Nuclear Science

ISBN 92-64-02331-3
NEA/NSC/DOC(2006)23

NEA NUCLEAR SCIENCE COMMITTEENEA COMMITTEE ON SAFETY OF NUCLEAR INSTALLATIONSBOILING WATER REACTOR
TURBINE TRIP (TT) BENCHMARK
Volume III: Summary Results of Exercise 2

November 2006

byBedirhan Akdeniz, Kostadin N. Ivanov
Nuclear Engineering Program
The Pennsylvania State University
University Park, PA, 16802 USA
Andy M. Olson
Exelon Nuclear
200 Exelon Way, KSA2-N
Kennett Square, PA, 19348 USA© OECD 2006
NEA No. 5437
NUCLEAR ENERGY AGENCY
ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENTUS NUCLEAR REGULATORY COMISSIONORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENTThe OECD is a unique forum where the governments of 30 democracies work together to address the economic,
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***This work is published on the responsibility of the Secretary-General of the OECD. The opinions expressed andarguments employed herein do not necessarily reflect the official views of the Organisation or of the governments of its
member countries.

NUCLEAR ENERGY AGENCYThe OECD Nuclear Energy Agency (NEA) was established on 1st February 1958 under the name of the OEEC
European Nuclear Energy Agency. It received its present designation on 20th April 1972, when Japan became its first
non-European full member. NEA membership today consists of 28 OECD member countries: Australia, Austria,
Belgium, Canada, the Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy,
Japan, Luxembourg, Mexico, the Netherlands, Norway, Portugal, Republic of Korea, the Slovak Republic, Spain,
Sweden, Switzerland, Turkey, the United Kingdom and the United States. The Commission of the European
Communities also takes part in the work of the Agency.
The mission of the NEA is:

to assist its member countries in maintaining and further developing, through international co-operation, thescientific, technological and legal bases required for a safe, environmentally friendly and economical use of
nuclear energy for peaceful purposes, as well as
to provide authoritative assessments and to forge common understandings on key issues, as input togovernment decisions on nuclear energy policy and to broader OECD policy analyses in areas such asenergy and sustainable development.

Specific areas of competence of the NEA include safety and regulation of nuclear activities, radioactive waste
management, radiological protection, nuclear science, economic and technical analyses of the nuclear fuel cycle, nuclear
law and liability, and public information. The NEA Data Bank provides nuclear data and computer program services forparticipating countries.
In these and related tasks, the NEA works in close collaboration with the International Atomic Energy Agency
in Vienna, with which it has a Co-operation Agreement, as well as with other international organisations in the nuclear
field.
© OECD 2006
No reproduction, copy, transmission or translation of this publication may be made without written permission.
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FOREWORDThe OECD Nuclear Energy Agency (NEA) completed under US Nuclear Regulatory Commission(NRC) sponsorship a PWR main steam line break (MSLB) benchmark against coupled systemthree-dimensional (3-D) neutron kinetics and thermal-hydraulic codes. Another OECD/NRC
coupled-code benchmark was completed for a BWR turbine trip (TT) transient and is the object of thepresent report. Turbine trip transients in a BWR are pressurisation events in which the coupling
between core space-dependent neutronic phenomena and system dynamics plays an important role.
The data made available from actual experiments carried out at the Peach Bottom 2 plant make thepresent benchmark particularly valuable. While defining and co-ordinating the BWR TT benchmark, asystematic approach and multi-level methodology was developed, which not only allowed for aconsistent and comprehensive validation process, but also contributed to the study of key parametersof pressurisation transients. The benchmark consists of three separate exercises, two steady states andfive transient scenarios.
The BWR TT benchmark is being published in four volumes as OECD/NEA reports. CD-ROMs
will also be prepared and will include the four reports and the transient boundary conditions, decay
heat values as a function of time, cross-section libraries and supplementary tables and graphs not
published in the paper versions. BWR TT Benchmark – Volume I: Final Specifications was issued in2001 [NEA/NSC/DOC(2001)1]. The benchmark team – Pennsylvania State University (PSU) in
co-operation with Exelon Nuclear and the OECD/NEA – was responsible for co-ordinating benchmark
activities, answering participants’ questions and assisting participants in developing their models, aswell as analysing submitted solutions and providing reports summarising the results for each phase.
The benchmark team was also involved in the technical aspects of the benchmark, including sensitivity
studies for the different exercises. In performing these tasks, the PSU team has been collaborating with
Andy M. Olson and Kenneth W. Hunt of Exelon Nuclear. Lance J. Agee, of the Electric Power
Research Institute (EPRI), also provided technical assistance for this international benchmark project.
BWR TT Benchmark – Volume II: Summary Results of Exercise 1 was published in 2004
[NEA/NSC/DOC(2004)21]. It summarised the results for Exercise 1 of the benchmark and identified
the key parameters and important issues concerning the thermal-hydraulic system modelling of the TT
transient with specified core average axial power distribution and fission power (or reactivity) timetransient history. Exercise 1 helped the participants initialise and test their system code models forfurther use in Exercise 3 on coupled 3-D kinetics/system thermal-hydraulics simulations.
Volume III summarises the results for Exercise 2 of the benchmark and identifies the key
parameters and important issues concerning the coupled neutronics/thermal-hydraulic core modellingwith provided core inlet and outlet boundary conditions. Exercise 2 helped the participants initialise andtest their core models for further use in Exercise 3 on coupled 3-D kinetics/system thermal-hydraulics
simulations.

3

Acknowledgements
The authors would like to thank Prof. J. Aragonés (UPM), Drs. T. Lefvert and S. Langenbuch(GRS) and Dr. F. Eltawila (US NRC), whose support and encouragement in establishing this benchmark
are invaluable.
This report is the sum of many efforts, the participants, the funding agencies and their staff – theUS Nuclear Regulatory Commission and the Organisation of Economic Co-operation and Development.
Special appreciation is due to: L. Agee (EPRI), Professor T. Downar (Purdue) University, B. Aktas(ISL Inc.), Drs. G. Gose and C. Peterson (CSA), Dr. A. Hotta (TEPSYS), Dr. P. Coddington (PSI) and
Dr. U. Grundmann (FZR). Their technical assistance, comments and suggestions have been very
valuable. We would like to thank them for the effort and time involved.
Of particular note are the efforts of Dr. F. Eltawila assisted by Drs. J. Han and J. Uhle of the US
Nuclear Regulatory Commission. Through their efforts, funding was secured for this project. We also
thank them for their invaluable technical advice and assistance.
Special appreciation goes to the report reviewers: Dr. A. Hotta, Dr. U. Grundman andProfessor G. Verdú (UPV). Their comments and suggestions were very valuable and significantly
improved the quality of this report.
The authors wish to express their sincere appreciation for the outstanding support offered by
Dr. E. Sartori, who is providing efficient administration, organisation and valuable technical advice.
Authors wish to specially thank all of the OECD/NEA BWR Turbine Trip Benchmark participants
for their valuable support, comment and feedback during this study.
Special thanks are due to all of authors’ family members for their encouragement, support andpatience throughout this work.
Finally, the authors are grateful to Amanda Costa for having devoted her competence and skills to
finalising this report for publication.

4

TABLE OF CONTENTS

Foreword ............................................................................................................................................

3

List of figures .....................................................................................................................................

7

List of tables .......................................................................................................................................

9

List of abbreviations ........................................................................................................................... 11
Chapter 1 INTRODUCTION......................................................................................................... 13
Chapter 2 DESCRIPTION OF EXERCISE 2..............................................................................
2.1 General.....................................................................................................................
2.2 Core and neutronics data..........................................................................................
2.3 Core thermal-hydraulic boundary conditions model and its
coupling with 3-D neutron kinetics model...............................................................
2.4 Initial steady-state conditions ..................................................................................
2.5 Transient calculations ..............................................................................................
Chapter 3 METHODOLOGIES TO QUANTIFY THE ACCURACY
OF THE CALCULATIONS ........................................................................................
3.1 Standard techniques for the comparison of results ..................................................
3.1.1 Integral parameter values ...............................................................................
3.1.2 One-dimensional (1-D) axial distributions .....................................................
3.1.3 Two-dimensional (2-D) radial distributions ...................................................
3.1.4 Time histories .................................................................................................
3.2 ACAP analysis.........................................................................................................
3.3 Statistical analysis of normalised parameters ..........................................................
3.3.1 Two-dimensional (2-D) core-averaged radial power distribution ..................
3.3.2 One-dimensional (1-D) core-averaged axial power distribution ....................
3.3.3 One-dimensional (1-D) core-averaged axial power distribution
for FAs 75 and 367 .........................................................................................
3.3.4 Multiple code dependencies ...........................................................................
Chapter 4 RESULTS AND DISCUSSION ...................................................................................
4.1 Steady-state results ..................................................................................................
4.1.1 Hot zero power (HZP) results.........................................................................
4.1.2 Hot power (HP) results...................................................................................
4.2 Transient results.......................................................................................................
4.2.1 Time histories .................................................................................................
4.2.2 Snapshot at the time of maximum power before scram .................................
4.2.3 Snapshot at the end of the transient (at 5 s)....................................................

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86
94

Chapter 5 CONCLUSIONS ........................................................................................................... 103
References .......................................................................................................................................... 105

5

Appendix A

Description of the computer codes used for analysis in Exercise 2of the OECD/NRC BWR TT Benchmark.................................................................... 107
CRONOS2/FLICA4 (CEA, France)............................................................................ 109
DYN3D (FZR, Germany)............................................................................................ 110
QUABOX/CUBBOX-ATHLET (GRS, Germany) ..................................................... 116
DNB/3D (NETCORP, USA) ....................................................................................... 116
TRAC-BF1/COS3D (NFI, Japan) ............................................................................... 117
TRAC-BF1/SKETCH-INS (NUPEC, Japan) .............................................................. 118
RETRAN-3D and CORETRAN (PSI, Switzerland) ................................................... 118
TRAC-BF1/NEM (PSU, USA) ................................................................................... 121
TRAC-BF1/ENTRÉE (TEPSYS, Japan)..................................................................... 123
RELAP5/PARCS (U.PISA, Italy) ............................................................................... 125
TRAC-BF1/NEM (UPV, Spain).................................................................................. 126
TRAB-3D (VTT, Finland)........................................................................................... 127
POLCA-T (Westinghouse, Sweden) ........................................................................... 128

Appendix B

Questionnaire for Exercise 2 of the OECD/NRC BWR TT benchmarck.................... 131
CRONOS2/FLICA4 (CEA, France) ........................................................................... 134
DYN3D (FZR, Germany) ........................................................................................... 137
QUABOX/CUBBOX-ATHLET (GRS, Germany)..................................................... 140
DNB-3D (NETCORP, USA) ...................................................................................... 143
TRAC-BF1/COS3D (NFI, Japan)............................................................................... 146
TRAC-BF1/SKETCH-INS (NUPEC, Japan) ............................................................. 149
RETRAN-3D (PSI, Switzerland)................................................................................ 152
CORETRAN-3D (PSI, Switzerland) .......................................................................... 157
TRAC-BF1/NEM (PSU, USA)................................................................................... 163
TRAC-BF1/ENTRÉE (TEPSYS, Japan) .................................................................... 166
RELAP5/PARCS (U.PISA, Italy)............................................................................... 169
TRAC-BF1/NEM (UPV, Spain) ................................................................................. 171
TRAB-3D (VTT, Finland) .......................................................................................... 177

Available on CD-ROM upon request
Appendix C

Reference results

Appendix D1

Participant deviations in integral parameters

Appendix D2Participant deviations axial parameters

Appendix D3

Participant deviations 2-D radial parameters

Appendix D4Participant deviations time histories

6

List of figures
Figure 2-1. Reactor core cross-sectional view..................................................................................
Figure 2-2. PB2 initial fuel assembly lattice.....................................................................................
Figure 2-3. PB2 reload fuel assembly lattice for 100 mil channels ..................................................
Figure 2-4. PB2 reload fuel assembly lattice for 120 mil channels ..................................................
Figure 2-5. PB2 reload fuel assembly lattice for LTA assemblies ...................................................
Figure 2-6. PSU control rod grouping ..............................................................................................
Figure 2-7. Radial distribution of assembly types ............................................................................
Figure 2-8. Fuel assembly orientation for ADF assignment.............................................................
Figure 2-9. Core orificing and TIP system arrangement ..................................................................
Figure 2-10. Elevation of core components........................................................................................
Figure 2-11. Exercise 2 vessel/core boundary condition model .........................................................
Figure 2-12. Reactor core thermal-hydraulic channel radial map ......................................................
Figure 2-13. PB2 HZP control rod pattern .........................................................................................
Figure 2-14. PB2 HP control rod pattern............................................................................................
Figure 3-1. FOM configuration in ACAP.........................................................................................
Figure 4-1. HZP keff ..........................................................................................................................
Figure 4-2. Core average relative axial power distribution at HZP..................................................
Figure 4-3. Relative power distribution for FA 75 at HZP...............................................................
Figure 4-4. Relative power distribution for FA 367 at HZP.............................................................
Figure 4-5. Mean radial power distribution at HZP (average of participants)..................................
Figure 4-6. Standard deviation of radial power distribution at HZP ................................................
Figure 4-7. HP keff.............................................................................................................................
Figure 4-8. Core average axial void fraction distribution at HP (Group 1)......................................
Figure 4-9. Core average axial void fraction distribution at HP (Group 2)......................................
Figure 4-10. Core average axial void fraction at HP (mean and deviation) .......................................
Figure 4-11. Core average relative axial power distribution at HP (Group 1) ...................................
Figure 4-12. Core average relative axial power distribution at HP (Group 2) ...................................
Figure 4-13. Core average relative axial power distribution at HP (mean and deviation) .................
Figure 4-14. Relative power distribution for FA 75 at HP (Group 1) ................................................
Figure 4-15. Relative power distribution for FA 75 at HP (Group 2) ................................................
Figure 4-16. Relative power distribution for FA 75 at HP (mean and deviation) ..............................
Figure 4-17. Relative power distribution for FA 367 at HP (Group 1) ..............................................
Figure 4-18. Relative power distribution for FA 367 at HP (Group 2) ..............................................
Figure 4-19. Relative power distribution for FA 367 at HP (mean and deviation) ............................
Figure 4-20. Mean radial power distribution at HP (average of participants) ....................................
Figure 4-21. Standard deviation of radial power distribution at HP...................................................
Figure 4-22. Transient power (fission) ...............................................................................................
Figure 4-23. Transient power (fission – zoom) ..................................................................................
Figure 4-24. Transient power (total)...................................................................................................
Figure 4-25. Transient power (total – zoom)......................................................................................
Figure 4-26. Total reactivity...............................................................................................................
Figure 4-27. Total reactivity (zoom) ..................................................................................................
Figure 4-28. Total reactivity (mean and deviation) ............................................................................
Figure 4-29. Total reactivity (mean and deviation – zoom) ...............................................................
Figure 4-30. Doppler reactivity ..........................................................................................................
Figure 4-31. Doppler reactivity (zoom)..............................................................................................
Figure 4-32. Doppler reactivity (mean and deviation) .......................................................................
Figure 4-33. Doppler reactivity (mean and deviation – zoom)...........................................................
Figure 4-34. Void reactivity ...............................................................................................................
7

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Figure 4-35. Void reactivity (zoom) ................................................................................................... 84
Figure 4-36. Void reactivity (mean and deviation)............................................................................. 85
Figure 4-37. Void reactivity (mean and deviation – zoom)................................................................ 85
Figure 4-38. Time of maximum power before scram......................................................................... 86
Figure 4-39. Core axial power profile at maximum power before scram (fission power used) ......... 87
Figure 4-40. Core axial power profile at maximum power before scram (total power used)............. 88
Figure 4-41. Core axial power profile at maximum power before scram(fission power used – mean and deviation).................................................................... 88
Figure 4-42. Core axial power profile at maximum power before scram(total power used – mean and deviation) ....................................................................... 89
Figure 4-43. Relative power of FA 75 at maximum power before scram (fission)............................ 89
Figure 4-44. Relative power of FA 75 at maximum power before scram (total) ............................... 90
Figure 4-45. Relative power of FA 75 at maximum power before scram(mean and deviation – fission power used).................................................................... 90
Figure 4-46. Relative power of FA 75 at maximum power before scram(mean and deviation – total power used) ....................................................................... 91
Figure 4-47. Relative power of FA 367 at maximum power before scram (fission).......................... 91
Figure 4-48. Relative power of FA 367 at maximum power before scram (total) ............................ 92
Figure 4-49. Relative power of FA 367 at maximum power before scram(mean and deviation – fission power used).................................................................... 92
Figure 4-50. Relative power of FA 367 at maximum power before scram(mean and deviation – total power used) ....................................................................... 93
Figure 4-51. Mean radial power distribution at maximum power before scram ................................ 93
Figure 4-52. Standard deviation of radial power distribution at maximum power before scram ....... 94
Figure 4-53. Core axial power profile at end of transient (fission) .................................................... 95
Figure 4-54. Core axial power profile at end of transient (total) ........................................................ 95
Figure 4-55. Core axial power profile at end of transient (mean and deviation – fission
power used).................................................................................................................... 96
Figure 4-56. Core axial power profile at end of transient (mean and deviation – total
power used).................................................................................................................... 96
Figure 4-57. Relative power of FA 75 at end of transient (fission).................................................... 97
Figure 4-58. Relative power of FA 75 at end of transient (total) ....................................................... 97
Figure 4-59. Relative power of FA 75 at end of transient (mean and deviation – fission
power used).................................................................................................................... 98
Figure 4-60. Relative power of FA 75 at end of transient (mean and deviation – total
power used).................................................................................................................... 98
Figure 4-61. Relative power of FA 367 at end of transient (fission).................................................. 99
Figure 4-62. Relative power of FA 367 at end of transient (total) ..................................................... 99
Figure 4-63. Relative power of FA 367 at end of transient (mean and deviation – fission
power used).................................................................................................................... 100
Figure 4-64. Relative power of FA 367 at end of transient (mean and deviation – total
power used).................................................................................................................... 100
Figure 4-65. Mean radial power distribution at end of transient ........................................................ 101
Figure 4-66. Standard deviation of radial power distribution at end of transient ............................... 101

8

List of tables
Table 1-1. List of participants in the Exercise 2 of the BWR TT benchmark..................................
Table 2-1. PB2 fuel assembly data...................................................................................................
Table 2-2. Assembly design 1 ..........................................................................................................
Table 2-3. Assembly design 2 ..........................................................................................................
Table 2-4. Assembly design 3 ..........................................................................................................
Table 2-5. Assembly design 4 ..........................................................................................................
Table 2-6. Assembly design 5 ..........................................................................................................
Table 2-7. Assembly design 6 ..........................................................................................................
Table 2-8. Decay constant and fractions of delayed neutrons..........................................................
Table 2-9. Heavy-element decay heat constants ..............................................................................
Table 2-10. Assembly design for Type 1 initial fuel..........................................................................
Table 2-11. Assembly design for Type 2 initial fuel..........................................................................
Table 2-12. Assembly design for Type 3 initial fuel..........................................................................
Table 2-13. Assembly design for Type 4 8 u 8 UO2 reload ...............................................................
Table 2-14. Assembly design for Type 5 8 u 8 UO2 reload ...............................................................
Table 2-15. Assembly design for Type 6 8 u 8 UO2 reload, LTA .....................................................
Table 2-16. Control rod data (movable control rods).........................................................................
Table 2-17. Definition of assembly types ..........................................................................................
Table 2-18. Composition numbers in axial layer for each assembly type..........................................
Table 2-19. Range of variables...........................................................................................................
Table 2-20. Key to macroscopic cross-section tables ........................................................................
Table 2-21. Macroscopic cross-section table structure ......................................................................
Table 2-22. PB2 HZP initial conditions .............................................................................................
Table 2-23. PB2 TT2 initial conditions from process computer P1 edit............................................
Table 2-24. PB2 TT2 scram characteristics .......................................................................................
Table 2-25. CRD position after scram vs. time ..................................................................................
Table 3-1. Exercise 2 parameters for steady-state statistical comparisons.......................................
Table 3-2. Exercise 2 parameters for transient statistical comparisons............................................
Table 4-1. Number of channels used and power submitted by the participants...............................
Table 4-2. Models used at HZP........................................................................................................
Table 4-3. HZP keff ...........................................................................................................................
Table 4-4. Models used at HP ..........................................................................................................
Table 4-5. HP keff .............................................................................................................................
Table 4-6. Models used in transient calculation...............................................................................
Table 4-7. Transient power, figure of merit .....................................................................................
Table 4-8. Total reactivity, figure of merit.......................................................................................
Table 4-9. Doppler reactivity, figure of merit ..................................................................................
Table 4-10. Void reactivity, figure of merit .......................................................................................
Table 4-11. Time of maximum power before scram..........................................................................

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LIST OF ABBREVIATIONS

1-D
2-D
3-D
ACAP
ADF
APRM
AVZ
BC
BE
BOC
BP
BPV
BVBO
BVFO
BWR
CA
CEA
CEPIR
DPIR
EOC
EOT
EPRI
EXELON
FA
FANP
FFT
FOM
FZR
GE
GRS
HFP
HP
HZP
IBER
LPRM
LWR
ME
MSIV
MSLB
MVCEP

One-dimensional
Two-dimensional
Three-dimensional
Automated Code Assessment Program
Assembly discontinuity factor
Average range power monitor
Above vessel zero
Boundary conditions
British Energy
Beginning of cycle
Burnable poison
Bypass valve
Bypass valve begins opening
Bypass valve full open
Boiling water reactor
Control assemblyCommissariat à l’énergie atomiqueCore exit pressure initial response
Dome pressure initial response
End of cycle
End of transientElectric Power Research InstituteExelon Corporation
Fuel assembly
Framatome ANP
Fast Fourier transform
Figure of merit
Forschungszentrum Rossendorf
General Electric
Gesellschaft fur Anlagen- und Reaktorsicherheit mbH
Hot full power
Hot power
Hot zero power
Iberdrola Ingenieria
Local power range monitor
Light water reactor
Mean error
Main steam isolation valve
Main steam line break
Maximum value per cent initial value of core exit pressure
11

NEA
NEM
NETCORP
NFI
NP
NPP
NRC
NRS
NSC
NSSS
NUPEC
OECD
PB
PB2
PECo
PSI
PSU
PWR
SRV
TEPSYS
T-H
TSV
TSVC
TT
TT2
UPI
UPV
VTT
VBA
WES

Nuclear Energy Agency
Nodal expansion method
Nuclear Engineering Technology Corporation
Nuclear Fuel Industries, Ltd.
Normalised power
Nuclear power plant
US Nuclear Regulatory Commission
Nuclear reactor systems
Nuclear Science Committee
Nuclear steam supply system
Nuclear Power Engineering Corporation
Organisation for Economic Co-Operation and Development
Peach Bottom Atomic Power Station
Peach Bottom Atomic Power Station Unit 2
Philadelphia Electric Company
Paul Scherrer InstitutePennsylvania State University
Pressurised water reactor
Safety relief valve
TEPCO Systems Corporation
Thermal-hydraulic
Turbine stop valve
Turbine stop valve closing
Turbine trip
Turbine trip test 2
University of Pisa
Universidad Politecnica de Valencia
Valtion Teknillinen Tutkimuskeskus
Visual basic for applications
Westinghouse Electric Company

12Chapter 1
INTRODUCTION

Prediction of a nuclear power plant’s behaviour under both normal and abnormal conditions has
an important effect on its safety and economic operation. Incorporation of full three-dimensional (3-D)
models of the reactor core into system transient codes allows for a “best-estimate” calculation ofinteractions between the core behaviour and plant dynamics. Recent progress in computer technology
has made the development of such coupled system thermal-hydraulic and neutron kinetics code
systems feasible. Considerable efforts have been made in various countries and organisations in thisdirection. To verify the capability of the coupled codes to analyse complex transients with coupled
core-plant interactions and to fully test thermal-hydraulic coupling, appropriate light water reactor(LWR) transient benchmarks need to be developed on a higher “best-estimate” level. The previous
sets of transient benchmark problems separately addressed system transients (designed mainly forthermal-hydraulic system codes with point kinetics models) and core transients (designed forthermal-hydraulic core boundary conditions models coupled with a 3-D neutron kinetics model). The
Nuclear Energy Agency (NEA) of the Organisation for Economic Co-operation and Development(OECD) has completed – under the auspices of the US Nuclear Regulatory Commission (NRC) –sponsorship of a pressurised water reactor (PWR) main steam line break (MSLB) benchmark [1]against coupled thermal-hydraulic and neutron kinetics codes. Similar benchmark against the coupledcodes for a boiling water reactor (BWR) plant transient was also established as an OECD/NRC
activity [2]. A turbine trip (TT) transient in a BWR is a pressurisation event in which the coupling
between core phenomena and system dynamics plays an important role. In addition, the available realplant experimental data [4,5] makes the such benchmark problem very valuable. The NEA, OECD and
US NRC have approved the BWR TT benchmark for the purpose of validating advanced systembest-estimate analysis codes.
The established benchmark project was designed to test the coupled system thermal-hydraulic/neutron kinetics codes for simulation of the Peach Bottom 2 (PB2 – a General Electric-designed
BWR/4) turbine trip transient with a sudden closure of the turbine stop valve. Three turbine triptransients at different power levels were performed at the PB2 nuclear power plant (NPP) prior to
shutdown for refuelling at the end of Cycle 2 in April 1977. The second test (TT2) is selected for thebenchmark problem to investigate the effect of the pressurisation transient (following the sudden
closure of the turbine stop valve) on the neutron flux in the reactor core. In a best-estimate manner thetest conditions approached the design basis conditions as closely as possible. The actual data werecollected, including a compilation of reactor design and operating data for Cycles 1 and 2 of PB2 andthe plant transient experimental data. The transient was selected for this benchmark because it is a
dynamically complex event and it constitutes a good problem to test the coupled codes on both levels:
neutronics/thermal-hydraulics coupling, as well as core/plant system coupling. In the TT2 test, thethermal-hydraulic feedback alone limited the power peak and initiated the power reduction. The void
feedback plays the major role while the Doppler feedback plays a subordinate role. The reactor scramthen inserted additional negative reactivity and completed the power reduction and eventual core
shutdown.

13

The purposes of this benchmark are met through the application of the three exercises, which aredescribed in Volume 1 of the OECD/NRC BWR TT Benchmark: Final Specifications [2]. The purposeof the first exercise is to test the thermal-hydraulic system response and to initialise the participants’system models. Core power response is provided to reproduce the actual test results utilising either
power or reactivity versus time data. The comprehensive analysis of the Exercise 1 was summarised
in Volume II of the OECD/NRC BWR TT Benchmark Volume II: Summary Results of Exercise 1 [3].
The purpose of Exercise 2 is to provide a clean initialisation of the coupled core models since thecore thermal-hydraulic boundary conditions are provided. The second exercise has two steady-state
conditions: hot zero power (HZP) conditions and the initial hot power (HP) conditions of TT2. The
last exercise, Exercise 3, is the best-estimate coupled 3-D core/thermal-hydraulic system modelling.
This exercise combines elements of the first two exercises of this benchmark and is an analysis of thetransient in its entirety. Exercise 3 also has extreme scenarios that provide the opportunity to better test
the code coupling and feedback modelling.
Comparative analysis of the submitted results for Exercise 2 has been performed and is summarisedin this report. In total, 18 results have been submitted by the participants representing 16 different
organisations from 9 different countries. A list of participants, who have submitted results to the PSU
benchmark team for the second exercise, along with the code used to perform the analysis, is listed inTable 1-1. A more detailed description of each code is presented in Appendix A, and the modellingassumptions made by each participant are given in Appendix B.
Chapter 2 contains a description of Exercise 2 including the initial conditions. Chapter 3 discusses
the utilised comprehensive statistical methodology for integral parameters, 1-D distributions, and time
histories. Chapter 4 provides comparative analysis of the final results for the second exercise. Finally,
Chapter 5 summarises the conclusions drawn from the analysis of Exercise 2.
Table 1-1. List of participants in the Exercise 2 of the BWR TT benchmark
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18

Participant*
Codes
Country
CEA-33 (33-channel model)
CRONOS2/FLICA4France
CEA-764 (764-channel model)
CRONOS2/FLICA4FranceRAMONA5-2.1
GermanyFANP
FZR (3-D model with 764 core channels)
DYN3D
GermanyQUABOX/CUBBOX-ATHLET Germany
GRS
RETRAN 3D–Mod 3.1
Spain
IBER
DNB-3DUSA
NETCORPTRAC-BF1/COS3D
Japan
NFI
TRAC-BF1/SKETCH-INS
Japan
NUPEC
PSI-A (pressure BC at core inlet and outlet)
RETRAN-3D MOD 003.1
Switzerland
PSI-B (flow rate BC at core inlet and pressure RETRAN-3D MOD 003.1
Switzerland
BC at core outlet)
CORETRAN
Switzerland
PSI-C
TRAC-BF1/NEM
USA
PSU
TRAC-BF1/ENTRÉEJapanTEPSYSRELAP5/ PARCS
Italy
UPI
TRAC-BF1/NEM
Spain
UPV
TRAB-3D
FinlandVTTPOLCA-T
SwedenWES* Participants’ full names can be found in the List of Abbreviations.

14

Chapter 2
DESCRIPTION OF EXERCISE 2

2.1 General
After participants’ system models are initialised and the thermal-hydraulic system responses of
their codes are tested in the first exercise, studies are focused on the second exercise of PB2 TT2benchmark. Exercise 2 consists of coupled reactor core calculations while the system thermal-hydraulics
is modelled through imposed boundary conditions. The purpose of this exercise is to test the coupledcore response and to initialise participant’s core models.
Steady-state analyses are performed for two conditions in Exercise 2: hot zero power (HZP)
conditions and the initial hot power (HP) conditions of TT2. The HZP state provides a clean initialisationof the core neutronics models since the thermal-hydraulic feedback is spatially uniform across the core.
The second exercise is to perform a coupled 3-D kinetics/thermal-hydraulic calculation for thereactor core using the PSU provided boundary conditions at core inlet and exit. The core boundary
conditions are provided utilising a combination of the calculated PSU results and test data.
A TT transient in a BWR type reactor is considered one of the most complex events to beanalysed because it involves the reactor core, the high pressure coolant boundary, associated valvesand piping in highly complex interactions with variables changing very rapidly. The PB2 TT2 test
starts with a sudden closure of the turbine stop valve (TSV) and then the turbine bypass valve begins
to open. From a fluid flow phenomena point of view, pressure and flow waves play an important role
during the early phase of the transient (of about 1.5 seconds) because rapid valve actions cause sonicwaves, as well as secondary waves, generated in the pressure vessel. The pressure oscillation generated
in the main steam piping propagates with relatively little attenuation into the reactor core. The induced
core pressure oscillation results in changes of the core void distribution and fluid flow. The magnitudeof the neutron flux transient taking place in the BWR core is affected by the initial rate of pressure risecaused by the pressure oscillation and has a spatial variation. The simulation of the power response to
the pressure pulse and subsequent void collapse requires a 3-D core modelling supplemented by 1-D
simulation of the remainder of the reactor coolant system. In Exercise 2 of the benchmark the later ismodelled by the same boundary conditions imposed to the 3-D core models.
The reference design for the BWR is derived from real reactor, plant and operation data for the
PB2 NPP and it is based on the information provided in EPRI reports [4-7] and some additionalsources such as the PECo Energy Topical report [8]. Although complete set of core/neutronics andthermal-hydraulics input specifications are provided in Volume I [2], the data relevant to Exercise 2
are given in this section for the convenience of the reader.
In the following subsections of this chapter, descriptions of core and neutronics data,
thermal-hydraulic core boundary conditions model and its coupling with the 3-D neutron kinetics
model, initial steady-state conditions and transient calculations are provided.

15

2.2 Core and neutronics data
The reference design for the BWR is derived from real reactor, plant and operation data for the
PB2 BWR/4 NPP and it is based on the information provided in EPRI reports and some additionalsources such as the PECO Energy Topical Report. This chapter specifies the core and neutronic data to
be used in the calculations of Exercise 2.
The radial geometry of the reactor core is shown in Figure 2-1. Radially, the core is divided into
cells 15.24 cm wide, each corresponding to one fuel assembly (FA), plus a radial reflector (shaded
area of Figure 2-1) of the same width. There are a total of 888 assemblies, 764 FAs and 124 reflector
assemblies. Axially, the reactor core is divided into 26 layers (24 core layers plus top and bottom
reflectors) with a constant height of 15.24 cm (including reflector nodes). The total active core heightis 365.76 cm. The axial nodalisation accounts for material changes in the fuel design and for exposureand history variations. Geometric data for the FA and fuel rod is provided in Table 2-1. Data fordifferent assembly designs is given in Tables 2-2 through 2-7. Fuel assembly lattice drawings,
including detailed dimensions, for initial fuel, reload fuel with 100 and 120 mil channels and the leadtest assemblies (LTA) are shown in Figures 2-2 through 2-5. The numbers 100 and 120 refer to thewall thickness of the channel (1 mil = 0.001 inches).
The core loading during the test was as follows: 576 fuel assemblies were the original 7 u 7 typefrom Cycle 1 (C1), and the remaining 188 were a reload of 8 u 8 fuel assemblies. One hundred andeighty-five control rods provided reactivity control. To build the participant’s given neutronic model,
these control rods can be grouped according to their initial insertion position. The control rod grouping
used by PSU to perform reference calculations is presented in Figure 2-6.
Two neutron energy groups and six delayed neutron precursor families are modelled. The energy
release per fission for the two prompt neutron groups is 0.3213 u 10–10 and 0.3206 u 10–10 W-s/fission,and this energy release is considered to be independent of time and space. It is assumed that 2% offission power is released as direct gamma heating for the in-channel coolant flow and 1.7% for the
bypass flow. Table 2-8 shows global core-wide decay time constants and fractions of delayed
neutrons. In addition delayed parameters are provided in the cross-section library for each of thecompositions. The prompt neutron lifetime is 0.45085 u 10–4.
It is recommended that ANS-79 be used as a decay heat standard model. In total 71 decay heatgroups are used: 69 groups are used for the three isotopes 235U, 239Pu and 238U with the decay heatconstants defined in the 1979 ANS standard; plus, the heavy-element decay heat groups for 239U and239
Np are used with constants given in Table 2-9. It is recommended that the participants also use theassumption of an infinite operation at a power of 3 293 MWt. For participants who are not capable ofusing the ANS-79 decay heat standard, a file of the decay heat evolution throughout the transient isprovided on CD-ROM and at the benchmark ftp site under the directory Decay-Heat. These predictions
are obtained using the PSU coupled code results. The effective decay heat energy fraction of the total
thermal power (the relative contribution in the steady state) is equal to 0.065583.
Nineteen assembly types are contained within the core geometry. There are 435 compositions.
The corresponding sets of cross-sections are provided. Each composition is defined by material
properties (due to changes in the fuel design) and burn-up. The burn-up dependence is a three-component
vector of variables: exposure (GWd/t), spectral history (void fraction) and control rod history.
Assembly designs are defined in Tables 2-10 through 2-15. Control rod geometry data is provided inTable 2-16. The definition of assembly types is shown in Table 2-17. The radial distribution of theseassembly types within the reactor geometry is shown in Figure 2-7. The axial locations ofcompositions for each assembly type are shown in Table 2-18.
16

A complete set of diffusion coefficients, macroscopic cross-sections for scattering, absorption,and fission, assembly discontinuity factors (ADFs), as a function of the moderator density and fueltemperature is defined for each composition. The group inverse neutron velocities are also provided
for each composition. Dependence of the cross-sections on the above variables is specified through a
two-dimensional table look-up. Each composition is assigned to a cross-section set containing separate
tables for the diffusion coefficients and cross-sections, with each point in the table representing a
possible core state. The expected range of the transient is covered by the selection of an adequate
range for the independent variables shown in Table 2-19. Specifically, Exercise 1 was used forselecting the range of thermal-hydraulic variables. A steady-state calculation was run using the
TRAC-BF1 code and initial conditions of the second turbine trip for choosing discrete values of thethermal-hydraulic variables (pressure, void fraction and coolant/moderator temperature). A transient
calculation was performed to determine the expected range of change of the above variables.
A modified linear interpolation scheme (which includes extrapolation outside the thermal-hydraulicrange) is used to obtain the appropriate total cross-sections from the tabulated ones based on the reactor
conditions being modelled. Table 2-20 shows the definition of a cross-section table associated with acomposition. Table 2-21 shows the macroscopic cross-section table structure for one cross-section set.
All cross-section sets are assembled into a cross-section library. The cross-sections are provided inseparate libraries for rodded (nemtabr) and un-rodded compositions (nemtab). The format of eachlibrary is as follows:x

The first line of data shows the number of data points used for the independent
thermal-hydraulic parameters. The parameters used in this benchmark include fuel temperatureand moderator density.

x

Each cross-section set is in the order shown in Table 2-21. Each table is in the format
described in Table 2-20. More detailed information on this format is presented in Appendix B.
First, the values of the independent thermal-hydraulic parameters (fuel temperature andmoderator density) used to specify that particular set of cross-sections are listed, followed by
the values of the cross-sections* and ADFs. Since there is one-half symmetry for all theassembly designs, two ADFs per composition per energy group are provided – West (widegap) and South (narrow gap). Because the fuel assembly designs employed in PB2 core
design have one-half symmetry, it is assumed that North is equal to West and East is equal toSouth (e.g. Figure 2-8). Detector parameters† are included after the two-group cross-sections
followed by the delayed neutron parameters for six groups. Finally, the group inverse neutron
velocities complete the data for a given cross-section set.

x The dependence on fuel temperature in the reflector cross-section tables is also modelled. Thisis because the reflector cross-sections are generated by performing lattice physics transport
calculations, including the next fuel region. In order to simplify the reflector feedback
modelling the following assumptions are made for this benchmark: an average fuel temperature
value equal to 550 K is used for the radial reflector cross-section modelling in both the initialsteady-state and transient simulations, and the average coolant density for the radial reflector
is equal to the inlet coolant density. For the axial reflector regions the following assumptions
are made: for the bottom, the fuel temperature is equal to the inlet coolant temperature (perthermal-hydraulic channel or cell) and the coolant density is equal to the inlet coolant density(again per channel); for the top, the fuel temperature is equal to the outlet coolant temperature(per channel) and the coolant density is equal to the outlet coolant density (per channel).
* Please note that the provided absorption cross-sections already take the xenon thermal cross-sections into account;however, at the participants’ request, the thermal macro and micro xenon cross-sections are listed in the cross-section sets.
†
Detector parameters were described in Volume I, Section 2.6.

17

All cross-section data, along with a program for linear interpolation, are supplied on CD-ROM
and at the benchmark ftp site under the directory XS-Lib in the format described above. Latticephysics calculations are performed by homogenising the fuel lattice and the bypass flow associatedwith it. When obtaining the average coolant density, a correction that accounts for the bypass channel
conditions should be included since this is going to influence the feedback effect on the cross-section
calculation through the average coolant density. The following approach should be applied:
A act U act  A byp U byp  U sat

U eff
act

2.1

A act

where U eff
act is the effective average coolant density for cross-section calculation, Ubyp is the averagemoderator coolant density of the bypass channel, Usat is the saturated moderator coolant density of the
bypass channel, Aact is flow cross-sectional area of the active heated channel and Abyp is the flowcross-sectional area of the bypass channel. Bypass conditions should be obtained by adding a bypass
channel to represent the core bypass region in the thermal-hydraulic model.
Table 2-1. PB2 fuel assembly data

1
168
0
7u7
15.24
1.875
49
0
0
7
0.225
1.183
4.128

2
263
261
7u7
15.24
1.875
49
0
4
7
0.225
1.183
4.128

3
333
315
7u7
15.24
1.875
49
0
5
7
0.225
1.183
4.128

4
0
68
8u8
15.24
1.623
63
1
5
7
0.225
1.353
4.128

5
0
116
8u8
15.24
1.623
63
1
5
7
0.225
1.353
4.128

LTA
special
6
0
4
8u8
15.24
1.623
62
2
5
7
0.225
1.353
4.128

0
222.44
222.44441
212.21212.65547
212.06212.61490
207.78208.27328
208.0
208.33313
207.14207.45Initial load
Assembly typeNo. of assemblies, initial core
No. of assemblies, Cycle 2
Geometry
Assembly pitch, cm
Fuel rod pitch, cm
Fuel rods per assembly
Water rods per assembly
Burnable poison positions
No. of spacer grids
Inconel per grid, kg
Zr-4 per grid, kg
Spacer width, cm
Assembly average fuel composition:
Gd2O3, g
UO2, kg
Total fuel, kg

ReloadReloadTable 2-2. Assembly design 1
Rod
type

No.
of rods

1
2
2s

31
17
01

Pellet density
UO2
UO2+Gd2O3(g/cm3)(g/cm3)
10.42
–
10.42
–
10.42
–

Stack
density(g/cm3)
10.34
10.34
10.34

Gd2O3
(g)

UO2
(g)

0
0
0

4 548
4 548
4 140

Pellet outer diameter = 1.23698 cm.
Cladding = Zircaloy-2, 1.43002 cm outer diameter u .08128 cm wall thickness, all rods.
Gas plenum length = 40.64 cm.

18

Stack
length(cm)
365.76365.76330.20Table 2-3. Assembly design 2
Rod
type

No.
of rods

1
1s
2
3
4
5A
6B

25
1
12
6
1
3
1

Pellet density
UO2
UO2+Gd2O3
3(g/cm )
(g/cm3)
10.42
–
10.42
–
10.42
–
10.42
–
10.42
–
–
10.29
10.42
10.29

Stack
density(g/cm3)
10.32
10.32
10.32
10.32
10.32
10.19
10.27

Gd2O3
(g)

UO2
(g)

0
0
0
0
0
129
54

4 352
3 935
4 352
4 352
4 352
4 171
4 277

Stack
length(cm)
365.76330.20365.76365.76365.76365.76365.76Pellet outer diameter = 1.21158 cm.
Cladding = Zircaloy-2, 1.43002 cm outer diameter u .09398 cm wall thickness, all rods.
Gas plenum length = 40.132 cm.

Table 2-4. Assembly design 3
Rod
type

No.
of rods

1
2
3
4
5A
6C
7E
8D

26
11
6
1
2
1
1
1

Pellet density
UO2
UO2+Gd2O3(g/cm3)(g/cm3)
10.42
–
10.42
–
10.42
–
10.42
–
–
10.29
–
10.29
10.42
10.25
10.42
10.25

Stack
density(g/cm3)
10.32
10.32
10.32
10.32
10.19
10.19
10.28
10.19

Gd2O3
(g)

UO2
(g)

0
0
0
0
129
117
43
129

4 352
4 352
4 352
4 352
4 171
3 771
4 292
4 172

Stack
length(cm)
365.76365.76365.76365.76365.76330.20365.76365.76Pellet outer diameter = 1.21158 cm.
Cladding = Zircaloy-2, 1.43002 cm outer diameter u .09398 cm wall thickness, all rods.
Gas plenum length = 40.132 cm.

Table 2-5. Assembly design 4
Rod
type

No.
of rods

1
2
3
4
5
WS

39
14
4
1
5
1

Pellet density
UO2
UO2+Gd2O3(g/cm3)(g/cm3)
10.42
–
10.42
–
10.42
–
10.42
–
–
10.29
–
–

Stack
density(g/cm3)
10.32
10.32
10.32
10.32
10.19
–

Gd2O3
(g)

UO2
(g)

0
0
0
0
98
0

3 309
3 309
3 309
3 309
3 172
0

Pellet outer diameter = 1.05664 cm.
Cladding = Zircaloy-2, 1.25222 cm outer diameter u .08636 cm wall thickness, all rods.
Gas plenum length = 40.64 cm except water rod.
Gd2O3 in rod type 5 runs full 365.76 cm.
Water rod (WS) has holes drilled top and bottom to provide water flow and little or no boiling.
Water rod is also a spacer positioning rod.

19

Stack
length(cm)
365.76365.76365.76365.76365.76–

Table 2-6. Assembly design 5
Rod
type

No.
of rods

1
2
3
4
5
WS

39
14
4
1
5
1

Pellet density
UO2
UO2+Gd2O3
3(g/cm )
(g/cm3)
10.42
–
10.42
–
10.42
–
10.42
–
–
10.33
–
–

Stack
density(g/cm3)
10.32
10.32
10.32
10.32
10.23
–

Gd2O3
(g)

UO2
(g)

0
0
0
0
66
0

3 309
3 309
3 309
3 309
3 216
0

Stack
length(cm)
365.76365.76365.76365.76365.76–Pellet outer diameter = 1.05664 cm.
Cladding = Zircaloy-2, 1.25222 cm outer diameter u .08636 cm wall thickness, all rods.
Gas plenum length = 40.64 cm, except water rod.
Gd2O3 in rod type 5 runs full 365.76 cm.
Water rod (WS) has holes drilled top and bottom to provide water flow and little or no boiling.
Water rod is also a spacer positioning rod.

Table 2-7. Assembly design 6
Rod
type

No.
of rods

1
2
3
4
5
WR,WS
ENDS

38
14
4
1
5
2
62

Pellet density
UO2
UO2+Gd2O3(g/cm3)(g/cm3)
10.42
–
10.42
–
10.42
–
10.42
–
–
10.33
–
–
10.42
–

Stack
density(g/cm3)
10.32
10.32
10.32
10.32
10.23
–
10.32

Gd2O3
(g)

UO2
(g)

0
0
0
0
63
0
0

3 125
3 125
3 125
3 125
3 037
0
223

Pellet outer diameter = 1.0414 cm.
Cladding = Zircaloy-2, 1.22682 cm outer diameter u .08128 cm wall thickness, all fuelled rods.
= Zircaloy-2, 1.50114 cm outer diameter u .07620 cm wall thickness, water rods.
Gas plenum length = 24.0792 cm.
Gd2O3 in rod type 5 runs full 355.60 cm.
Water rod (WS) has holes drilled top and bottom to provide water flow and little or no boiling.
Water rod is also a spacer positioning rod.

20

Stack
length
(cm)
355.6
355.6
355.6
355.6
355.6
–
25.4

Table 2-8. Decay constant and fractions of delayed neutrons
Group

Decay constant (s–1)

Relative fraction ofdelayed neutrons in %1

0.012813

0.01672

0.031536

0.1134

3

0.124703

0.1022

4

0.328273

0.21525

1.405280

0.08376

3.844728

0.0214

Total fraction of delayed neutrons: 0.5526%.

Table 2-9. Heavy-element decay heat constants
Group no.
(isotope)

Decay constant(s–1)

Available energy froma single atom (MeV)

70 (239U)

4.91 u 10–4

0.474

239

3.41 u 10

0.419

71 ( Np)–6

21

Table 2-10. Assembly design for Type 1 initial fuelRod type
1
2

23

U (wt.%)
1.33
0.71

Gd2O3 (wt.%)
0022

No. of rods
31
18

Table 2-11. Assembly design for Type 2 initial fuelRod type
1
2
3
4
5A
6B

235

U (wt.%)
2.93
1.94
1.69
1.33
2.93
2.93

Gd2O3 (wt.%)
0.0
0.0
0.0
0.0
3.0
3.0

23

No. of rods
26
12
06
01
03
01

Table 2-12. Assembly design for Type 3 initial fuelRod type
1
2
3
4
5A
6C
7E
8D

235

U (wt.%)
2.93
1.94
1.69
1.33
2.93
2.93
2.93
1.94

Gd2O3 (wt.%)
0.0
0.0
0.0
0.0
3.0
3.0
4.0
4.0

24

No. of rods
26
11
06
01
02
01
01
01

Table 2-13. Assembly design for Type 4 8 u 8 UO2 reload
Rod type
1
2
3
4
5
WS

235

U (wt.%)
3.01
2.22
1.87
1.45
3.01
–

Gd2O3 (wt.%)
0.0
0.0
0.0
0.0
3.0
0.0

25

No. of rods
39
14
04
01
05
01

Table 2-14. Assembly design for Type 5 8 u 8 UO2 reload
Rod type
1
2
3
4
5
WS

235

U (wt.%)
3.01
2.22
1.87
1.45
3.01
–

Gd2O3 (wt.%)
0.0
0.0
0.0
0.0
2.0
0.0

WS – Spacer positioning water rod.
G – Gadolinium rods.

26

No. of rods
39
14
04
01
05
01

Table 2-15. Assembly design for Type 6 8 u 8 UO2 reload, LTA
Rod type
1
2
3
4
5
WS
WR

235

U (wt.%)
3.01
2.22
1.87
1.45
3.01
–
–

Gd2O3 (wt.%)
0.0
0.0
0.0
0.0
2.0
0.0
0.0

WS – Spacer positioning water rod.
WR – Water rod.
G – Gadolinium rods.

27

No. of rods
38
14
04
01
05
01
01

Table 2-16. Control rod data (movable control rods)
Shape
Cruciform
Pitch, cm
30.48
Stroke, cm
365.76
Control length, cm
363.22Control material
B4C granules in Type-304, stainless steel tubes and sheath
Material density
70% of theoretical
Number of control material tubes per rod 84
Tube dimensions.47752 cm outer diameter by .0635 cm wall
Control blade half span, cm
12.3825
Control blade full thickness, cm.79248Control blade tip radius, cm.39624
Sheath thickness, cm.14224
Central structure wing length, cm
1.98501
Blank tubes per wing
None
Table 2-17. Definition of assembly types
Assembly type
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19

Assembly design(see Tables 2.10 through 2.15)
5
4
5
6
2
2
2
2
2
2
3
2
3
2
3
2
3
2
Reflector

28

29

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433 433
1 25 49 73 97 121 145 169 193 217 241 265 289 313 337 361 385 409 435
2 26 50 74 98 122 146 170 194 218 242 266 290 314 338 362 386 410 435
3 27 51 75 99 123 147 171 195 219 243 267 291 315 339 363 387 411 435
4 28 52 76 100 124 148 172 196 220 244 268 292 316 340 364 388 412 435
5 29 53 77 101 125 149 173 197 221 245 269 293 317 341 365 389 413 435
6 30 54 78 102 126 150 174 198 222 246 270 294 318 342 366 390 414 435
7 31 55 79 103 127 151 175 199 223 247 271 295 319 343 367 391 415 435
8 32 56 80 104 128 152 176 200 224 248 272 296 320 344 368 392 416 435
9 33 57 81 105 129 153 177 201 225 249 273 297 321 345 369 393 417 435
10 34 58 82 106 130 154 178 202 226 250 274 298 322 346 370 394 418 435
11 35 59 83 107 131 155 179 203 227 251 275 299 323 347 371 395 419 435
12 36 60 84 108 132 156 180 204 228 252 276 300 324 348 372 396 420 435
13 37 61 85 109 133 157 181 205 229 253 277 301 325 349 373 397 421 435
14 38 62 86 110 134 158 182 206 230 254 278 302 326 350 374 398 422 435
15 39 63 87 111 135 159 183 207 231 255 279 303 327 351 375 399 423 435
16 40 64 88 112 136 160 184 208 232 256 280 304 328 352 376 400 424 435
17 41 65 89 113 137 161 185 209 233 257 281 305 329 353 377 401 425 435
18 42 66 90 114 138 162 186 210 234 258 282 306 330 354 378 402 426 435
19 43 67 91 115 139 163 187 211 235 259 283 307 331 355 379 403 427 435
20 44 68 92 116 140 164 188 212 236 260 284 308 332 356 380 404 428 435
21 45 69 93 117 141 165 189 213 237 261 285 309 333 357 381 405 429 435
22 46 70 94 118 142 166 190 214 238 262 286 310 334 358 382 406 430 435
23 47 71 95 119 143 167 191 215 239 263 287 311 335 359 383 407 431 435
24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 435
434 434 434 434 434 434 434 434 434 434 434 434 434 434 434 434 434 434 434

Table 2-18. Composition numbers in axial layer for each assembly type

Table 2-19. Range of variables
T Fuel(qK)
0 400.00 800.0
1 200.0
1 600.0
2 000.0
2 400.00 400.00 800.0
1 200.0
1 600.0
2 000.0
2 400.00 400.00 800.0
1 200.0
1 600.0
2 000.0
2 400.00 400.00 800.0
1 200.0
1 600.0
2 000.0
2 400.00 400.00 800.0
1 200.0
1 600.0
2 000.0
2 400.00 400.00 800.0
1 200.0
1 600.0
2 000.0
2 400.0

Rho M.
(kg/m3)141.595
141.595
141.595
141.595
141.595
141.595
226.154226.154226.154226.154226.154226.154299.645299.645299.645299.645299.645299.645435.045435.045435.045435.045435.045435.045599.172599.172599.172599.172599.172599.172779.405
779.405
779.405
779.405
779.405
779.405

30

Table 2-20. Key to macroscopic cross-section tables
Tf1
Um1
61

Tf2
Um2
62

Tf3
Um3
...
...

Tf4
Um4

Tf5
Um5

Tf6
Um6

634

635

636

Where:– Tf is the Doppler (fuel) temperature (qK)
– Um is the moderator density (kg/m3)
Macroscopic cross-sections are in units of cm–1

Table 2-21. Macroscopic cross-section table structure************************************************************************
Cross-Section Table Input**
T FuelRho Mod.
66************ X-Section Set ##************************************************************************
Group No. 1************** Diffusion Coefficient Table************** Absorption X-Section Table************** Fission X-Section Table************** Nu-Fission X-Section Table************** Scattering From Group 1 to 2 X-Section Table************** Assembly Disc. Factor Table - W************** Assembly Disc. Factor Table - S************** Detector Flux Ratio Table************** Detector Microscopic Fission X-Section Table*31

************************************************************************
Group No. 2************** Diffusion Coefficient Table************** Absorption X-Section Table************** Fission X-Section Table************** Nu-Fission X-Section Table************** Xe Macroscopic X-Section Table************** Xe Microscopic X-Section Table************** Assembly Disc. Factor Table - W************** Assembly Disc. Factor Table - S************** Detector Flux Ratio Table************** Detector Microscopic Fission X-Section Table************** Detector Flux Ratio Table (not energy group dependent)************** Detector Microscopic Fission X-Section Table (not energy group dependent)************** Effective Delayed Neutron Yield in Six Groups************** Decay Constants for Delayed Neutron Groups************** Inv. Neutron Velocities

32

Figure 2-1. Reactor core cross-sectional view33Figure 2-2. PB2 initial fuel assembly latticeDim. ID
A
B
C
Dim. (in) 12.00 c5.27800 0.3750
Dim. (cm) 30.48 13.40612 0.9525
Dim. ID
K
L
M
0.18700
Dim. (in)0.47498
Dim. (cm)

D

N

E
F
G
H
0.0800 0.1750 0.14350 0.73800
0.2032 0.4445 0.36449 1.87452
O
P
Q
R

34

I

S
0.38000.9652

J

Figure 2-3. PB2 reload fuel assembly lattice for 100 mil channels

Dim. ID
A
B
C
Dim. (in) 12.00 05.27800 0.3550
Dim. (cm) 30.48 13.40612 0.9017
Dim. ID
K
L
M
0.16700
Dim. (in)0.42418
Dim. (cm)

D

N

E
F
G
0.100 0.14700 0.15300
0.254 0.37338 0.38862
O
P
Q

35

H
0.64001.6256R

I

S
0.38000.9652

J

Figure 2-4. PB2 reload fuel assembly lattice for 120 mil channels

Dim. ID
A
B
C
Dim. (in) 12.00 05.27800 0.3550
Dim. (cm) 30.48 13.40612 0.8509
Dim. ID
K
L
M
0.14700
Dim. (in)0.42418
Dim. (cm)

D

N

E
F
G
0.1200 0.14700 0.15300
0.3048 0.37338 0.38862
O
P
Q

36

H
0.64001.6256R

I

S
0.38000.9652

J

Figure 2-5. PB2 reload fuel assembly lattice for LTA assemblies

Dim. ID
A
B
C
Dim. (in) 12.00 05.27800 0.3550
Dim. (cm) 30.48 13.40612 0.9017
Dim. ID
K
L
M
0.16700
Dim. (in)0.42418
Dim. (cm)

D

N

E
F
G
0.100 0.15700 0.15800
0.254 0.39878 0.40132
O
P
Q

37

H
0.64001.6256R

I

S
0.38000.9652

J

38

0
0
0
0
0
0
0
0
0
0
0
0
0
0
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0

0
0
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0
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0
1
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3
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3
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4
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0
1
1
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6
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7
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1
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5
1
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5
5
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7
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1
1
6
6
1
1
1
1
0

0
1
1
1
1
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6
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7
1
1
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5
1
1
5
5
1
1
7
7
1
1
6
6
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0

0
1
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3
3
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1
5
5
1
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1
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5
5
1
1
3
3
1
1
0

0
1
1
3
3
1
1
5
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
5
1
1
3
3
1
1
0

0
1
1
1
1
6
6
1
1
7
7
1
1
5
5
1
1
5
5
1
1
7
7
1
1
6
6
1
1
1
1
0

0
1
1
1
1
6
6
1
1
7
7
1
1
5
5
1
1
5
5
1
1
7
7
1
1
6
6
1
1
1
1
0

0
1
1
4
4
1
1
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
1
1
4
4
1
1
0

0
1
1
4
4
1
1
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
3
1
1
4
4
1
1
0

Figure 2-6. PSU control rod grouping
0
1
1
1
1
8
8
1
1
6
6
1
1
7
7
1
1
7
7
1
1
6
6
1
1
8
8
1
1
1
1
0

0
1
1
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8
1
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6
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1
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7
1
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7
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1
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1
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6
1
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0
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39

19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19
19 19 11 5 6 5 6 6 6 6 6 6 6 5 5 11 19 19
19 19 19 6 6 1 5 1 6 1 1 1 1 5 1 6 1 6 6 19 19 19
19 7 13 13 1 10 1 10 1 10 12 14 10 1 9 1 10 1 15 13 8 19
19 19 6 7 1 14 12 14 15 16 15 15 16 17 15 16 15 10 15 1 7 6 19 19
19 19 19 13 10 1 16 1 15 3 15 1 15 2 2 17 1 15 3 15 1 15 1 10 13 19 19 19
19 8 6 9 1 15 10 15 14 15 14 17 14 17 17 18 17 14 15 14 17 10 15 1 10 6 8 19
19 19 12 7 1 15 4 15 3 17 3 15 2 15 15 14 17 2 15 3 17 3 16 4 15 1 7 13 19 19
19 19 6 13 1 16 10 17 15 17 17 15 15 17 14 17 17 15 15 14 17 13 17 14 16 10 15 1 13 7 19 19
19 11 6 1 16 1 15 3 17 2 15 2 15 2 15 2 2 17 2 15 2 17 2 15 3 17 1 15 1 6 11 19
19 5 1 10 10 15 12 17 16 15 14 17 15 15 14 17 17 13 17 15 15 15 17 14 15 14 15 10 10 1 5 19
19 6 6 1 16 3 17 3 15 2 15 2 17 2 17 17 15 17 2 17 2 15 2 15 3 17 3 15 1 6 5 19
19 6 1 9 16 17 14 16 15 15 14 16 15 17 17 17 17 15 17 14 17 15 15 14 15 14 16 16 9 1 6 19
19 7 5 1 17 3 15 2 15 2 15 2 17 2 17 2 2 17 2 17 2 15 2 15 2 17 1 15 1 5 6 19
19 6 1 10 15 16 15 15 15 17 15 17 17 17 15 15 17 15 17 15 17 13 15 17 15 14 15 16 10 1 6 19
19 6 1 12 16 2 16 13 16 2 17 15 17 2 15 15 15 15 2 17 15 15 2 17 13 17 2 15 14 1 6 19
19 7 1 12 15 2 17 15 15 2 15 15 15 2 16 17 15 15 2 17 15 17 2 17 13 16 2 17 12 1 6 19
19 6 1 10 16 17 15 15 15 17 14 17 15 17 15 16 15 17 17 15 17 13 15 15 16 13 15 15 10 1 6 19
19 6 6 1 15 1 17 2 15 2 15 2 17 2 17 2 2 17 2 17 2 17 2 15 2 17 1 15 1 5 6 19
19 6 1 9 16 17 12 16 15 15 14 17 14 17 14 17 17 15 17 16 17 14 15 15 15 14 16 17 9 1 6 19
19 6 6 1 16 3 17 3 15 2 15 2 17 2 17 16 15 17 2 17 2 15 2 15 3 15 3 15 1 6 6 19
19 5 1 10 10 17 14 15 14 17 15 15 15 17 14 15 17 15 17 14 15 14 15 14 15 14 15 10 10 1 5 19
19 11 5 1 16 1 17 3 15 2 17 2 15 2 17 2 2 15 2 17 2 15 2 15 3 17 1 14 1 5 10 19
19 19 7 13 1 16 10 15 14 15 15 15 15 17 16 17 18 14 17 15 15 15 17 14 17 10 16 1 14 6 19 19
19 19 13 7 1 15 4 15 3 15 3 15 2 17 14 14 17 2 17 3 17 3 17 4 15 1 7 13 19 19
19 8 6 10 1 17 10 17 12 15 14 17 13 17 17 13 16 14 15 12 15 10 15 1 10 6 8 19
19 19 19 13 10 1 16 1 17 3 17 1 17 2 2 17 3 15 3 16 1 16 1 9 13 19 19 19
19 19 6 7 1 16 10 16 16 18 18 15 16 17 18 16 16 10 16 1 7 6 19 19
19 7 11 15 1 10 1 9 1 10 10 10 10 1 10 1 10 1 15 13 7 19
19 19 19 6 6 1 6 1 6 1 1 1 1 6 1 5 1 6 6 19 19 19
19 19 11 5 6 6 7 6 6 6 6 7 6 6 5 11 19 19
19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19

Figure 2-7. Radial distribution of assembly types

Figure 2-8. Fuel assembly orientation for ADF assignment
Wide
G
a
p

North

West
East

G
a
p
South
Narrow

40

Figure 2-9. Core orificing and TIP system arrangement

41

Figure 2-10. Elevation of core components

422.3 Core thermal-hydraulic boundary conditions model and its coupling with 3-D neutron
kinetics model
PB2 is a GE designed BWR/4 with a rated thermal power of 3 293 MW, a rated core flow of
12 915 kg/s (102.5 u 106 lb/hr), a rated steam flow of 1 685 kg/s (13.37 u 106 lb/hr), and a turbine inlet
pressure of 6.65 MPa (965 psia). Nuclear steam supply system (NSSS) has turbine-driven feed pumps
and a two-loop M-G driven recirculation system feeding a total of 20 jet-pumps. There are totally foursteam lines and each has a flow-limiting nozzle, main steam isolation valves (MSIVs), safety relief
valves (SRVs), and a turbine stop valve (TSV). The steam bypass system consists of nine bypass
valves (BPVs) mounted on a common header, which is connected to each of the four steam lines.
In Exercise 2 steady-state and transient analyses, core thermal-hydraulic boundary conditions
model is used and it is coupled to the 3-D core neutron kinetics model. The full PB2 thermal-hydraulicmodel can be converted to a core thermal-hydraulic boundary condition model by defining inlet andoutlet thermal-hydraulic boundary conditions. The developed model for performing the 3-D core
thermal-hydraulic boundary condition calculation was built based on different TRAC-BF1 thermalhydraulic components as follows.
A basic 33-channel thermal-hydraulic core boundary condition model was obtained from the PB2TT2 TRAC-BF1 system model. Bottom and top boundary conditions are specified in this model using
the FILL and BREAK TRAC-BF1 components. The developed model is illustrated in Figure 2-11.
Figure 2-12 shows the thermal-hydraulic radial mapping scheme used to represent the PB2 reactor
core. The feedback, or coupling, between neutronics and thermal-hydraulics can be characterised bychoosing user supplied mapping schemes (spatial mesh overlays) in the radial and axial core planes.
Some of the inlet perturbations (inlet disturbances of both temperature and flow rate) are
specified as a fraction of the position across the core inlet. This requires either a 3-D modelling of thevessel, or some type of a multi-channel model. The PSU developed core multi-channel model consistsof 33 channels to represent the 764 fuel assemblies of the PB2 reactor core. The above core
thermal-hydraulic model was built according to different criteria. The fuel assemblies are ranked
according to the inlet orifice characteristics. The flow areas at channel inlet were adjusted in order tomatch the channel by channel flow rate distribution while preserving pressure drop across core support
plate. Another criterion is the fuel assembly type (e.g. 7 u 7 or 8 u 8). The model is developed without
lumping in a same core channel two or more fuel bundles of different types. This means that 8 u 8 fueltypes are never lumped with 7 u 7 fuel types in a same core channel. Thermal-hydraulic conditions arealso considered. For example, power peaking factors are re-normalised for the lumped channels andmass flows are taken into account during the lumping.
The 33 thermal-hydraulic channels shown in this figure are coupled to the neutronic code modelin the radial plane shown in Figure 2-13. Thermal-hydraulic channels identified with zeroes are treatedas reflector regions. This mapping scheme follows the spatial mesh overlays developed for the PB2
TRAC-BF1/NEM 3-D neutron kinetics/thermal-hydraulic model.
For the purposes of Exercise 2, it is recommended that an assembly flow area of 15.535 in2(1.0023 u 10–2 m2) for fuel assemblies with 7 u 7 fuel rod arrays, and 15.5277 in2 (1.0017 u 10–2 m2)
for fuel assemblies with 8 u 8 fuel rod arrays be used in the core thermal-hydraulic multi-channel
models. There are 764 fuel assemblies in the PB2 reactor core. At EOC 2, there are 576 fuel assembliesof 7 u 7 type, and 188 of the 8 u 8 type. The radial distribution of assembly types is shown in Figure 2-7
in which the assembly types from 1 to 4 identify a fuel assembly with 8 u 8 fuel arrays and theassembly types from 5 to 18 identify a fuel assembly with 7 u 7 fuel rod arrays. The core hydrauliccharacteristics (e.g. core pressure drop) can be found in Ref. [5].
43There are several files of data were provided to participants regarding the definition of the core
thermal-hydraulic boundary condition model. These data are taken from a combination of thebest-estimate core plant system code calculations performed and test data. The boundary conditions
provided to the participants are both steady state and time dependent. They are provided for the bottom
and top regions adjacent to the inlet and outlet region of the core region. These values are obtained fromthe lower and upper region of the vessel component of the TRAC-BF1 model [9-11]. The types ofboundary conditions that are provided to the participants are:x

At the inlet of the channels: mass flows (kg/s) and temperatures (K) from 0 s to 5 s. Thirty-three
files are provided since the model used to obtain these variables contains 33 thermal-hydraulicchannels. Also, a single file containing core mass flow and core inlet temperature vs. time isprovided to participants whose thermal-hydraulic models consist of a single average channel.

x

At the inlet and outlet of the thermal-hydraulic channels: pressure (Pa) from 0 s to 5 s. Since
all the channels have a common plenum, pressure is constant radially. Therefore, a single filecontaining pressure vs. time information is provided.
Figure 2-11. Exercise 2 vessel/core boundary condition model

44

Figure 2-12. Reactor core thermal-hydraulic channel radial map

2.4 Initial steady-state conditions
The initial conditions for performing PB2 hot zero power (HZP) core calculations are chosen as
552.833 K for fuel temperature, 753.9777 kg/m3 for average coolant density and 32.93 MW for thereactor power (see Table 2-22). The fixed thermal-hydraulic variables should be equally distributed
through the whole core. The initial power corresponds to 1% of the PB2 nominal power. Figure 2-13
shows the HZP control rod pattern that should be used for the analysis of this calculation. The initialconditions along with the control rod pattern produce a critical or very near to critical reactor core.
A similar control rod grouping approach as shown in Figure 2-13 could be useful to set up the control
rod mapping scheme for just two control rod groups.
Table 2-22. PB2 HZP initial conditions
Fuel temperature, K
Average coolant density, kg/m3
Reactor power, MW

552.8330
753.9777032.9300

Turbine trip test 2 (TT2) was initiated from steady-state conditions after obtaining P1 edits fromthe process computer for nuclear and thermal-hydraulic conditions of the core. PB2 was chosen for theturbine trip tests because it is a large BWR/4 with relatively small turbine bypass capacity. During thetest, the initial thermal power level was 61.6% rated 2 030 MW; core flow was 80.9% rated
10 445 kg/s (82.9 u 106 lb/hr); and average range power monitor (APRM) scram setting was 95% of
nominal power. Table 2-23 provides the reactor initial conditions for performing steady-statecalculations while Figure 2-14 shows the PB2 TT2 initial control rod pattern.
45

Figure 2-13. PB2 HZP control rod pattern

Table 2-23. PB2 TT2 initial conditions from process computer P1 edit
Core thermal power, MWt
Initial power level, % of rated
Gross power output, MWe
Feedwater flow, kg/s
Reactor pressure, Pa
Total core flow, kg/s
Core inlet subcooling, J/kg
Feedwater temperature, K
Core pressure drop, Pa
Jet-pump driving flow, kg/s
Core average exit quality, fraction
Core average void fraction, fraction
Core average power density, kW/l

2 030.000
61.600625.100
980.260
6 798 470.000
10 445.000
48 005.291
442.310113 560.700
2 871.240
0.097
0.304
31.280Figure 2-14. PB2 HP control rod pattern46

2.5 Transient calculations
Most of the important phenomena of interest during TT2 occurred in the first five seconds.
Therefore, the transient will be simulated for this time period. The thermal-hydraulics system transient
behaviour in Exercise 2 is modelled through boundary conditions imposed to the coupled core model.
The only event, which needs to be modelled in this exercise, is the scram simulation. Table 2-24
shows the scram initiation time and the delay time that should be used for performing Exercise 2.
Table 2-25 shows the average control rod density (CRD) position during reactor scram. An averagevelocity can be obtained from Table 2-24 for the scram modelling in the 3-D kinetics case.
An approximate value obtained from the above table is 2.34 ft/s (0.713 m/s) for the first 0.04 seconds
and 4.67 ft/s (1.423 m/s) thereafter.
Table 2-24. PB2 TT2 scram characteristics
APRM high flux scram set-point, % rated
Time delay prior to rod motion, msec
Time of scram initiation, sec
Initiates CR insertion, sec

95 (3 128.35 MWt)
120
0.63
0.75

Table 2-25. CRD position after scram vs. time
Time (sec)
0.000
0.120
0.160
0.247
0.354
0.457
2.500
3.080
5.000

Position (cm)000.00000.00002.85015.24030.48045.72310.90365.76365.7647

Chapter 3
METHODOLOGIES TO QUANTIFY THE ACCURACY OF THE CALCULATIONSAs mentioned briefly in Chapter 1, each of the 18 participants has submitted various results thatwere available for the statistical analysis. The submitted results for Exercise 2 can be classified in fourtypes of data. These are integral parameter values, 1-D distribution, 2-D distributions and time
histories. It was decided by the participants in the benchmark that the reference data used in the
Exercise 2 comparative analysis is the so-called “averaged data”. The reference solution for eachrequested parameter is based upon the statistical mean (averaged) value of all submitted results.
3.1 Standard techniques for the comparison of results
In Exercise 2, four types of data were analysed and the results of all participants were comparedbased on this classification. These data types were:
1) integral parameter values;2) one-dimensional (1-D) axial distributions;
3) two-dimensional (2-D) radial distributions;4) time history data.
It was necessary to develop a suite of statistical methods for each of these data types, which wereapplied in the comparative analysis. The statistical methods used in the comparative analysis of
Exercise 2 are described in Subsections, 3.1.1, 3.1.2, 3.1.3 and 3.1.4.
Table 3-1 and Table 3-2 summarise the submitted data types for Exercise 2 problem conditions
and the classifications of these data types.
Table 3-1. Exercise 2 parameters for steady-state statistical comparisonsCondition

HZP

HP

Submitted data for statistical analysis
keff
Normalised axial power
Relative power for FA 75
Relative power for FA 367
Normalised radial power
keffCore averaged axial void fraction
Normalised axial power
Relative power for FA 75
Relative power for FA 367
Normalised radial power

49

Classification
Integral value
1-D distribution
1-D distribution
1-D distribution
2-D distribution
Integral value
1-D distribution
1-D distribution
1-D distribution
1-D distribution
2-D distribution

Table 3-2. Exercise 2 parameters for transient statistical comparisonsCondition
Transient

Snapshot at
maximum power
before scram

Snapshot at theend of transient

Submitted data for statistical analysis
Core power
Total reactivity
Doppler reactivity
Void reactivity
Time of maximum power before scram
Normalised axial power
Relative power for FA 75
Relative power for FA 367
Normalised radial power
Normalised axial power
Relative power for FA 75
Relative power for FA 367
Normalised radial power

Classification
Time history
Time history
Time history
Time history
Integral value
1-D distribution
1-D distribution
1-D distribution
2-D distribution
1-D distribution
1-D distribution
1-D distribution
2-D distribution

3.1.1 Integral parameter values
These parameters include such values as keff for HZP and initial conditions of TT2 as well as timeof maximum power before scram. In the analysis of integral values, there is no need to condition thedata by isolating point of interest. Likewise, there are no curves to analyse. Thus, the mean value andstandard deviation should be sufficient to facilitate a comparison of the results. Mean value, standard
deviation, deviation and figure of merit (FOM) are calculated according to Eqs. (3.1), (3.2), (3.3) and(3.4), respectively.
(3.1)

N

¦x

i

i

x referenceN¦ x x
V r
i

2

(3.2)

referenceN 1

where V is the standard deviation, xi is the data submitted by each participant and N is the total numberof received results.
The deviation and FOM can be computed as:eixi  x reference

(3.3)

ei
V

(3.4)

)i

where ei is the difference between the participant’s value and the mean value.
3.1.2 One-dimensional (1-D) axial distributions
Exercise 2 contains many steady-state and transient snapshots of the axial distributions of certain
parameters through the core. The core average axial void fraction and power distributions are functions
50

of height or number of axial nodes. They can be displayed as an x-y plot. Similar methods of statisticalanalysis described in the previous section can be applied for each axial cell. One-dimensional axial
distributions are compared with the average data submitted by the participants. Analyses are performed
for each 1-D cell according to Eqs. (3.5), (3.6) and (3.7).

¦ x x
V r
i

2

(3.5)

referenceN 1

where xi is each participant’s data and N is the total number of received results. FOM is computed as:
ei
V

(3.6)

xi  x reference

(3.7)

)i

ei

For each participant, a single table is prepared that shows the deviations from mean and FOM ateach axial position.
3.1.3 Two-dimensional (2-D) radial distributions
Exercise 2 also contains steady-state and transient snapshots of the radial distribution through thecore for certain parameters. Due to the two-dimensional nature of such data, it is difficult to plot theresults as with time history data and 1-D distributions. However, the same statistical methods can beused to generate mean values, standard deviations and participant deviations, and figures of merit.
Mean and standard deviation for each 2-D cell can be computed according to Eqs. (3.1) and (3.2).
Such an analysis results in a 2-D map for mean values and standard deviations, rather than a single
value for each parameter. Comparisons can thus be made for each cell, rather than only specific cellsof interest.
The deviation and FOM can be computed according to Eqs. (3.3) and (3.4), respectively. For eachparticipant, a map will be generated that shows deviations from the mean at each radial position.
A second map will report the figures of merit.
3.1.4 Time histories
Participants were required to submit four different sets of time histories for Exercise 2. Theseare power (fission or total), total reactivity, Doppler reactivity and void reactivity histories for the
five-second transient period. The averaged values were used as reference data for the statisticalcomparison purpose in the comparative analysis of the time histories. The averaged data are calculated
according to the Eq. (3.8).
(3.8)

N

x reference

¦x

i

i

N

where xi is each participant’s data for the specified time interval and N is the total number of resultsreceived.
51

3.2 ACAP analysis
The comparative analysis was performed for code-to-code comparisons using the standard
statistical methodology with the Automated Code Assessment Program (ACAP) [11]. ACAP is a tool
developed to provide quantitative comparisons between nuclear reactor systems code results andexperimental measurements. This software was developed under a contract with PSU and the NRC for
use in PSU’s code consolidation efforts. ACAP’s capabilities are described as follows:xdraws upon a mathematical tool kit to compare experimental data and NRS code simulations;x

returns quantitative FOM associated with individual and suite comparisons;xaccommodates the multiple data types encountered in NRS environments;x

incorporates experimental uncertainty in the assessment;x

provides “event windowing” capability;x

accommodates inconsistencies between measured and computed independent variables(e.g. different time steps);x

provides a framework for automated, tunable weighting of component measures in theconstruction of overall FOM accuracy.

ACAP is a PC- and UNIX-station-based application that can be run interactively on PCs with
Windows 95/98/NT, in batch mode on PCs as a WINDOWS console application, or in batch mode on
UNIX stations as a command line executable. The D’Auria Fast Fourier Transformation (FFT) andmean error (ME) methods were used for the FOM calculations for time histories [12,13]. Figure 3-1
shows a snapshot of the FOM configuration for ACAP calculations in Exercise 2 of the benchmark.
These methods are advanced techniques for analysis of time history data. Eqs. (3.9) to (3.14) represent
the theory portion of the D’Auria FFT and ME methods [13].
Figure 3-1. FOM configuration in ACAP

52

The Discrete Fourier Transform (DFT) can be calculated as:
(3.9)

1 N
) i e 2 SImi N
N i1

¦

ˆm
)

The D’Auria measures are as follows:x

average amplitude (AA):M¦(3.10)

P̂m  Ôm

AA  m 0 M

¦ Ô

m

m 0

x

weighted frequency (WF):(3.11)

M¦ Pˆ  Oˆ x f
m

WF

m

m

m 0

M

¦ Pˆ  Oˆ
m

m

m 0

Mean error (ME) can be computed as:

ME

1 ­N
½
®¦ Oi  Pi ¾
N ¯i 1¿(3.12)

where N is the number of data values, i is the sample index, )i is the values spaced 't apart, Oi is thei-th datum in experimental set Pi is the i-th datum in computed set, and fm is the frequency of mode m.
The D’Auria and ME FOM equations are outlined below:

FOM D ’AURIA(3.13)1
2§ª¨ AA 2  § K · º
¨
¸ »
¨¨ «
© WF ¹ »¼
«
¬
©

1/ 2

·
 1¸¸
¸
¹

where K is the constant used to weight the relative importance of the weighted frequency (WF)
relative to the average amplitude (AA).

FOM ME1(3.14)ME  1

Note that the statistical FOM given by Eqs. (3.3) and (3.6) differs from the FOM calculated using
Eqs. (3.13) and (3.14). FOM indicates that the participant results are closer to the reference solution if
the former FOM [given by Eqs. (3.3) and (3.6)] is closer to zero, while the later FOM [given by
Eqs. (3.13) and (3.14)] has to be closer to unity (1) to indicate better agreement.

53

The following procedure was applied during the ACAP calculation:x

Step 1: Data synchronisation was necessary due to the varying time steps of submitted
participant data for the time histories. Regarding synchronisation, the cubic spline function
was written in Visual Basic for Applications (VBA) and macro module inserted into theMicrosoft Excel workbook file [14]. Then, all participants’ results were set to a time intervalof precisely 6 ms. The inserted module was outlined in the previous volume [3].

xStep 2: In order to avoid the effects of differing participant initialisation on the comparative
analysis, actual values of the time history data were set to zero and they were called “deltachanges”. The delta changes were calculated by subtraction of initial value (at time zero) fromthe all other transient values (as shown below where t represents time in seconds).
Delta Changes (t = 0.000) = Value (t = 0.000) – Value (t = 0.000)
Delta Changes (t = 0.006) = Value (t = 0.006) – Value (t = 0.000)
Delta Changes (t = 0.012) = Value (t = 0.012) – Value (t = 0.000)
Delta Changes (t = 0.018) = Value (t = 0.018) – Value (t = 0.000)
Delta Changes (t = 0.024) = Value (t = 0.024) – Value (t = 0.000)
Delta Changes (t = 0.030) = Value (t = 0.030) – Value (t = 0.000)…
and so on.

x Step 3: Using ACAP’s user-friendly interactive options, a configuration must be selected andFOM calculation should be performed in accordance with the reference data.
3.3 Statistical analysis of normalised parameters
In the Exercise 2 comparative analysis, some parameters require special attention, because undercertain circumstances the normalisation will become skewed. These parameters are:x

normalised axial power (snapshot) at the time of maximum power before scram;x

relative axial power for FAs 75 and 367 (snapshot) at the time of maximum power before
scram;

x

normalised radial power (snapshot) at the time of maximum power before scram;x

normalised axial power (snapshot) at the end of the transient (5 s);x

relative axial power for FAs 75 and 367 (snapshot) at the end of the transient (5 s);xnormalised radial power (snapshot) at the end of the transient (5 s).

Treating each of these parameters separately, the procedure for generating a comprehensive
analysis that preserves the normalisation will be discussed.
3.3.1 Two-dimensional (2-D) core-averaged radial power distribution
This parameter is collected for the transient snapshots. The goal of the statistical analysis is toderive an average normalised power for each assembly:54

(3.15)

pi
p FA

N Pi

where, for N participants, pi , the average power density in radial assembly location i, is:pi(3.16)

1 N
¦ pij
N j1

and p FA , the averaged assembly power density, is:(3.17)

1 N¦ pFA, j
N j1

p FA
Thus:

(3.18)

N

¦p

N Pi

ij

j 1
N

¦p

FA , jj 1

In the initial steady-state case the total core power is specified as Q = 2 030 MWt for the hot fullpower (HFP) conditions, so that the average power per fuel assembly is the same for all participants and:(3.19)

N

N Pi

¦p
1

ij

j 1

N p FA,c

1 N pij¦N j 1 p FA,c

1 N
¦ NPijN j1

where, given the total number of assemblies, M, is 764:

p FA,cQ
M(3.20)

Thus, for the transient snapshots, where total power level and power per assembly vary among theparticipants, the following corrected procedure must be applied.
x

Step 1: Convert normalised values into absolute values. Absolute values are achieved bymultiplying the normalised value in each 2-D cell for each participant by the average power
per assembly for the same participant, where the latter value is the total core power for thatparticipant divided by 764 fuel assemblies.

x

Step 2: Calculate participant-averaged average power per assembly. All participant values
for total core power are averaged by the standard averaging technique to get the average core
power. This value is divided by the number of fuel assemblies, 764, to get the average power
per assembly, averaged over all participants. The same result can be obtained by averaging
directly, with Eq. (3.1), all participants’ values for average power per assembly.
55

x

Step 3: Generate mean solution using absolute values. The map of absolute mean values isgenerated by the standard averaging procedure.

x

Step 4: Re-normalise mean solution. Normalisation is attained by dividing each cell of theabsolute map by the average power per assembly calculated in Step 2.

Unfortunately, the standard deviation and figure of merit can not be included in a normalised
form, since the meaning of these statistical functions would be lost. Therefore, three maps must be
provided instead of the usual two. Mean values and standard deviations are provided using absolute
powers, and are accompanied by maps of the normalised mean values. Participant deviations andfigures of merit are calculated relative to the absolute mean solution.
3.3.2 One-dimensional (1-D) core-averaged axial power distribution
This parameter is also collected for transient snapshots, and the final specifications require that all
participants divide the core into 24 equal axial nodes. Where this is the case, the statistical analysis
will be similar to that for the radial power distribution. The normalised mean axial power for a given
axial node is given by:(3.21)

p z ,iN Pz ,ipz

where, p z ,i , the average power density at axial layer i, is given by:

p z ,i1 N¦ p z ,ij
N j1

(3.22)

where p z , the core-averaged axial power density, is:pz

1 N p FA, j¦
N j 1 24

1 N
¦ pz, jN j1

(3.23)

Thus:(3.24)N¦p
N Pz ,i

z ,ij

j 1

p FA, j

N

¦ 24
j 1

For the steady-state cases, where the total core power level, Q, and average power per assemblyare constant for all participants:

N Pz ,i

1 1 N p z ,ij¦
N 24 j 1 p FA, j

56

1 N¦ NPz ,ij
N j1

(3.25)

As a result, the standard techniques for 1-D distribution can be applied for the steady-state cases;
however, for the transient snapshots, where the average power per assembly will vary among theparticipants, the following procedure must be utilised:x

Step 1: Convert normalised values into absolute values. Absolute values are achieved bymultiplying the normalised value in each axial node for each participant by the average power
per node in the average assembly for the same participant, where the latter value is the total
core power for that participant divided by 764 fuel assemblies and 24 axial nodes.

x

Step 2: Calculate participant-averaged average power per assembly. All participant values
for total core power are averaged by the standard averaging technique to get the average core
power. This value is divided by the number of fuel assemblies, 764, to get the average power
per assembly, which is finally divided by 24 to get the average power per axial node, averaged
over all participants. The same result can be obtained by averaging directly all participants’values for average power per axial node, using Eq. (3.1).

x

Step 3: Generate mean solution using absolute values. The table of absolute mean values isgenerated by the standard averaging procedure.

x

Step 4: Re-normalise mean solution. Normalisation is attained by dividing each cell of theabsolute map by the average power per node calculated in Step 2.

Once again, the standard deviation and figure of merit can not be included in a normalised form
and two axial tables will be provided. Absolute mean values and standard deviations are provided alongwith re-normalised mean values in one table. Participant deviations and figures of merit, calculated
relative to the absolute values, are presented in a second table. It should be noted that this procedure
could be applied only where the participants have used 24 equal axial layers. Results from participants
who do not adhere to this specification must first have their data converted to 24 equal nodes via acell-volume weighting procedure.
3.3.3 One-dimensional (1-D) core-averaged axial power distribution for FAs 75 and 367
For maximum power before scram and at the end of transient snapshot cases, one-dimensionalcore-average power distribution is collected for FAs 75 and 367. It is treated in a similar manner as forthe core-averaged axial power. Again, the specifications request that the fuel assembly be divided into
24 equal nodes. For the transient snapshots, the power in the assemblies 75 and 367 varies among theparticipants and the average normalised power per node is given by:(3.26)N¦p
N Pz ,i

z ,ij

j 1

p FA, j

N

¦ 24
j 1

where the total power in FAs 75 and 367 can be extracted from each participant’s 2-D core-averaged
radial power distribution. The following method must be applied in every transient case:57

x

Step 1: Convert normalised values into absolute values. The absolute values are found by
multiplying the normalised value in each axial node for each participant by the average power
per 3-D node in the core for the same participant, where the latter value is the total core power
divided by 764 assemblies and 24 axial nodes.

x

Step 2: Calculate participant-averaged average power per assembly. All participant values
for total core power are averaged by the standard averaging technique to get the average core
power. This value is divided by the number of cells in the core – 764 assemblies times
24 axial layers – to get the average power per 3-D node, averaged over all participants.

x

Step 3: Generate mean solution using absolute values. The map of absolute mean values isgenerated by the standard averaging procedure.

x

Step 4: Re-normalise mean solution. Normalisation is attained by dividing each cell of theabsolute map by the average power per node calculated in Step 2.

As with the previous two parameters, the results are reported in the form of mean values andstandard deviations of the absolute values along with a re-normalised mean solution. Participant
deviations and figures of merit are again calculated relative to the absolute mean solution.
3.3.4 Multiple code dependencies
It has been noted that some sets of results that have been submitted for this exercise are not fully
independent of each other. That is, certain participants have submitted multiple sets from codes thatdiffer from each other to varying degrees. In some cases, the differences are significant, and involvequite different kinetics models. In other cases, the differences are subtler. In the case of codes with
only subtle differences, it may not be appropriate to treat the results as fully separate, and therefore
subject to independent treatment in the averaging techniques described above.
To account for this circumstance, a two-step averaging process has been developed whereby setsof results that are determined to be “dependent” on each other are first averaged together, and thesubsequent mean participant values are then included in the final averaging process. However, after
examining the descriptions of each code that has been used in developing the submitted results, it wasdetermined that such a two-step averaging process is not necessary in the present case, and it has notbeen applied.

58

Chapter 4
RESULTS AND DISCUSSION

The results, presented in this chapter, demonstrate the importance of the neutronic and coupledneutronic/thermal-hydraulics core modelling for analysis of pressure transients for BWRs. The tables
and the figures of this chapter provide a comparison of the participants’ results with the reference
solutions as well as a discussion of observed agreement or disagreement.
It should be reminded that the second exercise consists of performing coupled-core boundary
conditions calculations. The purpose of the second exercise is to test and initiate the participants’ coremodels. Thermal-hydraulic boundary conditions are provided to the participants from the benchmark
team. The thermal-hydraulic core boundary conditions provided are the core inlet pressure, core exit
pressure, core inlet temperature and core inlet flow. In summary the second exercise is to perform a
coupled 3-D kinetics/T-H calculation for the reactor core using the PSU-provided boundary conditions
at core inlet and exit. Three-dimensional two-group macroscopic cross-section libraries are provided
to the participants. The core inlet flow is provided in two formats: total core flow as a function of timeand radially distributed flow as a function of time for 33 channels. In addition, the benchmark teamprovided the participants with normalised power vs. flow correlations for the different assembly types
based on the detailed modelling in which each assembly represented by a thermal-hydraulic channel
for the initial steady-state conditions. The studies performed by the benchmark team indicated thatthese correlations also apply reasonably well during the transient, which provided an opportunity forthe participants to develop their own core coupled spatial mesh overlays.
The participants in Exercise 2 are required to provide steady-state results for two different
conditions: hot zero power (HZP) and hot power (HP) conditions. For transient analysis, in addition totime histories, the participants are asked to submit results for two snapshots of the transient, one at thetime of maximum power before scram and the other is at the end of transient.
The outline of this chapter is as follows:x Steady-state results:–

HZP results;–

HP results.

x Transient results:–

time histories;–

results for the snapshot at the time of maximum power before scram;–

results for the snapshot at the end of transient.

The comparison is made for the parameters that have important effects on the steady-state andtransient scenarios. Statistical analysis was performed for each submitted parameter based on the59methodology extensively described in Chapter 3. The tables show values of the standard deviation andthe figure of merit for each participant’s result for a given parameter. The figures included in thischapter show the scatter of data about the reference solution.
The complete set of reference results with associated standard deviations are given in Appendix C
while the complete set of the deviations of submitted results for all parameters from the reference
solutions for each participant is given in Appendix D. This appendix is divided into four parts: D.1(integral parameters), D.2 [one-dimensional (1-D) axial distributions], D.3 [two-dimensional (2-D)
radial distributions] and D.4 (system and core averaged time histories). It should be noted that
Appendix C and Appendix D are only available in electronic format in the CD-ROM (electronic)
version of this report.
4.1 Steady-state results
Steady-state results consist of the results from HZP and HP conditions. For each condition,
participants are asked to submit the following parameters:
x

keff;

x

core averaged relative axial power distribution;x

relative power distributions for fuel assemblies 75 (rodded bundle) and 367 (un-rodded
bundle) – numbering the core fuel region from top to bottom and from left to right;

xradial power distribution – two-dimensional assembly normalised power distribution (for the
3-D kinetics options).

x

core averaged axial void fraction distribution (excluding the HZP state).

Table 4.1 presents the number of channels utilised in the thermal-hydraulics core models of theparticipants and the type of power model used in their calculations. This information should be taken
into account during the discussion of the participants’ deviations from the reference solutions. The
term “total” in the table below refers to the total power, which includes power from decay heat andfission power together.
4.1.1

Hot zero power (HZP) results

An additional steady state was defined in the framework of the second exercise – HZP state with
fixed thermal-hydraulic feedback. This allows for “clean” initialisation of the core neutronics models
and cross-section modelling algorithms.
The results in this section should be considered together with Table 4.2. Important modellingissues were identified such as: the impact of using assembly discontinuity factors (ADF model), which
are also provided to the participants in a similar table format as for the two group cross-sections; thexenon correction to account for the actual xenon concentration distribution at the initial steady-state
conditions of the turbine trip test 2 (xenon model); the spatial distribution of the decay heat (decay
model); and the bypass density correction (bypass model) in the cross-section feedback modelling toaccount for the deviations of bypass density from the saturated value used in the cross-section
homogenisation since the cross-sections are generated by homogenising the bypass region associatedwith the lattice. Although the xenon, bypass and decay models are irrelevant for HZP conditions, theutilisation of BWR type ADF and ADF rotation modelling are important for the results especially forkeff values and normalised radial power distributions.
60

Table 4-1. Number of channels used and power submitted by the participantsParticipant
CEA-33
CEA-764
FANP
FZR
GRS
IBER
NFI
NUPEC
PSI-A
PSI-B
PSI-C
PSU
TEPSYS
UPI
UPV
VTT
WES

No. of channels
33
764
33
764
764
1
33
33
33
33
764
33
33
33
33
764
764

Power submitted
FissionFissionFission
Total
Fission
Total
FissionFissionFissionFissionFission
Total
Total
Total
Total
FissionFissionTable 4-2. Models used at HZPParticipant
CEA-33
CEA-764
FANP
FZR
GRS
IBER
NFI
NUPEC
PSI-B
PSI-C
PSU
TEPSYS
UPI
UPV
VTT
WES

Xenon
No
No
No
No
No
No
Yes
No
No
No
No
No
Yes
Yes
No
No

ADF
No
No
Yes
Yes
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Bypass
No
No
Yes
No
No
No
No
No
Yes
Yes
No
No
Yes
Yes
Yes
Yes

Decay
No
No
Yes
No
No
No
No
No
No
No
Yes
Yes
Yes
Yes
Yes
No

Figure 4-1 presents a graphical comparison of participants’ keff predictions with the mean value asa reference value while Table 4-3 provides keff values with the mean and standard deviation. The
maximum deviated result is less thaQ  , showing that all participants’ results agree well with thereference (mean) solution. The reason for discrepancies of CEA-33, CEA-764 and GRS results fromthe mean value can be attributed to the lack of ADF modelling.
Figure 4-2, Figure 4-3 and Figure 4-4 show a very good agreement of the participants’ results for
1-D relative axial power distributions while Figures 4-5 and 4-6 show the mean of the radial power
distribution and its standard deviation in a graphical format. The only significant deviation is observed61for UPI results in Figure 4-4. The latter plot gives an idea about the observed deviations in radial
power distribution predictions. Since the participants use the same cross-section library and interpolation
routine and the same radial nodalisation (one node per assembly) these deviations are coming from thedifferent neutronics methods and utilisation or not of the ADFs. The mean values and standard
deviations can be found in Appendix C and the deviations of each participant’s solutions from themean value can be found in Appendix D.
Figure 4-1. HZP keff
Average=0.995779

1.002
1.000
0.998

0.994
0.992
0.990
0.988

Table 4-3. HZP keff
HZP
keff
0.991560
0.991560
0.997880
0.996910
0.991580
0.996788
0.994500
0.997200
0.998070
0.997190
0.9972100.999500
0.990940
0.998390
0.997410
0.995779
0.002923

CEA-33
CEA-764
FANP
FZR
GRS
PSU
NFI
NUPEC
PSI-B
PSI-C
TEPSYSUPIUPVVTTWESTINGHOUSE
Average =Standard deviation (V) =

62

HO
US
E

NG

3DUWLFLSDQWV

Participant

VT
T

PV
U
W

ES
TI

PS
TE U
PS
YS
U
.P
IS
A

FI
U
PE
C
PS
PS
I-C
I-B
O
R
ET
R
AN

N

N

S
G
R

EA

C

EA
/

D
EN

-3
/D
3
EN
-7
64
FA
NP
FZ
R3D

0.986

C

.HII

0.996

Deviation(ei)-0.004219-0.004219-0.002101-0.001131-0.004199-0.001009-0.001279-0.001421-0.002291-0.001411-0.001431-0.003721-0.004839-0.002611-0.001631

Figure 4-2. Core average relative axial power distribution at HZP
3.0
CEA-33
CEA-764

normalized axial power

2.5

FANP
FZR
GRS

2.0

NFI
NUPEC
PSI-B

1.5

PSI-C
PSU

1.0

TEPSYS
UPI
UPV

0.5

VTT
WES

0.0

AVERAGE

0

5

10

15

20

25

axial node

Figure 4-3. Relative power distribution for FA 75 at HZP
3.0

CEA-33

Normalized Axial Power

CEA-764
FANP

2.5

FZR
IBER

2.0

NFI
NUPEC
PSI-A

1.5

PSI-C
PSU
TEPSYS

1.0

UPI
UPV

0.5

VTT
WES
Average

0.0
0

5

10

15

20

Axial Node

63

25

30

Figure 4-4. Relative power distribution for FA 367 at HZP
3.0E+00

CEA-33
CEA-764

Normalized Axial Power

2.5E+00

FANP
FZR
NFI

2.0E+00

NUPEC
PSI-A

1.5E+00

PSI-C
PSU

1.0E+00

TEPSYS
UPI
UPV

5.0E-01

VTT
WES

0.0E+00
0

5

10

15

20

25

30

Average

Axial Node

Figure 4-5. Mean radial power distribution at HZP (average of participants)
28

1.500-1.750
1.250-1.500

25

1.000-1.250
0.750-1.000
0.500-0.750
0.250-0.500

190.000-0.250

7

22
16
13
10
4
1
1

4

7 10 13 16 19 22 25 28

Channels64Figure 4-6. Standard deviation of radial power distribution at HZP
29
25
21
17
13
9

0.25-0.3
0.2-0.25
0.15-0.2
0.1-0.15
0.05-0.1
0-0.0551
1 4 7 10 13 16 19 22 25 28

Channels
4.1.2 Hot power (HP) results
Hot power refers to the initial conditions of turbine-trip-test-at the EOC 2. Similar to the previous
section, the results of this section should be considered together with Table 4-4. Core bypass flow
density correction, xenon correction and BWR-type ADF and ADF rotation models are important for
the HP results while the decay heat modelling is important for the transient. In particular, theutilisation of ADFs is important for keff values and radial power distribution predictions, and the core
bypass flow density correction affects the axial power distributions.
Figure 4-7 presents a graphical comparison of participants’ keff predictions with the mean value asa reference value, while Table 4-5 provides keff values with the mean and standard deviation. If the
NETCORP solution is excluded as an outliner, the maximum deviated result can be found to be lessthen 2V that also shows a good agreement of all of the rest of participants’ results with the reference(mean) solution.
The most challenging part of the BWR steady-state analysis is the prediction of the void fraction
distribution. Participants’ core averaged axial void fraction distribution results are given in two
figures, Figure 4-8 and Figure 4-9, while the mean and standard deviation are given in Figure 4-10.
In principal the core averaged void fraction distribution results have a good agreement; however,
PSI-A and PSI-B have noticeable deviation at the lower part of the core. From Figure 4-10 it can beseen that the standard deviation increases in the lower (bottom) part of the core which indicatesdifferences in the void modelling in terms of sub-cooled boiling and vapour slip. Subsequently these
deviations are propagated in the axial power profile predictions due to the void feedback mechanism(see Figures 4-11, 4-12 and Figure 4-13). The axial power profile predictions are also affected byutilisation or not of core bypass flow density correction
The comparisons of participants’ relative axial power profile solutions for FAs 75 and 367 aregiven in Figures 4-14 through 4-19 and they show more pronounced deviations as compared to thecore average axial power profile results. This is especially valid for the rodded bundle 75. The reason
for such increased deviations are that at HP conditions the number of T-H channels and spatial meshoverlays with neutronics core model effect the local power predictions. The mean and standard
deviation of radial power distribution at HP are given in Figures 4-20 and 4-21. In addition to utilisation65

or not of ADFs the spatial mesh overlays also affect the radial power distribution predictions at HP.
The utilisation or not of the xenon correction also contributes to observed deviations. The mean values
and standard deviations of the submitted results can be found in Appendix C and the deviations ofeach participant’s prediction from the mean solution can be found in Appendix D.
Table 4-4. Models used at HP
Participant
CEA-33
CEA-764
FANP
FZR
GRS
IBER
NFI
NUPEC
PSI-A
PSI-B
PSI-C
PSU
TEPSYS
UPI
UPV
VTT
WES

Xenon
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No

ADF
No
No
Yes
Yes
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Bypass
Yes
Yes
Yes
Yes
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Decay
Yes
Yes
Yes
Yes
Yes
No
No
Yes
No
No
No
Yes
Yes
Yes
Yes
Yes
No

Figure 4-7. HP keff
1.015

Average=1.003943
1.010
1.005

I 1.000
H.
0.995
0.990
0.985

66

U
W
P
E
V
S
TI
N V
G T
H T
O
U
S
E

P
S
TE U
P
S
Y
S
U
.P
IS
A

N
FI
N
U
P
E
C
P
S
I-A
P
S
I-C P
O SI
R -B
E
TR
A
N

C
E
A
/D
C
E
FR EA
N
/D -33
A
M
E
N
A
TO -7
M 64
E
A
N
P
FZ
R
-3
D
IB
G
E
R RS
D
R
O
LA
N
E
TC
O
R
P

0.980

Table 4-5. HP keff
Participant
CEA-33
CEA-764
FANP
FZR
GRS
IBER
NETCORP
NFI
NUPEC
PSI-A
PSI-B
PSI-C
PSU
TEPSYS
UPI
UPV
VTT
WES
Average =Standard deviation (V) =HP keff
0.997330
0.995440
1.009890
1.004100
1.000740
1.006437
0.990400
1.005300
1.009900
1.008150
1.008830
1.0071301.004800
1.006500
1.005860
1.005300
1.002410
1.002450
1.003943
0.005189

Deviation (ei)-0.006613-0.008503-0.005947-0.000157-0.003203-0.002495-0.013543-0.001357-0.005957-0.004207-0.004887-0.003187-0.000857-0.002557-0.001917-0.001357-0.001533-0.001493

Figure 4-8. Core average axial void fraction distribution at HP (Group 1)
0.70
CEA-764

0.60
FANP
FZR

Void Fraction

0.50

IBER

0.40

GRS
NETCORP

0.30
NFI
AVERAGE

0.20

0.10

0.00
0

3

6

9

12

Axial Nodes

67

15

18

21

24

Figure 4-9. Core average axial void fraction distribution at HP (Group 2)
0.70
NUPEC
PSI-A

0.60

PSI-B
PSI-C

Void Fraction

0.50

PSU
TEPSYS
UPI

0.40

UPV
VTT

0.30

WES
AVERAGE

0.20

0.10

0.00

0

3

6

9

12

15

18

21

24

Axial Nodes

Figure 4-10. Core average axial void fraction at HP (mean and deviation)
0.70

0.60

Void Fraction

0.50

0.40

0.30

0.20

0.10

0.00
0

3

6

9

12

Axial Nodes

68

15

18

21

24

Figure 4-11. Core average relative axial power distribution at HP (Group 1)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2

CEA-33

CEA-764

FANP

GRS

NFI

NUPEC

PSI-A

PSI-B

PSI-C

VTT

WES

AVERAGE

0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-12. Core average relative axial power distribution at HP (Group 2)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
FZR

PSU

TEPSYSUPIUPVAVERAGE

0.4
0.2
0.0
0

5

10

15

Axial Nodes

69

20

25

Figure 4-13. Core average relative axial power distribution at HP (mean and deviation)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-14. Relative power distribution for FA 75 at HP (Group 1)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4

CEA-33

CEA-764

FANP

NFI

NUPEC

PSI-A

PSI-C

VTT

WES

AVERAGE

0.2
0.0

0

5

10

15

Axial Nodes

70

20

25

Figure 4-15. Relative power distribution for FA 75 at HP (Group 2)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2

FZR

GRS

IBER

PSU

TEPSYSUPIUPVAVERAGE

0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-16. Relative power distribution for FA 75 at HP (mean and deviation)
1.6

1.4

Normalized Power

1.2

1.0

0.8

0.6

0.4

0.2

0.0
0

5

10

15

Axial Nodes

71

20

25

Figure 4-17. Relative power distribution for FA 367 at HP (Group 1)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2

CEA-33

CEA-764

FANP

NFI

NUPEC

PSI-A

PSI-C

VTT

WES

AVERAGE

0.0

0

5

10

15

20

25

Axial Nodes

Figure 4-18. Relative power distribution for FA 367 at HP (Group 2)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2

FZR

GRS

PSU

TEPSYSUPIUPVAVERAGE

0.0
0

5

10

15

Axial Nodes

72

20

25

Figure 4-19. Relative power distribution for FA 367 at HP (mean and deviation)
1.6

1.4

Normalized Power

1.2

1.0

0.8

0.6

0.4

0.2

0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-20. Mean radial power distribution at HP (average of participants)

28
25

1.250-1.500
1.000-1.250
0.750-1.000
0.500-0.750
0.250-0.500
0.000-0.250

22
19
16
13
10
7
4
1
1

4

7 10 13 16 19 22 25 28

Channels73

Figure 4-21. Standard deviation of radial power distribution at HP

29
25
21
17
13
9
5

0.40-0.45
0.35-0.40
0.30-0.35
0.25-0.30
0.20-0.25
0.15-0.20
0.10-0.15
0.05-0.10
0.00-0.05

1
1 4 7 10 13 16 19 22 25 28

Channels
4.2 Transient results
The requested output in Exercise 2 in terms of transient results consists of core averaged time
histories, snapshot at the time of maximum power before scram, and snapshot at the end of the 5 stransient. Participants are asked to submit the following parameters for each relevant case:x Time histories:– core power;– total reactivity;– Doppler reactivity;– void reactivity.
x Snapshot at the time of maximum power before scram:– time of maximum power before scram;– core averaged relative axial power distribution;– relative power distribution for FA 75;– relative power distribution for FA 367;
– radial power distribution.
x Snapshot at the end of the transient:– core averaged relative axial power distribution;– relative power distribution for FA 75;– relative power distribution for FA 367;
– radial power distribution.

74

4.2.1 Time histories
In transient analyses of Exercise 2, core thermal-hydraulic boundary conditions model are utilised
to test and initialise the coupled core response. The complete PB2 system thermal-hydraulic model isconverted to a core thermal-hydraulic boundary condition model by defining inlet and outlet
thermal-hydraulic boundary conditions. The simulated transient and the comparison of submitted
results, presented in this section, not only provide an opportunity to understand the core reactivity
feedback phenomena during a turbine trip transient but also allow for a comprehensive testing of thecoupled neutronics/thermal-hydraulics core models.
The plots and tables given in this section provide a comparison of the participants’ results for theparameters that have the greatest effect on the Exercise 2 analysis. For this reason only core averaged
time histories were requested from the participants to be submitted. These histories are core power,
total reactivity, Doppler reactivity and void reactivity.
Please note that the participants have preformed in advance sensitivity studies on temporal coupling
schemes and time step sizes for obtaining converged solutions [16]. The results in this section should
be considered together with the Table 4-6 since all of the models given in the table are important for
the transient calculations.
Table 4-6. Models used in transient calculation
Participant
CEA-33
CEA-764
FANP
FZR
GRS
IBER
NFI
NUPEC
PSI-A
PSI-B
PSI-C
PSU
TEPSYS
UPI
UPV
VTT

Xenon
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

ADF
No
No
Yes
Yes
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Bypass
Yes
Yes
Yes
Yes
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Decay
Yes
Yes
Yes
Yes
Yes
No
No
Yes
No
No
No
Yes
Yes
Yes
Yes
Yes

The mean time histories are provided in this section as well as in Appendix C (supplied on the
CD-ROM). The standard deviations are represented as error bounds for the time histories. The figuresof merit are presented in the tables of this section. Additionally, the participant deviations and figuresof merit are presented in Appendix D (also supplied on the CD-ROM), and are listed in the same orderas the reference solutions.

75

In each case the figures (Figures 4-22 through 4-37) graphically illustrate the agreement or
disagreement of participants’ predictions. Statistical evaluation is employed to generate a mean
solution, which is also shown in the plots.
Core power time evolutions are presented in two groups (fission or total) depending on thesubmitted core power type. Comparisons of the predictions of fission power evolution and the total
power evolution calculated by each code throughout the transient (up to 5 seconds) are shown in
Figures 4.22 and 4.24, while Figures 2.23 and 4.25 are zooming on the first one second of the transient
where the power peak occurs. Table 4-7 provides figure of merit (FOM) for two different methods,
D’Auria FFT and mean error.
When analysing the power history results it has to be taken into account that in the TT2 test, thethermal-hydraulic feedback alone limited the power peak and initiated the power reduction. The void
feedback plays the mayor role while the Doppler feedback plays a subordinate role. The reactor scramthen inserted additional negative reactivity and completed the power reduction and eventual core
shutdown. The scram initiation time and the speed of the rod insertion were specified. The scram
initiation time was specified since one of the objectives of the benchmark is to test coupled codes’
capabilities to predict or not that the thermal-hydraulic feedback alone limits the power peak andinitiates the power reduction. The power response to the pressure wave caused by the turbine trip
(which is “seen” by the participants’ core models through the provided core boundary conditions) interms of timing and magnitude of power peak during the transient as predicted by different codes is afunction of the total reactivity time evolution. In Figure 4-23 (the fission power group), the predicted
power peak values of four participants, CEA-33, CEA/DEAN-764, PSI-B and NFI, are higher than themean value. In total power group (Figure 4-24), only the TEPSYS solution differs from the others, which
form a cluster. In reality, fission power (Figure 4-23) is slightly lower than total power which accounts
decay heat. In general, the power history results are in a good agreement including TEPSYS results.
Figure 4.26 through Figure 4.37 show comparisons of the predictions of the total, Doppler andvoid reactivity throughout the transient. The total reactivity has three components – the negative
tripped rod reactivity, moderator density (void) reactivity and Doppler feedback reactivity. The total
reactivity behaviour before the scram is dominated by the void reactivity feedback mechanism. The
fuel heat transfer parameters such as the UO2 conductivity and gap conductivity and direct heating(2% to in-channel flow and 1.7% to bypass flow) were specified. The sources of modelling uncertainties
in the void feedback model were identified in terms of sub-cooled boiling and vapour slip. Different
density correlations and standards for water/steam property tables incorporated into the codes havealso an important role on the void reactivity predictions by such codes (see Figures 4.34 and 4.37 andTable 4-10). As mentioned above the Doppler feedback plays a subordinate role. The discrepancies inthe Doppler reactivity time history predictions (see Figures 4.30 and 4.33 and Table 4-9) come fromthe discrepancies in the results for core averaged Doppler temperature time evolution. The later are
due to the different relations used for calculating the Doppler fuel temperature, and the radial and axial
nodalisation of the heat structure used (fuel rod). Discrepancies at the end of the transient are due todifferent predictions of the tripped control rod reactivity by the participants’ codes.

76Figure 4-22. Transient power (fission)
1.2E+10

CEA-33Fission Power Delta Changes (W)

1.0E+10

CEA-764FANP

8.0E+09

GRS
6.0E+09

NFI
NUPEC

4.0E+09

PSI-B
2.0E+09

PSI-C
VTT

0.0E+00

Average-2.0E+09-4.0E+09

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

time (s)Figure 4-23. Transient power (fission – zoom)
1.2E+10

CEA-33
CEA-764

Fission Power Delta Changes (W)

1.0E+10FANP
GRS

8.0E+09

NFI
NUPEC

6.0E+09

PSI-B
PSI-C

4.0E+09

VTT
Average

2.0E+09

0.0E+00

0.5

0.6

0.7

0.8

time (s)

77

0.9

1.0

Figure 4-24. Transient power (total)
1.2E+10

FZR-3D

1.0E+10PSU
6.0E+09

TEPSYS
UPV

4.0E+09

AVERAGE
2.0E+09

0.0E+00

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

-2.0E+09-4.0E+09

time (s)Figure 4-25. Transient power (total – zoom)
1.2E+10

FZR-3D

Total Power Delta Changes (W)Total Power Delta Changes (W)IBER
8.0E+09

1.0E+10IBER
PSU

8.0E+09

TEPSYS
UPV

6.0E+09

AVERAGE
4.0E+09

2.0E+09

0.0E+00
0.5

0.6

0.7

0.8

time (s)

78

0.9

1.0

Table 4-7. Transient power, figure of merit
Fission power used
D’Auria
Mean error
FFT(ME)
0.7566
0.99640.78420.99840.79530.99940.74470.99740.76020.99850.7914
0.99710.62340.98940.69680.99520.8231
0.99820.83900.9972

CEA-33
CEA-764
FANP
GRS
NFI
NUP
PSI-A
PSI-B
PSI-C
VTT

FZR
IBER
PSU
TEPSYS
UPV

Total power used
D’Auria
Mean error
FFT(ME)
0.76090.99220.72680.99740.7676
0.9976
0.69630.99790.7852
0.9925Figure 4-26. Total reactivity
0.05

Reactivity (dk/k)

0.00

-0.05
CEA-33
CEA-764
FZR

-0.10

GRS
NFI
PSI-A

-0.15

PSI-B
PSI-C
TEPSYS-0.20

VTT
AVERAGE

-0.25
0.0

1.0

2.0

3.0

time (s)

79

4.0

5.0

Figure 4-27. Total reactivity (zoom)
0.005
CEA-33
CEA-764
FZR

0.004

GRS

Reactivity (dk/k)

NFI
PSI-A
PSI-B

0.003

PSI-C
TEPSYSVTTAVERAGE

0.002

0.001

0.000
0.4

0.5

0.6

0.7

0.8

0.9

1.0

time (s)Figure 4-28. Total reactivity (mean and deviation)
0.05

Reactivity (dk/k)

0.00

-0.05

-0.10
(+) Deviation-0.15

Average(-) Deviation

-0.20

-0.25
0.0

1.0

2.0

3.0

time (s)

80

4.0

5.0

Figure 4-29. Total reactivity (mean and deviation – zoom)
0.006
0.004

Reactivity (dk/k)

0.002
0.000
-0.002(+) Deviation-0.004

Average(-) Deviation-0.006-0.008-0.010
0.4

0.5

0.6

0.7

0.8

0.9

1.0

time (s)Table 4-8. Total reactivity, figure of merit

CEA-33
CEA-764
GRS
NFI
PSI-A
PSI-B
PSI-C
VTT
FZR
TEPSYS

D’Auria FFT
0.81410.81710.67120.85770.84420.83870.88610.82340.88710.767081

Mean error (ME)
0.94130.94650.81270.95920.98380.98490.99880.9574
0.99100.8963

1.1

1.2

Figure 4-30. Doppler reactivity
0.004
0.003

Reactivity (dk/k)

0.002
0.001
NFI

0.000

PSI-A
PSI-B

-0.001PSI-C
TEPSYS-0.002AVERAGE-0.003
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

time (s)Figure 4-31. Doppler reactivity (zoom)
0.0001
NFI
PSI-A-0.0001

Reactivity (dk/k)

PSI-B
PSI-C

-0.0003

TEPSYSAVERAGE-0.0005-0.0007-0.0009-0.0011
0.5

0.6

0.7

0.8

0.9
time (s)

82

1.0

1.1

1.2

Figure 4-32. Doppler reactivity (mean and deviation)
0.004

Reactivity (dk/k)

0.003
0.002
0.001
0.000
(+) Deviation-0.001

Average(-) Deviation-0.002-0.003
0.0

1.0

2.0

3.0

4.0

5.0

time (s)Figure 4-33. Doppler reactivity (mean and deviation – zoom)
0.0005(+) Deviation

0.0003

Average

0.0001

Reactivity (dk/k)(-) Deviation-0.0001-0.0003-0.0005-0.0007-0.0009-0.0011-0.0013-0.0015
0.4

0.5

0.6

0.7

0.8

time (s)

83

0.9

1.0

1.1

1.2

Table 4-9. Doppler reactivity, figure of merit
D’Auria FFT
0.8636
0.84320.88930.85610.7693

NFI
PSI-A
PSI-B
PSI-C
TEPSYS

Mean error (ME)
0.98270.96280.9901
0.97270.9633Figure 4-34. Void reactivity
0.070
NFI

0.060

PSI-A

0.050

Reactivity (dk/k)

PSI-B

0.040

PSI-C
TEPSYS

0.030

AVERAGE

0.020
0.010
0.000
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

-0.010time (s)Figure 4-35. Void reactivity (zoom)
0.006
0.005

Reactivity (dk/k)

0.004
0.003
NFI

0.002

PSI-A

0.001
PSI-B
PSI-C

0.000

TEPSYS-0.001AVERAGE-0.002
0.4

0.5

0.6

0.7

0.8

time (s)

84

0.9

1.0

1.1

1.2

Figure 4-36. Void reactivity (mean and deviation)
0.070
0.060
(+) Deviation

0.050

Reactivity (dk/k)Average
0.040(-) Deviation

0.030
0.020
0.010
0.000
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

-0.010-0.020time (s)Figure 4-37. Void reactivity (mean and deviation – zoom)
0.006
0.005

Reactivity (dk/k)

0.004
0.003
0.002
0.001
(+) Deviation
0.000
Average-0.001(-) Deviation-0.002
0.4

0.5

0.6

0.7

0.8

0.9

1.0

time (s)Table 4-10. Void reactivity, figure of merit

NFI
PSI-A
PSI-B
PSI-C
TEPSYS

D’Auria FFT
0.71320.86400.87430.89730.639685

Mean error (ME)0.87870.97030.9791
0.99870.8412

1.1

1.2

4.2.2 Snapshot at the time of maximum power before scram
Participants’ results from snapshot at the time of maximum power before scram were analysed inorder to investigate coupled neutronics/thermal-hydraulics modelling and the code capabilities of theparticipants at the conditions where the maximum power is reached and scram is still not activated.
Figure 4-38 presents a graphical comparison of participants’ predictions of the time of maximum
power before scram with the mean value as reference while Table 4-11 provides the values with themean and standard deviation. In general results are in good agreement. If the PSI-A and PSI-B results
are excluded, all deviations are within 2V. The rest of the results in this section are presented in two
groups – one for the participants that used fission power and the other for the participants that used
total power. Small deviations are observed from the mean solution for the core average relative axial
power distribution results given in Figures 4-39 and 4-40, while the mean and standard deviations arepresented in Figures 4-41 and 4-42. In comparison to the HP results (Figure 4-13), the discrepancies
are in average of the same magnitude but in the snapshot case they are more evenly distributed over
the whole core height while in the HP case the maximum deviations are observed in the bottom part ofthe core. Good agreements are observed in the predictions of relative axial profiles for the selectedrodded and un-rodded fuel assemblies, as shown in Figures 4-43 through 4-50. One observation fromthe presented comparisons for axial power distributions is that the results in the total power groupagree better than the results fission power group. The major reason for this fact can be deducted in
inspecting Table 4-6. It can be seen that all of the participants using total power utilise the bypass
model (bypass density correction) while in the fission power group some participants utilise it andsome do not. For the total power group results of axial distributions the differences in the decay heatmodels still do not impact the comparisons since at this snapshot the fission power is the dominating
contributor to the total power and the radial fission power distribution in the snapshot is similar to theradial power distribution at the initial HP conditions. The mean solution for the radial power distribution
and the standard deviation are given in Figures 4-51 and 4-52. If compared to the initial HP conditions
the snapshot comparison of radial power distribution exhibits similar deviations since what reallychanged in the snapshot is the total power level and axial distribution but not the radial one since thescram is still not activated.
The complete list of the mean solutions and standard deviations can be found in Appendix C andthe deviations of each participant’s solutions from the mean value can be found in Appendix D. Bothappendices are provided only in the electronic copy of this report distributed via a CD-ROM.
Figure 4-38. Time of maximum power before scram
0.800
0.780

Average = 0.742 s

0.760

V 0.740
H 0.720P
LW 0.700
0.680
0.660

86

V
TT

U
P
V

P
TE SU
P
S
Y
S
U
.P
IS
A

N
N FI
U
P
EC
P
SI
P
-A
SI
-C P
S
O
R I-B
E
TR
A
N

C
E
A
C /DE
E
N
A
/D -33
E
N
-7
64
FA
N
FZ P
R
-3
D
IB
G
E
R
R
D S
R
O
LA

0.640

Table 4-11. Time of maximum power before scram
Time of max. power
before scram (s)
0.750
0.750
0.785
0.740
0.746
0.750
0.720
0.750
0.696
0.696
0.747
0.750
0.770
0.750
0.730
0.750
0.742
0.023

Participant
CEA-33
CEA-764
FANP
FZR
GRS
IBER
NFI
NUPEC
PSI-A
PSI-B
PSI-C
PSU
TEPSYSUPIUPVVTT
Average =Standard deviation (V) =Deviation(ei)-0.008-0.008-0.042-0.002-0.004-0.008-0.022-0.008-0.046-0.046-0.005-0.008-0.028-0.008-0.012-0.008Figure 4-39. Core axial power profile at maximum power before scram (fission power used)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6

CEA-33

CEA-764

FANP

NFI

NUPEC

PSI-A

PSI-B

PSI-C

VTT

0.4
0.2

AVERAGE

0.0
0

5

10

15

Axial Nodes

87

20

25

Figure 4-40. Core axial power profile at maximum power before scram (total power used)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6
FZR

PSU

TEPSYSUPIUPVAVERAGE

0.4
0.2
0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-41. Core axial power profile at maximum power before scram(fission power used – mean and deviation)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

Axial Nodes

88

20

25

Figure 4-42. Core axial power profile at maximum power before scram(total power used – mean and deviation)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-43. Relative power of FA 75 at maximum power before scram (fission)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6

CEA-33

CEA-764

FANP

GRS

NFI

NUPEC

PSI-A

PSI-B

PSI-C

VTT

AVERAGE

0.4
0.2
0.0

0

5

10

15

Axial Nodes

89

20

25

Figure 4-44. Relative power of FA 75 at maximum power before scram (total)
1.8
1.6

1.2
1.0
0.8
0.6
0.4

FZR

IBER

PSU

TEPSYSUPIUPVAVERAGE

0.2
0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-45. Relative power of FA 75 at maximum power before scram(mean and deviation – fission power used)
1.8
1.6
1.4

Normalized Power

Normalized Power

1.4

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

Axial Nodes

90

20

25

Figure 4-46. Relative power of FA 75 at maximum power before scram(mean and deviation – total power used)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-47. Relative power of FA 367 at maximum power before scram (fission)
1.8

1.6

1.4

Normalized Power

1.2

1.0

0.8

0.6

0.4

CEA-33

CEA-764

FANP

GRS

NFI

NUPEC

PSI-A

PSI-B

PSI-C

VTT

AVERAGE

0.2

0.0
0

5

10

15

Axial Nodes

91

20

25

Figure 4-48. Relative power of FA 367 at maximum power before scram (total)
1.8
1.6

Normalized Power

1.4
1.2
1.0
.

0.8
0.6
0.4

FZR

PSU

TEPSYS

0.2

UPI

UPV

AVERAGE

0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-49. Relative power of FA 367 at maximum power before scram(mean and deviation – fission power used)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

Axial Nodes

92

20

25

Figure 4-50. Relative power of FA 367 at maximum power before scram(mean and deviation – total power used)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-51. Mean radial power distribution at maximum power before scram
28
25

1.250-1.500
1.000-1.250

22190.750-1.000

160.500-0.750
0.250-0.500

13100.000-0.250

7
4
1
1

4

7 10 13 16 19 22 25 28

Channels93

Figure 4-52. Standard deviation of radial power distribution at maximum power before scram

29
25

0.12-0.15

21

0.09-0.12

17

0.06-0.09

13
9

0.03-0.06
0-0.0351
1

5

9 13 17 21 25 29
Channels

4.2.3 Snapshot at the end of the transient (at 5 s)
The conditions of the snapshot at the 5 s into the transient (the end of the simulated transient) are
different from the conditions of the snapshot at the time of maximum power before scram. The bypass
model still will play a role since the bypass density correction in the cross-section feedback modellingis to account for the deviations of bypass density from the saturated value used in the cross-section
homogenisation (please note that the cross-sections are generated by homogenising the bypass region
at saturated conditions associated with the lattice at actual conditions). The consistent utilisation of the
ADF and xenon models is also relevant to the agreement (or disagreement) of participants’ predictions
for this snapshot. Since the control rods were tripped during the scram some of the differences arecoming from the neutronics methods and control rod models. The decay modelling in total powergroup results for axial power distributions is very important because for this snapshot the decay heat is
dominating contributor to the total power and it is very important how the spatial distribution of the
decay heat is done – according to the fission power distribution at the initial HP conditions or
according to the fission power distribution at this snapshot.
The core average relative axial power distribution results are compared and analysed in
Figures 4-53 through 4-56. The relative power distribution results for selected un-rodded and rodded
fuel assemblies is shown in Figures 4-57 through 4-64. The mean radial power distribution andstandard deviation distribution are given in Figures 4-65 and 4-66. In summary, if compared to thecomparisons of power distribution results for the snapshot at the time of maximum time before scramcase, the discrepancies in the participants’ results are higher for the snapshot at the end of transient.
It should also be noted that there is a significant deviation in lower part of axial power profile for
NUPEC results in Figure 4-53.
The complete list of the mean solutions and standard deviations can be found in Appendix C andthe deviations of each participant’s solutions from the mean value can be found in Appendix D. Bothappendices are provided only in the electronic copy of this report distributed via CD-ROM.

94

Figure 4-53. Core axial power profile at the end of transient (fission)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6
0.4
0.2

CEA-33

CEA-764

FANP

NUPEC

PSI-A

PSI-B

PSI-C

VTT

AVERAGE

0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-54. Core axial power profile at the end of transient (total)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6
0.4

FZR

IBER

PSU

TEPSYSUPIUPVAVERAGE

0.2
0.0
0

5

10

15

Axial Nodes

95

20

25

Figure 4-55. Core axial power profile at the end of transient(mean and deviation – fission power used)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-56. Core axial power profile at the end of transient(mean and deviation – total power used)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

Axial Nodes

96

20

25

Figure 4-57. Relative power of FA 75 at end of transient (fission)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6
0.4
0.2

CEA-33

CEA-764

FANP

NUPEC

PSI-A

PSI-B

PSI-C

VTT

AVERAGE

0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-58. Relative power of FA 75 at end of transient (total)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6
0.4

FZR

IBER

PSU

TEPSYSUPIUPVAVERAGE

0.2
0.0
0

5

10

15

Axial Nodes

97

20

25

Figure 4-59. Relative power of FA 75 at end of transient(mean and deviation – fission power used)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-60. Relative power of FA 75 at end of transient(mean and deviation – total power used)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

Axial Nodes

98

20

25

Figure 4-61. Relative power of FA 367 at end of transient (fission)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6
0.4
0.2

CEA-33

CEA-764

FANP

NUPEC

PSI-A

PSI-B

PSI-C

VTT

AVERAGE

0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-62. Relative power of FA 367 at end of transient (total)
1.8
1.6

Normalized Power

1.4
1.2
1.0
0.8
0.6
0.4

FZR

IBER

PSU

TEPSYSUPIUPVAVERAGE

0.2
0.0
0

5

10

15

Axial Nodes

99

20

25

Figure 4-63. Relative power of FA 367 at end of transient(mean and deviation – fission power used)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

20

25

Axial Nodes

Figure 4-64. Relative power of FA 367 at end of transient(mean and deviation – total power used)
1.6
1.4

Normalized Power

1.2
1.0
0.8
0.6
0.4
0.2
0.0
0

5

10

15

Axial Nodes

100

20

25

Figure 4-65. Mean radial power distribution at end of transient28
25

1.250-1.500

22

1.000-1.250

190.750-1.000
0.500-0.750

160.250-0.500

10130.000-0.250

7
4
1
1

4

7 10 13 16 19 22 25 28

ChannelsFigure 4-66. Standard deviation of radial power distribution at end of transient28

0.15-0.18

25
22

0.12-0.15

19

0.09-0.12

16
13
10

0.03-0.06

7

0.00-0.03

41
1

4 7 10 13 16 19 22 25 28

Channels

101

0.06-0.09

Chapter 5
CONCLUSIONS

The developed multi-level methodology is employed to perform a validation of coupled codes for
BWR transient analysis. For this purpose, the application of three exercises was performed in the
BWR TT benchmark. These exercises include the evaluation of different steady states, and simulationof different transient scenarios. In this volume, Exercise 2 of the OECD/NRC BWR TT benchmark
was discussed in detail in order to meet the objectives of the validation of best-estimate coupled codes.
The second exercise consists of performing coupled-core boundary conditions calculations, thepurpose being to test and initiate the participants’ core models. Thermal-hydraulic boundary conditions
are provided to the participants from the benchmark team. The thermal-hydraulic core boundary
conditions provided are the core inlet pressure, core exit pressure, core inlet temperature and core inlet
flow. In summary the second exercise is to perform a coupled 3-D kinetics/T-H calculation for thereactor core using the PSU-provided boundary conditions at core inlet and exit. Three-dimensional
two-group macroscopic cross-section libraries are provided to the participants. The core inlet flow isprovided in two formats: total core flow as a function of time and radially distributed flow as a functionof time for 33 channels. In addition, the benchmark team provided the participants with normalised
power vs. flow correlations for the different assembly types based on the detailed modelling in which
each assembly represented by a thermal-hydraulic channel for the initial steady-state conditions. The
studies performed by the benchmark team indicated that these correlations also apply reasonably wellduring the transient, which provided an opportunity for the participants to develop their own core
coupled spatial mesh overlays. An additional steady state was defined in the framework of the second
exercise – hot zero power (HZP) state with fixed thermal-hydraulic feedback. This allows for “clean”
initialisation of the core neutronics models and cross-section modelling algorithms.
This benchmark problem has been well-accepted internationally, with 18 participants representing
9 countries. CEA submitted two sets of results using coarse core T-H nodalisation with 33 channels
and fine core T-H nodalisation with 764 core channels – one T-H channel per neutronics assembly.
PSI submitted two sets of results with RETRAN-3D using different sets of core boundary conditions
and one set of results using CORETRAN. The results submitted by the participants are used to makecode-to-code comparisons and a subsequent statistical analysis. The results encompass several typesof data for both thermal-hydraulic and neutronics parameters at the initial steady-state conditions
and throughout the TT transient, including integral parameters, 1-D axial distributions, 2-D radial
distributions and time histories.
Detailed assessments of the differences between the calculated results submitted by the participants
for this exercise were presented in Chapter 4 of this volume. Overall, the participants’ results for
integral parameters, core-averaged axial distributions, and core-averaged time histories are in good
agreement, considering some of the shortcomings in participants’ current models, uncertainties ofsome system parameters, and difficulties in interpreting some of the measured responses.
During the comparative analysis of the participants’ results for the second exercise the following
sources of modelling uncertainties were identified: core pressure drop in terms of local losses andfriction models, core bypass modelling, void feedback model in terms of sub-cooled boiling and103

vapour slip and time step size which is a user optional parameter. The fuel heat transfer parameters as
the UO2 conductivity and gap conductivity and direct heating (2% to in-channel flow and 1.7% tobypass flow) were specified. The scram initiation time and the speed of the rod insertion were also
specified. The scram initiation time was specified since one of the objectives of the benchmark is totest coupled codes’ capabilities to predict for TT2 that the thermal-hydraulic feedback alone limits thepower peak and initiates the power reduction. Other important modelling issues were identified suchas the impact of using assembly discontinuity factors, which are also provided to the participants in asimilar table format as for the two group cross-sections; xenon correction to account for the actual
xenon concentration distribution at the initial steady-state conditions of the turbine trip test 2; numberof thermal-hydraulic channels and spatial mapping schemes with the neutronics core model; decay
heat modelling; and bypass density correction in the cross-section feedback modelling to account forthe deviations of bypass density from the saturated value used in the cross-section homogenisation
since the cross-sections are generated by homogenising the bypass region associated with the lattice.
Different code formulations/correlations for Doppler temperature and moderator density, affected bothcore-averaged power and reactivity time histories and local distributions throughout the transient sincethese two parameters are the major feedback parameters for the cross-section modelling impacting inthis way the neutronics predictions.
While the purpose of the first exercise is to initialise and test the primary and secondary systemmodel responses, the purpose of the second exercise is to initialise and test the coupled-core
thermal-hydraulic/3-D neutronics response. Both exercises prepare the foundation of conducting
Exercise 3 in a consistent and systematic way. Exercise 3 is defined as a best-estimate coupled-core
plant transient modelling.
The PB TT2 test has previously been analysed elsewhere with different codes and models [6,7].
These analyses involved not only point kinetics and 1-D kinetics system simulations, but also 3-D
kinetics/core thermal-hydraulics boundary conditions calculations. Each of the organisations performing
these separate analyses generated their own point kinetics parameters, 1-D cross-sections and 3-Dcross-section libraries. It is thus not possible to directly compare the results of different organisations,especially for the parameters where the measured data is not available. In most of the 3-D coreboundary conditions analyses the cross-section functionalisation for instantaneous dependencies wasdone either by using polynomial fitting procedure or the procedure using multi-level tables with baseand partial cross-sections. In both cases the instantaneous cross-term effects (which are important for
the transient analysis) are not modelled completely, which led to different degree of underestimationof the void feedback (void coefficient) depending on the procedure used.
The current OECD/NRC BWR TT benchmark is designed to provide a validation basis for the
new generation best-estimate codes – coupled 3-D kinetics system thermal-hydraulic codes. Based on
previous experience, three benchmark exercises were defined in order to develop and verify, in aconsistent way, the thermal-hydraulic system model, the coupled-core model, and the coupled-core/system modelling. The three exercises defined also helped to identify the key parameters for modellinga turbine trip transient. This in turn allowed the evaluation of these key parameters, through theperformance of sensitivity studies, which allowed the benchmark team to assist the participants in themost efficient way. The participants use the cross-section library generated by the benchmark team,which removes the uncertainties introduced with using different cross-section generation and modelling
procedures. The defined benchmark cross-section modelling approach is a direct interpolation in
multi-dimensional tables with complete representation of the instantaneous cross-section cross-term
dependencies. Developing a more in-depth knowledge of the coupled computer code systems isimportant because 3-D kinetic/thermal-hydraulic codes will play a critical role in the future of nuclear
analysis. It is anticipated that the results of this benchmark problem will assist in the understanding of
the behaviour of the next generation of coupled computer codes.

104

REFERENCES[1]

Ivanov, K., T. Beam, A. Baratta, A. Irani, N. Trikouros, PWR MSLB Benchmark – Final
Specifications, NEA/NSC/DOC(97)15, Nuclear Energy Agency, October 1997.

[2]

Solis, J., K. Ivanov, B. Sarikaya, A. Olson, K. Hunt, Boiling Water Reactor Turbine Trip (TT)Benchmark – Volume I: Final Specifications, NEA/NSC/DOC(2001)1, Nuclear Energy Agency.

[3]

Akdeniz, B., K. Ivanov, A. Olson, BWR TT Benchmark – Volume II: Summary Results of
Exercise, NEA/NSC/DOC(2004)21, Nuclear Energy Agency.

[4]Larsen, N., Core Design and Operating Data for Cycles 1 and 2 of Peach Bottom 2, EPRI
NP-563, June 1978.

[5]

Carmichael, L., R. Niemi, Transient and Stability Tests at Peach Bottom Atomic Power Station
Unit 2 at End of Cycle 2, EPRI NP-564, June 1978.

[6]

Hornyik, K., J. Naser, RETRAN Analysis of the Turbine Trip Tests at Peach Bottom Atomic
Power Station Unit 2 at the End of Cycle 2, EPRI NP-1076-SR Special Report, April 1979.

[7]

Moberg, L., J. Rasmussen, T. Sauar and O. Oye, RAMONA Analysis of the Peach Bottom-2
Turbine Trip Transients, EPRI NP-1869, June 1981.

[8]

Olson, A.M., Methods for Performing BWR System Transient Analysis, Topical Report
PECo-FMS-0004-A, Philadelphia Electric Company (1988).

[9]

Borkowski, J., N. Wade, TRAC-BF1/MOD1 – Model Description, NUREG/CR-4356
EGG-2626, Vol. 1, Idaho National Engineering Laboratory, EG&G Idaho, Inc., August 1992.

[10] Steinke, R., V. Martinez, N. Schnurr, J. Spore, J. Valdez, TRAC-M/FORTRAN 90 (Version 3.0)
User’s Manual, NUREG/CR-6722, pp. 2-1 to 2-2, May 2001.
[11] Ivanov, K., M. Vela Garcia, J. Solis, Andy M. Olson, OECD/NRC BWR TT Benchmark: A Core
Boundary Condition Model Approach, TANSAO 85, 275-277 (2001).
[12] Kuntz, R., G. Kasmala, J. Mahaffy, Automated Code Assessment Program: Technique Selection
and Mathematical Prescription, Letter Report 3, Applied Research Laboratory, The Pennsylvania
State University, April 1998.
[13] Ambrosini, W., R. Bovalini, F. D’Auria, “Evaluation of Accuracy of Thermal-hydraulics CodeCalculations”, Energia Nucleare, Vol. 7, No. 2 (1990).
[14] Cubic Spline for Excel Workbook, SRS1 Software, February 2003, available on-line as follows:
http://www.srs1software.com.
[15] “OECD/NRC BWR Turbine Trip Benchmark Special Issue”, Nuclear Science and Engineering,Vol. 148, No. 2, October 2004.
105

Appendix A
DESCRIPTION OF THE COMPUTER CODES USED FOR ANALYSIS
IN EXERCISE 2 OF THE OECD/NRC BWR TT BENCHMARK

107

CRONOS2/FLICA4 (CEA, France)
CRONOS2CRONOS is the computer tool devoted to neutronic core computation in the SAPHYR system,
which also includes APOLLO2 for neutronic assembly calculation and FLICA4 for thermal-hydrauliccore calculation. CRONOS has been designed to provide all the computational means necessary for
nuclear reactor core calculations, including design, fuel management, follow-up and accidents.
CRONOS allows steady-state, kinetic, transient, perturbation and burn-up calculations. The power
calculation takes into account the thermal-hydraulic feedback effects. All of this can be done without
any limitation on any parameter (angular discretisation, energy groups and spatial meshes). CRONOS
was written with the objective of optimising its performance and its portability. It is based on a
modular structure that allows a great flexibility of use. A special user-oriented language, named
GIBIANE, and a shared numerical toolbox have been developed to chain the various computation
modules. The code solves either the diffusion equation or the even parity transport equation withanisotropic scattering and sources. Different geometries are available such as 1-, 2- or 3-D Cartesian,2- or 3-D hexagonal and cylindrical geometries. Four different solvers are available: PRIAM, MINOS,
CDIF and VNM. The PRIAM solver uses the second-order form of the transport equation and is basedon SN angular discretisation and a finite element approximation on the even flux (primal approximation).
This solver is mainly devoted to accurate reference calculation for either Cartesian or hexagonal
geometry. The MINOS nodal solver is based on mixed dual finite element for diffusion or simplified
PN equations. This solver performs very fast kinetic and static calculations. The CDIF solver uses
finite difference approximation for the diffusion equation, and is devoted to pin-by-pin rectangular
calculation. The VNM solver based on the VARIANT method will be soon connected to CRONOS.
It is based on a mixed primal method and PN approximation and will be mainly devoted to computationof fast breeder reactors.
References
Fedon-Magnaud, C., “Pin-by-pin Transport Calculation with CRONOS Reactor Code”, M&C Madrid,
27-30 September 1999.
Lautard, J., D. Schneider, A.M. Baudron, “Mixed Dual Methods for Neutronic Reactor Core
Calculations in the CRONOS System”, M&C Madrid, 27-30 September 1999.
Lautard, J., et al., “CRONOS – A Modular Computational System for Neutronic Core Calculation”,
IAEA Meeting, Cadarache, France (1990).
FLICA4
FLICA4 is the thermal-hydraulics code of the SAPHYR system, which also includes CRONOS2
for neutronic core calculations and APOLLO2 for neutronic assembly calculations. SAPHYR codes
are based on a modular structure that allows a great flexibility of use. A special user-oriented language,
named GIBIANE, and a shared numerical toolbox have been developed to chain the various computation
modules. FLICA4 is a 3-D two-phase compressible flow code, especially devoted to reactor core
analysis. The fluid is modelled by a set of four equations: mass, momentum, and energy conservation
for the two-phase mixture, and mass conservation for the vapour. The velocity disequilibrium is taken
into account by a drift flux correlation. A 1-D thermal module is used to solve the conduction in solids(fuel). Thanks to the modular design of the SAPHYR codes, numerous closure laws are available forwall friction, drift flux, heat transfer and critical heat flux (CHF), and many fluids can be calculated109

(liquids like lead or freons, gases like hydrogen or carbon dioxide). A specific set of correlations has
been qualified in FLICA3 for PWR applications. An extensive qualification program for FLICA4 isunderway, based on recent experimental data, in order to cover a wider range of flow conditions.
FLICA4 includes an object-oriented pre-processor to define the geometry and the boundary
conditions. Radial unstructured meshes are available, without any limitation on the number of cells.
Zooming on a specific radial zone can be performed by a second calculation using a finer mesh (forinstance a sub-channel calculation of the hot assembly). The fully implicit numerical scheme is basedon the finite volumes and a Roe solver. This kind of method is particularly accurate, with a low
numerical diffusion.
References
Toumi, I., A. Bergeron, D. Gallo, E. Royer, D. Caruge, “FLICA4: A Three-dimensional Two-phase
Flow Computer Code with Advanced Numerical Methods for Nuclear Applications”, Nuclear
Engineering and Design, 200, 139-155 (2000).
Bergeron, A., D. Caruge, P. Clément, “Assessment of the 3-D Thermal-hydraulic Nuclear Computer
Code FLICA4 on Rod Bundle Experiments”, NURETH-6, San Francisco, 3-8 October 1999.
Toumi, I., D. Caruge, “An Implicit Second Order Method for 3-D Two-phase Flow Calculations”,
Nuclear Science Engineering, 130, 213-225 (1998).
DYN3D (FZR, Germany)
Capabilities
DYN3D is a three-dimensional core model for dynamic and depletion calculations in light water
reactor cores with quadratic or hexagonal fuel assembly geometry. The two-group neutron diffusion
equation is solved by nodal methods. A thermal-hydraulic model of the reactor core and a fuel rod
model are implemented in DYN3D. The reactor core is modelled by parallel coolant channels which
can describe one or more fuel elements. Starting from the critical state (keff-value, critical boron
concentration or critical power) the code allows to simulate the neutronic and thermal-hydraulic core
response to reactivity changes caused by control rod movements and/or changes of the coolant core
inlet conditions. Depletion calculations can be performed to determine the starting point of thetransient. Steady state concentrations of the reactor poisons can be calculated. The transient behaviourof Xe and Sm can be analysed. The decay heat is taken into account based on power history andduring the transient. Hot channels can be investigated by using the nodal flux reconstruction inassemblies and the pin powers of the cell calculations. Cross-section libraries generated by different
cell codes for different reactor types are linked with DYN3D. Macroscopic cross-section libraries
created within the common software platform can easily be linked to DYN3D.
Methods of solution
Neutron kinetics
The neutron kinetic model is based on the solution of the three-dimensional two-group neutron
diffusion equation by nodal expansion methods. Different methods are used for quadratic andhexagonal fuel assembly geometry. It is assumed that the macroscopic cross-sections are spatially110constant in a node being the part of a fuel assembly. With Cartesian geometry, the three-dimensional
diffusion equation of each node is transformed into one-dimensional equations in each direction x, y, z
by transversal integrations. The equations are coupled by the transversal leakage term. In each energy
group, the one-dimensional equations are solved with the help of flux expansions in polynomials up to
the second order and exponential functions being the solutions of the homogeneous equation. The
fission source in the fast group and the scattering source in the thermal group as well as the leakage
terms are approximated by the polynomials. In the case of hexagonal fuel assemblies, the diffusion
equation in the node is transformed into a two-dimensional equation in the hexagonal plane and a onedimensional equation in the axial direction. The two equations are coupled by the transverse leakage
terms which are approximated by polynomials up to the second order. Considering the two-dimensional
equation in the hexagonal plane, the side-averaged values (HEXNEM1) or the side-averaged and thecorner point values (HEXNEM2) of flux and current are used for the approximate solution of the
diffusion equation. The method used for the one-dimensional equations of the Cartesian geometry isapplied for the axial direction. It is extended to two dimensions in the HEXNEM1 and HEXNEM2
methods. In the steady state, the homogeneous eigenvalue problem or the heterogeneous problem withgiven source is solved. An inner and outer iteration strategy is applied. The outer iteration (fission
source iteration) is accelerated by Chebychev extrapolation.
The steady-state iteration technique is applied for the calculation of the initial critical state, thedepletion calculations and the Xe and Sm dynamics. Concerning reactivity transients an implicit
difference scheme with exponential transformation is used for the time integration over the neutronic
time step. The exponents in each node are calculated from the previous time step or during theiteration process. The precursor equations are analytically solved, assuming the fission rate behaves
exponentially over the time step. The heterogeneous equations obtained for each time step are solved
by an inner and outer iteration technique similar to the steady state.
Thermal-hydraulics
The parallel channels are coupled hydraulically by the condition of equal pressure drop over all
core channels. Additionally, the so-called hot channels can be considered for the investigation of hot
spots and uncertainties in power density, coolant temperature or mass flow rate. Thermo-hydraulicboundary conditions for the core like coolant inlet temperature, pressure, and coolant mass flow rate orpressure drop must be given as input for DYN3D. The module FLOCAL comprises a one- or
two-phase coolant flow model on the basis of four differential balance equations for mass, energy andmomentum of the two-phase mixture and the mass balance for the vapour phase allowing thedescription of thermodynamic non-equilibrium between the phases, a heat transfer regime map fromone-phase liquid up to post-critical heat transfer regimes and superheated steam. A fuel rod model forthe calculation of fuel and cladding temperatures is implemented. A thermo-mechanical fuel rod
model allows the estimation of the relevant heat transfer behaviour of the gas gap during transients andthe determination of some parameters for fuel rod failure estimation.
The two-phase flow model is closed by constitutive laws for heat mass and momentum transfer,e.g. vapour generation at heated walls, condensation in the sub-cooled liquid, phase slip ratio, pressure
drop at single flow resistances and due to friction along the flow channels as well as heat transfer
correlations. Different packages of water and steam thermo-physical properties presentation can be used.
Coupling neutron kinetics/thermal-hydraulics
A two-time-step scheme consisting of thermal-hydraulic and neutron kinetic time steps is used forthe transient integration. One or several neutron kinetic steps are used within a thermal-hydraulic step.
111

Iterations between neutron kinetics and thermal-hydraulics are carried out in the steady state as well as
for each thermal-hydraulic time step. Based on the changes of the main physical parameters of thetransient process the time step size is controlled during the calculation.
Programming language
FORTRAN90 on Windows, Unix and Linux platforms.
Outstanding features
Special models
The assembly discontinuity factors (ADF) can be considered in the two geometries, Cartesian andhexagonal. The pin-wise flux reconstruction can be used for hot channel calculation during the
DYN3D run. A decay heat model based on the power history or the initial power distribution can betaken into account during the transient. The decay heat model integrated in the code is based on thefour fissionable isotopes 235U, 238U, 239Pu and 241Pu, the contributions from the decay of actinides
resulting from the neutron capture and the contributions from the decay of nuclides formed by neutron
capture in fission products. Based on perturbation theory, the reactivity contributions due to control
rod motions, changes of moderator properties and fuel temperatures are calculated.
A model for description of the mixing of coolant from different primary loops in the downcomer
and lower plenum of VVER-440 type reactors is implemented. It is based on the special feature of
VVER-440 type reactors, that the coolant flow in the downcomer is nearly parallel without large
re-circulation vortexes as they are known from Western-type PWRs. Thus the flow can be well describedin the potential flow approximation, where the Navier-Stokes equations can be solved analytically forthe 2-D flow in the downcomer. The velocity gradient in the radial direction was neglected. In thelower control rod chamber a parallel flow with constant velocity was assumed. With this approximationof the velocity field the diffusion equation for the temperature is solved. The solution is presented as aclosed analytical expression based on series of orthogonal eigenfunctions. The turbulence was taken
into account by constant scalar turbulent Peclet numbers defined individually for the downcomer andthe lower control rod chamber. The turbulent Peclet numbers describe the intensity of turbulent
diffusion and were adapted to experimental data. For the validation of the model, measured values
from an air operated 1:5 scaled VVER-440 model were used. Temperature measurements were taken
at the end of the downcomer and at the inlet of the reactor core. Further, the model was validated
against measured operational data from NPP with VVER-440 and CFD calculations.
Concerning the transport of boron gradients into the core at low velocities a particle-in-cell model
for avoiding the numerical diffusion can be applied in DYN3D. Integrated fuel rod model allows
considering dynamic changes in heat transfer conditions (gap behaviour) and fuel rod failure limits
estimation on-line during transient calculations.
Coupling with system codes and CFD
DYN3D is coupled with the system code ATHLET to analyse a wide range of transients.
Regarding the thermal-hydraulics of the core three different types of coupling are implemented:x
xx

internal coupling;external coupling;
parallel coupling.
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In the internal coupling, the neutron kinetics is described by DYN3D and ATHLET models thewhole thermal-hydraulics. Data exchange is performed via internal interfaces. In the external coupling,
the core, including neutron kinetics and thermal-hydraulics, is simulated by DYN3D, and the remaining
system is simulated by ATHLET. Boundary conditions at the core inlet and outlet are exchanged
during the calculation. The thermal-hydraulics of the core are analysed by the two codes DYN3D and
ATHLET in the parallel coupling. The code structure of DYN3D (data modules within FORTRAN90)
allows relatively easy coupling to other thermal-hydraulic system codes. Internal and external couplings
between DYN3D and RELAP5 realised by international partners (IPPE Obninsk, VUJE Trnava) also
exist. Off-line coupling with CFD for providing realistic boundary conditions at the core inlet withrespect to coolant mixing in the downcomer and lower plenum has been realised. A module based onsemi-analytical perturbation reconstruction (SAPR) has been developed and coupled to DYN3D
allowing the determination of boron concentration and coolant temperature distributions at the core
inlet from response functions obtained by CFD calculations or experimentally. Coupling of DYN3D
neutron kinetics module or DYN3D core model (including thermal-hydraulics) with other -D or 3-D
thermal-hydraulic modules (including CFD for open and porous media) is feasible based on common
software platform (SALOME).
Validation
DYN3D has been validated by numerous benchmarks (including experimental results) for both
Cartesian and hexagonal fuel element geometry.
Steady-state problemsx

3-D IAEA benchmark (Cartesian);x

2-D IAEA benchmarks modified for hexagonal geometry;x

2-D and 3-D Seidel benchmark for VVER-440 (hexagonal);x

3-D Schulz benchmark for VVER-1000 (hexagonal);x

Atomic Energy Research (AER) benchmark problem concerning control rod worth of
VVER-440 reactor (hexagonal);x

comparison of calculated reactor parameters (critical boron concentration, reactivity
coefficients, control rod efficiency) with measured data for different VVER-reactors;x

comparison of assembly-averaged and pin-wise neutron flux distribution measured at V-1000
zero power test facility (hexagonal).

Transient problemsxkinetic experiments at the zero power reactor LR-0 (hexagonal);x

1st through 3rd kinetic benchmarks of AER with ejection of asymmetrical control rods in a
VVER-440 (hexagonal);x

4th kinetic benchmark of AER of a boron dilution transient in a VVER-440 (hexagonal);x

NEACRP benchmarks on control rod ejections in PWR (Cartesian);x

NEA-NSC benchmarks on uncontrolled withdrawal of control rods at hot zero power in PWR(Cartesian);113

xOECD/NRC main steam line break benchmark – Exercise 2 (Cartesian);xOECD/NRC main steam line break benchmark – Exercise 3 analysed with DYN3D/ATHLET(Cartesian);x

5th kinetic benchmarks of AER on main steam header break in a VVER-440 with DYN3D/
ATHLET (hexagonal);x

comparison of DYN3D/ATHLET results with measured data for operational transients innuclear power plants with VVER type reactors;

x

DYN3D/ATHLET calculations of the turning-off of one feedwater pump from working two
in the Balakovo-4 VVER-1000 (hexagonal);x

DYN3D/ATHLET calculations for the load drop down to house load level in one of the twoworking turbines in Loviisa-1 VVER-440 (hexagonal);xOECD BWR turbine trip benchmark in the reactor Peach Bottom-2 – Exercise 2 analysedwith DYN3D (Cartesian);xOECD BWR turbine trip benchmark in the reactor Peach Bottom-2 – Exercise 3 analysedwith DYN3D/ATHLET (Cartesian);x

DYN3D/ATHLET calculations for drop of a single control rod and power control action in
the VVER 440/213 of NPP Bohunice 3 (hexagonal);x

DYN3D/ATHLET calculations for the coast-down of a second main coolant pump (start-uptest) in the VVER-1000/V-320 of Kozloduy 6 (hexagonal);x

DYN3D Calculations for the V-1000 test facility and comparisons with the measurements(hexagonal).

References
Grundmann U., U. Rohde, DYN3D/M2 – A Code for Calculation of Reactivity Transients in Cores
with Hexagonal Geometry, IAEA Technical Committee Meeting on Reactivity Initiated Accidents,
Vienna (1989), Report ZfK-690, Rossendorf (1989) or Report FZR 93-01, Rossendorf (1993).
Grundmann, U., J. Hádek, “Calculations of Neutron Kinetics Experiments on the LR-0 Reactor with
the Three-dimensional Code DYN3D/M1”, Kernenergie, 34, 12 (1991).
Grundmann, U., U. Rohde, “Investigations on a Boron Dilution Accident for a VVER-440 Type
Reactor by the Help of the Code DYN3D”, Proceedings of the 1994 Topical Meeting on Advances inReactor Physics, Vol. III, pp. 464-471, Knoxville, TN (USA), 11-15 April 1994.
Grundmann, U., The Code DYN3DR for Steady-state and Transient Analyses of Light Water Reactor
Cores with Cartesian Geometry, Report FZR-114, Rossendorf, November 1995.
Grundmann, U., U. Rohde, “DYN3D – A Three-dimensional Core Model for Steady State andTransient Analysis in Thermal Reactors”, Proceedings of the International Conference on the Physics
of Reactors (PHYSOR 96), Mito, Japan, 16-20 Sept. 1996.
Grundmann, U., U. Rohde, “The Reactor Code DYN3DR – Transient Calculations of NEACRP
Benchmarks for PWR and BWR”, Proceedings Jahrestagung Kerntechnik ’96, Mannheim (1996).

114

Selected Safety Aspects of WWER-440 Model 213 Nuclear Power Plants: Final Report of the IAEA
Project on Evaluation of Safety Aspects for WWER-440 Model 213 NPP, Vienna, International Atomic
Energy Agency, ISBN 92-0-101196-2 (1996).
Kyrki-Rajamäki, R., U. Grundmann, A. Kereszturi, “Results of Three-dimensional Hexagonal Dynamic
Benchmark Problems for VVER Type Reactors”, Proceedings of the Int. Conf. on the Physics ofReactors (PHYSOR’96), Mito, Japan, ,16-20 Sept. 1996, pp. J229-J238.
Grundmann, U., U. Rohde, Verification of the Code DYN3DR with the Help of International
Benchmarks, Report FZR-195, Rossendorf (1997).
Grundmann U., F. Hollstein, “A Two-dimensional Intranodal Flux Expansion Method for Hexagonal
Geometry”, Nuclear Science and Engineering, 133, 201-212 (1999).
Grundmann, U., “HEXNEM – A Nodal Method for the Solution of the Neutron Diffusion Equation in
Hexagonal Geometry”, Proceedings of the Conference on Mathematics and Computations in Nuclear
Applications (M&C’99), Madrid, 27-30 September 1999, pp. 1086-1095.
Grundmann, U., S. Kliem, U. Rohde, “Analysis of the Exercise 2 of the OECD – MSLB Benchmark
with the Code DYN3D/R”, Proceedings of the Conference on Mathematics and Computations in
Nuclear Applications (M&C’99), Madrid, 27-30 September 1999.
Kliem, S., U. Grundmann, U. Rohde, “Analysis of the OECD MSLB Benchmark Using the Coupled
Code DYN3D/ATHLET”, Proceedings of the 8th International Conference on Nuclear Engineering(ICONE 8), Baltimore (USA), 2-6 April 2000.
Grundmann, U., S. Kliem, “Analyses of the OECD MSLB Benchmark with the Codes DYN3D and
DYN3D/ATHLET”, Transactions of the American Nuclear Society, Volume 84, pp. 23-25, June 2001.
Mittag, S., S. Kliem, F-P. Weiß, R. Kyrki-Rajamäki, A. Hämäläinen, S. Langenbuch, S. Danilin,
J. Hadek, G. Hegyi, A. Kuchin, D. Panayotov, “Validation of Coupled Neutron Kinetic/ThermalHydraulic Codes. Part 1: Analysis of a VVER-1000 Transient (Balakovo-4)”, Annals of Nuclear
Energy, 28, pp. 857-873 (2001).
Kozmenkov, Y., Y. Orekhov, U. Grundmann, S. Kliem, U. Rohde, A. Seidel, “Development andBenchmarking of the DYN3D/RELAP5 Code System”, Proceedings of Jahrestagung Kerntechnik
2001, Dresden, 15-17 Mai 2001, pp. 15-18.
Grundmann, U., U. Rohde, “Analysis of the Boiling Water Reactor Turbine Trip Benchmark with theCode DYN3D”, Proc. Int. Conference on the New Frontiers of Nuclear Technology: Reactor Physics,
Safety and High-performance Computing (PHYSOR 2002), Seoul, Korea, 7-10 Oct. 2002.
Grundmann, U., S. Kliem, “Analyses of the OECD Main Steam Line Break Benchmark with theCodes DYN3D and ATHLET”, Nucl. Technol., 142, 146 (2003).
Grundmann, U., U. Rohde, “Different Simulations of Phase II of the OECD/NRC BWR Turbine Trip
Benchmark with the Code DYN3D”, Annual Meeting on Nuclear Technology, Berlin, 20-22 May 2003.
Mittag, S., P. Petkov, U. Grundmann, “Discontinuity Factors for Non-multiplying Material in
Two-dimensional Hexagonal Reactor Geometry”, Annals of Nucl. Energy, 30/13, pp. 1347-1364 (2003).
Grundmann, U., S. Kliem, U. Rohde, “Analysis of the Boiling Water Reactor Turbine Trip Benchmark
with the Codes DYN3D and ATHLET/DYN3D”, Nuclear Science and Engineering, forthcoming.
115

QUABOX/CUBBOX-ATHLET (GRS, Germany)
The code system QUABOX/CUBBOX-ATHLET is developed at GRS on the base of thermo-fluid
dynamic system cede ATHLET for analysis of the whole plant behaviour under accident conditions
and the core model code QUABOX/CUBBOX for the analysis of the 3-D reactor core behaviour.
The ATHLET code is a thermo-fluid dynamic system code for a wide range of applications
comprising anticipated and abnormal plant transients, small and intermediate leaks as well as large
breaks in PWRs and BWRs. The code offers the possibility of choosing between different models of
fluid dynamics. The two-phase flow is described either by a five-equation model or a full six-equation
model for mass, energy and momentum of both phases including models for non-condensables. The
code structure is highly modular, and allows an easy implementation of different physical models. The
basic modules are: thermo-fluid dynamics, neutron kinetics, general control simulation and numericalintegration method FEBE. ATHLET provides a modular network approach for the representation of athermal-hydraulic system. The analyses presented in the current work are made with the version of
ATHLET release 1.2E.
The 3-D reactor core behaviour is described by QUABOX/CUBBOX. This code solves the neutron
diffusion equations with two energy neutron groups and six groups of delayed neutron precursors.
The coarse mesh method is based on a polynomial expansion of neutron flux in each energy group.
The time integration is performed by a matrix-splitting method, which decomposes the solution into
implicit one-dimensional step for each spatial direction. The reactivity feedback is taken into accountby dependence of homogenised cross-section on feedback parameters, the functional dependence canbe defined in a very general and flexible manner.
The coupling approach for 3-D neutronics models implemented in ATHLET is based on a generalinterface, which separates data structures from neutronics and thermo-fluid dynamic code and performs
the data exchange in both directions. The approach has been successfully applied to couple other 3-D
neutronics codes. The internal coupling method has the following features: the fluid dynamic equations
for the primary circuit and the flow channels in the reactor core region are completely modelled andnumerically solved by ATHLET methods. The time integration in the neutronics code QUABOX/CUBBOX is performed separately. Therefore, both codes maintain their capabilities. The time step
size is synchronised during the transient, whereby the accuracy control is preferably done by the fluid
dynamic code. The coupling allows a flexible mapping defined by input between fuel assemblies of
the core loading and the thermo-fluid dynamic channels. Also, the axial meshes for neutronics andfluid dynamics can be defined independently. The coupled code ATHLET-QUABOX/CUBBOX has
already been applied to study complex plant transient conditions.
DNB/3D (NETCORP, USA)
DNB/3D is a FORTRAN 77 computer program that simulates the nuclear steam supply system of
a boiling water reactor under transient conditions. Geometry and system component options areprovided to represent any of the current BWR designs. The major features of DNB/3D are:x

Point, 1-D and 3-D neutronic kinetics models including Doppler, moderator density andcontrol rod feedback along with standard decay heat models. Initially subcritical cores can be
represented. A power forced option is also provided.

x

Multi-node radial and axial coolant channels and fuel rods.

xFixed nodalisation in the reactor vessel and steam lines.
116xOne-dimensional homogeneous equilibrium conservation of mass, energy and momentum.

x

Mechanistic non-equilibrium flow quality or profile fit model option to represent slip with thecoolant channels.

x

Steam line includes representation of the MSIV, turbine control and stop valves, RSV andsteam bypass valves.

x

Method of characteristics used to solve conservation equations in the steam lines.

x

Turbine representationx

Structural metal components represented. Reactor protection and safety systems represented.

x

Control systems represented. Complete self-initialisation of all components and models.

x

Provisions to represent a wide variety of transient and accident scenarios. Flexible restartcapability. British or Sl input/output option.

TRAC-BF1/COS3D (NFI, Japan)
NFI’s code system used for this benchmark is TRAC-BF1/COS3D. COS3D based on modified
one-group neutronics model is a three-dimensional core simulator. TRAC-BF1 is a plant simulator
based on two-fluid model. TRAC-BF1/COS3D is a coupled system of both codes, which areconnected using a parallel computing tool.
COS3D is a 3-D BWR core simulator used for designing and licensing analyses and coremanagements of commercial BWR plants in Japan. The neutronics model deals with three-dimensional
geometry of rectangular co-ordinates. The characteristics of COS3D neutron kinetics model are as
follows:x

modified one-group time-dependent diffusion equation derived from three-group diffusion
equation;x

six delayed neutron precursor groups;x

direct consideration of feedback effect due to changes of moderator density, fuel temperatureand control rod movement.

TRAC-BF1 includes a full non-homogeneous, non-equilibrium, two-fluid thermal-hydraulicmodel of two-phase flow. This also includes detailed modelling of a fuel bundle, thermal equilibrium
critical flow model and so on. RPV is treated as three-dimensional nodalisation, and the othercomponents are one-dimensional. The fundamental equations of thermal-hydraulics consist of mass,energy and momentum for each phase.
Instantaneous variables, namely, moderator density and fuel temperature are calculated at each
CHAN component of TRAC-BF1. Those variables are transferred from TRAC-BF1 to COS3D via
Parallel Virtual Machine (PVM). After COS3D calculates the neutronic condition according to thosevariables, it returns the power distribution data to TRAC-BF1. Then TRAC-BF1 calculates thethermal-hydraulic condition in the plant based on the power distribution. Such a data transfer is
executed by turns at every time step on Unix or Linux environments.

117

TRAC-BF1/SKETCH-INS (NUPEC, Japan)
NUPEC used the SKETCH-INS/TRAC-BF1 coupled-code system in Exercise 2. The coupled-code
system was originally developed at the Japan Atomic Energy Research Institute (JAERI) by a couplingof the best-estimate BWR transient analysis code TRAC-BF1 with the three-dimensional neutron
kinetics code SKETCH-N. The coupling between the codes is organised using an interface module
based on the massage-passing library called Parallel Virtual Machine (PVM).
TRAC-BF1 is the latest public domain BWR version of TRAC, which concerns thermal-hydraulics,
fuel heat transfer and plant systems. Thermal-hydraulics utilises the two-fluid model that solves six
balance equations of mass, momentum and energy for liquid and vapour phases. Two-phase flow in thecore region is treated as one-dimensional parallel vertical flows. The heat transfer model solves 1-D
radial heat conduction equations. Standard finite differential method with staggered mesh is used forspace integration of both fluid flow and heat conduction. Time integration of the fluid flow equations
is performed by the semi-implicit scheme with the stability enhanced two-step (SETS) method.
The SKETCH-INS code is a modification of the SKETCH-N code that was originally developed
at JAERI. The SKETCH-INS code deals with neutron kinetics, which solves time-dependent diffusion
equations in three-dimensional Cartesian co-ordinates. The code treats two neutron energy groups andsix groups of delayed neutron precursors. In order to improve the spatial resolution accuracy, anassembly discontinuity factor (ADF) was implemented in the code upon the original one. Reactivity
feedback is taken into account with moderator density, fuel temperature, and control rod motion andreactor scram. The ANS-1979 standard decay heat model has been implemented in the code. Direct
gamma heating is taken into account for the in-channel active coolant flow. Numerical methods for theneutronic calculations are as follows. Polynomial and semi-analytical nodal method based on the
nonlinear iteration procedure is used for spatial integration of diffusion equations. Time integration of
the neutron kinetics equations is performed by the fully implicit scheme.
RETRAN-3D and CORETRAN (PSI, Switzerland)
RETRAN-3D
Within the STARS project at PSI, the code environment for the coupled 3-D reactor kinetics/
thermal-hydraulics transient analyses of the Swiss light water reactors (LWRs) is based principally on
RETRAN-3D and CORETRAN, both for PWR and BWR systems. (It should be noted that the
TRACE code since recently gets more and more importance within and without the project and that
other codes are used for specific applications: e.g. RAMONA for BWR stability.) Both codes play
distinct roles in this environment; RETRAN-3D is used for the analysis of coupled 3-D core/plantsystem transients, while CORETRAN is used for core-only dynamic analysis. An important aspect isthat both codes are based on an identical neutronics algorithm, allowing the use of CORETRAN as aninterface code to help prepare the 3-D core model for RETRAN-3D. This approach forms the basis of
the PSI 3-D transient analysis methodology.
Participation in the OECD/NRC Peach Bottom 2 (PB2) turbine trip (TT) benchmark was
prompted by the following considerations. First, the PSI methodology has so far only been assessed
for neutronically-driven transients, and for a PWR system transient. As the benchmark addresses a
BWR transient driven by system thermal-hydraulic perturbations, it extends the range of the codes’
assessment. Secondly, the benchmark incorporates three different phases, which are, from the PSI
point of view, well suited to a comprehensive assessment of all the participating codes. Consequently,
PSI participated in all three phases of the benchmark.

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RETRAN-3D MOD003.1, which is used in all three phases of the benchmark, is developed by
EPRI to perform licensing and best-estimate transient thermal-hydraulic analyses of LWRs and it ismaintained by CSA/USA. RETRAN-3D is used to analyse thermal-hydraulic transients and requires
numerical input data that completely describe the components and geometry of the system being
analysed. The input data include fluid volume sizes, initial flow, pump features, power generation,
heat exchanger properties, and material compositions.
RETRAN-3D can calculate a steady-state initialisation from a minimal amount of information.
The steady-state option computes volume enthalpies from a steady-state energy balance, with therestriction that generally only one enthalpy may be supplied per flow system. The range of applicationsof RETRAN-3D contains also the spatial kinetics behaviour of multi-dimensional reactor cores.
RETRAN-3D also permits the analysis of systems with non-equilibrium thermodynamic conditions
and allows for the presence of non-condensable gases in the fluid stream.
CORETRAN
CORETRAN-01 [1] is a three-dimensional core simulation program developed by EPRI, aimed at
performing both core depletion and core transient analyses for LWRs. The code principally consists ofan explicit coupling between a neutronic module and a thermal-hydraulic module, both “internally”
built-in as part of the code. In both modules, the core is represented using a full representation, i.e. one
neutronic channel per fuel assembly coupled to one single thermal-hydraulic channel. In the neutronic
module reflectors are treated explicitly, while in the thermal-hydraulic module, one or several bypass
channels can be added. Moreover, because the neutronic model has also been implemented in the
RETRAN-3D program [2], CORETRAN can be used as an interface code to prepare the 3-D coremodel for RETRAN-3D, which is the methodology applied at PSI [2]. To summarise, CORETRAN
can be seen as a plenum-to-plenum full core analysis tool making it very suitable not only for an
accurate steady-state core follow analysis [3] but also for the 3-D simulation of reactivity-initiatedaccidents [4-5] as well as for the detailed analysis of the dynamical core response to “external”
perturbations (i.e. specified by means of appropriate plenum-to-plenum boundary conditions).
Neutronics
The neutronic module solves in Cartesian 3-D geometry the steady-state and transient two-groupneutron diffusion equations and the delayed neutron precursor equations for six groups. Two distinct
nodal kinetic models are available. The first model is provided by means of the ARROTTA module
implemented as part of the code and based on the Analytical Nodalisation Method (ANM). The second
neutronic model uses a Coarse Mesh Finite Difference (CMFD) non-linear iteration procedure where
the local two-node problems are solved using a hybrid ANM/Nodal Expansion Method (NEM) kernel.
For both models, a dynamic frequency transformation of both the neutron fluxes and the delayed neutron
precursor concentrations is employed and fully implicit or semi-implicit schemes can be used for the
temporal discretisation. The cross-section model is based on a multi-dimensional interpolation from a
set of 1-D, 2-D and 3-D tables produced with an assembly lattice code and containing cross-sections
for base depletion calculations (i.e. as function of burn-up and historical variables) and for branchcalculations (i.e. to model instantaneous feedback effects). A macroscopic depletion model can beapplied to perform steady-state core follow analyses and an explicit model for the treatment of thetime-dependent variation of four fission products (xenon, iodine, promethium and samarium) is alsoavailable. A pin power reconstruction module for both steady-state and transient applications isavailable and based on polynomial expansions for the fast intra-nodal flux and hyperbolic functions
for the thermal flux, combined with several options for the corner-fluxes estimates. Finally, the assembly
spatial discretisation allows for heterogeneous axial nodalisation while a 1 u 1 mesh is normally applied
for the radial assembly representation, although a 2 u 2 mesh can be used for PWR applications.
119Thermal-hydraulics
The thermal-hydraulic (T-H) module is principally based on the VIPRE code with the following
three main options to solve the channel hydraulics. The first option is based on a four-equation modelwith forced flow along with a drift flux formulation and solved using a semi-implicit method. The
second option is originally from the VIPRE-01 code and consists of a three-equation homogeneous
equilibrium model (HEM) along with void and slip correlation profiles and solved using a fully
implicit method. The third option is taken from the VIPRE-02 code and is based on a two-fluid
six-equation model solved using a fully implicit scheme. Any of these options can be applied to a fullcore analysis with explicit coupling to the neutronic module so that a single separate T-H flow channel
is assigned to each (neutronic) fuel assembly. A heterogeneous axial nodalisation of the T-H channels
can be applied in order to allow for axial variations of the fuel assembly design (flow area, wetted/heatedperimeters) and to allow for a detailed specification of pressure loss coefficients (inlet, spacers, outlet).
Leakage flows from the lower plenum and from the fuel assemblies to the bypass channel can bemodelled as well as water tube flows within fuel assemblies.
The boundary conditions can be specified for both steady-state and transient applications andinclude, among others, inlet enthalpy, total core flow (alternatively individual channel flow) and coreoutlet pressure (alternatively core pressure drop). When the total core flow and core outlet pressure are
specified, a flow split calculation is performed to determine the individual channel flows including
bypass with the condition for a uniform core pressure drop. A broad range of critical heat flux (CHF),
critical power ratio (CPR), two-phase and heat transfer correlations are available, as is the possibility
to enter “user” correlations. Additionally, PWR cross-flows can be taken into account when using theHEM or the two-fluid options. With these two options, detailed sub-channel analysis can also be
performed where a fuel assembly is divided into a number of channels that communicate laterally andwhere the (time-varying) axial power shape can be defined. (i.e. no coupling to neutronics). Concerning
the solution of the fuel heat conduction equation, an implicit finite-difference method is employed.
A non-linear iterative procedure with the channel hydraulic solution is used to ensure convergencewith regards to the wall heat fluxes, the rod temperatures and the channel flows. The heat conduction
model can treat nuclear fuel rods but also electric heater rods, hollow tubes and walls. Fuel properties
are based on the MATPRO code but can alternatively be specified by the user. A dynamic conductancemodel for the (fuel-cladding) gap, aimed at taking into account changes in fuel rod dimensions and fillgas pressure, is also available.
References[1]

Eisenhart, L.D., A.F. Dias, J.L. Westacott, T.J. Downar, H.G. Joo. CORETRAN-01: A Threedimensional Program for Reactor Core Physics and Thermal-hydraulics Analysis. Volume 1:
Theory and Numerical Analysis, EPRI Report WO-3574, Revision 3, November 2000 (2000).

[2]

Paulsen, M.P., C.E. Peterson, G.C. Gose, J.H. McFadden, J.G. Shatford, J.L. Westacott,P.P. Cebull, J.Y. Wu, P.J. Jensen, RETRAN-3D – A Program for Transient Thermal-hydraulic
Analysis of Complex Fluid Flow Systems. Volume 1: Theory and Numerics, EPRI Report
NP-7450 (A), Volume 1, Revision 5, July 2001 (2001).

[3]

Ferroukhi, H., F. Holzgrewe, P. Coddington, ”Towards a Best-estimates Steady-state andTransient Analysis Using the CORETRAN Code”, Proc. Int. Mtg. Best-estimate Methods in
Nuclear Safety Installation Analysis (BE2000), Washington, DC, USA, 12-16 November 2000
(2000).

120

[4]Ferroukhi, H., P. Coddington, “Uncontrolled Rod Bank Withdrawal Benchmark Analyses with
CORETRAN and RETRAN-3D”, Proc. Int. Mtg. Mathematical Methods for Nuclear
Applications (M&C 2001), Salt Lake City, Utah, USA, 9-13 September 2001 (2001).

[5]

Ferroukhi, H., P. Coddington. “The Analysis of Pressurised Water Reactor and Boling Water
Reactor Reactivity Transients with CORETRAN and RETRAN-3D”, Nuclear Technology,
Vol. 142, No. 1, pp. 19-34, April 2003 (2003).

TRAC-BF1/NEM (PSU, USA)
TRAC-BF1
TRAC-BF1 is an advanced best-estimate computer program for boiling water reactor accident
analysis [1]. The TRAC-BWR Code Development Program at the Idaho National Engineering
Laboratory (INEL) was a program developing versions of the Transient Reactor Analysis Code (TRAC)
to provide the US Nuclear Regulatory Commission (NRC) and the public with a best-estimate capability
for the analysis of accidents and transients in boiling water reactor (BWR) systems and related
experimental facilities. This effort began in October 1979 and resulted in the first publicly released
version of the code, TRAC-BD1, 1-1 which was sent to the National Energy Software Center in
February 1981. The mission of this first version of the code was to provide a best-estimate capability
for the analysis of design basis loss-of-coolant accidents (LOCAs) in BWRs. The code provided aunified and consistent treatment of the design basis LOCAs sequence beginning with the blowdown
phase, through heat-up, then re-flood with quenching, and finally ending with the refill phase of the
LOCA scenario. New models developed for TRAC-BD1 in order to accomplish its mission included(a) a full two-fluid non-equilibrium, non-homogeneous thermal-hydraulic model of two-phase flow inall parts of the BWR system, including a three-dimensional treatment of the BWR pressure vessel;(b) a detailed model of a BWR fuel bundle, which includes the following models: a radiation heattransfer model for thermal radiation between multiple fuel rod groups, the inner surface of the channel
wall, and the liquid and steam phases in the channel; a leakage path model; and a quench front
tracking capability for both falling films and bottom flooding quench fronts on all rod groups and theinner surface of the channel wall; (c) simplified models of BWR hardware components, such as thejet pump and separator-dryer; (d) a counter-current flow limiting model for BWR geometries;(e) a non-homogeneous critical flow model; and (f) flow regime-dependent constitutive relations forthe transfer of mass, energy, and momentum between the liquid and steam phases in two-phase flow
and between each phase and structure.
The mission of the second publicly released version of the code, TRAC-BD1/MOD1, was expanded
to include not only large- and small-break LOCAs but also operational transients and anticipatedtransients without scram (ATWS) for which point reactor kinetics is applicable. Models developed tosupport the broadening of the scope of the mission of the TRAC-BWR codes included:xbalance of plant models, such as turbine, feedwater heaters and condenser;xa simple lumped parameter containment model;xreactivity feedback model for use in the point reactor kinetics model;xsoluble boron transport model;x

non-condensable gas transport model;x

two-phase level tracking model;121xcontrol systems model;x

generalised component-to-component heat and mass transfer models;x

improved constitutive models for the transfer of mass, energy and momentum between thetwo phases and between the phases and structure.

User convenience features, such as free-format input and extensive error checking of the input
data, were also included in TRAC-BD1/MOD1.
The mission of TRAC-BF1/MOD1 was the same as for TRAC-BD1/MOD1, however the newcapabilities built into this code make it more suitable for that mission. The new models and capabilities
in TRAC-BF1/MOD1 include:xmaterial Courant-limit-violating numerical solution for all one-dimensional hydrauliccomponents;x

implicit steam separator/dryer model;x

implicit turbine model;x

improved interfacial heat transfer;x

improved interfacial shear model;xa condensation model for stratified vertical flow;x

one-dimensional neutron kinetics model;x

improved control system logic and solution method.

In addition to these code improvements, a preload processor was written for TRAC-BF1, itsgraphic routines were improved for adaptation to the Nuclear Plant Analyser (NPA) at the INEL, andmore than 95% of the coding has been converted to ANSI Standard FORTRAN 77.
TRAC-BF1/MOD1 can be applied to any BWR accident analysis or thermal-hydraulic test
facility, including those requiring reactivity feedback effects, control system simulation, and/or abalance-of-plant model. TRAC-BF1/MOD1 was applied to experimental facilities ranging from simple
pipe blowdowns, such as the Edwards pipe tests, to integral LOCA tests, such as the two-loop test
apparatus (TLTA) facility, and even to multi-dimensional test facilities such as the slab core test
facility (SCTF). BWR small-break LOCAs have also been simulated with TRAC-BD1. The BWR fuelbundle model is quite versatile and was used to simulate not only BWR fuel bundles within a BWR
reactor vessel but also stand-alone, single-bundle experiments in which advanced bundle hydraulics
and heat transfer models are required.
NEM-3D
The Nodal Expansion Method (NEM) is a 3-D multi-group nodal code developed and used at thePennsylvania State University (PSU) for modelling both steady-state and transient core conditions [2].
The code has options for modelling 3-D Cartesian, cylindrical and hexagonal geometry. This code isbased on the nodal expansion method for solving the nodal equations in three dimensions. It utilises atransverse integration procedure and is based on the partial current formulation of the nodal balance
equations. The leakage term in the one-dimensional transverse integrated equations is approximatedusing a standard parabolic expansion by using the transverse leakages in three neighbour nodes. The
122

nodal coupling relationships are expressed in partial current formulation and the time dependence ofthe neutron flux is approximated by a first order, fully explicit, finite difference scheme. This method
has been shown to very efficient although it lacked the precision of the advanced nodal codes. An
upgrade of the method has recently been completed, replacing the fourth-order polynomial expansion
with a semi-analytical expression utilising a more accurate approximation of the transverse leakage.
This code has been benchmarked for Cartesian, cylindrical and hexagonal geometry. NEM is coupledwith the Penn State versions of TRAC-PF1 and TRAC-BF1.
The NEM spatial model is based on the transverse integrated procedure. Two levels of
approximation are used: fourth-degree transverse integrated flux representation and the quadratic leakage
approximation. The nodal coupling relationships are expressed in a partial current formulation. The
time dependence of the neutron flux is approximated by a first order, fully implicit, finite-difference
scheme, whereas the time dependence of the neutron precursor distributions is modelled by a linear
time-integrated approximation. The coarse-mesh-rebalance and asymptotic extrapolation methods areused to accelerate convergence of the iterative solution process. Several benchmark problems wereused to assess the NEM model in both steady-state and transient conditions. Very good agreement was
obtained among the reference results and those from NEM.
TRAC-BF1 and NEM are coupled using parallel virtual machine (PVM) environment [3]. The
numerical scheme of the PVM coupling is a semi-implicit scheme for the calculated power [4].
In most cases (especially during steady state calculation), the number of times the three-dimensional(3-D) kinetics calculations performed can be optimised to speedup the calculation. For this purpose, amultiple time step marching scheme is implemented in TRAC-BF1/NEM calculation. This scheme
allows TRAC-BF1 solution to march several steps while NEM only marched one large time step.
References[1]

Giles, M., et al., TRAC-BF1/MOD1: An Advanced Best Estimate Computer Program for
Boiling Water Reactor Accident Analysis Volume 1: Model Description, NUREG/CR-4356
EGG-2626, pp. 1-1 to 1-2, May 1992.

[2]

Bandini, R., “A Three-dimensional Transient Neutronics Routine for the TRAC-PF1 Reactor
Thermal Hydraulic Computer Code”, PhD Thesis, The Pennsylvania State University (1990).

[3]

Geist, A., et. al., “PVM: Parallel Virtual Machine – A Users Guide and Tutorial for Networked
Parallel Computing”, The MIT Press, Cambridge, Massachusetts, London, England (1994).

[4]

Lu, S., “GE Simplified Boiling Water Reactor Stability Analysis in Time Domain”, PhD Thesis,
The Pennsylvania State University (1997).

TRAC-BF1/ENTRÉE (TEPSYS, Japan)
This system is composed of the 3-D nodal kinetic code ENTRÉE and the state-of-the-art
two-fluid thermal-hydraulic plant simulator TRAC/BF1. Numerical methodologies of ENTRÉE andthe parallel coupling techniques of these two codes were described in detail in a different paper writtenby the authors (see the reference below). Figure A-1 depicts the linkage of two codes applied in thisbenchmark.
Neutronic constants consist of macroscopic and microscopic cross-sections, discontinuity factors,
detector response parameters and so on. They are evaluated by the detailed two-dimensional assembly123transport code and are transformed into a binary library based on the multiple-table function of historicaland instantaneous variables. Exposure weighted moderator density, fuel temperature and control rod
density are classified as historical variables together with exposure. They are evaluated by the 3-D
steady-state core simulator. On the other hand, instantaneous variables consist of moderator densityand fuel temperature evaluated at test points. They are solved as state variables of CHAN components
in TRAC/BF1 and are updated at every time step. The control rod density is normally controlled by
ENTRÉE itself or it is transferred from TRAC/BF1 together with arbitrary trip signals.
Reference
Hotta, A., H. Ninokata A.J. Baratta, “Development of Parallel Coupling System Between Three
Dimensional Nodal Kinetic Code ENTRÉE and Two-fluid Plant Simulator TRAC/BF1”, J. Nucl. Sci.
Technol., 37 (10), 840 (2000).
Figure A-1. TRAC-BF1/ENTRÉE coupling scheme

124

RELAP5/PARCS (U.PISA, Italy)
RELAP5The light water reactor (LWR) transient analysis code, RELAP5, was developed at the Idaho
National Engineering Laboratory (INEL) for the US Nuclear Regulatory Commission (NRC). Codeuses include analyses required to support rule-making, licensing audit calculations, evaluation of
accident mitigation strategies, evaluation of operator guidelines and experiment planning analysis.
RELAP5 has also been used as the basis for a nuclear plant analyser. Specific applications haveincluded simulations of transients in LWR systems such as loss of coolant, anticipated transients
without scram (ATWS), and operational transients such as loss of feedwater, loss of off-site power,
station blackout and turbine trip. RELAP5 is a highly generic code that, in addition to calculating the
behaviour of a reactor coolant system during a transient, can be used for simulation of a wide variety
of hydraulic and thermal transients in both nuclear and non-nuclear systems involving mixtures ofsteam, water, non-condensable and solute.
The RELAP5/MOD3 code is based on a non-homogeneous and non-equilibrium model for thetwo-phase system that is solved by a fast, partially implicit numerical scheme to permit economical
calculation of system transients. The objective of the RELAP5 development effort from the outset was
to produce a code that included important first-order effects necessary for accurate prediction ofsystem transients but that was sufficiently simple and cost effective so that parametric or sensitivity
studies were possible.
The code includes many generic component models from which general systems can be simulated.
The component models include pumps, valves, pipes, heat releasing or absorbing structures, reactor
point kinetics, electric heaters, jet pumps, turbines, separators, accumulators and control systemcomponents. In addition, special process models are included for effects such as form loss, flow at anabrupt area change, branching, choked flow, boron tracking and non-condensable gas transport.
The system mathematical models are coupled into an efficient code structure. The code includes
extensive input checking capability to help the user discover input errors and inconsistencies. Also
included are free-format input, re-start, re-nodalisation and variable output edit features. These userconveniences were developed in recognition that generally the major cost associated with the use of asystem transient code is in the engineering labour and time involved in accumulating system data anddeveloping system models, while the computer cost associated with generation of the final result is
usually small.
The code development has benefited from extensive application and comparison to experimental
data in the LOFT, PBF, Semiscale, ACRR, NRU and other experimental programs.
The numerical solution is obtained with a semi-implicit scheme based on replacing the system ofdifferential equations with a system of finite-difference equations partially implicit in time. The method
has a material Courant time step stability limit. However, this limit is implemented in such a way thatthe single-node Courant violations are permitted without adverse stability effects.
PARCS
PARCS is a three-dimensional (3-D) reactor core simulator which solves the steady-state andtime-dependent neutron diffusion equation to predict the dynamic response of the reactor to reactivity
perturbations such as control rod movements or changes in the temperature/fluid conditions in thereactor core. The code is applicable to both PWR and BWR cores loaded with either rectangular or125hexagonal fuel assemblies. The neutron diffusion equation is solved with two energy groups for therectangular geometry option, whereas any number of energy groups can be used for the hexagonal
geometry option. PARCS is coupled directly to the thermal-hydraulics systems codes TRAC-M and
RELAP5 which provide the temperature and flow field information to PARCS during the transient.
The thermal-hydraulic solution is incorporated into PARCS as feedback into the few-groupcross-sections. Neutronically, the coarse mesh finite difference (CMFD) formulation is employed in
PARCS to solve for the neutron fluxes in the homogenised nodes. In rectangular geometry, theanalytic nodal method (ANM) is used to solve the two-node problems for accurate resolution of
coupling between nodes in the core, whereas the triangle-based polynomial expansion nodal (TPEN)
method is used for the same purpose in hexagonal geometry.
Numerous sophisticated spatial kinetics calculation methods have been incorporated into PARCS
in order to accomplish the various tasks with high accuracy and efficiency. For example, the CMFD
formulation provides a means of performing a fast transient calculation by avoiding expensive nodal
calculations at times in the transient when there is no strong variation in the neutron flux spatial
distribution. Specifically, a conditional update scheme is employed in PARCS so that the higher ordernodal update is performed only when there are substantial changes in the core condition to require
such an update. The temporal discretisation is performed using the theta method with an exponential
transformation of the group fluxes. A transient fixed source problem is formed and solved at eachtime point in the transient. For spatial discretisation, the stabilised ANM two-node kernel or themulti-group TPEN kernel is used to obtain the nodal coupling relation that represents the interface
current as a linear combination of the node average fluxes of the two nodes contacting the interface.
TRAC-BF1/NEM (UPV, Spain)
The coupled code used by the UPV for the Exercise 2 was the TRAC-BF1/NEM code.
TRAC-BF1
The TRAC code is an advanced, best-estimate computer program for BWR transient and accident
analysis. It belongs to the TRAC series of codes that are six-equation, non-equilibrium two-fluid
codes. The TRAC mathematical models are intended to solve a coupled set of field equations which is
set up to describe the T-H behaviour of the coolant flow in a BWR system as well as the flow ofenergy in the fuel elements and the structural components of the reactor. The two-fluid models for the
fluid flow in the BWR system are solved in TRAC in the one- and three-dimensional components.
This code is modular in nature. The above feature makes it easier to add or modify the code models.
NEM
The NEM code is a three-dimensional neutron kinetics model for performing steady-state andtransient simulations, based on the Nodal Expansion Method (NEM). Two levels of approximation
have been used: fourth-degree transverse-integrated flux representation and the quadratic leakage
approximation. The nodal coupling relationships are expressed in a partial current formulation. The
time dependence of the neutron flux is approximated by a first order, fully implicit, finite-difference
scheme, whereas the time dependence of the neutron precursor distributions is modelled by a linear
time-integrated approximation. The coarse-mesh-rebalance and asymptotic extrapolation methods areused to accelerate convergence of the iterative solution process. Several benchmark problems havebeen used to assess the NEM model in both steady-state and transient conditions.
126

The NEM models are based on two-energy-group diffusion theory equations with an option tochoose between Cartesian and hexagonal geometry. Calculations include six delayed neutron precursor
groups with definition for the delayed neutron precursor parameters in each spatial node. The NEM
solution has incorporated assembly discontinuity factors. The solution method also accounts for the
direct treatment of time dependence with an implicit integration scheme. To reproduce initialsteady-state conditions, a core-modelling methodology was developed. Some of the NEM code’s
advanced features include the selection of up to six energy groups, 1-D decay heat model, and an
efficient and flexible cross-section generation algorithm.
TRAB-3D (VTT, Finland)
TRAB-3D [1] is the latest member of the code system developed at VTT Energy for LWR reactor
dynamics calculations. The neutron kinetics model of the new code is based on the three-dimensional
VVER dynamics code HEXTRAN [2,3], but the nodal equations are solved in rectangular fuel assembly
geometry, instead of hexagonal. In the neutronics solution the two-group nodal fluxes are constructedfrom two spatial modes, the asymptotic or fundamental mode and the transient mode. The former
mode is approximated by polynomials and the latter by exponential functions. Also, flux discontinuity
factors can be specified on the transverse interfaces of nodes. The nodal flux model of TRAB-3D
contains eight degrees of freedom per group in a transverse cross-section and they are adjusted bycontinuity conditions for group fluxes and currents and for their first moments at nodal interfaces.
Thermal-hydraulics and fuel heat transfer models are the same as in the axially 1-D dynamics code
TRAB [4], which includes descriptions of both the reactor core and the BWR cooling circuit. Thus the
dynamic behaviour of the whole primary circuit of a reactor can be analysed with TRAB-3D. For PWR
dynamics the core model of TRAB-3D is coupled with the SMABRE PWR circuit model.
Comparisons with fine-mesh finite difference calculations have shown that TRAB-3D solves the
diffusion equations for homogeneous fuel assemblies of a two-dimensional reactor core with anaccuracy of better than 1% in assembly powers. The validation history of TRAB-3D, so far, includes
the calculation of OECD/NEACRP 3-D light water reactor benchmark problems and verification
against measurements from real BWR plant transients. Much of the validation, however, has alreadybeen done by various calculations with HEXTRAN and TRAB since the same models for neutron
kinetics and thermal-hydraulics description are used in TRAB-3D.
References[1]

Kaloinen, E., R. Kyrki-Rajamäki, “TRAB-3D a New Code for Three-dimensional Reactor
Dynamics”, CD-ROM Proceedings of ICONE-5, 5th International Conference on Nuclear
Engineering, Nice, France, paper ICONE5-2197 (1997).

[2]

Kyrki-Rajamäki, R., “HEXTRAN: Three-dimensional Reactor Dynamics Code for VVER-reactor
Cores”, Proc. of the Int. Topical Meeting on Advances in Mathematics, Computations andReactor Physics, Pittsburgh, USA, American Nuclear Society, pp. 30.2 4-1 to 30.2 4-5 (1990).

[3]

Kyrki-Rajamäki, R., “Three-dimensional Reactor Dynamics Code for VVER-type Nuclear
Reactors”, VTT Publications 246, Technical Research Centre of Finland, Espoo, Finland(Thesis for DrTech) (1995).

[4]

Rajamäki, M., TRAB. A Transient Analysis Program for BWR, Part 1. Principles, Report 45,
Technical Research Centre of Finland, Nuclear Engineering Laboratory, Helsinki, Finland (1980).
127

POLCA-T (Westinghouse, Sweden)
POLCA-T is a coupled 3-D core neutron-kinetics and system thermal-hydraulics computer code.
The code is able to perform steady-state and transient analysis of BWR. The code is based to different
extend on models and tools for BWR and PWR analysis used in POLCA7, BISON and RIGEL codes.
The code utilises new advanced methods and models in neutron kinetics, thermal-hydraulics andnumerics. The main features of the code can be summarised as follows:x

Full 3-D model of the reactor core: The neutronics models in the code are the same as those in
the well-known static core analyser POLCA7 with addition of proper 3-D kinetics model.

xAdvanced five-equation thermal-hydraulic model with thermal non-equilibrium description of
the steam-water mixture and its coupling to the heat structures. Separate mass and energybalances of the phases. Drift flux model that can handle all flow regimes.

xHeat transfer model that works also in post-dry-out.

x

The gas phase can consist of steam and non-condensable gases. The liquid phase can containdissolved non-condensable gas.

x

Boron transport model.

x

Use of the same thermal-hydraulics model for core and plant systems.

x

2-D fuel rod heat transfer model, gas gap model consistent with design code and complete
range of heat transfer regimes. Code is also able to model all plant heat structures.

x

Dry-out and DNB correlations (using pin power distributions model).

x

Full geometrical flexibility of the code: volume cells, flow paths, heat structures, materials,
pumps, measurements, controls, etc. are all input data. Code is able to analyse different power
plants and test facilities.

x

Balance of plant, control and safety systems: The reactor pressure vessel, external pump loops,
steam system and feedwater system, ECC systems and steam relief system are modelled to thedesired details. Large and valuable set of input models that already exists can be used.

x

Stable numerical method that allows long time steps, which is used also for steady-statesolution. The low dependence on the size of the time step is due to the implicit numericalintegration, which is close to second order by means of T-weighting.

Due to the above-mentioned features POLCA-T code makes possible a comprehensive approachto plant analysis with full consistency in steady-state and transient calculations. The consistency in
BWR core and system modelling, when transient analyses are performed, is also achieved by using thesame basic model and the same design database for core data (cross-section data, burn-up, xenon andother 3-D distributions obtained from depletion calculations), fuel thermal-mechanical behaviour(properties) and system data. Thus full consistency is also possible between predicted core and systemparameters and their behaviour over a very wide range of phenomena and processes important both fordesign and safety analyses.
The application areas of the POLCA-T code consist of three groups: BWR steady-state core
design, BWR stability, transients and accident analyses and modelling of experimental test facilities.

128

Applications for BWR steady-state core design are covered by the POLCA7 wide-range
capabilities regarding:x

evaluation of reactivity and power distribution at cold and hot core conditions;xdetailed thermal-hydraulic analysis;xcontrol operations (reactivity search modes: boron, power, flow, control rod, axial offset andminimum boron control);x

detectors simulation;x

evaluation of fuel pin and pellet powers and burn-up;

xevaluation of peaking factors based on pin results;xdry-out and DNB margin calculations (based on pin power distributions);x

fission heat load parameters (margins) calculations;xpellet cladding interaction calculations;xdepletion calculation with tracking of the most important fissile isotopes and fission products;xfuel bundle, control rod, fuel channel and fixed in-core detectors depletion;x

shutdown margins evaluation;x

shutdown cooling;x

xenon transients;xreactivity coefficients (void, burn-up, moderator temperature).

Applications to BWR safety analysis include operational transient, stability, RIA, ATWS, ATWC
and LOCA as follows:x

feedwater flow increase/feedwater temperature decrease transients;x

loss of feedwater flow transients;xpressure increase transients – analysis with regard to the cladding;xpressure increase transients – analysis with regards to the reactor coolant pressure boundary;xpressure decrease transients;x

re-circulation flow increase transients;x

re-circulation flow decrease transients;xcontrol rod withdrawal error;x

inadvertent loading transients;xcontrol rod drop accident;xstability analysis;xanticipated transients without scram (ATWS);x

anticipated transients without control rods (ATWC).

129

The POLCA-T code is well adapted to analyse the type of scenarios with a number of failing
control rods. Boron transport model makes it possible also to analyse different types of boron
shutdown scenarios. Applications to modelling of separate test facilities (such as FRIGG) are foreseen
not only for code validation but also for pre-test analysis and experiments planning and optimisation.
References
Panayotov, D., U. Bredolt, P. Jerfsten, “POLCA-T – Consistent BWR Core and Systems Modelling”,
ANS/AESJ/ENS Int. Conf. Top Fuel 2003, Paper 410, Wurzburg (G), 16-19 March 2003.
Lindahl, S-Ö., E. Müller, “Status of ABB Atom’s Core Simulator POLCA”, Int. Conf. PHYSOR96,
Mito, Japan, 16-20 September 1996.
Wijkström, H., “ABB Atom’s New Code for 3-D Static and Transient Analysis”, Proceedings of theGerman Nuclear Society Workshop on Thermal and Fluid Dynamics, Reactor Physics and Computing
Methods, Rossendorf, Germany, 31 January-1 February 2000.
Panayotov, D., “OECD/NRC BWR Turbine Trip Benchmark: Simulation by POLCA-T Code”,
PHYSOR2002 International Conference on the New Frontiers of Nuclear Technology: Reactor
Physics, Safety and High-performance Computing, Track H-2, Paper 3C-02, Seoul, Korea.

130

Appendix B
QUESTIONNAIRE FOR EXERCISE 2
OF THE OECD/NRC BWR TT BENCHMARK131QUESTIONNAIRE FOR EXERCISE 2

I.

Thermal-hydraulic core modela) Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D and number of channels orcells) – how are channels/T-H cells chosen?
b) Bypass channel modelling?
c) Number of heat structures (fuel rods) modelled?
d) Which core thermal-hydraulic initial and transient boundary conditions are used and how?
e) Radial and axial heat structure (fuel rod) nodalisation?
f) Used correlations for fuel properties vs. temperature?

II. Core neutronics modela) Number of radial nodes per assembly?
b) Axial nodalisation?
c) Radial and axial reflector modelling?
d) Cross-section interpolation procedure used?
e) Used method to get a critical reactor at the beginning of transient?
f) How xenon effect is modelled?
g) How Assembly Discontinuity Factor (ADF) is modelled?
h) Is bypass density correction used? If it is used, how it is modelled?
i) How decay heat modelling is modelled?
III. Coupling schemesa) Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
b) Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
c) Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
d) Temporal coupling scheme?
e) Coupling numerics – explicit, semi-implicit or implicit?
f) Coupling method – external or internal?
g) Coupling design – serial integration or parallel processing?
IV. Generala) User assumptions?
b) Specific features of the used codes?
c) Number of solutions submitted per participant and how they differ?

133

CRONOS2/FLICA4 (CEA, France)
I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
Two models were used (two sets of results): 33 channels, 1-D, as proposed by the benchmark
specifications and 764 channels, 3-D, i.e. one channel per fuel assembly. In both cases, there
are 37 axial nodes.

b)Bypass channel modelling?
One average bypass channel for the whole core.

c)Number of heat structures (fuel rods) modelled?
As many as channels, i.e. 33 and 764 heat structures.

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
We have used the specified boundary conditions, mass flow and temperature at core inlet,pressure at core outlet. Temperature is actually converted into enthalpy, using the specified
pressure at core inlet.

e)Radial and axial heat structure (fuel rod) nodalisation?
There are 10 radial nodes (6 in the fuel, 4 in the cladding) in each fuel rod, and 37 axial
nodes.

f)

Used correlations for fuel properties vs. temperature?
We have used the specified correlations for heat capacity, conductivity. Volumetric mass isconstant versus temperature (cf. specifications).

II. Core neutronics modela)

Number of radial nodes per assembly?
764 radial nodes.

b)

Axial nodalisation?
26 axial nodes.

c)Radial and axial reflector modelling?
The reflector has the same nodalisation as the fuel assemblies.

d)

Cross-section interpolation procedure used?
CRONOS2 internal procedure, based on the same linear interpolation algorithm as specified.
134

e)

Used method to get a critical reactor at the beginning of transient?
The fission is normalised by the steady-state eigenvalue.

f)

How xenon effect is modelled?
Xenon is not modelled, that means we do not correct the cross-sections for xenon effect.

g)

How Assembly Discontinuity Factor (ADF) is modelled?
ADF are not taken into account.

h)Is bypass density correction used? If it is used, how it is modelled?
Density is corrected for bypass as specified.

i)

How decay heat modelling is modelled?
Decay heat is modelled as specified: total decay heat versus time from the specifications, andconstant 3-D distribution (same as initial fission power).

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
There is one heat structure per hydraulic channel. The axial nodalisation is the same forhydraulic channels and heat structures.

b)

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
For axial direction, we use a standard linear projection algorithm implemented in FLICA4.
For radial direction, either the nodalisation is the same (764 channels), or (33 channels) a
specific method was developed to lump the fuel assemblies.

c)

Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
Same as b).

d)

Temporal coupling scheme?
The time step is the same for neutronics and thermal-hydraulics.

e)

Coupling numerics – explicit, semi-implicit or implicit?
Semi-implicit.

f)

Coupling method – external or internal?
External, using ISAS software.

g)

Coupling design – serial integration or parallel processing?
Parallel processing.

135

IV. Generala)User assumptions?
None.

b)

Specific features of the used codes?
?

c)Number of solutions submitted per participant and how they differ?
Two solutions were submitted. They differ only by thermal-hydraulics: 33 or 764 channels[cf. I.a)].

136

DYN3D (FZR, Germany)
I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
One T-H channel/fuel assembly.

b)Bypass channel modelling?
One average T-H channel for bypass in the core.

c)Number of heat structures (fuel rods) modeled?
One fuel rod/T-H channel.

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
Total mass flow through the core and core bypass, inlet temperatures, core exit pressure.

e)Radial and axial heat structure (fuel rod) nodalisation?
10 radial and 24 equal axial nodes.

f)Used correlations for fuel properties vs. temperature?
Specified.

II. Core neutronics modela)

Number of radial nodes per assembly?
One node/assembly.

b)

Axial nodalisation?
24 equal axial layers for the core and 2 layers for axial reflectors =26 layers.

c)

Radial and axial reflector modelling?
Radial reflector modelled by assemblies, each of axial reflectors were modelled by one layerof 15.24 cmd)

Cross-section interpolation procedure used?
Yes.

e)

Used method to get a critical reactor at the beginning of transient?
Eigenvalue keff.

137

f)

How xenon effect is modelled?
Given Xe concentration.

g)

How Assembly Discontinuity Factor (ADF) is modelled?
Explicitly.

f)

Is bypass density correction used? If it is used, how it is modelled?
Bypass densities were taken into account by using the specified formula of cross-section
calculation.

g)

How decay heat modelling is modelled?
The own decay heat model of DYN3D was used by assuming a very long fuel cycle with theinitial power distribution.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
One fuel rod/T-H channel, 24 equal axial core layers.

b)

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
One T-H channel/fuel assembly, 24 equal axial core layers.

c)Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
One fuel rod/fuel assembly, 24 equal axial core layers.

d)Temporal coupling scheme?
Several neutronic time steps/T-H time step.

e)

Coupling numerics – explicit, semi-implicit or implicit?
Explicit with iterations between neutronics and thermal-hydraulics.

f)Coupling method – external or internal?
Internal.

g)

Coupling design – serial integration or parallel processing?
Serial integration.

138

IV. Generala)User assumptions?
Use of the implemented boiling model of Molochnikov.

b)Specific features of the used codes?
See code description.

c)

Number of solutions submitted per participant and how they differ?
In addition to the three-dimensional solution a one-dimensional solution with cross-sections
condensed from several steady-state calculations were submitted.

139

QUABOX/CUBBOX-ATHLET (GRS, Germany)
I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
33 T-H channels, as specified, and 765 T-H channels (764 fuel assemblies + 1 reflector
assembly).

b)

Bypass channel modelling?
One bypass channel.

c)Number of heat structures (fuel rods) modelled?
33 (one average fuel rod for each T-H channel), 764 (one average fuel rod for each T-Hchannel).

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
As specified.

e)Radial and axial heat structure (fuel rod) nodalisation?
Axial: 24 nodes in active core and one node per upper and lower reflector, radial: one per
assembly.

f)

Used correlations for fuel properties vs. temperature?
Built-in ATHLET correlations (very similar to the specified).

II. Core neutronics modela)

Number of radial nodes per assembly?
1:1 modelling.

b)

Axial nodalisation?
24+2 nodes.

c)Radial and axial reflector modelling?
Yes.

d)

Cross-section interpolation procedure used?
Subr. lin4d.f – as specified.

e)Used method to get a critical reactor at the beginning of transient?
Keff search, adjustment of fission cross-sections.

140

f)

How xenon effect is modelled?
As specified (additional cross-section in the XS libraries).

g)

How Assembly Discontinuity Factor (ADF) is modelled?
ADF is not modelled.

h)

Is bypass density correction used? If it is used, how it is modelled?
Yes. Simplified model is developed based on non-boiling of the coolant in the bypass channels.

i)

How decay heat modelling is modelled?
The specified table values are implemented.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
1:1 scheme and as specified (33 T-H channels).

b)

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
1:1 scheme.

c)Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
1:1 scheme and as specified (33 T-H channels).

d)Temporal coupling scheme?
Specific synchronisation of time-step.

e)

Coupling numerics – explicit, semi-implicit or implicit?
Serial, semi-implicit.

f)

Coupling method – external or internal?
Internal.

g)

Coupling design – serial integration or parallel processing?
Serial.

IV. Generala)User assumptions?
No.

141

b)

Specific features of the used codes?
No.

c)

Number of solutions submitted per participant and how they differ?
Only one solution with 764 T-H channels.

142

DNB-3D (NETCORP, USA)

I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
The core T-H model is a 1-D homogeneous equilibrium model that consists of 185 channels
with each channel essentially representing 4 fuel bundles. Each T-H channel has 24 equal
length axial nodes. The void distribution that is used in the neutronic calculations uses a
profile fit model to obtain the effects of slip.

b)Bypass channel modelling?
The core bypass is represented by 1 channel that has a single axial node.

c)

Number of heat structures (fuel rods) modelled?
There is 1 average fuel rod per T-H channel. Each fuel rod has 24 axial nodes that correspondto the T-H nodes. Each fuel node is modelled by 7 concentric rings (5 in the oxide and 2 inthe cladding).

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
The initial and transient boundary conditions that were used corresponded to those provided
in the final specification and/or on the ftp site. The core inlet temperature and core inlet andoutlet pressures were used as input to calculate the core inlet enthalpy and core averagepressure. The flow distribution amongst the T-H channels was calculated based on thechannel flow distribution provided in the final specification and/or on the ftp site.

e)Radial and axial heat structure (fuel rod) nodalisation?
See I.c) above.

f)

Used correlations for fuel properties vs. temperature?
The fuel properties as contained in the final specification were used.

II. Core neutronics modela)

Number of radial nodes per assembly?
The core neutronic nodalisation was identical to the core T-H nodalisation, i.e. there were
185 radial nodes and 24 axial nodes per radial node.

b)

Axial nodalisation?
See II.a) above.

c)

Radial and axial reflector modelling?
The radial and axial reflector modelling used albedo boundary conditions for the core nodes
at the reflector interfaces.
143

d)

Cross-section interpolation procedure used?
The cross-section interpolation procedure was the one provided with the cross-sections; i.e.
lint4d.f.

e)Used method to get a critical reactor at the beginning of transient?
The initial criticality was established by an iterative eigenvalue calculation using a source
over-relation method.

f)

How xenon effect is modelled?
Xenon was modelled directly through the cross-sections provided in the final specification.

g)

How Assembly Discontinuity Factor (ADF) is modelled?
ADF was not modelled. Cross-sections provided in the final specification were used without
applying these factors.

h)Is bypass density correction used? If it is used, how it is modelled?
The core bypass density correction was not applied.

i)

How decay heat modelling is modelled?
The decay heat was modelled using the core average value provided by the final specifications
and distributing it throughout the core based on the initial relative power distribution.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
There is a direct one-to-one relationship between the T-H and heat structure nodes, so that
there are no spatial overlays per se.

b)

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
There is a direct one-to-one relationship between the T-H and neutronic nodes, so that there
are no spatial overlays per se.

c)Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
There is a direct one-to-one relationship between the heat structure and neutronic nodes, sothat there are no spatial overlays per se.

d)Temporal coupling scheme?
The temporal coupling scheme consists of solving the T-H, heat structure and neutronicmodels for a user-specified fixed time step. Each model is solved independently, andfeedback effects are updated at the beginning of the next time step. The T-H and heatstructure calculations utilise a Runge-Kutta 5th-order solution technique, while the neutronic
calculations employ a semi-implicit technique.
144

e)

Coupling numerics – explicit, semi-implicit or implicit?
The coupling numeric calculations are explicit as indicated in III.d) above.

f)

Coupling method – external or internal?
The coupling calculations are performed internally.

g)

Coupling design – serial integration or parallel processing?
The coupling calculations are performed using serial integration.

IV. Generala)User assumptions?
The model utilises 1 channel to represent essentially 4 fuel bundles. Thus, each channel isused to compute the average power for the 4 fuel bundles it represents. That average power
is distributed over the 4 bundles based on the initial relative power distribution provided in
the final specification and/or on the ftp site.

b)Specific features of the used codes?
The T-H calculations are based on a 1-D homogeneous equilibrium model; however the void
distribution that is used in the neutronic calculations uses a profile fit model to obtain theeffects of slip.

c)

Number of solutions submitted per participant and how they differ?
Not applicable, since only one solution was submitted.

145

TRAC-BF1/COS3D (NFI, Japan)

I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
1-D, 33 channels, 24 nodes per active fuel length. Radial T-H nodalisation is the same as theradial map shown in Figure 3.2.2 of BWRTT specifications.

b)

Bypass channel modelling?
No.

c)Number of heat structures (fuel rods) modelled?
Answer: 4 types of fuel assembly are modelled based on Figures 2.2.2, 2.2.3, 2.2.4 and 2.2.5
of BWRTT specifications.
7u7
8 u 8-100mil channel
8 u 8-120mil channel
8 u 8 LTAd)49 fuel rods
63 fuel rods and 1 water rod
63 fuel rods and 1 water rod
62 fuel rods and 2 water rods

Which core thermal-hydraulic initial and transient boundary conditions are used and how?
Core thermal-hydraulic initial and transient boundary conditions are provided as specifications,that is, initial and transient channel inlet flow rate and outlet pressure. We use these
specifications directly to conditions of 33 channels like Figure 3.2.1 of BWRTT specification.

e)Radial and axial heat structure (fuel rod) nodalisation?
Radial direction: 5-mesh for fuel pellet, 1 for gap region and 2 for fuel rod, axial direction:
24 node.
Spatial mesh

Fuel pellet

Fuel cladding
Gap

Radial direction

146

f)

Used correlations for fuel properties vs. temperature?
Fuel properties are used based on Section 3.3 of BWRTT specifications.

II. Core neutronics modela)

Number of radial nodes per assembly?
One.

b)

Axial nodalisation?
24 nodes per active fuel length.

c)Radial and axial reflector modelling?
We assume that the neutron flux at the reflector centre is equal to 0.0.

d)

Cross-section interpolation procedure used?
Provided cross-section interpolation procedure is used.

e)

Used method to get a critical reactor at the beginning of transient?
We get the initial steady state by null transient calculation.

f)

How xenon effect is modelled?
Provided xenon density is used. We assume that xenon density is constant during the transient.

g)

How Assembly Discontinuity Factor (ADF) is modelled?
ADF is not used.

h)

Is bypass density correction used? If it is used, how it is modelled?
No.

i)

How decay heat modelling is modelled?
Decay heat model is not included in Exercise2.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
Hydraulics/heat structure (fuel rod) spatial mesh (fuel rod group) is one. Radial peaking is
not considered.

b)Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
The spatial mesh is the same as the radial map shown in Figure 3.2.2 of the BWRTT
specifications.
147

c)

Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
Number of radial neutronics spatial mesh is 1 per assembly, therefore with regard toneutronics calculation the heat structure inner assembly is not considered.

d)Temporal coupling scheme?

e)Coupling numerics – explicit, semi-implicit or implicit?
Explicit.

f)Coupling method – external or internal?
External.

g)

Coupling design – serial integration or parallel processing?
Serial integration.

IV. Generala)User assumptions?
Nothing special.

b)Specific features of the used codes?
NFI’s code system used for this benchmark is TRAC-BF1/COS3D, which is a coupledsystem of TRAC-BF1 and 3-D core simulator, COS3D. COS3D adopts the modified onegroup neutronics model. Therefore, we use one-group cross-sections which are collapsed
from two-group macroscopic cross-sections provided for this benchmark. The adequacy ofthis method has been verified by means of the comparison between one-group and two-groupmodel analyses.

c)Number of solutions submitted per participant and how they differ?
One solution submitted.

148

TRAC-BF1/SKETCH-INS (NUPEC, Japan)

I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
The reactor pressure vessel is modelled in 1-D cylindrical coordinates with one radial ringand three axial levels. Thermal-hydraulic channels were treated as 1-D, 33 parallel channels
according to Figure 3.2.2 in the final specifications.

b)

Bypass channel modelling?
The reactor vessel simulated core bypass region. The core bypass flow was simulated with aleak path model from T-H channel to the vessel (core bypass) region. Gamma heating in thebypass region was neglected.

c)Number of heat structures (fuel rods) modelled?
33 heat structures, i.e. one heat structure for one T-H channel.

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
Table 5.2.1 in the final specifications was used for the initial condition. During the transient,the following boundary conditions are used, the data for which were obtained from CD-ROM:core inlet total flow rate, core inlet flow temperature, core exit pressure.

e)Radial and axial heat structure (fuel rod) nodalisation?
Radial: pellet 10 rings, gap 1 ring, crud 2 rings, axial: 24 nodes.

f)Used correlations for fuel properties vs. temperature?
MATPRO in TRAC-BF1, which is consistent with the final specifications.

II. Core neutronics modela)

Number of radial nodes per assembly?
One node.

b)

Axial nodalisation?
24 nodes.

c)

Radial and axial reflector modelling?
Radial: 1 node (Figure 2.4.2), axial: bottom 2 nodes, top one node.

d)

Cross-section interpolation procedure used?
Cross-section was fitted as a pronominal function of coolant density and fuel temperature.

149

e)

Used method to get a critical reactor at the beginning of transient?
keff was set 1 at the beginning of transient.

f)

How xenon effect is modelled?
Xenon absorption is excluded at HZP. Absorption cross-section with xenon absorption isused at HP and transient.

g)

How Assembly Discontinuity Factor (ADF) is modelled?
Same as the Code Smith model.

h)Is bypass density correction used? If it is used, how it is modelled?
Not used.

i)

How decay heat modelling is modelled?
Same as the ANS-1979.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
Radial: One heat structure per one T-H channel, axial: same noding.

b)Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
Radial: 33 T-H channels/764 neutronic channels, axial: same noding.

c)Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
Radial: 33 heat structure/764 neutronic channels, axial: same noding.

d)Temporal coupling scheme?
PVM coupling scheme.

e)Coupling numerics – explicit, semi-implicit or implicit?
Explicit.

f)Coupling method – external or internal?
External.

g)

Coupling design – serial integration or parallel processing?
Parallel processing.

150

IV. Generala)User assumptions?
None.

b)

Specific features of the used codes?
Polynomial and semi-analytical nodal method based on the non-linear iteration procedure(Zimin, et al., 1998) is used for spatial integration of diffusion equations. Time integration of
the neutron kinetics equations is performed by the fully implicit scheme.
Zimin, V.G., H. Ninokata, L. Pogosbekyan, “Polynomial and Semi-analytic Nodal Methods
for Non-linear Iteration Procedure”, Proc. ANS Int. Conf. on the Physics of Nuclear Scienceand Technology (PHYSOR), Long Island, New York, 5-8 October 1998, Vol. 2, pp. 994-1002(1998).

c)

Number of solutions submitted per participant and how they differ?
One solution submitted.

151

RETRAN-3D (PSI, Switzerland)

I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
In the core region, the flow from the lower plenum is mainly to the core inlet volume, with asmall fraction of the total core flow flowing through the core bypass volume. From the core
inlet volume, most of the coolant flows into the core, while again a small amount enters thecore bypass volume. The core region is represented by 34 thermal-hydraulic channels, eachwith 24 axial nodes, and the flow through each channel corresponds to the combined flow
through a certain number of fuel assemblies. The steam/water mixture flowing out of the topof the core channels flows into a single core exit volume and from there into the upper
plenum, where it mixes with the core bypass flow.
Figure 1. Nodalisation of the core region
To Standpipes
Upper plenumCore
exit vol.

Core,
34 TH
channelsCore
bypassCore inlet
vol.
From
Jet pumps

Lower Plenum

It consists of the core, the core inlet volume, the core exit volume and the core bypass
volume. 34 thermal-hydraulic channels represent the core itself, where each channel consistsof 24 axially stacked volumes levels. In the PSI methodology, the input required for
RETRAN-3D to perform a 3-D core calculation consists of three separate input files, two of
which are prepared by CORETRAN, and the remaining one forms part of the normal
RETRAN-3D input structure. The two files prepared by CORETRAN consist of a transientcross-section (tcs) file, and a file containing geometric information for all the individual fuelassemblies (cdi or CORETRAN Data Interface file). The additional information contained
within the standard RETRAN input includes a “map” which allocates each reactor fuelassembly to a given RETRAN core hydraulic channel (a total of 34 such channels were usedin the present analysis, see below). Thus, prior to the RETRAN-3D calculation, a CORETRAN
static calculation of Phase 2 (see above) was performed to provide well-founded parameters
for the 3-D core. Accordingly, in the benchmark Phase II and III calculations, the neutronics
152

parameters of each of the 764 fuel assemblies have been entered at 24 axial levels. The
combining, or “lumping”, of the flow through these assemblies into the 34 thermal-hydraulicchannels is that suggested in the benchmark specification (Figure 3.2.2 in Solis, et al., 2001),
except that since RETRAN-3D will not combine assembly types with different numbers offuel rods within the same hydraulic channel, Channel 26 in [Solis, et al., Figure 3.2.2] was
subdivided into two separate channels: Number 26 (for the 4 outermost fuel assemblies with
Assembly Design 5 [Solis, et al., Figure 2.4.2]), and Number 34 (for the 4 innermost fuelassemblies with Assembly Design 4).
Figure 2. Thermal-hydraulic channel radial map, with Channels 10, 34 highlighted
The + symbols represent differently inserted control rods
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 18 17 17 17 17 17 17 17 17 17 17 17 17 18 0 0
0 0 0 33 14 15 14 15 14 15 15 15 15 14 15 14 15 14 33 0 0 0
0 33 18 16 15 14 15 14 15 14 14 14 14 15 14 15 14 15 16 18 33 0
0 0 33 14 15 13 13 13 13 13 11 13 13 11 13 13 13 13 13 15 14 33 0 0
0 0 0 18 14 15 13 12 13 12 11 12 11 10 10 11 12 11 12 13 12 13 15 14 18 0 0 0
0 33 33 29 26 11 13 11 13 11 13 13 11 11 11 11 13 13 11 13 11 13 11 26 29 33 33 0
0 0 18 29 30 27 34 11 12 11 12 7 6 7 8 8 7 6 7 12 11 12 11 34 27 30 29 18 0 0
0 0 33 29 30 13 13 27 25 7 7 7 7 7 8 8 8 8 7 7 7 7 7 25 27 13 13 30 29 33 0
0 17 29 30 13 28 27 28 22 31 7 31 7 6 7 6 6 7 6 7 31 7 31 22 28 27 28 13 30 29 17
0 17 30 29 13 27 13 27 24 22 23 7 8 3 3 3 3 3 3 8 7 23 22 24 27 13 27 13 29 30 17
0 17 29 30 27 28 27 28 22 31 22 4 3 4 3 3 3 3 4 3 4 22 31 22 28 27 28 27 30 29 17
0 17 30 29 27 13 13 22 22 22 24 21 5 3 3 3 3 3 3 5 21 24 22 22 22 13 13 27 29 30 17
0 17 29 30 27 28 27 32 22 32 21 4 21 4 19 2 2 19 4 21 4 21 32 22 32 27 28 27 30 29 17
0 17 30 29 27 27 27 24 22 22 20 20 20 19 19 1 1 19 19 20 20 20 22 22 24 27 27 27 29 30 17
0 17 30 29 27 10 9 22 22 32 20 20 20 2 1 1 1 1 2 20 20 20 32 22 22 9 10 27 29 30 17
0 17 30 29 27 10 9 22 22 32 20 20 20 2 1 1 1 1 2 20 20 20 32 22 22 9 10 27 29 30 17
0 17 30 29 27 27 27 24 22 22 20 20 20 19 19 1 1 19 19 20 20 20 22 22 24 27 27 27 29 30 17
0 17 29 30 27 28 27 32 22 32 21 4 21 4 19 2 2 19 4 21 4 21 32 22 32 27 28 27 30 29 17
0 17 30 29 27 13 13 22 22 22 24 21 5 3 3 3 3 3 3 5 21 24 22 22 22 13 13 27 29 30 17
0 17 29 30 27 28 27 28 22 31 22 4 3 4 3 3 3 3 4 3 4 22 31 22 28 27 28 27 30 29 17
0 17 30 29 13 27 13 27 24 22 23 7 8 3 3 3 3 3 3 8 7 23 22 24 27 13 27 13 29 30 17
0 17 29 30 13 28 27 28 22 31 7 31 7 6 7 6 6 7 6 7 31 7 31 22 28 27 28 13 30 29 17
0 0 33 29 30 13 13 27 25 7 7 7 7 7 8 8 8 8 7 7 7 7 7 25 27 13 13 30 29 33 0
0 0 18 29 30 27 34 11 12 11 12 7 6 7 8 8 7 6 7 12 11 12 11 34 27 30 29 18 0 0
0 33 33 29 26 11 13 11 13 11 13 13 11 11 11 11 13 13 11 13 11 13 11 26 29 33 33 0
0 0 0 18 14 15 13 12 13 12 11 12 11 10 10 11 12 11 12 13 12 13 15 14 18 0 0 0
0 0 33 14 15 13 13 13 13 13 11 13 13 11 13 13 13 13 13 15 14 33 0 0
0 33 18 16 15 14 15 14 15 14 14 14 14 15 14 15 14 15 16 18 33 0
0 0 0 33 14 15 14 15 14 15 15 15 15 14 15 14 15 14 33 0 0 0
0 0 18 17 17 17 17 17 17 17 17 17 17 17 17 18 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0+ + ++ + + +
+ + + + ++ ++ + + +
+ +
+ +
+ + +
+ + +
+ +
+ +
+ + +
+ + +
+ +
+ +
+ +
+ + + +
+ + + + ++ + + +
+ + +

b)

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Bypass channel modelling?
The core bypass (as in the Phase I calculation) is modelled as a RETRAN-3D volume, whichis connected to the lower plenum, core inlet and upper plenum volumes. For the coupling of
the thermal-hydraulics with the neutronics calculations in the core, the RETRAN-3D code
separates the core bypass volume into 24 axially stacked volumes.

c)Number of heat structures (fuel rods) modelled?
The flow in the core is lumped into 34 thermal-hydraulic channels at 24 axial levels and an
additional bypass channel and the same number heat structures (34*24) are modelled by
RETRAN-3D. Bypass heating is taken into account.

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
We have submitted two solutions using RETRAN-3D, called PSI-A and PSI-B. The
RETRAN-3D solutions described in this section read initial conditions from CORETRAN,
including the flow distributions in the thermal-hydraulics channels. From the initial flow
distributions the loss coefficients are also calculated and used for the transient calculation in
RETRAN-3D.

153

For both RETRAN-3D calculations the upper plenum pressure is used as (outlet) boundary
condition and the same lower plenum fluid enthalpy is used. In the PSI-A calculation thepressure in the lower plenum is used as the inlet boundary condition. In a second option,
PSI-B, the total flow rate through the lower plenum into the core region, i.e. the sum of thecore and bypass flows, is used as the inlet boundary condition into the lower plenum.
e)

Radial and axial heat structure (fuel rod) nodalisation?
The flow in the core is lumped into 34 thermal-hydraulic channels at 24 axial levels and an
additional bypass channel and the same number heat structures (34*24) are modelled by
RETRAN-3D. Each of these heat structures is defined to consist of fuel, gap and cladding.

f)Used correlations for fuel properties vs. temperature?
All specified correlations for fuel and cladding properties have been used.

II. Core neutronics modela)

Number of radial nodes per assembly?
Same radial nodalisation as in CORETRAN, see PSI CORETRAN questionnaire.

b)

Axial nodalisation?
Same axial nodalisation as in CORETRAN, see PSI CORETRAN questionnaire.

c)

Radial and axial reflector modelling?
Same procedure as in CORETRAN, see PSI CORETRAN questionnaire.

d)

Cross-section interpolation procedure used?
Same procedure as in CORETRAN, see PSI CORETRAN questionnaire.

e)

Used method to get a critical reactor at the beginning of transient?
Same procedure as in CORETRAN, see PSI CORETRAN questionnaire.

f)

How xenon effect is modelled?
Same procedure as in CORETRAN, see PSI CORETRAN questionnaire, except that xenon
number distributions are read from an additional RETRAN-3D input file.

g)

How Assembly Discontinuity Factor (ADF) is modelled?
Same procedure as in CORETRAN, see PSI CORETRAN questionnaire.

h)

Is bypass density correction used? If it is used, how it is modelled?
Same procedure and assumptions as applied for the PSI CORETRAN calculation, except thatbypass heating is taken into account and noting that the actual nodal moderator density is
obtained from the RETRAN-3D channel hydraulic solution and that the bypass conditions
are calculated using the non-conducting heat exchanger option.

154

i)

How decay heat modelling is modelled?
The RETRAN-3D decay heat model used is based on the 1979 ANS standard.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
A total of 34 heat structures are used to model an average fuel pin in each of the 34 heatedthermal-hydraulic channels (see next question). The radial distribution of the fuel pins hencecorresponds to the thermal-hydraulic channel representation. For the axial nodalisation, eachfuel pin is discretised in a similar manner as the corresponding thermal-hydraulic channel,
i.e. 24 axial volumes.

b)

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
All of the 764 fuel assemblies are modelled as single neutronic channels mapped on
34 thermal-hydraulic channels. For the axial nodalisation, 24 uniform volumes nodes are
consistently used in the neutronic and thermal-hydraulic representation of the active fuel part.

c)

Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
Same as above, see a) and b).

d)Temporal coupling scheme?
The complete mathematical model used in RETRAN-3D consists of a very large system ofdifferential and algebraic equations that describe the numerous physical phenomena that
occur in complex thermal-hydraulic systems. A variety of numerical methods are required
due to the nature of the equations that make up the complete RETRAN-3D model and thewide range of analyses for which the code is used. The differential equation models in
RETRAN-3D include:x

mass, momentum, and energy equations for the coolant fluid;x

conduction equation for heat transfer in solids;xmulti-dimensional (3-D) kinetics for power generation in the core;x

model equations for some equipment components and special physical processes.

In general, these equations are coupled in the following manner. The neutron kinetics
equations give the power generated in the fuel rods, which provides the internal volumetricheat generation rate for the conduction equations for the fuel rods. In this application theCoarse Mesh Finite Difference (CMFD) non-linear iteration procedure is used, where thelocal two-node problems are solved using a Nodal Expansion Method (NEM). The coupling
between the kinetics and the heat conduction equations is explicit. The heat conduction
solution uses implicit coupling between the heat transfer correlations and the source term forthe energy equations. Feedback between the thermal-hydraulic equations and the kinetics
equations is also treated explicitly in this application.
e)

Coupling numerics – explicit, semi-implicit or implicit?
Explicit coupling, see also answer to d).
155

f)

Coupling method – external or internal?
Internal coupling.

g)

Coupling design – serial integration or parallel processing?
Serial integration.

IV. Generala)User assumptions?
For the benchmark calculation the same bypass density correction has been implemented in
RETRAN-3D as for the PSI CORETRAN calculation and consequently also a uniform flow
area ratio is assumed.

b)Specific features of the used codes?
For the core bypass heating the non-conducting heat exchanger option in RETRAN-3D isused. An effective core bypass density correction is implemented according to the benchmark
specifications in RETRAN-3D as in CORETRAN, which is non-standard for both codes.
The same thermal fuel and cladding properties as before in CORETRAN have been enteredin RETRAN-3D using tables. An algebraic slip equation based on drift flux model of
Chexal-Lellouche (recommended option) is used for the thermal-hydraulic calculation. The
neutron void reactivity is calculated from profile fit equation.

c)

Number of solutions submitted per participant and how they differ?
We submitted two solutions using RETRAN-3D, called PSI-A and PSI-B. Both RETRAN-3D
calculations differ in the inlet boundary condition only. (Thus in particular the hot zero
power (HZP) calculation is identical for cases.) In the PSI-A calculation the pressure in thelower plenum is used as the inlet boundary condition. In a second option, PSI-B, the total
flow rate through the lower plenum into the core region, i.e. the sum of the core and bypass
flows, is used as the inlet boundary condition into the lower plenum. Both calculations use
the same lower plenum fluid enthalpy provided in the benchmark specifications for the inlet
boundary condition. The inlet pressure boundary condition case PSI-A results in a slightly
smaller inlet flow rate for the core (relative to the flow boundary condition case PSI-B).
In addition, the core exit flow rate is also reduced. Together, this results in a slightly reduced
net flow of water into the core region before the time of the power maximum, which in turnmeans a smaller increase in the (void) reactivity. These slight differences in the flow
behaviour lead to a power peak for the pressure boundary condition case about 20% lower
than that for the flow boundary condition case. This illustrates the sensitivity of the power
peak to small changes in the system parameters; namely, in the lower plenum flow rate andpressure.

156

CORETRAN-3D (PSI, Switzerland)

I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
The CORETRAN code consists of the ARROTTA module for the neutronics calculations
and the VIPRE-02 module for the thermal-hydraulic (T-H) solution. For Peach Bottom 2, afull core T-H representation is used through VIPRE-02, i.e. 764 parallel channels aremodelled. Each of these channels corresponds to one unique neutronic channel, i.e. fuelassembly modelled in ARROTTA. However, to take into account the unheated zones at theassembly inlet and outlet, the axial nodalisation for the T-H channels differ slightly from theneutronic one as shown in the figure below. It is important to emphasise that in the active
fuel axial zone, the same nodalisation is used for a neutronic channel and its corresponding
T-H channel. Moreover, an additional T-H channel is modelled in VIPRE-02 to represent thebypass region (see answer to question b). Parallel (1-D) flow is assumed in each channel.
Figure 1. CORETRAN neutronic and T-H full core representation
VIPRE-02

ARROTTA
174.0 in.
Node 30
168.0 in.
Node 29
162.0 in.
Node 28156.0 in.
Node 26

Node 27150.0 in.

Node 25

Node 26
144.0 in.

Power

FIBWR Model
Lateral Assembly Leakage
Water Rods

T/H Feedback

24.0 in.
Node 4

Leakage ThroughCore Support
Plate

Node 518.0 in.

Node 3

Node 412.0 in.

Node 2

Node 2

Node 12.0 in.
0.0 in.

b)¾ Leakage defined

Node 36.0 in.

LKP3
LKP2
LKP1

w ith pressure-drop versus flowcorrelations

Node 1

Bypass channel modelling?
The bypass channel is in CORETRAN only implemented in the T-H model (i.e. VIPRE-02).
This is done by modelling, in addition to the 764 individual flow channels, an extra T-H
channel to represent the bypass region. The geometry required for this extra channel is theflow area and the wetted perimeter. This data is derived by lumping the following unheated
coolant regions in the core:x

between fuel assemblies;x

between the peripheral fuel assemblies and the core shroud.
157

The intra-assembly bypass, i.e. the water rods are not taken into account for this bypass
channel. To derive the geometry of the bypass channel, the diameter of the core shroud DCS
was estimated from Figure 25 in the EPRI Report NP-563 (Larsen, N.H., Core Design andOperating Data for Cycle 1 and 2 of Peach Bottom 2) as follows:
DCS | 220.47 in. = 5.6 m
Thereafter, the assembly outer pitch was estimated, assuming it uniform for all channels, as:
POUT | 5.374. in. = 0.1365 m
The bypass area was thereafter calculated, without including the area for water rods, as:
2

ABYP

§D ·
2
S  ¨ CS ¸  764  POUT
| 21.7  14.235 | 7.464 m 2© 2 ¹

11569.22 in.

Similarly, the wetted perimeter was calculated as:
WPBYP

c)

ª
§ DCS · º
«2  S  ¨ 2 ¸ »  >764 u 4 u POUT @ | 433.67 m©
¹¼¬

Number of heat structures (fuel rods) modelled?
For each T-H flow channel (except the bypass), the geometry and the number of fuel pins are
explicitly defined for each T-H axial node, based on the benchmark specifications [1] for thefuel design type of the T-H given channel. However, in the active zone, VIPRE-02 uses anaverage-pin when solving the fuel heat conduction equations. Hence for the 764 T-H
channels, a single “average” fuel pin is used yielding a total of 764 heat structures.

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
For the steady-state results, a flow split option is used to determine the coolant flow in each
T-H channel including the bypass channel. The boundary conditions are the uniform core
inlet temperature, the total core inlet mass flow and the uniform core exit pressure.
For the transient analysis, the specified time-dependant functions for the uniform core inlet
temperature, the channel inlet mass flow for all 764 plus bypass channel (“reconstructed”
from the specified flow for 33 channel groups) and the uniform core exit pressure are used.

e)

Radial and axial heat structure (fuel rod) nodalisation?
Axial heat conduction is neglected and only radial conduction is taken into account. The
pellet is discretised in 6 concentric mesh rings, 2 rings are used for the gap and the cladding.
Axially, each fuel pin is discretised in 24 equal-sized nodes.

f)Used correlations for fuel properties vs. temperature?
All specified correlations for fuel and cladding properties have been used.

158

II. Core neutronics modela)

Number of radial nodes per assembly?
A 1 u 1 radial assembly mesh is used (i.e. 1 radial node per assembly).

b)

Axial nodalisation?
The neutronics model contains 24 active nodes and two reflector nodes (bottom and top). All
nodes have equal size.

c)Radial and axial reflector modelling?
Both radial reflectors and axial reflectors are explicitly modelled. The geometry andnodalisation for the radial reflectors is identical to the one used for the active fuel assemblies
and contains hence 26 axial nodes (i.e. 24 + 2 reflector nodes).

d)

Cross-section interpolation procedure used?
The specified cross-section tables and the provided interpolation routine have been
implemented and used.

e)

Used method to get a critical reactor at the beginning of transient?
Normalisation of the fission cross-section with the initial (steady-state) Keff value.

f)

How xenon effect is modelled?
A SIMULATE summary file containing the nodal xenon number density distributions wasprovided by the benchmark organisers and used to define a CORETRAN restart filecontaining only the xenon nodal distributions (i.e. all other distributions set to zero). Then, a
two-step procedure was used for the xenon correction during the cross-section evaluation.
Step 1: Evaluate the thermal macroscopic absorption cross-section with no xenon as:

6 aNoXe,2

6 a , 2  6 Xe

where 6a,2 is the thermal absorption cross-section (interpolated from the specified cross-section
data tables) and 6Xe is the macroscopic xenon cross-section (interpolated from the specified
cross-section data tables).
Step 2: Compute the corrected thermal absorption macroscopic cross-section as:
6 Corra ,2

6 aNoXe,2  n Xe  V Xe

where nXe is the (nodal) xenon number density read from the restart file, VXe is the xenon
microscopic cross-section (interpolated from the specified cross-section data tables) and6 aNoXe,2 is the nodal macroscopic thermal absorption cross-section with no xenon (obtained
from Step 1).

159

g)

How Assembly Discontinuity Factor (ADF) is modelled?
The ADFs are modelled to correct for heterogeneous flux condition at the interfaces. They
are treated as all other specified cross-sections (i.e. tables and interpolation procedure).

h)Is bypass density correction used? If it is used, how it is modelled?
The bypass density correction is applied with a two-step procedure.
Step 1: First, the nodal moderator density (for an active fuel node) obtained from the T-H
solution is corrected to take into account bypass density changes as follows:
U eff
act

U act ABypAact

 U byp  U sat

where Uact is the nodal density calculated by VIPRE-02, Ubyp and Usat are the bypass actual
ABypand saturation density respectively andis the ratio of the bypass flow are to the active
Aactflow area.
Step 2. The corrected moderator density of step 1 is then used by the neutronic module toevaluate the cross-sections (i.e. by interpolation from specified tables).
Note 1. An approximation is made by using a uniform bypass-to-active area ratio

AByp

for
Aact
all active nodes based on the observation that fuel type design 2 and 3 were the predominant
assembly types. Hence, the geometry of these bundles was considered significantly
representative for all fuel channels. The geometry for the fuel design type 2 is shown infigure below.
Figure 2. Geometry of fuel type 2 with surrounding bypass waterC

PB2 Fuel Assembly ([1 ], Fig. 2.2.2)• B = 13.4061 cm• C = 0.9525 cm• E = 0 .2032 cm

E
B

To derive the ratio based on the geometry above, a constant gap between fuel channels was
assumed and the eventual presence of control rod blades was neglected. The assumed gap
was chosen as D = 2*C. Thereafter, the ratio used for all fuel nodes is evaluated as:

160

ARatioAbypAact

B  2  C  2.  E  B  2 E
FA2

2| 0.56141

where FA is the active fuel channel area which for simplicity was defined as constant for all
channels with the value FA= 100 cm2.
Note 2. The bypass heating (1.7%) is not applied.
i)

How decay heat modelling is modelled?
The decay heat model is not used.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
There are 764 thermal-hydraulic channels (one for each fuel assembly) and corresponding
764 heat structures (an average fuel pin is computed from the intra-nodal pin layout
description and geometry). The heat structures are only modelled in the active part of thecore where the same axial nodalisation as for the T-H channel representation is used.

b)

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
Neutronically, 764 active “channels” are used for the fuel assemblies (plus additional radialreflectors). Thermal-hydraulically, there are 764 “channels” plus an additional bypass channel.
Each of the 764 neutronic channels is coupled to a single T-H channel. The neutronic
reflectors channels and the T-H bypass channel are not coupled. The axial nodalisation for
the active zone of each channel is identical in the neutronics and the T-H representation (seefurther details provided with answer to Question I).

c)Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
Same as above [answers a) and b)]d)Temporal coupling scheme?
The neutronics are solved by the ARROTTA module using the Analytical Nodalisation
Method and an implicit (Crank-Nicholson) temporal discretisation scheme. The VIPRE-02
module handles the thermal-hydraulics, in solving both of the fuel heat conduction equations
and the channel hydraulics. Fuel heat conduction equations are solved using a semi-implicit
method. The channel hydraulics solution scheme is based on a 6-equation, 2-fluid formulation
solved using a fully implicit procedure.

e)Coupling numerics – explicit, semi-implicit or implicit?
Explicit coupling between the T-H module (VIPRE-02) and the neutronic module(ARROTTA). Within the T-H solution scheme, an iterative procedure is used between thefuel heat conduction and the channel hydraulic solutions until temperatures, heat fluxes andflows are converged.

161

f)

Coupling method – external or internal?
CORETRAN uses an internal coupling between ARROTTA and VIPRE-02. CORETRAN is
used as a stand-alone, i.e. not coupled with an external code. The specified thermal-hydraulicboundary conditions are applied to the core inlet and the core outlet via the VIPRE-02
module.

g)

Coupling design – serial integration or parallel processing?
CORETRAN uses a serial integration procedure.

IV. Generala)User assumptions?
The following assumptions were made:b)x

approximate reactor and assembly data to derive the bypass channel geometry [seeanswer to Question I.b)];x

uniform flow area ratio (i.e. applied to all active core nodes) for the bypass density
correction [see answer to Question II.h)].

x

bypass heating of 1.7% was neglected [see answer to Question II.h)].

Specific features of the used codes?
The nominal CORETRAN version used is CORETRAN-01 MOD001 (Nov. 2000). However,
several modifications were implemented to comply with the benchmark specification:c)x

VIPRE-02 internal fuel and cladding property tables have been replaced by specified
correlations [see answer to Question I.f)].

x

The CORETRAN nominal cross-section model was replaced by using specified
cross-section tables and interpolation routine [see answer to Question II.d)].

x

The bypass density correction is not normally used in CORETRAN and was only
implemented for this benchmark [see answer to Question II.h)].

Number of solutions submitted per participant and how they differ?
One CORETRAN solution for the steady-state analysis and one solution for the transient
analysis were submitted.

162

TRAC-BF1/NEM (PSU, USA)

I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
Based on 1-D TRAC-BF1 model 33 core channels were connected 33 BREAK components
at the core inlet and 33 BREAK components at the core outlet. In addition to the core channels
two bypass channels were modelled in order to simulate core bypass flow phenomenab)

Bypass channel modelling?
Two bypass channels one for centre orifice and another for peripheral orifice.

c)Number of heat structures (fuel rods) modelled?
One per channel.

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
Core inlet and outlet pressure boundary conditions were applied.

e)

Radial and axial heat structure (fuel rod) nodalisation?
Radial: 5 pellet + 1 gap + 2 cladding, axial: 24 active + 1 lower ref. + 1 upper ref.

f)

Used correlations for fuel properties vs. temperature?
PBTT benchmark specifications.

II. Core neutronics modela)

Number of radial nodes per assembly?
One per assembly.

b)

Axial nodalisation?
24 active + 1 lower ref. + 1 upper ref.

c)

Radial and axial reflector modelling?
One reflector at radial boundaries and axially, one node for upper and one node for lower
boundaries of the channels.

d)

Cross-section interpolation procedure used?
Linear interpolation.

e)

Used method to get a critical reactor at the beginning of transient?
Eigenvalue solution and fixed source solution are used.

163

f)

How xenon effect is modelled?
Microscobic cross-sections and number densities provided by benchmark team were used.

g)

How Assembly Discontinuity Factor (ADF) is modelled?
Values from cross-section libraries were used. Those libraries were provided by benchmark
team.

h)

Is bypass density correction used? If it is used, how it is modelled?
Yes. Methodology is consistent with the final specification.

i)

How decay heat modelling is modelled?
Answer: ANS-1979 Std.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
One-by-one mapping.

b)

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
According to methodology specified in the final specification.

c)Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
Same as one applied for hydraulics/neutronics spatial mesh overlays.

d)Temporal coupling scheme?
T-H state variables of previous step were fixed.

e)

Coupling numerics – explicit, semi-implicit or implicit?
Explicit coupling.

f)Coupling method – external or internal?
External.

g)

Coupling design serial integration or parallel processing?
Parallel Virtual Machine (PVM).

IV. Generala)User assumptions?
Assumptions are based on the specifications.
164

b)

Specific features of the used codes?
N/Ac)

Number of solutions submitted per participant and how they differ?
One solution was submitted.

165

TRAC-BF1/ENTRÉE (TEPSYS, Japan)

I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
1-D channel model by TRAC/BF1: 35 regions (33 active + 2 bypass).

b)

Bypass channel modelling?
Two regions (one for centre orifice and another for peripheral orifice).

c)

Number of heat structures (fuel rods) modelled?
One for each channel.

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
Transient boundary conditions were applied.

e)

Radial and axial heat structure (fuel rod) nodalisation?
Radial: 5 pellet + 1 gap + 2 cladding, axial: 24 active + 1 lower ref. + 1 upper ref.

f)

Used correlations for fuel properties vs. temperature?
As specified in Final Specification (default of TRAC/BF1).

II. Core neutronics modela)

Number of radial nodes per assembly?
One per assembly.

b)

Axial nodalisation?
24 active + 1 lower ref. + 1 upper ref.

c)

Radial and axial reflector modelling?
Radial: one per reflector, axial: one for lower and another for upper reflector.

d)

Cross-section interpolation procedure used?
Linear interpolation regarding to independent instantaneous variables.

e)Used method to get a critical reactor at the beginning of transient?
Eigenvalue solution + fixed source solution.

166

f)

How xenon effect is modelled?
Production of Xe micro cross-section (given by OECD/NEA) and Xe number density (alsogiven by OECD/NEA).

g)

How Assembly Discontinuity Factor (ADF) is modelled?
General Equivalence Theory (same as SIMULATE3).

h)

Is bypass density correction used? If it is used, how it is modelled?
Yes. According to methodology specified in the final specification.

i)

How decay heat modelling is modelled?
ANS-1979 Std.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
One-by-one mapping.

b)

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
According to methodology specified in the final specification.

c)Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
Same as one applied for hydraulics/neutronics spatial mesh overlays.

d)Temporal coupling scheme?
T-H state variables of previous step were fixed.

e)

Coupling numerics – explicit, semi-implicit or implicit?
Explicit coupling.

f)Coupling method – external or internal?
External.

g)

Coupling design serial integration or parallel processing?
PVM.

IV. Generala)User assumptions?
N/A

167

b)

Specific features of the used codes?
Automatic time-step-control method introduced considering changing rate of state variables.

c)

Number of solutions submitted per participant and how they differ?
N/A

168

RELAP5/PARCS (U.PISA, Italy)

I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – How are channels/T-H cells chosen?
3-D, 33 channels according to the benchmark specification core mapping.

b)

Bypass channel modelling?
Yes. One bypass channel is modelled.

c)Number of heat structures (fuel rods) modelled?
33 heat structures.

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
The considered boundary conditions are those provided in the NEA/BWRTT CD-ROM (coreinlet mass flow rate, core inlet temperature, core outlet pressure).

e)Radial and axial heat structure (fuel rod) nodalisation?
24 axial nodes and 33 radial nodes.

f)Used correlations for fuel properties vs. temperature?
Tables are used (fuel properties variation with temperature).

II. Core neutronics modela)

Number of radial nodes per assembly?
1b)

Axial nodalisation?
24c)Radial and axial reflector modelling?
888d)Cross-section interpolation procedure used?
Bi-linear.

e)

Used method to get a critical reactor at the beginning of transient?
The convergence of the schema calculating Keff.

f)

How xenon effect is modelled?
Yes.
169

g)

How Assembly Discontinuity Factor (ADF) is modelled?
ADFs are read from the cross-section tables.

h)Is bypass density correction used? If it is used, how it is modelled?
No.

i)

How decay heat modelling is modelled?
The ANS-79 is considered.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
33/33 radial per 24/24 axial nodes.

b)

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
34/19 radial per 24/24 axial nodes.

c)Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
34/19 radial per 24/24 axial nodes.

d)Temporal coupling scheme?
Contemporary in parallel process.

e)

Coupling numerics – explicit, semi-implicit or implicit?
Semi-implicit.

f)

Coupling method – external or internal?
Internal.

g)

Coupling design – serial integration or parallel processing?
Parallel processing.

IV. Generalh)User assumptions?

i)Specific features of the used codes?
RELAP5 is a largely validated system code, PARCS allows simulating the whole core(taking into account all the fuel assemblies) and allows pin-to-pin flux reconstruction.

j)

Number of solutions submitted per participant and how they differ?
One solution submitted.
170

TRAC-BF1/NEM (UPV, Spain)

I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
The nodalisation, which was the proposed in specifications, has 33 thermal-hydraulicchannels and 26 axial levels (24 core layers plus top and bottom reflectors).
Axial nodalisation

Core thermal-hydraulic channel radial map

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

b)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 18 17 17 17 17 17 17 17 17 17 17 17 17 18 0 0
0 0 0 33 14 15 14 15 14 15 15 15 15 14 15 14 15 14 33 0 0 0
0 33 18 16 15 14 15 14 15 14 14 14 14 15 14 15 14 15 16 18 33 0
0 0 33 14 15 13 13 13 13 13 11 13 13 11 13 13 13 13 13 15 14 33 0 0
0 0 0 18 14 15 13 12 13 12 11 12 11 10 10 11 12 11 12 13 12 13 15 14 18 0 0 0
0 33 33 29 26 11 13 11 13 11 13 13 11 11 11 11 13 13 11 13 11 13 11 26 29 33 33 0
0 0 18 29 30 27 26 11 12 11 12 7 6 7 8 8 7 6 7 12 11 12 11 26 27 30 29 18 0 0
0 33 29 30 13 13 27 25 7 7 7 7 7 8 8 8 8 7 7 7 7 7 25 27 13 13 30 29 33 0
17 29 30 13 28 27 28 22 31 7 31 7 6 7 6 6 7 6 7 31 7 31 22 28 27 28 13 30 29 17
17 30 29 13 27 13 27 24 22 23 7 8 3 3 3 3 3 3 8 7 23 22 24 27 13 27 13 29 30 17
17 29 30 27 28 27 28 22 31 22 4 3 4 3 3 3 3 4 3 4 22 31 22 28 27 28 27 30 29 17
17 30 29 27 13 13 22 22 22 24 21 5 3 3 3 3 3 3 5 21 24 22 22 22 13 13 27 29 30 17
17 29 30 27 28 27 32 22 32 21 4 21 4 19 2 2 19 4 21 4 21 32 22 32 27 28 27 30 29 17
17 30 29 27 27 27 24 22 22 20 20 20 19 19 1 1 19 19 20 20 20 22 22 24 27 27 27 29 30 17
17 30 29 27 10 9 22 22 32 20 20 20 2 1 1 1 1 2 20 20 20 32 22 22 9 10 27 29 30 17
17 30 29 27 10 9 22 22 32 20 20 20 2 1 1 1 1 2 20 20 20 32 22 22 9 10 27 29 30 17
17 30 29 27 27 27 24 22 22 20 20 20 19 19 1 1 19 19 20 20 20 22 22 24 27 27 27 29 30 17
17 29 30 27 28 27 32 22 32 21 4 21 4 19 2 2 19 4 21 4 21 32 22 32 27 28 27 30 29 17
17 30 29 27 13 13 22 22 22 24 21 5 3 3 3 3 3 3 5 21 24 22 22 22 13 13 27 29 30 17
17 29 30 27 28 27 28 22 31 22 4 3 4 3 3 3 3 4 3 4 22 31 22 28 27 28 27 30 29 17
17 30 29 13 27 13 27 24 22 23 7 8 3 3 3 3 3 3 8 7 23 22 24 27 13 27 13 29 30 17
17 29 30 13 28 27 28 22 31 7 31 7 6 7 6 6 7 6 7 31 7 31 22 28 27 28 13 30 29 17
0 33 29 30 13 13 27 25 7 7 7 7 7 8 8 8 8 7 7 7 7 7 25 27 13 13 30 29 33 0
0 0 18 29 30 27 26 11 12 11 12 7 6 7 8 8 7 6 7 12 11 12 11 26 27 30 29 18 0 0
0 33 33 29 26 11 13 11 13 11 13 13 11 11 11 11 13 13 11 13 11 13 11 26 29 33 33 0
0 0 0 18 14 15 13 12 13 12 11 12 11 10 10 11 12 11 12 13 12 13 15 14 18 0 0 0
0 0 33 14 15 13 13 13 13 13 11 13 13 11 13 13 13 13 13 15 14 33 0 0
0 33 18 16 15 14 15 14 15 14 14 14 14 15 14 15 14 15 16 18 33 0
0 0 0 33 14 15 14 15 14 15 15 15 15 14 15 14 15 14 33 0 0 0
0 0 18 17 17 17 17 17 17 17 17 17 17 17 17 18 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

4
3
2
1

Bypass channel modelling?
The bypass is modelled by a TRAC channel component.

c)Number of heat structures (fuel rods) modelled?
There are a total of 888 assemblies, 764 fuel assemblies and 124 reflector assemblies. 576
fuel assemblies are 7 u 7 type and the remaining 188 are 8 u 8 type.

d)

Which core thermal-hydraulic initial and transient boundary conditions are used and how?
The boundary conditions are imposed by the FILL and BREAK components of TRAC-BF1.
The boundary conditions are the proposed in the specifications. See figure below.

171

33 channels
BREAK
26

CHAN

4
3
2
1

FILL
1

e)

2

3

4

33

Radial and axial heat structure (fuel rod) nodalisation?
The thermal power is calculated for each node by the neutronic code, and this power isallocated in the correspondent axial and radial node of the heat structure.

f)

Used correlations for fuel properties vs. temperature?
No.

II. Core neutronics modela)

Number of radial nodes per assembly?
We have used 1 radial node per assembly.

b)

Axial nodalisation?
There are 26 axial levels, 24 core layers plus top and bottom reflectors.

c)Radial and axial reflector modelling?
The radial and axial reflector are modelled. The distribution of reflector is the proposed in
specifications.

d)Cross-section interpolation procedure used?
The cross-sections are interpolated linearly with a subroutine that uses four-point linear
interpolation to calculate t real cross-section based on two-group total eight cross-section data.

172

e)

Used method to get a critical reactor at the beginning of transient?
We have calculated the steady state and we assure that the eigenvalue keff is approximately 1.
After that, we normalised dividing Nu fission by keff., and then, we start the transient.

f)

How xenon effect is modelled?
The effect of xenon is introduced in the absorption cross-section coefficients for the 764 fuelassemblies and for the 24 core levels by means of the following equation:
6 ia*,2i
6 ia ,2  6 iXe ,2  N Xe
V iXe ,2

where 6 ia*,2 is the modified absorption cross-section coefficient for node i and group 2, 6 ia ,2is the absorption cross-section coefficient for node i and group 2, 6 iXe ,2 is the xenon
macroscopic cross-section coefficient for node i and group 2, V iXe ,2 is the xenon microscopiciis the xenon concentration for node i.
cross-section coefficient for node i and group 2, and N Xeg)

How Assembly Discontinuity Factor (ADF) is modelled?
The values of ADF obtained from the files nemtab and nemtabr are taken by the neutroniccode and used in the calculations integrated in the code.

h)Is bypass density correction used? If it is used, how it is modelled?
When obtaining the average coolant density, a correction that accounts for the bypass
channels conditions are included by the following equation:
U eff
act

Aact U act  Abyp ( U byp  U sat )Aact

where U eff
act is the effective average coolant density for cross-section calculation, Ubyp is theaverage coolant density for cross-section calculation, Usat is the saturated moderator coolant
density of the bypass channel, Aact is the flow cross-sectional area of active heated channeland Abyp is the flow cross-sectional area of the bypass channeli)

How decay heat modelling is modelled?
With subroutines of TRAC-BF1 with 1-D neutron kinetics.

173III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
There are 33 TRAC-BF1 channel components with 26 channel hydraulic cells.
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 18 17 17 17 17 17 17 17 17 17 17 17 17 18 0 0
0 0 0 33 14 15 14 15 14 15 15 15 15 14 15 14 15 14 33 0 0 0
0 33 18 16 15 14 15 14 15 14 14 14 14 15 14 15 14 15 16 18 33 0
0 0 33 14 15 13 13 13 13 13 11 13 13 11 13 13 13 13 13 15 14 33 0 0
0 0 0 18 14 15 13 12 13 12 11 12 11 10 10 11 12 11 12 13 12 13 15 14 18 0 0 0
0 33 33 29 26 11 13 11 13 11 13 13 11 11 11 11 13 13 11 13 11 13 11 26 29 33 33 0
0 0 18 29 30 27 26 11 12 11 12 7 6 7 8 8 7 6 7 12 11 12 11 26 27 30 29 18 0 0
0 0 33 29 30 13 13 27 25 7 7 7 7 7 8 8 8 8 7 7 7 7 7 25 27 13 13 30 29 33 0 0
0 17 29 30 13 28 27 28 22 31 7 31 7 6 7 6 6 7 6 7 31 7 31 22 28 27 28 13 30 29 17 0
0 17 30 29 13 27 13 27 24 22 23 7 8 3 3 3 3 3 3 8 7 23 22 24 27 13 27 13 29 30 17 0
0 17 29 30 27 28 27 28 22 31 22 4 3 4 3 3 3 3 4 3 4 22 31 22 28 27 28 27 30 29 17 0
0 17 30 29 27 13 13 22 22 22 24 21 5 3 3 3 3 3 3 5 21 24 22 22 22 13 13 27 29 30 17 0
0 17 29 30 27 28 27 32 22 32 21 4 21 4 19 2 2 19 4 21 4 21 32 22 32 27 28 27 30 29 17 0
0 17 30 29 27 27 27 24 22 22 20 20 20 19 19 1 1 19 19 20 20 20 22 22 24 27 27 27 29 30 17 0
0 17 30 29 27 10 9 22 22 32 20 20 20 2 1 1 1 1 2 20 20 20 32 22 22 9 10 27 29 30 17 0
0 17 30 29 27 10 9 22 22 32 20 20 20 2 1 1 1 1 2 20 20 20 32 22 22 9 10 27 29 30 17 0
0 17 30 29 27 27 27 24 22 22 20 20 20 19 19 1 1 19 19 20 20 20 22 22 24 27 27 27 29 30 17 0
0 17 29 30 27 28 27 32 22 32 21 4 21 4 19 2 2 19 4 21 4 21 32 22 32 27 28 27 30 29 17 0
0 17 30 29 27 13 13 22 22 22 24 21 5 3 3 3 3 3 3 5 21 24 22 22 22 13 13 27 29 30 17 0
0 17 29 30 27 28 27 28 22 31 22 4 3 4 3 3 3 3 4 3 4 22 31 22 28 27 28 27 30 29 17 0
0 17 30 29 13 27 13 27 24 22 23 7 8 3 3 3 3 3 3 8 7 23 22 24 27 13 27 13 29 30 17 0
0 17 29 30 13 28 27 28 22 31 7 31 7 6 7 6 6 7 6 7 31 7 31 22 28 27 28 13 30 29 17 0
0 0 33 29 30 13 13 27 25 7 7 7 7 7 8 8 8 8 7 7 7 7 7 25 27 13 13 30 29 33 0 0
0 0 18 29 30 27 26 11 12 11 12 7 6 7 8 8 7 6 7 12 11 12 11 26 27 30 29 18 0 0
0 33 33 29 26 11 13 11 13 11 13 13 11 11 11 11 13 13 11 13 11 13 11 26 29 33 33 0
0 0 0 18 14 15 13 12 13 12 11 12 11 10 10 11 12 11 12 13 12 13 15 14 18 0 0 0
0 0 33 14 15 13 13 13 13 13 11 13 13 11 13 13 13 13 13 15 14 33 0 0
0 33 18 16 15 14 15 14 15 14 14 14 14 15 14 15 14 15 16 18 33 0
0 0 0 33 14 15 14 15 14 15 15 15 15 14 15 14 15 14 33 0 0 0
0 0 18 17 17 17 17 17 17 17 17 17 17 17 17 18 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

b)

26

4
3
2
1

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
The core is divided into 888 assemblies. 764 fuel assemblies and 124 reflector assemblies.
There are 19 different types of fuel assemblies distributed as it is in the figure with thecharacteristics described in the specifications.
19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19
19 19 11 5 6 5 6 6 6 6 6 6 6 5 5 11 19 19
19 19 19 6 6 1 5 1 6 1 1 1 1 5 1 6 1 6 6 19 19 19
19 7 13 13 1 10 1 10 1 10 12 14 10 1 9 1 10 1 15 13 8 19
19 19 6 7 1 14 12 14 15 16 15 15 16 17 15 16 15 10 15 1 7 6 19 19
19 19 19 13 10 1 16 1 15 3 15 1 15 2 2 17 1 15 3 15 1 15 1 10 13 19 19 19
19 8 6 9 1 15 10 15 14 15 14 17 14 17 17 18 17 14 15 14 17 10 15 1 10 6 8 19
19 19 12 7 1 15 4 15 3 17 3 15 2 15 15 14 17 2 15 3 17 3 16 4 15 1 7 13 19 19
19 19 6 13 1 16 10 17 15 17 17 15 15 17 14 17 17 15 15 14 17 13 17 14 16 10 15 1 13 7 19 19
19 11 6 1 16 1 15 3 17 2 15 2 15 2 15 2 2 17 2 15 2 17 2 15 3 17 1 15 1 6 11 19
19 5 1 10 10 15 12 17 16 15 14 17 15 15 14 17 17 13 17 15 15 15 17 14 15 14 15 10 10 1 5 19
19 6 6 1 16 3 17 3 15 2 15 2 17 2 17 17 15 17 2 17 2 15 2 15 3 17 3 15 1 6 5 19
19 6 1 9 16 17 14 16 15 15 14 16 15 17 17 17 17 15 17 14 17 15 15 14 15 14 16 16 9 1 6 19
19 7 5 1 17 3 15 2 15 2 15 2 17 2 17 2 2 17 2 17 2 15 2 15 2 17 1 15 1 5 6 19
19 6 1 10 15 16 15 15 15 17 15 17 17 17 15 15 17 15 17 15 17 13 15 17 15 14 15 16 10 1 6 19
19 6 1 12 16 2 16 13 16 2 17 15 17 2 15 15 15 15 2 17 15 15 2 17 13 17 2 15 14 1 6 19
19 7 1 12 15 2 17 15 15 2 15 15 15 2 16 17 15 15 2 17 15 17 2 17 13 16 2 17 12 1 6 19
19 6 1 10 16 17 15 15 15 17 14 17 15 17 15 16 15 17 17 15 17 13 15 15 16 13 15 15 10 1 6 19
19 6 6 1 15 1 17 2 15 2 15 2 17 2 17 2 2 17 2 17 2 17 2 15 2 17 1 15 1 5 6 19
19 6 1 9 16 17 12 16 15 15 14 17 14 17 14 17 17 15 17 16 17 14 15 15 15 14 16 17 9 1 6 19
19 6 6 1 16 3 17 3 15 2 15 2 17 2 17 16 15 17 2 17 2 15 2 15 3 15 3 15 1 6 6 19
19 5 1 10 10 17 14 15 14 17 15 15 15 17 14 15 17 15 17 14 15 14 15 14 15 14 15 10 10 1 5 19
19 11 5 1 16 1 17 3 15 2 17 2 15 2 17 2 2 15 2 17 2 15 2 15 3 17 1 14 1 5 10 19
19 19 7 13 1 16 10 15 14 15 15 15 15 17 16 17 18 14 17 15 15 15 17 14 17 10 16 1 14 6 19 19
19 19 13 7 1 15 4 15 3 15 3 15 2 17 14 14 17 2 17 3 17 3 17 4 15 1 7 13 19 19
19 8 6 10 1 17 10 17 12 15 14 17 13 17 17 13 16 14 15 12 15 10 15 1 10 6 8 19
19 19 19 13 10 1 16 1 17 3 17 1 17 2 2 17 3 15 3 16 1 16 1 9 13 19 19 19
19 19 6 7 1 16 10 16 16 18 18 15 16 17 18 16 16 10 16 1 7 6 19 19
19 7 11 15 1 10 1 9 1 10 10 10 10 1 10 1 10 1 15 13 7 19
19 19 19 6 6 1 6 1 6 1 1 1 1 6 1 5 1 6 6 19 19 19
19 19 11 5 6 6 7 6 6 6 6 7 6 6 5 11 19 19
19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19

174

26

4
3
2
1

c)

Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
See figure below.

d)Temporal coupling scheme?
See figure below.
REACTOR POWER (tn)

SOLUTION HEAT TRANSFEREQUATIONS (tn)

THERMAL-HYDRAULIC SOLUTION WITH
TRAC-BF1 (tn)

FUEL TEMPERATURE (tn)

THERMAL-HYDRAULIC FEATURES (tn+1)
Moderator Temperature (tn+1)
Moderator Pressure (tn+1)
Void Fraction (tn+1)
Moderator Density (tn+1)

CROSS-SECTION CALCULATION

3D NEUTRONIC SOLUTION WITH NEM

3D POWER DISTRIBUTION (tn+1)

tn=tn+1175e)Coupling numerics – explicit, semi-implicit or implicit?
Semi-implicit.

f)

Coupling method – external or internal?
Internal.

g)

Coupling design – serial integration or parallel processing?
Serial integration.

IV. Generala)User assumptions?

b)Specific features of the used codes?

c)Number of solutions submitted per participant and how they differ?

176

TRAB-3D (VTT, Finland)

I.

Thermal-hydraulic core modela)Core thermal-hydraulic (T-H) model and nodalisation (1-D, 3-D, and number of channels orcells) – how are channels/T-H cells chosen?
1-D channels, one channel per fuel assembly, 764 active core channel, 24 axial meshintervals of equal height.

b)

Bypass channel modelling?
Two core bypass channels with 24 axial mesh intervals of equal height. The first channel
corresponds to the flow between central core assemblies with direct heating and feedback toneutronics. Second channel corresponds to the peripheral bypass, and is not coupled to theneutronics calculation.

c)

Number of heat structures (fuel rods) modelled?
One fuel rod per fuel assembly, 764 fuel rods.

d)Which core thermal-hydraulic initial and transient boundary conditions are used and how?
Outlet pressure and total mass flow, as well as inlet temperature, used as steady-state andtransient boundary conditions. Inlet pressure and flow distribution checked to be adequately
correct in steady state.

e)Radial and axial heat structure (fuel rod) nodalisation?
Five radial points for fuel rods, two more radial mesh points for the cladding, 24 axial layersof equal height.

f)Used correlations for fuel properties vs. temperature?
As specified in Section 3.3 of the final specifications.

II. Core neutronics modela)

Number of radial nodes per assembly?
One node per assembly.

b)

Axial nodalisation?
24 axial nodes of equal height.

c)

Radial and axial reflector modelling?
Reflector nodes not modelled. Albedo boundary conditions calculated from the reflector
cross-sections given in the specifications.

177

d)

Cross-section interpolation procedure used?
Linear interpolation.

e)

Used method to get a critical reactor at the beginning of transient?
Number of neutrons from fission divided by calculated keff.

f)

How xenon effect is modelled?
The suggested xenon correction used for the full power steady state and the transient withthe xenon number density kept constant during the transient. No correction for the HZP
calculation.

g)

How Assembly Discontinuity Factor (ADF) is modelled?
ADFs interpolated from tables similarly as the cross-sections.

h)Is bypass density correction used? If it is used, how it is modelled?
Yes, as specified, from the first bypass channel [cf. question b)].

i)

How decay heat modelling is modelled?
Time evolution of decay heat (ANSI-79 standard) followed dynamically in each assembly.
For axial distribution the initial steady-state fission power distribution is used through thetransient.

III. Coupling schemesa)Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial and axial plane)?
One-to-one mapping. Each hydraulics channel corresponds to one heat structure with thesame axial nodalisation.

b)

Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and axial plane)?
One-to-one mapping. Each neutronics node corresponds to one hydraulics mesh intervalradially and axially.

c)Heat structure/neutronics spatial mesh overlays mapping schemes in radial and axial plane)?
One-to-one mapping. One fuel rod modelled for each fuel assembly with the same axial
nodalisation.

d)Temporal coupling scheme?
Thermal-hydraulics and neutronics iterated during each time step inside the same outer
iteration loop (equal time step).

e)

Coupling numerics – explicit, semi-implicit or implicit?
Implicit.

178

f)

Coupling method – external or internal?
Internal.

g)

Coupling design – serial integration or parallel processing?
Serial integration.

IV. Generala)User assumptions?

b)Specific features of the used codes?

c)Number of solutions submitted per participant and how they differ?
One solution.

179

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