ML19310H054
| ML19310H054 | |
| Person / Time | |
|---|---|
| Site: | Washington Public Power Supply System |
| Issue date: | 08/01/1986 |
| From: | Holmberg B WASHINGTON PUBLIC POWER SUPPLY SYSTEM |
| To: | Martin J NRC OFFICE OF INSPECTION & ENFORCEMENT (IE REGION V) |
| References | |
| REF-PT21-86-266-000 GO1-86-0113, GO1-86-113, PT21-86-266, PT21-86-266-000, NUDOCS 8608150026 | |
| Download: ML19310H054 (2) | |
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%ISn%QCDtSE PROPnET4aY Ct.466 2 Patt.tsussay i i
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i SCALING ANALYSIS FOR AP600 CONTAINMENT i
,. PRESSURE DURING DESIGN BASIS ACCIDENTS
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. June 1996
, by .
l D. R. Spencer ;
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! This document contains information propnetary to Westingbouse Elecuic Corporauon, it is submited in confidence and is to be used solely for the purpose for which it is furnished and returned upon request. This i document and such informauon is not to be reproduced, transeunad. disclosed or used otherwise in whole or in part without pnor wnnen authoruauon of Wesunghouse Electnc Corporanon, Energy Busmess Systems Unit.
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- WESTINGHOUSE ELEC11 tlc CORPORA 110N ,
i Systems and Major Projects Division
- . P. O. Box 355 l Pittsburgh, Pennsylvania 15230 355 i
C 1996 Westinghouse Electric Corporation All Rights Reserved l 4
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.e r 4 9608150026 960808 PDR ADOCK 05200003
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- TABLE OF CONTENTS ;
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PREFACE . . .... . . ........ .... .. ................. , ,..... ,,,, 7
SUMMARY
. . ... ........................ ....................... .... 11
1.0 INTRODUCTION
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.0 The AP600 PI RT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 i
3.0 Energy. Pressure and Momentum Equadons , , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 l.
3.1 Containment Gas Energy and Pressure . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 17 3.2 PCS Air Flow Path Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Heat Sink Energy Equadons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3.1 Energy Equadon for Internal Drops . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3.2 Energy Equadon for the Break Pool . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 l> 3.3.3 Energy Equadon for the IRWST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 !
3.3.4 Energy Equadon for the Liquid Film . . . . . . . . . . . . . . , . . . . . . . . . . . . 20 ,
' 3.3.5 Energy Equation for internal Solid Heat Sinks . . . . . . . . . . . . . . . . . . . ... 21 3.3.6 Energy Equadon for the Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3.7 Energy Equadon for Baffle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 i 3.3.8 Energy Equadon for Shield Building . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3.9 Energy Equadon for the Chimney . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.0 Constitutive Equations for Heat. Mass and Radiadon Transfer . . . . . . . . . . . . . . . . . . . . . . 26 4.1 R adiadon Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2 Convection Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 26 4.2.1 Turbulent Free Convecdon Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2.2 Laminar Free Convection Heat Transfer . . . . . . . . . . , , . . . . . . . . . . . . 26 4.2.3 Turbulent Forced Convection Heat Transfer . . . . . . . . . . . . . . . . . , , . . . 27 4.3 Condensation and Evaporation Mass Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.4 Coedensadon and Evaporation Heat Transfer . . . , . . . . . . . . . . . . . . . . . . . . . . . 32 4.5 Liquid Film Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.6 Heat Si nk Conductances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.0 Di mensionless Quantides . . '. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.1 Constant Dimensionless Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.2 Variable Dimensionless Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 ;
5.2.1 Values of Dimensionless Quandties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.2.2 Heat Sink Surface Areas During Transients . . . . . . . . . . . . . . . . . . . . . . . 37
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utmvcout PROPRIEhRY Ct.rss 3 5.2.3 Heat Sink Characteristics During Transient . . . . . . . . . . . . . . . . . . . . . . . 39 5.2.3.1 Drops . . . . . . . . .. ... ..................... . 39 5.2.3.2 Break Pool . ...... . ......... ... .. ........ 39 5.2.3.3 Heat Sinks . .. ....... . .... .. ....... ....... 40 5.2.3.4 Containment Shell . . ...................... .... 41 6.0 Normallied. Dimensionless Rate of Pressure C!.ange Equadon . . . . . . ............,.. 42 6.1 Pre s s ure Term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 6.2 Break Source Gas Term . . . . . . . . . . .......................... ..... 42 6.3 B reak Source Liquid Term . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6.4 I RWST Source Te rm . . . . . . . . . . . . . . . . . . . . . . . . . ' . . . . . . . . . . . . . . . . .. 43 6.5 Condensadon/ Evaporation Phase Change Terms . . . . . . . . . . . ............. 43 ;
6.5.1 Phaic Change Mass Transfer Term . . . . . . . . . . ............, . 43 -
45 i 6.5.2 Convection and Radiadon Heat Transfer Terms . . ................
6.6 Normalized. Dimensionless Heat Sink Energy Equations . . . . . . . . . . . . . . ..... 45 l
- 6. 6.1 Source Drops . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 l 6. 6. 2 B reak Pool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .' . . . . . . . . . . . . . 46 6.6.3 Heat Sinks . . . . . . . . . . ................................... 47 .
4 6. 6.4 S he l l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
- 6. 6.5 B attle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.6.6 Chimney /S hicId Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 l
I 7.0 Val ues for PI Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 ' -
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t 7.1 Energy Conductance Pi Values . . . . . . . . . . . . . . . , , . . . . . . . . . . . . . . . .' . . . . . 52 7.2 Heat Sink Energy Pi Values . . . . . . . . . . . . . . . . . . . . . . . . . . . ..,.......... 53
- 7. 2 .1 D rops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 53 l
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- 7. 2.2 B re ak Pool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 I 7.2.3 Solid Heat Sinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
- 7. 2.4 S he l l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 7.2.5 B affle and Chi mney . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 7.3 Columinment Pressure Pi Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ 55 8.0 PCS Air Flow Path Momentum Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 8.1 Dimensionless PCS Momentum Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 l 8.2 Dimensionless, Normalized PCS Momentum Equations . . . . . . . . . . . . . . . . . . . . . 61 8.3 Numerical Values for Scaled Momentum Groups . . . . . . . . . .. . . . . . . . . . . . . . . . . 61 9.0 Test Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................... 63 9.1 Condensadon Mass Transfer Test Scaling . . . . . ......................... 63 9.2 Evaporation Mass Transfer Test Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 l
l 9.3 Forced Convection Heat Transfer . . . . . . . . . . . . . . . ..................... 65 9.4 PCS Air Flow Path Flow Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 i
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u rsn%cuotst Paorantav Ct. Ass 2 9.5 Wind Effects . . . . . . . . ..... .... ... . . ........ ,,. .... . . . 66 i
9.6 Wetting Stability . . . . . . . . . . . . . .... .... ................ ... 66 10.0 Containment Momenutm Scaling . . . . . . . ..... ....... ....... .... . ... . 68 10.1 Froude Number Relationships . . . ... .. .... ....... . . .. ... 68 10.1.1 Forced / Buoyant Jet . . . . . . . . . . . . . . ........ ... .. ... 68 10.1.2 Containment Stability . . ................... .. .. .. . 69 10.2 Ap' :icadon to AP600 . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ .... 70 10.2.1 Loss of Coolant Accident . . . . . . . .................... ... . 72 ,
10.2.2 Main Steam Line Break ........................ . . ..... 73 10.3 Application to Large Scale Tests . . . . . . .................... ... .... 73 10.2.1 Loss of Coolant Accident . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
- 10. 2.2 M ai n S t e am Li ne B re ak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 10.3 Application to Large Scale Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , 75 10.3.1 LOCA Configuration . . . . . . . . . . . . . . . . . . . . . . . . ............. 77 10.3.2 MSLB Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 1 1.0 Conc l u si o ns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I 12.0 Nome nc l ature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 3.0 R e fere nce s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDICES A Development of Containment Pressurization Equadon A1 B Tables of Pt Group Calculation Results B1
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%r3TINGnOlsE PROPRIE14kV Cl.ASE 2 l
LIST OF TABLES I.Rhl.t ERE i
Table 2-l Phenomena Idendfication and Ranking Table Summary . . . ............ .. .. 16 ,
Table 41 Heat Sink Conductances . . . . . . . . ........ ... ....... ...... .. . . . . 33 Table 51 Reference Values for Dimensionless Parameters . . . . . . . . .... ..... ... 36 Table 5 2 Heat Sink Areas During DECLG and MSLB Transients . . . . . ..... .. 37 Table 71 Energy Transfer Conductances to Heat Sinks Scaled to Shell . . . . . . . . . . .. 52
. Table 7 2 Drop Specific and Characteristic Frequencies . . . . . . . . . . . . . . . . . . . . . . . . .... 53 Table 7 3 Pool Specific and Characterisde Frequency . . . . . . . . . . . . . . . . . . . . . ......... 54 Table 7 4 Solid Heat Sink Specific and Characteristic Frequencies . . . . . . . ... .. . ..... 54 ;
Table 7 5 Shell Specific and Characteristic Frequencies . . . . . . . . . . . . . . . . . ........... 55 Table 7-6 Baffle and Chimney Specific and Characterisde Frequencies . . . . . . . . . . . . . . . . . . . 55 Table 7 7 RPC Pt Group Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . ...... 56
, Table 8 1 PCS Air Flow Path Momentum Equadon Groups . . . . . . . . . . . . . . . . . . . . . . . . . 62 ,
1- . Table 9 1 Test Scaling for AP600 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 l Table 9 2 Comparison of AP600 Operating Range to Tests for Liquid Film Stability . . . . . .. 67
Table 101 Geometric Parameters and Critical Froude Numbers for AP600 and LST LOCA andMSLB........................................................ 70
- LIST OF FIGURES
- TJsst East Figure i PCS Test and Analysis Process Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Figure 2 One. Dimensional Energy Balance and Temperatwes for Energy Transfer Resistance to Solid H e at S i nks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 i
Figure 3 One Dimensional Energy Balance and Temperatwes for Energy Transfer Conductance through the Containment Shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Figure 4 Temperstwe and'Concentrauon Dependence of the Dynamic Viscosity of an Air Steam Gas Mixture............................................................... 29
. Figure 5 Temperature and Concentration Dependence of the Thermal Conductivity of an Air Steam Mixture............................................................... 30 Figure 6 Temperature and Concentration Dependence of the Prandtl and Schmidt Numbers for an Air-S te am Mi xture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 ,
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%rsmcuotst PoorsurTany Ct. Ass 2 Figure 7 AP600 Containment Pressure during Blowdown . . . . . . . . . . . .... .... ,,. 3g ,
I Figure 8 Passive Cooling System Air Flow Path Momentum Parameters . . . . . . . . 59 l
Figure 9 Free Convection Condensadon Data from the Large Scale Test Compared to the ;
Correlation and the AP600 Operating Range . . . . . . . . . . . . . . . . . . . . .... ... . 64 l Figure 10 Forced Convection Evaporadon Data Compared to the Correladon and the AP6(O Range of Operadon ...................... ................ .. .. .. 64 Figure iI Mixed Consection Heat Transfer Data Comparison to die AP600 Operadng Range . . . 67 ,
. Figure 12 Froude Numbers inside Containment for the AP600 DECLG . . . . . . . . . . . . . . . . . . 71 ,
Figure 13 Main Steam Line Break Jet and Volumetric Froude Numbers . . . . . . . . . . . . . . . . . . 71
. Figure 14 Steam Mixing Data above and below the Operating Deck from the LST . . . . . . . . . 72 1
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l wtsnscuot.st Paoesurraav ct. Ass 2 ,
l PREFACE -
i This report docurwnts the scaling evaluadons performed to support the PCS DB A evaluation model.
Additional primary reports documenting evaluation model bases include the accident specification and !
+ PIRT repon", the WGOTHIC code description and validadon repon'. and the' WGOTHIC applications !
repon . Test data reports, test analysis reports, and phenomenological model repons are incorporated
- into the primary repons by reference. Although the focus of this repon is to develop the sealing laws for AP600 PCS performance and relevant tests, a background section is provided to show how the !
overall program fits together.
Background
The evaluation model for the PCS Design Basis Analysis (DB A) has been developed using elements of sealing (top-down modelling of the integrated components), testing, and analysis (bottom:up !
phenomenological models and evaluadons). The results have been used to identify bounding models i
and input values for use in the DBA evaluadon model 'the results of the evalua' ion model provide conservative predictions of design basis transient pressure and temperature response for the containment. L The PCS DBA methodology has followed an approach which can be organized into four elements as -
shown in Figure 1. The elements include tasks which together provide a structured, traceable, and :
pracdcal method for 1
- specifying the scenario,
- identifying phenomena imponant to the transient.
- evaluating data and scale effects,
- documendng and validating the computer code, ,
a assessing margins and uncenainties, and
- developing and applying the evaluadon model:
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The process is represented as a once-through flow diagram for simplicity. The actual process followed includes many iterations between the various tasks. For example, to better represent the observadons of the LST dome temperature distribution due to the subcooling of the film applied to the LST, the l
initial WGOTHIC code version used in 1992 was augmented by the addition of a model for convective heat transpon for the liquid film. In addidon, extensive review by representadves of regulatory agencies, industry, and academia were incorporated into the process. The end result is documentation which describes the PCS DBA evaluation model and its bases in an auditable, traceable manner. Following is a brief descripdon of the process elements and reference to documentation.
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HErrocnou,E PeoraET4aY Ct. Ass 2 !
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. l l Element I AP600 PCS Requirements and Code Capabilities l f
I l The PCS DBA methodology development process began with a review of the AP600 design and DB A I
scenarios and an identificadon of phenomena important for AP600 containment pressurization. From i t
, this review, an initial test program was defined and a computer code was selected.
A Phenomena identification and Ranking Table (PIRT) is developed to identify the key thermal- !
hydraulic phenomena which govern the transients of interest. The PIRT" ranks phenomena according l to their relative importance to the pardcular transient phase of interest. The PIRT process included
- input and review by representative; of academia, regulatory authorities, and cross-functional
, Westinghouse technical reviews. The nases for high, medium, and low rankings are documented with the PIRT. A key result of the PIRT is that the dominant phenomena for transferring heat from the l
containment is mass transfer condensadon on the inside and evaporadon on the outside.
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In parallel with bottom up phenomena evaluations, the WGOTHIC computer code was selected, ,
upgraded, and frozen to allow explicit modelling of many of the phenomena identified in the initial
! review. As the scaling analysis and tesdng programs progressed, code upgrades to better model j experimental results were completed according to guidelines consistent with lifecycle management i IJ identified in NQA 2a Part 2.7. Extensive hand calculations and spreadsheets were used to verify correct programming of the upgrades as documented within the Westinghouse QA program. ;
Documentation of the code used in the evaluation model has been issued.W j Element 2 Assess Code Versus Tests and important Procesass .
Analyses and computer code validadon were used to identify the most appropriate models and biases :
to use in the PCS DBA. The PCS test program includes separate effects tests, as well as a Large i Scale Test (LST) that provided data for simultaneous extemal evaporadon and internal condensation in an integral setting. The LST was not designed to simulate a particular AP600 transient response.
Rather, the LST varied boundary conditions over significant portions of the AP600 range to gain insight into the physics, confirm the selection of mass transfer correlations that were based on smaller ;
scale tests, and examine the performance of the WGOTHIC computer code in modelling the AP600 phenomena. Where the LST does not well represent the AP600, other data and scaling consideradons
- j. were used together with bottom up phenomena modelling to develop a bounding approach.
. The PCS test results were documented, including separate effects" and integral effects'. The PCS test data and other data from the literature were used to provide input to code validadon'. Validation was used to study how the oversimplification inherent in the lumped parameter WGOTHIC formuladon applies to the AP600. Tne lumped parameter limitations lead to the potendal for compensating errors, so that a methodology to bound the effects of compensating errors was identified (Reference 1, page 8-9). The effects of noding on WGOTHIC results were an important output of validation, insight from validadon was used to develop a bounding evaluation model in Element 3. Validadon with LST data was also performed using the distributed parameter WGOINIC formulation. The more detailed 9.
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i wrsnscr.ast reormanav Ctans 2 distributed parameter model(Reference 1. Appendix A) better represents phenomena, more closely !
matches the LST data, and helped confirm the ranking of phenomena in the PIRT. !
A scaling evaluadon of AP600 was performed which provided additional confirmadon of the PIRT phenomena and ranking. Scaling identified the appropriate nondimensional parameters and the effects of facility scales. Scaling also provided insight into the ranges of parameters expected in AP6mL The results of scaling, testing, and code validation were used to establish a bounding analysis approach for each of the PIRT phenomena. Section 2 summarizes the PIRT high and medium ranked phenomena and the approach that is used to address each.
Element 3 Assess Uncertainties and Develop Bounding Models Uncertaindes were assessed and together with the results of code validation were used to develop a method of applying me WGOllilC lumped parameter formuladon to create a bounding DBA evaluation model. Key results are summarized as follows.
The effects of uncertainty contributors which were not readily quantified as bias and distribudon were 3 quantified separately using sensitivity calculations and ranging of the parameters which influence l l
! pressure. Such phenomena are bounded by applying conservadve boundary conditions or introdring i biases into the evaluation model as discussed in Section 2.
~ Element 4 Perfonn DBA Calculations and Compare to Success Criteria The evaluadon model was developed as described above to produce conservative, bounding pressure transients for each accident phase. The acceptance criteria are that the peak pressure must remain below the design pressure of 45 psig, and the pressure at 24 hours2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> must be less than,1/2 of the design ,
i pressure. Road maps' have been provided which show, for each phenomenon, 1
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- relevant model in the code,
- test basis, i
+ report references.
- summary report conclusions.
- applicability of LST, ,
e validation basis summary, i
- how validation results are used, and ,
- how uncertainty is bounded.
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, Wamwasotas PuermartARY CIA 38 2 Element Objective OUTPUT i
+ scenenoisenunashon Select and freeze computer code j based on phenomenological + N W W Ap000 , e ,,,,, ,,,,,,,
containment preneure pressatione
+ evensmonuses me**mems i
(
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+ Scahng Asemas code capaldtity to needel
+ .
- 2 important phenomena by comparteen '+ c.s.
(opease) mi con -
. to test data and select bounding anahmte approach .
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+ casovaNeason l, report and
- noene sweenos If Assees uncertainees and range of. + Appearessememod 3 par = net == to d aion kaunians *r=== *ea=*
l m ter input saue I + Presen APeso noene i
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1f 4 perform Ap000 DBA esloadadone + connnusonman and compare to success cratoria ,
i Figure 1 PCS Test and Analysis Process Overview Fweuremos 10 9
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wisnscuotst roomanav ct.us a ;
SUMMARY
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This document presents the scaling analysis for the pressure in the AP600 containment during a design basis accident with the following bases:.
- The double ended cold leg guillotine (DECLG) pipe break and the main steamline break l initiated from 1029r power, identified in the SSAR' as the I.OCA and MSLB with the Umiting pressure responses, were selected for evaluation. l
- The integrated stmeture for technical issue resolution (IS11R), presented in NUREG/CR 5809,'
and the scaling example by Wulff' were used for guidance in the preparation of tlus document.
- Containment pressure, energy, conductances, internal momentum, and external momentum were evaluated.
- Previous iterations on the scaling analysis were performed and documented.""
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- Comments received from the NRC and ACRS review were addressed and incorporated. ,
The major elements of this scaung analysis are:
- Control volume equadons were developed to describe the rate of change of the containment gas energy and pressure. These equadons were coupled by conductances to energy equations for internal heat sinks and to the external PCS through the shell.
- Closure reladonships (phenomenological models) were selected for the dominant transport processes.1he closure relationships are dimensionless, scalable, and valid for applicadon to AP600 and the tests. ,
- Scaling groups (pi groups) were developed by normalizing and 'nondimensionalizing the conservados equadons, using initial and boundary conditions, in a form that shows,the-important dimensionless parameters in each pi group.
- Values were calculated for the pi groups during each time phase to quantify the relative importance of the transport processes and components.
- The dominant energy transport process inside containment (free convection condensation mass transfer) and the dominant transport process outside containment (forced convection evaporadon mass transfer) were scaled and compared to test data and the range of AP600 operating parameters L
f 11 e
wasmcnotst Pnopeuttant ct. Ass 2 The process satisfied the AP600 needs for scaling which are:
1 Quantatively evaluate the relathe magnitude of transport processes and physical components as they affect energy, pressure, and momentum inside the AP600 containment and in the AP600 air flow path.
Use the quantitative evaluation to rank the importance of components and transpon processes and thereby confirm the PIRT. ,
Confirm the PIRT to define the processes and components that must be included in, or bounded by, the evaluadon model Identify the important dimensionless groups and their range needed to scale test results to AP600. .
The informadon presented in this document meets the AP600 needs for scaling analysis.
8 t
9 4
6 I
i i
'S g
wisnscuot6t Peormarraav Ct. Ass 2 ;
4 l
l l
1.0 INTRODUCTION
l l
This report presents the scaling analysis for pressurization of the AP600 containment. The scaling i
analysis was performed to identify the phenomena necessary to be modeled for accurate predictions of pressure within the AP600 containment during a design basis accident (DB A) and to permit a scaled '
comparisori of the supporting separate effects and integral effects tests to the AP600 performance.
Specifically addressed are:
j The development of the energy and rate of pressure change (RPC) equadons for the ;
containment gas volume, and the energy equadons that couple the internal heat sinks and euernal passive cooling system (PCS) to the containment gas.
. t The dimensionless groups needed to scale jet and plume momentum (mixing and stradfication) in the containment volumes are presented and reladonships between AP600 and the LST are discussed.
i The development of the momentum equadon for the air flow through the FCS air flow path ,
that includes the downcomer, riser, and chimney.
'he i dimensionless, normalized pressure, energy, and air path mor.Ntum equations that produce the pl groups requireo to scale containment pressure, heat sink energy interactions, i energy transfer resistances, and PCS momentum. .
Quandficadon of the pi group values for the AP600 phenomena, providing:
Identificadon of the dominant transport processes and components (phenomena)
- necessary for an evaluation model to predict containment pressurization.
l l Validation of the ranking of PIRT phenomena.
Disnensionnem groups necessary to scale separate effects and integral effects test l '
j phenomena.
The evaluation of pi groups in this document assumes the containment steam / air atmosphere is well-mixed. The actual effect of stratification in AP600 is to reduce the effectiveness of some internal heat sinks and improve others, which will change the magnitude of pi groups representing heat and mass transfer to portions of the concrete and steel heat sinks. However, the actual effects of mixing and stratification do not change any of the conclusions of this report about the relative magnitude and-timing of phenomena in AP600 The effects of stratification on AP600 are conservatively treated in the evaluation model as discussed in the mixing and stratification repost".
13 l' .
CEmvasotC3 PeoPREfray class 2 i
This documenteses guidance from the scaling methodology for severe accidents presented in NUREG/CR 5809', and the example presented by W.Wulff" for scaling interconnected regions.
The Westinghouse containment scaling analysis has evolved through a series of issued documents, presentations, and reviews. Extensive input has been received from the USNRC and the ACRS Thermal Hydraulies Subcommittee.
Westinghouse issued Reference i1, Passive Containment Cooling System Preliminary Scaling l Report", July 1994 Westinghouse presentation to USNRC,"AP600 Passive Containment Cooling System (PCS)
Scaling . Iteration i Report Review Kickoff Meeting, July 26,1994.
Westinghouse issued Reference 12, Scaling Analysis for AP600 Passive Containment Cooling System, October,1994.
. Westinghouse presentation to ACRS Thermal Hydraulics Subcommittee, March 29,1995.
' NRC presentation of (LASL) review comments on Containment Scaling, June 20 22, 1995.
NRC issued several requests for additional information that are answered in this document.
This document was prepared for submittal to the USNRC to support design certification of the Westinghouse AP600.
e l'
t, 14
wtsmcCDL$t Paorma74ay ct.AEG 2 j 2.0 The AP600 PIRT The phenomena considered for the AP600 containment pressure calculadon were listed and ranked in f the PIRT". Those ranked high or medium are listed in Table 21 and most are quandfied in the scaling analysis. Some are addressed by separate, detailed evaluadons in which AP600 parameters were ranged to derive bounding inputs for the evaluation model. These include: ..
Mixing and Stradficadon A summary of the consequences of mixing and stradficadon on containment scaling was presented in Section 1.0. The mixing of air and steam inside containment, and the transpon rates between interconnected gas volumes (compartments) is addressed in detail in the mixing and stradficadon report".
i intercompartment Flow The mass flow rate of air and steam between interconnected gas !
volumes affects heat sink udilzation and is addressed in the mixing and stratificadon report.
i ,
Source Fog Source droplets (fog) occur during blowdown and increase the steam source density, thereby reducing its buoyancy. However, during blowdown, mixing inside containment is momentum and pressure dominated, not buoyancy dominated. After blowdown .
> drops do not occur in the break source, so the post blowdown source buoyancy is not affected.
. The effect of drops is addressed in the mixing and stratification report. However, the effect of droplets as heat sinks is addressed in this scaling document.
Liquid Film Stability - Liquid film stability affects the amount of surface area that can be covered by the PCS cooling wpter. TWpl shows the wetted surface area increases while the shell surface heats, and by 660 sec.,(af 120 gpm PCS water flow rate) the entire applied flow rate is evaporated. Documentation is provided in the liquid film stability repon",
4 e
e, 15
. c ,
1 wisre,cuout Peorannar Ct.us 2 l Table 21 Phenomena identification and Ranking Table Summary !
HIGH RANKED PHENOMENA Phenomenon Effect on Containment Break Source Direction and momentum can dominate circulation Miting and Stratificadon Lack of circuladon and air blankedng can affect access of steam to heat l
...".$$$E.P$.$$$...$..., sinks for condensation heat removal Heat Sink L'Ulization Fluid Compliance Stores mass and energy in atmosphere, increasing pressure Source Fog Affects circuladon, stradficadon, buoyancy Mass Transfer The dominant process for removing mass and energy from the containment gas and from the evaporating external liquid film.
Internal Heat Conduction Limits conduction heat transfer into heat sinks and through shell Resistance Heat Transfer Through Water and noncondensable layer on upward facing horizontal surfaces Hcrizontal Liquid Films limits heat and mass transfer to horizontal heat sinks PCS Natural Circulation . Convective tir flow provides effective convective heat and mass transfer
. from containment shell.
Film Stability Affecu the upper limit for water coverage on ' enternal shell MEDIUM RANKED PHENOMENA Heat Transfer Convective heat transfer to shell, heat sinks, riser, and downcomer Radiation Transfers heat from gas to surfaces, and from shell to baffle and shield i Film Thermal Carries 15% of condensadon energy to the IPWST and break pool, and Capacitance absorbs 5% of energy from the external shell sarface.
Liquid Level Rising liquid levels block certain circulation flow paths as the transient progresses
, l 4
16
wrsnwootst Pnormartany Chas 2 f
3.0 Energy. Pressure and Momentum Equations 3.1 Containment Gas Energy and Pressure The conservadon of mass and energy equadons for a gas volume with sources, sinks, and convective {'
flows, and the RPC equadon are derived in Appendix A. The derivadon includes a statement of ,
assumpdons, the definidon of mixture properdes for the binary alt / steam gas mixture, and the j manipuladon of the thermodynamic equadons of state and conservadon of mass and energy for a control wlume to produce the energy and pressure equadons for the gas volume inside containment.
l l l The containment gas energy equation is:
(g) mb = m,(h -h) + m,(h,-h) +
[h,,, (h, h,) + h,y+ h,,) A,(T,-T))
p dt + .P dm i dt ,
The containment gas pressure equadon is: i e
f i
' T T (1 +yZT ) P (1 +yZT ) P 4
(1 +Z ) y dP ' ** h, -h, + y( I + Z ) P Z,,R ~
(y - 1) Ji
~
(y - 1 p ZR ,
f (y - 1) K "" (y-IT Y K'
f '
h"'-h" + y(I +Z ) P Z.,R., . y(1 +ZT ) P Z,,R,,
+ m .
(y - 1) pT (y - 1) p ZR
.."'( ,
s ( ,
.p h, ,, "
, y(t .z T) p Z,,,R,, , (t .yz T)1 (y - 1) p ZR (y -1)
+ h,'d+ h,,, A,(T, -T)
(h,- h,) p,, . (2) ,
lhe mass flows in Equadons (1) and (2) include the break and IRWST sources with given time histories, convected mass Dows ( i subscripted) through openings between compartments, if the equadon is applied to interconnected Mrapartments, and phase change mass flows (j subscripted) due
! to evaporadon or condensadon between the gas and the heat sinks. In addition, wherever there are heat sinks, radiados and convection heat transfer may also occur, The mass and energy that enter the gas control volume are stored in the gas volume and cause the gas pressure, temperature, and density to increase. Storage in the gas volume is reduced by condensation ;
and energy transfer to the heat sinks and to the containment shell.
.The thermodynamic state of the control volume is defined by the total pressure, temperature, the mass of air, and the mass of steam, and therefore, all of the thermodynamic properties in Equadons (1) and (2) are specified by these parameters. The convected mass flows are zero if the control volume includes all of the containment gas, or may be calculated from a flow network model if individual compartments are considered. The phase change mass flows depend on both the thermodynamic state of containment, and the state of the heat sinks. The state of the heat sinks depends on the time history .
of the heat sink mass and energy interactions with the containment gas, which are tracked using 17 i
- - ~ - - .,.-..-.c - --.,7 --
_ ._ . - _ _ _ . _ __ _ _ _ _ _ _ _ _ _ . . _ _ _ _ ~ - _ - . _ _ _ _ _ _ _ _ - _ _ . _ . _ . . _ _ _ _ _ _ _ _ _ _ _
%ISI1%Cnot4 PROMUET4ay Cialis 2 energy equadons developed for the individual heat sinks.
3.2 PCS Air Flow Path Momentum The equation derived by Wulff" for buoyancy driven flow through the primary loop is also valid for ;
the downcomer riwr chimney air flow path. The transient equation includes the buoyancy and drag terms derived previously":
r s K, + f,- (3) de,t L' dy l
_ $2 T di Li M 4 2
where i represents each segment of the closed path around the PCS air flow path.
3.3 Heat Sink Energy Equailons Heat sinks reduce containment pressure by absorbing energy that reduces the mass and energy stored in the gas atmosphere. Heat sinks are both solid and liquid Solid heat sinks are composed of steel or 4 concrete and include walls, floors. ceilings, exposed structural steel, equipment, and the containment shell Liquid heat sinks include drops, pools, and films.
Soild heat sinks include steel, concrete, and steel jacketed concrete. These are treated as distinct heat sinks because each has a different thermal conduction characteristicts. Heat transfer to steel heat sinks is limited by the heat and mass transfer coefficient, and to concrete is is limited by internal conduction resistance. Solid heat sinks are affected by condensation, radiation, and convection heat transfer.
Evaporation from solid heat sinks requires a continuous liquid source which is not present inside containment. Consequently, solid heat sinks only reject heat by radiation and convection.
Liquid heat sinks include drops, the break pool, the IRWST, and films. These, can interact with the '
containment gas by both evaporation and condensation, as well as by radiation and convection heat transfer, The shell is separased into three regions, each with a disdncdy different external energy transfer resistance. The three regions are subcooled, evaporating and dry, conesponding to the dominant
- process on the outside of the shell, in the subcooled region, the liquid film is the heat sink.
Evaporation, radiation, and convection from the subcooled film are neglected. In the evaporating region all of the energy is transferred to the riser by evapotation and convection, and to the baffle by radiation. In this scaling analysis, the evaporating film is assumed to have no sensible heat capacity, in the dry region, there is no external liquid film: heat is rejected by convection heat transfer to the riser gas and by radiation to the baffle.
18
. . . . . - . ,, - - ~ , . - - - - , .
e wasmonots: PaorannaY class 2 I
l A general form.of the energy equadon for liquid and solid heat sinks is:
l
= th.c,(T -T) - 6,,c,(T,, - T) + 4 - 4, (4) !
inc, where the convective flow terms may be present for liquid heat sinks, but are absent for solid heat ,
sinks. Equadon (4) is modified as necessary for each of the heat sinks. Each of the q terms in Equadon (4) may include the three parallel energy transfer components: mass transfer, convecdon heat transfer, and radiation heat transfer. Using the subscripts c, r, and m to denote convection heat transfer, radiation heat transfer, and condensatiorvevaporation mass transfer, and adding an x for the
- exterior of containment:
d) d=d+4"+([' and d=d+d+d l Each of these energy transfer terms can be written as the product of a conductance and a tempera'ture t
difference,4" = HAT. In addition, the mass flut is written in terms of mass conductance, temperature l difference, and enthalpy change, th" = h,AT/(h,.h,). The subscript e is useil to denote an equivalent heat transfer coefficient when conductances are combined in series and/or parallel. .
- 3.3.1 Energy Equation for laternal Drops Drops, or fog particles, are created when the blowdown break source steam disrupts and disperses a fraction of the break liquid along with the gas. The drops of imerest are those with a diameter of 0.001 inch or less that are transported with the break steam and do not readily settle out. Although
- the drops may persist for some time, they have a settling rate and hence, the conservation equadons include both in and out convecdve mass terms. The drop mass conservation equation is:
&n g " *m - *se ~ sene ,,
l The drops are assumed to enter containment as saturated liquid at the containment total pressure. This introduces saturated drops with a temperature and steam partial pressure higher than the containment
- temperature and steam partial pressure. Consequently, the liquid drops evaporate to the containment gas and also transfer heat to the gas by convection and radiation. The energy equation for the drop is: ,
er (7) an.c.,j %c,,(T -T) - 6.c,,(T,,-T) - h,A(T -T) where h, = h. + h, + 1. 4 3.3J Energy Equation for the Break Pool The liteak pool is created from the blowdown break liquid that is not dispersed along with the gas and pours into the bonom of the steam generator and reactor cavities. The break liquid is assumed to leave the break sanarated at the containment total pressure. The resulting temperature is always greater 19
- _ ~ _ . - . - _ - - - - - - _ - _ - - - - _ ~ - _ - - - - . - - - - - - - _
J wtsrwcmotst reorannar ct.us 2 l
l
- 1
- i than the containmenf gas temperature, since the containment temperature remains approximately at the l saturation temperature corresponding to the steam partial pressure. Liquid from drop fallout and l
! condensation below the operaung deck also drain into the break pool. Liquid *..at condenses and falls 7 l out above the operating deck drains into the IRWST. i l The energy equadon for the pool is: :
m, c,, 4T' = thm,c,,(T -T) + th w ,,(T. c -T) - h, A(T, -T) t81 i
where h, = h,, + h, + h,. ;
! 3.3.3 Energy Equation for the IRWST L
! 1he IRWST collects the condensate from above deck, and aRer the primary system depressurires.
- provides a gravity flow of borated water into the reactor. The gas space above the water level is dead-ended and does not circulate because the gas above deck is less dense than that in the IRWST gas i volume. The above deck gas is less dense because the initial temperature of the IRWST water is 120 "F or less, and the saturadon temperature of the warmer condensate liquid that drains into the tank is less than that of the atmosphere above, otherwise it would not have condensed. While flowing across the floor to the tank the water may heat, but at most it can only heat until the saturadon pressure of i the water reaches the steam partial pressure of the atmosphere at the operating deck. Consequently,it cannot become a vapor source by headng from the atmosphere, either while above deck or after draining into the tank. (The draining fluid is assumed to stratify Pad spread across the surface without ,
mixing with the cooler, deeper water). Consequendy, the water in the IRWST, and the gas in :he space above the water level both remain stably stratified relative to the atmosphere in the above <leck volume above the tank.
! i l As a stably stratified, dead-ended volume, only the small volume of steam forced into the IRWST gas volume by containment pressuritation will condense. With only 0.7% of the contalmnent volume, the 4
net effect of the small, stably stratified, dead-ended IRWST gas volume and its interactions with the IRWST water and the containment atmosphere is negligible. Thus, it is not necessary to perfor'n scaling calculations for the IRWST.
3.3.4 Energy Egustles for the Liquid Film J For containment analysis, liquid films can be categorized as draining films or stagnant films. Films that form on structures with slopes greater than l' drain and remain thin. The film on the shell was
! determined to be less than approximately 0.005 inches thick and have a heat transfer coefficient of approximately 900 B/hr ft2 *F. Horizontal surfaces facing downward show similarly high heat .
I transfer Coefficients '.
20 4
i !
%Es11%CuoL5E P90 PRE 14av CIA 6s 2 ;
The rado of the heat capacity of a draining film to that of the average steel heat sink can be expressed as:
% , (P O C.)fa. , 60 0.005 1 = 0.012 !
t u (p o c,). 490 0.5 0.11 l i .
1 Since the film heat capacity is only 1% of the heat sink heat capacity, the film absorbs to little heat t
that its mass can be neglected relative to the mass of the heat sink in ter.ns of transient performance, Although the film heat capacity is neglected in the scaling analysis, the film conductance is included in the conductance term that couples the gas to the heat sink, as described in Section 3.3.5.
Stagnant films are those that do not drain effectively and consequently build up sufficient thickness to l
lead to a significant heat transfer resistance to the surfaces on which they form. They also present large surface areas for evaporation / condensation mass transfer interactions that is, they behave as a l l
large shallow pool. However, having formed by condensadon on cooler surfaces, the film is cooler than the atmosphere and behaves as a heat sink until reheated by the atmosphere. The sensible heating ;
can only progress to the point that the film partial pressure is equal to that of the atmosphere. After condensing, the films can have little net effect on containment heat removal or addition.
Consequently, horizontal liquid film energy transport is neglected and only their thermal conductance is considered.
' . ne P
i Liquid films can form to sufficient depth on nearly horizontal surfaces that their conductance beccmes' significant in limiting heat transfer. However, rather than tracking draining film flow rates, estimating the flow paths, and calculating film conductances, a more conservadve approach of eliminating heat transfer surface area is used in the evaluation model. That is, the surfaces are assumed to be adiabatic, i
For concrete floors this effectively eliminates the heat capacity of the floor.
The only steel structures of any size with upward facing horizontal surfaces are the crane rail, stiffener l
i ring, and hatch covers. These are modeled by eliminating the upward facing surface area, while retaining the mass, since the downward facing surface area is still active.
Summarizing for liquid films, the heat capacity of draining film is neglected relative to the heat capacity of the surface they fonn on, and the conductance is included in the heat transfer coellicient.
The heat capacity of stagnant films constitutes a heat sink for the gas, so is conservadvely neglected, and the conductance to the' horizontal surface is assumed to be so poor that the horizontal surface heat capacity is neglectea.
3.3.5 Energy Equation for laternal Solid Heat Sinks The conduction terms necessary to couple the containment atmosphere to the heat sink surface are defined using the one-dimensional energy balance from the containment atmosphere to a heat sink shown in Figure 2. The energy balance shown assumes the total energy flux out of the containment g
21
,I wisnwuolSE PRortEnRY Ct.us 2 l
gas is reduced by the liquid enthalpy of the condensed film prior to entering the liquid film, rather than midway through the film as is believed to be most correct. However, the conductance of the film is more that 10 times that of the conductance from the atmosphere to the film, and the energy carried away by the liquid is only 1/10 that of the condensing gas energy, so the error introduced by assuming the liquid energy is removed at the surface rather than midway through the liquid film is negligibly , i small. This assumption greatly simplifies the resulting mathematics.
The energy fluxes can be related to the series temperature drops by assuming thermal conduction through the liquid film, and condensation, convection and radiation heat transfer to the liquid surface.
For time greater than zero, the heat conducted into the solid and the solid surface temperature can be calculated by various analytical models. The analytical models depend on whether the solid is modeled as a lumped mass, a thick wall, or a semi-infinite conductor, such as concrete.
Containment inner Film Heat Sink 4". s .
- h. .
4 Y h, 7 > h,, > ,
-r , h 4.
- -, 4 y e
,th,,w T T,,, Tw :
f Figure 2 One Dimensional Energy Balance and Temperatures for Energy Transfer Resistance to Solid Heat Sinks
~
h temperature drop relationships to the heat flunes are developed from Figure 2 for the containment to inner film surface, and inner film surface to solid heat sink surface:
T -T,, = d'% + h, + h,)*' and T,,-T, = ('(h,yi (10).
These two equations are added, so T T, remains on the left side of the equation, and only multipliers on 4," remain on the right side of the equation:
(11)
(7.T,3 = gN .h, .h,)* + (h,))
The term in brackets defines the inverse conductance from the inside of containment to the solid heat
. sink surface. The effective heat sink conductance is defined h, = [(h + h,4 h,y' + hi' T' and is combined with the energy equation to give:
. age, #T = h, A(T -T,) (12)
' 6e rg 22
r l
%ESTi%GlootbE PROP 9tIET4ay Ct. Ass 2 3.3.6 Energy Equation for the Shell The conduedon terms necessary to couple the containment atmosphere to the shell, and the shell to the riser are defined from the one-dirnensional energy balance shown in Figure 3. As was done for the heat sinks (Section 3.3.5) the total energy Oux out of the containment gas is first reduced by the liquid enthalpy of the condensed film. The shell has such a high heat capacity that it cannot be neglected until several thousand seconds into the transient. The energy Ouxes in and out of the shell can be related to the series temperature drops by assuming thermal conduction through the Olm, condensadon and evaporation mass transfer, and convecdon and radiation heat transfer. The ten.perature drop rela:.lonships to the heat fluxes are presented in the following equations.
]' Baf0e Inner l e External '
gntainment Film Shell Film Riser h.,, Q"g {
4".*,h.%
4",
- h, 4" -'P- 4",g-i >- 4"g-P 4"4 ho - q"o-4", ,h, ,
h, i
h,, f h,
\ v 4%
\ '( \
hsh" i , m"c,T T T,, , T., T.,, T., T,,, T. T, Figure 3 One Dimensional Energy Ba' awe and Temperatures for Energy Transfer Conductance through the Containment Shell
- -QC #
The temperature drops through each of the conductances into the shell are shown in Figure 3 and are the same as for energy transfer into the heat sink developed in Section 4.3. That is:
(13)
(T -T,3 . gg .h, + hy' + (b,)*')
where the inverse of the term in brackets is the conductance from the containment atmosphere to the shell inner surface, h,.. = [(h. + h, + h,) + hi' T 3
Energy transfer out of the shell through each of the conductances to the riser and baffle are also shown in Figure 3. The shell outer surface to external film outer surface temperature drop is:
Tu -T,=d (14) and the external film outer surface with convection heat transfer and evaporation to the riser bulk flow, and radiation to the baffle is:
f bl T,,,-T, = 4 " hjh o " IIN
+h, (T,,,-T,)
r ,g 23 1
- - . -.~. - - -
Wisrt%CnotSE PROPn5'14ay Ct.46s 2 These two equadons are added, resuldng in the equation:
i f I*h (16) l (T,s, -T,) = q.,.,,(hy'+ h , + h,., + h,, (T * - T,,,)
(T,,, - T,) i
. ( s. 1
- The term in brackets represents the inverse conductance for the outside of the shell, h,. = [+ Ni' + th,
+ h, + 4 ) ' l. Equations (13) and (16) can be combined with the general energy equation for a heat sink, Equation (4), to give:
m e, dT* = hw ,(T A -Ty - hw A,(Tu -T ) (17) 6
- Steadv. State .
At steady. state the transient shell term drops out of the energy equadon so the containment gas can be coupled directly to the riser. With q, = % the energy equadon becomes:
(18)
- (" = (T -T )[(h, +h, +hyl + (h,)*8 + (hg8 + (hg8 + (h, +h, +h,) l) i where the bracketed term is the equivalent conductance, h,.
3.3.7 Energy Equation for Bame The energy equation for the baffle is formulated assuming radiation heat transfer from the shell to the baffle, and convection heai and mass transfer from the riser to the baffle on the inside. On the outside, the baffle radiates to the shield and transfers heat by convection to the downcomer. The baffle is a thin steel member with such a small Blot number that it is well represented as a lumped mass with idendcal bulk and surface temperatures. Both sides of the baffle are subject to forced l
convection. The forced convecdon is always dry on the downcomer side and is dry on the riser side until approalineesty 300 sec. (at 220 gpm PCS water flow rase) when the second weir begins to spill over. Thereafter, the riser side of the baffle may be wet or dry, depending upon the radiation heat transfer rate to the baffle and the convection heat transfer from the baffle to the riser and downcomer.
The energy equation for the baffle is:
d (19) gc,[r = h,A(T-T) - h,A(T -T )
l I where the effective conductances are defined h,, = [(h + h, + h,r' + hi' l'8 and h , = (+ hi' + (h.
+ h, + h,r' l,
L sg 24
wwrr,cuotse emesurr$av class 2 3.3.8 Energy Equation for Shield Building The shield building is a concrete heat sink with dry forced convection to the riser and radiation heat transfer from the baffle. Because it is so thick, it is modeled as a semi infinite solid with the same j energy equation as the heat sink concrete.
(he shield building can potentially effect the downcomer air flow rate by heating the downeomer air, thereby inducing buoyancy that counteracts the riser and chimney buoyancy. The maximum effect j results if all the radiation from the baffle,is assumed to be deposited into the downcomer, rather than some being absorbed in the concrete. It will be shown that both the energy magnitude is very small, l
! and the counterflow buoyancy is small, so it is reasonable to simplify the analysis by neglecting the
! shield energy interactions and allowing the haffle radiation to be deposited directly into the downcomer, 3.3.9 Energy Equation for the Chimney The chimney and upper part of the shield building is a large concrete structure that can cool the PCS air flow before it exits from the chimney, and thereby reduce the natural circulation buoyancy force.
l The concrete was modeled with the same equation as for the internal heat sinks, except that radiation 7
l to the concrete is aeglected. Neglecting radiation reduces the heating rate and overpredicts the heat j removal from the air flow path, thereby minimizing the air flow rate.
The effective heat sink conductance is defined h, = [(h + h, y' + hi' t' and is combined with the l general energy equation for a heat sink to give:
m .c, dT* = h, A(T -T,) - (E i dt l'
1 25
l I
wrsny,notse PaormErramy cuss 3 )
I 4.0 Constitutive Equations for Heat. Mass, and Radiation Transfer j 4.1 Radiation Heat Tran'sfer ]
'"he energy transfer due to radiation heat transfer is calculated from:
4," = a e (T * -T' ) or 4," h,(T -T,) (21) 2 i where the conductance is h, = ocf(T.Tm) and f(T.Tm) = (T + Tm)(T + T m). The character e is the product of the emissivity and beam length for radiation from the containment gas to the surface.
4.2 Convection Heat Transfer The convection heat transfer can be written in terms of a conductance and a temperature difference:
4," = h,(T -T,) (22) where the conductance, h, is given by one of the following constitutive correlations.
> 4.2.1 Turbulent Free Convection Heat Transfer The correlation selected" for scaling turbulent free convection heat transfer is used for all surfaces inside containment, horizontal as well as vertical, except for drops:
t h, = hw - 0.13 L(Gr Pr)W = 0.13 g
k h*pr W (23)
(v/3)W t Pe 2
~
, et, C The term (ap/p) is the difference between the bulk density and surface density, divided by the bulk density. Note that in this form the Grashof number with its length dependence no longer appears and ,
the heat transfer coefficient is dependent only on local properties. This is valid for turbulent free
' convection heat transfer for which Gro < 10', which is the case over all but the lower 2 to 3 feet of height of heat sinks and the shell, after the first few seconds of the transient. The turbulent free convection correlation underacimmes heat and mass transfer at lower Grashof numbers, so its use'is conservative then. The turbulent free convection correlation is shown in Section 9 in a dimensionless form compared to the LST condensation data. The correlation compares well with the data, especially considering that the LST is 1/8 geometric scale and therefore has more of its total height within the 2 to 3 foot height limit for turbulent free convection. i 4.2.2 Laminar Free Convection Heat Transfer Laminar free convection heat transfer is considered for the drops that result from the break liquid during blowdown, because their diameter is so is so small (- 10' ft) that Gr a 1. For this case, Kreith" presents the correlation for small spheres:
L l
. *i 26
i l
i wumcuotst enormarTrav Class 2 I
h, = hw =2 (24) f 4.2.3 Turbulent Forced Convection Heat Transfer In the riser the heat transfer is turbulent forced convection for shell surface temperatures more than 2 1 above the environment air temperature". The correlation selected" for turbulent forced convection in a channel is:
h, = h% = 0.023 Ref'Pr W (25) where the hydraulic diameter is 2 times the riser width.
On the inside of containment, turbulent forced convection is expected during blowdown, and produces heat and mass transfer rates significantly greater than free. convection. However, forced convection is ,
conservatively neglected during blowdown, free convection is assumed. This conservatism results in underpredicted heat sink energy absorption during blowdown, and a small overprediction of .
< containment pressure. The assumption does not change the conclusions of the scaling analysis.
.4.3 Condensation and Evaporat ion Mass Transfer .
l The rate of evaporation and condensation mass transfer is determined from the heat and mass transfer
- analogy. The analogy can be expressed as Sh/Nu = (Sc/Pr), or, in terms of the mass trahsfer i coefficient:
sW k = _ h,PD' r 3c - (26)-
s 1 RTPm k (Pr;
! With the definition m" = k,M,.AP,, an expression for condensation or evapcration mass flux is:
2 gi, , h,M.PD, AP. 'g W RTPu k ( Pr, ,
I J
With the steam density defined p., = M.,P/RT the mass flux is:
j
& ,, =
h, p D, AP. '-Sc' W (28) k P (Pr, 1
a Condensation and evaporation mass transfer are calculated from Equation (28) and the appropriate heat transfer correladon from Section 4.2. Three distinct mass transfer correlations result from the turbulent 27
l wEsnvCDLsE Phorturr4RY Lt.ASE 2 free, turbulent forced, and landnar free convection heat transfer correlations. For turbulent free comection mass transfer:
4 = 0.13 (v:/g)W Pu1 ph Sc
" ' " (29)
For turbulent forced convection mass transfer:
thlL = 0.023 * ' *Rc['Sc W (30)
~ ;
' l For laminar free convection mass transfer to the drops: i l
.s P iW (31) mm = 2.0 .D, L AP.
P ,i'sc-Pr, A correlation for the air steam diffusion coefficient is available to use in the mass transfer correlation":
a 14.2W f T M 2 (32)
D, = 0.892 R/hr P 4grR, The temperature in the diffusion coefficient is the absolute boundary layer temperature: the arithmetic mean of the bulk and surface temperatures.
The dynamic viscosity, thermal conductivity, Prandtl, and Schmidt numbers in the heat and mass transfer correlations are evaluated at the boundary layer steam mole fraction and the boundary layer temperature. These parameters have been evaluated over a range of temperatures and air / steam
.ompositions and are presented in Figure 4, Figure 5 and Figure 6. The boundary layer steam mole l
fraction is assumed to be the arithmetic mean of the bulk and surface values.
1'
's 4
28 l _ _ _
WasnwgotSE PROPRETARY CLA56 2 j l
I i
i l
I L
1.6 l
- - - ~ ~ - - - - - - - ~ ~ ~ ~ ~ ~ ~ ~ - ~ ~ ~ ~ ~ - ~ ~ ~ ~ ~ - -
1.5-1 l- o 240 F
- - ~ ~ - - ~~-- ~~~- -~~--~~-
8 1.4- - -
210 F -
1.3 . . . . .... .... . . . . .....1.80...F................................ .
150 F l 69 NF - - - ~ ~ ~ - - - ~ ~ -
E $ 1.2- - - - - - -~ ~ -
l l ',
{
i 3.3 5 1- --~~~ ---~~~~~~-- -- --- -- - - - -
.e. g I-
- ~ ~ ~ ~ ~ ~ ~ - - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -- ~ ~ ~
0.9-
}l .
- - - ~ ~ ~ ~ ~ - - - - - - - ~ ~ - - - - - - - " - - - ~ ~ " - - - - - - - -
0.8-0.7 . . . . . . . . .
0 0.1 0.2 0.3 0.4 0.5 ' O.6 0.7 0.8 0.9 1 Mole Fracta dSteam f .
Figure 4 Temperante ami Concentrauon Dependence of the Dynamic Viscosity of an Air Steam
. Gas Mixture l
I h
t u
i f
U l
29
- - - , - , ,m e - ,, , - - - - - - - - - -
s
.I e f i
%EsmcaotsE PaonusTray Ct. Ass 2
- 1 i
e n
0 4
l 1 t
Ia l
0.02 l
~ ~ - - ~ ~ ~ - - ~ ~ ~ ~ - - ~ ~ - - - ~ ~ ~ ~ - ~ ~ ~ - - - ~ ~ ~ ~ ~
I 0.019-
\
l QQ,g3g-- . - - - - - - . . ~ . - - - . - - - ~ ~ ~ . . - ~ ~ . ~ - - . . - ~ ~ . . . - . - - - . . -
a.
~~~~~- - - ~ ~ ~ - - - E~~~~~-~~~-----
l
, $_ 0.017- 10 --F
.i 0.016- - -- - ~ ~ - ~ ~ ~ ~ - - -- - - - ~ ~ - -
MF
~~~---- ---"- - - - - - - - ~ ~~ ~ ~~-- - - - -
0.015- 50 F 0.014- ~ ~ ~ ~ ~ ~ - ~ ~ - - - - - WF~- - - - - - ---
- ~ - - ~ ~ - ~ ~ ~ ~ ~ - - ~ ~ ~ ~ ~ ~ - - - - - - ~ ~ - -
1 0.013-y 0.012- ~~~~:-~~~~~~~--~~~~~~-----~~~~~~~~~-
- - ~ ~ ~ ~ ~ ~ ~ - - ~ ~ ~ ~ ~ - ~ ~ ~ ~ ~ ~ ~ - - - - - - - - - ~ ~
0.011- .
0.01 . . . . . . . . .
0 0.1 0.2 0.3 0.4 0.5 - 0.6 0.7 0.8 0.9 1 l
Mole FracDon of Steam I
Figure 5 Temperange and Concentration Dependence of the 'Ihermal Conductivity of an Air-
! Steam Mixture l
1 I
t I
e l
l tw
! g~4 1
1 t
r 1 1
wEsmonotst enoramrmv Cuss 2 4
l l
l l
1 J
I I
i I
I 1 l' 1
t
. . 4 ce %_ 4 ..... ...........
g.e, rm - .... .. . . . .. . .. . . .. .. . . ... . . .. . . .. .
mc 0.8- - - - " - - - - - - - - - - " " - " - - - - - - " - - -
120 F 0.7- ---~~PMM----------------.-...---.---.------. s i
r QJ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
l:' .~~~~--------------
. . . . . . . . .. . . . . . . . . gggggg. . . . .. . 110,F, , , , , , , , ,,,,,,
0.5- ---
====w44e.....-
- l Schmdt Number 240 F 1 j b 0.4- - - - ~ ~ - - - ~ ~ - ~ ~ - - - ~ ~ ~ ~ - - - - - -
0.3- - - - - - - - - - - - - - - - - - - - - - - - ~ ~ ~ - - - - - - - - - - - - - -
l 1 l
0.2- ~ ~ ~ ~ - - - - - - ~ ~ ~ ~ ~ - - - - - - - - - ~ ~ ~ ~ ~ -
i j-..............................................m.............................................. ,
1 1
0 . . . . . . . . ;
i 0 0.1 02 ~ 0.3 0.4 0.5 0.6 0.7 0.8 0'.9 1 ;
Mole Fracton of Sloam i 1
i i
s f
l Figure 6 Temperature and Concentration Dependence of the Prandtl and Schmidt Numbers for an )
l F Air. Steam Mixture r
I I
I i
e i
l'k 31 l
I
r wtrnscuotse reocaaway ct. Ass 2 .,
i l 4.4 Condensation and Evaporation Heat Transfer The heat transferred by condensation and evaporation mass transfer is the product of the mass transfer -
rate and the enthalpy transported. For condensation, the condensed mass leaves the gas control' volume with gas enthalpy, h,, and the condensate retains the liquid enth,ilpy, hr. The difference, h, ,hr is greater than h,, since the gas temperature is generally higher than the liquid temperature. For evaporation, the evaporated mass leaves the liquid surface at the liquid surface temperature, so the enthalpy change is he,. Using the subscripts m for condensation mass transfer and mx for evaporation, the corresponding heat transfer rates in terms of conductances are:
d = h.(T,,-T) and d = h ,(T,,-T) and the mass transfer rates for condensation and evaporation are:
,, h,(T -T,) ,,
h,,(Ty -T,,) ,
(h, - h,) h, e
4.5 Liquid Film Conductance .
)
The conductance through both the inner film (if), and the external film (xf) can be adequately modeled l
l for the scaling analysis using a constant thickness of 0.005 inches, and a thermal conductivity val,ue
. for water of 0.38 BTU /hr ft F. The conductance is determined from:
h, = h,, = ir/6 .
(35)
Although the film flow rates vary considerably both inside and outside containment, a detailed evaluation'* showed the films quickly achieve a thickness of approximately 0.005 inches, and do not increase much thereafter due to the cube root dependence of thickness on flow rate. An addidonal consideration is that the conductance value is 912 B/hr ft2 F, which is approximately 10 times greater than the limiting conductance from the gas to the surface, so the error introduced by this ,
approximation is not significant.
4.6 Heat Sink t'a=dactances The conductances for the heat sink energy equations presented in Section 3.3 are determined from the constito'ive correladoes presented in Sections 4.1 to 4.5. The correlations for the individual and combined conductances are presented in Table 4-1. .
l l
A 32 l
-- - - . ~ , .--I
~
b .
~
f wastepm;essurw Peorsteactans naw 2 .
Table 4-1 Heat Sink Condisctances l Equiv Conductance g Ce.uhn1ance Cimup.ments-laden /H Sink l t Drops (h, + h, + h,) 2(h,-h,)p,, D, AP., 'Sc "" 2k 2 th,-h,)p_D, 'se "" dP !
h = MT,J) W AT = W h, -
(T -T)d P, Pr, d
P,d ( Pr , di
'ap tW 2 Break Pool (( + h, + h) , 0.13 4,-h,) p,,D, AP,, , 0.13k ' a p n' h, = o e f(T,T,) i (T-T,)(v /g)W Pt p 2 , (v 2/g)V3 ( p a ;
3 Secci r g y t -8 0.13(b,-h,)p.D, AP. ' a p T V3 0.13k 'ApM N = o e f6J,) N=h 4 Concsete ,
+
(T-T,)(v 2/3)v3 Fwt p ,
(v2fggys ( p 6, 5 Jackened A '
II Chesency Shell inside r y g 1 -8 0.13(h,-h,)p D, AP. < ap V2 0.13k ' Ap h'" A = a e fFJ,) N=b 6 Evapawanag
. + (T-T,)(v jg)vs P 2 (p (v 2fg)v3 ( p 6, 7 Subcuoted a 8 Dry , l' 0.023h k, 6 Evaporanag r g , -i g p.D, AP. as y3 , 0.023k ge hW ( = oef6 J ,)
Shell Outsule, g
(T -T,)D, Pw DL N = 6, 9 Bame nasade t + {>
7 Subcooled hg2 h, = 2 k,/ 6, l Shell Outside 8 Dry SheH (b, + h,) g . 0.023k ge hV2 4 = aef6J,)
9 Bame Oueside d, i 10 Simeld !
i t
33 :
l wasnotst PeoramT4mv cts 2 l 5.0 Dimensionless Quantities -
I'
\
1 Dimensionless parameters can be defined for each of the quantities that appear in the RPC and energy equations. De dimensionless parameters, identified by a " * " superscript are defined from initial or boundary values, identified by a "o" subscript, and the dimensioned parameter: x = x,x* Many of the
)
dimensioned parameters are either constants, or can be shown to vary so little over the range of l conditions during the transients that they may be approximated as constants. De dimensionless value of constant parameters is 1.0.
5.1 Constant Dimensionless Quantities 1
De water, steel, and concrete density, thermal conductivity, and specific heat are approximated as f
t constants. Linear dimensions of the solid heat sinks are constants, and the liquid film thickness is, approximated as a constant as discussed in Section 2.5. The heat sink thickness is a constant that is defined by the total volume divided by :.he total surface area. Values for other constants are defined' below.
Water density p, = pr., = 60 lbm/ft' 3 Water thermal conductivity '
k, = kr., = 0.38 BTU /hr ft F Water specific heat c, , = c,,, = 1.0 BTU / ibm-F Steel density p. = p , = 488 lbm/ft' Steel thermal conductivity k, = . k,,, = 26 BTU /hr ft-F l Steel specific heat c, , = c,. = 0.11 BTU /lbm F ;
Concrete density p, = p,., = 140 lbm/ft' Concrete thermal conductivity k, = k = 0.83 BTU /hr ft-F . J Concrete specific heat c, = c,..
= 0.19 BTU /lbm-F Water film thickness 6= 6, = 0.005 in
[ 6. = . 8., = 1.625 in 9, C. . .
' Steel shell thickness Steel heat sink thickness 8=
% 8g, = g0.50 in ,,
( Radiation constant o= o, = 0.1714x10ra BTU /hr fts - R' l Emissivity e= c, = 0.9 l Containment volume V= V., = 1.74x10' ft2 I
! Figure 6 shows the Schmidt numtr is nearly constaat at approximately 0.51 over all air steam concentrations, so l Schmidt Number Sc = Sc, = 0.51 (
5.2 Variable Dimensionles Quantities i l The following are dimensionless variables. De reference values can differ for each time phase and are tabulated in Appendix B j4
- E
. 4 34
WisnscootsE PaoMurTany C1. Ass 2 I I
1 Heat sink surface area A, = AA*
Drop diameter d= dod*
Diffusion Coefficient D, = D, ,D,
- Gas thermal cond k= k,k
- Steam density p.,, = paa# *.i.
Drop srf containment temp diff (T3 -T) = (T T)AT*d :
Pool srf-containment temp diff (T,-T) = (T, T)AT*,
IRWST srf containment temp diff (TrT) = (TrT)AT*,
! Liquid film srf-containment temp diff (Tr-I') = (TeT)AT*,
Steel HS srf-containment temp diff (T. T) = (T. PAT *,
l Concrete srf-containment temp diff (T -T) = (T, T)AT*,
Jacketed srf-containment temp diff (T.-T) = (T. T)AT*,
i Shell srf containment temp diff (T. T) = (T. T)AT%
Shell'stf riser temp diff (T.-T ) = (T.-T,)AT%
Baffle srf-riser temp diff (Tort ) = (T rT )ATN ,
Baffle srf downcomer temp diff (TorTJ = (T., TJAT%
Shield srf-downcomer temp diff (T,,-TJ = (T,,-TJAT%
. Radiation heat trans coefficient h, = h,.A*
Convection heat trans coefficient h, = h,.A*
Cond/evap energy transfer coefficient h, = 'h ),*
Effective energy transfer coefficient h, = h,.h,*
Gas volume Vi V,V*
Gas volume fraction a a,a*
Air enthalpy difference (ig - h ) = (h ,-h.)Ah%,
Steam enthalpy difference (h , - h ) = (h ,-ly)Ah*, ,
Break steam enthalpy difference (tw-h,)=(tw ly)Ah% .
. Steam density p., = p, p%
l Air density- p, = p p%
( . Compressibility functions ~ (l+Zr) (g gry,gt.
l (1+Yl') = (1+YZ'),(1Z'l*
Speci6c heat ratio y= y.f Specific heat difference (71)=(71),7.
Break steam flow rate r% = r% 2%
! Break liquid flow rate r%. = r%., 2%.,
Air flow rate m ,= m .,2 %
IRWST liquid flow rate mm n=mawn m%wn Break steam enthalpy % = % .,h %
Time t= to t*
b A 35
wIsrp.cCatst enoramTany ct.4ss 3 l
i
, Pressure is normalized by the maximum containment pressure, defined in terms of other initial - C conditions. By defining the reference pressure P, = Cpm,.ih%dy, IVyjl+Z T ),,, a simplification of the normalized form of the RPC equation results. The value of the coefficient C is calculated to give P, = P , = 60 psia. - i Total pressure P= P,P
- Steam pressure P., = P oP.,*
l Air pressure P, = P,P,*
1 It is desired to scale the RPC for four LOCA time phases: blowdown, reflood, post reflood, and peak pressure, and for du MSLB blowdown. The dimensionless variables take on different values for each
[ time phase. Initial values for each variable are used for each time phase except blowdown. For blowdown, the time average pressure values are used to define all dimensionless thermodynamic propenies, since several essential variables are zero at time zero. (For example, the break flow starts at zero, and the initial steam and pool masses inside containment are zero).
5.2.1 Values of Dimensionless Quantities i> The containment pressure during the blowdown phase of a DECLG is shown in Figure 7. The pressures were obtained from the WGOTHIC code as a reasonable estimate. The specific pressure history does not significandy affect the results or conclusions of this study. The time averaged pressure is 44 psia at 240 'F, consisting of 19 psia of air and 25 psia of steam. The average blowdown steam mass flow rate is 10,300 lbm/sec and the liquid mass flow rate is 20,000 lbm/hr, both from the mass histories. The break source flow is assumed to enter containment at the saturation temperature,273 'F. Given these conditions, the reference values used to make the parameters
! dim'ensionless in the RPC and energy equations are calculated and presented in Table 5-1. Reference values for subsequent time periods, reflood, post reflood, peak pressure, are based on the initial conditions for each time period and are presented in Table 5-1.
Table 5-1 Reference Values for Dimensionless Parameters DECLG LOCA MSLB Parameter Blowdown Reflood Post-reflood Peak P Blowdown
]
Containment gas temperature,7 240 252 244 268 300 Total Pressure, psia P, 44 50 46 60 50 Saturation Temp T 273 281 276 293 2349 l
Coefficient for ref, pressure, C 0.532 0.522 0.542 0.5W 0.528 Bulk air pressure, psia, P ., 18.9 19.3 19.0 19.7 20.6 Bulk steam pressure, psia P , 25.0 30.7 26.9 40.3 29.4 Bulk stm density, Ibm /ft', p , 0.0587 0.0705 0.0627 0.0901 0.641
!L
- sy
, 36
Mtsmcuotst PaoraETrav Ct.us 2 Bulk air density, Ibm /ft', p.,, 0.0732 0.0732 0.0732 0.0732 . 0.732 Total density, Ibm /ft', p. - 0.1320 0.1437 0.1358 0.1632 0.1373 Liquid density, Ibm /ft', pt, 60.0 60.0 60.0 60.0 60.0 Specific heat ratio, y, 1.34 1.33 1.33 1.33 1.35 Break stm excess enthalpy. B/lbm 1084 1086 1084 1090 1101 Enthalpy diff (h .., h .), B/lbm i 1.0 9.4 10.4 7.7 51.2 j
r l Compressibility Functions, (l+Z'), 1.%5 1.080 1.074 1.103 1.031 f
l Compressibility Function (1+#'), 1.087 1,106 1.098 1,137 1.042 l- Break steam flow rate, ihm/sec,mn . 10,300 10,300 200 70 500 Break liquid flow rate, Ibm /sec mr , 20,000 0 200 200 0 IRWST liq flow rate, Ibm /sec,mt, 0 0 200 70 . 0 5.2.2 Heat Sink Surface Areas During Transients Surface area is a very important parameter for calculating the heat and mass transfer to the heat sinks.
'~
7he surface area of some heat sinks change over time: the break pool volume and surface area increase with time, and the wetted area of the external shell initially increases, then varies with time 'as the source flow rate changes and the containment pressure causes the shell heat flux to change. The areas of the heat sinks are summarized in Table 5 2.
l f
Table 5 2 Heat Sink Areas During DECLG and MSLB Transients 2
(Units are ft )
Blowdown Reflood Post reflood Peak Press Blowdown Evaporating Shell 0 0 31,600 21,000 0 Dry Shell 52,600 52,600 31,600 21,000 52,600-Subcooled Shell 0 0- 1316 1316 0 Drops 2x10' 2x10' 2xIOP 2x10' 0 l
Break Pool '17,000 17,000 2000 2000 0 Steel 159,000 159,000 159,000 159,000 19,700 Concrete 50,800 50,800 50,800 50,800 8,300 Steet/ Concrete 35,600 35,600 35,600 35,600 8,500 l
l l,
37
%EsTisaCDLsE PaortsTaaY Ct.ASE 2 i
l d
I e
l l
i 55 . . . . 1
! : 1 I I I i i t
50
- - - l-- -
"I" *-+"- '
+- -
I I I I
. I 1 I I I I i J- Pig;- - 1" -y - - ' "L--- "I- J- - -
45 l--
i i i i i i
- i i I I I
I~ l" I- - - I" - - I- - "I-40 -- -
I I I 9-1 I I I I I 8, I I I
' ~ I I .I
. I- - . . . . . . - . . . - . - - . .
t I . .- .
o 3$ -- . . ... . - - . . . .
i l i i-g i
= 1 I I I I I o -
1 I I I I-
I
. d: 30 --
- }- - '"'"T"' ' "l'"
"T' '"i"' ' "1" '
I I I I 1 I
1 I I I I I "I" ' "1" 25 -
1- - 7-I" '
"T" 1 I I I I I I I 1
- I I I l
20 _- -
-r - - "l-
- - t - - -- - l- -
-t-l 1 I I I i l
I I I I I i 15 4 8 12 16 20 24 28 0
Time (sec)
Figure 7 AP600 Containment Pressure during Blowdown I
J 1
b 4
I.
~
.4 38 i
i
wrsrtvCDtst PaorastamY Ct. Ass 2 i
5.2.3 Heat Sink Characteristics During Transient The heat sinks have to be tracked by their energy equations during the transient to create a temperature history for each heat sink. As the heat sink temperature changes, the boundary layer and surface properties that appear in the transport equations also change. Consequently, for each heat sink, several properties must be determined.
l
- 5.2.3.1 Drops l
De fraction of break liquid that is transformed into drops by the blowdown processes is not easily calculated'. Consequently, an upper limit on the blowdown drop mass is estimated to be 50% of the 4_
gas mass and is used as a reference value. The blowdown gas mass is approximately 150.000 lbm, so the upper limit liquid mass is 75.000 lbm. The corresponding liquid volume is 1254 ft', which gives a containment liquid volume fraction of 7.2x10". (De void fraction is greater than 99.93%). Using an 2
assumed drop diameter of 0.001 inch, the drop surface area is 9x10' ft De drop specific length, is.
l L' = V/A, = D/6 = 1.39x10-5 ft, and the characteristic length of the liquid drops in the containment
- volume is L = V/A, = 0.97 ft. j l ,
u After blowdown, the break fluid that exits the steam generator end of the break is all steam, while the fluid from the other end is mostly water with only a few percent by mass of gas 'thus, there is little i or no drop mass entrained in the break gas after blowdown. However, the drops created during blowdown continue to be transported with the gas for a long period of time, and continue to affect the effective gas density and heat capacity, A detailed tabulation of properties and parameters used to calc'ulated the pi groups for drops is 4 presented in Appendix B.
5.2.3.2. Break Pool i
During blowdown the break liquid flow rate is approximately twice the gas flow rate, and the fraction of liquid that is not transformed into drops by the blowdown processes (Section 4.1) is assumed to be the break liquid flow rate.
De total blowdown liquid mass is used as the reference value. The total blowdown liquid mass is approximately 300,000.lbe, so the bounding break pool mass (total minus drops) is 225,000 lbm. De 8
corresponding break pool volume is 3750 ft . The vigor of blowdown causes extensive liquid splashing that wets most of the surface area in the break steam generator and the stairwell. This additional surface area is included in Table 5 2 along with the pool surface area as the effective pool heat transfer surface area during blowdown.
The break liquid is assumed to enter containment as saturated liquid at the containment total pressure.
At the initial containment pressure of 15.7 psia the initial liquid temperature is 215 "F. The liquid is 39
wrsnscuoat PooramT4mv Ct. Ass 2 ,
surrounded by the containment air at 120 'F and bounded by concrete heat sinks initially at 120 "F.
Consequently, the liquid evaporates to the containment gas, transfers heat to the gas by convection and radiation, and transfers heat by convection and conduction heat transfer to the concrete walls. The energy transfer rate to the solid heat sinks will likely be gre uer than to the atmosphere. However, an upper limit estimate is desired for the evaporation to the atmosphere. Consequently, to maximize the evaporation rate, the maximum pool temperature should be used. Assuming the pool stratifies -
strongly, which to some extent will be the case, the pool surface temperature is the same as that of the incoming liquid through the time of the peak pressure. This provides the surface temperature and saturation pressure needed to calculate heat and mass transfer to the gas.
An additional consideration when the containment is cooling is that the large heat capacity of the pool causes it to remain hot after containment temperature begins to drop. Consequently, a lumped mass calculation of the pool temperature, assuming only heat interactions with the atmosphere, will be performed and the pool surface temperature will be taken from the larger of the two: the lumped mass temperature, or the surface temperature at saturation at the total pressure, ,
A detailed tabulation of properties and parameters used to calculated the pi groups for the break pool is presented in Appendix B. ,
t
, 5.2.3.3 Heat Sinks m d,b 0.5 inches. The Biot number for The average steel tij,ckness, c,agated from the steel volume / area is ,
the average steel is Bi = 0.08., so it is clear that the steel can be modeled as a lumped mass. With this l
assumption, the surface heat flux and total stored energy in the heat sink can be related to the heat sink surface temperature and average temperature. The lumped mass assumption provides the means to track the surface and average temperatures necessary to use the steel heat sink equations in Section 3.3.5.
The thermal boundary layer can not penetrate the thickness of the concrete during the 24 hour2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> period of interest, so the concrete can be modeled as always thermally thick. Its surface temperature and
. surface heat flux can be calculated by coupling the time h%ry of steam and air partial pressures and temperature to the surface, using the integral equations 28, 29, and 30 from Reference 10 for thermally thick structures.
- ~Ah .OC 8 A large portion of the concrete is jacketed thick steel b(~0.5 plate. Initially, the composite inch behaves like steel, and later as concrete. The composite can be conservatively modeled (conservative in terms of underestimating heat flux and total heat storage) by modeling the two structures in parallel and taking the larger of the two as the instantaneous heat tiux. This neglects the concrete heat capscity during the early part of the transient, when the steel absorbs fastest, and neglects the steel heat capacity later in the transient when the concrete absorbs fastest. In the long term, the conductance of the jacket is 624 B/hr ft2-F, so ts conductance is not significant in comparison to that of the gas conductance (see Appendix B).
S
,g
Hisrnceotst Paoma74my tuss 2.
5.2.3.4 Containment Shell As time progresses, the thermal boundary layer advances through the tNckness of the shell and eventually reaches the (nearly) adiabatic outer surface of the shell (thetwa pnetration). The time of thermal penetration is an important characteristic time for modeling energy transfer into the shell.
Internal processes are not coupled to the riser until the thermal boundary layer reaches the outside of the shell. Using the correlation developed by Wulff". the thermal boundary layer reaches the outside
~
of the shell in 22 seconds. Thus, the steel shell is modeled as a thermally thick structure during "' Y hiowdown and as a thermally thin structure thereafter. Because the energy transfer from the shell
, outer surface is very low until it wets sometime after 300 seconds, the shell can be modeled with an adiabatic outer surface to 300 sec. and with evaporation heat transfer thereafter. -
t l
- .5 i
1 l
I l
[h rg 41 h
% F5n%oCDLsE PaoreKTARY CIAss 2 6.0 Normalised, Dimensionless Rate of Pressure Change Equation The RPC derived in ApperElix A is made dimensionless by substituting the expressions for the dimensioned variables defined in Section'3.0. and is normalized by dividing each term in the RPC by the reference break excess enthalpy flow rate, m, A, Ah,,,,,is the difference between the break ,p gas enthalpy and the liquid enthalpy at 120 F, the maximum possible enthalpy change. Note that thi9 /
. is approximately the energy rate that must be removed to condense the source energy rate. The following sections present the normalizadon, dimensionless substitutions, and pl groups that result for
,each term of the RPC.
6.1 Pressure Term T T T Q,C T
(1+Z ) V dP , (l *Z ),Z
- V,V 'C p. Ahw(y - 1). dP' Z *V
- dPf50)
T dt*
(Y~l) % A b e di (y - 1),y
- y,(1 + Z ),ng Ahw t odt
- y where J
J and t =
"** (51) x * . .C. Y.
- An,se .
, ~
The selection of the parameters defining the coefficient C, presented in Section 5.2, greatly simplifies the pressure pi group, and as shown subsequently, also simplifies the expressions for compression work pi groups.
6.2 Break Source Gas Term The first term on the right side of the RPC represents the break source steam enthalpy and work. The dimensionless substitutions and normalization give:
~ ,
r , -QC
'b ' h Y(1 +Z 3 P,, ,
8%4 . Ah ,., ( ,, - h"" (y+ - 1) p ., ,
rh ,, ,th * , , (h,, -h,,), Ah,*,
y,y *(I +Z r),ZT* C p., Ah,,.,(y - 1),P,*" (52)
'hme.e Ah . , (y .1),y;(1 +Z ), T Ahm,y,p m,p;, ,
T
= x Ahl,,Q + x,,,, I *Z , P"'" Q Y. p where -
x* . b-Y' Ah%
and x"" = C (53)
. r 4
42 n ., . . . - ~ ,- -
wtsriscuotu PRoPRETARY Ct. Ass 3 6.3 Break Source Liquid Term
- The break source liquid displaces gas from the containment volume, and hence, does work on the containment gas. The normalized, dimensionless term is :
(i C, I T #
libes (1 + y2 T
) P_ , Ibr N (I + YZ ),Z
- C p.,,, A(,(y - 1),P
- ti4t . Ah w , (y - 1) p, tigg, Ah ,,,, (y _ g),y- y,(g .z T), p, p,- (54)
T
- 8 e (yZ )' riQ P
- t Y. Pr l where IIbef.. P , C(1 + yZT),
IB T -L wt44 Pr Y.(1 + Z ), ,
. 6.4 IRWST Source Term -
l The IRWST liquid changes phase as it flows through the r'eactor. The removal pf liquid from the IRWST increases the containment gas volume, then decreases the volume when the steam condenses. ,
However, Since steam condensation is considered separately, the IRWST flow must al'so be tracked.
The normahc't. di ensionless term is :
l -
thewsrs T (1 + yZ T
) P_ , mmwrrs,.bs (I
- YZ *).(yZ )* C p.,,, AQ(y - 1),P,* --@C j _
m wne AI4tp (Y - I) Pr Mwn ,Ahmte. (y - 1),y* T y,(1 +Z ),pg,pg*
l T
a
" 8 e (yZ ). m'twrrsP' Y. Pr where thawers, Pw C(I
- TI ).
, p thwn, p,, y,(1 +ZT),
6.5 Condensation / Evaporation Phase Change Terms The third line of the RPC, Equation 2, represents the energy transfer associated with the heat sinks, and, because it is unwieldy, will be separated into phase change mass transfer, convection heat transfer, and radiation heat transfer terms. The mass transfer portion will be further broken down as described below. . ;
6.5.1 Phase Change Mass Transfer Term The steam that flows between the containment gas ar.d the i:-at sinks gives rise to three pressure terms corresponding to euthalpy, gas work, and liquid work:
43 1
wESTiscuotst PaorsurTARY class 2
.@C (T,,3- T) , y(1.z T) P. ' (1 yzT) p' "J "
J (h, - h,) (y - 1) p, (y - 1) {, _
De portion of the equation outside the large parentheses represents the mass flow rate, expressed in terms of the conductance from the containment gas to the surface of the solid or liquid heat sink. De portion of the equation inside the large parentheses represents the enthalpy excess of the Dow, the work on the gas volume due to mass transfer, and the work on the gas volume due to displacement by the liquid. The mass and the enthalpy/ work portions are normalized and made dimensionless separately as follows.
. De mass transfer ratio, expressed in terms of conductance, normalized by the source mass now rate, l = 4, C and made dimensionless is:
hw j(T,3 A -T) ,
h g.h,*,g A9A'j (T,3 -T). AT j , , hM* AT[ (59)
! 'Nteo@s- h,) m%@,- h,), AQ Ah[,
where:
,* , hws u(T,,3-
, A T), (g)
% @,-h,), e
- ~
The enthalpy/ work portion is normalized by the source excess enthalpy:
Sc 1 y(1 +Z7 ) P , (1 +yZT) P' @uma -h.), Ahl,,a Ah% (y - 1) p. (y -1) 5, g Ab%
T T T yoy*(1 +Z T
),Z
- C p., Ah%'y - 1),Pk , (1 + yZ ),(yZ )* C p,,, Ah%(y - 1),P@l)
T (y - 1),y *,
T Ah% y,(1 + Z ), p , p * , (y - 1),y
- Ah%y,(1 +Z ).pe,pr' ,
y zT P. i (yZ T)* Pk
- #aaJA h ., a + x ,,3 , ,
-sg e , ,
- y. Pa, ya Pr l where:
i (b ,;-h ,,), , , C(1 + yZr), pe,, {g)
, * , d, Ah% y,(1 +ZT), pr, De resulting pi groups'for mass transfer to the heat sinks are the product of the mass and l -
enthalpy/ work pi groups. Dat is: ,
h,,g, Ap (T,,3 -T), (hg -h.), b A3(T,3-T),
l , ,
W, %,,,@, - h,),
Ibi ,@,-%), AA.,, {g) f h,,3 p(T,,3-T),
A C(1 + yZ r), p,,,
e ,,@, - %), y,(1 +ZT), pg, g
~
b
@4 44
u tstocuot.st reoramtrav class 2 1 i 6.5.2 Convection and Radiation Heat Transfer Terms ,
a The energy transferred between the gas and the heat sinks includes a convecdon heat transfer term and i a radiation heat transfer term. These terms are normalized and made dimensionless as follows: g'g (he .g
- huJ) A;(Tj -T) ,
h,q,h,*q ,AA3 [(T)-T), ATj' , hua h d3A A pj'(T -T), j AT j' ,
ug ,,, Ah i,,,,,, m ,,,, Ah ,,,,,, i%
ng,,, a h,,,,,,,
=xh*g[AT[+shdaj'AT' q A g A j where
- hw. A ,6j i. hua ^j,6j - D*
, , 1
,' (65) ng ,, AIg ,,, ng ,,,, Ah ,,,,,
6.6 Normalized, Dimensionless Heat Sink Energy Equations I
j 'Ihe heat sink energy equations derived in Section 3.0 are transformed into'the normalized and dimensionless form nedssary to define the pi groups. The containment gas time constant is used to .
make time dimensionless in each equation. The heat transfer coefficients are normalized to the shell conductance (with inorganic zinc coating on each side) and define as pi groups. Finally, " local scaling" is perforn.ed to define the specific and characteristic frequencies for each heat sink.
! 6.6.1 Source Drops s
Equation (7) is normalized by the break source excess enthalpy flow rate, rt%c,.t,(T,Q,, and is made
~
dimensionless with the system time constant and additional substitutions from Section 4.0: .,
g m u c,u(T, - T),4,,,, . E,' , s oc,u(T,-T), . . , h,,hl A,(T,-T),A ' ATJ Ebt tg,,,(T,-T),p%V, dt* t o c,,o(T,-T), s oc,,o(T,-T). (66)
! CE -
i
- z,m,' c' = z_6/ ATJ + z,hl A
- ATJ dt j .
where the drop pi terms are defined:
i z, . g'#
Ed,bbe,y
," , g ,* , b *8 c,C+ A* (67) i 8e Pne,y 0 ,4 IN The individual conductance terms for mass evaporation, heat convection, and radiation from the drop to the containment atmosphere are scaled by dividing each term by the shell conductance, h , =
k./5., so that:
i Oe , 2tg,p D,, y V3 AP. ,
o , 2 k, ,
o.,,
gg[
k., d.(T -T), er , , r , s k.,, d, k**
iM 45 l
f I % EsrI%(CDL5E PROPRIETARY Ct.rss 2
\
Local Scaline -
The specific frequency (effect on the drops) of the energy transfer rate from the drops to the gas atmosphere is the ratio of the energy transfer rate to the energy capacity of the drops and is equal to I/t: ,
c I hoA,(T,-T), ho 1 (69)
, w' = . . -
t m,,, c,,,,(T, - D, p,,,c,,,, L
- where the speci0c length L' = V,/A.,= d/6. The characteristic frequency (effect on the gas) of energy transfer from the drops to the gas is the ratio of energy transfer rate to the energy capacity of the l
containment atmosphere: .oc i h,,, A,(T, - D, h,,,g, - D, I (70) u, . p Au, L
m, Au,
! where the characteristic length L = V/A,.
l 6.6.2 Break Pool Equation (8) is normalized by the initial break liquid excess enthalpy flow rate of sty.,,c..r (T ,..-T),
)
and is made dimensionless with the system time constant and the substitutions in Section 4.0:
' . 4,C N c. ,(T,-T), . . c, " ihw,,c.u g w-T), .
mw,,c.u(Tw - T), p,v,"' "'* e - mw ,c,,,(Tw -T),
ho h,' A,(T, -T), A * (T,-T)*
+ the..,c.u(T. -T),th ,,, A T , , , - (7l}
%c,u(Tw-T), %c,ug -T), .
or c =x iha, ATb + z 6 BAT - x,h,' A
- AT,*
5,mlc,',, de where the pool groups are defined:
, . N 6 ,-T), x " , (l) s" , gc,,,U. me ,3(Tw c
-D, 4
3%es,.6w-T),pg ,V, - T)* (72) h, A,6, - T),
x* . 3% ass c ,f,.6 w - D.
~'
+ 1he individual conductance terms from Table 4-1 for mass evaporation, heat convection, and radiation
! from the drop to the containment atmosphere are normalized by dividing each term by the shell conductance, h., = Iq/6., so that:
i
~
46
wrsnsacat.st reoraanny crus a 4, C og,0,13hy p. D,,AP..' g W , o ,g 0,13 k, 'g W ,
o, g
k,g (v2 /3),(T,-T); Pu, i p ,, kg, (v:/g), i p ,,
k,**
g 173)
Local Scaling i
The specific frequency (effect on the pool) for the energy transfer rate from the pool to the p i atmosphere is the energy transfer rate divided by the energy capacity of the pool and is equal to 1/t: ,4
~
hoA,(T, -T), h,,, /
' w _l fp Wr. .C,f,o7p -T),
pg,,c,y, La
_1 (74)
' ~
where the specific length L' = V,./A, De characteristic frequency (effect on the gas) of the energy transfer rate from the pool to the gas is the energy transfer rate divided by the energy capacity of the
~
containment atmosphere: 4, (
h,, A,(T, -T), h,,(T, -T), I (75) w' .
m, Au, p Au, L --
' here w the characteristic length L = V/A 6.6.3 Heat Sinks Equation (12) is normalized by the initial energy transfer rate to the heat sink, and is made dimensionless with the system time constant and the substitutions in Section 3.0:
~ Q, C NC,.',(T - T,),% M * ,
h,,h,' A,(T - T,), AT,*,
ho A,(T -T,),p% ,Vdg
- hoA,(T -T,),
a, (76) y.
8m I " 8.h,' AT,*,
dt where the pi groups are defired:
z , . N * bV x*-(1) (77) b ^eP w ,
De individual conductance terms from Table 4-1 are normalized to the shell conductance, ha,, to produce the pi groups for scaling the heat sink conductances: -
) Q, C
,*. W ,, .
W __
1 + (h,, + hy + ty)/hy,, 1 + (hg+hu + h,,,)/h,, 47g)
- h,,jhg ,
.' x, - w 1 + (h,,, + ( + h,A, ,
~
De equations developed to model the heat sinks assume the heat sink surface temperature is known.
De steel heat sink was assumed to behave as a lumped mass, so the surface and average temperature i are easily tracked by integrating Equation (76) forward in time.
1 47 4
WErrl%GCDt5E PaoramTray Ct. Ass 2 The surface ternperature of the concrete was tracked using integral methods for thermally thick structures developed by Wulff" by integrating forward in time. The containment boundary condition was modeled as a step function over each time phase, with initial conditions determined from the final surface and average temperature from the prior time phase.
l - 0, C
- ne steel jacketed concrete was modeled by considering the steel and concrete to be exposed in parallel, rather than series, to the containment atmosphere, and using the larger of the two surface heat fluxes during any time phase. The result is conservative, since the heat capacity of the member not selected is neglected. -
~
l i 1.ocal Scaline i
The heat Mnk specific frequency is the energy transfer rate to the heat sink, divided by the energy storage capachy of the heat sink, and is equal to 1/t: .
G, c I = b A.(T,-T), =
Ig,,, t (79) w( = ag,,c,,(T,- T),
pm,,c,, L'
- h. .
where the specific length L' = Vs/A, The characteristic frequency (effect on the gas) is the energy .
3 transfer rate to the heat sink, divided by the energy storage capacity of the atmosphere:
, -aC /
hw A
,(T -T,), = hw(T-T,), t_
.,,= (so) m, Au, p, Au, L -
l ,
i-where the characteristic length L = V/A 6.6.4 Shell Equation (17) is normalized by the initial energy transfer rate into the shell and is made dimensionless .
with the system time constant and the substitutions in Section 3.0: OC/
m.,c,,,(T -Tu),% miRd , ho h,' A,(T-Tu), , ,
h,,,,,lg* A,(Tu-Td, ,
he, A,(T -Tu ),p,V, dt* h A,(T -T ), h,,,A,(T -Tu ),
ar z m ' C*' = zg h,* A
- ATu - z,lg* A
- ATi, t
di (81) l where the pi groups are defined: -
0 44C va b I Pe4 ," (g) ,** . k s464,-T), (gy) hy,, pg ,V, h,,i,(T -Tu ), ,
The shell energy equation was formulated in terms of the shell inner and outer surface temperatures.
The integral relationships developed by Wulff* for thermally thick structures are used to track the shell surface and average temperatures for appropriately short values of time, and Wulff' for thermally l
thin structures with heat transfer from two sides. Both the thermally mick and thin regimes are f
\c 4
48
unmcuotst PaorasTray ca. Ass 2 modeled assuming the environment changes as a step function over the Ome phase of interest.
The steady-state energy transfer rate due to condensation and evaporation mass transfer on the AP6'.O I
jhell are scaled by normalizing the energy transfer rates to the reference break enthalpy flow rate: .
tC
=
t h, -h,), 0.13 p,,,,D, , AP,,, ap Se h, 3 0.02 3 p ,,, , D, , AP,,,, Re
,,,,og Sc
/
n "w -
n " = o
% o ( vi,/g f ' m,,,, , , P ,,, , p , 4,, D,m m,, P m, ,
Local Scaling
- The shell specific frequency is the energy transfer rate to the shell, divided by the energy storage capacity of the shell and is equal to 1/t : 4,C.
h,, A,(Tg -T), h, , t 4.Ib .
IN.C.JT,,,-T),
p ,c,., L *
<s4) where the specific length L' = A/V .uThe characteristic frequency (effect on the gas) is the energy transfer rate to the heat sink, divided by the energy storage capacity of the atmosphere: ,, # C
_ )
h,, A,(T -T,,,), h,,(T -T,,,), I g- .,_ (as) m,au, p,au, u .
where the characteristic length L = A/V Similarly, a specific frequency can be defined for heat transfer out of the shell to the riser, and a characteristic frequency for energy transfer to the riser gas:
I h,,,, 1 ,, ( A,(T,-T), /
4;T w pw c,,, L
- A(mu),i,,
~
l l 6.6.5 Baffle Equation (19) is normalized by the initial energy transfer rate into the baffle and is made dimensionless with the system time constant and the substitutions in Section 3.0: .,
gg
~
mw ho,,b,*A,(Tv-T)* A
- ATy
- c. (T-Tw ).% =?c? . h .h,* A,(T-T)* A
- ATE h,,i,, A,(Tw-T ),p% V , dt* h A,(T -Tw), b A,(T-Tw), (g.7) or zwas dt = z g h,* A
- ATE - x,,,h,* A
- ATE,,
where the pi groups are defined: .
Pw,0w,c,,,sh,,,,, ho ,,(Tv -T), (as) x, - x"3 - (1) x,,, -
h,,3,, pu,,V, h,,i,,(T -Tw),
The shell energy equation is formulated in terms of the shell inner and outer surface temperatures.
The shell inner and outer surface temperatures are modeled using a lumped mass approach as discussed in Section 3.3.7.
l l.
lQ 49
% rsriscuot.sr. PeoraETany Ct. Ass 2 Local Scalina .
De baf0e specific frequency is the energy transfer rate to the shell, divided by the energy storage capacity of the shell and is equal to 1/ts ,g C 1
1 h,, A,(T,,, - T), h,, _i wy . . . 019
) ,
T w mw ,c,,(T,-T), pg,,c,, L
- _
where the specific length L' = %/A,. The characterisue frequency (effect on the gas) is the energy transfer rate to the baffle, divided by the energy storage capacity of the atmosphere: _pg h A,(T -T,), . o(T h -T,), 1
_ ._ (90) w, .
m,Au, p,Au, L -
where the characteristic length L = V/A Similarly, a specific frequacy can be defined for heat transfer out of the baffle to the downcomer, and a characteristic frequency for energy transfer to the downeomer gas: ac
"' *I
- w',._1_. "* _I- and uw= p,Au, L
(91) ,
pw,c,, L' t
- T m -
J
- 6.6.6 Chimney / Shield Building Equation (20) is normalized by the energy storage capacity of the atmosphere and made dimensionless with the system time constant and the substitutions in Section 3.0.
a,c m.,c,,(T -T,),% dT1 , ho h,' A,(T -T,), ATy h A,(T -T,),p% V, dt
- h, A,(T - T,),
or (92) dT**
z.h,'ATy ,-
=. dt where the pi groups are defined:
' ****" (93) x, . x*=(1) h, A,p% V, ._
De individual conductance terms from Table 4-1 are normalized to the shell conductance, h.,, to produce the pi groups for scaling the heat sink conductances. Radiation to the concrete is neglected, resulting in more heat transfer from the gas, and consequently, less buoyancy to drive the natural circulation air flow. The liquid film is assumed to be 0.005 inches thick, as for all other films.
, a/ c h.Jhe h,,,4 (94h n= - i . (h,, .m. x, - x, = hy )h.,
i.(h,,. % .
De time history of the chimney and shield building concrete surface temperature is predicted using the same integral methods for thermally thick structures as for the internal concrete. De boundary condition was modeled as a step function over each time phase, with initial conditions determined L !
cg 50
wisnscuotst enoran14av cuss 2 from the final surface and average temperature from the prior time phase.
Local Scaling The chimney characteristic frequency (effect on the gas) is the energy transfer rate to the heat sink, divided by the energy storage capacity of the containment atmosphere: , , a c.
w, . b^.(T - T,), . ((T -T,d, I_ i95) m,Au, p, Au, L .,
where the characteristic length L = v/A I
l 1
l l
~
l 1
i l
l, 51
- - . - - -. . . . . ~ _ . _ . - - . - .. . - - . - - . - . _ - . - __
%EsnscuotsE PatMuETARY CIAss 2 7.0 Values for Pt Groups The pi groups were evaluated using the reference values presented in Section 5.0 and the equations presented in Section 6.0. Pi group values are presented in the following subsections for energy conductances. heat sink energy, and containment pressure.
7,1 Energy Conductance Pi Values Table 71 presents the energy transfer conductance pi values for each heat sink and time phase. The conductance pi was defined in Section 6.5 by normalizing the equivalent conductance (for radiation, convection, mass transfer, and liquid film) to the shell conductance. Additional detail on the individual series and parallel conductances is presented in Appendix B.
Table 71 Energy Transfer Conductances to Heat Sinks Scaled to Shell Heat Sink Blowdown Reflood Post reflood Peak Press MSLB Drops 823 972 877 1175 --
Break Pool 0.53 0.61 0.55 0.73 --
4 Steel Heat Sink O.30 0.38 0.37 0.51 0.26 Concrete Sink O.33 0.40 0.27 0.51 0.07 ,
- l Shell
Dry Inside 0.30 0.37 0.36 0.60 0.27 Dry Outside 0.01 0.01 0.01 0.02 0.01 Subcooled Inside -- -- 0.36 0.52 ,
Subcooled Outside -- -- 7.8 7.8 -
I Evaporaung Inside -- -- 0.36 0.56 --
Evaporating Outside -- -- 0.04 0.55 --
Baffle inside 0.01 0.01 0.01 0.01 0.01 Baffle Outside 0.01 0.01 0.01 0.01 0.01 Chimney 0.01 0.0 L 0.01 0.04 0.01 Table 7 2 shows the conductances for the drops are extremely high, so the drops quickly re'ach thermal equilibrium with the gas and subsequently follow changes in the gas temperature with no significant lag. The dry shell external conductance is I to 2 orders of magnitude less than the internal conductance. The external conductance on the evaporating shell at the time of peak pressure is nearly
. equal to the internal conductance, and both are 60% of the shell conductance. The baffle inside and outside both operate dry and have low conductances. The chimney operates with low conductances, even when condensate forms, due to the high noncondensable concentration.
- s 52 i
wisnscuotst Peopertaav Ctass 2 7.2 Heat Sink. Energy PI Values
! The " local scaling" specific and characteristic frequencies defined in Section 6.5 are presented in t ables 7 2 to 7 5 for each heat sink.
7.2.1 Drops l
! The specific and characteristic frequencies of the drops are presented in Table 7 2.
1 i
Table 7 2 Drop Speci.'ic and Charactensuc Frequencies m'/sec w Iruual Blowdown 494000 169,600/sec Blowdown 59,800 0.66/hr
- Reflood 70.200 0.04/hr Post reflood 63.300 0.007/hr Peak Pressure 84,800 0.0003/hr .
i .
l; The drop time constant is t = 1/w'. Because the initial time conste.nt is so small, the drops almost
' instandy cool to the containment gas temperature, and subsequently remain strongly thermally coupled j
to the containment gas. The result is the drop temperature changes at the sar.w rate as the contalament i gas after the initial appearance of the drops.
t l
Although the drops evaporate very rapidly, only a small amount of evaporation is required 10 bring the drops into equilibrium with the gas. Equating the drop energy change, me,AT to the energy of evaporation, Amh,,, it is estimated that Am/m = 0.098, or less than 10% of the drop evaporates to cool the drop to the ambient temperature. After blowdown, as the transient progresses and the containment temperature changes, the drop energy changes even less and very slowly. The characteristic frequency and pi group show that the effect of the drop energy transfer on the containment gas is relatively small.
7.2.2 Break Peel The specific and charactertsdc frequencies for the pool are presented in Table 7 3. The MSLB break does not release liquid, so the break pool does not form during an MSLB. 3 l
. S l
0 53
! wisn%cCDtst l'aonuticav Ctes 2 l
i . Table 7 3 Pool Specific and Charactensuc >
' Frequency j 1 ot/hr uVhr i Blowdow n l 230 u, 40 i .
Renood 266 0.41 ';
1
- Post reflood 242 U.05 :
Peak Pressure 319 0.05
{ !
De specific frequency represents the surface layer of the pool. De value shows the pool surface
, temperature changes within a few seconds to closely follow the bulk gas saturation pressure. The very l small characteristic frequency shows the pool has a very weak influence on the containment gas
- energy.
l 1
! 7.2.3 Solid Heat Sinks I ,
he specific and characteristic frequencies for the steel and concrete heat sinks are presented in Table 7 4.
f 3
i Table 7-4 Solid Heat Sink Specific and Characteristic
- Frequencies ;
~
1 !
1 Sicel Concrete of/hr avhr oWhr Blowdown 29.1 7.5 0.75 Reflood 36.0 8.5 0.91 Post Reflood 35.7 6.0 0.03 ,
Peak Pressure 49.2 8.9 0.33 M5LB 24.9 1.2 0.04 7
From the steel specific frequency. the LOCA heat sink time constant is 50 to'100 sec., so the steel responds rapidly relative to the time of peak pressure (1500 sec). The characteristic frequencies show l
the steel heat sinks have a factor of 5 larger affect than concrete on containment energy, and that it is significant by the time of the peak pressure. The MSLB frequencies show the steel thermally saturates by the time of the peak pressure (300 sec), but the effect on containment energy is small for both the i steel and concrete. Specific frequency, the ratio of heat flux to heat capacity, is not calculated for
~'
concrete since itsheat capacity increases with time.
7.2.4 Shell The values of the shell groups are presented in Table 7 5 for the subcooled, evaporating, and dry regions during each of the four time phases.
- L
- 4 54 i .
. _ _ _ . _ _ _ _ . _ _ _ _ _ . . _ _ _ _ _ _ _ _ _ _ . - _ _ - . . . . _ _ , . . _ . - _ = , . . _ . - . _ . . _ . _ . . _ _ _, ... , . _ . , . . , _
Mrsnscuotst Peormstray CtAss 2 l l
. Table 7 5 Shell Specific and Charactensuc Frequencies j Dry Shell Subcooled Shell Evaporaung Shell m'ihr ohhr m'/hr uhr m'ihr phr ;
Blowdow n M.9 2.6 - - - - j RcDood 10.9 3.0 - - - -
0.054 !
Post reflood 10.7 1.3 10.7 10.7 11.9 l
Peak Pressure 17.7 u.7 15.5 0.07) 16.7 0.9 M5LB 8.1 2.7 - - .. -
The shell frequencies show the shell absorbs is a significant fraction of its heat capacity during ,
I blowdown and reflood. The post reflood values are much smaller due to the falling internal pressure and temperature. At the time of peak pressure. the dry shell and evaporating shell are absorbing at a
! significant rate. The subcooled film locally absorbs at a significant rate, but over a small area m the
'effect on containment energy is not significant. ,
7.2J Baffle and Chimney a The values of the specific and characteristic frequencies are presented in Table 7 6 for the baffle and
! . shield building chimney during each of the four time phases.
I Table 7 6 Baffle and Chimney Specific and Characteristic Frequencies Baffle inside Baffle Chimney Outside w7hr ovhr avhr ovhr Blowdown 2.1 0.0004 0.0007 0.0007
~
Reflood 2.1 0.0003 0.0005 0.0002 Post reflood 2.3 0.0011 0.0022 0.0002 Peak Pressure 3.0 0.0053 0.0211 0.0241 M5LB !.3 0.00Z7 0.0055 , 0.0U76 7.3 Containment Presure M Values i
The values for the RPC pi groups are presented in Table 7 7. A detailed tabulation of the initial and boundary conditions used to calculate the RPC pi groups is presened in Appendix 8.
1
~
e
%tsnscuotst Peorsurtsav Ct. Ass 2
- Table 7 7 RPC PI Group Values Pi Group Blowdown Rellood Post Rellood Peak Press .NI5LB i Containment Gas I
t,,, 9.9 -- 544 2234 222 ,
K,. ,. u.3960 0.3912 0.4078 0.3822 0.393l 0.010I O 0.0096 UAU71 0.t 45 K~ui mim 0.5324 0 0.5424 0.507I o.5283
- K~. p..
OMO8 O u.0004 0.0u17 0 i Kwo. i,, ,,, .
0 0 0.0004 0.0006 0 f Kt am sT ..
Drop K..,,,, 0.0000 0.0000 0.0000 0.0000 --
K,,,,.n. 0.0000 0.0000 0.0000 0.0000 -
j K. , 0.0000 0.0000 0.0000 0.0000 -
K,.. 0.0016 0.0000 0.0009 0.0000 -
K,,,....
i 0.0000 0.0000 0.0000 0.0000 -
i Break Pool 0.0000 0.0000 0.0002 0.0005 -
- l. K,.. ,,,,
0.0003 K, 0.0000 0.0000 0.0001 -
f' . ,.n, i I
K, 0.0000 0.0000 0.0001 0.0002 --
l K, .. 0.0009 0.0009 0.0058 0.0166 -
Ki ,,,. . 0.0000 0.0000 0.0000 0.0000 -
l Steel Heat Sinks K,... , 0.0008 0.0076 0.0LTrt 0.094I 0.0034 l K,o,,,.n,,, 0.0014 0.0014 0.0402 0.I482 0.0060 0 0 0 0 0 K,%
0.0169 0.0195 0.7376 3.1201 0.0522 K,
0.0uuu 0.0000 0.0006 0.0036 0.0000 K. i Concrete Heat Sinks K,,~ . - 0.vuuu 0.0000 0.0002 0.0041 0.0006 K u ,,,,.n ,- 0.uuuu 0.0000 0.0000 0.0011 0.0002 K% 0 0 0 0 0 0.0019 0. ort 23 0.0036 0.1262 0.0017 K,
O.vuuu 0.0000 0.vuuu 0.0001 0.0000 K i .. ..
l Steel Jacketed Heat Sinks X, 0.0002 0.0002 0.0063 0.0211 0.0015 0.0003 O.0003 0.0090 0.0332 0.0026 l K.o 0 0 0 0 0 i K.,,,,,,
0.0037 0.0044 0.I651 0.6986 0.0225 K,.
0.0000 0.0000 0.0001 0.0005 0.0000 K i .. ..
- 1. -
56
_ _.m_ _ .__ _ _ . . _ _ . _ _ _ . _ . . . . _ . . . _ _ _ _ _ _ . _ _ . _ . -__ _ _ _ _ _ . _ _ _ _ _ . .
l
%tsTI%GuothE PROP 9utT4RY Ct.Ans 2 :
Dry Shell .
K, 0.0003 0.tn O3 0.0062 0.0074 0.0077 Ke n .- 0.0005 0.(R A>5 0.0094 0.0074 0.0115 U U U U 0
%e K g . ,, 0.tO56 0.0007 0.1578 0.2776 0.1206 K ,. . .. O.t x t'O OAnn 0 01M Ol 0.un13 0.th a u f Subcooled Shell K,. ~ - 0.0003 0.0007 ..
K-.cwn - ~ 0.0004 0.0011 ~
K - ~ 0 0 ..
' K m.m ~ ~ 0.0066 0.0250 -
Kn.,4.. ~ ~ 0.0000 0.0000 ..
Evaporaung Shell !
4
- ~ 0.0041 0.0087 ..
- K,. . l K..cw. ~ ~ 0.0062 0.01I2 -
K enw - ~ 0 0 .. j Km ~ ~ 0.1052 0.3116 -
.e
' Ka, .. ~ ~ 0.0002 0.0002 ..
l The pi groups in Table 7 7 show that during the blowdown and reflood phases, the internal heat sinks reduce the rate of pressure change by only 8 to 10% of the source. During the post reflood and peak pressure phases the heat sinks and shell reduce the pressure rate of change more than the source can increase it, so pressure begins to decrease. The work due to mass removal is the only significant pressure reduction process: radiation and convecuon heat transfer are typically lower by a factor of 20 or more. The enthalpy pi group shows that for most of the heat sinks there is no effect, except for the pool which becomes a small additional pressure source after the peak pressure. The pi groups clearly show the dominance of condensation mass transfer as the process that affects the rate of pressure change after blowdown. - ,
4 l '.
4 57
' uisnscuoat reormaicar ctass a .
8.0 PCS Air Flow Path Momentum Equation The wind positive character of the PCS air flow path is neglected and the PCS air flow is modeled as entirely buoyancy driven". De posidve buoyancy is provided by air headng and the evaporadon of low density steam into the riser and chimney. A small amount of negative buoyancy is provided by heating from the baffle and shield walls in the downcomer, and heat and mass transfer to the cool shield building and chimney at the outlet. Wind induced recirculation was shown to hase a negligible impact on PCS performance."
De downcomer, riser, and chimney are modeled as distinct, interconr.:cted flow paths using Equation (3). De single loop system is shown in Figure 8. It is assumed that the heat and masa are added to, or removed from, each leg of the path at thermal centers that are located to minimize the PCS air flow rate.
~
Following the example of Wulff, the system of momentum equations for a single loop can be written in vector form where the overline ladicates vectors: .
(96) l
. TT# = G - K iKEy Ils the geometry dependent inertia vector:
(M)
T = ((L/ A), , (L/ A), , (L/ A).) .
Hiis the mass flow rate vector:
m, , m ) (#)
15 = (m G'is the buoyancy defined by integrating around a closed path, the density times the' dot product of the j gravity and displacement vectors:
G = fp g ds = [p gdz +[p gdz +[p gdz+ [p gdz (99) s . . . _
I e
4 l
l
(
h 58
I l
i MisTWCotst PaoPRET4mv CLA55 2 i
4 I f 1 j .
i 6
J ,
i . .N /
t t
1 9 .1 e r 1 2,; c; : ;
/ .
va- s r;v3 4
i
- v .
= _ . _ , r
?.. e,- t l - ev 'O !
l =-
i a= g j \ / a 45:0 j
' \ , / >
\ /
t
\ /
.= =. 6
\
,/ l,
\/
243 y
> - }
- s l
i
\ I /
/
/ I*.a 412
- ew .
.. ; 7_,
(- 1 L
t
- ::-e- ! , 9d d
/A 4:e
, see .. .-
- V '
,, i ,
I 1
.g ,
y # I
- 157e 1 i
~
i . :
l 1 I
u t
135' e
l Figure W Passive Cooling System Air Flow Path Momentum Parameters l
1 E
i I
i e l
! l
- .t. l
- g.4 j i 59 1 l
. 1
wasmcuotst PnorarrraY CtAss 2 l i
i
- R is the impedance vector and R, is the sum of the form and friction resistance for each segment i
determined from the I/6 scale pressure drop test":
i i
t K' + f'L'y
/d ' (t00)
K= where R, =
l 2 p. A,i(R, , R,, , R,) (A,IA,7 l
K5 is the vector of kinetic energies: ,
(101) l mn = (mi , m,' , mi) .
l
- where m, = rho., and % + m , = m,, = rh.. Since the evaporadon mass flow rate is known
!. (treated parametrically), there is only one unknown flow rate.
l N.I Dimensionless PCS Momentum Parameters i
f The matrix elements are made dimensionless by setting each equal to the product of a reference value and a dimensionless value:
1
! Inertia I, = 1,l,* where I, = E 1,..
!' Mass flow rate m,= m om,*
Buoyancy G = G.G
- where p, = p, the ambient air density ;
Density p, = pop,*
Flow resistance R, = R.R,* where R, = the total PCS loss t
The reference mass flow rate comes from the reference buoyancy term, which is used to normalize the inertia and resistance terms. The reference buoyancy is the steady state soludon to the momentum equation, that is, the soludon to the momentum equadon without the inertial term. The buoyancy term is given, in terms of thermal center differences (Figure 8): .
t (102)
! O, = fpi df = p,g(H,-H ) 3+p,,g(H 3-H ) +p g(H 3-H )+p,,,g(H,-H i) 3 s
1 where:
PM* T = T,+ ( (103) p = RT, M. = M. m, c,,
, 4, + m,,c,,(Tu -T,)
P M, ,
rh, + rn,, ,
l " "
m,c,, + :h,,c, l
p" , KT, m,,,/ M, + m,,/ M,,
l 1
1 1
60
w rsmcaotst PeoriurTaar Ctass 2 m, + m,,,- m m 4, + m c,,,(T ,-T,)
p* , PM, g* , "
m, e, , + m,,, c, ,, - moqq$,)
RT, m,/ M, + ( m,,, - m,,,,)/ M,,
The Q terms represent the net heat transfer into the gas, m,is the same in all terms, and P is one atmosphere. All terms can be calculated by guessing a value of m, and selecting a parametric value of m,,, that is known to be consistent with evaporation limits. The result is the buoyancy term that is used in the momentum equatien to calculate the value for m, . This process converges rapidly using back substitution.
he areas, lengths, and loss coefficients for the AP600 air flow path are shown in Figure 8. From these values the R and I vectors are:
g
- p/g T = (0.089 , 0.275 , 0.048) and K= ,(0.30 , 1.38 , 0.82) (106) 29,Al With I, = II, = 0.412 and R = IR/(2p A,3) = 2.5/(2p,A,8), the normalized vectors are and K = R,7 = R,(0.12 , 0.55 , 0.33 ) (107)
T = I,T = I,(0.21, 0.67 , 0.12) .
' ~
1 8.2 Dimensionless, Normalized PCS Momentum Equations i The dimensionless and reference variables defined in Section 8.1 are substituted into Equation (96),
and each term is normalized by the reference buoyancy. The result is:
- i d = G*- iF or x _i- = x %, G ' - x,,,,,7 T V Im R, m,'
where t- x_= x %, = 1 x ,, =
l 8.3 Numerical Values for Scaled Momenten Groups I
The reference PCS buoyancy is eticulated using heat fluxes calculated from the equations presented in Section 6.6, and the reference mass flow rate is determined from tim buoyancy. The time constant and pi groups are then calculated for each time phase (except blowdown, during which there is no PCS air flow). The rado of the branch buoyancy to the total buoyancy, G/G,is presented to show the relative contribution of the downcomer, riser, and chimney to the total buoyancy.
I 61 ,
wtsmcuotst PaoramTray Class 2
- Table 81 PC5 Air Flow Path Momentum Equation Groups Blowdown Reflood Post Reflood Peak Pressure M5LB 401 209 69 153 t 325 x, _
- 0. I 6 0.16 0.13 0.I3 0.10 1.0 1.0 1.0 1.0
- n. 1.0 1.20 1.00 1.02 1.0 t x,, ,
1.23 0 0 0.07 0.15 0 GdG, 0.41 0.47 0.53 0.38 0,/G, 0.36 0.63 0.59 0.60 0.62 0.62 GdG, 28.000 54,000 145,000 68.000 R e.,,,, 35.000 The pi groups show the inenial effect is relatively minor early and by the post reflood phase the llow solution is determined only by buoyancy and resistance. The effect of the downcomer on the net buoyancy is relatively small. The air flow Reynolds number is high even during blowdown. (During blowdown it is due to the assumed initial condition of I17.5 7 shell temperature and 115 7 riser air.)
t I
- i i
l l
l l
6 62
l WF5nNGnotM PROraKTARY class 2
?
9.0 Test Scaling The AP600 phenomena listed in Table 91 are validated by test data. The pl groups that scale the phenomena are identified for each and discu'ssed in the following subsections. Momentum scaling for
- the LST is discussed in Section 10.0.
~
Table 91 Test Scaling for AP600 Phenomena Pi Group ,,
,GC I
Condensation Mass k,,M A, AP,,, 0.13 D,, P, Kw = where k,, = '_ap "Sc,in Transfer m ... RT,(v /g)") P,_ ,
3 p,
i F.vaporation Mass k, ,M, A, AP"** -
- where o I
l Transfer m ,,,, k'" . RT,D, hw Re",Sc "'
Forced Convection h,, A,(T,,, -T,)*
- Heat Tansfer in Riser **_ w ere h, = ' '
m ,,ah,q, Ou Air Flow Padt Flow I R,m,'
W convection, and **
Resistance K '" _ forced convection ;
l 2 p , A,2G, 2 p, A,2AP 9.1 Condensation Mass Transfer Test Scaling The prediction of pressure inside AP600 requires a correlation for condensadon mass transfer that depends on local property values. Table 91 shows condensation mass transfer inside containment depends on the product of the mass transfer coefficient and the steam partial pressure difference from the bulk to the wall. The free convection mass transfer coefficient can be represented by the Sherwood number and expressed.as a function of the Schmidt number and (Ap/p)"'. The basis for ;
replacing the Grashof number with ap/p was discussed in Section 4.2.1. Figure 9 shows the range of l
l parameters covered by the LST envelopes the operating range of AP600 and the test data agree well I
l with the free convection mass transfer correlation. The data and correlation are discussed in more detail in Reference 17.
i 1
63
) WEsn%GuoL5E PROPmETARY C1. Ass 2 t
, t i ;
- O, C l 02 ,
l a
! i
- 0 15 -
1 s
con. i.
l I
- o .t O oo 01 -
On
[ o o o ;
! o oo o o l G 0 06 -
o o eW o ,
s ee w g i
0 0.7 04 04 05 06 (delta-rho /ft o)'* .,
Figure 9 Free Convecdon Condensadon Data from the Large Scale Test Compared to the Correladon and the AP600 Operadng Range -
-QC '
9 t
1000 .
sn. o oexa./'(sef*
f 100 -
10 -
l i o w a e.- i i
)l 1 i amoa i l i ,
I 100E.04 1.00E+05 1.00Ed 100E+03 1 Reynoide Number. Re, Figure 10 Forced Convecdon Evaporadon Data Compared to the Correladon and the AP600 Range of Operadon 64
%Esn%GCDLSE Pa0PaKT4RY Ct. Ass 3 9.2 Evaporation Mass Transfer Test Scaling
-QC#
The predicdon of heat rejection from the outside of AP600 requires a correlation for evaporation mass transfer that depends on the local propeny values. Table 91 shows the evaporadon mass tiux depends on the forced convection mass transfer coefficient and the steam partial pressure difference from the liquid surface to the riser. The evaporadon mass transfer coefficient can be represented by the Sherwood number and expressed as a function of the Reynolds and Schmidt numbers. De range of Sherwood and Reynolds numbers for AP600 operadon is shown in Figure 10 to be within the range covered by the LST and Gilliland and Sherwood test data. The figure also shows the data agree well with the forced convection mass transfer correlation. Note that although the Gilliland and Sherwood data range is shown on the figure the actual data were not local, so are not included on the plot. The data and correlation are discussed in more detail in Reference 17.
9.3 Forced Convection Heat Transfer Although a second-order phenomena, the prediction of heat rejection from the outside of AP600
- includes a correlation for forced convection heat transfer that depends on the local property values.
Table 91 shows the evaporadon mass flux depends on the forced convecdon heat transfer coefficient and the temperature difference from the Uquid surface to the riser. The forced convection heat transfer-coefficient can be represented by the Nusselt number and expressed as a function of the Reynolds and Prandtl numbers. Figure 11 shows the test Nusselt and Reynolds numbers envelope the operaung range for AP600. The data shown in the figure are from tests that operated in mixed free and forced convection and show significantly greater scatter than expected for typical forced convection heat transfer data. The data and correlation are discussed in more detail in Reference 17.
9.4 PCS Air Flow Path flow Resistance The flow resistance in the PSC air flow path was measured in the 1/6 scale air flow' test". Although' AP600 operates in natural circulation and the test was fan forced. the buoyant pressure, G, and the.
forced pressure drop, AP are interchangable in the pi groups. Consequently, a fan forced test produces a flow resistance that is equally valid for a buoyancy forced system.
l The overall pressure loss coefficient for the system is a combination of form losses and fristion losses.
It is known from the test that the form and fric: ion losses are approximately equal. Thus it is expected that the resistance should be a weak function of the Reynolds, number, with approximately 1/2 the Reynolds number dependence of the friction factor at the same Reynolds number.(The RMS roughness of the inorganic zinc coating on three STC tests ranged from 150 to 250 micro inches per j inch, and the roughness of the commercial steel baffle is esdmated to be no worse. Consequently, r/dn = 0.00012 in the riser where most of the friction occurs. At this relative roughress and the l
Reynolds number at the peak pressure, the exponent for the dependence of friction on the Reynolds number is -0.20. Thus, the loss coefficient is expected to be of the form C Re". 4 1
65 l
Wrstrwootst PaorsurTAny class 2 The loss coefficient is defined by setting x,,, = 1 and expressing the loss coefficient as the ratio of.
pressure drop to stagnation pressure: ,
4' AP*
I R' = C Re,* ' =
th,#/ (2 p, A,')
The 1/6 scale test report presented a loss coefficient of 2.37 at Re = 105,000. Subsequent design ,
changes increased the loss coefficient to 2.50. This gives a loss coefficient correlation of IR, = 7.94x Re*". At the peak pressure, Re = 135,000, so IR, = 2.44. At the minimum Reynolds number of 35,000, IR, = 2.79. ,
It is concluded that the 1/6 scale test results can be scaled to AP600 for turbulent air llow using the relationship:
IR, = 7.94x Re* *.
~
9.5 Wind Effects .
A series of tests were conducted in wind tunnels to characterize the effect on the AP600 PCS air flow of environmental wind speeds up to the AP600 design limit of 214 mph. The particular concern was the effect of upwind terrain and obstructions that could subject the PCS air flow path to pressure fluctuations that might induce reversed flow in the riser, Such fluctuations might produce a worse condition than the assumed zero environmental afffect. The Reynolds number for the plant was examined in facilities at two different scales to insure the appropriate flow regime was sumulated in the tests. The test evaluation22showed the wind posidve characteristic of AP600 more than off set the effect of fluctuations.
'the recirculation of the chimney outflow (warmer and more humid than the environment) to the downcomer inlets was evaluated2 s and determined to have an insignificant effect. ,
9.6 Wetting Stability Heated and unheated water distribution measuremerds were made on tests to support the modeling of water coverage on the external shell of AP600. The model and its application to AP600 is presented in Referencel5. The dimensionless groups appropriate for scaling water coverage are defined in the literature and those that are most significant for AP600 are the film Reynolds number, Marangoni number, and Bond number, defined respectively as:
Re = $
p Ma = b dT 2k p 8
- ' B=N 8
'the range of these groups for AP600 and two of the tests are presented in Table 9-2.
66
w rstr.cuotst enormanny Ct.rss 2
~ _qg Film Reynolds Number:
Upper Sidewall 1100 60 to 800 600 to 1300 Bottom of PCS surface 600 49 to 1100 na Marangoni Number:
l Upper Sidewall 2600 120 to 4700 unheated Bottom of PCS surface 720 33 to 1500 unheated Bond Number:
Upper Sidewall 0.009 0.003 to 0.016 0.014 to 0.018 Bottom of PCS surface 0.005 0.002 to 0.010 na Table 9 2 Comparison of AP600 Operating Range to Tests for Liquid Film Staoility The comparisons show the range of AP600 operation is adequately covered by the test data.
4 2 ,
. Nu a 0 Ot*Re)"(PO
1.5
- h. s .
a!
g .:.i. ..
- . : 1 , : ;, , .
] 1 n' , .
s..
i n
g
.i . , . t* '
g l ll
.. * /*
0.5 - *I
, v
" l n 1.00E+t 1.00E+03 1.00EW 1.00E+05 Reynold. Number Re Figure !! Mixed Convection Heat Transfer Data Comparison to the AP600 Operating Range 67
. . - . _ , - - - . - _ ~ ~ _ . _ _ - - - - - _ ~ _ . - -
%r5r1%GCDLSE PROPRIET4aY Ct. Ass 2
- s i
i 10.0 Containment Momenutm Scaling The scaling of momentum from forced and buoyant jets in large stratified volumes, such as the compartments and above deck volumes in AP6to, has been addressed by Peterson". Baines '
f Turner" presented scaled reladonships for density gradients in a stratified volume as a function of l
) dimensiordess plume characteristics. These references provide analytical bases for evaluating the et'fe .
' of jets and plumes on enclosed volumes, and present equations for scaling the effects. Those i references provide the analytical basis for scaling momentum in AP600 as it affects mixing and
! . stradfication and heat sink utilization duri ng DBA. ,
i l
This section presents some of the important consideradons for scaling the LST results to AP600. The I application to AP600 is documented in the mixing and stratification report.'
J 10.1 Froude Number Relationships ,
The internal mixing and stratification phenomena teltJve to the steam jet can be represented by the jet i Froude number, or the Richardson number which is 1/Froude. The Froude number can be considered 3
1 as a ratio of kinetic energy to potential energy, or pU /opgH. The Froude number is sometimes defined as the ratio Re'/Gr. In AP600, interest is focused on the extent that the jet kinede energy <
I enhances mixing inside containment. During a design basis transient, the jet potential energy varies a factor of 2 to 3, while the kinetic energy varies by many orders of magnitude. The Froude nutuber l is a more direct measure of the kinetic energy than its inverse, the Richardson number, and thus, the
' Froude number is used for scaling the AP600 internal phenomena.
i
' The internal containment phenomena that are of interest for AP600 scaling are:
i The jet t'ype, whether predominantly forced or buoyant, is important because it determine way the jet interacts with the containment volume. .
If the jet kinede energy is sufficient to disrupt stabic t,tratification, it may also be sufficient l
energede to virtually eliminate vertical gradients in the upper containment volume and to a induce mixing between the above deck and below deck regions.
1 It is desired to use Froude number formulations that represent these phenomena in both AP600 an LST to permit scaled inferences between the tests and AP600. The appropriate form of the F number is different for each of the above phenomena.
10.1.1 Forced / Buoyant Jet Peterson recommended the following equation to determine the elevation where a forced jet transl to a buoyant jet:
68
%rsmcCDLSE PhortuET4aY Class 2
/ . %L4 f Vid f )
~
PoVl g z,,, ,
gggg
( p , -p ..) g d. p, d, A jet Froude number can be defined, based on the jet source velocity, density, and diameter, and the ambient containment density:
Fr P" " (117) g = E(P.-Pold, Rewriting Equation (116)in terms of the jet Froude number gives:
f M f M4 b (IIII Frg b = or ""* = Fr/o" p, P. """,
d3 do According to Equation (118), jet transition is not a function of the containment height or volume: the transition elevation only depends upon the jet source characteristics. Equation (118) is equally valid for predicting jet transidons in AP600 and the LST. ,
10.1.2 Containment Stability Peterson also presented equadons for jets in large stratified fluid volumes. Peterson defined a stably stratified fluid as one in which the horizontal gradients of temperature, density, and concentration are negligible everywhere except at the boundanes of jets and wall boundary layers. Vertical gradients of .
temperature, density, and concentration remain. His equation for a stably stratified volume,is:
r Mr3 f WS (p,-pJgde H ;.
do
,{
(gg,)
P. Uo' ,
lo 4daH, Taylor's jet entrainment parameter, a, can be assumed to be a constant with a value of 0.05, l A volumetric Froude number can be defined that is the square of the jet Reynolds number, divided by t the containment Grashof number:
P0 (120)
Fr' = '
t g tp,-po)H 8 Rewriting Equation (119) for stable stratification in terms of the volumetric Froude number gives:
f M
- do (121)
Fr, < l+
( 46aH , l As a meaure of stability, or lack thereof, the volumetric Froude number can also be used to correlate I vertical density gradients. It is shown in Section 10.2 that stability corresponds to a volumetric Froude l number on the order of unity. Volumetric Froude values orders of magnitude greater than unity imply Reynolds number (or kinetic energy) dominated phenomena, while Floude numbers much less than unity imply that the Reynolds number is not an important parameter for mixing inside containment, j 69
wismenotSt PaonurTray Ct.ru 2 t
l i
Equation (121),is equally valid for AP600 and the LST jets with similar rm /d.
t ;
10.2 Application to AP600 l
L . t Values of the geometric parameters used to evaluate the jet and volumetric Froude numbers for APNx) j and the LST are presented in Table 101. The values of the Froude numbers at the stability limit .md l for the jet transition elevation are summarized in Table 10-1.
I
~
LST/AP6m >
. .6 M O Lil
. LOCA:
Height. H. (ft) 109 13.2 1/8.26 Source Diameter, d,, (ft) i1.1 1.66 1/6.69 Fr. at Stability Limit 2.96 3.57 1.21 l Fr,,, at is 0.lH 1.46 0.62 0.42 Fr,.o at y= H 1.46:10' O t>2x10' O.42 1
MSLB:
Height. H. (ft) 2.46 .256 t/9.61 Source Diameter, dn, (ft) 74.8 9.01 1/8.30 j
' Fr, at Stability Limit 1.52 1.44 0.95 ;
Fr,.oa t rm=0.1 H 138 227 1.64
. Fr,.o at z =H 138x10' 227x10' l.64 -
Table 10-1 Geometric Parameters and C itical Froude Numbers for AP600 and LST LOCA and I MSLB l L
f h
l
\
l 1
l J
70
l WESTI%G90tbE PROPMETARY class 2 a/ L.
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...... . . . .. . . . .. .u . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . ..
. . . . . . . . . . . . . . . . . . . . . . . . .g, 11 :q HomemmeHI HueHe HHe:HHein HiHopO.QQ1 u.=
1
.HsHHei:l.
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. t.t.tt.t.t
. t.t.t.i.
t t.tt.t.t.t.tt.t.t.t.t.tt.t.
. .... g.. . .. .. .. .. ~ ..... . . .
E 0.1 in mumm : m LsT =n. l0.0001 I. m. . n..u..n..u.n.a..n.n.l.il.
. . .. .. ... .. .u.n.n. ..n. .i n.: !!.e mum Ihme .n..u u.n.u..n. n'!.!.!.e n:
. . . . . . .. . . .. . . . . . . . . .. . .. .. .d.
. ......l.mmu..a
.......u....u..... .. .
0.01 j
!l, llllllllllllll]lllllllll
.........................t..
.ll.l.ll.ll.ll.l.l.l.lllllll.ll.ll..ll.l..llllll.ll.ll.l.ll.l.l(..
. . . . . . . . . . . .l1 E.05 0.001 . .. ..u. . . . . .. .......................=.9.......
. . ....u. . . ..- 1E 06 1 10 100 1000 10000
. Tme(Seconds) .
- Jet Froude ~~~ Volumome Froude Figure 12 Froude Numbers inside Containment for the AP600 DECLG
-^^^^^
. - 4a/
1 NH u. . n. a. n. .n..m. 100
. . .... ..n.........u..m. . u. .n. u. n..u.
m.
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- m. ...n. . . ... ..... . u.n.t n.u..u..n.
. .n.. a. . . . . . . . . . . .
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. . ? %,. ............................................
. . . . . . . . . . . . . . . . . . .......u..............u............u.....
. Amen... .
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jM gjh s.a.s.s.a.s. s a s u..s.. 443 gatsss..s s. s.s.s. s s.s.s. ss s s.s.s. s s.s.s s s s s.s.s.s.s.s.s a.s t n e s.s a.s.t as.i 7.. .s.t s. s.a.
s s a. ,
....u.u.....................
....m.. . ..w . ..... .
% ..u......................s....... %
W 100 m gim...u..m...a.m..mmnunmunm'. n. I same um ni il e..e. . . .. . .... . . . . . . . . . . . . . . . . . . , .
k.....
.'..'..u....a..
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. .. . . ..........u...............
........................... .1 .. .
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......................u.... . . . . . ..
j@l j tt.tt
. t.t.t... t t t.t.t.t
. . .t.t. s.t.s . t s.tt.t.t.t.t
. . .t tt . t.t
. tt.t
. .t.t.t.a
. . rt.t.t.t.t
. . . t.t . t.t.t. t.t
. t.t
. it.t.t.t
. . .t.t.t . . .lt.tt.i
. t.stt.i.s t.t.tt.t
-Q,j t.t.t l [
..m.........................................
. ......................u.............. ..u... .
. < ..................u................un.... . . . . . . . .
. .~ . . . . . . . , .........u.......u. . . . ...
- 80%Susved 100 . . . . . . . . . . . . . . . . . . . . . ... 0.01 1 10 100 1000 Time (seconds) s
- Jet Froude --~ Volumpgic Fr Figure 13 Main Steam Line Break Jet and Volumetric Froude Numbers 71
I 1 J
% Eyrt%cHOLSE PROPRIET ARY Ct. Ass 3 ,
1 I
d n
- -,M j 10.+....~...~...............................~..............~...............
j i
i t
5
- +
T j 1.:.:.::.:.::.:.::*a.. *:::::::::::::::::::::::::::::::
...9........... . . . . ::::::
. . . . . . . . . . . . . . . . . . . . . . . .m.
.. s.gp. .
. ...............m..................g.
. . . . . . . . . . . . . . . . . . . ...... ...... . . W.
........................................................... \
......................................4........
. ......................................................m............ {
. ............................................g...............................................................
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E
......................W.........W**W********************~********************************************
l e = a E l
0.1 r... ...:.:::..:::::
... a. .:.m..:.:.:.:.:..::::::::::::::::::::::.::::::.::::::::::::::::::::::::::::::::::::::::.::::::.:::..::.
t
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b i
4 y y yy ieyy y 1 Y WT Tuvv .T T U TIv y y y v i yy a evi T u I T <vvea v i iT eisa 1E.06 1E.05 0.0001 0.001 0.01 0.1 1 Volumetnc Froude Number i
p
- LOCA, F
i I .
l Figure 14 Steam Mixing Data above and below the Operating Deck from the LST l l 4 t
J 10.2J Los of Coolant Accident i
The volumetric and jet Froude numbers were calculated for the AP600 DECLG. with the assumption that the ambient density is that of a well. mixed containment. The results are presented in Figure 12.
1 The fact that the jet and volumetric Froude numbers differ by a factor of 1000 simply results from the fact that (H/do)' = 1000, approximately. The jet Froude numbers show that the jet is mixed forced and ,
l buoyant over the Srst 27 sec. of the tranient and is buoyant over 90% or more of its height after 27 l
sec. The volumetric Froude numbers indicate that the containment 4 stably strati 6ed aher 4 sec. into the DECLG. Because containment is stably stratified. the jet flow rate can cause the density gradients to increase or decrease. but cannot disrupt the stably stratified containment. AAer approximately 1000 seconds, the time when external cooling becomes important. the volumetric Froude number is less than
< lx10'. This is four orders of magnitude less than the stability limit. Consequently, it is expected that mixing between elevauons above and below the jet source and above and below the operating deck is limited to that induced by the large. scale circulation due to the rising buoyant jet. Furthermore, the very small magnitude of the volumetric Froude numbers (after 1000 sec.) indicate that the jet Reynolds j I
72 )
- l
wumscCDur PoormaTray class 2 l
number is nc; a factor in containment mixing during a LOCA.
10.2.2 Main Steam Line Brehk De volumetric and jet Froude numbers were calculate.1 for a MSLB, with the assumption that the ambient density is that of a well. mixed containment. The results are presented in Figure 13. The jet . ;
Froude number indicates that the jet is mixed over the entire transient with a minimum transition l elevation of 28 ft at 150 sec and a maximum transition elevadon of 45 ft. at 30 sec. The volumetric ,
Froude number indicates that the containment volume is unstable over the first 40 seconds of the 400 second transient, and stable thereafter. It can be anticipated that this instability has the potential to ,
induce a well. mixed state inside containment, both above and below the jet source elevation. and if the ,
Froude number is high enough the vigorocs mixing may even penetrate into the below deck elevation.
Comparison to the LST will indicate the effectiveness of mixing. ,
10.3 Application to Large Scale Tests The LST were conducted in several different internal configurations. The LST configuration with the ,
steam source exiting from a diffuser located under the simulated steam generator approximates the geometric configuration of a LOCA, and the LST configuradon with the steam source elevated 6 ft.
above the deck and exiting from a 3 inch ID pipe approximates the geometric configuration of an MSLB. ,
10.3.1 LOCA Configuration
.4 Twenty.five LST were conducted in the LOCA configuration, i.e., with the diffuser located under the steam generator model, he jet Froude numbers ranged from 0.0016 to 0.231 and the volumetric Froude numbers ranged from 5x104 to 6x10 . The LST Froude number ranges are compared to the d
AP600 DECLG Froude numbers in Figure 12. De figure shows that the LST data span the range of AP600 postew etting operation. De jet Froude numbers indicate that over 92% of the LSTjet height is buoyant, consistent with the post-blowdown buoyant height of 90% or more in AP600. The volumetric Froude numbers indicate that the LST containment atmosphere, like the post blowdown i AP600, is stably stratifled with negligible momentum.
It is concluded that both the LST and AP600 jets are predominantly buoyant plumes, and the internal jet induced mixing phenomena in the post. blowdown AP600 lies within the range of the LST.
~
- (f' b As a further measure of mixing in the LST, steam concentrations just above the deck and below the deck near the bottom of the vessel are presented in Figure 14. The plotted values are the ratio of the measured local steam partial pressure to the partial pressure of steam assuming perfect mixing. A value of 1.0 indicates perfect mixing. The values show the above deck ratios generally range from 0.6 l
to 1.0 and the below deck values range from 0.1 to 0.4. De data show no significant trend with the Froude number, as expected at these very low values of volumetric Froude number. These data l
73 ;
l
%tsmcuotbE PROPRET4aY Cl.A&E 3 l
1
! support the fact that the jet Reynolds number is not a significarit f actor in containment mixing dur the post wetting phase of the DECLO.
10.3.2 MSLB Configuration
.- qb Four LST were conducted in the MSLB configuration two with the steam jet directed horizontally and two wi:h the jet directed upward. The jet Froude numbers ranged from 7.900 to 22.000 and the volumetric Froude numbers ranged from 0.286 to 0.695. The jet transitions from forced to buoyant in the LST at 2510 35% of the containment height compared to 40 to 71% in AP600. The greater '
- forced height in AP600 will cause better mixing. The comparison of LST to AP600 volumetric Froude numbers in Figure 13 shows the LST lie at the minimum AP600 values. The mixing data l measured in the LST and presented in Figure 14 show that even at the lower volumetric Froude numbers mixing is nearly ideal. .
1 The LST mixing data show that nearly ideal mixing occurs at volumetric Froude numbers as low as the minimum values that occur in AP600 during a MSLB. 'these results are vali,d for both horizontally and vertically directed jet sources, it is expected that the high jet momentum during an
- MSLB will pmduce very effective mixing throughout the above-deck region of AP600 i
r
' l 1
i' .
e i
e 8 4 6
' l l
1 74
l
% Estisot St PaoMurTany Ct. Ass 2 j l
11.0 Conclusions .
The pl groups were defined and evaluated for containment energy and pressurizadon conductances to heat sinks and the shell, air flow path momentum, and internal momentum. The values of the pi groups and discussions presented show the following are the dominant components and transport ;
processes in APNO. .
For Containment Pressure:
The break source steam mass flow rate because it drives pressurizadon The gas volume because it relates presssure to stored mass and energy (volumetric compliance or capacitance) [
1he internal steel, concrete, and steel Jacketed concrete heat sinks that absorb energy and condense steam mass, thereby reducing pressure.
The shell because it is a major heat sink and the only energy transfer path out of containment to the riser.
The liquid condensate that carries away part of the enthalpy of the condensed steam.
Liquid film stability because it can limit the area for evaporation, and evaporation is the dominant energy transfer from the shell.
For Energy Transfer Resistances:
The conductance of the shell and the heat sinks limits energy absorydon and transfer rates The condensadon and evaporation mass transfer conductances transport most of the energy to the shell and heat sinks, and from the shell to the riser. l l
Horizontal liquid films can produce low conductances that ir.sulate upward-facing horizontal :
i surfaces.
. l Stratificadon can increase the concentration of dense noncondensables and locally limit the udlization of heat sinks and conductors.
Air Flow pat mornentum:
Buoyancy and flow resistance determine the air flow rate and have a strong effect on the evaporadon rate.
75
wtsriscuotst PeorairTamY Class 2 De downcomer is not a significant contributor to the air flow path momentum.
For Internal containment momentum:
De above deck atmosphere remains weakly stradfied during the DECLG LOCA and is well. ,
mixed during a MSLB. Intra compartment stradfication and the effects of large scale -
circuladon can affect internal heat sink utilization. Dese are complex phenomena that must be evaluated and bounded in the evaluation model.
The dimensionless groups derived from the scaling analysis shows the dominant transport processes.
- which are condensadon inside containment and evaporadon outside containment, are properly scaled to represent the AP600, and that the range of test data covers the range of AP600 operation.
e J
76
wumscootst enormataar cuss 2 -
l 12.0 Nomencloture ,
Symbol Quantity Letters 1 A Area ,
c, Constant pressure specific heat e, Constant volume specific heat d Hydraulic diameter i d., Hydraulic diameter of jet at source D, Gas phase diffusion coefficient :
. g Gravitational acceleration h Convective heat transfer coefficient h, Gas phase enthalpy ;
h, Liquid phase enthalpy h,, Liquid-to gas enthalpy H Height, height of containment above steam source k 1hermal conductivity
.k, Gas phase mass transfer coefficient i
L Length m Mass
[
m Mass flow rate m" Mass flux l P Pressure or partial pressure P,, Log mean pressure difference = (P P i)/In(P /P i) i 4 Heat flow rate ,
4" Heat flux Q Volumetric flow rate "R Universal gas constant .
T Temperature - :
u, Liquid phase internal energy u, Gas phase internal energy ,
l u,, Liquid-to-gas internal energy Ua Velocity of jet at source V Volume 4,,, Elevation for jet transition from forced to buoyant Subscripts a - Ambient containment air Air bf Baffle brk Break source i
77 i
l wumwmotst rnonurraar Ct. ass 2 ,
I c Convection heat transfer ec Concrete .
ch Chimney ,
cond Condensate t ct Containment gas -
! ex External convection l 1
d hydraulic diameter, or droplet value de Downcomer ,
c Equivalent heat transfer coefficient
, evap Evaporation .
. ex External l hs Heat sink if Internal liquid film in inlet value i
j Jet value t If Liquid film r m Mass transfer, or mixture value mx External mass transfer t
out Outlet value .
pl Pool '
r Radiadon rx External radiation ri Riser , t IR IRWST water ,
se Subcooled external liquid film sd Shield building sh Containment shell ;
i sat Saturated .
srf Su'rface :
l st Structure stm Steam v Volumetric value I xf External liquid 81, I o Inidal or boundary value for nondimensionalizing O Value at jet nozzle ~ exit Supersedpts ,
?
- Nondimensional value T T used on compressibility to indicate a normalized partial derivadve Z = (T/ZX&Z/&T)
Greek htters ;
78 f
l wcsnwmotn PaoramTraY class 2 l a Taylor's jet entrainment constant value is 0.05 6 Thickness
.i Difference e Product of emissivity and beam length in radiation heat transfer p Density c Radiation constant v Kinematic viscosity .
t Time constant Dimensionless Groups ,
Froude number p/Un:/g(p.-pn)do or po Uo:d//g(p -po) !' l Fr Gr Grashof number g(p, po)H'/p v or g(p po)d//p,v or, g(p2 pi)L'/p2v Nu- Nusselt number = hUk Pr Prandtl number = pc/k ,
Re Reynolds number = U4/v -
Sc Schmidt number = p/pD, ,
Sh Sherwood number = kATP ,UD,P
[] Dimensionless Scaling Group c 4
e 9
4 e
8 4 i
79
wesweceous raonurtAny ca. ass 2 13.0 References
- 1. WCAP 14382, "WGdTHIC Code Description and Validation," May 1995, "WGOTHIC Application to AP600", (to be issued). l 2.
- 3. NTD NRC 95-4563, " GOTHIC Version 4.0 Documentation" September 21,1995.
- 4. NTD NRC 5 4577, " Updated GOTHIC Documentation". October II. ;995.
- 5. NTD NRC 95-4595, "AP600 WGOTHIC Comparison to GOTHIC," November 13, 1995. ,
- 7. NTV NRC 95 4545, "AP600 PCS Design Basis Accident Road Maps," August 31,1995. ;
- 8. "AP600 Standard Safety Analysis Report". Westinghouse Electric Corporation, June 26,1992.
- 9. NUREG/CR 5809 EGG 2659, "An lategrated Structure and Scaling Methodology for Severe Accident Technical Issue Resolution," INEL EG&G Idaho, Inc. ,
- 10. W. Wulff, " Scaling of Thermohydraulic Systems", BNL-62325, May 1995, Brookhaven National Laboratory.
- 11. Letter, N. J. Liparulo (Wesdaghouse) to R. W. Borchardt (US NRC), "AP600 Passive Containment Cooling System Preliminary Scaling Report". NTV NRC-94 4246, July 28,1994, i
- 12. D. R. Spencer, Scaling Analysis for Ap600 Passive Containment Cooling System", WCAP-14190 October 1994, Westinghouse Electric Corporadon, Proprietary Class 2.
- 13. D. R. Spencer, " Accident SpeciScation and Phenomena Evaluation for AP600* Passive Containment Cooliog System,' NSD NRC-96 4643, February 12,1996, ,
- 14. NSD NRC 96 4763, " Assessment of Mixing and StratiScation Effect on AP600", July 1, l
1996,
- 15. Letter, B. A. McIntyre (Westinghouse) to T. R. Quay (USNRC), "AP600 PCS Film Coverage Model" NSD-NRC-96-4728, May 21,1996.
i
- 16. NTD NRC 94-4100, Letter, N. J. Liparulo (WQ..wase) to R. W. Borchardt (US NRC),
' AP600 Passive Containment Cooling System Letter Reports: ' Radiation Heat Transfer through L Fog in the Passive Containment Coo ling System Air Gap", and " Liquid Pilm Model Validation".
l l
' 17. R. P. Ofstun, " Experimental Basis for the AP600 Containment Vessel Heat and Mass Transfer Correladons", WCAP-14326, March 31,1995, Westinghouse Electric Corporation.
I '
- 18. F. Kreith, Principles of Neat Transfer,1965, International Textbook Company.
wrsnscuotst reorairrany ct. ass a
{
4 d
- 19. Letter, N. J. Liparulo (Westinghouse) to R. W. Borchardt (US NRC), " Supporting Infctmation for the Use of Forced Convection in the AP600 PCS Annulus", NTD NRC 95 4397, February 16, 1995.
- 20. E. R. G. Eckert and R. M. Drake, Jr., Analysis of Heat and Mass Transfer,1972, McGraw.
Hill.
- 21. W. Wulff, " Integral Methods for Simulating Transient Conduction in Nuclear Reactor Components", Nuclear Engineenng and Design 151 (1994) 113-129.
4
- 22. NTD NRC-95-4467, " Analysis of AP600 Wind Tennel Testing f >r PCS Heat Removal [PCS-T2C-059)," June 2,1995.
- 23. . NTD NRC 94-4166, "AP600 Passive Containment Cooling S' stem Letter Report " Enclosure 1, " AP600 Containment Plume Investigation," June 10,199/,
24.' W. A. Stewan and A. T. Pieczynski, " Tests of Air Flow Path for Cooling the AP600 Reactor Containment", WCAP - 13328,1992, Westinghouse Electric Company, Proprietary Class 2.
4
- 25. Lener, N. J. Liparulo (Westinghouse) to Document Control Desk (USNRC). NTD-NRC 94- -
i 4166, "AP600 Passive Containment Cooling System Letter Reports: AP600 Conta!nment Plume Investigation," by R. L. Haessler, June 10,1994
- 26. E. Hihara and P. F. Peterson," Mixing in Thermally Stratified Fluid Volumes by Buoyant Jets", ASME/JSME 1hermal Engineering Conference: Volume 1, ASME 1995. .
- 27. P. F. Peterson, " Scaling and Analysis of Mixing in Large Stratified Volumes", International Journal of Heat and Mass Transfer, Vol. 37, Supplement 1, pp 97106,1994.
- 28. P. F. Peterson, V. E. Schrock, and R. Grief, " Scaling for Integral Simulation of Mixing in Large, Stratified Volumes", Sixth International Topical Meeting on Nuclear Thermal Hydraulics, October 5 8,1993, Grenoble, France.
- 29. W. D. Baines and J. S. Turner, " Turbulent Buoyant Convection from a Source in a Confined Region", Journal of Fluid Mechanics, Vol. 37. Part 1, pp 5158, (1969).
I 81
..__ _... __ . _ ._- _.m_-- _ _ _ _ _ .__ _ _ _ _ - _ _ _ ___.___
~
PREl!%GN4ay WEsnscBOLSE PROPluETARY Class 2 APPENDIX A -
, . DEVELOPMENT OF THE RPC EQUATION De goal for this part of the scaling analysis is to develop an equation that represents the containment gas rate of pressure change (RPC) due to the sources and heat and mass transfer to the containment shell and l
- i. .
Internal heat sinks (steel, concrete, fain, fog, and pools), and to couple the RPC equation to the shell and heat sinks by thermal resistances. The equation should be in a form that minimizes unknowns.
i
' Assumptions for the development of the equations are:
We mass of the gas mixture is the sum of the individual air and steam masses: m = m, + m o.
- The internal energy of the mixture, U, is the sum of the individual air and steam internal energies, i that is, there is no reaction between the two: U = mu = m,u, + mo u..
Re Dalton rule for additive partial pressures: the total pressure is the sum of the air and steam l
partial pressures P = P, + P,..
l I
Air can be approximated as an ideal gas due to high reduced temperature and low reduced
. pressure (T, > 2 and P, < 0.05). Thus P,V = Z,m,R T where the compressibility factor Z, =
1.
L l
Steam is a real gas with equation of state P ,V = Z,,m R.,T where the compressibility factor Z,, = Zo(P o .T). Steam properties are from steam tables.
There is no liquid-vapor phase change within the gas control volume. Phase change occurs after the gas passes out of the gas control volume.
Intensive properties are Extensive properties are & fined in terms of the gas mixture P. Tim,, and m,..
defined in terms of P. T, and the steam mass concentration, C. De gas mixture relationships are defined. '
The RPC equation is developed from the conservation of mass and energy equations for a control volume.
De equation of state is used to eliminate the variable T from the RPC, and the derivative of the equation of state is used to eliminate the variable dT from the final expression. The condensation / evaporation mass transfer terms are related to conductances, and the conductances are substituted into the final form of the RPC.
i Gas Mixture Relationships l
.Ma.si1 On a mass basis the mass of mixture is the sum of the masses of the individual gasses:
(1) m = m, + m,, -
On a molar basis for a non-reacting mixture, the number of moles of gas mixture is the sum of the moles of individual gasses: j (2) !
n = n, + n,,
i' hLo,1,g;gjg Weinht Because the number of moles is defined n = m/M, the mixture molecular weight can be defined from (2):
A1
i PREtt\n%ARY WESTINGMOLSE PROrguETARY CLASE 2 m,m,, m"* M= ""**"" (3) mdM, + m,/M, M M, M ,,,
Gas Constant
~
The mixture gas constant can be determined from (3) and the detinition of the gas constant R = R/M
- "*' so R= "" " " " " (4)
R= m (m, + m,,)
Defining the steam concentration C = m,Jm, the air concentration is (I C), so Equation (4) can be written:
(5)
R = (1 - C)R, + C R, l Enthalov The mixture enthalpy can be derived from the definition of enthalpy H = mh = mu + PV, the internal f energy of the mixture, mu = m,u, + mo u,,, and the Dalton rule, P = P + P ,: .
l mh = m,u, + m,,,u,, + P,V + P V (O
f so h= m"h" + m""h"" or h = (1 -C)h, + C h, m
i Soecific Heat I
The mixture constant pressure specific heat can be derived by taking the partial derivative of mh with l
respect to temperature, and noting that the masses are not functions of temperature:
Bh Sh Bh i 3 so m p=m + m,,
7(mh) = a (m,h, + m,,h,,)
m"c'" + m""e' "" or c, = (1 -C)C,, + C c,,
- and c, = m i
A similar approach can be applied to the internal energy to derive the mixture constant volume spe f heat:
(8) c, a '# * ' ' "
or c, = (1 -C)C,, + Cc,,
m I
Gas Comoressibility The gas mixture compressibility, Z, can be derived from the Dalton rule and the equation of state:
+ (Z n),, (9)
P = P, + P,, and P= so Zn = (Zn) 4
' Deleting RTIV from each term and divide by n:
4-1 l
A2
l i'
PRELI\g uay WrSrtNGCDlsE PROPRETARY Ct. Ass 2 7 , n,Z, + n.Z" (10)
" l With nR = mR, Equation (10) can be written:
ZmR = Z,m,R, + Z m.R. or ZR = (1 -C)Z,R, + CZ R. (11)
)
The derivative of ZR is:
I d(ZR) = -Z,R,dC +(1 -C)(Z,dR, + P dZ,) + Z,,R dC+C(Z dR.+ R .
o dZ.) (12)
The values of Z,, R , and R are constants, so Equation (12) can be simplified to:
d(ZR) = dC(Z.R.-Z,R ) + CR dZ. (13)
Whereas the concentration, C, can range from 0 to 1; Z,,is limited to the range 0.97 to 1.0. Therefore, the derivadve dZocan be neglected and dZR expressed:
d(ZR) = dC(Z.R.-Z,RJ (14)
T The property Zr, where Zr = (T/Z)3Z /3T, can be expressed in terms of Z , and Z' with Equadon (10):
a( Z ,+ " Z d e n ,aZ. (15)
Zn Z n Zn a since n, nm, ny., and Z, are not functions of temperature. With the substitution Z,,n ,/Zn = Po /P:
T n,, aZ,, , Z. n. T dZ. , P. ,p g)
Zn a Z - n Z,, R P For steam at 40 psi and 280 *F the magnitude of Z',, is 0.13. Consequently, the temperature derivative of the compressibility factor may be significant.
Mixture Enthalpy The gas mixture total enthalpy, H = mh = m h, + m h.,is a function of the four independent variables P, T, m,, m 1he derivative of H can be written:
Sh d(mh) = m dT + m TPdP + h, dm,am" dm, + h,, &m,,am""d (17) so d(mh) = me,dT + m dP + h,dm, + h,,dm,,
Examinadon of the steam tables shows that along the saturation line from 38 to 42 psia, oh = 1.9 B/lbm, while c,aT = 3.0 B/lbm and (3h/3P)AP = 1.1 B/lbm. Ahhough containment pressuriration does not follow the saturation line exactly, it does follow with at most a modest superheat. Consequently, the rate of change of enthalpy due to pressure is approximately -l/2 of the total, while that due to temperature is 3/2 of the total. Clearly, the pressure derivadve of enthalpy may be substantial, and tNs may contribute A-3
( wEste,caOL5E PROPRIETARY class 2 PREUAG%RY i
to pressurization. The presence of air inside containment will somewhat reduce the magnitude of the l enthalpy rate of change with pressure.
l i From thermodynamic relationships, the partial derivative of enthalpy with respect to pressure can be I wriiten in tertas of a temperature derivative:
Sh f =v-T* 08) dP W .
!. With the equation of state v = ZRT/P, and considering Z and v to be functions of the independent
- variables P. T, and C, the pressure derivative of enthalpy is
i Bh
=v-T 'RTBZ ZR' so Sh
=-T v BZ (g9) 7 77 + p s l With this expression and the abbreviation Zr = (T/Z)(8Z/3T), dmh can also be written:
(20) d(mh) = me,dT - VZ TdP + h,dm, + oh dm.
l Specific Heat From the definition of the constant pressure and constant volume specific heats, and the definition of enthalpy:
i h , du , 3(u + N , Bu BPy so (21) c' - c' = W W BT W c' - c' = 7 -
Substituting the equation of state. Pv = ZRT:
' ST T BZ (22) so e' - e' = 3(ZRD dT = ZRW + RTWc' - c' = ZR(1 +YW)
With the substitution Zr = (T/Z)BZ/8T T (23) c, - c, = ZR(1 +Z )
With the specific heat ratio y = c/c,, the ratio c,/ZR can be expressed:
"E - Y' T (24)
ZR (y -1)(1 +Z )
Equation of State 3
~ Starting with the equation of state T = PV/ZmR and differentiating:
'd(PV) , d(ZR) , dm' (25)
M=T ZR m
< PV >
Substituting' Equation (14) for d(ZR):
e i
&=T d(PV) , (Z,R -Z,R,)dC ,
dm (26)
PV ZR T, Or, in terms of the individual air and steam masses:
. A-4
PREttNUNARY Wrstv.cCDLSE PROPRETARY class 2 l
d(PV) Z, R,, d m., Z,,R o dm,, (27)
&=T ,
ZR ZR PV ,
Rate of Change of Internal Energy i
The total derivative of the gas mixture internal energy can be expressed in terms of enthalpy and pressuref 8) d(mu) = d(mh-PV) = d(mh) - d(PV)
Substituting Equation (20) for dmh:
T - d(PV) (29) d(mu) = me,dT - VZ dP + h,dm, + h,,dm ,
l Now substitute Equatien (26) for dT:
l l
I i
t .
[ "* R,, -Z, R,) dC dm - VZ dP T
+ h,dm,, + h,,dm - d(PV) d(mu) 4 me,T d(PV._I .
f PV ZR m ;
(30)
Substitute PV/ZR for mT and combine coefficients on dPV:
r _
T
" " dC + dm - VZTdP + h,dm, 4 h,,dh d(mu) = ( ZR.f -1)d(PV) ZR- g ZR m, '
! Substitute Equation (24) for c,/ZR and combine dP terms:
y(1+Z ) py (Z R,,-Z,R,)
T d(mu) = II
- VdP + II*Y ) PdV I
(Y - 1) ZR (32) l (Y - 1) (Y -1) '
Y(1+Z9 py dm + h,dm, + h,,dm , 1 f (Y - 1) m l I
Or in terms of air and steam mass, instead of total mass and concentration:
gg,) , (1+Z i) VdP + II *TZ 7) PdV TII* PV " "dm, (Y - 1) (Y - 1) (Y - 1) Y (33) )
T
_ y(1+Z ) py Z R" dm,, + h,ds, + h,,dm,,
(Y - 1) ZR ,
l d
A5
i .
WEKrl%CHOLSE PaorsuETARY class 2 PRE 1.DU%ARY
(
l CONSERVATION OF MASS AND ENERGY i
{ 1he conservation equations are written for a gas control volume with multiple steam sources and sinks.
and with multiple convective inflows and outflows.
[
- Conserve Mass l Conservation of mass applied to a control volume can be stated as "the rate of change of mass in a control l volume is equal to the sum of the mass fluxes in and out of the control volume" The equation for I conservation of mass for a control volume encompassing only the containment gas can be written:
I
- =m (34) m + { (m,m +m m ) + { mm ,
dt
' where the inde'x i represents convective air and steam terms, and j repr'esents condensation or evaporation steam mass transfer terms. Positive flows are into the control volume and negative flows are out.
Conservation of mass can also be applied to each gas species (air and steam) with the result:
! dm dm
.dt dt Conservation of mass can also be applied to the liquid that forms part of the gas control volume. The l
total liquid mass includes tne masses of the IRWST, break pool, drops, and liquid films. These are the liquid masses that displace gas in the containment volume, and cause the containment pressure to change.
l The liquid mass conservation equation is; j =%-sawrr -[dlw (36)
The break liquid includes the drops, as well as the liquid that pours into the break pool. The term m,
= -mt,, that is, the mass of gas tha: changes phase (either condensed from or evaporated to) the atmosphere is equal in magnitude, but opposite in sign to the mass of liquid that changes phase. The
' IRWST flow drains into the reactor (hence the minus sign) and subsequently is released from the break .
as liquid and/or steam, lhe liquid and steam from the primary cooling system (piping, pumps, steam generators, accumulators, and pressurizer) only appear as break source terms.
Conserve Enerny Conservation of energy for a control volume can be stated as "the rate of change of internal' energy in a control volume is equal to the sum of the enthalpy fluxes and the heat transfer in and out of the control volume. Conservadon of energy for the control volume encompassing only the containment gas can be wrinen:
$"h, + { (m ,h,, +m m ,h ) + [(th,h, + h A,(T,-T)) (37) d 2
where h is the total break steam enthalpy, hm = h + v /2 + gz. Elevation is negligible, as is v /2 for 2
all but the break source during blowdown. (Post-blowdown, y < 200 ft/sec, so v /2 < 0.8 BTU /lbm).
1 With Equations (1), (6), (28), and (35), the energy equation can be written:
A-6
}
Partenway wEsmcaot.sr rnomaway class 2 P dm 43g) m $ = m ,(h%-h) + { rh,(h,-h) + { (mm,(h,,, -h) + h A,(T, -T)) + , , ,
p dt dt.
RATE OF PRESSURE CHANGE EQUATION A rate of pressure change equation can be written by combining the equation for the rate of change of -
internal energy, Equation (32) with conservation of energy, Equation (37), and rearranged in terms of the pressure derivative:
dm"
( l + Z r) V dP = mm h, + { {m,,h,,,, + m,,,h,,,) + { (m,,,h,,, + h, A,(T, -T)) - h,
_( y -1) di dt(39)
T T dmn . y(1 +yZT ),y (Z,,,R,,-Z,,,R,,,) dC y(1 +yZ )p y dm _ (1 +yZ ), dV
- h"" dt (y - 1) ZR dt (y - 1) dt (y - 1) dt The dm.,,/dt and dm,,,/dt terms in Equation (39) can be replaced by Equation (35), giving:
- I V .dP = m (h, - h,,) + { [m,,(h,,,, - h,,,) + m,,,(h,,, - h,,)] + .{ (m,,,(h',,, -h,,) + h A,(T, -T)J
, ty -1) dt T y(1 +Z r) py (Z,,R,,-Z,,,R,,,) dC , (1 +yZ )p dV
. PV y(I +Z r) dm m (y - 1) dt"
~
(y - 1) (ZR) dt (y - 1) T (40) .
The first term on the right side of the equation represents the enthalpy flow rate of break steam. The second term, the summation over i, consists of two parts that represent the enthalpy flow rates of air and of steam convected in and out of the control volume, such as, through openings between compartments.
Wherever there is an opening, both air and steam are expected to flow simultaneously. The third term, the summation over j, also consists of two parts. One part is mass transfer (condensation or evaporation) and the other part is convective heat transfer between the atmosphere and the shell, steel, concrete, drops, or pools. The fourth term (dm/dt)is the work done on the gas by mass addition. The fifth term (dC/dt) is the work done on the gas by the changing concentration. The sixth term is the work done on the gas by volume change; the displacement of ges by liquid in the fixed containment volume.
The pressure equation shows pressure increases when: ,
The enthalpy of influx source i is greater than the enthalpy of the gas already in the volume.
The enthalpy influx from surface j is greater than h, or Tu is greater than T.
The net mass flux is > d.
t The steam concentration increases ( the coefficient on dC/dt is > 0 since R.,is nearly twice R.,,).
l The gas volume decreases.
Attematively, the energy equation can be combined with Equation (33) to give:
l A-7
PREt.1%nuny WESTP=G90LSE PROMUETARY Ct. Ass 2 1
l
)V = mm(h m - h,,) + { [m,,,(h,,, - h,,) + m,,,(h,,, - h,,)] + { m,,,(h,,, -h,,)
_g T y
+ { h A' (T'-T) +(yy(1 +Z )ZRP Z,,R,
- 1) p dt dm, (y -, 1) y(!p .z ZRT) p Z,,R,, dt dm (y - 1), , (1 dyl) +yz T)p dV Substituting (35) for the time derivatives of air and steam mass gives:
) .
r T T Z,,,R,,
(1 +Z ) V_dP =m m h* -h"" + y(I +Z ) P _
(y - 1) dt (y - 1) p ZR '
\ , r 7 (42)
+ y(I +Z ) P Z,,R,,
- [ M, u h,,,- h, + y(1 +Z r) p Z,,R.,+ m , ,, h,,,, -h ,
( . -
s 3
. < y h"*' -h"" + y(1 + Z 9 {.R""
u Z +h A'(T -T) II*Y2 PY.
+{ ,
m"* ' (y - 1) p ZR ,
8 (y - 1) di The containment gas volume only changes due to displacement by liquid water. The gas vow. .:. is the containment volume minus the liquid volume, V = V, - Vi , so dV/dT = - dV/dt. The liquid volume can be expressed as the liquid mass divided by the liquid density, V, = m/pi. It is sufficient to ignore the small liquid density variation with temperature. Consequently, with Equation (36), the volume rate of change term can be written:
7 T
. (1 +YZ ), dV , (1 + yZ ) P_ _ _ (43)
(y - 1) di (y-1) pi
'With this equation, the RPC is expressed entirely in terms of mass flow rates and convective heat transfer Each mass tiow term ca: Ties.enthalpy and does work on the gas volume. The work includes portions due to the change of gas mass, change of gas composition, and change of gas volume. The RPC is:
f i
7 Z R,, (1 +yz T) p (1 +yz T) P (1 +Z r) V_dP = rta, h,-h,, + y(1 +Z ) P _ +mm -m mwsT (y - 1) p, (y - 1) dt (y - 1) p ZR ,
(y - 1) p,
, r Y r
T Z,,R,,
+ m**' h"*'-h"" + y(1 +Z ) P
,{ m"' h"' -h" + TI(y*- 1) p ZR (y - 1) p ZR
- o
- L. ,
T T
+{ m"*' h"*' -h"" + (y y(1 +Z ) PZRZ,,R. ,(y(1
- 1) p
+yZ )+h
- 1) p,,
1 A'(T -T) 8
, (44)
In this form, the ' rate of pressure change is expressed in terms of the containment gas properties, the temperature of the heat sinks, and the i and J subscripted mass flow rates. The break gas and liquid flo rates, and the IRWST liquid flow rate are known boundary conditions. The convective (i subscripted) flows can be calculated with a network momentum equation, or parametrically treated. The condensation and evaporation () subscripted) mass flow rates can be calculated using a mass transfer conductance tha couples th containment atmosphere to the heat sinks or to the PCS air flow path.
The condensation / evaporation mass transfer rate expressed in terms of conductance, and the heat transfer coefficient expressed as a combination of radiation and convection conductance (heat transfer) coefficients are:
A-8
l pag.Lousany
' WESTt%HotsE PaoramTraY class 2 rh " (h8 -h,)
h,,, = and h = (h,, + h,,)
(T, -T)
With these substitutions the RPC becomes: -
T T Z,,R ,. (1+yZT) P (1 +yZ r3 p (1+Z )v dP =rh , h, -h,,, + y(I +Z ) P +m, m - mm37 {y , ) _
7 (y _ g ) Y'
" i f f
T Z,R, '
h,,, -h,, + 7( g .z T) p Z,,R,,
+[ s ., h,,-h, + y(Ily+Z )P
- 1) p ZR
+ m , ,,
p, ZR
. .. ( , g ,-(y - 1) ,,
f h ., . y(1 +ZT ) P Z,,R,, (g +yz T) p A '(T' -T)
,{
(y - 1) p ZR (y - 1) p, + hd+ h,'d, (46)
, ,(h,-h,) ,
e 6
4 4
A-9
I"E ^"Y wEmwoolsE PROPRIETARY CIAss 2 Appendix B l Initial Conditions, Boundary Values, and PI Group Values i
ne following tables present the initial and boundary conditions used to make parameters dimensionless.
f l De pi groups are tabulated for each component and time phase, and are derived from the initial and )
i boundary conditions by the equations presented in the scaling report. J
- \
QCl I Containment System Values MSLB Post Refl Peak init Blow Blowdow Reflood 252 244.2 247.7 300 240.16 240.16 50 44 50 46 60 P42 #@ psia 44 .
TEOQ)F mdategistIbm/sec 10300 10300 10300 200 70 500 0 200 200 0 mhDGghIbm/sec 20000 20000 0 0 200 70 0' lbm/sec 0 60 q$jlbm/ft3 rigstd 60 60 60 60 60 292.677 249 2485 T-sat F 273.0749 273.0749 281.0198 275.8166 psia 18.95261 18.95261 19.2731 19.06197 19.69809 20.57241 P air P stm psia 25.04739 25.04739 30.7269 26.93803 40.30191. 29.42759 C 0.5324 0.5324 0.521703 0.542397 0.507062 0.528339 rho stm Ibm /ft3 0.058661 0.058661 0.070486 0.062653 0.090066 0.064125 0.07319 0.073191 0.07319 0.073188 rho air Ibm /ft3 0.073191 0.073191 rho Ibm /ft3 0.131852 0.131852 0.143677 0.135843 0.163255 0.137313 Gamma 1.344507 1.344507 1.333759 1.330049 1.326791 1.343856 (1 +ZT)o 1.064669 1.064669 1.079826 .1.073995 1.103523 1.031355' (1 + GZT)o 1.086948 1.086948 1.106469 1.096417 1.137353 1.042136 1101.09 1083.557 1083.557 1086.04 1064.422 1089.557 hg ht B/lbm hbrk-hstm B/lbm 10.97863 10.97863 9.391419 10.43985 7.71867 EM Delta rho . BTU 92.19015 92.19015 92.19014 92.19014 92.19012 92.19009 .
e
' e B-1
.__ _ _ _ _ _ _ __m _ _ _ _ _ . _ . _ _ _ _ . _ _ _ _ . _ . _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _
i !
PRELL%G%ARY i WEKHSG80LSE PRortuETARY Ciass a I
i
._ QC #
i .
Calculate Z, TdZ/ZdT,Cp, Cv, gamma; using constant pressure inputs from steam tables f 25 25 32 27 40 24 98n Press 340 l 250 260 250 280 l T1) s 4 250 19.628 16.561 16.561 13.062 15.307 10.711
- U$211' /?$ 1210 1165.6 1165.6 1168.5 1165 1176.5 l t$$$ 244.36 267.25 320 l jd 240.07 240.07 254.05 l .
Ti")
yF N. 16.303 1160.6 16.303 1160.6 12.94 1165.4 1'5.17 1162 10.498 1169.7 19.111 1200.4 l ht a 22 0.978644 0.978644 0.974274 0.976904 0.971644 0.988173 21 0.977068 0.977068 0.97322. 0.975916 0.969025 0.986824 l
TdZ/ZdT stm 0.113602 0.113602 0.129897 0.126355 0.154121 0.053275 TdZ/ZdT mix 0.064669 0.064669 0.079826 0.073995 0.103523 0.031355 0.24 0.24 0.24 0.24 0.24 ,
Cp air 0.24 Cv air 0.171517 0.171517 0.171517 0.171517 0.171517 0.171517 l 0.48 Cp stm 0.503525 0.503525 0.521008 0.531915 0.533333 Cp-mix 0.357242 0.357242 0.37786 0.374635 0.401828 0.352079 i ZR mix B/lbm-R 0.085977 0.085977 0.087565 0.08656 0.089686 0.087349 Cv mix 0.265705 0.265705 0.283305 0.28167 0.302857 0.261992 f 1.344507 1.344507 1.333759 1.330049 1.326791 1.343856 i Gamma-mix
[ System PI groups:
PI press 0.395982 0.395982 0.3911 " 0.407803 0.382172 0.393151 Tau sys sec 9.886934 9.886934 11.6, ci- o43.8259 2233.632 222.6409 i
PI enth-brk 0.010132 0.010132 0 0.009627 0.007084 0.046499
[ 0.5324 0 0.542397 0.507062 0.528339 ,
PI work brk-g 0.5324 0 0.000436 0.001689 0 PI work brk-f 0.000767 0.000767 0 0 0 0.000436 0.000591 0'
mio P
W 1
s l
B-2
- . - - - . - . - - - - . - . , . . . . - - . ~. .. --.. - .- - - -. -
PRELLMINARY Wasm.csoLSE PRoraETARY class 2
- Q C.
i --
Peak Init Blow Blowdow Reflood Post-Reflo DROPS ft 1.39E 05 1.39E 05 1.39E-05 1.39E 05 1.39E 05 ft 0.000869 0.000869 0.000869 0.000869 0.000869
[] 2E+09 A ]h ft2 2E+09 2E+09 60 2E+09 60 2E+09 60 60 Rhos " @ lbm/ft3 60 1 1 1 ,
1 Cet? ' i B/lbm F 1 267.7
' 273.16 240.16 252 244.2 T Surf F 2.962963 -0.16667 0.0315 -0.00075 WT g d F/sec 267.7 256.66 240.16 252 244.2 1 T-Bl F 33 2.97E-07 1.4E 08 2.98E-09 5.3E-11 l ,
M[t@ F 33 2.97E-07 1.4E-08 2.98E-09 5.3E-11 Calc D T F 0.671 0.459 0.546 0.488 ,
l Mjl Psi /F 44 44 50 46 60 Ps Suri Psia X-stm bl 0.784629 0.784629 0.807269 0.792805 0.835849 Ibm /ft3 0.100676 0.105421' O 117805 0.109581 0.,138316 rho stm hstmj hst B/lbm 11.00558 1.04E-07 -4.8E-09 1.03E-09 -1.7E 11 hfg B/It:m 930.4239 952.4183 944.6491 949.7819 934.1383 ,
Dv ft2/br 0.643908 0.617325 0.559987 0.596666 0.485447 in(PRa) 6.864015 fr R3 1.47E+091.37E+091.44E+09 1.4E+09 1.54E+09
~ 0.91 0.91 0.91 0.91 0.91 0.0163 0.0163 0.0163 0.0163 B/hr ft F 0.0163 0.5 0.5 0.5 Mgg 0.5 0.5 -
Drop Heat Transfer Coefficients hr B/hr-ft2 F 2.27239 2.117899 2.22717 2.154772 2.377773 2347.2 2347.2 2347.2 2347.2 he B/hr-ft2-F 2347.2 hm B/hr-ft2-F 1479974 177081.1 208262.5 187542.9 252047.3 he B/hr-ft2 F 1482323 179430.4 210612 189692.3 254396.8 hsh B/hr ft2-F 216.5817 216.5817 216.5817 216.58h' 216.5817 l Drop Pl Groups 1 . pi-r 0.C10492 0.009779 0.010283 0.009949 0.010979 10.83748 10.83748 10.83748 ,10.83748 10.83748 pi-c pi-m 6833.328 817.6178 961.5887 865.9222 1163.751 1174.6 pi-o 6644.176 828.465 972.4365 876.7696 Taudrop sec 0.000126 0.001044 0.000889 0.000966 0.000736 PI r 3.737136 3.13E 08 1.6E 09 1.65E-08 -9.2E 10
-9.1 E-07 PI-c 3860.167 3.47E-05 -1.7E-06 1.8E 05 Pl' mass 2834529 0.002981 -0.00017 0.001638 -0.00011 PI enth 28790.04 2.85E 13 7.51E 16 1.56E-15 1.78E-18 PI-gas 1509104 0.001587 -8.8E 05 0.000888 -5.8E-05 PI-liq 1120.336 1.18E-06 -8E-08 7.13E-07 -6.7E 08 Omega-s 1/sec 494107.8 59810.13 70203.99 63297.42 84798.94 Omega 1/sec 169611 0.000185 1 E-05 1.96E-06 -4.7E-08 ~
B-3 l
- _ WEFUNGBOlst Pnot RETrav class 2 PRELL%GNAaY l 7 --. . Q, C.
t POOL - Blowdow Reflood Post-Refl Peak MSLB
[ ft 0.008333 0.008333 0.008333 0.008333 No pool i ft 101.7647 .101.7647 865 865 f Agese( ft2 17000 17000 2000 2000 l rhe%g;j lbm/ft3 60 60 60 60 l Ov[ N B/lbm F 1 1 1 1 -
l T-8urf % F 273.0749 281.0198 275.8166 292.677 .
l T BI F 256.6175 266.5099 260.0083 280.1885 Delt T F 32.91493 29.01979 31.61661 24.97698 i Ps Sud Psia 34.5237 40.36345 36.46902 50.15096 l X stm bl 0.676944 0.710903 0.689207 0.753774
!' rho-sud Ibm /ft3 0.113987 0.126574 0.118199 0.147199 l rho bl Ibm /ft3 0.122919 0.135125 0.127021 0.155227 rho stm Ibm /ft3 0.103 0.115452 0.107175 0.135982 l hstmj-hst B/lbm 10.97863 9.391419 10.43985 7.71867 l hg-hf B/lbm 963.3969 954.0405 960.2217 941.857 l
Dv ft2/hr 0.643838 0.580813 0.62113 0.500631 In(PRa) 0.693147 0.693147 0.693147 0.693147
! fr R3 1.47E + 09 1.53E + 09 1.49E + 09 1.62E + 09
[*
k, g B/hr ft F 0.91 0.0163 0.91 0.0163 0.91 0.0163.
0.91 0.0163 7
l l 0.5 0.5 0.5 0.5
" lbm/ft-sec '
1.13E-05 1.13E-05 1.13E-05 1.12E-05 l (nu2/g)1/ ft O.000641 -0.000602 0.000627 0.000545
! Pool Heat Transfer Coefficients hr B/hr ft2-F 2.27198 2.36707 2.304279 2.503018
[
l- hc B/hr-ft2-F. 1.646171 1.679331 1.659045 1.738723 !
l hm B/hr ft2-F 111.2906 128.9445 116.8278 155.4644 ;
- he B/hr ft2-F 115.2087 132.9909 120.7911 159.7061 hsh B/hr-ft2-F 216.5817 216.5817 216.5817 .216.5817
{ pi-r 0.01049 0.010929 0.010639 0.011557
! pi-c 0.007601 0.007754 0.00766 .0.008028 l l pi-m 0.51385 0.595362 0.539417 0.717809 pi-e 0.531941 0.614045 0.557716 0.737394 PI r 3.16E-05 2.9E-05 0.000187 0.000455
. PI c 2.29E-05 2.06E-05 0.000134 0.000316 i PI' mass 0.001743 0.001798 0.010685 0.03272 4
PI-enth 1.77E 05 1.55E-05 0.000103 0.000232
- PIgas 0.000928 0.000938 0.005796 0.016591
- . PI-liq 6.89E 07 8.47E-07 4.65E-06 1.93E-05
{ Omega s 1/hr 230.4174 265.9818 241.5822 319.4123 Omega 1/hr 0.4042 0.411372 0.047891 0.050022 1 - .
l B-4
WEgnM;80LSE PROrkE"TARY Ct. Ass 2 PRELDG%ARY
,l
- ~
4, C i STEEL HEAT SINK Blowdow Reflood Post Refl Peak MSLB
- ft 0.042 0.042 0.042 0.042 0.042 ft 10.9434 10.9434 10.9434 10.9434 88.32487 Af8e% ft2 .159000 159000 159000 159000 19700 rtiesSv 3lbm/ft3 490 490 490 490 490 C W
- l B/lb m F 0.11 0.11 0.11 0.11 0.1 )
T-8tst jF 120 143.5272 169.2084 186.8319 120 T-BI F 180.08 197.7636 206.7042 227.266' 210' Delt T F 120.16 108.4728 74.99165 80.86806 180 Ps Surf Psia 1.692843 3.161547 5.884486 8.724482 1.692843 X stm-bl 0.303866 0.338884 0.356767 0.408553 0.311204 rho surf Ibm /ft3 0.202145 0.218647 0.188091 0.236985 0.230119 rho bl Ibm /ft3 0.166998 0.181162 0.161967 0.20012 0.183716-tho-stm Ibm /ft3 0.115316 0.127518 0.115744 0.146453 0.1'2519 hstmFhst B/lbm 0 0 0 0 0 hg hf B/lbm 1083.557 1062.513 1035.213 1022.725 @MM Dv ft2/hr 0.524796 0.485172 0.540407 0.437728 0.501631 dPs/ Pima 0.803015 0.887994 0.744068 0.956692 0.853629 fr R3 1.06E + 09 1.15E + 09 1.19E + 09 1.3E + 09 1.22E + 09 I l I[ 0.91 0.91 0.91 0.91 0.91 l B/hr-ft F 0.0163- 0.0163 0.0163 0.0163 0.0163 0.5 0.5 0.5 0.5 0.5 lbm/ft sec 1.22E-05 1.23E 05 1.24E-05 1.26E-05 1.3E 05 l (nu2/g)1/ ft 0.00055 0.000524 0.000567 0.000498 0.000538 Steel Heat Sink Heat Transfer Coefficients hr B/hr-ft2-F 1.632396 1.767932 1.834359 2.009965 1.889315 he B/hr-ft2 F 3.028951 3.157833 2.63309 3.164585 3.348623 l
hm B/hr-ft2-F 66.69912 85.39102 85.00491 123,3402 55.17841 .
hif B/hr ft2-F ,
840. 840 840 840 ,
840 he B/hr ft2-F 65.77287 .81.54868 80.85962 111.4618 56.36251 hsh B/hr ft2-F 216.5817 216.5817 216.5817 216.5817 216.58.17 Steel Heat Sink Pt Groups l pi r 0.006947 0.00737 0.007654 0.008049 0.008138 pi-c 0.01289 0.013165 0.010987 0.012673 0.014424 pi-m 0.283849 0.355991 0.354703 0.493919 0.237675 pi-o 0.303686 0.376526 0.373345 0.514641 0.260237 PI-r 0.000776 0.000757 0.028013 0.094127 0.00338 PI-c 0.00144 0.001352 0.040211 0.148197 0.005991 PI' mass 0.031717 0.037381 1.359852 6.15346 0.098722 PI-enth 0 0 0 0 0
! PI-gas 0.016886 0.019502 0.73758 3.120188 0.052158 PI liq 1.25E-05 1.76E-05 0.000592 0.003638 4.19E 05 Omega-s 1/hr 29.05419 36.02292 35.71853 49.23659 24.8973 Omega 1/hr 7.833757 8.76801 6.010463 8.934424 1.245936 .
B5
PREttul%4av
. WnTINcnotst PaoPRETARY class 3 l
a, c Blowdow Reflood Post Reft Peak MSLB
! CONCRETE HEAT SINK CM ft from Biot delta number l LM ft 34.25197 34.25197 34.25197 34.25197 209.6386 50800 50800 50800 50800 8300 l Asse d ft2 140 140 Ibm /ft3 140 140 140 0.19 0.19 thof CW ]M B/lbm F 0.i 9 0.19 0.19 242.7 258.3 242.7 T-S wt~ j F 205.5 218.6 222.83 235.3 243.45 263 271.35 T BI F 34.66 33.4 1.5 9.4 57.3 l Delt T F 12.90131 16.72938 26.2151 34.42481 26.2151 c Ps Surf Psia X stm bl 0.431235 0.474563 0.577752 0.622723 0.556427 rho surf Ibm /ft3 0.158889 0.173942 0.138738 0.176701 0.154129 l
rho bl Ibm /ft3 0.14537 0.158809 0.137291 0.169978 0.145721 rho-stm Ibm /ft3 0.108097 0.120634 0.109698 0.139215 0.114688 0 0 0 0 0 hstmFhst B/lbm 998.0569 987.4405 961.7217 951.257 4 i
hg-hf B/lbm
! Dv ft2/hr 0.589946 0.53644 0.595516 0.479787 0.587836 0.495224 0.545964 0.037224 0.261101 0.1451 dPs/ Pima
- fr R3 1.27E + % 1.35E + 09 1.39E + 09 1.51 E + 09 1.57E + 09 0.09 0.08 0.08 0.081 0.081
- $[@P 0.0163 0.0165 0.0168 0.0168 B/hr-ft F 0.016 0.5 0.5 0.5 0.5 0.5 l
! lbm/ft-sec 1.22E-05 1.23E-05 1.24E-05 1.26E C5 1.26E-05 (nu2/g)1/ ft 0.000735 0.000687 0.000735 0.000634 'O.000722 Concrete Heat Sink Heat Transfer Coefficients hr B/hr ft2-F 1.965761 2.075298 2.147897 2.332097 2.417437 hc B/hr-ft2 F 0.716526 0.791441 0.348519 0.646482 0.650464 hm B/hr ft2-F 75.32752 93.41536 60.65673 124.9598 11.86261 840 840 840 840 840 hit B/hr ft2-F he B/hr ft2 F 71.38076 86.38098 58.73715 111.0295 14.66976 6sh 1 B/hr ft2-F 216.5817 216.5817 216.5817 216.5817 216.5817 Concrete Heat Sink Pt Groups pi-r 0.008305 0.008597 0.009224 0.009344 0.010967 pi-c 0.003027 0.003278 0.001497 0.002598 0.002951 pi-m 0.318247 0.386963 0.26048 0.500702 0.053815 pi-e 0.329579 0.398838 0.271201 0.512645 0.067733 Pl r 8.61 E-05 8.74E 05 0.00021 0.004056 0.00058 PI-c 3.14E-05 3.33E-05 3.4E-05 0.001128 0.000156 PI' mass 0.003584 0.004329 0.006675 0.248922 0.003204 j 0 0 0 PI enth 0 0 PIgas 0.001908 0.002258 0.003621 0.126219 0.001693 PI-liq 1.42E 06 2.04E 06 2.91E-06 0.000147 1.36E-06 Omega 1/hr 0.783501 0.913681 0.027902 0.330519 0.043493 B-6
wrsnOSE PaomETAnY Cuss 2 PREton%aY 1
Q, C JACKETED CONCRETE Blowdow Reflood Post Refl Peak Calculate heat transfer to 1/2 inch steel and to concrete in parallel and estimate
- behavior to the composite as the larger of the two. This underestimates heat flux.
Ases] ^ j ft2 35600 35600 35600 35600 8500 PI-r 0.000174 0.00017 0.006272 0.021075 0.001458 PI c 0.000322 0.000303 0.009003 0.033181 0.002585 PI' mass 0.007101 0.00837 0.30447 1.377756 0.042596 PI enth 0 0 0 0 0 PIgas 0.003781 0.004366 0:165144 0.698608 0.022505 PI liq 2.81 E-06 3.94E 06 0.000133. 0.000815 1.81E 05 e
e B-7 9
PRELLMARY WErnNcaoLSE PROMUETARY class 2 '
- ct, C.
Post Reft 24-hour MSLB l
EVAPORATING SHELL INSIDE ft 0.135417 0.135417 none
(([ 82.60226 82.60226 ft 21064.8 21064.8 i Apesf ft2 490 490 i its);4] lbm/ft3 0.11 0.11 i .OvPf ]. B/lb m F 159.4 214.57
- -T-Surf iF 241.135 F
201.8 T BI l 84.8 53.13 Delt T F Psia 4.673911 15.46319
( Ps Surf
- 0.343608 0.464709 i
X stm-bl 0.193075 0.21699 rho surf Ibm /ft3 l 0.164459 0.190123 l rho bl Ibm /ft3 0.113601 0.143556 rho stm . Ibm /ft3 0
[ 0 hstmj-hst B/lbm 994.987 1045.022 hg hf O/lbm 0.533233 0.453847 Dv ft2/hr - '
0.773799 0.815795 i '
dPs/ Pima .
1.16E+ 091.38E+ 09 fr R3 ~
0.91 0.91
[
l 0.0163 0.0163 B/hr ft F 0.5 l
0.5
- i 1.24E-05 1.26E-05
' lbm/ft sec 0.000561 0.000515 j
(nu2/g)1/ ft Evaporating Shell inside Heat Transfer Coefficients 1.79586 2.129812 hr B/hr-ft2 F 2.742056 2.752264 he B/hr ft2 F 81.69309 137.6609 hm B/hr ft2 F -
840 840 hit B/hr ft2-F 78.203-121.8634 l he. B/hr-ft2-F :
l 216.5817 216.5817 hsh B/hr ft2-F Evaporating Shellinside Pt Groups 0.00752 0.006407 pi-r O.011482 0.010864 pt'-c 0.342077 0.543396 pi m 0.361078 0.562667
~
pi-o 0.004100 0.008681 PI r 0.006273 0.011219 PI-c 0.193946 0.614454 Pl' mass 0 0
PI-enth 0.105196 0.311567 PI-gas 8.45E-05 0.000363 PI liq 10.71427 16.69601 Omega-s 1/hr 0.870849 0.850231 Omega 1/hr ,
asse B-8
PRELDGNAny WF.smcaotst PaornEETraY Ct. Ass 2
~
EVAPORATING SHELL OUTSIDE Post Reft Peck QC '
~'
ft 0.135417 0.135417 3 82.60226 82.60226 l ft
- d[% ft 21064.8 2
21064.8 2 l l
Assadd ft2
, Ariesi?x ft2 412 412 490 490 )
rho [ w } lbm/ft3 i
.Cyt; c jB/lbmF 0.11 0.11 .
T Riser F 118.8709 139.8883 ;
137 198.4 T-Osstl?[3F T Baffle F 116.2 154.74 T Bl F 127.9355 169.1442 Delt T F 18.12908 58.51167
~
PsalAgd Psia 2.2 2.9 Ps Suri Psia 2.673504 11.15112 X stm bl 0.165765 0.477929 rho stm - Ibm /ft3' O.041943 0.039196 hfg B/lbm 958.7287 897.3287 Dv ft2/hr 1.346879 1.522579 ,
dPs/Plma 0.038616 1.201468 fr R3 8.08E+081.03E+09 0.72 0.72 B/hr ft F 0.0159 0.0165 E^" Ibm /ft sec 0.5 0.5 .
1.29E-05 . 1.39E-05 l
Red 53962.52 145072.3 Evaporating Shell Outside Heat Transfer Coefficients h'r B/hr ft2 F 1.429433 1.189059 bc B/hr ft2-F 1.000501 2.290331-hm B/hr ft2-F 6.428649 135.1678 l
hit B/hr ft2-F 840 840 he B/hr ft2-F 8.766136 119.0047 hsh B/hr ft2 F 216.5817 216.5817 Evaporating Shell Outside Pt Groups pi r 0.006531 0.004712 pi-c 0.004571 0.009077 l 0.029373 0.535679 l pi-m pi-e 0.040475 0.549468
[ 0.000099 0.005338 PI r Pl c C.000489 0.010281 PI' mass 0.003557 0.736751 PI-enth 0.003557, 0.736751 PIgas 0.001929 0.373579 PIliq 1.55E-06 0.000436 l
I Omega-s 1/hr 1.201012 16.30434 Omega 1/hr 0.020869 0.914388 B9
Paruwuny wesm.csotst enoramT4av cuss 2 DRY SHELL INSIDE Blowdow Reflood Post Reft Peak MSLB 0.135417 0.135417 0.135417 0.135417 0.135417 l .%$@ftft 33.0409 33.0409 55.06817 55.06817 33.0409 !
l L.
31597.2 52662 Ases W. ft2 52662 52662 31597.2 490 490 490 490 490 l
} st6E 3 lbrn/ft3 0.11 0.11 0.11 0.11 0.11 j l Ovh h f B/lbm F !
T-Surf ,LF 117.5 135.6 159.4 239.2 158.8 l i I T-SI F 178.83 193.8 201.8 253.45 229.4 F 122.66 116.4 84.8- 28.5 141.2 j
- Delta-T Ps Surf Psia 1.57872 2.577654 4.673911 24.61362 4.607269 )
>. X stm bi 0.302569 0.333046 0.343608 0.540963 0.340349 i
l rho surf Ibm /ft3 0.203223 0.222564 0.193075 0.195921 0.210852
! rho-bl Ibm /ft3 0.167537 0.183121 0.164459 0.179588 0.174082 :
rho stm Ibm /ft3 0.115542 0.128291 0.116601 0.141078 0.121667 l
0 0 0 0 0 l i hstmj hst B/lbm !
hg hf 1086.057 1070.44 1045.022 970.357 1062.29 l - B/lbm Dv ft2/hr 0.522943 0.479893 0.533233 0.468378 0.528229, i l 0.805709 0.900383 0.773799 0.585805 0.791401 dPs/ Pima 1 fr . R3 1.05E + 09 1.13E + 09 1.16E + 09 1.45E + 09 1.32E + 09 0.91 4
0.91 0.91 0.91 0.91 0.0163 0.0163 0.0163 0.0163 0.0163
- i B/hr ft F 0.5 0.5 0.5 0.5 0.5 l
. . .. [._ Ibm /ft sec 1.22E 05 1.23E-05 1.24E-05 1.26E-05 1.26E 05 l
(nu2/g)1/ ft 0.000549 0.00052 0.000561 0.000535 0.000546 l
Dry Shell Inside Heat Transfer Coefficients hr B/hr ft2 F 1.623505 1.738105 1.79586 2.241698 2.042951 l
h he B/hr ft2 F 3.050906 3.235 2.742056 2.244607 3.052385 l hm B/hr ft2-F 66.08172 82.8675 81.69309 148.6509 58.69065 840 840 840 840 840 l hif B/hr-ft2-F
, he B/hr-ft2-F 65.25913 79.52455 78.203 129.5241 59.2842 hsh B/hr ft2 F 216.5817 216.5817 216.5817 216.5817 216.5817 I Dry ShellInside Pt Groups
! pi r 0.006914 0.007265 0.00752 0.008754. 0.008767 i pi c 0.012992 0.013523 0.011482 0.008766 0.'013099
- pi m 0.281408 0.346392 0.342077 0.580518 0.251861 pi o 0.301314 0.36718 0.361078 0.590038 0.273727 l
' .PI r 0.000261 0.000265 0.006163 0.007352 .0.007665 PI-c 0.00049 0.000492 0.00941 0.007382 0.011452 j PI' mass 0.0106 0.012798 0.290919 0.54743 0.228237 0 0 0 0 0
- PI-enth PI-gas 0.005643 0.006677 0.157794 0.277581 0.120586 l
}
PI liq 4.19E 06 6.03E-06 0.000127 0.000324 9.69E-05
- Omega s 1/hr 8.940882 10.89533 10.71427 17.74557 8.122282 l Omega 1/hr 2.627894 3.03891 1.306274 0.727128 2.748131 __
m i B 10 s . l 1
1 t.
pumcaots: reornETA V c u ss 2 paruwwny l
i
- a, C l DRY SHL ' UTSIDE Blowdow Reflood Post Refl Peak MSLB ft 0.1354 0.1354 0.1354 0.1354 0.1354 TNdli 4 LM ft 33.0409 33.0409 55.06817 55.06817 33.0409 M ' i!$ ft 2 2 2 2 2 Assedd$ ft2 52662 52662 31597.2 31597.2 52662 Ibm /ft3 490 490 490 490 490
.%]#f Omid# B/lbm F 0.11 116.06 0.11 115.83 118.865 0.11 0.11 139.9 0.11 121.26 T-Bulk ' F TMj@@ F 117 5 116.7 137.3 230.2 137.3 T Baffle F 115 115 116.2 154.74 115
- Delt T F 1.44 0.87 18.435 90.3 16.04 fr R3 7.65E + 08 7.64E + 08 8.08E + 08 1.11 E + 09 8.06E + 08 l 0.72 0.72 0.72 0.72 0.72
. B/hr-ft F 0.0157 0.,0157 0.0159 0.0165 0.0165
[E}[* 0.5 0.5 0.5 0.5 0.5 :
[ lbm/ft sec 1.29E-05 1.29E 05 1.29E-05 1.39E-05 1.39E-05 ,
Red 34657.94 20072.55 53962.52 145072.3 67891.32 (
Dry Shell Outside Heat Transfer Coefficients hr B/hr ft2 F 2.049867 2.302354 1.427093 1.437056 1.728213 l
he B/hr-ft2 F 0.693248 0.585696 1.000501 2.290331 1.247619 he B/hr-ft2-F 2.743115 2.888049 2.427594 3.727388 2.975832 hsh B/hr ft2 F 216.5817 216.5817 216.5817 216.5817 216.5817 pi r 0.009465 0.01063 0.006589 0.006635 0.007979
' pi c 0.003201 0.002704 0.00462 0.01'0575 0.005761 pi-o 0.012665 0.013335 0.011209 0.01721 0.01374.
PI r 3.87E-06 2.62E-06 0.001065 0.014933 0.000737 Pl-c 1.31E-06 6.66E-07 0.000746 0.0238 0.000532 Omega-s 1/hr 0.375889 0.395728 0.332636 0.510737 0.407757' Omega 1/hr 0.001297 0.000825 0.008815 0.066299 0.01567
~
7 B ll
i i
ParLLutNAny WFsnsceotsE PaormETARY Cii== 2 i
l -
- G, C. 1 l SUBCOOLED SHELL INSIDE Post Reft Peak ft 0.1354 0.1354 ft 1321.636 1321.636 h ft2 1316.55 1316.55 490 490 l
%hy.)jlbm/ft3 CM ~ i B/lbm F 0.11 0.11 I T-Surf.;_., j F 159.4 191.3 T BI F 201.8 229.5 l
1 DebMj F 84.8 76.4
! Ps-Surf Psia 4.673911 9.60327 I X-strh-bl 0.343608 0.415877 rho surf Ibm /ft3 0.'193075 0.233974 l
rho-bl Ibm /ft3 0.164459 0.198615 l l
rho-stm Ibm /ft3 0.116601 0.145979 l hstmj-hst B/lbm 0 0 t hg hf B/lbm 1045.022 -1018.257 Dv ft2/hr 0.533233 0.440307 dPs/ Pima 0.773799 0.939405 fr R3 1.16E+ 091.32E+09 0.91 MQ)k AggiM4 B/hr-ft F 0.91 0.0163 0.0163 Sc 0.5 0.5
@@djlbm/ft-sec 1.24E-05 1.26E 05 (nu2/g)1/ ft 0.000561 0.0005 Subcooled Shell Inside Heat Transfer Coefficients hr B/hr ft2-F 1.79586 2.028837 he B/hr-ft2-F 2.742056 3.105252 hm B/hr ft2-F 81.69309 125.571 hit B/hr-ft2-F 840 840 t he B/hr ft2 F 78.203 113.1057 hsh B/hr ft2-F 216.5817 216.5817 Subcooled ShellInside Pl Groups pi r 0.00752 0.006106 pi-c 0.011482 0.012407 pi-m 0.342077 0.501718
. pi-e .
~
0.381078 0.522231 PI r 0.000257- 0.000743 PI c 0.000392 0.001138 l 0.012122 0.049222 PI' mass
~
PI enth 0 0 '
PIgas 0.006575 0.024959
- PI-liq 5.28E-06 ~ 2.91E-05 i Omega-s 1/hr 10.71559 15.49804 Omega 1/hr 0.054428 0.070922 i B-12 l
Parusas4mv wrsnscnotse Puorastiny cuss 2 i
- Q, C.
Post Reft Peak SUBCOOLED SHELL OUTSIDE 0.1354 0.1354 M@ffit I 0.000208 0.000208 l .dj ' tj?jft W) ft 1321.636 1321.636 f 1316.55 1316.55
- M$$lft2 11 41.7 Delt-T F l- ,
l
- Subcooled Shet! Outside Heat Transfer Coefficients .
1680 1680 l hxf B/hr ft2 F 1680 1680 l 4
he B/hr ft2 F hsh B/hr-ft2 F 216.5817 216.5817 l l
pi-o 7.756887 7.756887 j
- Omega-s 1/hr 230 1982 230.1982-l Omega 1/hr-0.151672 0.574975 l -
a b
I i
l 1
B-13
L 1 PRELacMay
{ WEsnCOE PROPRIETARY Cl. ASS 2 I
l
a, C l- BAFFLE Blowdow Reflood Post Reft 24 hour2.777778e-4 days <br />0.00667 hours <br />3.968254e-5 weeks <br />9.132e-6 months <br /> MSLB I- ft 0.010417 0.010417 0.010417 0.010417 0.010417 l
M]11ft d4130F 2 6
2 6
2 6
2 6
2 6
l "desumes ft l
Lhj ft 33.0409 33.0409 33.0409 33.0409 33.0409 ,
1
- 52662 52662 52662 52662 52662 l l Areandft2 412 412 412 412 AlflagrMQ ft2 41 2 l
1272 1272 1272 1272 i ~ A;Mj ft2 1272 490 490 490 490 490 ;
thei/E7 g Ibm /ft3
'Q i$ f k B/lb m F 0.11 0.11 -
0.11 0.11 0.11 ,
i' OeMsd3 858.8155 878.7269 869.5359 1597.611 1015.588 Ogef[ 7.37722 7.572956 7.001658 10.27586 8.11336 f l l
- 115.0571 116.2164 154.7502
! ,N~F 115' 115 116.2 154.74 115 T Shell F 117.5 116.7 137 198.4 137.3
%3 Psia 115.53 1,47 1.47 115.415 117.5325 1.47 2.9 147.32 1.47 118.13 T-BI F Delt T F -1.06 -0.83 -2.665 14.84 -6.26 fr sh-bf R3 7.69E+08 7.66E+08 8.36E+081.1E+09 8.36E+08 l fr bf-sd .R3 7.6E+08 7.6E+08 7.63E+08 8.54E+08 7.6E+08 0.72 0.72 0.72 0.72 0.72 f %qc4j ki Q. B/hr-ft-F 0.0157 0.0157 -0.0159 0.0165 0.0165 l Sc 0.5 0.5 - 0.5 0.5 0.5 L @@ Ibm /ft see 1.29E-05 1.29E-05 1.29E-05 1.39E 05 1.39E-05 Red-riser 34657.94 20072.55 53962.52 145072.3 67891.32 f
l Red-downc 33677.05 27278.05 52435.28 135876.2 65969.87 Baffle Heat Transfer Coefficients
> hr sh-bf B/hr-ft2 F 1.185846 1.181742 1.290043 1.702704 1.290349 hr bf-dc B/hr-ft2-F 1.173051 1.173051 1.177617 .1.317603 1.173051 f 0.693248 0.585696 1.000501 2.290331 1.247619 l he bt ri B/hr ft2 F hc bf-dc B/hr ft2-F 0.225836 0.190799 0.325928 ,0.724476 0.40643 hsh B/hr ft2-F 216.5817 216.5817 216.5817 216.5817 216.5817 l Omega-s 1/hr 2.112082 2.104772 2.297664 3.032645 2.298209 l Omega-in 1/hr -0.00041 -0.00032 -0.00113 0.008295 -0.00265 Omega o 1'/hr -0.00073 -0.00053 -0.00219 0.021107 -0.00581 i
i
).
- l 4
B 14 j
i WErmarotsE PaoMurTA::V Ct. Ass 2 m m aY
_ Q C.
Tin = 115 Cp air = 0.24 Cp stm = 0.45 l
219 Chimney 270 Outlet 307 l Downcom 219 Riser '
Tsat.xf,shell F M i % $ $ $itgiM F i p #$ t W 4 G d #
f i Tsat.xf.chimn F MMN@$jMhhM'$d@390AM,. .
I Guess m dot air (Ibm /sec) , ![W,1'7]44{'[14I('Z~4N,4 f'{',i38,4j ' "
l y, ly'7'S'% M'yS;;;gy *,; g [ ' g m dot stm (Ibm /sec)
J'm A' % %SS,1' y:y m dot ch (ibm /sec) l T downcomer out F W .tWFyW l 'l ,'~
1 90ttCM T riser out F l
T chimney out F $h
"[1SSjtM No stm No stm No stm no stm Calculate heat fluxes .O q bf dc B/sec. 0 0 20.01487 1027.306 q bf-ri B/sec -10.7495 -7.11123 39.0041 497.1953 114.249 q sh-ri B/sec 57.78317 36.75519 265.4178 1959.968 698.2447 2.3831 9.823 55.366 315.229 -101.981 q ch-sd B/sec m ch sd Ibm /sec 0.028614 0.007221 0.008758 0.970518 0.303304 115 115 115.5616 125.6904 115 Downcomer Tout F Riser Tout F 117.1278 116.6557 122.1603 154.0863 127.5171 Chimney Tout F 117.02 116.1071 120.5516 150.347 125.3313 '
Rho downcomer out 0.069131 0.069131 0.069061 0.067869 0.069131 Rho riser outlet 0.068876 0.060933 0.068281 0.062084 0.067658 Rho chimney outlet 0.068868 0.060992 0.068466 0.062549 0.067804 Rho environment 0.069131 0.089131 0.069131 0.069131 0.069131 Buoyancy, Go, Ibm /ft sec2 -0.73277 0.49245 -2.19004 -19.4149 -4.00065 R dot KE lbm/ft sec2 0.725545 0.492194 2.190481 19.41407 4.025628 ERROR = -0.00722 -0.00025 0.000438 -0.00081 0.024982 Riser V (ft/sec)= .
3.245585 2.626737 5.097474 15.65361 6.974003 Air Flow Path Momentum Pl Groups ,
sec 324.7442' 400.9242 208.57 69.49104 153.8526 l Tau PI-inertia 0.159459 0.155674 0.129343 0.131434 0.130124 1 1 1 1- 1 PI buoyancy 1.233085 1.203818 1.0002 1.016368 1.006244 PI resistance 0 G-downcomer Ibm /ft-sec2 0 0 -0.19903 -3.41475 G-riser Ibm /ft sec2 0.303825 0.236807 1.202573 11.81038 1.755641
' G-chimney Ibm /ft sec2 0.535894 0.338971 1.532607 13.98906 2.861853 0 0.07424 -0.15268 0 pi-downcomer 0 pi-riser 0.361904 0.411077 0.47231 0.528082 0.380215 pi-chimney 0.638096 0.588923 0.60193 0.624603 0.619785
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B-15
l wesmcaotu raoramAny ct. Ass 2 ratu e rav i
! - - gc SHIELD BUILDING / CHIMNEY Blowdow Reflood Post-Reft Peak MSLB ft from Biot delta number
!- ft 108.2493 108.2493 108.2493 108.2493 108.2493 l ft 36 36 36 36 36 Sist ft2 16074 16074 16074 16074 -16074 f 4500 4500 4500 4500 4500
! Plow Asse ft2 140 140 140 140 140
- timis s
- llbm/ft3 0.19 0.19 0.19 0.19 0.19
- Cd d B/lbr.tF l T@g F 115 115.9 1 21.3 124.6 115 0.05 l M psi /F 0.05 0.05 0.05 0.05 j T BI F 116.0639 116.2779 121.7301 139.3431 121.2585 Delt-T F 2.127834 0.755717 0.860293 29.48625 12.51706 l' Ps Surf Psia 1.471273 1.509206 1.754936 1.921404 1.d71273 1 l
l rho-surf Ibm /ft3 0.066507 0.066335 0.065285 0.064624 0.066507 I rho bi Ibm /ft3 0.067691 0.067634 0.066783 0.063354 0.067082 l
rho-stm ibm /ft3 0.042807 0.042792 0.042391 0.041145 0.042425 drho/ rho .0.002847 0.001013 0.001161 0.039022 0.016597 f 0 0 j hstmj-hst B/lbm 0 0 0 i
hg-hf B/lbm 1029.444 1028.345 1025.254 1035.151 1033.793-
! Dv ft2/hr 1.298058 1.29893 1.321259 1.394552 1.319321 f dPs/ Pima 0.008042 0.002865 0.003323 0.115374 0.0.4731 0.72 0.72 0.72 0.72 0.72
! 0.016 B/hr ft-F 0.016 0.01 6 0.01 6 0.016 0.5 0.5 0.5 0.5' O.5 l
lbm/ft sec 1.25E-05 1.25E-05 1.25E-05 1.25E-05 1.25E-05 l
(nu2/g)1/ ft 0.00102 0.001021 0.001029 0.001066 0.001026 l
Chimney Heat Transfer Coefficients he B/hr-ft2-F 0.259092 0.18352 0.190425 0.593237 0.463482 hm B/hr ft2-F 3.100415 2.200712 2.337632 7.63073 5.61032.
! hit B/hr-ft2-F 840 840 840 840 840 he B/hr ft2-F 3.346125 2.377484 2.520471 8.144232 6.030199
- - hsh B/hr-ft2-F 216.5817 216.5617 216.5817 216.5817 216.5817 Chimney Concrete Pl Groups pi c 0.001192 0.000645 0.000877 0.002713 0.002125 l
pi-m 0.014258 0.010132 0.010761 0.034891 0.025718 ,
pi-e 0.01545 0.010977 0.011638 0.037604 0.027843 l PI c 2.21E-07 5.54E-08 3.37E 06 0.001024 4.71E-05
. PI' mass 2.78E-06 7.01E-07 4.38E-05 0.013865 0.000607 PI-enth 0 0 0 0 0 j PI-gas 1.48E-06 3.66E-07 2.38E-05 0.00703 0.00032 l
- PI liq 1.1 E-09 3.3E 10 1.91E-08 3.2E-06 2.58E-07
- Omega 1/hr 0.000713 0.00018 0.000217 0.024064 0.007564 B-16
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