"COBRA-FLX: A Core Thermal-Hydraulic Analysis Code Topical Report".

725 Pages·2010·6.56 MB·English

by  Framatome Technologies Inc

ANP-10311NP
Revision 0

COBRA-FLX: A Core Thermal-Hydraulic Analysis Code

Topical Report

March 2010

AREVA NP Inc.

(c) 2010 AREVA NP Inc.
Copyright © 2010
AREVA NP Inc.
All Rights Reserved
AREVA NP Inc. ANP-10311NP

COBRA-FLX: A Core Thermal-Hydraulic Analysis Code
Topical Report Page i
Nature of Changes

Section(s)
Item or Page(s) Description and Justification
AREVA NP Inc. ANP-10311NP

COBRA-FLX: A Core Thermal-Hydraulic Analysis Code
Topical Report Page ii

Contents
Page
List of Tables .............................................................................................................................iv
List of Figures ..............................................................................................................................v
Nomenclature ............................................................................................................................xxi
1.0 Introduction....................................................................................................................1-1
1.1 Code Applications..............................................................................................1-5
1.2 Requested Code Review and Approval..............................................................1-6
1.3 References.........................................................................................................1-9
2.0 Problem Formulation and Solution.................................................................................2-1
2.1 Mixture Balance Equations.................................................................................2-1
2.1.1 Two-Phase Flow Definitions...................................................................2-1
2.1.2 Local-Instantaneous Navier-Stokes Equations.......................................2-7
2.1.3 Averaging Operators.............................................................................2-12
2.2 Subchannel Formulation of the Basic Equations..............................................2-15
2.2.1 Fuel Rod Array Geometry.....................................................................2-17
2.2.1.1 Lateral scaling of crossflow resistance factor...........................2-22
2.2.1.2 Lateral scaling of turbulent mixing............................................2-22
2.2.1.3 Lateral scaling of the lateral momentum parameter..................2-23
2.2.2 Subchannel Mass Conservation Equation............................................2-24
2.2.2.1 Diversion Crossflow..................................................................2-26
2.2.2.2 Turbulent Interchange...............................................................2-26
2.2.3 Subchannel Momentum Balance Equations.........................................2-27
2.2.3.1 Axial Momentum Equation........................................................2-27
2.2.3.2 Lateral Momentum Balance......................................................2-30
2.2.4 Subchannel Energy Conservation Equation.........................................2-32
2.2.5 COBRA-FLX Basic Equations..............................................................2-35
2.2.5.1 Mass Conservation...................................................................2-35
2.2.5.2 Momentum Balance Equations.................................................2-35
2.2.5.3 Energy Conservation................................................................2-37
2.2.5.4 Equation of State......................................................................2-39
2.3 COBRA-FLX Numerical Solution Methodology................................................2-40
2.3.1 SCHEME Solution Methods..................................................................2-43
2.3.1.1 COBRA-FLX Finite-Difference Equations.................................2-43
2.3.1.2 General Computational Procedure...........................................2-54
2.3.1.3 Crossflow SCHEME Solution Logic..........................................2-59
2.3.1.4 Pressure SCHEME Solution Logic............................................2-61
2.3.2 Pressure-Velocity (PV) Solution Method..............................................2-66
2.3.2.1 Thermal-Hydraulic Model Equations.........................................2-67
2.3.2.2 Control Volume Equations........................................................2-72
2.3.2.3 Closure Relationships...............................................................2-90
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COBRA-FLX: A Core Thermal-Hydraulic Analysis Code
Topical Report Page iii
2.3.2.4 PV Numerics.............................................................................2-92
2.4 Boundary Conditions......................................................................................2-119
2.4.1 Inlet Enthalpy / Inlet Temperature.......................................................2-119
2.4.2 Power .................................................................................................2-119
2.4.3 System Pressure................................................................................2-121
2.4.4 Exit Pressure Distribution...................................................................2-121
2.4.5 Inlet Flow............................................................................................2-122
2.4.6 Transient Forcing Functions...............................................................2-122
2.5 References.....................................................................................................2-123
3.0 Code Structure And Flow Logic Description..................................................................3-1
4.0 Subroutine Description...................................................................................................4-1
5.0 Verification and Validation..............................................................................................5-1
5.1 Conservation of Mass and Energy.....................................................................5-2
5.2 Experimental Validation of the Fluid Flow Solution............................................5-4
5.2.1 Inter-Bundle Diversion Cross-Flow Tests...............................................5-4
5.2.2 MARIGNAN Crossflow Tests................................................................5-12
5.3 Experimental Validation of Empirical Correlations............................................5-18
5.3.1 Critical Heat Flux Correlations..............................................................5-19
5.3.2 Validity of Steady-State Critical Heat Flux (CHF)
Correlations in Transient Applications..................................................5-19
5.4 Comparisons of Solution Algorithms (Solution Schemes)................................5-21
5.5 Modeling Size...................................................................................................5-27
5.6 Heat Transfer Package....................................................................................5-28
5.7 Comparison of Fluid Flow Solution to Other Subchannel codes......................5-32
5.7.1 Steady-State Comparisons to Other Codes.........................................5-32
5.7.1.1 2-Channel Calculations with No Crossflow...............................5-32
5.7.1.2 38-Channel Calculations With Crossflow..................................5-35
5.7.1.3 Examination of Void Model Impacts Between Codes...............5-39
5.7.2 Transient Comparisons with Other Codes............................................5-41
5.7.2.1 4 Pump Coastdown Transient...................................................5-42
5.7.2.2 Locked Rotor Transient.............................................................5-48
5.7.2.3 Main Steam Line Break Transient.............................................5-49
5.8 Verification and Validation Conclusions...........................................................5-50
5.9 References.......................................................................................................5-52
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COBRA-FLX: A Core Thermal-Hydraulic Analysis Code
Topical Report Page iv
List of Tables
Page
Table 1-1: The Extent of the COBRA-FLX Review and Approval Requests.............................1-7
Table 1-2: Empirical Correlation Application for Requested Review and Approval..................1-8
Table 5-1: Example of COBRA-FLX Heat and Exit Mass Balance Errors................................5-3
Table 5-2: Summary of COBRA-FLX Predictions Using the SCHEME-Pressure
(P) and Pressure-Velocity (PV) Solution Methods versus Test Values
for IBDCF Tests......................................................................................................5-7
Table 5-3: Summary of COBRA-FLX Predictions Using the Pressure-Velocity
(PV) Solution Methods versus Test Values for the Severe Inlet Flow
Asymmetry IBDCF DCF Tests................................................................................5-8
Table 5-4: DNBR Comparison During a 4 Pump Coastdown Using the P and PV
Solution Methods..................................................................................................5-23
Table 5-5: Statistics for the P and PV Based Predictions for Subchannel
Enthalpies.............................................................................................................5-26
Table 5-6: Minimum DNBR Predictions for Various Core Model Sizes for a 4
Pump Coastdown .................................................................................................5-28
Table 5-7: COBRA-FLX Heat Transfer Modes.......................................................................5-29
Table 5-8: Summary of DNBR Comparison for the 12-Channel Model for the 4
Pump Coastdown .................................................................................................5-43
Table 5-9: COBRA-FLX and LYNXT Minimum DNBR Sensitivity to Modeling
Parameters for the 4 Pump Coastdown................................................................5-45
Table 5-10: Summary of DNBR Comparison for the 12-Channel Model for the
Locked Rotor ........................................................................................................5-48
Table 5-11: COBRA-FLX and LYNXT Minimum DNBR Sensitivity to Modeling
Parameters for the Locked Rotor..........................................................................5-49
Table 5-12: Summary of DNBR Comparison for the 17-Channel Model for the
Main Steam Line Break.........................................................................................5-50
AREVA NP Inc. ANP-10311NP

COBRA-FLX: A Core Thermal-Hydraulic Analysis Code
Topical Report Page v
List of Figures
Page
Figure 1-1: ARCADIA® Code System.......................................................................................1-4
Figure 1-2: Typical COBRA-FLX U.S. Application Input/Output Interfaces...............................1-6
Figure 2-1: Arbitrary Eulerian Control Volume..........................................................................2-2
Figure 2-2: Vertical Flow Past Fuel Rods.................................................................................2-3
Figure 2-3: Subchannel Control Volume.................................................................................2-15
Figure 2-4: Relation of Subchannel Control Volume to Reactor Core....................................2-16
Figure 2-5: A Pair of Subchannels..........................................................................................2-19
Figure 2-6: Example of Subchannel Numbering.....................................................................2-21
Figure 2-7: General Solution Flow Chart................................................................................2-43
Figure 2-8: Nodal Designation for Channels and Axial Location Indexes...............................2-45
Figure 2-9: SCHEME Solutions Sequence.............................................................................2-56
Figure 2-10: [ ]..........................................2-65
Figure 2-11: [ ]...................................................2-65
Figure 2-12: Pair of Interconnected Subchannels...................................................................2-75
Figure 2-13: Axial Nodal Indices for Control Volumes............................................................2-77
Figure 2-14: Control Volume for Mass Equation.....................................................................2-78
Figure 2-15: Control Volume for Energy Equation..................................................................2-79
Figure 2-16: Control Volume for Axial Momentum Equation...................................................2-84
Figure 2-17: Control Volume for Lateral Momentum Equation ...............................................2-90
Figure 2-18: PV Solution Sequence......................................................................................2-118
Figure 2-19: Example of Rod with Multiple Fluid Connections.............................................2-121
Figure 3-1: COBRA-FLX Code Structure..................................................................................3-2
Figure 3-2: COBRA-FLX High Level Solution Logic.................................................................3-7
Figure 3-3: SCHEME Solution Logic.........................................................................................3-9
Figure 3-4: Pressure-Velocity (PV) Solution Logic..................................................................3-10
Figure 5-1: Radial Node Scheme for the 12-Channel Model of a 193 Fuel Assembly
Core (1/8th Core Symmetry)..................................................................................5-3
Figure 5-2: Two-Bundle Isothermal Crossflow Test Apparatus for the IBDCF Tests................5-5
Figure 5-3: Cross-Sectional View of IBDCF Test Arrangement................................................5-6
Figure 5-4: Cross-Sectional View of the IBDCF Test Arrangement Showing the 4
Channel Model Definition......................................................................................5-9
Figure 5-5: Axial and Crossflow Velocity for Channel 1 of IBDCF Test 147 Using PV
Solution Method..................................................................................................5-10
Figure 5-6: Axial and Crossflow Velocity for Channel 2 of IBDCF Test 147 Using PV
Solution Method..................................................................................................5-10
Figure 5-7: Axial and Crossflow Velocity for Channel 3 of IBDCF Test 147 Using PV
Solution Method..................................................................................................5-11
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COBRA-FLX: A Core Thermal-Hydraulic Analysis Code
Topical Report Page vi
Figure 5-8: Axial and Crossflow Velocity for Channel 4 of IBDCF Test 147 Using PV
Solution Method..................................................................................................5-11
Figure 5-9: MARIGNAN Test Configuration with Two Adjacent Fuel Assemblies with
Defined Subchannels (lateral view).....................................................................5-13
Figure 5-10: Location of the Velocity Measurements in the MARIGNAN Test
Configuration (Full View).....................................................................................5-14
Figure 5-11: Location of the Velocity Measurements in the MARIGNAN Test
Configuration (Exploded View)............................................................................5-15
Figure 5-12: Axial Velocity Comparisons by Subchannel Row at the Relative Axial
Location of Y= - 200.0 mm in the MARIGNAN Test............................................5-16
Figure 5-13: Axial Velocity Comparisons by Subchannel Row at the Relative Axial
Location of Y= - 7.5 mm in the MARIGNAN Test................................................5-17
Figure 5-14: Axial Velocity Comparisons by Subchannel Row at the Relative Axial
Location of Y= +7.0 mm in the MARIGNAN Test................................................5-17
Figure 5-15: Axial Velocity Comparisons by Subchannel Row at the Relative Axial
Location of Y= +200.0 mm in the MARIGNAN Test............................................5-18
Figure 5-16: DNBR Response During a 4 Pump Coastdown Using the P and PV
Solution Methods.................................................................................................5-22
Figure 5-17: DNBR Response During a 4 Pump Coastdown Using the P and PV
Solution Methods for the Axial Range of 200 to 350 cm.....................................5-23
Figure 5-18: DNBR-Limiting Subchannel Mass Flux versus Axial Location at Three
Times during a 4 Pump Coastdown for the P and PV Solution Methods............5-24
Figure 5-19: DNBR-Limiting Subchannel Enthalpy versus Axial Location at 0.0 Seconds
During a 4 Pump Coastdown for the P and PV Solution Methods......................5-25
Figure 5-20: DNBR-Limiting Subchannel Enthalpy versus Axial Location at 3.4 Seconds
during a 4 Pump Coastdown for the P and PV Solution Methods.......................5-25
Figure 5-21: DNBR-Limiting Subchannel Enthalpy versus Axial Location at 4.8 Seconds
during a 4 Pump Coastdown for the P and PV Solution Methods.......................5-26
Figure 5-22: Transient “A” Progression through Heat Transfer Modes...................................5-30
Figure 5-23: Transient “A” Clad Wall Temperature Response................................................5-30
Figure 5-24: Transient “B” Progression through Heat Transfer Modes...................................5-31
Figure 5-25: Transient “B” Clad Wall Temperature Response................................................5-31
Figure 5-26: 2-Channel Model with No Crossflow for Code Comparisons..............................5-32
Figure 5-27: Normalized Axial Pressure Drop Comparison for the 2-Channel Model with
No Crossflow.......................................................................................................5-33
Figure 5-28: Axial Void Fraction Comparison for the 2-Channel Model with No Crossflow....5-34
Figure 5-29: Coolant Density Comparison for the 2-Channel Model with No Crossflow.........5-34
Figure 5-30: Coolant Enthalpy Comparison for the 2-Channel Model with No Crossflow.......5-35
Figure 5-31: Radial Node Scheme for the 38 Channel Model (1/8th Core Symmetry) With
Crossflow for Code Comparisons........................................................................5-36
Figure 5-32: Mass Velocity Comparison for the 38-Channel Model With Crossflow...............5-37
Figure 5-33: Void Fraction Comparison for the 38-Channel Model with Crossflow................5-38
Figure 5-34: Coolant Enthalpy Comparison for the 38-Channel Model with Crossflow..........5-39
AREVA NP Inc. ANP-10311NP

COBRA-FLX: A Core Thermal-Hydraulic Analysis Code
Topical Report Page vii
Figure 5-35: Mass Velocity Comparison for the 38-Channel Model Using the
Homogenous Void Model....................................................................................5-40
Figure 5-36: Void Fraction Comparison for the 38-Channel Model Using the
Homogenous Void Model....................................................................................5-40
Figure 5-37: Void Fraction Comparison for the 2-Channel Model Using the Homogenous
Void Model..........................................................................................................5-41
Figure 5-38: Radial Node Scheme for a 17-Channel Model (1/8th Core Symmetry) for
the Main Steam Line Break Event.......................................................................5-42
Figure 5-39: DNBR Comparison for the 12-Channel Model for the 4 Pump Coastdown........5-43
Figure 5-40: Mass Velocity Comparison for the 12-Channel Model for the 4 Pump
Coastdown..........................................................................................................5-44
Figure 5-41: Thermodynamic Quality for the 12-Channel Model for the 4 Pump
Coastdown..........................................................................................................5-44
Figure 5-42: DNBR Comparison for the Combined Effect of All Modeling Parameters in
Table 5-9 for the 4 Pump Coastdown..................................................................5-46
Figure 5-43: Mass Velocity Comparison for the Combined Effect of All Modeling
Parameters in Table 5-9 for the 4 Pump Coastdown at the Time of
Minimum DNBR...................................................................................................5-47
Figure 5-44: Thermodynamic Quality Comparison for the Combined Effect of All
Modeling Parameters in Table 5-9 for the 4 Pump Coastdown at the Time
of Minimum DNBR...............................................................................................5-47
Figure 5-45: DNBR Comparison for the 12 Channel Model for the Locked Rotor..................5-48
Figure 5-46: DNBR Comparison for the 17-Channel Model for the Main Steam Line
Break in the Limiting Subchannel........................................................................5-50
AREVA NP Inc. ANP-10311NP
Revision 0
COBRA-FLX: A Core Thermal-Hydraulic Analysis Code
Topical Report Appendix Page viii
Table of Contents
Page
Appendix A : Empirical Correlations........................................................................................A-1
A.1 Introduction........................................................................................................A-1
A.2 Water Properties...............................................................................................A-1
A.3 Friction Factor ...................................................................................................A-1
A.3.1 Single-phase Flow..............................................................................A-2
A.3.2 Two-phase Flow.................................................................................A-5
A.4 Void Fraction Correlation...................................................................................A-7
A.4.1 Bulk Void.............................................................................................A-7
A.4.2 Subcooled Void.................................................................................A-18
A.5 Heat Transfer Coefficients...............................................................................A-23
A.6 DNBR Iteration Scheme..................................................................................A-38
A.7 References......................................................................................................A-39
Appendix B : COBRA-FLX Development History.....................................................................B-1
B.1 History...............................................................................................................B-1
B.2 History of COBRA Development.......................................................................B-1
B.2.1 COBRA Versions Leading to COBRA 3-CP.......................................B-2
B.2.2 Creation and Further Development of COBRA 3-CP.........................B-5
B.3 References........................................................................................................B-8
Appendix C : Critical Heat Flux Correlation Validation.............................................................C-1
C.1.1 Validation Process..............................................................................C-1
C.2 The ACH-2 CHF Correlation .............................................................................C-4
C.2.1 Measured to Predicted CHF Performance..........................................C-5
C.2.2 Design Limit DNBR.............................................................................C-8
C.2.3 Ranges and Limitations......................................................................C-9
C.3 The BHTP CHF Correlation.............................................................................C-10
C.3.1 Predicted to Measured CHF Performance........................................C-10
C.3.2 Statistical Design Limit......................................................................C-12
C.3.3 Ranges and Limitations....................................................................C-13
C.4 The BWU-Z CHF Correlation for Mark-BW17 Fuel with MSMGs....................C-14
C.4.1 Measured to Predicted CHF Performance........................................C-15
C.4.2 Statistical Design Limit......................................................................C-16
C.4.3 Ranges and Limitations....................................................................C-18
C.5 The BWU-Z CHF Correlation for Mark-BW17 Fuel.........................................C-18
C.5.1 Measured to Predicted CHF Performance........................................C-19
C.5.2 Statistical Design Limit......................................................................C-21
C.5.3 Ranges and Limitations....................................................................C-23