ML20246B116
| ML20246B116 | |
| Person / Time | |
|---|---|
| Site: | Comanche Peak  |
| Issue date: | 06/30/1989 |
| From: | Giap H, Sung Y TENNESSEE VALLEY AUTHORITY |
| To: | |
| Shared Package | |
| ML20246B114 | List: |
| References | |
| RXE-89-002, RXE-89-2, NUDOCS 8907070204 | |
| Download: ML20246B116 (109) | |
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VIPRE-01 CORE THERMAL-HYDRAULIC .
I ANALYSIS METHOD 3 FOR COMANCHE PEAK STEAM ELECTRIC l STATION LICENSING APPLICATIONS June, 1989
).
Yi-Iing Sung Haan B. Giap A [g
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Prepared by: , e #/ / Date:
Yi-fing Sung [
Reviewed by: M Date:
James H. Holderness Consulting Engineer Reviewed by:
Date: A N Stephen M. Maier Supervisor, Trans**nt Analysis Approved by: --T d . N' - ~~ Date: h/ K/f![7 Brent L. Rice Manager, Safety Analysis Approved by: -
Date:
Aushf Husain Director, Reactor Engineering
1UELECTRIC l
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DISCLAIMER The information contained in this report was prepared for the specific requirements of Texas Utilities Electric Company (TUEC), and may not be l appropriate for use in situations other than those for which it was
, specifically prepared. TUEC PROVIDES NO WARRANTY HEREUNDEP., EXPRESS OR 1
IMPLIED, OR STATUTORY, OF ANY KIND OR NATURE WHATSOEVER, RECARDING THIS l REPORT OR ITS USE, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES ON MERCHANTABILITY OR FITNESS FOR A PARTICUIAR PURPOSE. .
By making this report available, TUEC does not authorize its use by others, i.
and any such use is forbidden except with the prior written approval of
- TUEC. Any such' written approval shall itself be deemed to incorporate the disclaimers of liability and disclaimers of warranties provided herein. In j no event shall TUEC have any liability for any incidental or consequential l
damages of any type in connection with ths use, authorized or unauthorized, of this report or the information in it.
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1 ABSTRACT This report describes the TU Electric VIPRE-01 model to be used for Komanche Zeak Eteam Electric Etation (CPSES) core thermal-hydraulic analyses.
. Sensitivity studies are presented to provide justification for the selection of model options. The adequacy of the model is demon 0trated through sample calculations and benchmark analyses for selected events V.encared in the CPSES Zinal Eafety Analysis Report (FSAR).
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p TABLE OF CONTENTS PAGE DISCLAIMER.................................................. 11 ABSTRACT................................................... iii TABLE OF CONTENTS............... .......................... iv LIST OF TABLES............................................. vi LIST OF FIGURES............. .............................. vii CHAPTER
- 1. INTRODUCTION...-............................................ 1-1 1.1 Purpose............................................... 1-1
- 1.2 Report Outline........................................ 1-4
- 2. GENERAL DNB ANALYSIS METH0DS............................... 2-1 2.1 0bjective................................. ........... 2-1 2.2 TUE-1 DNB Correlation................................. 2-2 2.3 DNBR Design Limit..................................... 2-3 l 3. VIPRE-01 DESCRIPTION....................................... 3-1 3.1 VIPRE-01............................................c.. 3-1 3.2 VIPRE-01 SER Conditions............................... 3-2 l 1
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- 4. CPSES VIPRE-01 Model Description.......................... 4-1 {
.i 4.1 Genera 1............................................... 4-1 4.2 Core Geometry........................................ 4-2 l 4.3 Fuel Rod Modeling..................................... 4-6
[ 4.4 Power Distributions................................... 4-9 4.5 Thermal-Hydraulic Parameters.......................... 4-11 4.6 Operating Condition Parameters........................ 4-21 4.7 Numerics Parameters................................... 4-21 4.8 Engineering Uncertainties............................. 4-22 4
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l TABLE OF CONTENTS (continued)
PAGE CHAPTER
- 5. SENSITIVITY STUDIES........................................ 5-1 5.1 Genera 1............................................... 5-1 5.2 Ra d ia l N od ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 5.3 Axial Noding.......................................... 5-3 5.4 Crossflow Parameters............. .................... 5-4 5.5 Turbulent Mixing Parameters.......................... 5-5 5.6 Axial Friction Factor................................. 5-6 5.7 Two-Phase Flow correlations........................... 5-7 5.8 Heat Transfer Correlations............................ 5-8
- 6. DEMONSTRATION ANALYSES..................................... 6-1 6.1 Genera 1............................................... 6-1 6.2 Nominal Operating Conditions.......................... 6-2 6.3 Complete Loss of Flow Transient....................... 6-3 6.4 Uncontrolled Fast Rod Withdrawal Transient............ 6-4 6.5 Uncontrolled Slow Rod Withdrawal Transient............ 6-5 6.6 Comparison with FSAR Analyses....................... .. 6-6
- 7. CONCLUSION................................................. 7-1
- 8. REFERENCES................................................. 8-1 APPENDIX
- 1. CPSES-1 FSAR BENCHMARK ANALYSES............................ Al-1 A1.1 General............................................... Al-1 A1.2 Nominal Operating Conditions................ 4 ........ Al-4 A1.3 Core Safety Limit Curves.............................. Al-5 A1.4 Complets Loss of Flow Transient....................... Al-6 A1.9 Uncontrolled Fast Rod Withdrawal at Power............. Al-7 /
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A1.6 Uncontrolled Slow Rod Withdrawal at Power............. Al-8 q A1.7 Summary............................................... Al-10 i
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LIST OF TABLES TABLE PAGE 2-1 TUE-1 DNB Correlation...................................... 2-4 1 CPSES-1 Core Thermal-Hydraulic Parameters (Cycle 1)......... 4-25 4-2 CPSES VIPRE-01 Model Summary (CPSES-1 Cycle 1)............. 4-26 5 Steady State Sensitivity Study operating conditions........ '5-10 5-2 Radial Noding Sensitivity Study............................ 5-11 5-3 Axial Noding Sensitivity Study............................. 5-12 5-4 Crossflow Parameters Sensitivity Study..................... 5-13.
5-5 Turbulent Mixing Parameters Sensitivity Study.............. 5-14 5-6 Axial Friction Factor Sensitivity Study.................... 5-15 5-7 Two-Phase Flow Model Sensitivity Study..................... 5-16 Al-1 CPSES-1 Core Safety Limit Curve Benchmark.................. Al-11 l
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l LIST OF FIGURES FICURES PAGE 4-1 CPSES-1 Cycle 1 Core Arrangement............................ 4-27 4-2 Westinghouse Standard 17x17 R-grid Fuel Assembly ,
Cross Section.............................................. 4-28 4-3 Westinghouse Standard 17x17 R-grid Fuel Assembly Axial View................................................. 4-29 f
4-4 CPSES-1 VIPRE-01 Model Radial Noding....................... 4-30 4-5 CPSES-1 VIPRE-01 Model Axial Noding........................ 4-31 4-6 CPSES-1 VIPRE-01 Model Reference Radial Power Distribution............................................... 4-32 5-1 Sensitivity Study Reference Radial Power Distribution...... 5-17 5-2 40 channels - 42 Rods, 1/8th Core Mode 1.................... 5-18 j 5-3 12 Channels - 14 Rods, 1/8th Core Mode1.................... 5-19
,5-4 26 Channels - 35 Rods, 1/4th Core Mode 1.................... 5-20 )
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5-5 Heat Transfer Correlations Sensitivity Study............... 5-21 6-1 CPSES-1 Complete Loss of Flow Demonstration Analysis Transient Forcing Functions................................ 6-9
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6-2a CPSES-1 Complete Loss of Flow Demonstration Analysis....... 6-10 j 6-2b CPSES-1 Complete loss of Flow FSAR Analysis . . . . . . . . . . . . . . . . 6-10 l 6-3 CPSES-1 Fast Rod Withdrz.wal Demonstration Analysis l Transient Forcing Functions................................ 6-11 1 6-4a CPSES-1 Fast Rod Withdrawal Demonstration Analysis......... 6-12 ]
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LIST OF FIGURES (continued)
FIGURE PAGE l
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6-4b CPSES-1 Fast Rod Withdrawal FSAR Ana2ysis.................. 6-12
- j. 6 CPSES-1 Slow Rod Withdrawal Demonstration Analysis
> Transient Forcing Functions (2 Sheets)............ ....... 6-13
! 6-6a CPSES-1 Slow Rod Withdrawal Demonstration Analysis......... 6-15 l-6-6b CPSES-l' Slow Rod Withdrawal FSAR Analysis.................. 6-15
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l Al-1 CPSES-12 Core Safety Limit Curve Benchmark................. Al-12 Al-2 CPSES-1 Complete Loss of Flow Benchmark l Hot Channel Heat Flux Results.............................. Al-13 1
1 Al-3 CPSES-1 Complete Loss of Flow Benchmark W-3 MDNBR Results.......................................... Al-13 Al-4 CPSES-1 Fast Rod Withdrawal Benchmark Hot Channel Heat Flux Results.............................. Al-14 Al-5: CPSES-1 Fast Rod Withdrawal Benchmark W-3 MDNBR Results.......................................... Al.14 Al-6 CPSES-1 Slow Rod Withdrawal Benchmark Heat Flux Forcing Function................................. Al-15 I
Al-7 'CPSES-1 Slow Rod Withdrawal Benchmark W-3 KDNBR Results.......................................... Al-15 i
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CHAPTER ONE.
INTRODUCTION I
i 1.1 Purpose The purpose'of this report'is to demonstrate TU Electric's core thermal-hydraulic analysis capability for Somanche feak Eteam Electric Etation (CPSES) licensing applications. TU Electric intends to use this capability to perform peparture from Eucleate Eoiling (DNE) calculations for core safety limit evaluations, reactor protection system setpoint analysis, and safety analyses for normal operation and selected plant transients.
A qualified core thermal-hydraulic analysis capability must have the following attributes:
o An approved core thermal-hydraulic analysis code. TU Electric will use the VIPRE-01 code [1], which has been generically approved by the Euclear Regulatory Eommission (NRC) for use in pressurized Eater l Eeactor (PWR) licensing calculations, with the limitations stated in ;
1 the VIPRE-01 Eafety Evaluation Eeport (SER) [2].
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o Documentation of code usare. In the VIPRE-01 SER [2], the NRC states that each VIPRE-01 user is required to submit a document describing the proposed code applications, the computer codes with which VIPRE-01 will interact, the source of each input variable, the selected modeling options and correlations, and justification for using such options and correlations. This submittel is intended to satisfy the documentation requirements stated in the VIPRE-01 SER for the intended applications discussed in chis report.
o An approved DNB correlation and associated 95/95 limit. As required by the VIPRE-01 SER, TU Electric will use an NRC approved DNB correlation, with a 95/95 limit that is approved for use with the TU Electric VIPRE-01 model. The TUE-1 DNB correlation has been submitted to the NRC in a separste report [3), and is intended to be used for CPSES analyses with Westinghouse R-grid fuel.
o Demonstration of the code user's cualiffeation for verformine the analyses. :lRC Generic Letter 83-11 [4] requires that users of safety analysis codes demonstrate their proficiency in using the codes by submitting qualification analyses p. rformed by the users themselves.
This submittal is intended to satisfy the user qualification requirements of Generic Letter 83-11.
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L The intent of this report is to present and qualify a basic VIPRE-01 modeling methodology for DNB analysis, and thus no specific CPSES licensing analyses are included. The basic VIPRE-01 core thermal-hydraulic analysis I
methodology described in this report is applicable to both CPSES units (CPSES-1 and CPSES-2), although the specific models and analyses presented in this report are for Westinghouse standard 17 x 17 R-grid fuel, which is
- l. used for CPSES-1 Cycle 1. The application of the CPSES VIPRE-01 model for alternate fuel designs will be addressed in the appropriate reload analysis reports.
The VIPRE-01 modeling methodology presented in this report is applicable to DNB analyses for CPSES normal operation and plant transients, with the
-limitations stated in the VIPRE-01 code manuals [1] and the VIPRE-01 SER
[2]. Applications of the VIPRE-01 model for low flow rate, buoyancy dominated flow conditions are beyond the scope of this submittal. In addition, justification for applications of the VIPRE-01 model for post-DNB conditions is not included in this report.
In summary, this submittal is made for the purpose of obtaining NRC staff f concurrence that:
- 1) The CPSES VIPRE-01 modeling methodology described in Chapter 4 of I
this report is acceptable for the intended licensing applications l stated in this submittal.
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2)- TU Electric has fulfilled the user documentation requirements stated in the VIPRE-01 SER [2] for the description of a basic modeling methodology.
- 3) TU Electric has satisfactorily demonstrated its proficiency in using VIPRE-01,4 as required by NRC Generic letter 83-11 [4) .
1.2 Report Outline The main body of this report is organized as follows:
o General DNB Analvais Methods. In Chapter 2, a discussion is presented on the objectives of DNB analysis, the use of a core thermal-hydraulic analysis code, the use of a DNB correlation and its associated 95/95 limit, and the use of a DNBR " design" limit which includes plant and cycle-specific allowances and retained margin.
o VIPRE-01 Description. A brief description of the VIPRE-01 code is presented in Chapter 3. The specific limitations and conditions i
stated in the VIPRE-01 SER [2] are listed and addressed individually.
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o CPSES VIPRE-01 Model Description. A complete description of the l
l CPSES VIPRE-01 modeling methodology is provided in Chapter 4, with justification for the source of each input paramete.r. As an illustration of the TU Electric methodology, specific input parameters are given for the CPSES-1 Cycle 1 model, which uses Westinghouse 17x17 standard R-grid fuel.
o Sensitivity Studies. Sensitivity studies are presented in Chapter 5 to demonstrate the adequacy and conservatism of TU Electric's choice of key input parameters and modeling options, o Demonstration Analyses. Sample analyses for CPSES-1 Cycle 1, using the CPSES VIPRE-01 model with the TUE-1 correlation, are presented in Chapter 6 to demonstrate the model adequacy for plant licensing j applications.
IL o Conclusions. The conclusions of this report are stated in Chapter 7. '
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l i- o Benchmark Analyses. Comparisons to current CPSES-1 FSAR analyses are provided in Appendix 1, with the use of a modified benchmark model j which includes the use of the W-3 DNB correlation to facilitate the comparison between the CPSES VIPRE-01 model and the FSAR analyses, i
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L CHAPTER TWO j GENERAL DNB ANALYSIS METHODS l
2.1 Obiective l:
l One of.the basic objectives of PWR core thermal-hydraulic analysis is to g demonstrate, with a high degree of confidence, that core coolant conditions 1
l do not result in DNB, which is also referred to as boiling crisis, burnout, l or Ecitical Heat Elux (CHF). The DNB phenomenon is characterized by i.
unstable film boiling at the fuel rod surface, which results in a drastic increase in the rod surface temperature and eventually leads to fuel clad failure. Section 4.4 of NUREG-0800 [5] imposes the DNB acceptance criterion that there be at least a 954 probability at a 95% confidence level (95/95) that the most limiting fuel rod in a PWR core does not experience DNB during normal operation or anticipated operational occurrences. Traditionally, DNB
- j. :is evaluated in terms of the Departure from Eucleate loiling Eatio (DNBR),
which is the ratio of the predicted DNB heat flux calculated by an empirical I
l correlation to the actual local heat flux. The DNB correlation is typically i
developed from experimental data that simulate the PWR fuel geometry and L
core operating conditions. The required core protection is ensured if the )
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1 minimum DNBR (MDNBR) is greater than the 95/95 DNBR design limit for the DNB j correlation.
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f' A core thermal-hydraulics analysis code, such as VIFRE-01, is used to provide the predictions of fluid conditions and heat transfer that are required as input to the DNB correlation. It is important to ensure proper coupling between the DNB correlation and the core thermal-hydraulics code (and model). The thermal-hydraulics code and associated modeling methodology which are intended to be used for licensing applications must be used to confirm that the 95/95 limit for the selected DNB correlation is appropriate for use with that particular code and model. Typically, this requires the statistical evaluation of comparisons of DNB predictions with applicable experimental data, using the code and modeling methodology which is intended to be used for licensing applications.
2.2 TUE-1 DNB Correlation The TUE-1 DNB correlation was developed by TU Electric using selected test data from the Columbia University DNB data base, which simulated Westinghouse R-grid mixing vane fuel assemblies at typical FWR operating conditions. The VIFRE-01 code was used in the correlation development for predicting thermal-hydraulic conditions in the subchannel model of the test sections, with a modeling methodology consistent with the methodology described in this report. The 95/95 DNBR limit of the TUE-1 correlation has 3 been determined to be 1.16 [3]. The statistical properties and the applicable range of the TUE-1 correlation are given in Table 2-1. ;
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2.3 DNBR Desien Limit A plant and cycle-specific DNBR design limit will be used as part of the Til Electric DNB analysis methodology. A TUE-1 DNBR limit higher than the correlation 95/95 DNBR limit will be specified by TU Electric as the "DNBR design limit" for CPSES DNB analysis. The use of this DNBR design limit is intended to provide sufficient margin to offset anticipated DNBR penalties resulting from plant and cycle-specific considerations and generic issues such as fuel rod bowing [6] and the Eeactor Goolant Eystem (RCS) flow anomaly [7]. The specification of this design DNBR limit and thc. evaluation of DNBR margin penalties will be performed on a plant / cycle-specific basis.
Therefore, the actual specification of the DNBR design limit and the calculation of DNB margin penalties is beyond the scope of this submittal.
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TABLE 2-1 TUE-1 DNB Correlation i
STATISTICAL PROPERTIES Data Sample Size 934 !
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.MDNBR Mean 1.0018 MDNBR Standard Deviation 0.0884 95/95 DNBR Limit 1.16 APPLICABLE RANGE Pressure 1485 - 2435 psia Local Mass Flux 0.93 -
3.53' M1bm/hr-ft 2 local Quality -0.15 - 0.30 1.15 MBtu/hr-ft 2 Local Surface Heat Flux 0.14 -
Inlet Subcooling' 30 - 350 Btu /lbm Mixing Vane Grid Spacing 20 - 32 inches Heated Length 96 - 168 inches 0.37 Wetted Hydraulic Diameter -
0.51 inches i
Heated Hydraulic Diameter 0.46 -
0.58 inches 2-4
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,_ CHAPTER THREE l
l l VIPRE-01 DESCRIPTION L
3.1 VIPRE-01 f
l i VIPRE-01 was developed by the Battelle Pacific Northwest Laboratories, under
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the sponsorship of the Electric Zower Research Institute (EPRI), for reactor l core thermal-hydraulic analyses involving the calculation of local heat
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flux, fluid conditions, and DNBR. With the VIPRE-01 code, the reactor core can be modeled as a number of quasi-one-dimensional flow paths or channels that communicate laterally by diversion crossflow and turbulent mixing. The fluid field is assumed to be homogeneous, incompressible, and thermally
) expandable, with models added to reflect subcooled boiling and co-current liquid / vapor slip. Conservation equations of mass, axial +d lateral l momentum, and energy are solved for the liquid enthalpy, axial flow rate, lateral flow rate per unit length, and momentum pressure drop. The detailed VIPRE-01 code description, input instructions, and code verification analyses can be found in Reference [1].
l VIPRE-01 is capable of modeling reactor transients using time-varying I
boundary conditions, or " forcing functions", of inlet flow, enthalpy, system i l
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pressure, and core power. These boundary conditions are taken from a system transient analysis code such as RETRAN-02 [8).
o TU Electric has modified VIPRE-01 to install the TUE-1 DNB correlation and to produce additional summary tables for DNB correlation and sensitivity studies. However, the code modifications do not alter the fundamental
_VIPRE-01 computational methods. The modified version of VIPRE-01 is maintained in accordance with TU Electric's QA procedures for the control of quality-related softn re.
3.2 yJfRE-01 SER Conditions In December, 1984, the Utility group for Eegulatory Applications (UGRA) submitted VIPRE-01 for NRC staff review. The NRC subsequently issued an SER which states that VIPRE-01 is acceptable for PWR licensing calculations, with certain limitations and conditions [2]. The VIPRE-01 SER limitations and conditions are listed below, with a discussion of how TU Electric intends to address each one.
(1) The application of VIPRE-01 is limited to PWR licensing calculations with heat transfer regimes up to critical heat flux (CHF) (i.e.,
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DNB). Any use of VIPRE-01 in BWR calculations or post-CHF calculations will require prior NRC review and approval.
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,TU Electric Response: The intended applications of VIFRE-01 discussed in this report do not include post-CHF calculations. Any such application will be submitted for NRC review and approval with a separate report.
(2) Use of a steady-state DNB correlation with VIFRE-01 is acceptable for reactor transient analysis provided that the DNB correlation and its DNBR limit have been reviewed and approved by the NRC and that the application is within the range of applicability of the correlation including fuel assembly geometry, spacer grid design, pressure, coolant mass velocity, quality, etc. Use of any DNB correlation which has not been approved will require the submittal of a separate topical report for staff review and approval. The use of a DNB correlation which has been previously approved for application in connection with another thermal-hydraulic code other than VIFRE-01 ,
will require an analysis showing that, given the correlation data base, VIPRE-01 gives the same or a conservative safety limit, or a new and higher DNBR limit must be used, based on the analysis 1
results.
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TU Electric Response: TU Electric intends to use the TUE-1 DNB correlation for analysis of Westinghouse standard 17x17 R-grid fuel. l The correlation has been been submitted for NRC review in a separate report [3]. The TUE-1 correlation was developed with the VIPRE-01 I
( code, using modeling techniques consistent with the those used in the l CPSES VIPRE-01 model described in this report. TU Electric will not use the TUE-1 DNB correlation outside of its approved range of
, applicability. Any use of DNB correlations for alternate fuel 1
designs or thermal-hydraulic conditions outside the range of the l TUE-1 correlation will be justified in accordance with the SER conditions stated above.
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l (3) Each organization using VIPRE-01 for licensing calculations should submit separate documentation describing how they intend to use VIPRE-01 and providing justification for their specific modeling assumptions, choice of particular two-phase flow models and correlations, heat transfer correlations, DNB correlation and DNBR limit, input values of plant specific data such as turbulent mixing coefficient, slip ratio, grid loss coefficient, etc., including 1
defaults.
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TU Electric Response: This report is intended to satisfy the i
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, requirements of the above SER condition, Intended applications were 1'
discussed in Chapter 1, and a complete description of the CPSES VIPRE-01 model is given in Chapter 4.
'(4) 'If a profile fit subcooled boiling model (such as Levy and EPRI
.models) which was developed from steady-state data is used in boiling rransients, care should be taken in the time step size used for transient analysis to avoid the Courant number less than one.
TU Electric Resoonse: The EPRI subcooled boiling model is used in the CPSES VIPRE-01 model, as described in Chapter 4 of this report.
For transient applications, appropriate time steps will be selected to ensure numerical stability and accuracy. '
(5) The VIPRE-01 user should abide by the Quality Assurance (QA) procedures described in Section 2.6 of the SER.
TU Electric Response: TU Electric will comply with the QA program described in the SER. TU Electric's QA program for control of quality-related software ensures that only the approved version of VIPRE-01 will be used for licensing applications.
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CHAPTER FOUR
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CPSES VIPRE-01 MODEL DESCRIPTION j l
1 4.1 Eineral A complete description of the basic CPSES VIPRE-01 modeling methodology is presented in this chapter. Although the specific model input parameters presented in this chapter are based on CPSES-1 Cycle 1 data, the basic modeling methodology has geners.1 applicability for both CPSES units and alternate fuel designs. The CPSES-1 Cycle 1 specific model is presented in order to illustrate the application of the CPSES VIPRE-01 modeling methodology for a specific core design.
CPSES consists of two Westinghouse 4-loop PWRs, each with a rated thermal power of 3411 NW. The core configuration for CPSEO-1 Cycle 1 is shown in Figure 4-1, and the core thermal-hydraulic parameters are summarized in Table 4-1. Tne fuel assembly design for Westinghouse standard 17x17 R-grid fuel, used for CPSES-1 Cycle 1, is illustrated in Figures 4-2 and 4-3.
The TU Electric VIPRE-01 modeling methodology has been developed in accordance with the modeling guidelines in the VIPRE-01 code manuals [1] and the modeling requirements specified in the VIPRE-01 SER [2]. Each input 4-1
parameter in the CPSES VIPRE-01 model is conservatively selected from CPSES plant design documents, results of sensitivity studies, or justifiable engineering approximations. In addition, the CPSES VIPRE-01 model is consistent with the VIPRE-01 model used for the development of the TUE-1 correlation [3), which ensures consistent coupling between the CPSES model
.and the TUE-1 correlation and its associated 95/95 limit.
A summary of the CPSES VIPRE-01 model is provided in Table 4-2. As discussed above, specific input parameters are chosen for CPSES-1 Cycle 1 in order to illustrate the application of the TU Electric VIPRE-01 modeling methodology. The VIPRE-01 model description presented in this chapter is organized into the following general sections: 1) core geometry, 2) fuel rod modeling, 3) power distribution, 4) thermal-hydraulic parameters, 5) operating conditions, 6) numerics parameters, and 7) engineering uncertainties.
4.2 Core Geometry 1 i
t 4.2.1 Sinnie State Core DNB Analveis l
Historically, DNBR calculations for PWR cores have been performed using the {
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multi-stage or multi-pass analysis method [9,10,11], in which the reactor '
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l core and the " hot" fuel assembly (the assembly in which MDNER occurs) are
! modeled in different simulations. In this method, a core-wide analysis is first performed to generate assembly crossflow boundary conditions to be b
used for the subsequent hot assembly analysis. In the core-wide analysis, f each fuel asadmbly is modeled as a single flow channel. In the hot assembly analysis, the assembly is modeled as a number of subchannels that are i defined as the flow channels formed by four fuel rods (standard channel) or three fuel rods and one thimble tube (thimble channel) in a rectangular array. The multi-stage approach reflects a compromise between the desired degree of detail for hot channel analysis and the modeling capabilities of earlier subchannel codes.
Presently, the single-stage or one-pass approach [12,13) is commonly used with advanced codes such as VIPRE-01, COBRAIIIC/MIT [13], and LYNIT [14),
where subchannels and fuel assemblies are modeled together in one i
simulation. In a single-stage analysis, the reactor core is modeled as a {
number of subchannels surrounding the hot fuel rods, with several lumped i channels representing the rest of the core. In this way, the entire core can be modeled with a relatively small number of flew channels, while maintaining a sufficient level of detail and accuracy in the vicinity of the hot channels. Because it has been proven to be an economical and highly reliable alternative to the traditional multi-stage analysis, the single stage approach is used by TU Electric for CPSES DNB analysis.
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4.2.2 Radial Nodinn In the CPSES VIPRE-01 model, the core is modeled with a number of flow-l channels of various sizes and shapes. While the limiting (" hot")
subchannels and their immediate surroundings are modeled in detail, the
.subchannels farther away from the hot channels can be lumped together into large channels which may include several fuel assemblies. The VIPRE-01 SER
[2] states that:
"As long as at least one full row of subchannels are placed to completely surround the hot channel to adequately resolve the details of the flow field in the vicinity of the hot' channel, the hot channel flow conditions are very insensitive to the core radial layout or how the rest of the hot bundle and core are modeled".
A sensitivity study of radial noding performed by TU Electric confirmed this conclusion for the CPSES VIPRE-01 model. This sensitivity study is discussed further in Chapter 5 of this report. By choosing a design power shape and an inlet flow distribution symmetric to the core center, a 1/8th core symmetric model can be used with the hot assembly located at the core center. Within the hot assembly, bounding hot channels are defined which are the most limiting channels in the reactor core for DNBR calculations.
4-4
o TU Electric has developed a 16-channel model for the CPSES core as shown in T
l Figure 4-4, consisting of twelve subchannels and four lumped channels. Two het channels are defined for the CPSES VIPRE-01 model: a hot standard channel formed by four fuel rods, and a hot thimble channel formed by three fuel rods and one thimble tube. The hot standard channel is Channel 7, and the hot thimble channel is Channel 4 as shown in Figure 4-4. The subchannel configuration is selected such that there are two subehannel rows bordering i
every side of the hot channels The rest of the subchannels in the hot assembly are lumped into one channel. Then, the rest of the 1/8th core is lumped into three channels, with an increasing number of fuel assemblies included in the outer channels. The lumped channel configuration is such that the difference in the flow areas of adjacent channels is less than an order of magnitude, as recommended in the VIPAE-01 manual [1].
4.2.3 Axial Nodine.
The finite difference method used in the VIPRE-01 code requires that care be taken to ensure that an adequate number of axial noder are provided to !
resolve the detail in the flow field and the axial power profila. The CPSES l VIPRE-01 model described in this report uses 38 axial nodes with a nonuniform nodal length along the fuel rod. The nodal length in the MDNBR region (about 80" to 127 from the bottom of fuel rod) is 3 inches. In 1 I'
addition, the axial nodes are specified such that there is an axial node 4-5
.i t
1 within 2 inches of the center of each of the mixing vane grid locations.
l~
L Figure 4-5 illustrates the axial noding for the CPSES VIPRE-01 model. The L VIPRE-01.SER [2] states that:
l "The VIPRE-01 predictions are sensitive to axial noding in that.
I s
enough nodes must be provided to resolve the detati in the axial
)
power profile and the flow field such as-flow redistribution'n around
' area changes, local pressure drop and local boiling. Once a sufficient accuracy.is obtained, the VIPRE-01 prediction becomes insensitive to further axial node refinement."
A sensitivity. study performed by TU Electric confirmed that the axial noding used in the CPSES VIPRE-01 model described in this report is adequate. This ce'nsitivity study is discussed further in Chapter 5.
4.3 Fuel R2d Modeline With VIPRE-01, fuel rods can be modeled either as dummy rods or conduction rods, as discussed below. L... heated rods such as guide thimble tubes or instrumentation thimble tubes are used in calculating the subchannel geometry parameters, but are not considered for heat transfer. The CPSES VIPRE-01 model accounts for the fact that a fraction of core power is 4-6
f i
l generated directly in the coolant due to gamma heating and neutron L absorption. For the CPSES VIPRE-01 model described in this report, 97.4% of the reactor power is generated within the fuel rods, and 2.6% of the power is generated directly in the coolant, consistent with the values specified by Westinghouse for CPSES-1 Cycle 1 [15].
4.3.1 Dummy Rod Model For steady-state DNB analysis, the CPSES VIPRE-01 model uses a dummy rod model to represent the fuel rods. In a dummy rod model, there is no calculation of the heat conduction and temperature distribution within the fuel rods, and the rod surface heat flux is specified as an input parameter.
4.3.2 Conduction Rod Model For transient analyses where fuel stored energy and thermal inertia effects are important, a conduction rod model is used to represent the fuel rods.
With the conduction rod model, the rod surface heat flux is calculated at each time step by solving the energy equations for the fuel rods and coolant, using appropriate input for fuel rod geometry, fuel pellet radial power distribution, gap conductance between fuel pollet and clad, and fluid heat transfer correlations.
4-7
M A uniform radial power shape is assumed within the fuel rods. The small internal thermal neutron flux depression expected in CPSES fuel rods is not l
significant for DNB analysis. As recommended by the VIPRE-01 manual, six 1
radial nodes are specified in a fuel pellet, which is adequate for the rod conduction solution. The material properties of UO2 and zircaloy are evaluated using the VIPRE-01 built-in property correlations [1].
The pellet-clad gap conductance is used for modeling the heat transfer across the gap between the fuel pellet and clad, as given below:
Hg ,p = q"/(Tp, - Tge) (4-1) where Hg ,p = gap conductance q" = surface heat flux T,p - pellet outer surface temperature T ge = clad inner surface temperature In a reactor transient with a rapid power change, the calculated transient heat flux (and thus DNBR) is sensitive to the gap conductance < The exact value of the gap conductance is difficult to determine due to the complexity of the heat transfer mechanism within the gap. The CPSES VIPRE-01 transient model will use a constant Bap conductance value which is conservative with respect to the DNBR calculation. The bounding value for the gap conductance ,
1 is selected on a transient specific basis. I 4-8 I
In the VI2RE-01 conduction rod model, heat transfer correlations are used to provide the connection between the rod conduction equation and fluid conservation equations. The code contains several correlations for each of the major segments of the boiling curve ranging from single-phase forced convection to film boiling. However, only single-phase convection and nucleate boiling are important for DNB analyses. TU Electric's sensitivity studies, presented in Chapter 5, indicate that DNBR is not very sensitive to the choice of heat transfer correlations. The VIPRE-01 recommended correlations are selected for the CPSES model based on considerations of numerical stability and the correlation ranges. The Dittus-Boelter correlation is used for single-phase convection, and the Thom correlation plus single-phase convection is used for subcooled and saturated nucleate boiling.
I !
l 1 4.4 Power Distributions j 1
In the VIPRE-01 model, each fuel rod is assigned a radial power factor that l determines the rod power relative to the average core power. An axial power profile is utilized to specify how much power each axial node receives )
l relative to the average.
l 4-9 l
l 1
4.4.1 EJLdial Power Distribution The radial power distribution of a reactor core at full power is a function of the fuel and burnable poison loading pattern and the presence or absence of control rods. For the CPSES VIPRE-01 model, a reference radial power distribution within the hot assembly is conservatively specified such that there is a gradual power gradient which peaks around the hot channels. The hot assembly power factor, which is the average of all rod power factors within the assembly, is also assigned to the assemblies immediately adjacent to the hot assembly. Lower power factors are then assigned to the remainder of the core, such that the power factors are normalized to unity on a core-wide basis.
For the reference radial power distribution shown in Figure 4-6,, the peak rod power is set to the Technical Specification limit of F N at full power. FN is defined as the ratio of the integral of the j linear power along the rod with the highest integrated power to that for the average power rod. The current F NAH limit for CPSES-1 at full power is 1.55 [16]. The peak rod power factor in the reference radial power distribution will be selected to ensure conservatism on a transient specific basis, since in some events the radial power peak may exceed the Technical Specification peaking limit.
4-10
4.4.2 Axial Power Distribution 1
1 I
l The core axial power profile is affected by moderator and Doppler reactivity 1
feedback, xenon distribution, fuel burnup, and control rod position. A chopped cosine with a 1.55 peak-to-average ratio is used as the reference ,
l' axial power shape for the CPSES VIPRE-01 model, consistent with the shape currently used by Westinghouse for CPSES-1 analyses [16]. Although the reference axial shape is expected to be conservative with respect to the axial power profiles encountered in normal plant operation, other axial power shapes may be more DNB limiting for some events. The conservatism of the axial power shape in the CPSES VIPRE-01 model will be confirmed for each specific application.
4.5 Thermal-tydraulie Parameters The thermal-hydraulic input parameters in the VIPRE-01 model include crossflow parameters, turbulent mixing parameters, hydraulic loss I coefficients, two-phase flow models, and water property functions.
4.5.1 Crossflow Parameters I In the VIPRE-01 code, the gap width, centroid length and axial node length l 4-11 ,
define the control volume for crossflow between adjacent channels. The gap width is the width of the space through which the adjacent channels communicate, and is determined from the fuel assembly geometry. The centroid length is the distance between the centroids of the adjacent j channels. For lumped channels, the gap width is the sum of all gap vidths connected with the neighboring channels, and the centroid length is f
increased from the subchannel value in proportion to the number of rod rows between the channel centroids. If a channel has several sides connected with a lumped channel (for instance, Channel 12 in Figure 4-4), the largest centroid distance is used in the model.
The crassflow resistance coefficient is the coefficient of form drag in the gap between adjacent channels. In the CPSES VIPRE-01 model, the subchannel crossflow resistance coefficient is modeled with a constant value of 0.5, which is the VIPRE-01 recommended value [1]. For lumped channels, a VIPRE-01 option is selected to multiply the subchannel crossflow resistance coefficient by the ratio of the centroid distance and rod pitch for each gap, in order to calculate the correct effective crossflow resistance, as j j
recommended by the VIPRE-01 modeling guidelines [1].
l 1
l
)
The VIPRE-01 SER [2] states that:
"For most of normal VIPRE-01 applications when the axial flow is 4-12 l
predominant relative to the crossflow, the gap-to-length ratio (s/1) and crossflow resistance (kgj) have insignificant effects on the mass flux and the DNBR."
TU Electric performed sensitivity studies, which are presented in Chapter 5, to confirm that the CPSES VIPRE-01 model is insensitive to the modeling of these crossflow parameters for the range of flow conditions encountered in the intended model applications discussed in this report.
4.5.2 Turbulent Mixine In VIPRE-01, the turbulent mixing model accounts for the exchange of energy and momentum between adjacent channels due to turbulence. The VIPRE-01 turbulent mixing parameters include the turbulent mixing coefficient (ABETA) and the turbulent momentum factor (FTM).
The VIPRE-01 SER states that:
"The hot chattnel flow conditions and DNBR are sensitive to the turbulent mixing. Use of a higher turbulent mixing coefficient will result in smoothing the hot channel flow conditions, i.e., a decrease in enthalpy and increase in flow rate and DNBR. Therefore, unless the value of the turbulent mixing coefficient can be verified by 4-13
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ____ _ . - - - - __ __ _ J
i) .
s 3
experimental 1' data, either.no . turbulent mixing or a- conservatively small mixing ' coefficient should be. used in licensing calculations.
The VIPRE-01 user should justify the value of the turbulent mixing
. coefficient in-the application."
. TU Electric studies have confirmed that DNB analyses with the CPSES VIPRE-01
- model are sensitive to the turbulent mixing coefficient, as discussed in Chapter 5. Therefore a conservative treatment-of turbulent mixing will be used for the CPSES VIPRE-01 model, as described below.
The following correlation form is selected for the VIPRE-01 turbulent mixing model: -
W' = ABETA
- S
- C,y, (4-2) where W' - turbulent flow rate between the channels l ABETA = turbulent mixing coefficient S = gap width G,y, = average mass flux in the adjacent channels The energy transferred by turbulent mixing is W' times the lateral enthalpy difference. ABETA corresponds to the thermal diffusion coefficient (TDC) used by Westinghouse in the THINC code [9), and Equation 4-2 is similar to 4-14
i the THINC thermal mixing model [16]. TU Electric intends to use this model with a conservatively small ABETA value which is dependent on the fuel
' design.
ABETA for mixing vane grid fuel is a function of grid spacing and rod array [17). Experimental results indicate that the mean, or best estimate, value of ABETA for Westinghouse 17x17 fuel assemblies with 26 inch grid spacing is 0.059 [16), and that the ABETA value increases with decreasing grid spacing [18). For the CPSES-1 Cycle 1 model described in this report, a conservatively small ABETA value of 0.038 is used, which is consistent with the Westinghouse TDC value used for the current FSAR analyses [16].
Turbulent mixing is a subchannel phenomenon. In lumped channel modeling, the mixing correlation must account for the effects of lumping many gaps, j and ABETA must be reduced accordingly. As recommended in the VIPRE-01 manual, ABETA for lumped channels can be approximated as follows [1):
- subchannel centroid distance (4-3)
ABETA1 = ABETAs lumped channel centroid distance where I
ABETAy - ABETA for a lumped channel ABETA, = ABETA for subchannels 4-15
'i I.
r The turbulent momentum factor, FTM, determines how effectively the turbulent crossflow mixes momentum. FTM can be specified on a scale of 0.0 to 1.0, where 0.0 indicates that the crossflow mixes enthalpy only but not momentum, and 1.0 indicates that the crossflow mixes both enthalpy and momentum at the same strength. Although the VIPRE-01 recommended FTM value is 0.3, it is more appropriate to use a lower value of FTM for models involving large lumped channels. An FTM value of 0.0 is conservatively used in the CPSES VIPRE-01 model. TU Electric performed a sensitivity study, which is presented in Chapter 5, that showed that the use of FTM - 0.0 is conservative, although the solution is relatively insensitive to a variation in the FTM parameter.
4.5.3 Axial-Hydraulic Losseg The axial pressure losses due to friction drag are modeled with the use of axial friction and local loss coefficients. The VIPRE-01 recommended model [1] for the axial friction factor is used in the CPSES model, as given below:
f - max (fturbulent* flaminar) (4~4) where f turbulent = 0.32
- Re-0.25 (Blasius correlation) f laminar - 64.0 / Re 4-16
L i
I For the Reynolds numbers encountered in PWR analyses, the axial friction 1
i factor is determined by the turbulent friction factor relation, which is the Blasius correlation for an isothermal smooth pipe. TU Electric performed a l sensitivity study, discussed in Chapter 5, which concluded that the CPSES VIPRE-01 model is not sensitive to the selection of axial friction factor correlations.
l l
VIPRE-01 also has a built-in Rohsenow-Clark model for a hot wall correction which accounts for the effect of the temperature and viscosity gradient in the fluid near the rod surface. However, since the temperature difference between the hot wall and fluid is relatively small in the regimes of single-phase and nucleate boiling, the Rohsenow-Clark model'is not used for the CPSES model.
Loca*. loss coefficients are used for simulation of the local hydraulic loss ;
caused by area cariation and turbulence at the bottom nozzle, the lower core plate, the grid 6 pacers, the upper core plate, and the top nozzle in the
.j core. These coefficients are chosen based ott information supplied by the ]
i fuel vendor. Its the CPSES VIPRE-01 model, local losses due to the core )\
bottom nozzle, the lower core plate, and the bottom simple grid are modeled I
with one local loss coefficient. Similarly, local losses due to the core top nozzle, the upper core plate, and the top simple grid are modeled with a single loss coefficient. The bundle average loss coefficients are converted 4-17
)-
1 1
into subchannel values to account for the d'.fferent flow areas in the standard fuel channels and the guide thimble channels. Using a method suggested by Rehme's correlation [19), the channel dependent loss coefficients are calculated based on the square ratio of total area and flow area in a channel, with the following assumptions: 1) the projected grid frontal area is uniformly distributed over the entire assembly area, and
- 2) the loss coefficients for a lumped channel are the came as the assembly average. loss coefficients. The method is described below:
[(S/A),/(S/A),]2 = [(At/A),/(At/A),]2 (4-5) where -
S = grid projected frontal area A = channei flow area At = channel total r.rea (or lattir.e area)
Subscripts: s - subchannel a - assembly The subchannel local loss coefficient is then given as:
k, = k,*((At/A),/(At/A),))2 (4-6) where 4-18
u
,a k, - local loss coefficient for a subchannel l:
l .. k, - assembly average local loss coefficient-
.This same method _of modeling local loss coefficients was used in the
.VIPRE-01 model for TUE-1 correlation development [3),
4.5.4 Two-Phase Flow Models l-Empirical correlations are used in VIPRE-01 to model two-phase flow effects. The two-phase correlations fall into three categories:
l.
- 1) subcooled void correlations, 2) bulk void models, and 3) two-phase
' friction multipliers. A subcooled void correlation is used for modeling the nonequilibrium transition from single-phase to nucleate boillag. The bulk (saturated) void model relates flowing quality with void fraction, accounting for phase slip. The two-phase friction multiplier is the traditional means of modeling the effect of two-phase flow on the friction pressure drop with a homogeneous equilibrium model. It is applic.d as a multiplier on the celculated single-phase friction pres.ture drop.
The VIPRE-01 recommended models are used in the CPSES VIPF.E-01 sodel. The EPRI void model, which consists of the EPRI subcooled vo'td and bu'.k void correlations, and the Columbia /EPRI two-phase friction multip15,ar, are selected for use in the CPSES model. The NRC staff stated in the VIPRE-01 4-19
)
l lL
\
I 1
SER [2] that:
"...we conclude that the EPRI void model and the the EPRI correlation for two-phase friction are acceptable for licensing calculations. In l
l some applications other correlations or combination of correlations '
may provide better results. It may be advisable, therefore, for the user to ... determine which correlations would give the best results l' for a particular application."
TU Electric performed a sensitivity study, as discussed in Chapter 5, to investigate other choices of two-phase flow models. This study indicated that for CPSES VIPRE-01 model applications, the choice of two-phase flow models does not have a significant effect on the DNBR calculation. .
-4.5.5 Water Procerties In the CPSES VIPRE-01 model, water properties-are obtained from the EPRI water property functions installed in VIPRE-01, using an internally generated interpolating table. The VIPRE-01 SER [2] states that:
"Aside from a possible local pressure effect, VIPRE-01 is insensitive to the way fluid properties are computed by either the interpolation of the table entries or the direct evaluation of internal properties functions."
4-20 l
l' l
1 The fluid properties are evaluated at the VIPRE-01 reference pressure (i.e.,
core exit pressure), rather than the calculated local pressure. The VIPRE-01 solution is not sensitive to the use of core exit pressure for evaluating water properties for the range of pressures encountered in CPSES l
l DNB analysis, l
4.6 Operatine Condition Parameters Operating condition parameters such as inlet temperature, pressure, inlet mass flux, and power serve as the input boundary conditions for VIPRE-01 calculations. These parameters are provided by a system code such as RETRAN-02 [8].
4.7 Numerics Parameters Numerics options in VIPRE-01 include the choice of a solution method and convergence control parameters. The direct UPFIDW solution method is used for the CPSES VIPRE-01 model. In this solution method, the energy equation matrix and the momentum equation matrix are solved by the direct elimination technique. The convergence of the VIPRE-01 numerical solution is controlled by both convergence limits and damping factors. Damping factors are input 4-21 l
l
weighting-factors used in the numerical iterative process to obtain a tentative value of an updated parameter from the values of the previous iteration. Values of convergence limits and damping factors are adjusted in the CPSES VIPRE-01 model in order to optimize the code efficiency and to ensure solution convergence within a reasonable degree of accuracy.
4.8 Engineering Uncertainties The following engineering uncertainties will be discussed in this section:
- 1) engineering enthalpy rise hot channel factor (FE ), 2) core inlet flow maldistribution, and 3) engineering heat flux hot channel factor (FEq ),
4.8.1 Encineerine Enthalov Rise Hot Channel Factor FE accounts for variations in fuel fabrication variables which affect the heat generation rate along the flow channel. These variables include pellet diameter, density, and U235 enrichment. FE g, modeled as a multiplier on the heat deposited in the hot channels from the surrounding fuel rods in the CPSES VIPRE-01 model. The value of E
F is evaluated based on fuel fabrication data, and is typically j supplied by the fuel vendor.
{
4-22
)
1 l
4.8.2 Inlet Flow Ma1 distribution A design basis 5% reduction of coolant flow to the hot assembly is used in the CPSES VIPRE-01 model to ensure a conservative inlet flow distribution for DNB analysis. In order to conserve the total mass flow rate, the relative flow rate at the core peripheral assemblies (Channel 16 in Figure.4-4) is increased to slightly greater than 1.0. The VIPRE-01 SER [2]
states that:
"The inlet flow distribution has a very small effect on the the VIPRE-01 results in the upper half of the core since the flow redistribution recovers the inlet flow maldistribution within the first few feet."
Even'though the VIPRE-01 results are not very sensitive to this small inlet flow maldistribution, it will be used in the CPSES VIPRE-01 model for consistency with the current FSAR analysis methodology.
l-l 4.8,3 Encineerine Heat Flux Hot Channel Factor E
F g is an allowance that accounts for heat flux spikes resulting from J manufacturing tolerances which include local variations in enrichment, pellet density and diameter, surface area of the fuel rod and eccentricity i
. 4-23
i of the gap between pellet and clad. Westinghouse has demonstrated that
! lthere is no DNB penalty for the relatively low intensity heat flux spikes
) caused by variations in fabrication parameters [20]. TU Electric has l
performed a similar study 'tsing VIPRE-01 and the TUE-1 DNB correlation. In this study the calculated MDNBRs for a CHF data set with heat flux spikes were compared with the MDNBRs for a matching CHF data set without heat flux spikes but with the same test geometry and operating conditions. The study results indicate that no additional DNBR penalty is required to account for heat flux spikes. Therefore, FEg is not used for DNB analyses with the CPSES VIPRE-01 model.
4-24
)
I 1
I 1
1 1
-l TABLE 4-1 CPSES-1 Core Thermal-Hydraulic Parameters (Cycle-1)
Core Heat Rate (NWth) 3411 Pressurizer Pressure (psia) 2250 Reactor Coolant System Thermal Design Flow Rste (gpm) 382,800 Core Nominal Inlet Temperature (F) 559.6 Bundle Length (in) 151.63 Active Cort Length (in) 144.0 Number of Fuel Assemblies 193 Effective Flow Area for Heat Transfer (ft2) 3g,1 Assembly Lattice 17 x 17 Fuel Rods per Assembly 264 Goide Thimble Tubes per Assembly 24 Instrumentation Thimble Tubes per Assembly 1 Assembly fitch (in) 8.426 Fuel Rod Diameter (in) 0.374 Guide Thimble / Instrumentation Thimble Diameter (in). 0.482 Rod Pitch (in) 0.496 Number of Crids 8*
Mixing Vane Grid Spacing (in) 20.55
- 6 R-type mixing vane grids & 2 simple supporting grids 4-25
LT l
i TABLE 4-2 1
CPSES VIPRE-01 Model Summary (CPSES-1 Cycle 1)
- f. '
16' Channels, 20 Rods (12 subchannels & 4 lumped channels, Fig.-4-4)
- 38 Axial nodes (3" nodal length in MDNBR region, Fig. 4-5)
Reference Radial Power Distribution (Fig. 4-6) with Peak / Avg = F N gg l.
[ - Reference Chopped Cosine Axial Power Distribution with Peak / Avg = 1.55
- i. - Percent of Heat Generated in Fuel Rods - 97.4%
- Turbulent Crossflow Mixing, ABETA = 0.030 l - No Turbulent Momentum Mixing, FTM = 0.0 (enthalpy mixing only)
Axial Friction Factor = 0.32*Re-0.25 l
Crossflow Resistance Coefficient = 0.5 l- ;
- Channel Flow Area Dependent Local Loss Coefficients l i 1 - 20.55" Crid spacing (6 mixing vane grids & 2 supporting grids) '
- EPRI Two-Fhase Flow Correlations
- 5% Flow Reduction in the Hot Assembly E
- F modeled as a multiplier on heat deposited to the hot channels
- Direct UPFlDW Solution Scheme i
- TUE-1 DNB Correlation l l
- Conduction Model Parameters: i 1
- Ct.p Conductance, Bounding Constant Value
- Uniform Power Distribution and 6 Radial Nodes within Fuel Rods
- Default Heat Transfer Correlations ;
)
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i i . ,
e i i e ,
I I ,' !
--r- . ,. {
l i i q i i i l 1
l ! .' I
(
i I
{
FIGURE 4-6. CPSES VIPRE-01 Model Reference Radial Power Distribution (
4-32 l
CHAPTER FIVE SENSITIVITY STUDIES 5.1 General Several sensitivity studies were performed by TU Electric to assess the effect of the VIPRE-01 modeling options on the CPSES mocel results. The input parameters evaluated in the sensitivity studies include radial and axial noding, crossflow parameters, turbulent mixing parameters, friction correlations, and two-phase flow correlations. In addition, the heat transfer correlations used with the conduction rod model for transient calculations were also studied. The sensitivity of the TUE-1 KDNBR to changes in the input parameters was investigated in each study.
1 I
The sensitivity of each parameter was studied at two different sets of operating conditions, as shown in Table 5-1: 1) the nominal operating conditions, and 2) the MDNBR conditions for the complete loss of flow transient. Because these studies were performed in the process of the CPSES VIPRE-01 model development, the VIPRE-01 model used as the " reference case" in the steady-state sensitivity studies is slightly different from the CPSES I model described in Chapter 4. However, the minor modeling differences are i
not expected to affect the conclusions of the sensitivity studies. These l
modeling differences are discussed below:
I 5-1
I I-I
- 1) A clightly differer.t radial power distribution was used, as -
l l -
shown in Figure 5-1.
- 2) A small pitch reduction factor was applied to the hot channels. ,
I 3) A constant axial friction factor of 0.0155 was used, as calculated from the Moody chart, which accounts for surface roughners.
I
- 4) TheIdel'chikcorrelation[21),2.66*Re{0.2,wasusedfor the crossflow resistance coefficient. .
I The CPSES transient model with conduction rods, as described in Chapter 4, was used as the reference case for the sensitivity study of the heat transfer correlations.
I .
5.2 Radial Nodine A radial noding (channel layout) sensitivity study was performed in which several subchannel configurations were evaluated to determine the sensitivity to radial noding detail. Three 1/8 core cases were er.amined, including the reference case, one case with a more detailed subchannel -
5-2 I
a j
i l
.model, and one case with a less detailed subchannel model. In addition, one
-1/4 core case was examined, with similar subchannel modeling detail as the reference case. The casec are listed below:
Case 1: 40 channels - 42 rods, 1/8th core model (Figure 5-2).
Case 2: 16 channels - 20 rods, 1/8th core model (Figure 4-4).
(Reference)
Case 3: 12 channels - 14 rods, 1/8th core model (Figure 5-3).
Case 4: '26 channels - 35 rods, 1/4th core model (Figure 5-4). '
The sensitivity study results in Table 5-2 show that the calculated MDNBRs for the four cases are within 1% of each other. This indicates that the MDNBR is insensitive to radial noding, as long as the hot channel is surrounded by at least one row of subchannels.
5.3 Axial Nodine I
A sensitivity study of axial noding was perfrrmed to de' ermine the effect of the axial noding detail and the use of nonuniform axirl noding. Three nonuniform axial noding cases were examined, including the reference case, one case with a larger axial node size, and one case vith a smaller axial node size. In addition, one uniform axial noding case was examined, with the noding in the MDNBR region equal to the reference case. The cases are listed below:
5-3
Case 1: Uniform axial noding with 6" nodal length in the heated region (0.6" to 144.6").
Case 2: Nonuniform axial noding with 3" nodal length in the NDNBR (Reference) region (Figure 4-5).
Case 3: Nonuniform axial noding with 2" nodal length in the MDNBR region (72.6" to 114.6") and 6" nodal length elsewhere. 1 Case 4: Uniform axial noding with 3" nodal length in the heated region.
The results shown11n Table 5-3 indicate that calculated MDNBR is not sensitive to axial noding for the cases examined. The MDNBR differences among the four cases are within 2%. The results of this sensitivity study indicate that the use of a 3" nodal length in the MDNBR region in the CPSES VIPRE-01 model is sufficient to predict the MDNBR accurately along the fuel rods.
5.4 Crossflow Parameters 5.4.1 Channel Centroid Distance In this sensitivity study, the channel centroid distances, used in the crossflow equations, were varied from half of the reference values to 1.5 times the reference values. The results in Table 5-4 show that the effect of different centroid distances on the VIPRE-01 solution is insignificant.
5-4 '
l u
h e-l l
f There'is virtually no MDNBR change at the operating condition selected for l
l the sensitivity study.
l
".5.4.2 Crossflow Resistance l
In the sensitivity study of crossflow resistance, the MDNBR results using the Idel'chik correlation were compared with the results using the constant value of.d.5 recommended in the VIPRE-01 manual [1], which was used in the.
CPSES VIPRE-01 model described in Chapter 4. The results in Table 5-4 show no significant MDNBR difference between the two cases.
5.5 Turbulent Mixine Parameters 5.5.1 ABETA The turbulent mixing coefficient, ABETA, was varied from 0.0 to the best estimate value of 0.059 for the 17x17 fuel assembly in this sensitivity study. As expected, the calculated MDNBR is a strong function of ABETA, as shown in Table 5-5. The calculated MDNBR decreases with decreasing ABETA, with the differences becoming more significant for smaller ABETA values.
1 4
5-5
t-c-
5.5.2 EId The turbulent mixing factor, FTM, was varied from 0.0 to 1.0 in'this sensitivity' study. The_results in Table 5-5 show that the calculated MDNBR increases slightly with increasing FTh 5.6 Axial Friction Factor A sensitivity study was performed to determine the effect of the axial friction factor on the calculated MDNBR. The constant axial friction factor for the reference case was calculated from the Moody chart using the nominal operating conditions and accounting for rod surface roughness. Two other cases were examined, using the McAdam and Blasius smooth tube correlations, j . The Blasius correlation is used in the CPSES VIPRE-01 model described in 1
Chapter 4. The cases are listed below:
Case 1: A constant friction factor, 0.0155 (Reference)
Case 2: Blasius correlation, 0.32*Re-0.25 ,
I Case 3: McAdam correlation [22), 0.184*Re-0.2 1
)
The axial friction factor calculated by the Blasius and McAdam friction correlations is smaller than the value of 0.0155. The results of the
)
5-6
~ , '
sensitivity study shown in Table 5-6 indicate that the calculated KDNBR l-I decreases slightly with decreasing axial friction loss. The MDNBR results L shown in Table.5-6 indicate that the maximum MDNBR difference is about 1%
for the three cases studied.
I 5.7 Two-Phase Flow Correlations j TU Eit.ctric performed a sensitivity to determine the effect of various two !
phase flow models in VIPRE-01 on the calculated MDNBR. The following combinations of two-phase flow correlations, which are applicable to CPSES operating conditions, were selected for this sensitivity study:
i Case a Subcooled Void Saturated Void Tro-Phase Friction 1 (Reference) EPRI EPRI EPRI 2 Levy Homogeneous Homogeneous 3 None Homogeneous Homogeneous 4 Levy Zuber/Findlay Homogeneous 5 None Armand Armand -l l
Although the flowing quality and axial void profiles are affected if a subcooled void model is not used, the MDNBR results shown in Table 5-7 indicate that the MDNBR is not very sensitive to the different covibinations 5-7
7 i
.y j
1 "of' correlations. .The maximum MDNBR' difference'is less than 2% for'the cases studied.
'5.8. ' Heat-Transfer Correlations
~
TU Electric performed a sensitivity study to determine the effect on-the calculated MDNBR resulting from the use of different heat transfer correlations available in the VIPRE-01~ code. In order to conduct this n- .
study, a transient model was used.
The CPSES VIPRE;01 transient model with conduction rods, as described:in.
Chapter.4,.was used as the reference case'for.the sensitivity study of the heat transfer. correlations. The " fast" (75 pcm/sec) rod. withdrawal event, a i .relatively rapid power increase transient, was selected as an appropriate 1
transient to illustrate the sensitivity of the VIPRE-01 solution to the L choice of heat transfer correlations. The power and pressure forcing functions were obtained from the fast rod withdrawal transient presented in tha CPSES-1 FSAR, which are shown in Figure 6-3. The coolant inlet temperature and the inlet flow rate were held constant, and the gap conductance was set to a conservatively large value of 10,000 Btu /hr-ft2 *F.
Only single-phase convection and nucleate boiling heat transfer are o
important in DNBR calculations, since the fluid conditions do not exceed the DNB point. .The following combinations of heat transfer correlations available in the.VIPRE-01 code [1], which are applicable to CPSES conditions, were selected for the sensitivity study:
1 Case # Sinnle-Phase Cubcooled Boiline Saturated Boilino 1 (Reference) EPRI Thom/ single-phase Thom/ single-phase 2 EPRI Thom Thom 3 Dittus-Boelter Jens-Iottes Thom 4 Dittus-Boelter Chen Chen The results shown in Figure 5-5 indicate that the calculated MDNBR is not sensitive to the choice of heat transfer correlations. The MDNBR differences for all of the cases are within 1% of the reference value.
However, when the Jens-Iottes correlation was selected for the subcooled boiling regime, the VIPRE-01 heat transfer coefficient iteration did not
- j. converge for several time steps after the MDNBR occurred at 3.0 seconds.
The non-convergent data points are not plotted in Figure 5-5.
I .
5-9
TABLE 5-1 Steady-State Sensitivity Study Operating Conditions NOMINAL CONDITIONS Reactor Power, MWth 3411 Core Inlet Temperature, OF 559.6 Core Inlet Mass Flux, Mlbm/hr-ft 2 2.62 Pressurizer Pressure, psia 2250 psia MDNBR CONDITIONS FOR THE COMPLETE LOSS OF FLOW Reactor Power, MWth 3343 Core Inlet Temperature, OF 565 7 Core Inlet Mass Flux, M1bm/hr-ft 2 2.04 Pressurizer Pressure, psia 2220 psia 5-10
~
L l'
f.
TABLE 5-2 Radial Noding Sensitivity Study l
l Nominal Loss of Flow Case
- Description MDNBR MDNBR 1 40 Channels - 42 Rods 2.032 1.565 (Figure 5-1) 2* 16 Channels - 20 Rods- 2.034 1.564 (Figure 4-4) 3 12 Channels - 14 kods 2.036 1.567- 'q (Figure 5-2) 4 26 Channels - 35 Rods 2.042 1.577 (Figure 5-3)
- Reference Case ,
5-11
g
't 0
L..,.. TABLE 5 Axial Noding Sensitivity Study Nominal Loss of Flow Case # -Description MDNBR MDNBR 1- Uniform, 6" Nodal Length 2.036 1.580 in Heated Region. 2* Nonuniform, 3" Nodal Length 2.034 1.564 in MDNBR region (Figure 4-5) 3 Nonuniform, 2" Nodal 2.039 1.569 Length in MDNBR Region
- 4 Uniform 3" Nodal Length
- 2.032 1.570 in Heated Region
- Reference Case 5-12 a
)
I 1 TABLE 5-4 Crossflow Parameters Sensitivity Study )
'f Centroid Distance:
Nominal Loss of Flow Case # b acrintion MDNBR MDNBR 1* Reference Values 2.034' 1.564 2' O.5 x Reference Values 2.034. 1.559 3 1.5 x Reference Values 2.035 1.569 Crossflow Resistance: Nominal loss of Flow Case # Description MDNBR MDNBR 1* 2.66* Reg-0.2 2.034 1.564 2+ 0.5 2.034 1.563 I }
- Reference Case
+ CPSES VIPRE-01 Model (Chapter 4) 1 5-13
e TABLE 5-5 Turbulent Mixing Parameters Sensitivity Study ABETA: Nominal Loss of Flow Case e Description MDNBR MDNBR 1 ABETA = 0.0 1.926 1.370 2 ABETA = 0.013 1.989 1.489 3 ABETA = 0.025 2.017 l'.537 4* ABETA = 0.038 2.034 1.564 5+ ABETA = 0.059 2.050 1.591 ETE: Nominal Loss of Flow Case e Description MDNBR MDNBR 1* FTM = 0.0 2.034 1.564 2 FTM = 0.4 2.058 1.578 3 FTM = 0.8 2.073 1.588 4 FTH = 1.0 2.075 1.590
- Reference Case
+ Best Estimate Value
! 5-14 l )
'1 i
TABLE 5 6 Axial Friction Factor Sensitivity Study Nominal Loss of Flow Case # Description MDNBR MDNBR 1* 0.0155 2.034 1.564 2+- 0.32*Re-0.25- 2.013 1.544 3 0.184*Re-0.2 2.018 1.549
- Reference Case l
l
+ CPSES VIPRE-01 Model (Chapter 4) l l
I i 1 l 5-15
TABLE 5-7 Two-Phase Flow Model Sensitivity Study l Nominal Loss of Flow Case # Description + MDNBR MDNBR 1* EPRI,EPRI,EPRI 2.034 1.564 2 NONE, HOMO, HOMO 2.013 1.582 3 NONE,ARMA,ARMA 2.038 1.581 4 LEVY, HOMO. HOMO 2.038 1.581 5 LEVY,ZUBR, HOMO 2.038 1.592
+
Two phase flow models are listed in order of 1) subcooled void model,
- 2) saturated void model, and 3) two phase friction multiplier.
Reference Case 5-16
y 2 0 ,' -
) ... e,.
) .r. ,.3,
,.s, 1.,0 . [06 34 I$,
)O900e
)@ O @e O O i 20000000 b
\
l Rod Number XX X.XX Normali2ed Power f actor e # i , I e
..T I
8 i ' I I I 8 ' t
. i
- +....,....u
. 4, . . . . - -
l 8 I
' I g .j i i ! ' 8 7...g.. 3---
1 I i i a i FICURE 5-1. Sensitivity Study Reference Radial Power Distribution 5-17 I
v.
*
- Channel 10 - Hot Thimble Channel J & 5 Channel 14 - Hot Standard Channel
^ 11 1 11 6 12 t IJ li16 1 13 l' 13 16 4 17 16 6 17 d 88 19 20 21
}- 14 3, 20 21 2. 22 i 23 > 26 23 e 26 21 .5 25 26 27 28 ' ) 2, i ao . n 32 . 33 3 ' is a
;1 32 J3 36 15 36 37 38 't 37 d
channels 1 - 37
\x i
4 38h , i ' i n l
..;___4-__,
l6) l i , e e l f 40 , e j I f I g
..........__6.-
e s I
. . p _ _ .; - _ _ -; _ _ _ + _ _ _ ' _ _ _
i e e i , t ! '
. . r . . . .! . . 3__.'
- e i i e
. e i e f f FICUrJE 5-2. 40 Channels - 42 Rods, 1/8th Core Model 5-18
~
i Channel 2 - Hot Thimble Channel Channel 4 - Hot Standard Channel y )O -
)o
, , . ,, n . ,
L )o
)o MDOOOOO 10000000 i
Channels 1 -9
\x l
toh ;
- I l !!
I l i
- i s t: l l 8 *
....._,.._s.._ i l 8
-7 i .
I : ' i , l 8 I 1 g i y-__' l I I i 1 1 FICURE 5-3, 12 Channels - 14 Rods, 1/8th Core Model 5-19
V V %::# V V %=# V V q
) O1 ,
2 > 0 t
)O',>4
- 2 7
00,,O O~ 9 10 11 ,, 12 13 7 8 9 + 10 ' - 11 12 14 15 16 17 18 19 20 7 13 14 ' 13
) 21 22 23 s 6 7 2,
og oo 18 19 20
)o 2e 27 28 XR,00DOO O ,
ch.nn.1 1 22 20000000 i i ,
; 4
____{____.___4___L__2____ 24 j @ l ___i____ ___ l l l __7___ l ! . l l l
.1___4@l ,
_r-__,___ 7 l 2> l
' l
' ' l l ,
_ _ _ .t. _ _ __i_ _ ._ _t __.___.,..__m______,___4___. I e i
, i I
l I i !
, a I l 26 i
_ _, p _ _ _ 4. _ _ _ .; _ _ _ + - _ _ } _ _ _ i i
' l l l l
..,....;___4___-
l t i I I I l ' t 6 i Channe1 9 - Hot Thimble Channel i Channe1s 10 & 15 - Hot Standard Channels FIGURE 5-4, 26 Channels - 35 Itods, 1/4th Core Model 5-20 l
6 e S
.t 26 2.5 -
/
2a-2.3 - / 2.2 - g' 2.1 - o 2-5 1.9 8
*~
1.8 - - 1,7 - 1.6 - 1.5 - 1.4 - 1.3 , 0 2 ' 1 6 TIME (SEC) O BASE -o THOW a JENS X CHEN FIGURE 5-5. Heat Transfer Correlations Sensitivity Study Case # Sinnle-Phase Subcooled Boilina Saturated Boiline 1 (Reference) EPRI Thom/ single-phase Thom/ single-phase 2 (Thon) EPRI Thom Thom 3 (Jens) Dittus-Boelter Jens-Lottes Thom 4 (Chen) Dittus-Boelter Chen Chen 5-21 l - _-_____- -- I
CHAPTER SIX '. DEMONSTRATION ANALYSES 6.1 General Four demonstration DNBR calculations were performed with the CPSES VIPRE-01 model described in Chapter 4, using the TUE-1 DNB correlation; 1) nominal steady-state operating conditions, 2) the complete loss of flow transient,
- 3) the uncontrolled fast-rod withdrawal transient, and 4) the uncontrolled slow rod withdrawal transient. In this chapter, the-results of the four demonstration analyses are presented individually, followed by a general discussion of the differences between the current FSAR analyses and the TU Electric demonstration analyses. These calculations, which were performed using a CPSES-1 Cycle 1 model, are presented to illustrate the DNB analysis methodology which TU Electric intends to use for CPSES licensing applications. The use of specific input values in these demonstration analyses is not intended to imply that the same values will be used in actual TU Electric licensing calculations.
In the demonstration analyses presented in this chapter, input boundary' conditions are obtained from the current CPSES-1 FSAR. In actual TU Electric licensing analyses, the input operating conditions will be 6-1 I i
)
calculated by the RETRAN-02 code. For the transient calculations, the CPSES transient model with conduction rods was used. In addition, the following assumptions were made in the transient calculations: 1 1
- 1) The core axial and radial power distributions, including the rod internal radial power profile and the fraction of heat generated in the fuel rods, were held constant with time. ,
i i
- 2) The hot channel location, hot channel factors, and inlet flow I reduction to the hot assembly were held constant with time.
The TU Electric analyses presented in this chapter generally show higher MDNBRs than the corresponding CPSES-1 FSAR analyses, due to the correlation differences between TUE.-l and W-3 and the modeling differences discussed in Section 6.6. Appendix 1 of this report describes the CPSES-1 FSAR benchmark analyses using VIPRE-01 and the W-3 DNB correlation. 6.2 Nominal Operating Conditions l l The CPSES steady-state (dummy rod) model was used in the calculation for nominal conditions. The operating conditions vers taken from the FSAR values given in Table 5-1. At the nominal operating conditions, the MDNBRs 1 6-2
,1
I predicted by the VIPRE-01 model with the TUE-1 correlation are 2.08 and 2.24 I for the hot thinble channel and the hot standard channel, respectively. The thimble channel is more limiting than the standard channel because of the cold wall DNB penalty factor in the TUE-1 correlation and a lower coolant mass flow rate resulting from higher a2ial flow resistance. 'I I 6.3 Complete Loss of Flow Transient The CPSES transient model with conduction rods was used for this demonstration calculation, with the core power and inlet mass flux forcing [,, I functions shown in Figure 6-1. As in the current FSAR analyses, the core i inlet temperature and the system pressure were held constant at their initial values of 565.1 0F and 2220 psia, respectively. The gap conductance was set to a conservatively low constant value of 400 Btu /hr-ft 2,o F. A low gap conductance was specified for this event to maximize initial fuel stored energy and thermal inertia, resulting in a delay in the reduction of the rod surface heat flux following reactor trip. A plot of the calculated transient MDNBR is presented in Figure 6-2a. Once again, the MDNBR occurs in the hot thimble channel (Channel 4), for the same reasons as discussed above for the nominal steady-state case. The MDNBR calculated by VIPRE-01 displays the same trends as the current FSAR 6-3 lI _
I rIk v.x <. i. l l analysis, shown in Figure-_6-2b. ' Initially, the MDNBR decreases due to the I . decrease in core flow, and then the MDNBR begins to' increase as the core power is rapidly reduced after-the reactor trip. I 6.4. ' Uncontrolled Fast Rod Withdrawal Transient l-1 i The demonstration DNBR calculation for the uncontrolled fast rod withdrawal '- transient was performed using the CPSES VIFRE-01 transient model with conduction rods, with the core power and pressure forcing functions shown in Figure 6-3. As in the' current FSAR analysis, the inlet temperature and mass u [O . flux were held constant during the transient.at their initial values of 565.l'0F and 2.60 M1bm/hr-ft2, respectively. The gap conductance-was set to a conservatively high value of 10,000 Btu /hr-ft 2 - F to minimize the fuel thermal inertia, resulting in a more rapid increase in rod surface l
. heat flux for this power increase transient.
A plot of the calculated transient MDNBR is presented in Figure 6-4a. The MDNBR occurs in the hot thimble channel (Channel 4), for the same reasons as discussed previously. The CPSES VIFRE-01 calculated MDNBR displays the same trends as the current FSAR analysis, shown in Figure 6-4b. Initially, the MDNBR decreases due to the increase in core power, and following the reactor trip.the MDNBR increases as the core power is reduced. k 6-4 4 l l 1 i
I I l' I I 6.5 Uncontrolled Slow Rod Withdrawal Transient 1 The CPSES transient model with conduction rods was also used in the I demonstration DNBR calculation for the uncontrolled slow rod withdrawal j 1 transient. The core power and pressure forcing functions were taken from the current FSAR analysis, as shown in Figure 6-5. The transient core inlet temperature and mass flow rate forcing functions, also shown in Figure 6-5, were inferred from the FSAR core average temperature plot. The gap conductance for this event was set to a conservatively high value of 10,000 Btu /hr-ft 2 -F, to minimize the fuel thermal inertia, resulting in a more rapid increase in the rod surface heat flux for this power increase transient. However, due to the relatively slow rate of power increase for this transient, the calculation is not sensitive to the specified fuel rod conduction model parameters. A transient MDNBR plot is presented in Figure 6-6a, which shows that the CPSES VIPRE-01 calculated MDNBR trends are the same as for the current FSAR analysis results, shown in Figure 6-6b. Initially, the MDNBR gradually decreases due to the increase in core power, and following the reactor trip the MDNBR increases as the core power is reduced. 6-5
l 1 l l 6.6 Comoarison with FSAR Analyses The TU Electric demonstration calculations indicate an increase in the DNB 1 margin as compared qualitatively with the CPSES-1 FSAR results. Several ) l features in the CPSES VIPRE-01 model contribute to the MDNBR increase, as discussed below:
- 1) The VIPRE-01 model uses the TUE-1 DNB correlation, which is a 1 modern mixing vane grid correlation developed specifically for application to Westinghouse R-grid fuel. The improved 1
statistical performance of this correlation results in a ) reduction in the excess conservatism that was required for the V-3 correlation. { i i
- 2) The VIPRE-01 model does not use an engineering heat flux hot l
channel factor, FEq , for the reasons discussed in Chapter 4. This results in a 3% increase in the calcarated MDNBR for the I VIPRE-01 model as compared with the FSAR analyses. 1
- 3) The VIPRE-01 model uses 8 grid locations with 20.55" grid spacing l
l instead of the 7 grid locations with 26.19" grid spacing used in j the CPSES-1 FSAR analyses. The grid locations used in the VIPRE-01 model represent the actual CPSES-1 Cycle 1 core l 6-6 1
i;
' j f ^~
i {' P
,, . II !
J l configuration. This difference has.a significant effect, l, especially for the TUE-1 correlation, which is a mixing vane correlation that is' sensitive to grid spacing.
- 4) The VIPRE-01 model does not' include a hot channel pitch reduction l
L factor. This difference results in an increase of approximately 3% in the predicted MDNBR for the CPSES VIPRE-01 model as L compared to the FSAR results. L > L.2 ' 0ther'VIPRE-01 modeling features do not result in significant differences in the MDNBR calculations. The CPSES-1 FSAR benchmark analyses presented in l l( Appendix 1, which utilize a modified VIPRE-01 model that more closely matches the Westinghouse'model, further demonstrate that the differences Is I between the VIPRE-01 calculations and the FSAR results are primarily due to . I the four key modeling differences discussed above. [' 1 From the above discussion there is the appearance of a reduction in the
~ degree of conservatism for the proposed TU Electric methodology as compared ,
.to the current FSAR methodology. However, each of the differences listed
'above are well understood and justifiable. In addition, it should be noted L. i that several of the FSAR conservation listed above are credited as part of )
the " generic" DNB margin philosophy used by Westinghouse for the current CPSES-1 FSAR analyses. TU Electric's proposed retained margin approach, )j l. i- i I 6-7 j
,)
? ,j:
.]'
l .?
.]v which involves the use'.of a higher DNBIL " design" limit as discussed-in i
[ Chapter 2, will'. result in the came or greater safety margin for the plant
;1icensing analyses.
i l i i l i 1 6-8
.r ..,
s l TIME (stcoes)
.O 5 '80
. 15 20 25
, 30 E I I l l 1.0 - 1 2.
=
! 5 - l = 0.8 I 8 5 l ,5 0.6 - L _= 2 f 0.s - [ G
~
O )~ I ) I' l.0 l-F 0.8 - 5 3 m B
= 0.6 -
,2, 1 W
= ,
1^ - l 3 0.s - ! w T S o.2 - t I I l j o ! l , 0 5 to 15 20 ;$ 33 IlME(SECCNDS) FIGURE 6-1. CPSES-1 Complete Loss of Flow Demonstration Analysis Transient Forcing Functions 6-9 _ . _ _ _ _ = _ - . _ _ - _ _ _ _ _ _ ._.
. i
- $.0 -
2.4 - 2.3 - 2.2 - 2.1 -
$ 2-5 .
i .-s a _ 15-1.7 - 1.6 - ' 1$- i 1.4 = 1.3 0 ; 6 Time (SOConOS) FICURE 6-2a. CPSES-1 Complete Loss of Flow Demonstration Analysis 2.50 2.25 - \ l 2.00 - a b 1.75 -
?
- =
1.50 1 l.25 -
.N 1.00 ! I
- 0 2 4 6 TIME (SECOND$)
FIGURE 6-2b. CPSES 1 Complete Loss of Flow FSAR Analysis 6-10
TlHE(SECONDS) 0 1 2 3 4 5 6 7 1.50 I l I l l l 1.25' -
.g I.00 wa hh* j
= 0.75 -
0% d Eg 0.50 - U E t 0.25 - 0.00 1 TIME (SECONDS) 0 1 2 3 4 5 6 7 8 L 2400 - i l I I i l I i 2350 - 2300 - w E a 2250 - as 3 2200 -
=t .1 E 1 g 2150 -
1 Y a- l 1 2l00 - 2050 -
)
I 2000 l l l FIGURE 6-3. CPSES-1 Fast Rod Withdrawal Demonstration Analysis Transient Forcing Functions 6-11 '
3.6' 3.4-el
-)
i: J 3-2.5 - f
)
- h. 2.6 -
l 5 3
- 2.4 - l 1.5 -
.: -g s5-14-1.2 L '
O- 2 4 6 he (secones; FIGURE 6-4a. CPSES-1 Fast Rod Withdrawal Demonstration Analysis 3.00 2.75 - 2.50 - g 2.25 - o M A 2.00 - 1 I.75 - 3.50 - I I , , , 3.25 4 5 6 7 TlHE(SECCNDS) FIGURE 6-4b. CPSES-1 Fast Rod withdrawal FSAR Analysis 6-12 3
1 TlHE (SECONDS) 0 5 10 15 20 25 30 35 40 1.2 l l l l l I - l 1.0 - C I 5E 0.8 - 3E m 5 05 - 55 8;
- bl 0.4 -
5 0.2 - 0.0 TIME (SEC6HDS) 0 5 10 15 20 25 30 35 u0 2400 I i i i i l l 2350 - 5 2300 - 2 g 2250 - S n E 2200 - N 2150 -- { 5 ' w" 2 2l00 - 2050 - 2000 FIGUPI 6-5. CPSES-1 Slow Rod Withdrawal Demonstration Analysis Transient Forcing Functions (Sheet 1 of 2) 6-13
)
i l _ _ _ _ _ . _ . _ _ I.
590.00 585.00 - 580.00 - E j $75.00 - a-E 570.00 - _^ 5 565.00 - e o u 560.00 -
$55.00 -
'550.00 . , , , , ,
0 10 20 30 40 Time (swones) 145.00-144.00 -
?
N 14s.00 - E e 142.00 - d
$ 141.00 -
e 140.00 -' - g
!39.00 -
2
)
1
]e 138.00 -
a 137.e0 - 1 i 136.00 - i 135.00 , , , , , , j 0 to 20 30 40 l nme (ex.nos) ( FIGURE 6-5. CPSES-1 Slow Rod Withdrawal Demonstration Analysis ; ) Transient Forcing Functions ' (Sheet 2 of 2) . 6-14
- 2.S 2.4 -
2.3 - 2.2 - 2.1 - O
- h. '2-E 1,9 4 1.5 -
1.7 - 1.6 - 1.5 - 1.4 - 1.3 0 to 20 so T.m (seconos) FIGURE 6-6a. CPSES-1 Slow Rod Withdrawal Demonstration Analysis 3.00 2.75 - i 2.50 - cr 2.25 - I m s 2.00 - 1.75 - 1.50 - I I I 1.25 I l I I 0 5 10 15 20 25 30 35 40 TIME (SECONDS} FIGUPI 6-6b. CPSES-1 Slow Rod Withdrawal FSAR Analysis l 6-15
CHAPTER SEVEN CONCLUSION The descriptions and analyses presented in this report have demonstrated the TU Electric core thermal-hydraulic analysis capability for CPSES licensing applications. The conclusions of this report are as follows:
- 1) The CPSES VIPRE-01 modeling methodology described in Chapter 4 of this report is acceptable for the intended licensing applications stated in this submittal.
2), TU Electric has fulfilled the user documentation requirements stated in the VIPRE-01 SER [2] for the description of a basic modeling methodology. l
- 3) TU Electric has satisfactorily demonstrated its proficiency in using VIPRE-01, as required by NRC Generic Letter 83-11 [4).
l 7-1
{ f l 1 l l CHAPTER EIGHT REFERENCES
- 1. Stewart,LC. W. et al., "VIPRE-01: A Thermal-Hydraulic Code for Reactor Cores", Vol.1-3 (Rev.2), Vol.4, & Vol.5, NP-2511-CCM, Electric Power Research Institute.
- 2. Rossi, C. E., " Acceptance for Referencing of Licensing Topical Report, EPRI NP-2511-CCM, 'VIPRE-01: A Thermal-Hydraulic Analysis ,
Code for Reactor Cores', Volume 1, 2, 3, and 4", NRC Letter to J. A. ' Blaisdell, UGRA Executive Committee.
Attachment:
" Safety Evaluation Report on EPRI NP-2511-CCM VIPRE-01", May, 1986,
- 3. Ciap, H. B. , et~ al. , "TUE-1 Departure from Nucleate Boiling Correlation", RXE-88-102-P, TU Electric, January, 1989.
- 4. Eisenhut, D. C., " Licensee Qualification for Performing Safety Analyses in Support of Licensing Actions (Generic Letter No. 83-11)",
NRC Letter to all operating reactor licensees, February 8,1983.
- 5. " Standard Review Plan", NUREC-0800, Rev.1, Nuclear Regulatory Commission, July, 1981.
- 6. Skaritka, J., " Fuel Rod Bow Evaluation", WCAP-8691-R1, Westinghouse Electric Corporation, July, 1979.
- 7. Carner, D. C., et al., "RCS Flow Anomaly Investigation Report",
WCAP-il528, Westinghouse Electric Corporation, April, 1988.
- 8. McFadden, J. H., et al., "RETRAN A Program for Transient Thermal-Hydraulic Analysis of Complex Fluid Flow Systems",
NP-1850-CCM-A, Rev.3, Electric Power Research Institute, June 1987.
- 9. Hochreiter, L. E. et al., " Application of the THINC-IV Program to PWR Design", WCAP-8054, Westinghouse Electric Corporation, September, 1973.
- 10. Hao, B. R., et al., "LYNI1: Reactor Fuel Assembly Thermal-Hydraulic Analysis Code", BAW-10129, Babcock & Wilcox Co., October, 1976.
- 11. "LYNK2-Subchannel Thermal-Hydraulic Analysis Program", BAW-10130, Babcock & Wilcox Co., October, 1976.
8-1
- 12. Jones, J. H., et al., "One-Pass Modeling", Transactions of the American Nuclear Society, Vol.49, TANSAO 49.1-474, 1985.
- 13. Sliz, F. W., et al., "VEPCO Reactor Core Thermal-Hydraulic Analysis Using the COBRAIIIC/MIT code", VEP-FRD-33-A, Virginia Electric and Power Co., October, 1983.
- 14. Jones, J. H., et al., "LYNIT-Core Transient Thermal-Hydraulic Program", BAW-10156, Babcock & Wilcox Co., February, 1984.
- 15. Priore, R. J., et al., "The Nuclear Design and Core Physica
- Characteristics of the Comanche Peak Unit 1 Nuclear Power Plant Cycle 1", WCAP-9806, Rev.1, Westinghouse Electric Corporation, October, 1986.
- 16. " Comanche Peak Steam Electric Station Finsi Safety Analysis Report",
Chapters 4 and 15.
- 17. Cadek, F. F., "Interchannel Thermal Mixing with Mixing Vane Grids",
WCAP-7667-P-A, Westinghouse electric Corporation, January, 1975.
- 18. Motley, F. E., et al., "The Effect of 17x17 Fuel Assembly Geometry on Interchannel Thermal Mixing", WCAP-8298-P-A, January, 1975.
- 19. Tong, L. S. & Weisman, J., " Thermal Analysis of Pressurized Water Reactors", 2nd Edition ANS Publication, 1979.
- 20. Hill, K. W., et al., "Effect of Local Heat Flux Spikes on DNB in l
Non-Uniform Heat Rod Bundles", WCAP-8174, Westinghouse Electric L Corporation, August, 1973.
- 21. Chelemer, H., et al., "THINC-IV - An Improved Program for Thermal-Hydraulic Analysis of Rod Bundle Cores", WCAP-7956, Westinghouse Electric Corporation, 1973.
l 22. Rust, J. B., " Nuclear Power Plant Engineering", Haralson Publish Co., i 1980. l 23. "LOFTRAN Code Description", WCAP-7907-P-A, Westinghouse Electric l Corporation, 1984.
- 24. Hargrove, H. G. , "FACTRAN - A FORTR.LN IV Code for Thermal Transients i in a UO2 Fuel Rod", WCAP-7908, Westinghouse Electric Corporation, I
July, 1972.
)
, 8-2 l 1 _--______-_____-_--.._ _ _ - - A
. APPENDII ONE CPSES-1 FSAR BENCHMARK ANALYSES f
A1.1 General TU Electric has benchmarked several current CPSES-1 FSAR analyses using a modified CPSES VIPRE-01 model to provide an additional illustration of the adequacy of the TU Electric modeling methodology. For these benchmark analyses, the CPSES VIPRE-01 model described in Chapter 4 was modified to be as consistent as possible with the Westinghouse modeling methodology in order to facilitate the comparison between the TU Electric and Westinghouse models. The analyses and comparisons presented in this appendix are intended to demonstrate that the CPSES VIPRE-01 model can produce results that are comparable to the current FSAR analyses if the W-3 correlation and i Westinghouse's modeling methods are used. These analyses will highlight the j differences between the TU Electric methods described in Chapter 4 and the Westinghouse methodology used for the CPSES-1 FSAR analyses, and provide an additional basis for the justification of the modeling options selected by TU Electric. 1 Al-1 I
i l 1 1 i The Westinghouse DNB analysis methodology for CPSES-1 utilizes the THINC code and the W-3 DNB correlation. Although THINC is different from VIPRE-01 I in code structure and computational method, the two codes are essentially equivalent for predicting core and hot channel thermal-hydraulic conditions. The V-3 correlation has a DNBR design limit of 1.30 for CPSES-1 applications [16). l l In order to more closely match the Westinghouse modeling methodology used for the current CPSES-1 FSAR analysis, the following changes were made to the CPSES VIPRE-01 model:
- 1) Th6 TUE-1 correlation was replaced by the W-3 correlation.
- 2) The 8 grid configuration with 20.55" spacing was replaced by a 7 grid configuration with 26.19" spacing [16).
- 3) A pitch reduction factor vas applied to the hot channels [16).
- 4) The cale.ulated MDNBR was divided by FE q , 1.033 [16).
- 5) For steady-state calculations, a constant axial friction factor of 0.0155, calculated from the Moody chart accounting for surface roughness, was used to approximate the Novendstern-Sandberg correlation used in the THINC code [21).
Al-2
s I
- 6) A slightly modified radial power distribution was used, as shown '
in Figure 5-1. 7). The Idel'chik correlation [21] was used for the crossflow resistance coefficient instead of the constant value of 0.5. The resultant VIPRE-01 model is referred to as the CPSES-1 benchmark model.- The DNB correlation and grid spacing changes have a significant effect on the DNB results, with the changes resulting in much lower DNBR predictions ifr the CPSES benchmark model than for the CPSES VIPRE-01 model described in Chapter 4. E The changes in pitch reduction and F g result in moderately lower DNBR predictions for the CPSES benchmark model. The other changes do not have a significant effect on the DNBR results. . For the transient DNBR benchmark calculations, conduction rods were used in 1 the CPSES 1 benchmark model to account for fuel stored energy and thermal inertia effects. In addition, the following assumptions were made in the transient calculations: L
- 1) The core axial and radial power distributions, including the rod internal radial power profile and the fraction of heat generated in the fuel rods, were held constant with time.
Al-3
l 1 1
- 2) The hot channel location, hot channel factors, and inlet-flow l
l 1 reduction to the hot assembly were held constant with time. 1 l' l The CPSES-1 FSAR DNB analyses selected for the benchmark study are:
- 1) nominal steady-state operating conditions, 2) the reactor core safety limit curves, 3) the complete loss of flow transient, 4) the uncontrolled fast rod withdrawal at power transient, and 5) the uncontrolled slow rod withdrawal at power transient.
l A1.2 Nominal Ooeratine Conditions A DNB analysis for the nominal steady-state operating conditions shown in Table 5-1 was performed with the CPSES-1 benchmark model for comparison with the CPSES-1 FSAR. The VIPRE-01 results are in good agreement with the FSAR values calculated by THINC. The W-3 MDNBRs calculated by VIPRE-01 are 1.70 and 2.02 for the hot thimble channel and the hot standard channel, respectively, which are within 1% of the corresponding FSAR values of 1.70 and 2.04. Al-4
i A1.3 Core Safety Limit Curves The CPSES-1 core safety limits are curves of RCS inlet temperature vs. reactor power fraction and pressure that define a region of permissible operation with respect to DNB and hot leg boiling. VIPRE-01 calculations for the DNB limit lines at 1860 psia, 2250 psia, and 2400 psia were performed using the CPSES-1 benchmark model for comparison with the CPSES-1 FSAR. At each pressure level, an iteration on the inlet temperature for different power levels was performed until the W-3 MDNBR limit of 1.30 (1 0.005) was reached. Although the core inlet volumetric flow rate was held constant at the thermal design value, the core inlet mass flux was varied with inlet temperature because of the coolant density change. In N addition, for power levels less than 100%, F AH was adjusted according to the CPSES-1 Technical Specification equation given below: i
'l N
F g (P) - 1.55*(1 + 0.2*(1 - P)) (Al-1) where P is the fraction of full power. i The VIPRE-01 results are shown in Table Al-1. A comparison of the i calculated inlet te.mperature vs. power curves is shown in Figure Al-1. The results from the CPSES-1 benchmark model are in good agreement with the corresponding FSAR safety limit curves. I Al-5 l
l 'l i A1.4 Complete Loss of Flow Transient A DNBR benchmark calculation for the complete loss of flow transient was performed, following the Westinghouse analysis methodology presented in the FSAR. The Westinghouse analysis utilized the LDFTRAN code [23) to provide core operating conditions, the FACTRAN code [24) for the' transient heat flux calculation, and the THINC code for the DNBR calculation. The CPSES-1 benchmark model with conduction rods was used for this analysis, with the following additional modeling assumptions:
- 1) The gap conductance was set to a conservatively small value of 400 Btu /br-ft2.op,
- 2) Transient core flow and power were input as forcing functions, using the FSAR values, as shown in Figure 6-1.
- 3) The core inlet temperature and the system pressure were assumed to remain constant throughout the transient at their initial values of 565.1 0F and 2220 psia, respectively.
The benchmark results for the VIPRE-01 calculation are in good agreement with the FSAR results. As shown in Figure Al-2, the average hot channel heat flux calculated by VIPRE-01 matches well with the FSAR curve. This Al-6
1 1' 1 l l 1 indicates that the VIPRE-01 conduction model with a gap conductance of 400 l l Btu /hr-ft2 - F gives results that are similar to Westinghouse's FACTRAN l model for the heat flux calculation in this transitat. The transient DNBR 1 plot in' Figure Al-3 demonstrates that the CPSES-1 benchmark model is l comparable to the THINC model for DNBR calculations. The MDNBR difference 1 1 is less than 1%. 1 A1.5 Uncontrolled Fast Rod Withdrawal at Power l ) A DNBR calculation was performed using the CPSES-1 benchmark model with conduction rods for the fast (75 pcm/sec) uncontrolled rod withdrawal transient, following the Westinghouse analysis methodology, for comparison with the CPSES-1 FSAR. The uncontrolled rod withdrawal was analyzed by Westinghouse using the LOFTRAN code, with a lumped fuel model for the calculation of core heat flux and a partial derivative approximation of the core safety limit lines for the DNBR calculations [23]. The following assumptions were made in the calculation:
- 1) For this event, the gap conductance was set to a conservatively large value of 10,000 Btu /hr-ft2 op,
- 2) The coolant flow rate and core inlet temperature were assumed i
Al-7 i i I l l
s constant at their initial values of 2.60 M1bm/hr-ft2and 565.1 F, respectively.
- 3) The transient core power and system pressure were input as forcing functions, using the FSAR curves shown in Figure 6-3.
Figure Al-4 shows a comparison between the VIPRE-01 results and the FSAR for the calculated core heat flux. The peak heat flux calculated by VIPRE-01 is slightly lower than the FSAR value, which was calculated by the lOFTRAN lumped fuel model. The difference in the heat flux affected the DNBR calculation, but the MDNBR difference was still less than 1%, as shown in Figure Al-5. The simplified LOFTRAN DNB,model is expected to match the DNBRs calculated by VIPRE-01 only in the vicinity of the DNBR limit, due to ! the nature of the partial derivative approximation of the core safety limit in the LOFTRAN code. Consequently, Figure Al-5 shows that the DNBR differences between VIPRE-01 and LOFTRAN increase when the DNBR is not close to the 1.30 limit of the W-3 correlation. L A1.6 Uncontrolled Slow Rod Withdrawal at Power l \ 1 The VIPRE-01 model was also benchmarked with the FSAR analysis for the l l uncontrolled slow (3 pcm/sec) rod withdrawal transient at power. Conduction Al-B
rods were not used in this calculation, bec.ause the effects of thermal inertia and fuel stored energy are not important for this relatively slow transient. The CPSES-1 benchmark model was used for this calculation, with the following additional modeling assumptions:
- 1) The transient core inlet flow, core inlet temperature, and pressure forcing functions were obtained from the FSAR, as shown in Figure 6-5.
- 2) The core heat flux was taken form the FSAR curve shown in Figure Al-6. For this relatively slow changing event, the transient heat flux response is essentially the same as the core power i response shown in Figure 6-5.
1
)
Figure Al-7 shows the DNBR comparison between the VIFRE-01 results and the FSAR. The MDNER calculated by VIFRE-01 agrees well with the FSAR value, j with a differences of less than 1%. Because the FSAR DNBRs were calculated by the LOFTRAN derivative approximation of the core safety limit curves, the
]
DNBR difference between VIFRE-01 and LOFTRAN increases when the DNBR is not close to the DNB limit of 1.30. Al-9 l l f
A1.7 Summary The benchmark analyses presented in this Appendix have shown that a modified CPSES VIPRE-01 benchmark model can produce results that are similar to those presented in the CPSES-1 FSAR. Because the differences between the benchmark model used for the analyses in this Appendix and the CPSES VIPRE-01 model described in Chapter 4 are well understood and justifiable, the analyses in this Appendix give further assurance of the adequacy of the 1 l CPSES VIPRE-01 modeling methodology. i 9 L Al-10
)
l l TAB 12 Al-1 CPSES-1 Core Eafety Limit Curve Benchmark VIPRE-01 FSAR L Pressure Power T-inlet T-inlet (osia) Fraction (OF) (OF) 1860 1.10 554 555 1860 1.15 545 544 l 1860 1.20 536 533 2250 1.00 588 590 2250 1.05 580 582 2250 1.10 572 573 2250 1.15 564' 564 2250 1.20 557 557 2400 1.00 594 597 2400 1.05 586 588 2400 1.10 579 580 2400 1.15 572 572 2400- 1.20 565 563 Al-11
( 610 ,, l 600 -
]'
2250psNe . 2400 psio j 580 - .Nx . i l - I ~ ! D 570 - 7 '3-g 560 -
\ '
50 - 1860 as.o
- se -
530 - l ) 520 , , , 0.6 0.5 1 1.2 POwCR FRACTION Ax ? vlPRE/w-3
- F5AR FIGURE Al-1. CPSES-1 Core Safety Limit Curve Benchmark Al-12
I. 1.3 1.2 - 1.1 - I - E O 6 09 - -s 3 ' E < g 0.7 - 06-0.S O 2 4 6 u Time (secOnes) VIPRE/w-3 9 r5AR FIGURE Al-2. CPSES-1 Complete loss of Flow Bench = ark Hot Channel Heat Flux Results 2.0 2.4 - 2.5 - 2.2 - 2.1 - 2-g 1.9 - D ^ g 1.5 - 7 1.7 - 1.6 - 1.5 - 1.4 - 1.3 - . _ __ _ - 12 - 1 1
- i I O O
2 Time (SeCDPOS) vlPRC/w.3 ,a, 4 r$ag 6 FIGURE Al-3. CPSES-1 Complete Ioss of Flow Benchmark W-3 MDNBR Results Al-13 I - - - -
7 ..
.f w ,f g
(-. Iff ' l-I
.k.
A ){
.p 1.4 I
x i .s - l l.
.1.2 -
_M - ~ - '-- jg. -- bk ' g' 1 - 2 09 - T j '. ,[ i O 'Ag l .' t 6 0.7 - , II' 06 - l . 0.5 - 0.4 1 O- 2
- l. ' 6 l-x Tems (StCOMOS) weec/w-s v rse L.
I J FIGURE Al-4. CPSES-1 Fast Rod Withdrawal Benchmark Hot Channel Heat Flux Results i 1 s 2.9 -
' 2.a -
' 2.1 -
2.6 - 2.5 - 2.4 - /
' 2.s - /
/
/
., 2.2 -
/j.
@ 2.1 -
2-
/ /
2 1.9 - /'/ 4 i .e - 4
/
1.7 - 16, s 1,$ - 14 - i 13 - - _ _ _ _ - 12 - ! u-t O 2 4 5 o tm. csec oaes) vlP#C/w.3 g qq FIGURE Al-5. CPSES-1 Fast Rod Withdrawal Benchmark V-3 MDNBR Results Al-14 I l-
4 ..
-l t
l i
'l 1.2 3
l.0 -
.a.
- h s' h ao 0.8 -
w=
>=. W 5
= 0.6 -
p ,~ m-
= 1 I ..
l g W g vg 0.4. - 5 0.2. - I 0.0 I I O 5' 10 15 20 25 30 35 u0 TIME (SECONDS) FIGURE Al-6. CPSES-1 Slow Rod Withdrawal Benchmark
' Heat Flux Forcing Function 3
2'.9 - 2.8 - . 2.7 - 2.6 - 2.5 - 2.4 - 2.3 - 4 g 2.2 -
@ 2.1 -
0 2-7 1.9 - I 1.5 - 1.7 - 1.6 y ~ 1.5 '
- 1. 4 -
1,3 -
/
1,2 - 1.1 - 1 0 10 20 30 40 Teme (seconos) o vrPRE/w-3 a r$AR FIGURE Al-7. CPSES-1 Slow Rod Withdrawal Benchmark W-3 MDNBR Results Al-15 - - _ _ _ - _ - _ _ - - - _ _ _ _ _ _ _ _}}