRAULIC EQUATIONS CALLS THE FOLLOWINO ROUTINES:
CONVAR DTSTEP HTADV HYDRO RKIN TIMEL TRIP TSTATE
- New routines added in RELAPSYA x
C-35 L______________ _ _ i
. \
l 9 l SUBROUTINE TRIP
)
TESTS TRIP CONDITIONS AND SETS TRIP CONDITIONS AND TIME OF TRIP. l l SUBROUTINE TRNCTL CALLS TRNSET TO SET UP ARRAYS AND INDEXES AND CALLS TRAN'TO DO THE l TRANSIENT ADVANCEMENT. CALLS THE FOLLOWING ROUTINES: l TRAN TRNFIN TRNSET SUBROUTINE TRNFIN I REACQUIRE SCM. LCM SPACE AND DELETE ALL SCM FILES. I CALLS THE FOLLOWING ROUTINES: DELETE FTBEXP FTBSFT ISFDES NEXTID NFUNIT l SUBROUTINE TRNSET i PROTECTS AND CHECKS CODING FOR TRANSIENT ADVANCEMENT, LOAD REQUIRED j FILES FROM DISK, COMPUTES INDEXES OF ACTUAL LOCATIONS FOR COMPONENT ' AND JUNCTION BLOCKS, CALLS SUBROUTINES TO ACQUIRE MATRIX SOLUTION SPACE AND CONTROLS FOR LOADING PATRIX, AND CALLS SUBROUTINE TO
~
RELEASE EXCESS SPACE. CALLS THE FOLLOWING ROUTINES: DELETE DMPLST FABEND FTBCHK FTBIN FTBORG FTBRDC FTBRSV FTBSFT ISUMRY LCONTG NEXTID TCNVSL TSETSL SUBkOUTINE TRNSIS TRANSITION PROCESSING SUBROUTINE, NOT OPERATIONAL i C-36 i
. ? I, I
}#:
1 L.
,I d . ,
k[ i f SUBROUTINE TSETSL OBTAINS SPACE AND SETS ARRAYS NEEDED TO, CONTROL LOADING AND SOLVING OF PR*SSURE EQUATIONS.
' CALLS THE FOLLOWING ROUTINES:
DMPFIL DMPLST FTBRSV FTBSFT LCONTG NEXTID ZEROUT SUBROUTINE TSTATE' STEAM. WATER STATE CALCULATION WITH AIR PRESENT FOR TIME DEPENDENT VOLUMES AND JUNCTIONS CALLS THE FOLLOWING' ROUTINES: POLATS PSATPD STH2XB STH2XF STH2X0 STH2X1 STH2X2 STH2X31
'STH2X6 O .SUBRO'UTINE VALVE CHECKS: TRANSIENT FLOW, PRESSURE, AND TRIP TO DETERMINE VALVE STATUS CALLS THE FOLLOWING ROUTINES:
POLATS ~ SUBROUTINE VEXPLT VEXPLT CALLS THE PUMP (CENTRIFUGAL) AND ACCUMULATOR SUBROUTINES, COMPUTES INTERMEDIATE ESTIMATED PHASE VELOCITIES, INITIALIZED
- CERTAIN SOURCE TERMS USED IN ECFINL, AND COMPUTES THE DISSIPATION TERMS AND PV TERM FOR THE ENERGY EQUATION.
CALLS THE FOLLOWING ROUTINES: ACCUM HEADLN HELPHD HELPTR PUMP a O C-37 E - - _ _ _ - _ _ _ _ _ . _ _ _ _ - - - - - _ . .- . - _ _
l i { SUBROUTINE VFINL VFINL COMPUTES FINAL NEW TIME PHASE VELOCITIES BASED ON NEW AND OLD TIME PRESSURE DIFFERENCES, AND COMPUTES THE JUNCTION MASS FLOW RATE. CHOKED, PUMP AND ACCUMULATOR JUNCTIONS HAVE FINAL VELOCITIES CALCULATED PRIOR TO THIS SUBROUTINE. CALLS THE FOLLOWING ROUTINES: HELPTR FUNCTION VISC00 CALCULATES WATER VAPOR VISCOSITY. CALLS THE FOLLOWING ROUTINES: VISCOL FUNCTION VISCOL CALCULATES LIQUID WATER VISCOSITY. CALLS THE FOLLOWING ROUTINES: FABEND STH2X0 SUBROUTINE VOLVEL CALCULATES AVERACE VOLUME VELOCITIES BY AVERAGING THE AVERAGE JUNCTION VELOCITIES IN AND OUT OF THE VOLUME CALLS THE FOLLOWING ROUTINES: HELPTR SUBROUTINE WRPLID WRITE TWO RECORDS ON RSTPLT TO IDENTIFY DATA ON PLTREC RECORDS FOR STRIPPING AND PLOTTING. FIRST WORD OF EACH RECORD IS "PLOTALF" AND "PLTNUM". REMAINING WORDS ARE ALPHANUMERIC AND NUKSER PORTIONS CF VARIABLE REQUEST CODES FOR INFORMATION PLACED ON "PLOTREC" RECORDS. THERE IS A ONE TO ONE CORRESPONDENCE BETWEEN THE POSITONS OF EACH RECORD. O l C-38 '}}