1

Nuclear Science

NEA/NSC/DOC (2010)

VVER-1000 COOLANT TRANSIENT

BENCHMARK

Phase 2 (V1000CT-2)

Volume IV: Summary results of Exercise 2 on

coupled 3D kinetics/core-vessel thermal hydraulics

and Exercise 3 on core-plant MSLB simulation

N.P.Kolev, I.Spasov, T.Tzanov

INRNE, Bulgaria

E. Royer

INSTN, Saclay, France

OECD 2010

NUCLEAR ENERGY AGENCY

ORGANIZATION FOR ECONOMIC COOPERATION AND DEVELOPMENT

2

ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT

Pursuant to Article 1 of the Convention signed in Paris on 14th December 1960, and which came into force on

30th September 1961, the Organisation for Economic Co-operation and Development (OECD) shall promote

policies designed:

to achieve the highest sustainable economic growth and employment and a rising standard of

living in Member countries, while maintaining financial stability, and thus to contribute to the

development of the world economy;

to contribute to sound economic expansion in Member as well as non-member countries in the

process of economic development; and

to contribute to the expansion of world trade on a multilateral, non-discriminatory basis in

accordance with international obligations.

The original Member countries of the OECD are Austria, Belgium, Canada, Denmark, France, Germany,

Greece, Iceland, Ireland, Italy, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland,

Turkey, the United Kingdom and the United States. The following countries became Members subsequently

through accession at the dates indicated hereafter; Japan (28th April 1964), Finland (28th January 1969), Australia

(7th June 1971), New Zealand (29th May 1973), Mexico (18th May 1994), the Czech Republic (21st December

1995), Hungary (7th May 1996), Poland (22nd November 1996) and the Republic of Korea (12th December 1996).

The Commission of the European Communities takes part in the work of the OECD (Article 13 of the OECD

Convention).

NUCLEAR ENERGY AGENCY

The OECD Nuclear Energy Agency (NEA) was established on 1st February 1958 under the name of 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 all OECD Member countries, except New

Zealand and Poland. The Commission of the European Communities takes part in the work of the Agency.

The primary objective of the NEA is to promote co-operation among the governments of its participating

countries in furthering the development of nuclear power as a safe, environmentally acceptable and economic

energy source.

This is achieved by:

encouraging harmonization of national regulatory policies and practices, with particular

reference to the safety of nuclear installations, protection of man against ionising radiation and

preservation of the environment, radioactive waste management, and nuclear third party liability

and insurance;

assessing the contribution of nuclear power to the overall energy supply by keeping under review

the technical and economic aspects of nuclear power growth and forecasting demand and supply

for the different phases of the nuclear fuel cycle;

developing exchanges of scientific and technical information particularly through participation in

common services;

setting up international research and development programmes and joint undertakings.

In these and related tasks, the NEA works in close collaboration with the International Atomic Energy Agency

in Vienna, with which it has concluded a Co-operation Agreement, as well as with other international

organisations in the nuclear field.

© OECD 2009

Permission to reproduce a portion of this work for non-commercial purposes or classroom use should be obtained

through the Centre français d‟exploitation du droit de copie (CCF), 20, rue des Grands-Augustins, 75006 Paris,

France, Tel. (33-1) 44 07 47 70, Fax (33-1) 46 34 67 19, for every country except the United States. In the United

States permission should be obtained through the Copyright Clearance Center, Customer Service, (508)750-8400,

222 Rosewood Drive, Danvers, MA 01923, USA, or CCC Online: http://www.copyright.com/. All other

applications for permission to reproduce or translate all or part of this book should be made to OECD Publications,

2, rue André-Pascal, 75775 Paris Cedex 16, France.

3

Foreword

The OECD NEA has completed LWR benchmarks for coupled thermal-hydraulic/ neutron

kinetics codes. In the course of these benchmarks, a systematic approach has been

established to validate best estimate coupled codes. This approach employs a multi-level

methodology that allows for consistent and comprehensive validation process and

contributes to prepare a basis of licensing application of the coupled calculations for a

specific reactor type.

The OECD VVER-1000 Coolant Transient Benchmark project started in 2002 with an

overall objective to assess computer codes for safety analysis of VVER power plants,

specifically for their use in reactivity transients. It consists of two phases. Phase 1, labeled

V1000CT-1 and led by Pennsylvania State University (PSU) is a main coolant pump

(MCP) start-up while three other MCP are in operation. Phase 2, labeled V1000CT-2 and

led by the French Commissariat à l‟Energie Atomique (CEA) includes calculation of

coolant mixing experiments and a main steam line break (MSLB) analysis.

Coupled code benchmarks have identified the coolant mixing in the reactor vessel as

an unresolved issue in the analysis of complex plant transients with reactivity insertion. In

order to support the necessary development work, Phase 2 of the VVER-1000 Coolant

Transient Benchmarks (V1000CT-2) was launched to provide a framework for:

Assessment of single-phase vessel mixing models

Assessment of coupled codes in MSLB simulations using validated mixing models

The V1000CT-2 benchmark consists of a computation of a plant experiment at

Kozloduy-6 in Bulgaria and core-vessel and core-plant MSLB simulations for the same

NPP unit. The testing process includes pure thermal-hydraulic and coupled calculations

and allows code-to-experiment and code-to-code comparisons.

The V1000CT-2 benchmark team is from the Institute for Nuclear Research and

Nuclear Energy (INRNE), Bulgaria and CEA and PSU. The V1000CT-2 benchmark

sponsors are the OECD Nuclear Energy Agency (NEA) and CEA. The Kozloduy NPP is

providing technical support and the AER Working Group D is collaborating in the

benchmark activities.

The V1000CT-2 benchmark reports are being published by the NEA in four volumes.

Volumes 1 and 2 provide the specifications of the VVER-1000 vessel mixing and MSLB

benchmarks. In addition, the transient boundary conditions, cross section libraries and

decay heat values as function of time are available on the NEA website and CD ROM.

Volume 3 summarizes the results of V1000CT-2 Exercise 1 and identifies the

important issues of the single-phase vessel mixing modeling. The reference problem is a

Kozlodyy-6 flow mixing experiment. The plant experiment is specially designed to have

approximately separable thermal hydraulics and neutron kinetics. Plant data, including

distributions are available for validation and assessment of the vessel thermal hydraulic

models to be used for coupled code MSLB analysis.

The present Volume 4 summarizes the results of V1000CT-2 Exercises 2 and 3.

Exercise 2 is a core-vessel coupled simulation with given MSLB vessel boundary

4

conditions. A realistic and a pessimistic scenario are considered. The main objective is to

evaluate the response of the coupled 3D N/TH in code-to-code comparison. A specific

objective is to provide an additional test of the vessel mixing models with MSLB

boundary conditions, by comparing coarse-mesh solutions and reference CFD results for

the core inlet distributions. Exercise 3 is a coupled full plant simulation.

Readers are kindly invited to note that the figures in the report were prepared in color.

Color versions are available on the NEA website at 0Hwww.nea.fr/

html/science/ergslib/v1000ct/ .

5

0BAcknowledgments

This report is the sum of many efforts of the participants, the benchmark team and the

funding agencies – the CEA France and OECD/NEA and their staff. Special thanks are

due to D. Caruge and R. Lenain from CEA Saclay whose support and encouragement in

establishing and preparing this benchmark are invaluable.

Particular appreciation goes to U. Bieder from CEA Grenoble who participated in the

preparation of the specifications.

The authors would like to thank Prof. J. Aragones from Universidad Politecnica de

Madrid – member of the NSC/NEA and Prof. F. d‟Auria from the University of Pisa,

member of the NEA Committee on the Safety of Nuclear Installations, for their support in

establishing the OECD benchmark on VVER vessel mixing and MSLB.

Special thanks are due to the Kozloduy NPP personnel for providing plant data,

simulator time and expertise. Of particular note is the support of J. Kostadinov, former

Executive Director of KNPP.

The authors thank the V1000CT-2 Benchmark participants and the members of the

AER Working groups D and C for their valuable support, comments and feedback.

Special appreciation goes to Dr. T. Hoehne from FZD who provided a supporting

CFX transient solution for the vessel thermal hydraulics obtained with MSLB boundary

conditions. This solution is taken as reference for coarse-mesh vessel mixing calculations.

The authors wish to express their sincere appreciation for the outstanding support

offered by Dr. Enrico Sartori who provided efficient administration, organization and

valuable technical recommendations.

The specifications of this benchmark were prepared with the CATHARE2 code,

developed in a joint effort by CEA, IRSN, AREVA and EDF, and with the TRIO_U and

CRONOS/FLICA codes developed by CEA.

6

Table of contents

FOREWORD ....................................................................................................................... 3

0BAcknowledgments ........................................................................................................... 5

List of abbreviations ........................................................................................................... 14

Chapter 1: Introduction ...................................................................................................... 15

1.1 Exercise 1 – Computation of a vessel mixing experiment ....................................... 15

1.2 Exercise 2 – Computation of a VVER-1000 MSLB transient with given vessel

boundary conditions ....................................................................................................... 15

1.3 Exercise 3 – Best-estimate coupled core-plant MSLB simulation ........................... 16

1.4 Benchmark documentation ....................................................................................... 16

Chapter 2: VVER-1000 MSLB benchmark problem ......................................................... 18

2.1 MSLB Scenario 1 ..................................................................................................... 18

2.2 MSLB Scenario 2 ..................................................................................................... 19

2.3 Core neutronics and cross-section library ................................................................ 19

2.4 Steady state conditions ............................................................................................. 20

2.5 Transient calculation ................................................................................................ 20

Chapter 3: Methodology of comparison............................................................................. 23

3.1 Integral parameters ................................................................................................... 23

3.3 Two-dimensional (2D) distributions ........................................................................ 24

Chapter 4: Assessment of vessel mixing models in MSLB calculations ........................... 25

4.1 The vessel mixing models ........................................................................................ 26

4.2 Coarse-mesh vs. CFD calculations........................................................................... 27

4.3 Qualitative comparison with plant data .................................................................... 27

4.4 Conclusions .............................................................................................................. 28

Chapter 5: Results of exercise 2 ......................................................................................... 43

5.1 HZP results ............................................................................................................... 43

5.2 Initial HFP state results ............................................................................................ 59

5.3 Transient results ....................................................................................................... 64

5.3.1 Scenario 1 .............................................................................................................. 64

5.3.2 Scenario 2 .............................................................................................................. 77

Chapter 6: Results of Exercise 3 ........................................................................................ 96

6.1 Scenario 1 results ..................................................................................................... 96

6.2 Scenario 2 results ..................................................................................................... 96

6.3 Time histories ........................................................................................................... 97

Chapter 7: Summary and conclusions .............................................................................. 119

References ........................................................................................................................ 122

APPENDIX A: Two-dimensional radial power distributions in the steady states .......... 125

APPENDIX B: Initial HFP results of Exercise 2 ............................................................. 146

APPENDIX C: Exercise 2 Scenario 1 results .................................................................. 153

7

APPENDIX D: Exercise 2 Scenario 2 results .................................................................. 156

APPENDIX E: Exercise 3 Scenario 1 results .................................................................. 160

APPENDIX F: Description of computer codes used for analysis of the VVER-1000

MSLB benchmark ............................................................................................................ 182

APPENDIX G: Participants‟ provided computational details ......................................... 190

8

List of tables

Table 1.1: List of participants in V1000CT-2 Exercise 2 .................................................. 17 Table 1.2: List of participants in V1000CT-2 Exercise 3 .................................................. 17

Table 2.1: Expected sequence of major events in Scenario 1 ............................................ 21

Table 2.2: Expected sequence of major events in Scenario 2 ............................................ 22

Table 4.1: Participant‟s codes and meshing of the down-comer and lower plenum .......... 25

Table 5.1: Definition of the steady states ........................................................................... 43

Table 5.2: Computed parameters in HZP state 0 and deviations from the mean ............... 47

Table 5.3: Computed parameters in HZP state 0 and deviations from the mean of all codes

............................................................................................................................................ 47

Table 5.4: Computed parameters in HZP state 1a and deviations from the mean of four

codes ................................................................................................................................... 49

Table 5.5: Computed parameters in HZP state 1a and deviations from the mean of all

codes ................................................................................................................................... 49

Table 5.6: Computed parameters in HZP state 1b and deviations from the mean of four

codes ................................................................................................................................... 51

Table 5.7: Computed parameters in HZP state 1b and deviations from the mean of all

codes ................................................................................................................................... 51

Table 5.8: Computed parameters in HZP state 3 and deviations from the mean of four

codes ................................................................................................................................... 53

Table 5.9: Computed parameters in HZP state 3 and deviation from the mean of all codes

............................................................................................................................................ 53

Table 5.10: Tripped and stuck rods worth. Reference is the CRONOS FEM 24N solution

............................................................................................................................................ 53

Table 5.11: Computed parameters in HZP state 5 and deviation from the mean of all codes

(XS library for Scenario 2) ................................................................................................. 55

Table 5.12: Computed parameters in HZP state 6 and deviations from the mean of all

codes (XS library for Scenario 1) ....................................................................................... 57

Table 5.13: Tripped and stuck rods worth (XS library for Scenario 1) ............................. 57

Table 5.14: Computed parameters in HZP state 6 (XS library for Scenario 2) ................. 58

Table 5.15: Computed HFP state parameters ..................................................................... 60

Table 5.16: Comparison of HFP results with core inlet BC as obtained from the

considered system code. Reference is the Cobaya3/Cobra3 result .................................... 63

Table 5.17: Comparison of HFP state simulations with flat core inlet BCs ...................... 64

Table 5.18: Comparison of Fxy and Fz ................................................................................ 85

Table 5.19: COBAYA results: Comparison of Fxy and Fz .................................................. 85

9

List of figures

Figure 2.1: Reference core of Kozloduy-6 at the end of Cycle 8....................................... 19

Figure 4.1: MSLB Scenario 1, time of maximum overcooling (166s): Temperature

distribution in the down-comer at elevation 5800 mm ...................................................... 29 Figure 4.2: MSLB Scenario 1, time of maximum overcooling (166s): Temperature

distribution in the down-comer at elevation 2500 mm ...................................................... 29 Figure 4.3: MSLB Scenario 2, time of maximum overcooling (69s): Azimuthal

temperature distribution in the down-comer at elevation 5800 mm .................................. 30

Figure 4.4: MSLB Scenario 2, time of maximum overcooling (69s): Azimuthal

temperature distribution in the down-comer at elevation 2500 mm .................................. 30

Figure 4.5: MSLB Scenario 2, time of maximum overcooling: Azimuthal velocity

distribution in the down-comer at elevation 5800 mm ...................................................... 31 Figure 4.6: MSLB Scenario 2, time of maximum overcooling: Azimuthal velocity

distribution in the down-comer at elevation 2500 mm ...................................................... 31 Figure 4.7: Assembly-by-assembly core inlet temperatures at highest return to power .... 32 Figure 4.8: Assembly-by-assembly core inlet mass flow rates at highest return to power 32 Figure 4.9: Plant data from the Kozloduy-6 vessel mixing experiments: Disturbed sector

and azimuthal turn of the loop #4 flow centre. Blue color corresponds to loop-to-

assembly mixing coefficients of 92-100% or ΔTi = Tin,i - Tcold leg 4 < 1.5 K, i =1,163

............................................................................................................................................ 33

Figure 4.10: MSLB Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: CFX computed disturbed sector and angular turn of loop #4 flow centre, in terms

of temperature differences between the assembly inlets and cold leg #4 (ΔTi = Tin, i – T

cold leg 4, i =1,...,163) ....................................................................................................... 34 Figure 4.11: Scenario 2 at time of max overcooling, with stuck rods in #117 and #140:

SMABRE/HEXTRAN computed disturbed sector and azimuthal shift of the loop#4 flow

centre (ΔTi = Tin, i - Tcold leg 4, i =1,...,163) .................................................................. 35 Figure 4.12: Scenario 2 at time of max overcooling, with stuck rods in #117 and #140:

HEXTRAN/SMABRE vs. CFX computed assembly-by-assembly core inlet temperatures

............................................................................................................................................ 35 Figure 4. 13: Scenario 2 at time of max overcooling, with stuck rods in #117 and #140:

Differences between the HEXTRAN-SMABRE and CFX predicted assembly inlet

temperatures (ΔT = Tin – Tin, ref) .................................................................................... 36

Figure 4.14: Scenario 2 at time of max overcooling, with stuck rods in #117 and #140:

ATHLET/DYN3D computed disturbed sector and angular turn of loop#4 flow centre

(ΔTi = Tin, i – T cold leg 4, i =1,...,163)............................................................................ 37 Figure 4.15: Scenario 2 at time of max overcooling, with stuck rods in #117 and #140:

HEXTRAN/SMABRE vs. CFX calculated assembly-by-assembly core inlet temperatures

............................................................................................................................................ 37 Figure 4.16: Scenario 2 at time of max overcooling, with stuck rods in #117 and #140:

Differences between ATHLET/DYN3D and CFX predicted assembly inlet temperatures

(ΔT = Tin – Tin, ref) .......................................................................................................... 38

Figure 4.17: Scenario 2 at time of max overcooling, with stuck rods in #117 and #140:

RELAP3D/NEM predicted disturbed sector and angular turn of loop #4 flow centre (ΔTi

= Tin, i – T cold leg 4, i =1,...,163) .................................................................................... 39 Figure 4.18: Scenario 2 at time of max overcooling, with stuck rods in #117 and #140:

RELAP3D/NEM vs. CFX calculated assembly-by-assembly core inlet temperatures ...... 39

10

Figure 4.19: MSLB Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: Differences between the RELAP3D/NEM and CFX predicted assembly inlet

temperatures (ΔT = Tin – Tin, ref) ..................................................................................... 40 Figure 4.20: Scenario 2 at time of max overcooling, with stuck rods in #117 and #140:

CATHARE2/PKin predicted disturbed sector and angular turn of loop#4 flow centre (ΔTi

= Tin, i – T cold leg 4, i =1,...,163) .................................................................................... 41 Figure 4.21: Scenario 2 at time of max overcooling, with stuck rods in #117 and #140:

CATHARE2 vs. CFX calculated assembly-by-assembly core inlet temperatures.

CATHARE 24-sector vessel model used ........................................................................... 41 Figure 4.22: MSLB Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: Differences between the CATHARE and CFX predicted assembly inlet

temperatures (ΔT = Tin – Tin, ref) ..................................................................................... 42

Figure 5.1: Core-averaged axial power distribution in HZP state 0 ................................... 48

Figure 5.2: Core-averaged axial power distribution in HZP state 0 (mean of all codes and

standard deviation) ............................................................................................................. 48 Figure 5.3: Core-averaged axial power distribution in HZP state 1a ................................. 50 Figure 5.4: Core-averaged axial power distribution in HZP state 1a: (mean of all codes

and standard deviation) ...................................................................................................... 50

Figure 5.5: Core-averaged axial power distribution in HZP state 1b ................................. 52

Figure 5.6: Core-averaged axial power distribution (mean of all codes and standard

deviation) ............................................................................................................................ 52 Figure 5.7: Core-averaged axial power distribution in HZP state 3 ................................... 54

Figure 5.8: Core-averaged axial power distribution in HZP state 3 (mean of all codes and

standard deviation) ............................................................................................................. 54 Figure 5.9: Core averaged axial power distribution in HZP state 5 ................................... 55 Figure 5.10: Core averaged axial power distribution in HZP state 5 (mean of all codes and

standard deviation) ............................................................................................................. 56 Figure 5.11: Core averaged axial power distribution in HZP state 6 (XS lib for Sc1) ...... 57

Figure 5.12: Core-averaged axial power distribution in HZP state 6 (XS lib for Sc2) ...... 58 Figure 5.13: Computed core average axial power distributions in the HFP state .............. 60 Figure 5.14: Computed core average axial power distributions in the initial HFP steady

state (mean of all codes and standard deviation)................................................................ 60 Figure 5.15: HEXTRAN/SMABRE computed assembly powers vs. mean of all codes in

the initial HFP state ............................................................................................................ 61

Figure 5.16: RELAP3D/NEM computed assembly powers vs. mean of all codes in the

initial HFP state .................................................................................................................. 61 Figure 5.17: DYN3D/ATHLET computed radial power distribution vs. mean of all codes

in the initial HFP state ........................................................................................................ 62 Figure 5.18: CRONOS/FLICA4 computed radial power distribution vs. mean of all codes

in the initial HFP state. CRONOS/Flica used flat core inlet BC ....................................... 62 Figure 5.19: COBAYA3/COBRA3 computed radial power distribution vs. mean of all

codes in the initial HFP state. COBAYA3/COBRA3 used CATHARE2 calculated core

BC....................................................................................................................................... 63 Figure 5.20: Time history of hot leg 1 temperature for Scenario 1 .................................... 66 Figure 5.21: Time history of hot leg 2 temperature for Scenario 1 .................................... 66

Figure 5.22: Time history of hot leg 3 temperature for Scenario ....................................... 67 Figure 5.23: Time history of hot leg 4 temperature for Scenario 1 .................................... 67 Figure 5.24: Scenario 1: Time history of the total power (or fission power for VTT and

FZK solutions).................................................................................................................... 68

Figure 5.25: Scenario 1: Time history of the total reactivity ............................................. 68

11

Figure 5.26: Scenario 1: Time history of the core average moderator density .................. 69 Figure 5.27: Scenario 1: Time history of the core average Doppler temperature .............. 69 Figure 5.28: Scenario 1: Time history of the maximum nodal Doppler temperature ........ 70 Figure 5.29: Scenario 1: Time history of Fxyz .................................................................. 70 Figure 5.30: Scenario 1 with stuck rod in #90. Core-average axial power distribution at

time of maximum overcooling (166s) ................................................................................ 71 Figure 5.31: Scenario 1 with stuck rod in #90. Core-average axial power distribution at

time of maximum overcooling (166s)- mean and standard deviation ................................ 71 Figure 5.32: Scenario 1 with stuck rod in #90. Core-average axial power distribution at

600s .................................................................................................................................... 72

Figure 5.33: Scenario 1 with stuck rod in #90. Core-average axial power distribution at

600s- mean and standard deviation .................................................................................... 72 Figure 5.34: Scenario 1 with stuck rod in #90. Axial power distribution in the stuck rod

assembly at 166s................................................................................................................. 73 Figure 5.35: Scenario 1 with stuck rod in #90. Axial power distribution in the stuck rod

assembly at 166s- mean and standard deviation ................................................................ 73 Figure 5.36: Scenario 1 with stuck rod in #90. Axial power distribution in the stuck rod

assembly #90 at 600s.......................................................................................................... 74

Figure 5.37: Scenario 1 with stuck rod in #90. Axial power distribution in the stuck rod

assembly #90 at 600s- mean and standard deviation ......................................................... 74 Figure 5.38: Scenario 1 with stuck rod in #90. DYN3D/ATHLET computed radial power

distribution at 166s. Reference is the mean result of DYN3D/ATHLET, TRACE/PARCS,

CRONOS/FLICA and COBAYA3/COBRA3. .................................................................. 75

Figure 5.39: Scenario 1 with stuck rod in #90 RELAP5/NEM computed radial power

distribution at 166s. Reference is the mean result of DYN3D/ATHLET, TRACE/PARCS,

CRONOS/FLICA and COBAYA3/COBRA3. .................................................................. 76

Figure 5.40: Time history of hot leg 1 temperature ........................................................... 79 Figure 5.41: Time history of hot leg 2 temperature ........................................................... 79

Figure 5.42: Time history of hot leg 3 temperature ........................................................... 80 Figure 5.43: Time history of hot leg 4 temperature ........................................................... 80 Figure 5.44: Time history of the total power (MW) .......................................................... 81

Figure 5.45: Time history of the total power (MW) .......................................................... 81 Figure 5.46: Comparison of the total reactivity (%) .......................................................... 82

Figure 5.47: Comparison of the total reactivity (%) .......................................................... 82

Figure 5.48: Comparison of the maximum nodal fuel temperature ................................... 83 Figure 5.49: Comparison of the core-average Doppler temperature .................................. 83 Figure 5.50: Time history of the core average coolant density .......................................... 84

Figure 5.51: Scenario 2 with stuck rods in #117&140: Time history of Fxy The core inlet

conditions for COBAYA/COBRA were obtained from a CATHARE 24-sector vessel

model .................................................................................................................................. 84 Figure 5.52: Scenario 2, stuck rods in #117&140. Time history of Fxyz .......................... 85 Figure 5.53: Core-average axial power distribution at time of maximum overcooling

(69s), for Scenario 2, with stuck rods in #117&#140 ........................................................ 86 Figure 5.54: Impact of the vessel mixing model on the core-average axial power

distribution at 69s, for Scenario 2, with stuck rods in #117&#140 .................................... 86

Figure 5.55: Core-average axial power distribution at 200s, for Scenario 2, with stuck rods

in #117&#140 ..................................................................................................................... 87 Figure 5.56: Impact of the mixing model meshing on the core-average axial power

distribution at 200s, for Scenario 2, with stuck rods in #117&#140 .................................. 87

12

Figure 5.57: Axial power distribution in stuck rod position #117 at 69s, for Scenario 2,

with stuck rods in #117&#140 ........................................................................................... 88 Figure 5.58: Scenario 2, stuck rods #117&#140. Impact of the mixing model meshing on

the axial power distribution in stuck rod position #117 at 69 s ......................................... 88 Figure 5.59: Scenario 2, stuck rods in #117&#140. Axial power distribution in stuck rod

position #117 at 200s.......................................................................................................... 89 Figure 5.60: Scenario 2, stuck rods in #117&#140. Impact of the mixing model meshing

on the axial power distribution in stuck rod position #117 at 200s.................................... 89 Figure 5.61: Scenario 2, stuck rods in #117&#140. Axial power distribution in stuck rod

position #140 at 69s............................................................................................................ 90

Figure 5.62: Scenario 2, stuck rods in #117&#140. Impact of the mixing model meshing

on the axial power distribution in stuck rod position #140 at 69s...................................... 90 Figure 5.63: Scenario 2, stuck rods in #117&#140. Axial power distribution in stuck rod

position #140 at 200s.......................................................................................................... 91 Figure 5.64: Scenario 2, stuck rods in #117&#140. Impact of the mixing model meshing

on the axial power distribution in stuck rod position #140 at 200s.................................... 91 Figure 5.65: Scenario 2, with stuck rods in #117&#140. Snapshot of the

HEXTRAN/SMABRE computed assembly powers at 69s................................................ 92

Figure 5.66: Scenario2, with stuck rods in #117&#140. Snapshot of the

DYN3D/ATHLET computed assembly powers at 69s ...................................................... 93 Figure 5.67: Scenario2, with stuck rods in #117&#140, and 12-sector model calculated

core BC. Snapshot of COBAYA3/COBRA3 predicted assembly powers at 69s .............. 94

Figure 5.68: Scenario2, with stuck rods in #117&#140, and 24-sector model calculated

core BC. Snapshot of the COBAYA3/COBRA3 predicted assembly powers at 69s ........ 95

Figure 6.1: Total break flow rate, kg/s ............................................................................... 99 Figure 6.2: Integrated total break flow rate, kg .................................................................. 99

Figure 6.3: Integrated liquid break flow rate, kg.............................................................. 100 Figure 6.4: BRU-K total flow rate, kg/s ........................................................................... 100

Figure 6.5: Integrated BRU-K total flow rate, kg ............................................................ 101 Figure 6.6: BRU-SN total flow rate, kg/s ........................................................................ 101 Figure 6.7: Integrated BRU-SN total flow, kg ................................................................. 102

Figure 6.8: Average pressure above the core, Pa ............................................................. 105 Figure 6.9: Cold leg 1 pressure, MPa ............................................................................... 105

Figure 6.10: Cold leg 2 pressure, MPa ............................................................................. 106

Figure 6.11: Cold leg 3 pressure, MPa ............................................................................. 106 Figure 6.12: Cold leg 4 pressure, MPa ............................................................................. 107 Figure 6.13: Main steam header pressure, MPa ............................................................... 102

Figure 6.14: SG1 pressure, MPa ...................................................................................... 103 Figure 6.15: SG2 pressure, MPa ...................................................................................... 103 Figure 6.16: SG3 pressure, MPa ...................................................................................... 104 Figure 6.17: SG4 pressure, MPa ...................................................................................... 104 Figure 6.18: Average core coolant temperature, K .......................................................... 107

Figure 6.19: Temperature of cold leg 1, K ....................................................................... 108 Figure 6.20: Temperature of cold leg 2, K ....................................................................... 108 Figure 6.21: Temperature of cold leg 3, K ....................................................................... 109

Figure 6.22: Temperature of cold leg 4, K ....................................................................... 109 Figure 6.23: Temperature of hot leg 1, K ......................................................................... 110 Figure 6.24: Temperature of hot leg 2, K ......................................................................... 110 Figure 6.25: Temperature of hot leg 3, K ......................................................................... 111

Figure 6.26: Temperature of hot leg 4, K ......................................................................... 111

13

Figure 6.27: Core average Doppler temperature, K ......................................................... 112 Figure 6.28: Maximum nodal fuel temperature, K........................................................... 112 Figure 6.29: Core average coolant density, kg/m3........................................................... 113 Figure 6.30: Fission power, W ......................................................................................... 113 Figure 6.31: Total core power, W .................................................................................... 114

Figure 6.32: SG1 mass of fluid, kg .................................................................................. 114 Figure 6.33: SG2 mass of fluid, kg .................................................................................. 115 Figure 6.34: SG3 mass of fluid, kg .................................................................................. 115 Figure 6.35: SG4 mass of fluid, kg .................................................................................. 116 Figure 6.36: SG1 exchanged power, W ........................................................................... 116

Figure 6.37: SG2 exchanged power, W ........................................................................... 117

Figure 6.38: SG3 exchanged power, W ........................................................................... 117 Figure 6.39: SG4 exchanged power, W ........................................................................... 118

14

List of abbreviations

BOC Beginning of Cycle

BOL Beginning of Life

BPG Best Practice Guidelines

BRU-K Steam dump to condenser

BRU-SN Steam dump to house needs

CEA Commissariat à l‟Energie Atomique

DTC Doppler Temperature Coefficient

EFPD Effective Full Power Days

FA Fuel Assembly

FZD Forschung Zentrum Dresden

FZK Forschung Zentrum Karlsruhe (Karlsruhe Institut of Technology)

GRS Geselschaft fur Reaktorsicherheit

HP Hot Power

HRP Highest Return to Power

HZP Hot Zero Power

INRNE Institute for Nuclear Research and Nuclear Energy

KI Kurchatov Institute

KNPP Kozloduy Nuclear Power Plant

LWR Light Water Reactor

MCP Main Coolant Pump

MSH Main Steam Header

MSLB Main Steam Line Break

NEA Nuclear Energy Agency

NRC Nuclear Regulatory Commission

OECD Organization for Economic Cooperation and Development

PSU Pennsylvania State University

PWR Pressurizer Water Reactor

RCS Reactor Coolant System

RPC Reactor Power Controller

RPV Reactor Pressure Vessel

SG Steam Generator

SIV Steam Isolation Valve

SST Shear Stress Transport

TH Thermal Hydraulics

UNIPI University of Pisa

UPM Universidad Politecnica de Madrid

6N, 24N 6 or 24 nodes/triangles per hexagon

15

Chapter 1: Introduction

Recently developed best-estimate computer code systems for modeling of 3D coupled

neutronics/thermal hydraulic transients and for the coupling of core and system dynamics

need to be validated against experimental results and compared against each other.

International benchmark studies have been set up for this purpose.

Coupled code benchmarks identified the coolant mixing as an unresolved issue in the

analysis of complex plant transients with reactivity insertion. In order to support the

necessary development work, Phase 2 of the OECD/NEA VVER-1000 Coolant Transient

Benchmarks (V1000CT-2) was defined (Kolev et al, 2004; 2006). The objective is to

provide a framework for

Assessment of single-phase vessel mixing models

Assessment of coupled codes in MSLB simulations using validated mixing

models.

The benchmark includes a complete set of input data and consists of three exercises as

summarized below. In addition to the definition of the benchmark exercises, technical

specifications including CFD grade thermal-hydraulics data as well as neutronics and

secondary circuit data are given in Volumes 1 and 2.

1.1 Exercise 1 – Computation of a vessel mixing experiment

The vessel mixing problem (Kolev et al, 2004; Bieder et al, 2005) is based on VVER-

1000 plant experiments at Kozloduy Unit 6 in Bulgaria (Topalov and Popov, 2004). The

objective is to test the capability of the reactor vessel thermal-hydraulic models to

represent single-phase flow mixing. The reference problem is a coolant transient initiated

by steam generator isolation at low power, considered as a pure thermal hydraulic

problem. The available plant data permit code validation on different scales:

Separate effects

Component level (reactor pressure vessel)

System level

For CFD codes, the task is to assess the ability of CFD to reproduce the

experimentally observed angular turn of the loop flow centres (swirl) and the assembly

inlet temperatures given the vessel boundary conditions and the pressure above the core.

The calculation of the vessel outlet parameters (loop-to-loop mixing) is an option.

For system codes, the task is to assess the ability of coarse-3D models and multi-1D

vessel models with cross flow to reproduce the swirl and the assembly inlet temperatures

as well as the vessel outlet temperatures. Given vessel boundary conditions or full plant

simulation can be used.

1.2 Exercise 2 – Computation of a VVER-1000 MSLB transient with given vessel

boundary conditions

The task is to model the core and the vessel only, using the validated coolant mixing

models and pre-calculated vessel MSLB boundary conditions. A realistic and a

16

pessimistic scenario are considered. The overall objective is to evaluate the response of

the coupled 3D neutronics/core-vessel thermal hydraulics in code-to-code comparison. A

specific objective is to provide an additional test of the vessel mixing models with MSLB

boundary conditions, by comparing coarse-mesh and CFD results for the core inlet

distributions. For this purpose, a CFX transient solution for the down-comer and core inlet

parameters was made available by FZD (Hoehne, 2007). Supplementary plant estimated

data from the Kozloduy-6 mixing experiments (Popov, Topalov, 2004) can also be used

for qualitative comparison of the disturbed sector formation and the angular turn of the

loop flows.

1.3 Exercise 3 – Best-estimate coupled core-plant MSLB simulation

This exercise is an extension of Exercise 2 to core-vessel-plant simulation. It is a best-

estimate analysis of the transient in its entirety, for a realistic and a pessimistic scenario.

1.4 Benchmark documentation

Background information on this benchmark with complete list of participants can be

found in the summaries of the seven V1000CT workshops held in Saclay, France

[NEA/NSC/DOC(2003)6]; Sofia, Bulgaria [NEA/NSC/DOC(2004)9]; Garching,

Germany [NEA/NSC/DOC(2005)1]; Avignon, France [NEA/NSC/DOC(2005)18]; Pisa,

Italy [NEA/NSC/DOC(2006)7]; Vancouver, BC, Canada [NEA/NSC/DOC(2006)21] and

Paris, France [NEA/NSC/DOC(2007)5].

The V1000CT-2 benchmark is documented in four volumes. Volumes 1 and 2 contain

the specifications of the vessel mixing problem and the VVER MSLB problem

respectively. Volume 3 summarizes the comparative analysis of the submitted results for

Exercise 1 on vessel mixing simulation.

The present Volume 4 contains summary results of Exercises 2 and 3 on MSLB

simulation. There are seven submitted solutions for Exercise 2 and three results for

Exercise 3, see Tables 1.1 and 1.2 below. The list includes recently obtained COBAYA

and COBAYA/COBRA3 solutions (Spasov et al, 2009), (Spasov et al, 2010).

Chapter 2 of this report gives a summary description of Exercises 2 and 3. Chapter 3

discusses the methodology of comparison of the results. Chapter 4 presents additional

tests of the coarse-mesh mixing models (once validated in Exercise 1), in comparison with

support CFD results obtained using MSLB boundary conditions (Hoehne, 2007). Chapter

5 shows the results of coupled core-vessel calculation with vessel boundary conditions.

Chapter 6 presents results of the full plant simulation. Appendices A and B contain results

of the steady state HZP and HFP calculations. Appendix C presents results of Exercise 2

Scenario 1. Appendix D shows results from Exercise 2 Scenario 2. Appendix E presents

results from Exercise 3. Appendix F describes the codes and Appendix G contains the

participant provided calculation details.

17

Table 1.1: List of participants in V1000CT-2 Exercise 2

Organisation Country Code Type

FZD Germany DYN3D/ATHLET System

FZK Germany PARCS/TRACE System

GRS/KI Germany/Russia BIPR8/ATHLET System

INRNE/CEA Bulgaria/France CRONOS/FLICA Core

INRNE/UPM Bulgaria/Spain COBAYA/COBRA Core

VTT Finland HEXTRAN/SMABRE System

UNIPI Italy NEM/RELAP3D System

Supplementary solutions

FZD Germany CFX CFD

INRNE Bulgaria CATHARE2 – Vessel

TH

System

Table 1.2: List of participants in V1000CT-2 Exercise 3

Organisation Country Code Type

GRS/KI Germany/Russia BIPR8/ATHLET System

VTT Finland HEXTRAN/SMABRE System

UNIPI Italy NEM/RELAP3D

RELAP3D

System

18

Chapter 2: VVER-1000 MSLB benchmark problem

The analyzed transient is initiated by a main steam line break in a VVER-1000 between

the steam generator (SG) and the steam isolation valve (SIV), outside the containment.

This event is characterized by significant space-time effects in the core caused by

asymmetric cooling and assumed stuck-out control rods after scram. One of the major

concerns for this case is the possible return to power and criticality after scram, due to

overcooling. Because of this concern, the main objective of the study is to clarify the local

3-D feedback effects depending on the vessel mixing.

A burnt core with three-year fuel loading is considered. The reference plant is

Kozloduy-6, at Cycle 8. The reactor is at the end of cycle (EOC) and at hot full power

(HFP). The SG water inventory is about the possible maximum at HFP. The break is

assumed to occur in Main Steam Line 4 (MSL-4).

Two scenarios are considered. The first is close to the current licensing practice. The

second is a pessimistic one, derived from Scenario 1 by assuming that all MCP remain in

operation and by reducing the tripped rods worth. The purpose of Scenario 2 is to enhance

the code-to-code comparison.

The specification of the VVER-1000 MSLB benchmark in V1000CT-2 Volume 2

(Kolev et al, 2010a) completely defines Exercises 2 and 3.

2.1 MSLB Scenario 1

Following the break and the scram signal, one of the most reactive peripheral control rod

assemblies remains stuck out of the core and is assumed to be close to the location of

maximum overcooling (not necessarily in the faulted loop sector). The MCP in the faulted

loop trips to mitigate the overcooling, with a coast down time of 55s. Starting from a

symmetric initial state, the reactor cooling system makes a transition to reversed flow in

one loop and three MCP running normally during the transient.

A mechanical failure of the large feed water control valve in the broken line is

assumed. At the time of the break the valve starts to open from about 70% to 100% and

then remains stuck in the open position. The main feed water flow to the faulted SG is

terminated by closure of the feed water block valve in 52s. The mass of feed water in the

piping between the isolation valve and the affected SG, estimated to about 7 500 kg, also

contributes to the overcooling. The intact SG feed water temperature after the reactor trip

varies from 220°C to about 164°C during the transient. The FW temperature to the faulted

SG varies from 220°C to about 130°C in the first 160s of the transient. For the purposes of

this benchmark the temperature is conservatively fixed to 160°C to the broken SG and

170°C to the intact ones.

The steam isolation valve in line #4 starts to close and the check valve in the broken

line closes to isolate the MSH from the break. Turbine stop valves close on protection

signal 10 s after scram. The turbine bypass to condenser starts to open and switches to

MSH pressure control mode. Secondary circuit controllers and off-site electric power are

assumed to be available. Overcooling of about 50 K relative to the initial state occurs in

loop #1 next to the faulted loop and the corresponding core sector. A part of this coolant

reaches the inlet of some fuel assemblies practically unmixed.

19

2.2 MSLB Scenario 2

This is a pessimistic case derived from Scenario 1. The MCP in the faulted loop fails to

trip on signal and all MCP remain in operation. The tripped rods worth is reduced

(through adjustment of the cross-sections). The maximum overcooling is approximately

80 K and occurs in the faulted loop.

From a thermal-hydraulic viewpoint this test problem is similar to the vessel mixing

experiments: asymmetric temperature and flow disturbance with sector formation.

2.3 Core neutronics and cross-section library

The problem is to be solved in 2-group diffusion approximation, with six delayed neutron

groups. The ANS-79 decay heat standard is the recommended decay heat model. A decay

heat table is provided to the participants as an option. Twenty-eight assembly types (see

Figure 1.1) axially discretized to 30 nodes define the core geometry by 840 un-rodded and

330 rodded compositions.

Figure 2.1: Reference core of Kozloduy-6 at the end of Cycle 8

Assembly #5, enrichment 4.4 w/o, twice burnt, 27.04 MWd/kgU 4.4w/o

20

A HELIOS1.9 generated wide-range XS library in the NEMTAB format is provided

(Ivanov et al, 2006). Burn-up dependence is a vector of (Tmod, Den_mod, T_dopp,

exposure). The boron concentration is constant and equal to 53ppm. For each

composition, the benchmark defines a set of cross-sections, diffusion coefficients, inverse

velocity and kinetic parameters. The cross-sections implicitly include the assembly

discontinuity factors (ADF). Sufficiently wide parameter range is considered. The

dependence on the state parameters is modeled through a table look-up. For details, see

the MSLB benchmark specification in V1000CT-2 Volume 2 (Kolev et al, 2010a).

2.4 Steady state conditions

The reactor is at the end of the cycle (EOC) with an average core exposure of 270.4

Effective Full Power Days (26.18 MWd/kgU) and boron concentration of 53 ppm and

equilibrium Xe and Sm concentrations. Control rods groups from 1 to 9 are completely

withdrawn. Group 10 is 80% withdrawn (283.2cm from the bottom of the core).

2.5 Transient calculation

Exercise 2 is a vessel boundary condition problem with pre-calculated MSLB thermal-

hydraulic boundary conditions. In Scenario1, involving pump trip in the faulted loop, the

application points of the boundary conditions for loop #4 reverse with the flow reversal.

For this purpose the hot leg #4 temperature and cold leg #4 pressure boundary conditions

are also given. The use of boundary conditions after flow reversal may require small

adjustment (regulation) of the loop #4 singular losses so that the computed reversed cold

leg#4 flow matches the mass flow boundary condition to the hot leg #4.

For a detailed description of the modeling conventions, see the benchmark

specification in V1000CT-2 Volume 2.

The expected sequence of events is as described in Tables 2.1 and 2.2.

21

Table 2.1: Expected sequence of major events in Scenario 1

Time, s Event Hardware Action

0 HFP state at EOC

Break opens FW regulation valves to SG-4 starts to open to

100% due to mechanical failure

Ts1 – Ts2 750C for SG-4

S4.P49T&DT:

P2 4.9MPa and Ts1 – Ts2 750C

and T primary 2000C (for MSL-4)

Start of HPI pumps (TQ3, TQ4)

(no injection by TQ3 before

P above core < 10.75MPa)

Signal to close SIV-4

on S4.P49T&DT

SIV-4 starts to close

S4.P44T&DT:

P2 4.4MPa and Ts1 – Ts2 750C

and T primary 2000C

MCP-4 trip signal on P44T&DT

MCP-4 trips

Switchover signal to BRU-SN

on MCP-4 trip and P_MSH > 5.5MPa

Bypass to House Consumption Header

(BRU-SN) starts to open

Signal to close FW-4 isolation valve

on P44T&DT

FW isolation valve to SG-4 starts to close

SCRAM signal

on S4.P49T&DT

Start of SCRAM with 0.3s delay

Stuck rod: (a) in FA#90 of 1/4 Sector #1

(b) in FA#63 of 1/4 Sector #4

Check valve of the broken MSL is closed

Low pressure above the core PRZ heaters ON

Control rods fully inserted

SIV-4 closes

Protection signal: TSV 10 s after scram Turbine Stop Valves start to close

TSV closed

BRU-K switches to pressure control mode

Intact SG-1,2,3 level 100 mm

Auxiliary FW pumps start to feed

P_MSH > 6.67MPa BRU-K starts to open with 15s opening time

Terminated forced FW flow

to the broken SG

Block valve in FW line #4 closes

PRZ Level < 4.2 m PRZ heaters OFF

Terminated main FW flow to intact SG

(BC)

Main FW Pumps in bypass mode

P_MSH < 5.79MPa BRU-K closes, P_MSH recovers a few minutes

and is stabilized by the controller

Max overcooling at core inlet

IF (P above core < 10.75MPa) HPIS begins to inject

(No credit taken for boron reactivity insertion)

PMSH 5.297MPa and Reactor tripped

and TSV closed

BRU-SN valves start to close

BRU-SN valves closed

Transient ends

22

Table 2.2: Expected sequence of major events in Scenario 2

Time, s Event Hardware Action

0 HFP state at EOC

Break opens FW regulation valves to SG-4 start to open

to100% due to mechanical failure

P-S4.DTS75:

Ts1 – Ts2 750C for SG-4

S4.P49T&DT:

P2 4.9MPa and Ts1 – Ts2 750C

and T primary 200oC (for MSL-4)

Start of HPI pumps (TQ3, TQ4)

(no injection by TQ3 before

P above core < 10.75MPa)

Signal to close SIV-4

on S4.P49T&DT

SIV-4 starts to close

with 0.3s delay

S4.P44T&DT:

P2 4.4Mpa and Ts1 – Ts2 75oC

and Primary temperature 200oC

MCP-4 trip signal on P44T&DT

MCP-4 does not trip (Sc2 assumption)

Signal to close FW-4 isolation valve

on P44T&DT

FW isolation valve to SG-4 starts to close

SCRAM signal

on S4.P49T&DT

Start of SCRAM with 0.3s delay

Stuck rod: (a) in FA #140 of 1/4 Sector #4

(b) in FA #140 and #117

Check valve of the broken MSL is closed

Low pressure above the core PRZ heaters ON

Control rods fully inserted

SIV-4 closes

Protection signal: TSV 10 s after scram Turbine Stop Valves start to close

TSV closed

Bypass to condenser (BRU-K)

switches to pressure control mode

Switchover signal to BRU-SN

on Closing 2 of 4 Turbine Stop Valves

(BRU-SN algorithm in load following

mode)

Bypass to House Consumption Header

(BRU-SN) starts to open

Intact SG-1,2,3 level 100 mm

Auxiliary FW pumps start to feed

P_MSH > 6.67MPa BRU-K starts to open with 15s opening time

P_MSH < 6.67MPa BRU-K maintains P_MSH < 6.28MPa

PRZ Level < 4.2 m PRZ heaters OFF

Terminated forced FW flow

to the broken SG

Block valve in FW line #4 closes

Max local overcooling at core inlet

Min pressure above the core

Maximal total core power

Terminated main FW flow to intact SG

(BC)

Main FW Pumps switch to bypass mode

PRZ Level > 4.2 m PRZ heaters ON

Transient ends

23

Chapter 3: Methodology of comparison

The MSLB situation target analysis presented here comprises three scales:

separate effects (mixing in the down-comer and the lower plenum; neutronics)

component scale (core and core-vessel)

system scale

The following comparisons are considered:

system code vs. CFD vessel mixing calculations with MSLB vessel BC

code-to-code comparison of vessel TH and coupled core-vessel N/TH solutions

code vs. mean results of all codes

In accordance with the Best Practice Guidelines (Mahaffy et al, 2007), the ability of

the validated vessel thermal-hydraulic models in system codes to reproduce main flow

features was tested vs. plant data and CFD results. For this purpose, supplementary plant

data for loop #4 from the Kozloduy-6 vessel mixing experiments and a transient CFX-5

calculation (Hoehne, 2007) with MSLB vessel boundary conditions were used as

reference. The domain of the CFD solution is from the vessel inlet to the core inlet. Plant

data were used in a qualitative manner only - to assess the disturbed sector formation and

the angular turn of the loop #4 flow centre.

The following target variables are chosen for comparison: integral parameters and

their time history as well as 1D power profiles, and 2D distributions of power,

temperature and flow rates. The applied metrics is discussed below.

3.1 Integral parameters

The statistical criteria used are as follows:

Mean value: N

x

x

N

i

i

ref

(3.1)

Standard deviation:

1

2

N

xx refi (3.2)

Relative deviation: refii xxe (3.3)

Figure of merit:

ii

e (3.4)

3.2 One-dimensional (1D) distributions

Mean value: N

x

x

N

i

i

ref

(3.5)

24

Standard deviation:

1

2

N

xx refi (3.6)

3.3 Two-dimensional (2D) distributions

The criteria used are as follows:

1. Mean error (ME):

N

i

refii xxN

ME1

, )(1

(3.7)

2. Maximum in modulus error: refiii xxe ,max, max (3.8)

where ei,max is the absolute value of the maximum difference of computed datum xi to

the reference value xi,ref

3. Average in modulus error (MEABS):

N

i

refiiABS xxN

ME1

,

1 (3.9)

where MEABS is the average of the absolute values of the deviations from the

reference.

For the assessment of vessel mixing models, xi,ref is a CFX result with MSLB vessel

BC, in a computational domain from the vessel inlet to the core inlet.

For benchmarking standalone neutronics solvers, because of the observed clustering of

the results in two groups, we consider two comparisons, where:

(a) “reference” is the mean of all codes solutions

xi,ref =

_

ix and

(b) “reference” is the mean of PARCS, DYN3D, CRONOS and COBAYA solutions.

A CRONOS 2nd order FEM solution with 24 triangles per hexagon (24N) also serves as

reference.

For coupled code solutions, “reference” is the mean of five coupled codes:

PARCS/TRACE, DYN3D/ATHLET, CRONOS/FLICA, COBAYA/COBRA and

HEXTRAN/SMABRE

xi,ref =

_

ix

25

Chapter 4: Assessment of vessel mixing models in MSLB

calculations

This chapter presents results from the assessment of coarse-mesh vessel mixing models

against CFD calculations with MSLB vessel boundary conditions. The objective is to

analyze the modeling of separate effects - flow mixing in the down-comer and the lower

plenum. A transient CFX solution (Hoehne, 2007) serves as reference. It has been

obtained with the SST turbulence model, unstructured mesh with 4 700 000 cells and the

upwind advection scheme. The domain of solution is from the reactor inlet to the core

inlet. The task is to calculate the flow parameters in the down-comer and at the core inlet,

given the vessel boundary conditions and the pressure above the core. The boundary

conditions correspond to MSLB Scenario 2, with all MCP in operation.

The vessel mixing models (coarse-mesh and CFD) used in this comparison have been

validated against plant data in Exercise 1 of this benchmark - see the V1000CT-2 Volume

3 (Kolev et al, 2010b). The considered calculation with MSLB boundary conditions is an

additional test of the validated models. It requires modeling of a different configuration

where the faulted loop is #4 and the temperature and flow disturbances are much stronger.

It is worth noting that the main coolant loops of a VVER-1000 are asymmetrically

connected to the vessel. There is an experimentally observed counter clockwise swirl in

the vessel, looking from the top. The azimuthal turn of loop #4 flow is app. +8 degrees ±

20% clockwise (estimated from loop heat-up experiments), while for loop #1 the shift is -

26 degrees counter clockwise (Topalov and Popov, 2004), (Kolev et al, 2009). Since the

hypothetical MSLB overcooling transient with all pumps in operation features single-

phase flow and high Reynolds numbers, the plant data from loop heat-up experiments

could be used to assess the ability of the model to reproduce the disturbed sector

formation as well as the angular shift of the loop flow.

For the present study, the analysis includes:

coarse-mesh to CFD comparison of the flow parameters in selected points in the

down-comer and at fuel assembly inlets

qualitative code-to-experiment comparison of the predicted azimuthal turn of loop

#4 flow centre with respect to the cold leg axis.

The CFX solution is used as an approximate reference, keeping in mind the following

uncertainties:

it has been obtained with ATHLET calculated vessel boundary conditions which

are slightly different from the CATHARE calculated ones (Kolev et al, 2005)

it is a first post-test calculation and tends to overestimate the clockwise angular

turn of loop #4 flow centre - see Figures 4.9 and 4.10 below and the results in

V1000CT-2 Volume 3

Table 4.1 summarizes the coarse-mesh r, vessel discretization used in each code for

this comparison.

Table 4.1: Participants’ codes and meshing of the down-comer and lower plenum

26

Organisation Code Vessel model Nodalization

FZD ATHLET/

DYN3D Multi-1D

4 sectors in the vessel

2 axial nodes in the DC

2 axial nodes in the LP

FZK (KIT) TRACE/

PARCS Coarse-3D

6 sectors in the DC and LP

3 radial rings in the LP

4 axial nodes in the DC

2 axial nodes in the LP

INRNE CATHARE2 Multi-1D

24 sectors in the vessel

12 axial nodes in the DC

2 axial nodes in the LP

VTT SMABRE/

HEXTRAN Multi-1D

6 sectors in the vessel

2 axial nodes in the DC

2 axial nodes in the LP

UNIPI RELAP3D/

NEM Coarse-3D

20 sectors in the DC

60 sectors in the upper LP

8 radial rings in the upper LP

20 axial nodes in the DC

4 axial nodes in the LP

4.1 The vessel mixing models

In this study, the coarse-3D models used 3D modeling without turbulence. The TRACE

user model had 6 sectors in the vessel and 3 radial rings in the lower plenum. The

RELAP3D model of UNIPI had 20 sectors in the down-comer and variable r,-meshing of

the lower plenum depending on the elevation: three axial layers in the lower plenum with

up to 60 sectors and 8 radial rings at the core inlet.

The multi-channel models with cross-flow used lower vessel nodalization as follows:

ATHLET: 4 sectors in the vessel. A sector formation model is tuned to fit CFD

results

SMABRE: 6 sectors in the vessel, one radial node and two axial nodes in the lower

plenum. Parallel channels with cross flow and aproximate turbulence modeling

CATHARE2: 24 sectors in the vessel, one radial node and two axial nodes in the

lower plenum. Parallel channels with cross flow governed by the local pressure

drops, without turbulence

The CFX-5 simulation used the SST turbulence model and unstructured mesh with

4 700 000 cells and upwind advection scheme.

For details, see Appendix F of this report and V1000CT-2 Volume 3 (Kolev et al,

2010b).

27

4.2 Coarse-mesh vs. CFD calculations

Down-comer flow parameters

Scenario 1: Figures 4.1 and 4.2 show a code-to-code comparison of the computed down-

comer temperature distribution at elevations 5800 mm and 2500 mm, in the moment of

max overcooling (166 s). The MCP #4 trips and the other three pumps are in operation.

The flow in the faulted loop #4 reverses and because of the cross-flow in the outlet ring of

the reactor vessel, the maximum overcooling (43 K) occurs in loop #1. The results show a

reasonable agreement of the coarse-mesh predictions when using 24-60 azimuth meshes.

At the same time, the 6-sector coarse-3D model solution illustrates the limitations of the

too coarse mesh.

Scenario 2: Figures 4.3 and 4.4 show the comparison of coarse-mesh vs. CFX

computed down-comer temperature distributions at elevation 5800 mm and 2500 mm

from the bottom of the reactor vessel, in the moment of maximum overcooling (app. 69s).

All main coolant pumps are in operation. The temperature of the faulted loop #4 is 74 K

lower than that in the initial state. The results show a good overall agreement with the

CFX prediction. Larger discrepancies can be seen at the borders of the disturbed sector

depending on the spatial resolution and the predicted azimuthal turn of loop #4 flow.

Figures 4.5 and 4.6 illustrate the corresponding down-comer velocity distributions. The

coarse-mesh models without turbulence cannot reproduce the detailed velocity

distribution and the predicted values are near the average ones.

Assembly inlet flow parameters

Figures 4.7, 4.12, 4.15, 4.18 and 4.21 show the computed assembly-by-assembly core

inlet temperatures, in comparison with the CFX results at time of highest return to power.

The core maps in Figures 4.13, 4.16, 4.19 and 4.22 show the corresponding differences to

CFD results. The maximum deviation varies from a few K (for 60 azimuth meshes) to

14K (for 24 meshes) or 25K (for 6 meshes). The results of the V1000CT-2 Exercise 1 on

vessel mixing simulation suggest that the actual maximum deviations can be a little

smaller than those observed here, in view of the uncertainty in the first CFX solutions.

Note that the very good agreement of RELAP3D and CFD results can be associated

with a similar sector formation and similar overestimation of the angular turn of the loop

flow, observed in V1000CT-2 Exercise 1. The CATHARE predicted disturbed sector is

rather similar to that of CFX, with some quantitative differences in the angular turn of the

main loop flow and in the transitional (border) regions.

The coarse-mesh solutions show a reasonable agreement with the CFX results in the

regions of strong or very weak disturbances, for all models. At the borders of the

disturbed sector, which are transitional regions, the coarse-mesh resolution is acceptable

when using at least 16-24 sectors in the down-comer and the lower plenum.

The results with 4- and 6-sector models illustrate the limitations in local resolution of

the too coarse azimuth meshes.

4.3 Qualitative comparison with plant data

Figure 4.9 shows the experimentally observed azimuth shift of loop #4 flow centre

relative to the cold leg axis, see the V1000CT-2 Exercise 1 specification (Kolev et al,

2009). It is +8 ±20% clockwise and opposite to that of -26 degrees observed for loop #1.

The plant data is used for qualitative comparison with the MSLB Scenario 2 results,

assuming all MCP in operation during the transient.

28

Figure 4.10 illustrates the CFX results at time of maximum overcooling (highest

return to power). The CFD solution shows an overestimation of the angular turn that may

cause larger discrepancies at the disturbed sector borders, if the solution is used as

reference. This should be kept in mind when comparing with other code solutions.

Figures 4.11, 4.14, 4.17 and 4.20 illustrate the angular turn of the loop flow as

predicted by the coarse-mesh user models. It is defined as the centerline of the zone of

minimum mixing. The disturbed sector is estimated in terms of temperature differences

between the assembly inlets and the cold leg. The zone of minimal difference (dark blue)

is the zone of minimal mixing. In this test, the CATHARE and SMABRE results are in

reasonable agreement with the plant data, while the RELAP3D and FZD ATHLET

solutions overestimate the angular turn.

4.4 Conclusions

Coarse-3D and multi-1D vessel thermal-hydraulic models with cross-flow, validated

against coolant mixing experiments and CFD calculations, can produce acceptable

accuracy in MSLB transient calculations, provided that a sufficiently fine azimuthal mesh

is used.

29

Figure 4.1: MSLB Scenario 1, time of maximum overcooling (166s):

Temperature distribution in the down-comer at elevation 5800 mm

Figure 4.2: MSLB Scenario 1, time of maximum overcooling (166s):

Temperature distribution in the down-comer at elevation 2500 mm

30

Figure 4.3: MSLB Scenario 2, time of maximum overcooling (69s): Azimuthal

temperature distribution in the down-comer at elevation 5800 mm

Figure 4.4: MSLB Scenario 2, time of maximum overcooling (69s): Azimuthal

temperature distribution in the down-comer at elevation 2500 mm

31

Figure 4.5: MSLB Scenario 2, time of maximum overcooling: Azimuthal

velocity distribution in the down-comer at elevation 5800 mm

Figure 4.6: MSLB Scenario 2, time of maximum overcooling: Azimuthal

velocity distribution in the down-comer at elevation 2500 mm

32

475

495

515

535

555

0 20 40 60 80 100 120 140 160

Te

mp

era

ture

, K

Assemblies

FZD - CFX5

UNIPI RELAP5-3D

VTT - HEXTRAN-SMABRE

FZD ATHLET/DYN3D

INRNE - CATHARE2

Figure 4.7: Assembly-by-assembly core inlet temperatures at highest return to power

100.5

102.5

104.5

106.5

108.5

110.5

112.5

114.5

116.5

118.5

120.5

0 20 40 60 80 100 120 140 160

Assembly #

Ma

ss

flo

w r

ate

, k

g/s

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

Figure 4.8: Assembly-by-assembly core inlet mass flow rates at highest return to

power

33

Figure 4.9: Plant data from the Kozloduy-6 vessel mixing experiments: Disturbed

sector and azimuthal turn of the loop #4 flow centre. Blue color corresponds to

loop-to-assembly mixing coefficients of 92-100% or

ΔTi = Tin,i - Tcold leg 4 < 1.5 K, i =1,163

34

Figure 4.10: MSLB Scenario 2 at time of max overcooling, with stuck rods in

#117 and #140: CFX computed disturbed sector and angular turn of loop #4

flow centre, in terms of temperature differences between the assembly inlets

and cold leg #4 (ΔTi = Tin, i – T cold leg 4, i =1,...,163)

35

Figure 4.11: Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: SMABRE/HEXTRAN computed disturbed sector and azimuthal shift of the

loop#4 flow centre (ΔTi = Tin, i - Tcold leg 4, i =1,...,163)

475

495

515

535

555

0 20 40 60 80 100 120 140 160

Te

mp

era

ture

, K

Assemblies

FZD - CFX5

VTT - HEXTRAN-SMABRE

Figure 4.12: Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: HEXTRAN/SMABRE vs. CFX computed assembly-by-assembly core inlet

temperatures

36

-33,0

155

20,6

151

5,5

149

6,4

139

5,0

103

-2,6

89

26,9

62

7,7

49

-7,2

16

-7,7

7

-1,7

5

0,8

15

-1,5

6

-0,4

2

-0,3

1

0,7

157

0,7

148

-0,5

115

-2,0

102

1,3

75

0,9

61

0,7

25

0,7

147

-31,6

145

-22,4

144

-3,5

143

5,7

140

0,5

131

-0,7

3

-1,1

4

-0,3

8

-0,3

9

-0,5

10

-0,9

11

-2,2

13

-1,6

12

0,9

14

-7,7

17

-0,3

18

-0,3

19

-0,6

20

-1,3

21

-2,1

22

1,0

23

0,8

24

-5,4

26

-6,8

27

-7,4

28

-0,2

29

-0,4

30

-1,0

31

-1,8

32

1,0

33

0,8

34

0,8

35

0,7

36

-1,2

37

-3,0

38

-5,1

39

-6,6

40

0,2

41

-0,5

42

-1,5

43

1,1

44

0,8

45

0,8

46

0,8

47

0,8

48

7,5

50

4,1

51

0,6

52

-2,7

53

2,9

54

0,2

55

1,6

56

1,0

57

0,9

58

0,9

59

0,9

60

23,3

63

22,2

64

18,9

65

15,1

66

9,3

67

10,0

68

5,2

69

1,9

70

1,4

71

1,4

72

1,3

73

1,3

74

41,9

76

41,1

77

40,6

78

38,9

79

35,7

80

27,1

81

0,6

82

1,3

83

-2,4

84

-2,9

85

-3,0

86

-3,1

87

-3,2

88

-1,0

90

-1,4

91

-1,3

92

-1,8

93

-5,8

94

-22,3

95

-11,5

96

1,3

97

-0,9

98

-1,4

99

-1,6

100

-1,7

101

4,5

104

4,6

105

4,7

106

3,0

107

-9,6

108

-8,1

109

-27,8

110

0,9

111

0,1

112

-0,2

113

-0,5

114

6,2

116

6,2

117

6,1

118

5,0

119

-2,3

120

3,1

121

-21,6

122

-32,0

123

0,8

124

0,5

125

0,3

126

0,2

127

6,4

128

6,3

129

5,4

130

10,9

132

-13,3

133

-28,5

134

-33,2

135

0,7

136

0,6

137

0,5

138

2,0

141

17,4

142

-33,7

146

2,7

150

4,2

152

-14,6

153

-28,0

154

-33,9

156

23,0

158

7,2

159

-8,7

160

-21,6

161

-29,9

162

-33,5

163

Figure 4. 13: Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: Differences between the HEXTRAN-SMABRE and CFX predicted assembly

inlet temperatures (ΔT = Tin – Tin, ref)

37

Figure 4.14: Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: ATHLET/DYN3D computed disturbed sector and angular turn of loop#4 flow

centre

(ΔTi = Tin, i – T cold leg 4, i =1,...,163)

475

495

515

535

555

0 20 40 60 80 100 120 140 160

Te

mp

era

ture

, K

Assemblies

FZD - CFX5

FZD ATHLET/DYN3D

Figure 4.15: Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: HEXTRAN/SMABRE vs. CFX calculated assembly-by-assembly core inlet

temperatures

38

1,0

155

-12,6

151

-0,7

149

0,2

139

-1,2

103

-8,8

89

-35,5

62

15,4

49

0,5

16

0,0

7

1,0

5

0,0

15

0,4

6

-0,2

2

-0,1

1

0,0

157

0,0

148

-1,2

115

-2,7

102

0,7

75

0,1

61

-0,1

25

0,0

147

2,4

145

11,6

144

-36,7

143

-0,5

140

-5,7

131

-0,5

3

-0,9

4

-0,1

8

-0,1

9

-0,3

10

-0,7

11

0,5

13

1,1

12

0,1

14

0,0

17

-0,1

18

-0,1

19

-0,4

20

-1,1

21

0,6

22

0,2

23

0,0

24

2,3

26

0,9

27

0,3

28

0,0

29

-0,2

30

-0,8

31

0,9

32

0,2

33

0,0

34

0,0

35

-0,1

36

6,5

37

4,7

38

2,6

39

1,1

40

0,4

41

-0,3

42

1,2

43

0,3

44

0,0

45

0,0

46

0,0

47

0,0

48

15,2

50

11,8

51

8,2

52

5,0

53

3,1

54

0,4

55

0,8

56

0,2

57

0,1

58

0,1

59

0,1

60

-39,2

63

-40,3

64

26,6

65

22,8

66

17,0

67

11,0

68

4,4

69

1,1

70

0,6

71

0,6

72

0,5

73

0,5

74

-20,5

76

-21,3

77

-21,8

78

-23,5

79

-26,7

80

-35,3

81

-1,2

82

6,0

83

2,3

84

1,8

85

1,7

86

1,6

87

1,5

88

-7,2

90

-7,6

91

-7,5

92

-8,0

93

-12,0

94

-28,5

95

13,6

96

0,6

97

-1,6

98

-2,1

99

-2,3

100

-2,4

101

-1,7

104

-1,6

105

-1,5

106

-3,2

107

-15,8

108

-41,0

109

6,2

110

0,2

111

-0,6

112

-0,9

113

-1,2

114

0,0

116

0,0

117

-0,1

118

-1,2

119

-8,5

120

-30,1

121

12,4

122

2,0

123

0,1

124

-0,2

125

-0,4

126

-0,5

127

0,2

128

0,1

129

-0,8

130

-22,3

132

-46,2

133

5,5

134

0,8

135

0,0

136

-0,1

137

-0,2

138

-4,2

141

-15,8

142

0,3

146

-3,5

150

-29,0

152

-47,5

153

6,0

154

0,1

156

-9,4

158

-26,0

159

-41,9

160

12,4

161

4,1

162

0,5

163

Figure 4.16: Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: Differences between ATHLET/DYN3D and CFX predicted assembly

inlet temperatures (ΔT = Tin – Tin, ref)

39

Figure 4.17: Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: RELAP3D/NEM predicted disturbed sector and angular turn of loop #4 flow

centre (ΔTi = Tin, i – T cold leg 4, i =1,...,163)

475

495

515

535

555

0 20 40 60 80 100 120 140 160

Te

mp

era

ture

, K

Assemblies

FZD - CFX5

UNIPI RELAP5-3D

Figure 4.18: Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: RELAP3D/NEM vs. CFX calculated assembly-by-assembly core inlet

temperatures

40

-13,3

155

-11,9

151

-0,1

149

0,3

139

2,8

103

-2,6

89

-5,2

62

-10,7

49

-1,2

16

-1,7

7

-0,7

5

-1,2

15

-0,8

6

-1,4

2

-1,4

1

-1,7

157

-1,7

148

-2,3

115

-2,0

102

-1,0

75

-1,4

61

-1,3

25

-1,7

147

-12,8

145

-10,7

144

-29,9

143

-0,4

140

-4,0

131

-1,6

3

-0,8

4

-1,4

8

-1,3

9

-1,4

10

-0,7

11

-0,7

13

-0,6

12

-1,1

14

-1,7

17

-1,6

18

-1,4

19

-1,5

20

-0,4

21

-0,9

22

-1,1

23

-1,2

24

-2,4

26

-0,8

27

-2,0

28

-1,6

29

-1,5

30

-1,1

31

-0,9

32

-1,1

33

-1,2

34

-1,2

35

-1,3

36

1,8

37

0,1

38

-1,5

39

-1,6

40

-2,4

41

-1,6

42

-0,8

43

-1,0

44

-1,2

45

-1,3

46

-1,2

47

-1,2

48

10,6

50

5,4

51

1,1

52

-1,3

53

0,4

54

0,1

55

-0,5

56

-1,1

57

-1,2

58

-1,2

59

-1,4

60

5,0

63

2,9

64

6,9

65

5,5

66

8,7

67

9,4

68

2,4

69

-0,6

70

-1,2

71

-1,2

72

-1,4

73

-6,0

74

8,9

76

6,8

77

5,4

78

1,5

79

4,0

80

15,2

81

4,3

82

-3,6

83

-2,4

84

-2,4

85

-2,6

86

-2,8

87

-3,0

88

-0,3

90

-7,2

91

-1,0

92

-1,7

93

-5,5

94

-15,5

95

-17,0

96

-2,5

97

-3,2

98

-3,2

99

-3,3

100

-3,7

101

2,5

104

-1,0

105

-0,1

106

-2,0

107

-13,6

108

-14,4

109

-5,9

110

-3,0

111

-2,1

112

-2,3

113

-2,5

114

0,1

116

0,1

117

0,3

118

-1,1

119

-7,1

120

-18,4

121

-12,4

122

-6,3

123

-2,4

124

-2,1

125

-1,7

126

-1,8

127

0,3

128

0,2

129

-0,7

130

-16,1

132

-19,0

133

-11,6

134

-5,9

135

-2,2

136

-1,8

137

-1,5

138

-3,1

141

-12,2

142

-5,9

146

-2,8

150

-24,1

152

-25,3

153

-14,8

154

-4,9

156

-8,8

158

-21,2

159

-21,5

160

-8,7

161

-11,1

162

-4,5

163

Figure 4.19: MSLB Scenario 2 at time of max overcooling, with stuck rods in #117

and #140: Differences between the RELAP3D/NEM and CFX predicted assembly

inlet temperatures (ΔT = Tin – Tin, ref)

41

Figure 4.20: Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: CATHARE2/PKin predicted disturbed sector and angular turn of loop#4 flow

centre (ΔTi = Tin, i – T cold leg 4, i =1,...,163)

475

495

515

535

555

0 20 40 60 80 100 120 140 160

Te

mp

era

ture

, K

Assemblies

FZD - CFX5

INRNE - CATHARE2

Figure 4.21: Scenario 2 at time of max overcooling, with stuck rods in #117 and

#140: CATHARE2 vs. CFX calculated assembly-by-assembly core inlet

temperatures. CATHARE 24-sector vessel model used

42

0,0

155

-7,6

151

1,2

149

1,9

139

0,4

103

-7,0

89

-10,1

62

-11,8

49

-0,3

16

0,1

7

0,5

5

0,1

15

0,1

6

0,1

2

0,2

1

0,3

157

0,4

148

-0,3

115

-0,2

102

0,9

75

0,3

61

0,1

25

0,3

147

1,3

145

-1,4

144

-6,5

143

1,4

140

-3,6

131

-0,1

3

-0,2

4

0,1

8

0,2

9

0,0

10

-0,3

11

0,1

13

0,4

12

0,2

14

0,0

17

0,1

18

0,2

19

0,0

20

0,0

21

0,2

22

0,3

23

0,2

24

-0,3

26

0,1

27

0,0

28

0,2

29

0,1

30

-0,3

31

0,4

32

0,3

33

0,2

34

0,2

35

0,1

36

-0,3

37

-1,1

38

0,7

39

0,6

40

0,6

41

0,0

42

0,2

43

0,4

44

0,2

45

0,2

46

0,2

47

0,2

48

-2,2

50

3,2

51

3,0

52

3,7

53

3,3

54

1,2

55

0,8

56

0,4

57

0,3

58

0,3

59

0,3

60

-9,3

63

-6,4

64

-2,3

65

4,1

66

9,7

67

10,8

68

4,2

69

1,3

70

0,8

71

0,8

72

0,7

73

0,7

74

-18,0

76

-18,8

77

-18,4

78

-16,6

79

-16,3

80

-16,6

81

-0,9

82

4,3

83

1,2

84

1,2

85

1,5

86

1,5

87

1,4

88

-5,5

90

-5,9

91

-5,9

92

-6,4

93

-10,3

94

-21,4

95

11,4

96

1,1

97

-0,9

98

-1,1

99

-0,9

100

-0,5

101

-0,1

104

0,0

105

0,1

106

-1,5

107

-12,9

108

0,6

109

6,1

110

0,6

111

-0,2

112

-0,4

113

-0,5

114

1,6

116

1,6

117

1,6

118

0,5

119

-6,1

120

-11,2

121

4,7

122

2,0

123

0,5

124

0,2

125

0,0

126

-0,1

127

1,9

128

1,8

129

1,0

130

-16,5

132

1,1

133

3,6

134

0,9

135

0,4

136

0,3

137

0,2

138

-2,2

141

-10,3

142

0,5

146

-1,5

150

-17,8

152

2,2

153

-0,4

154

0,4

156

-4,9

158

-20,1

159

-1,0

160

-4,6

161

2,8

162

-0,4

163

Figure 4.22: MSLB Scenario 2 at time of max overcooling, with stuck rods in #117

and #140: Differences between the CATHARE and CFX predicted assembly inlet

temperatures (ΔT = Tin – Tin, ref)

43

Chapter 5: Results of Exercise 2

This chapter presents the results of Exercise 2 of the VVER-1000 MSLB Benchmark. The

coupled 3D neutronics/TH codes were tested in the following sequence of calculations:

Hot zero power (HZP) states, as defined in Section 5.1

Initial hot full power (HFP) steady state

Transient

The steady state problems allow all standard steady state nodal calculations, from

clean tests to simple coupled N/TH calculations.

Six complete solutions and additional partial solutions for separate steps were

submitted. Section 5.1 shows HZP results of the evaluation of standalone nodal neutronics

models and solvers. Section 5.2 shows HFP results from coupled calculations. Section 5.3

presents the transient results.

5.1 HZP results

Table 5.1 shows the steady states to be calculated. The parameters of the zero power states

are as follows: total power of 300 kW, fuel/moderator temperature of 279.15°C (552.15

K) and moderator density of 766.5 kg/m3.

This section discusses the comparison of Keff, rod worth, peaking factors and axial

core power distributions. Appendix A illustrates the two-dimensional distributions and

their deviations from the mean.

Table 5.1: Definition of the steady states

State

no.

TH

conditions

Control rod positions Scenario

0 HZP Groups 1-10 ARO+ 1

1a HZP

(near critical) Groups 1-5 out, 6 - 81% wd, 7-10 in 1

1b HZP Groups 1-10 ARI 1

2 HFP Groups 1-9 ARO Group 10 is 80% wd 1

3 HZP Groups 1-10 ARI, #90 is 100% wd 1

4 HZP Groups 1-10 ARI, #63 is 100% wd 1

5 HZP Groups 1-10 ARI, #140 is 100% wd 2

6 HZP Groups 1-10 ARI, #140 and #117 100% wd 2

ARO – all rods out, ARI – all rods in

The comparison in the sequel shows that the submitted HZP results cluster in two groups:

one including DYN3D, PARCS, CRONOS2 and COBAYA3 results, and another

consisting of NEM and HEXTRAN results. The two groups differ in Keff and the core

power distributions, the differences being of systematic nature, with maximal

discrepancies of up to 13-15%. Similar clustering appears in the results of V1000CT-1

44

benchmark (Ivanov et al, 2006b). It is due to the properties of the considered nodal flux

approximations. NEM and HEXTRAN solvers use polynomial nodal expansion methods

without node subdivision. The results indicate that they need some improvements to

produce converged solutions for large hexagonal nodes and regions of steep gradients.

Because of this clustering, we consider two comparisons: (a) with the mean of all

codes results used as „reference‟ solution, and (b) with the mean of DYN3D, PARCS,

CRONOS and COBAYA solutions as reference. CRONOS 2nd

-order finite-element

solutions with 24 nodes/triangles per hexagon (24N) also serve as reference.

In the discussion to follow, reference is the mean result of all codes unless explicitly

stated otherwise.

HZP state 0

All control rod groups are out of the core (ARO).

Tables 5.2 and 5.3 show the computed Keff and peaking factors, along with the deviations

from the mean. The finer-mesh CRONOS 24N and COBAYA 24N results tend to

converge to the same solution. The coarse-mesh results are in good agreement and are

close to the mean and the 24N solutions.

Figure 5.1 shows the computed axial power distributions. The results of DYN3D,

PARCS, CRONOS and COBAYA are in excellent agreement. The NEM and HEXTRAN

results show certain deviations, which are larger in the upper part of the core. The relative

deviation in Fz is +6% for HEXTRAN and -5.5% for NEM. These discrepancies are due

to differences in the reflector modeling and the neutronics models as applied to large

hexagonal nodes.

Figure 5.2 presents the mean of all codes solutions and the standard deviations.

Figures A.1-A.6 in Appendix A show 2D maps with the computed radial power

distribution vs. mean of DYN3D, PARCS, CRONOS 6N and COBAYA 6N solutions.

The individual DYN3D, PARCS, CRONOS 6N and COBAYA 6N results are in very

good agreement with the mean values (max relative deviation of 0.6%, PARCS). The

finer-mesh CRONOS 24N and COBAYA 24N solutions tend to converge to the same

solution.

The maximal systematic deviation in the NEM computed radial power distribution is

13% and that of the HEXTRAN solution is up to 15%.

HZP state 1a

The reactor is near critical. Control rod groups 1-5 are fully withdrawn. Group number 6

is 81% withdrawn and groups 7-10 are fully inserted. The rodded assemblies are marked

in blue in the core maps (see Figures A.7 - A.12).

Tables 5.4 and 5.5 show the participants results for Keff and the peaking factors, in

comparison with the mean. HEXTRAN results are not available because of incorrectly

filled submittal template.

The peaking factors predicted by DYN3D, PARCS, CRONOS 6N and COBAYA 6N

are in very good agreement with the mean. The NEM computed Fxy differs by 3.4%.

Figure 5.3 shows a very good agreement of the predicted core average axial power

distributions for all codes, except the NEM solution for which the relative difference in Fz

to the mean of all codes is 4.6%.

45

HZP state 1b

All control rod groups are fully inserted (ARI).

Tables 5.6 and 5.7 show the comparison of the computed Keff and peaking factors.

The results of DYN3D, PARCS, CRONOS and COBAYA are in very good agreement.

The NEM results differ from the mean of the above four codes by -216 pcm in Keff,

8.24% in Fxy and – 10.57% in Fz.

Figure 5.5 shows a good agreement of the axial core power distributions for DYN3D,

PARCS, CRONOS and COBAYA.

Figures A.13-A.18 in Appendix A show 2D maps with the computed radial power

distribution vs. mean of DYN3D, PARCS, CRONOS 6N and COBAYA 6N solutions.

The individual DYN3D, PARCS, CRONOS 6N and COBAYA 6N results are in very

good agreement with the mean.

HZP state 3

HZP states 3 and 4 are similar stuck rods states with different locations of the stuck rods.

For this analysis, we consider only HZP state 3. All control rods are fully inserted except

the one in assembly #90 which is fully withdrawn.

Table 5.8 presents the results for Keff and the peaking factors compared with the

mean value of DYN3D, PARCS, CRONOS 6N and COBAYA 6N solutions. Table 5.9

gives the deviations from the mean of all codes results. Table 5.10 shows the tripped and

stuck rods worth in comparison with the CRONOS 24N solution.

Figure 5.7 shows the computed axial power distributions. Figures A.19-A.23 in

Appendix A show 2D maps with the computed radial power distribution vs. mean of

DYN3D, PARCS, CRONOS 6N and COBAYA 6N solutions.

The comparison shows that the results of DYN3D, PARCS, CRONOS 6N and

COBAYA 6N are in very good agreement, and those of NEM have systematic deviations.

The NEM result differs from the mean by -99 pcm in Keff, 6.46% in Fxy and -8.9% in Fz.

HZP state 5

All control rods are fully inserted, except the rod in #140 which is fully withdrawn. This

calculation uses the XS library for Scenario 2.

Table 5.11 shows the computed Keff and peaking factors and the deviations from the

reference. Figure 5.9 illustrates the computed axial power distributions. Figure A.29 in

Appendix A shows a comparison CRONOS 6N and COBAYA 6N solutions.

The coarse-mesh COBAYA and CRONOS results are in very good agreement – with

each other and with the reference. The NEM results differ from the mean by -251 pcm in

Keff, 7.3% in Fxy and -6% in Fz.

46

HZP state 6

All control rods are fully inserted except the rods in #117 and #140 which are fully

withdrawn. This analysis includes calculations with the XS libraries for Scenario 1 and 2.

The results in Tables 5.12 and 5.13, and Figure 5.11, obtained with the XS library for

the realistic Scenario 1 show a very good code-to-code agreement for DYN3D, PARCS,

COBAYA3 and CRONOS2 results.

Table 5.14 gives a comparison of the computed Keff and peaking factors, using XS

library for Scenario 2. The COBAYA and CRONOS results are close to each other and in

good agreement with the mean.

Figure 5.12 presents the predicted core averaged axial power distributions and the

standard deviation. The CRONOS and COBAYA solutions are in good agreement with

the reference. The NEM solution shows certain deviations, similar to those observed in

the other calculated states.

Figure A.30 shows a code-to-code CRONOS and COBAYA comparison of the

computed radial power distributions. The solutions are in good agreement, with a

maximum deviation in the order of 3% in the vicinity of stuck rods.

47

Table 5.2: Computed parameters in HZP state 0 and deviations from the mean

of four codes

Code/Parameter keff keff, pcm Fxy δ Fxy,% Fz δ Fz,% AO

VTT HEXTRAN 1.03480 474 1.258 -6.08 3.071 3.94 0.820

FZD DYN3D 1.02988 -4 1.337 -0.19 2.949 -0.19 0.803

UNIPI NEM 1.02821 -166 1.284 -4.14 2.786 -5.70 0.772

FZK PARCS 1.02986 -6 1.341 0.11 2.957 0.08 0.805

INRNE CRONOS 6N 1.02989 -3 1.341 0.11 2.954 -0.02 N/A

INRNE CRONOS 24N 1.02996 4 1.339 -0.04 2.951 -0.12 N/A

INRNE/UPM COBAYA 6N 1.03006 13 1.339 -0.04 2.958 0.12 0.805

INRNE/UPM COBAYA 24N 1.03003 10 1.340 0.04 2.962 0.25 0.806

Reference* 1.02992 1.340 2.955 N/A

Reference* = mean of PARCS, DYN3D, CRONOS 6N and COBAYA 6N

Table 5.3: Computed parameters in HZP state 0 and deviations from the mean

of all codes

Code/Parameter keff keff, pcm Fxy δ Fxy,% Fz δ Fz,% AO

VTT HEXTRAN 1.03480 433 1.258 -4.87 3.071 4.15 0.820

FZD DYN3D 1.02988 -44 1.337 1.11 2.949 0.02 0.803

UNIPI NEM 1.02821 -206 1.284 -2.9 2.786 -5.51 0.772

FZK PARCS 1.02986 -46 1.341 1.41 2.957 0.29 0.805

INRNE CRONOS 6N 1.02989 -43 1.341 1.41 2.954 0.19 N/A

INRNE CRONOS 24N 1.02996 -37 1.339 1.26 2.951 0.08 N/A

INRNE/UPM COBAYA 6N 1.03006 -27 1.339 1.26 2.958 0.32 0.805

INRNE/UPM COBAYA 24N 1.03003 -30 1.340 1.33 2.962 0.46 0.806

Reference 1.03034 1.322 2.949 N/A

Standard deviation 0.00190 0.03249 0.07727 N/A

48

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 50 100 150 200 250 300 350

Axia

l p

ow

er

pro

file

Elevation, cm

Average

DYN3D

PARCS

NEM

HEXTRAN

COBAYA

CRONOS

Figure 5.1: Core-averaged axial power distribution in HZP state 0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 50 100 150 200 250 300 350

Axia

l p

ow

er

pro

file

Elevation, cm

Average

Figure 5.2: Core-averaged axial power distribution in HZP state 0 (mean of

all codes and standard deviation)

49

Table 5.4: Computed parameters in HZP state 1a and deviations from the mean

of four codes

Code/Parameter keff keff, pcm Fxy δ Fxy,% Fz δ Fz,% AO

FZD DYN3D 0.99755 1 1.416 0.11 1.863 -0.25 0.481

UNIPI NEM 0.99665 -90 1.463 3.43 1.791 -4.11 0.455

FZK PARCS 0.99745 -10 1.414 -0.04 1.874 0.33 0.488

INRNE CRONOS 6N 0.99745 -10 1.410 -0.32 1.863 -0.25 N/A

INRNE CRONOS 24N 0.99761 7 1.414 -0.04 1.865 -0.15 N/A

INRNE/UPM COBAYA 6N 0.99773 19 1.418 0.25 1.871 0.17 0.487

INRNE/UPM COBAYA 24N 0.99764 10 1.415 0.04 1.873 0.28 0.488

Reference* 0.99755 1.415 1.868 N/A

* Reference = mean of PARCS, DYN3D, CRONOS 6N and COBAYA 6N

Table 5.5: Computed parameters in HZP state 1a and deviations from the mean

of all codes

Code/Parameter keff keff, pcm Fxy δ Fxy,% Fz δ Fz,% AO

FZD DYN3D 0.99755 11 1.416 -0.38 1.863 0.32 0.481

UNIPI NEM 0.99665 -79 1.463 2.92 1.791 -3.56 0.455

FZK PARCS 0.99745 1 1.414 -0.52 1.874 0.91 0.488

INRNE CRONOS 6N 0.99745 1 1.410 -0.80 1.863 0.32 N/A

INRNE CRONOS 24N 0.99761 17 1.414 -0.52 1.865 0.42 N/A

INRNE/UPM COBAYA 6N 0.99773 29 1.418 -0.24 1.871 0.75 0.487

INRNE/UPM COBAYA 24N 0.99764 20 1.415 -0.45 1.873 0.85 0.488

Reference 0.99744 1.421 1.857 N/A

Standard deviation 0.00036 0.01849 0.02953 N/A

50

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 50 100 150 200 250 300 350

Axia

l p

ow

er

pro

file

Elevation, cm

Average

DYN3D

PARCS

NEM

COBAYA

CRONOS

Figure 5.3: Core-averaged axial power distribution in HZP state 1a

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 50 100 150 200 250 300 350

Axia

l p

ow

er

pro

file

Elevation, cm

Average

Figure 5.4: Core-averaged axial power distribution in HZP state 1a: (mean of all

codes and standard deviation)

51

Table 5.6: Computed parameters in HZP state 1b and deviations from the mean

of four codes

Code/Parameter keff keff, pcm Fxy δFxy,% Fz δFz,% AO

FZD DYN3D 0.96213 8 1.383 -0.07 2.342 0.35 0.481

UNIPI NEM 0.95997 -216 1.498 8.24 2.087 -10.57 0.455

FZK PARCS 0.96192 -14 1.387 0.22 2.338 0.18 0.488

INRNE CRONOS 6N 0.96192 -14 1.378 -0.43 2.33 -0.16 N/A

INRNE CRONOS 24N 0.96210 5 1.384 0.00 2.322 -0.50 N/A

INRNE/UPM COBAYA 6N 0.96223 19 1.388 0.29 2.325 -0.37 0.487

INRNE/UPM COBAYA 24N 0.96216 11 1.383 -0.07 2.334 0.01 0.488

Reference* 0.96205 1.384 2.334 N/A

* Reference = mean of PARCS, DYN3D, CRONOS 6N and COBAYA 6N

Table 5.7: Computed parameters in HZP state 1b and deviations from the mean

of all codes

Code/Parameter keff keff, pcm Fxy δFxy,% Fz δFz,% AO

FZD DYN3D 0.96213 37 1.383 -1.22 2.342 4.51 0.481

UNIPI NEM 0.95997 -188 1.498 6.99 2.087 -20.99 0.455

FZK PARCS 0.96192 15 1.387 -0.94 2.338 4.11 0.488

INRNE CRONOS 6N 0.96192 15 1.378 -1.58 2.33 3.31 N/A

INRNE CRONOS 24N 0.96210 34 1.384 -1.15 2.322 2.51 N/A

INRNE/UPM COBAYA 6N 0.96223 47 1.388 -0.87 2.325 2.81 0.487

INRNE/UPM COBAYA 24N 0.96216 40 1.383 -1.22 2.334 3.71 0.488

Reference 0.96178 1.400 2.297 N/A

Standard deviation 0.00080 0.04327 0.09280 N/A

52

0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250 300 350

Axia

l p

ow

er

pro

file

Elevation, cm

Average

DYN3D

PARCS

NEM

COBAYA

CRONOS

Figure 5.5: Core-averaged axial power distribution in HZP state 1b

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 50 100 150 200 250 300 350

Axia

l p

ow

er

pro

file

Elevation, cm

Average

Figure 5.6: Core-averaged axial power distribution (mean of all codes and standard

deviation)

53

Table 5.8: Computed parameters in HZP state 3 and deviations from the mean of

four codes. XS library for Scenario 1

Code/Parameter keff keff, pcm Fxy δFxy,% Fz δFz,% AO

FZD DYN3D 0.96866 7 6.470 -0.32 2.12 0.49 0.481

UNIPI NEM 0.96763 -99 6.910 6.46 1.922 -8.90 0.455

FZK PARCS 0.96843 -16 6.486 -0.07 2.114 0.20 0.488

INRNE//UPM COBAYA 6N 0.96884 25 6.543 0.80 2.099 -0.51 0.487

INRNE//UPM COBAYA 24N 0.96869 10 6.490 -0.01 2.108 -0.08 0.488

INRNE CRONOS 6N 0.96843 -16 6.464 -0.41 2.106 -0.18 N/A

INRNE CRONOS 24N 0.96867 8 6.501 0.16 2.098 -0.56 N/A

Reference* 0.96859 6.491 2.110 N/A

* Reference = mean of PARCS, DYN3D, CRONOS 6N and COBAYA 6N

Table 5.9: Computed parameters in HZP state 3 and deviation from the mean of all

codes

Code/Parameter keff keff, pcm Fxy δFxy,% Fz δFz,% AO

FZD DYN3D 0.96866 19 6.47 -1.25 2.12 1.87 0.481

UNIPI NEM 0.96763 -88 6.91 5.46 1.922 -7.64 0.455

FZK PARCS 0.96843 -5 6.486 -1.01 2.114 1.59 0.488

INRNE/UPM COBAYA 6N 0.96884 37 6.543 -0.14 2.099 0.86 0.487

INRNE//UPM COBAYA 24N 0.96869 22 6.49 -0.95 2.108 1.30 0.488

CEA CRONOS 6N 0.96843 -5 6.464 -1.34 2.106 1.20 N/A

CEA CRONOS 24N 0.96867 20 6.501 -0.78 2.098 0.82 N/A

Reference 0.96848 6.552 2.081 N/A

Standard deviation 0.00040 0.14809 0.06531 N/A

Table 5.10: Tripped and stuck rods worth. Reference is the

CRONOS 24N solution

Parameters Tripped RW, pcm Scram W, pcm Stuck RW, pcm

FZD DYN3D -6509 -6837 -328

UNIPI NEM -6437 -6914 -476

FZK PARCS -6533 -6858 -326

INRNE/UPM COBAYA 6N -6509 -6844 -335

INRNE//UPM COBAYA 24N -6522 -6848 -326

CEA CRONOS 6N -6536 -6861 -325

CEA CRONOS 24N -6517 -6848 -331

54

0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250 300 350

Ax

ial p

ow

er

pro

file

Elevation, cm

Average

DYN3D

PARCS

NEM

COBAYA3

CRONOS

Figure 5.7: Core-averaged axial power distribution in HZP state 3

0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250 300 350

Ax

ial p

ow

er

pro

file

Elevation, cm

Average

Figure 5.8: Core-averaged axial power distribution in HZP state 3 (mean of all codes

and standard deviation)

55

Table 5.11: Computed parameters in HZP state 5 and deviation from the mean of all

codes (XS library for Scenario 2)

Code/Parameter keff keff,

pcmδFxy, δFxy,% Fz δFz,% AO

Tripped

RW,

pcm

UNIPI NEM 0.99635 -251 2.37 7.29 2.15 -6.04 0.58 -3110

INRNE/UPM COBAYA

6N 0.99977 91 2.159 -2.26 2.34 2.26 0.639 -2922

INRNE/UPM COBAYA

24N 0.99960 74 2.148 -2.76 2.334 2.00 N/A -2958

INRNE CRONOS 6N 0.99972 86 2.159 -2.26 2.329 1.78 N/A -2943

Average 0.99886 2.209 2.288 N/A

Standard deviation 0.00167 0.10746 0.09228 N/A

0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250 300 350

Axia

l p

ow

er

pro

file

Elevation, cm

Average

RELAP5-3D

COBAYA

CRONOS

Figure 5.9: Core averaged axial power distribution in HZP state 5

56

0.0

0.5

1.0

1.5

2.0

2.5

0 50 100 150 200 250 300 350

Axia

l p

ow

er

pro

file

Elevation, cm

Average

Figure 5.10: Core averaged axial power distribution in HZP state 5 (mean of all

codes and standard deviation)

57

Table 5.12: Computed parameters in HZP state 6 and deviations from the mean of

all codes (XS library for Scenario 1)

Code/Parameter keff keff, pcm Fxy δFxy,% Fz δFz,% AO

FZD DYN3D 0.97691 -3 8.542 -0.16 2.003 0.15 0.535

FZK PARCS 0.97667 -27 8.568 0.14 2.004 0.20 0.537

INRNE/UPM COBAYA 6N 0.97717 24 8.575 0.22 1.993 -0.35 0.533

INRNE/UPM COBAYA 24N 0.97700 6 8.539 -0.20 2.000 0.00 0.536

Mean 0.97694 8.556 2.000 N/A

Standard deviation 0.00021 0.01817 0.00497 N/A

Table 5.13: Tripped and stuck rods worth (XS library for Scenario 1)

Reference is the COBAYA 24N solution

Code/Parameter Tripped RW, pcm Scram W, pcm Stuck RW, pcm

FZD DYN3D -5584 -6837 -1253

FZK PARCS -5609 -6858 -1249

INRNE/UPM COBAYA 6N -5575 -6844 -1268

INRNE/UPM COBAYA 24N -5591 -6848 -1257

0,000

0,500

1,000

1,500

2,000

2,500

0 50 100 150 200 250 300 350

Axia

l p

ow

er

pro

file

Elevation, cm

Average

DYN3D

PARCS

COBAYA

CRONOS

Figure 5.11: Core averaged axial power distribution in HZP state 6 (XS lib for Sc1)

58

Table 5.14: Computed parameters in HZP state 6 (XS library for Scenario 2)

Code/Parameter keff keff,

pcm δFxy,% δFxy Fz δFz,% AO

Tripped

RW, pcm

UNIPI NEM 0.99830 -220 3.535 9.51 2.124 -6.15 0.572 -2913

INRNE/UPM

COBAYA 6N 1.00133 83 3.132 -2.97 2.315 2.29 0.632 -2783

INRNE/UPM

COBAYA 24N 1.00111 61 3.114 -3.53 2.31 2.07 N/A -2791

INRNE CRONOS 6N 1.00125 75 3.131 -3.00 2.304 1.80 N/A -2784

Mean 1.00050 3.228 2.263 N/A

Standard deviation 0.00147 0.20483 0.09294 N/A

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350

Axia

l p

ow

er

pro

file

Elevation, cm

COBAYA

CRONOS

NEM

Average

Figure 5.12: Core-averaged axial power distribution in HZP state 6 (XS lib for Sc2)

59

5.2 Initial HFP state results

The HFP steady state core parameters are as given in the V1000CT-2 Exercise 2

specification (Kolev et al, 2006). The cross-section library for Scenario 1 is used.

Table 5.15 and Figure 5.13 show a code-to-code comparison of the computed core

parameters. The results have been obtained with DYN3D/ATHLET (FZD), CRONOS2/

FLICA4 (INRNE/CEA), COBAYA3/COBRA3 (INRNE/UPM), NEM/RELAP3D

(UNIPI) and HEXTRAN/SMABRE (VTT) codes, using modeling assumptions as

described in Appendix G. Reference is the mean result of all codes.

The CRONOS and COBAYA nodal flux solvers used subdivision to 6 triangles/nodes

per hexagon. FLICA4 and COBRA3 used one point per hexagon. CATHARE2 calculated

thermal-hydraulic boundary conditions were imposed on the core, using a 24-sector

mapping scheme.

The DYN3D, NEM and HEXTRAN nodal solvers used one point per hexagon. In the

NEM/RELAP3D calculation the core boundary conditions were obtained through a

detailed mapping scheme with 60 channels in the upper part of the lower plenum. In the

HEXTRAN/SMABRE and DYN3D/ATHLET calculations, coarse-mesh mapping

schemes were used.

The CRONOS/FLICA, COBAYA/COBRA and NEM/RELAP3D results for Keff are

in good agreement with the reference. The HEXTRAN/SMABRE result differs by + 380

pcm and the DYN3D/ATHLET result shows a difference of -351 pcm, most of which can

be attributed to the fuel gap conductance model and the spatial N/TH coupling.

The maximum difference in Fxy and Fz (to the mean of all codes) is -1.36% and

-3.02% respectively. The discrepancies are mainly due to differences in the core and the

vessel thermal hydraulic models, leading to differences in the temperatures at the core

inlet and in the core.

Figures 5.15-5.19 present the coupled code computed relative assembly powers, in

comparison with the mean. The DYN3D/ATHLET and COBAYA/COBRA3 solutions are

close to each other despite the differences in the spatial coupling. In these solutions, the

differences in fuel Doppler temperature (see Appendix B) are relatively uniform and

affect mainly Keff (see T|able 5.15). Because of the observed clustering of the solutions,

there is a significant spread around the mean of all codes: up to 7.2% for

HEXTRAN/SMABRE and up to 4.9% for the other codes.

Appendix B documents details of the code-to-code comparison of 2D maps and graphs

displaying the assembly-by-assembly Doppler temperatures and core inlet parameters.

In order to separate the effects, the benchmark team performed a systematic code-to-

code comparison using the same core inlet BC for each pair of codes. The

COBAYA3/COBRA3 solution served as reference. The results in Тables 5.16 and 5.17,

and Figures B.5, B.7 and B.11-B.13 show that

CRONOS2/FLICA4 and PSU PARCS/TRACE results are in good agreement with

the COBAYA3/COBRA3 results

DYN3D/ATHLET and HEXTRAN/SMABRE results are in good agreement with

the COBAYA3/COBRA3 predicted peaking factors, but give a δk of 320-410 pcm

due to differences in the neutronics solver and the computed Doppler temperature

60

Table 5.15: Computed HFP state parameters

Code/Parameter Keff Δk, pcm Fxy δFxy,% Fz δFz,% AO

VTT HEXTRAN/SMABRE 1.00210 380 1.303 1.04 1.187 1.78 N/A

FZD DYN3D/ATHLET 0.99481 -351 1.283 -0.96 1.18 1.08 -0.050

UNIPI NEM/RELAP3D 0.99800 -31 1.303 1.04 1.139 -3.02 -0.028

INRNE/UPM

COBAYA/COBRA 0.99823 -8 1.279 -1.36 1.177 0.78 -0.048

INRNE/CEA CRONOS/FLICA 0.99841 10 1.295 0.24 1.163 -0.62 N/A

Reference 0.99831 1.293 1.169

Standard deviation 0.0026 0.0112 0.0190

0,6

0,7

0,8

0,9

1,0

1,1

1,2

0 50 100 150 200 250 300 350

Ax

ial p

ow

er p

rofi

le

Elevation, cm

Average

VTT - HEXTRAN/SMABRE

FZD - DYN3D/ ATHLET

UNIPI - RELAP5/NEM

INRNE/CEA - CRONOS/FLICA

INIRNE/UPM - COBAYA3/COBRA3

Figure 5.13: Computed core average axial power distributions in the HFP state

0,6

0,7

0,8

0,9

1,0

1,1

1,2

0 50 100 150 200 250 300 350

Ax

ial p

ow

er p

rofi

le

Elevation, cm

Average

Figure 5.14: Computed core average axial power distributions in the initial HFP

steady state (mean of all codes and standard deviation)

61

7,2

0,772

28

5,3

0,974

27

5,2

0,971

18

7,1

0,771

13

1,6

1,195

26

-4,9

0,739

1

-4,8

0,789

2

-4,6

1,021

3

-3,8

1,023

4

-2,1

1,084

5

-0,2

0,853

6

2,8

1,039

7-4,7

0,998

8

-4,0

0,920

9

-2,9

0,989

10

-1,4

0,955

11

1,4

1,190

12-4,0

0,920

14

-2,8

0,876

15

-1,8

0,958

16

0,6

1,296

17-2,7

0,994

19

-0,6

0,988

20

0,8

1,137

21

5,0

1,023

22-0,4

0,979

23

0,8

1,303

24

5,1

1,025

25

2,8

1,039

7

Figure 5.15: HEXTRAN/SMABRE computed assembly powers vs. mean of all codes

in the initial HFP state

4,5

0,753

28

3,6

0,958

27

3,5

0,955

18

4,4

0,751

13

0,4

1,181

26

-3,9

0,747

1

-3,4

0,800

2

-2,4

1,044

3

-2,0

1,042

4

-1,5

1,092

5

-0,2

0,853

6

2,5

1,036

7-2,6

1,020

8

-2,5

0,934

9

-1,6

1,002

10

-1,4

0,955

11

0,2

1,176

12-2,5

0,934

14

-1,9

0,885

15

-1,6

0,961

16

0,5

1,294

17-1,4

1,008

19

-0,6

0,988

20

0,3

1,132

21

3,2

1,005

22-0,4

0,980

23

0,8

1,303

24

3,3

1,007

25

2,5

1,036

7

Figure 5.16: NEM/RELAP3D computed assembly powers

vs. mean of all codes in the initial HFP state

Assembly #

Relative power

((RELAP5-3D-mean)/mean)*100%

Assembly #

Relative power

((HEXTRAN/SMABRE-mean)/ mean)*100%

62

-4,4

0,689

28

-3,5

0,892

27

-3,6

0,889

18

-4,5

0,687

13

-0,8

1,168

26

4,8

0,814

1

4,5

0,866

2

3,4

1,106

3

2,8

1,093

4

1,7

1,127

5

0,6

0,860

6

-2,3

0,987

73,6

1,085

8

3,3

0,990

9

2,1

1,040

10

0,5

0,974

11

-1,0

1,162

123,4

0,991

14

2,6

0,926

15

0,6

0,982

16

-1,0

1,275

172,3

1,045

19

1,8

1,011

20

-0,5

1,123

21

-3,3

0,942

221,5

0,998

23

-0,8

1,282

24

-3,3

0,943

25

-2,3

0,987

7

Figure 5.17: DYN3D/ATHLET computed radial power distribution vs. mean of all

codes in the initial HFP state

-2,0

0,706

28

-1,1

0,914

27

-1,3

0,911

18

-2,2

0,704

13

0,4

1,182

26

-0,5

0,773

1

-0,2

0,827

2

0,4

1,074

3

0,4

1,067

4

0,4

1,113

5

-0,2

0,853

6

-0,4

1,006

70,3

1,050

8

0,2

0,960

9

0,1

1,020

10

-0,4

0,965

11

0,2

1,176

120,3

0,961

14

0,0

0,902

15

-0,4

0,972

16

0,4

1,293

170,4

1,026

19

1,0

1,004

20

0,4

1,133

21

-1,2

0,962

220,8

0,991

23

0,7

1,302

24

-1,1

0,964

25

-0,4

1,006

7

Figure 5.18: CRONOS/FLICA4 computed radial power distribution vs. mean of all

codes in the initial HFP state. CRONOS/FLICA used flat core inlet BC

Assembly #

Relative power

((CRONOS-mean)/mean)*100%

Assembly #

Relative power

((DYN3D - mean)/mean)*100%

63

-5,3

0,683

28

-4,3

0,885

27

-3,8

0,888

18

-4,9

0,684

13

-1,6

1,158

26

4,5

0,812

1

4,0

0,862

2

3,2

1,104

3

2,6

1,091

4

1,5

1,125

5

0,0

0,855

6

-2,5

0,985

73,4

1,083

8

3,0

0,987

9

2,3

1,042

10

2,6

0,994

11

-0,8

1,164

122,9

0,987

14

2,1

0,921

15

3,2

1,008

16

-0,6

1,279

171,4

1,037

19

-1,6

0,978

20

-0,9

1,118

21

-3,6

0,939

22-1,5

0,969

23

-1,6

1,272

24

-3,9

0,937

25

-2,5

0,985

7

Figure 5.19: COBAYA3/COBRA3 computed radial power distribution vs. mean of

all codes in the initial HFP state. COBAYA3/COBRA3 used CATHARE2 calculated

core BC

Table 5.16: Comparison of HFP results using core inlet BC as obtained from the

considered system code. Reference is the COBAYA3/COBRA3 result

DYN3D/ATHLET COBAYA3/COBRA3 Abs. deviation

Keff 0.99481 0.99810 -329 pcm

Fxy 1.283 1.284 -0.001

Fz 1.180 1.178 0.002

Axial offset -0.050 -0.048 -0.002

HEXTRAN/SMABRE COBAYA3/COBRA3 Abs. deviation

Keff 1.00210 0.99796 +414 pcm

Fxy 1.303 1.278 0.025

Fz 1.170

NEM/RELAP3D COBAYA3/COBRA3 Abs. deviation

Keff 0.99844 0.99696 +148 pcm

Fxy 1.303 1.276 0.027

Fz 1.139 1.204 -0.066

Assembly #

Relative power

((COBAYA3 - mean)/mean)*100%

64

Table 5.17: Comparison of HFP state simulations with flat core inlet BCs

Flat BCs at the core inlet PSU PARCS/TRACE COBAYA3/COBRA3 Abs. deviation

Keff 0.99759 0.99823 -64 pcm

Fxy 1.293 1.279 0.016

Fz 1.170 1.177 -0.007

Flat BCs at the core inlet CRONOS/FLICA* COBAYA3/COBRA3 Abs. deviation

Keff 0.99750

0.99823 -73 pcm

Fxy 1.295 1.279 0.014

Fz 1.163 1.177 -0.014

* The compared CRONOS/FLICA* solution is not sufficiently converged

5.3 Transient results

Two transient scenarios are considered which differ in the

worth of negative tripped rod reactivity inserted during the scram

sequence of events

5.3.1 Scenario 1

The task is to calculate the core-vessel MSLB transient with imposed vessel boundary

conditions, corresponding to the realistic Scenario 1. This scenario is more complex for

thermal-hydraulic simulation because the MCP in the faulted loop trips and the loop flow

reverses. On the other hand, the total power after the reactor trip is at the level of decay

heat. The main objective is to test the improved vessel thermal-hydraulic modeling in a

coolant transient involving asymmetric loop cool-down and pump trip.

Time histories

Figures 5.20-5.28 show the time histories of main reactor parameters, such as

temperatures, coolant density, pressure, total power, total reactivity, power peaking factor

and the average and maximum nodal Doppler temperature. The results are compared

code-to-code and the figures graphically illustrate the agreement or disagreement of

participant‟s predictions.

In this scenario, the tripped rods reactivity is sufficient to prevent return to power after

scram. The power of the tripped reactor is at the level of decay heat. The differences in the

predicted hot leg temperatures are mainly due to the vessel thermal hydraulic models.

The RELAP3D solution shown in Figure 5.23 has been obtained with a 60-sector,

coarse-3D model of the uppermost layer of the lower plenum. However, the modeling of

the upper plenum is 1D which smears the response in reactor outlet temperatures. The

result indicates that this simulation does not take into account the reversal in the boundary

condition for the faulted loop.

The PARCS/TRACE solution in Figure 5.23 has been obtained with a coarse-3D, six-

sector, 18-channel model throughout the vessel.

65

The HEXTRAN/SMABRE result has been obtained with a 6-sector, multi-channel

vessel model using approximate turbulence modeling.

The DYN3D/ATHLET solution has been obtained with a 4-sector, multi-channel

vessel model. The lower plenum mixing is described by an empirical model tuned to fit

CFX calculation results for the flow re-distribution in case of pump trips. There is no

mixing in the upper plenum.

The UNIPI and FZD results in Figure 5.23 show significant discrepancies to the VTT

and INRNE solutions, which indicate a difference in the modeling of the reversal in the

boundary condition for the faulted loop. The rips in the ATHLET results seem to be due

to the controller used to fit the imposed boundary condition.

The CATHARE2 solution is supplementary, with point kinetics. It is possible to

compare the results with the coupled code solutions because the total power is at the level

of decay heat. The vessel thermal hydraulics is described with a 24-sector multi-channel

model with cross flow governed by the local pressure drops.

Figure 5.29 illustrates the evolution of Fxyz as predicted by COBAYA3/COBRA3 and

DYN3D/ATHLET. In this simulation, COBAYA/COBRA used CATHARE2 calculated

core BCs. The observed difference is significant and is mainly due to differences in the

spatial coupling.

Snapshots

Figures 5.30 and 5.32 show the comparison of the computed core-average axial power

distributions at time of maximum overcooling (166s) and at the end of transient (600s).

The results indicate a grouping consistent with that in HZP states. PARCS/TRACE and

DYN3D/ATLET results are close to each other, independently of the different detail in

vessel thermal-hydraulic models.

Figures 5.34 and 5.36 show the comparison of the computed axial power distributions

in the position of stuck rod, at time of maximum overcooling (166s) and at the end of

transient (600s). The observed grouping of the results is consistent with that in HZP states.

Figures 5.38 and 5.39 illustrate the resulting core power distribution at time of

maximum overcooling, as predicted with DYN3D/ATHLET and PARCS/TRACE.

For more details of the core inlet distributions, see Appendix C.

66

490

500

510

520

530

540

550

560

570

580

590

600

0 100 200 300 400 500 600

Te

mp

era

ture

, K

Time, s

FZD - DYN3D/ATHLETVTT - HEXTRAN-SMABREUNIPI - RELAP 3DFZK - TRACE / PARCSINRNE - CATHARE2

Figure 5.20: Time history of hot leg 1 temperature in Scenario 1

515

525

535

545

555

565

575

585

595

0 100 200 300 400 500 600

Te

mp

era

ture

, K

Time, s

FZD - DYN3D/ATHLET

VTT - HEXTRAN-SMABRE

UNIPI - RELAP 3D

FZK - TRACE / PARCS

INRNE - CATHARE2

Figure 5.21: Time history of hot leg 2 temperature in Scenario 1

67

510

520

530

540

550

560

570

580

590

600

0 100 200 300 400 500 600

Te

mp

era

ture

, K

Time, s

FZD - DYN3D/ATHLET

VTT - HEXTRAN-SMABRE

UNIPI - RELAP 3D

FZK - TRACE / PARCS

INRNE - CATHARE2

Figure 5.22: Time history of hot leg 3 temperature in Scenario 1

1

450

470

490

510

530

550

570

590

610

0 100 200 300 400 500 600

Te

mp

era

ture

, K

Time, s

FZD - DYN3D/ATHLETVTT - HEXTRAN-SMABREUNIPI - RELAP 3DFZK - TRACE / PARCSINRNE - CATHARE2

Figure 5.23: Time history of hot leg 4 temperature in Scenario 1

68

0

500

1000

1500

2000

2500

3000

3500

0 100 200 300 400 500 600

Po

we

r, M

W

Time, s

FZD - DYN3D/ATHLET

VTT - HEXTRAN-SMABRE

UNIPI - RELAP 3D

FZK - TRACE / PARCS

Figure 5.24: Time history of the total power (or fission power

for VTT and FZK solutions) in Scenario 1

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

0 100 200 300 400 500 600

Time, s

Re

ac

tiv

ity

, d

k/k

FZD- DYN3D/ATHLET

FZK- TRACE/PARCS

Figure 5.25: Time history of the total reactivity in Scenario 1

69

710

730

750

770

790

810

0 100 200 300 400 500 600

De

ns

ity,

kg

/m3

Time, s

FZD - DYN3D/ATHLET

UNIPI - RELAP 3D

VTT - HEXTRAN-SMABRE

FZK - TRACE / PARCS

Figure 5.26: Time history of the core average moderator density in Scenario 1

500

600

700

800

900

1000

0 100 200 300 400 500 600

Te

mp

era

ture

, K

Time, s

FZD - DYN3D/ATHLETUNIPI - RELAP 3DVTT - HEXTRAN-SMABREFZK - TRACE / PARCS

Figure 5.27: Time history of the core average Doppler temperature in Scenario 1

70

500

600

700

800

900

1000

1100

1200

0 100 200 300 400 500 600

Te

mp

era

ture

, K

Time, s

FZD - DYN3D/ATHLET

UNIPI - RELAP 3D

VTT - HEXTRAN-SMABRE

FZK - TRACE / PARCS

Figure 5.28: Time history of the max nodal Doppler temperature in Scenario 1

0,0

1,0

2,0

3,0

4,0

5,0

6,0

0 100 200 300 400 500 600

Fx

yz

Time, s

DYN3D/ATHLET - FZD

COBAYA3/COBRA3 - INRNE/UPM

Figure 5.29: Time history of Fxyz in Scenario 1

71

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 50 100 150 200 250 300 350

Ax

ial p

ow

er p

rofi

le

Elevation, cm

VTT - HEXTRAN-SMABRE

FZD - DYN3D/ATHLET

UNIPI - RELAP 3D/NEM

FZK - TRACE / PARCS

Average

Figure 5.30: Scenario 1 with stuck rod in #90. Core-average axial power

distribution at time of maximum overcooling (166s)

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 50 100 150 200 250 300 350

Elevation, cm

Axia

l p

ow

er

pro

file

Average

Figure 5.31: Scenario 1 with stuck rod in #90. Core-average axial power

distribution at time of maximum overcooling (166s) - mean and standard deviation

72

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 50 100 150 200 250 300 350

Ax

ial p

ow

er p

rofi

le

Elevation, cm

VTT - HEXTRAN-SMABRE

DYN3D/ATHLET - FZD

UNIPI - RELAP 3D/NEM

FZK - TRACE / PARCS

Average

Figure 5.32: Scenario 1 with stuck rod in #90. Core-average axial power

distribution at 600s

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 50 100 150 200 250 300 350

Elevation, cm

Ax

ial

po

we

r p

rofi

le

Average

Figure 5.33: Scenario 1 with stuck rod in #90. Core-average axial power

distribution at 600s - mean and standard deviation

73

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 50 100 150 200 250 300 350

Ax

ial p

ow

er d

istr

ibu

tio

n

Elevation, cm

UNIPI - RELAP 3D/NEM

FZD - DYN3D/ATHLET

VTT - HEXTRAN-SMABRE

Average

Figure 5.34: Scenario 1 with stuck rod in #90. Axial power distribution in the stuck

rod assembly at 166s

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 50 100 150 200 250 300 350

Elevation, cm

Axia

l p

ow

er

dis

trib

uti

on

Average

Figure 5.35: Scenario 1 with stuck rod in #90. Axial power distribution in the stuck

rod assembly at 166s - mean and standard deviation

74

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 50 100 150 200 250 300 350

Ax

ial p

ow

er d

istr

ibu

tio

n

Elevation, cm

UNIPI - RELAP 3D/NEM

DYN3D/ATHLET - FZD

VTT - HEXTRAN-SMABRE

Average

Figure 5.36: Scenario 1 with stuck rod in #90. Axial power distribution in the stuck

rod assembly #90 at 600s

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 50 100 150 200 250 300 350

Ax

ial p

ow

er d

istr

ibu

tio

n

Elevation, cm

Average

Average

Figure 5.37: Scenario 1 with stuck rod in #90. Axial power distribution in the stuck

rod assembly #90 at 600s - mean and standard deviation

75

0,4

0,349

15

Figure 5.38: Scenario 1 with stuck rod in #90. DYN3D/ATHLET computed radial

power distribution at 166s

Assembly #

Assembly power, MW

Relative assembly power, %

0,5

0,454

155

0,5

0,514

151

0,6

0,540

149

0,9

0,844

139

2,0

1,840

103

1,6

1,474

89

1,0

0,947

62

1,1

1,066

49

0,8

0,765

16

0,6

0,526

7

0,6

0,527

50,4

0,349

15

0,4

0,368

6

0,7

0,645

2

0,5

0,483

1

0,4

0,387

157

0,6

0,525

148

0,5

0,478

115

0,4

0,345

102

0,4

0,341

75

0,5

0,467

61

0,5

0,473

25

0,5

0,441

147

0,4

0,340

145

0,3

0,316

144

0,4

0,340

143

0,7

0,630

140

0,7

0,628

131

0,7

0,669

3

0,7

0,624

40,7

0,670

8

0,6

0,545

9

0,8

0,785

10

0,5

0,476

11

0,5

0,426

13

0,7

0,670

12

0,5

0,479

140,6

0,604

17

0,5

0,474

18

0,4

0,399

19

0,4

0,344

20

0,4

0,328

21

0,4

0,329

22

0,4

0,350

23

0,4

0,400

240,9

0,886

26

1,0

0,965

27

0,5

0,451

28

0,7

0,636

29

0,6

0,524

30

0,3

0,317

31

0,5

0,439

32

0,5

0,481

33

0,3

0,304

34

0,6

0,588

35

0,5

0,506

361,1

1,001

37

0,7

0,685

38

0,5

0,448

39

0,6

0,583

40

0,5

0,501

41

0,5

0,506

42

0,5

0,452

43

0,4

0,393

44

0,4

0,414

45

0,3

0,273

46

0,4

0,377

47

0,5

0,504

481,3

1,230

50

0,5

0,503

51

0,5

0,423

52

0,6

0,577

53

0,7

0,613

54

0,4

0,412

55

0,5

0,503

56

0,4

0,420

57

0,3

0,271

58

0,3

0,279

59

0,6

0,584

601,1

1,025

63

0,7

0,668

64

0,8

0,754

65

0,7

0,640

66

0,5

0,481

67

0,5

0,437

68

0,4

0,386

69

0,4

0,361

70

0,4

0,413

71

0,4

0,406

72

0,3

0,303

73

0,4

0,392

741,8

1,677

76

1,1

1,073

77

1,1

1,058

78

0,7

0,672

79

0,8

0,709

80

0,5

0,465

81

0,3

0,305

82

0,4

0,373

83

0,5

0,482

84

0,4

0,377

85

0,5

0,462

86

0,4

0,336

87

0,5

0,459

882,3

2,185

90

1,0

0,949

91

0,9

0,851

92

0,7

0,663

93

0,5

0,476

94

0,5

0,430

95

0,4

0,395

96

0,4

0,366

97

0,4

0,418

98

0,4

0,409

99

0,3

0,301

100

0,4

0,396

1012,1

2,011

104

0,7

0,698

105

0,5

0,458

106

0,6

0,579

107

0,6

0,599

108

0,4

0,408

109

0,6

0,523

110

0,5

0,439

111

0,3

0,276

112

0,3

0,279

113

0,6

0,598

1141,6

1,506

116

1,0

0,918

117

0,5

0,503

118

0,6

0,597

119

0,5

0,493

120

0,5

0,496

121

0,5

0,467

122

0,4

0,415

123

0,5

0,442

124

0,3

0,301

125

0,4

0,398

126

0,6

0,525

1271,2

1,098

128

1,2

1,099

129

0,5

0,467

130

0,5

0,510

132

0,3

0,316

133

0,5

0,459

134

0,5

0,515

135

0,4

0,335

136

0,7

0,648

137

0,6

0,553

1380,5

0,470

141

0,4

0,389

142

0,4

0,378

1460,7

0,654

150

0,8

0,731

152

0,5

0,454

153

0,7

0,689

154

0,6

0,524

1560,5

0,452

158

0,6

0,594

159

0,7

0,622

160

0,6

0,605

161

0,6

0,553

162

0,4

0,397

163

76

0,5

0,640

155

0,6

0,669

151

0,6

0,727

149

0,9

1,064

139

1,7

2,003

103

1,4

1,626

89

0,9

1,086

62

1,1

1,242

49

0,8

0,992

16

0,6

0,709

7

0,7

0,776

50,5

0,573

15

0,5

0,576

6

0,7

0,826

2

0,6

0,647

1

0,5

0,627

157

0,7

0,840

148

0,7

0,801

115

0,5

0,588

102

0,5

0,577

75

0,7

0,770

61

0,7

0,768

25

0,5

0,636

147

0,4

0,454

145

0,4

0,414

144

0,4

0,431

143

0,6

0,748

140

0,6

0,746

131

0,7

0,854

3

0,7

0,838

40,7

0,856

8

0,5

0,641

9

0,8

0,943

10

0,5

0,576

11

0,5

0,591

13

0,8

0,911

12

0,6

0,736

140,6

0,716

17

0,5

0,562

18

0,4

0,455

19

0,3

0,399

20

0,3

0,401

21

0,4

0,435

22

0,4

0,497

23

0,5

0,586

241,0

1,112

26

1,0

1,157

27

0,4

0,509

28

0,6

0,726

29

0,5

0,602

30

0,3

0,370

31

0,5

0,573

32

0,6

0,654

33

0,4

0,424

34

0,8

0,897

35

0,7

0,821

361,0

1,203

37

0,7

0,764

38

0,4

0,486

39

0,6

0,654

40

0,5

0,552

41

0,5

0,575

42

0,5

0,559

43

0,4

0,503

44

0,5

0,566

45

0,3

0,385

46

0,5

0,562

47

0,7

0,822

481,2

1,357

50

0,4

0,519

51

0,4

0,436

52

0,5

0,629

53

0,6

0,688

54

0,4

0,469

55

0,5

0,639

56

0,5

0,551

57

0,3

0,361

58

0,3

0,396

59

0,8

0,902

600,9

1,048

63

0,6

0,660

64

0,7

0,771

65

0,6

0,671

66

0,4

0,517

67

0,4

0,489

68

0,4

0,470

69

0,4

0,458

70

0,5

0,552

71

0,5

0,570

72

0,4

0,434

73

0,5

0,590

741,5

1,792

76

0,9

1,072

77

0,9

1,046

78

0,6

0,669

79

0,7

0,762

80

0,4

0,516

81

0,3

0,351

82

0,4

0,473

83

0,5

0,640

84

0,4

0,506

85

0,6

0,660

86

0,4

0,503

87

0,6

0,745

881,9

2,216

90

0,8

0,914

91

0,7

0,852

92

0,6

0,693

93

0,4

0,523

94

0,4

0,503

95

0,4

0,483

96

0,4

0,470

97

0,5

0,563

98

0,5

0,578

99

0,4

0,434

100

0,5

0,603

1011,8

2,084

104

0,6

0,683

105

0,4

0,474

106

0,6

0,644

107

0,6

0,700

108

0,4

0,485

109

0,6

0,666

110

0,5

0,573

111

0,3

0,373

112

0,3

0,401

113

0,8

0,949

1141,4

1,680

116

0,8

0,974

117

0,5

0,533

118

0,6

0,675

119

0,5

0,562

120

0,5

0,596

121

0,5

0,583

122

0,5

0,528

123

0,5

0,598

124

0,4

0,417

125

0,5

0,599

126

0,8

0,879

1271,1

1,299

128

1,1

1,273

129

0,5

0,527

130

0,5

0,625

132

0,3

0,385

133

0,5

0,602

134

0,6

0,694

135

0,4

0,459

136

0,8

0,975

137

0,8

0,891

1380,5

0,579

141

0,4

0,482

142

0,5

0,532

1460,7

0,876

150

0,9

1,009

152

0,5

0,620

153

0,8

0,989

154

0,7

0,802

1560,6

0,662

158

0,7

0,872

159

0,8

0,922

160

0,8

0,915

161

0,7

0,851

162

0,5

0,631

163

0,5

0,573

15

Figure 5.39: Scenario 1 with stuck rod in #90. RELAP3D/NEM computed radial

power distribution at 166s

Assembly #

Power in MW

Relative power, %

77

5.3.2 Scenario 2

The task is to calculate the core-vessel MSLB transient with imposed vessel boundary

conditions, corresponding to the pessimistic Scenario 2. In this scenario the MCP in the

faulted loop fails to trip on MSLB signal and all MCP remain in operation. In order to

enhance the testing of the coupled codes, the cross sections are adjusted so that the scram

reactivity is about a half of the real one. A significant return to power after scram is

expected.

This scenario is of particular interest for the testing of vessel mixing models and 3D

N/TH coupling schemes. In the analysis to follow, we consider the case with stuck rods in

assemblies #117 and #140.

Time histories

Figures 5.40-5.43 show the computed hot leg temperatures at the reactor outlet.

The NEM/RELAP3D solution was obtained with a 3D 60-sector model of the lower

plenum and 1D model of the upper plenum, which explains the deviations from the other

codes results.

The HEXTRAN/SMABRE and DYN3D/ATHLET results are in reasonable agreement

for the undisturbed loops and show a significant difference for the faulted loop. As the

predicted total powers and total reactivities are close to each other (see Figures 5.44 and

5.46), the loop differences can be attributed to the combined effect of:

mixing models in the down-comer and the lower plenum

spatial N/TH coupling in terms of number of TH channels

mixing models in the upper plenum (weak mixing in SMABRE and no mixing in

the ATHLET user model)

The results in Figures 5.45, 5.47 and 5.52 present a sensitivity study with

COBAYA3/COBRA3 to illustrate the impact of using finer mesh in the flow-mixing

model.

Figures 5.49 and 5.50 show the computed time histories of the maximum nodal fuel

temperatures and the core average Doppler temperatures. The dynamic gap conductance

model used in DYN3D/ATHLET predicts a considerably higher fuel temperature

compared to that of HEXTRAN/SMABRE and NEM/RELAP3D. This has an impact on

the total power dynamics, compensated in part by other mesh related effects.

The predicted time history of Fxy and Fxyz is shown in Figures 5.51 and 5.52. The

COBAYA/COBRA results were obtained from a coupled N/TH solution, with

CATHARE2 multi-1D calculated core inlet BCs using 6-, 12- and 24-sector azimuth

meshing. The results provide insight of the sensitivity of the 3D peaking factor to

modeling refinements in the vessel and the core.

In the overall, since the predicted integral core parameters in the considered

simulations are relatively close to each other (except the Doppler temperature), and the

same vessel boundary conditions are used, the main difference in the participants

solutions comes from the different modeling of local 3D effects in the vessel and the core.

The observed differences require further attention.

78

Snapshots

The computed peaking factors at time 0 s (HFP), 69 s (HRP) and 200 s are shown in

Tables 5.19 and 5.20. The results show that Fxy and Fz are sensitive to mesh refinement

in the vessel mixing models and in spatial coupling.

Figures 5.53-5.56 present the participants computed core-averaged axial power

distributions. The analysis shows that they are sensitive to refinement of the vessel mixing

models, the spatial coupling schemes and the decay heat distribution during the transient.

It is interesting to note that in Figure 5.54 the difference between COBAYA/COBRA

results with 24- and 6-sector BC is in the order of magnitude of the difference between

COBAYA/COBRA 24-sector BC and HEXTRAN/SMABRE with 6-sector BC in Figure

5.53.

Figures 5.57-5.64 show snapshots of the computed axial power distributions in the

stuck rod positions. They are sensitive to angular mesh refinement in the vessel mixing

models and to the spatial coupling.

The radial core power distributions in Figures 5.65 and 5.66 illustrate coarse-mesh

coupling results obtained with multi-1D thermal-hydraulic models: DYN3D/ATHLET

with 4 sectors in the vessel and HEXTRAN/SMABRE with 6 sectors. The results of the

two codes are similar, with the 6-sector modeling being closer to the results produced by

finer spatial coupling (see Figures 5.66 and 5.67).

The radial core power distributions in Figures 5.67 and 5.68 illustrate the effect of

finer spatial coupling. The results were obtained with COBAYA3/COBRA3 using one

point per hexagon in COBRA3 and core BC from CATHARE2 12-sector and 24-sector

vessel calculations.

Tables 5.24 and 5.25, and Figures 5.52, 5.54, 5.58 and 5.60 illustrate the impact of

spatial mesh and spatial coupling. The peaking factors are sensitive to spatial mesh and

spatial coupling, especially in case of steep flux gradients.

Appendix D shows additional snapshots of core inlet distributions and the assembly-

by-assembly fuel Doppler temperatures.

79

540

550

560

570

580

590

600

0 100 200 300 400 500

Te

mp

era

ture

, K

Time, s

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

Figure 5.40: Hot leg 1 temperature

540

550

560

570

580

590

600

0 100 200 300 400 500

Te

mp

era

ture

, K

Time, s

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

Figure 5.41: Hot leg 2 temperature

80

540

550

560

570

580

590

600

0 100 200 300 400 500

Te

mp

era

ture

, K

Time, s

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

Figure 5.42: Hot leg 3 temperature

500

510

520

530

540

550

560

570

580

590

600

0 100 200 300 400 500

Te

mp

era

ture

, K

Time, s

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

Figure 5.43: Hot leg 4 temperature

81

0

500

1000

1500

2000

2500

3000

0 100 200 300 400 500

Po

we

r, M

W

Time, s

HEXTRAN-SMABRE - VTT

DYN3D/ATHLET - FZD

COBAYA3/COBRA3 24 sect

Figure 5.44: Total power

Figure 5.45: Total power. Impact of the meshing in the vessel mixing model

82

-3,5

-3,0

-2,5

-2,0

-1,5

-1,0

-0,5

0,0

0,5

0 100 200 300 400 500

Re

ac

tivit

y, %

Time, s

HEXTRAN-SMABRE - VTT

DYN3D/ATHLET - FZD

COBAYA3/COBRA3 24 sect. BC

Figure 5.46: Total reactivity

-2,5

-2,0

-1,5

-1,0

-0,5

0,0

0,5

0 100 200 300 400 500

Re

ac

tivit

y, %

Time, s

COBAYA3/COBRA3 6 sect. BC

COBAYA3/COBRA3 12 sect. BC

COBAYA3/COBRA3 24 sect. BC

Figure 5.47: Total reactivity. Impact of the vessel mixing model meshing

83

400

600

800

1000

1200

1400

1600

0 50 100 150 200 250 300 350 400 450 500

Time, s

Tem

pera

ture

, K UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

Figure 5.48: Maximum nodal fuel temperature

500

600

700

800

900

1000

0 100 200 300 400 500

Te

mp

era

ture

, K

Time, s

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

Figure 5.49: Core average Doppler temperature

84

660

680

700

720

740

760

780

800

0 100 200 300 400 500

Time, s

Den

sit

y, kg

/m3

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

Figure 5.50: Core average coolant density

1

3

5

7

9

11

0 100 200 300 400 500

Fx

y

Time, s

HEXTRAN-SMABRE - VTT

COBAYA3/COBRA3 24 sect

Figure 5.51: Scenario 2 with stuck rods in #117&140: Time history of Fxy

Core inlet conditions for COBAYA/COBRA from a CATHARE 24-sector

vessel calculation

85

1

3

5

7

9

11

0 100 200 300 400 500

Fx

yz

Time, s

COBAYA3/COBRA3 6 sect. BC

COBAYA3/COBRA3 12 sect. BC

COBAYA3/COBRA3 24 sect. BC

Figure 5.52: Scenario 2, stuck rods in #117&140. Time history of Fxyz

Impact of the meshing in the vessel mixing model

Table 5.18: Comparison of Fxy and Fz

DYN3D/ATHLET HEXTRAN/SMABRE COBAYA/COBRA

Fxy-HFP 1.283 1.303 1.279

Fxy-HRP* 4.051 4.011 3.937

Fxy-200s 2.816 2.878 2.575

Fz-HFP 1.180 1.187 1.151

Fz-HRP 1.272 1.400 1.268

Fz-200s 1.815 2.043 1.722

Fz#140-HRP 1.213 1.160 1.184

Fz#140-200s 1.552 1.799 1.592

Fz#117-HRP 1.195 1.180 1.171

Fz#117-200s 1.554 1.763 1.588

Table 5.19: COBAYA results: Comparison of Fxy and Fz

COBAYA 6sect. COBAYA 12sect. COBAYA 24 sect.

Fxy-HFP 1.279

Fxy-HRP 3.534 3.854 3.937

Fxy-200s 2.531 2.561 2.575

Fz-HFP

Fz-HRP 1.439 1.282 1.268

Fz-200s 1.735 1.725 1.722

Fz#140-HFP

Fz#140-HRP 1.263 1.166 1.184

Fz#140-200s 1.641 1.597 1.592

Fz#117-HFP

Fz#117-HRP 1.21 1.154 1.171

Fz#117-200s 1.635 1.592 1.588

* HRP – at highest return to power

86

0,3

0,5

0,7

0,9

1,1

1,3

1,5

0 50 100 150 200 250 300 350

Ax

ial p

ow

er

pro

file

Elevation, cm

HEXTRAN-SMABRE - VTT

DYN3D/ATHLET - FZD

COBAYA3/COBRA3 24 sect. BC

Figure 5.53: Core-average axial power distribution at time of maximum overcooling

(69s), for Scenario 2 with stuck rods in #117&#140

0.3

0.5

0.7

0.9

1.1

1.3

1.5

0 50 100 150 200 250 300 350

Elevation, cm

Axia

l p

ow

er

pro

file

COBAYA3/COBRA3

6 sect. BC

COBAYA3/COBRA3

12 sect. BC

COBAYA3/COBRA3

24 sect. BC

Figure 5.54: Impact of the vessel mixing model on the core-average axial power

distribution at 69s, for Scenario 2 with stuck rods in #117&#140

87

0,1

0,3

0,5

0,7

0,9

1,1

1,3

1,5

1,7

1,9

2,1

0 50 100 150 200 250 300 350

Ax

ial p

ow

er

pro

file

Elevation, cm

HEXTRAN-SMABRE - VTT

DYN3D/ATHLET - FZD

COBAYA3/COBRA3 24 sect. BC

Figure 5.55: Core-average axial power distribution at 200s, for Scenario 2 with stuck

rods in #117&#140

0.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

2.1

0 50 100 150 200 250 300 350

Elevation, cm

Axia

l p

ow

er

pro

file

COBAYA3/COBRA3

6 sect. BCCOBAYA3/COBRA3

12 sect. BCCOBAYA3/COBRA3

24 sect. BC

Figure 5.56: Impact of the meshing in the vessel mixing model on the core average

axial power distribution at 200s, for Scenario 2 with stuck rods in #117&#140

88

0,5

0,6

0,7

0,8

0,9

1,0

1,1

1,2

1,3

1,4

0 50 100 150 200 250 300 350

Ax

ial p

ow

er

dis

trib

uti

on

Elevation, cm

DYN3D/ATHLET - FZD

HEXTRAN-SMABRE - VTT

COBAYA3/COBRA3 24 sect. BC

Figure 5.57: Axial power distribution in stuck rod position #117 at 69s,

for Scenario 2 with stuck rods in #117&#140

0,5

0,6

0,7

0,8

0,9

1,0

1,1

1,2

1,3

1,4

0 50 100 150 200 250 300 350

Ax

ial p

ow

er

dis

trib

uti

on

Elevation, cm

COBAYA3/COBRA3 6 sect. BC

COBAYA3/COBRA3 12 sect. BC

COBAYA3/COBRA3 24 sect. BC

Figure 5.58: Scenario 2 with stuck rods in #117&#140. Impact of the mixing model

meshing on the axial power distribution in stuck rod position #117 at 69 s

89

0,1

0,3

0,5

0,7

0,9

1,1

1,3

1,5

1,7

1,9

0 50 100 150 200 250 300 350

Ax

ial p

ow

er

dis

trib

uti

on

Elevation, cm

DYN3D/ATHLET - FZD

HEXTRAN-SMABRE - VTT

COBAYA3/COBRA3 24 sect. BC

Figure 5.59: Scenario 2 with stuck rods in #117&#140. Axial power distribution

in stuck rod position #117 at 200s

0.1

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

0 50 100 150 200 250 300 350

Elevation, cm

Axia

l p

ow

er

dis

trib

uti

on

COBAYA3/COBRA3

6 sect. BC

COBAYA3/COBRA3

12 sect. BC

COBAYA3/COBRA3

24 sect. BC

Figure 5.60: Scenario 2 with stuck rods in #117&#140. Impact of the mixing model

meshing on the axial power distribution in stuck rod position #117 at 200s

90

0,5

0,6

0,7

0,8

0,9

1,0

1,1

1,2

1,3

1,4

0 50 100 150 200 250 300 350

Ax

ial p

ow

er

dis

trib

uti

on

Elevation, cm

DYN3D/ATHLET - FZD

HEXTRAN-SMABRE - VTT

COBAYA3/COBRA3 24 sect. BC

Figure 5.61: Scenario 2 with stuck rods in #117&#140. Axial power distribution in

stuck rod position #140 at 69s

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

0 50 100 150 200 250 300 350

Elevation, cm

Axia

l p

ow

er

dis

trib

uti

on

COBAYA3/COBRA3

6 sect. BC

COBAYA3/COBRA3

12 sect. BC

COBAYA3/COBRA3

24 sect. BC

Figure 5.62: Scenario 2 with stuck rods in #117&#140. Impact of the mixing model

meshing on the axial power distribution in stuck rod position #140 at 69s

91

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

0 50 100 150 200 250 300 350

Ax

ial p

ow

er

dis

trib

uti

on

Elevation, cm

DYN3D/ATHLET - FZD

HEXTRAN-SMABRE - VTT

COBAYA3/COBRA3 24 sect. BC

Figure 5.63: Scenario 2 with stuck rods in #117&#140. Axial power distribution in

stuck rod position #140 at 200s

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 50 100 150 200 250 300 350

Elevation, cm

Axia

l p

ow

er

dis

trib

uti

on

COBAYA3/COBRA3

6 sect. BC

COBAYA3/COBRA3

12 sect. BC

COBAYA3/COBRA3

24 sect. BC

Figure 5.64: Scenario 2 with stuck rods in #117&#140. Impact of the mixing model

meshing on the axial power distribution in stuck rod position #140 at 200s

92

14,2

1,257

155

23,9

2,115

151

28,9

2,559

149

37,3

3,301

139

28,6

2,530

103

18,7

1,655

89

10,2

0,899

62

11,2

0,994

49

7,5

0,659

16

5,1

0,454

7

4,5

0,399

53,0

0,262

15

3,3

0,287

6

5,1

0,454

2

4,1

0,364

1

7,2

0,636

157

8,1

0,715

148

5,6

0,491

115

3,9

0,344

102

3,3

0,289

75

4,1

0,365

61

3,9

0,343

25

8,9

0,790

147

11,4

1,006

145

12,9

1,144

144

15,5

1,371

143

41,6

3,676

140

26,6

2,355

131

5,3

0,469

3

5,1

0,450

46,0

0,532

8

5,2

0,462

9

6,7

0,588

10

4,7

0,418

11

4,2

0,376

13

6,2

0,546

12

4,1

0,363

146,7

0,588

17

4,9

0,430

18

4,4

0,391

19

4,1

0,365

20

4,8

0,420

21

3,8

0,338

22

3,4

0,299

23

3,8

0,338

249,0

0,794

26

10,1

0,897

27

5,8

0,513

28

7,0

0,619

29

5,8

0,515

30

4,1

0,359

31

5,0

0,445

32

5,0

0,445

33

3,3

0,295

34

5,2

0,456

35

4,2

0,372

3610,4

0,921

37

8,6

0,760

38

6,8

0,597

39

7,6

0,675

40

6,6

0,580

41

5,9

0,518

42

5,3

0,466

43

4,9

0,429

44

4,7

0,412

45

3,3

0,296

46

3,9

0,341

47

4,3

0,381

4813,8

1,218

50

8,0

0,703

51

7,8

0,693

52

8,1

0,713

53

7,8

0,691

54

5,6

0,493

55

6,1

0,536

56

5,0

0,444

57

4,1

0,362

58

3,6

0,316

59

5,4

0,480

6012,5

1,105

63

9,9

0,872

64

11,7

1,035

65

10,2

0,906

66

8,2

0,727

67

6,6

0,582

68

5,6

0,494

69

5,2

0,464

70

5,3

0,469

71

5,1

0,447

72

3,7

0,329

73

4,2

0,371

7417,2

1,525

76

13,1

1,156

77

16,4

1,447

78

13,1

1,159

79

13,1

1,159

80

8,9

0,788

81

7,1

0,628

82

6,2

0,549

83

7,0

0,619

84

5,6

0,497

85

5,8

0,511

86

3,9

0,344

87

4,8

0,421

8823,5

2,077

90

18,3

1,621

91

19,3

1,710

92

16,3

1,443

93

13,7

1,207

94

11,0

0,975

95

8,6

0,764

96

7,2

0,639

97

6,6

0,586

98

6,0

0,528

99

4,4

0,385

100

5,0

0,446

10137,8

3,342

104

21,7

1,919

105

16,7

1,480

106

18,6

1,642

107

18,4

1,626

108

12,1

1,072

109

12,2

1,077

110

8,4

0,747

111

5,4

0,479

112

4,9

0,431

113

7,5

0,667

11435,1

3,098

116

37,1

3,278

117

23,3

2,062

118

24,0

2,125

119

20,0

1,770

120

16,1

1,426

121

13,4

1,184

122

11,3

1,002

123

9,1

0,805

124

6,1

0,536

125

6,3

0,559

126

6,6

0,585

12738,1

3,368

128

45,4

4,009

129

24,5

2,164

130

19,7

1,744

132

13,8

1,217

133

14,0

1,236

134

13,0

1,146

135

7,4

0,656

136

10,1

0,890

137

7,6

0,671

13823,2

2,054

141

18,2

1,610

142

9,5

0,841

14632,6

2,879

150

27,3

2,416

152

17,8

1,571

153

21,5

1,901

154

12,4

1,098

15619,9

1,756

158

22,6

1,995

159

21,6

1,909

160

19,3

1,705

161

16,4

1,447

162

11,3

0,997

163

0,16

2,968

15

Figure 5.65: Scenario 2 with stuck rods in #117&#140. Snapshot of the

HEXTRAN/SMABRE computed assembly powers at 69s

Assembly #

Relative power, %

Absolute power, MW

93

10,1

0,839

155

28,7

2,394

151

28,2

2,356

149

37,3

3,112

139

29,7

2,479

103

20,0

1,666

89

13,9

1,159

62

12,9

1,079

49

6,9

0,572

16

4,5

0,376

7

3,8

0,315

52,6

0,215

15

2,7

0,224

6

4,6

0,384

2

3,7

0,306

1

5,1

0,430

157

6,2

0,521

148

4,7

0,393

115

3,3

0,271

102

2,8

0,235

75

3,7

0,307

61

3,5

0,290

25

7,2

0,598

147

9,1

0,759

145

11,6

0,968

144

17,9

1,494

143

44,4

3,706

140

30,5

2,549

131

4,6

0,388

3

4,3

0,361

45,8

0,481

8

5,1

0,429

9

6,4

0,534

10

4,4

0,365

11

3,9

0,322

13

5,5

0,460

12

3,7

0,312

146,5

0,546

17

5,0

0,420

18

4,6

0,387

19

4,1

0,345

20

3,9

0,323

21

3,6

0,302

22

3,3

0,275

23

3,7

0,306

248,7

0,724

26

10,3

0,856

27

6,1

0,511

28

7,6

0,633

29

6,3

0,527

30

4,2

0,354

31

5,0

0,421

32

5,1

0,424

33

3,4

0,282

34

5,0

0,416

35

3,8

0,316

3610,9

0,907

37

9,4

0,781

38

7,4

0,615

39

8,4

0,698

40

7,4

0,613

41

6,6

0,547

42

5,7

0,474

43

5,1

0,424

44

4,7

0,396

45

3,3

0,279

46

3,7

0,312

47

3,9

0,323

4816,3

1,359

50

9,4

0,788

51

8,3

0,692

52

9,3

0,776

53

9,1

0,759

54

6,3

0,526

55

6,6

0,552

56

5,3

0,439

57

3,7

0,310

58

3,5

0,296

59

5,2

0,436

6018,1

1,507

63

14,2

1,183

64

14,7

1,231

65

12,7

1,061

66

10,0

0,834

67

7,7

0,640

68

6,2

0,514

69

5,6

0,468

70

5,5

0,456

71

5,1

0,423

72

3,7

0,310

73

4,0

0,334

7423,6

1,970

76

18,2

1,522

77

23,3

1,948

78

18,8

1,568

79

18,6

1,553

80

11,9

0,993

81

7,2

0,601

82

6,5

0,546

83

7,2

0,602

84

5,6

0,470

85

5,7

0,476

86

3,7

0,312

87

4,3

0,357

8827,4

2,285

90

22,2

1,851

91

24,2

2,017

92

20,7

1,724

93

16,9

1,413

94

12,9

1,079

95

8,9

0,742

96

7,4

0,618

97

6,7

0,560

98

6,0

0,497

99

4,3

0,356

100

4,7

0,390

10141,6

3,474

104

25,0

2,087

105

20,0

1,666

106

22,2

1,852

107

21,7

1,808

108

13,9

1,161

109

11,5

0,961

110

8,2

0,685

111

5,3

0,441

112

4,7

0,389

113

6,9

0,574

11435,6

2,970

116

40,0

3,342

117

26,3

2,193

118

27,7

2,312

119

23,2

1,936

120

18,8

1,569

121

12,7

1,061

122

9,8

0,818

123

8,3

0,694

124

5,6

0,463

125

5,6

0,470

126

5,5

0,460

12738,3

3,193

128

48,5

4,051

129

27,5

2,299

130

23,4

1,957

132

13,7

1,146

133

12,0

1,004

134

10,5

0,880

135

6,4

0,537

136

8,6

0,715

137

6,1

0,511

13826,2

2,185

141

22,1

1,840

142

7,3

0,605

14634,9

2,913

150

32,5

2,708

152

18,7

1,561

153

16,8

1,402

154

8,4

0,703

15622,0

1,833

158

25,7

2,141

159

23,0

1,918

160

15,3

1,280

161

11,1

0,927

162

6,9

0,579

163

0,16

2,968

15

Figure 5.66: Scenario2 with stuck rods in #117&#140. Snapshot of the

DYN3D/ATHLET computed assembly powers at 69s

Assembly #

Relative power, %

Absolute power, MW

94

9,6

0,917

155

22,0

2,091

151

23,1

2,201

149

30,9

2,940

139

24,9

2,365

103

16,4

1,562

89

11,5

1,096

62

12,9

1,224

49

7,1

0,673

16

4,6

0,437

7

3,7

0,355

52,5

0,242

15

2,7

0,255

6

4,5

0,432

2

3,7

0,348

1

4,9

0,469

157

5,9

0,560

148

4,4

0,417

115

3,1

0,291

102

2,7

0,261

75

3,6

0,339

61

3,4

0,324

25

7,0

0,665

147

8,5

0,811

145

10,7

1,016

144

14,0

1,334

143

36,6

3,485

140

24,9

2,373

131

4,5

0,432

3

4,2

0,402

45,8

0,554

8

5,3

0,504

9

6,3

0,602

10

4,5

0,424

11

4,0

0,383

13

5,5

0,520

12

3,7

0,355

146,8

0,650

17

5,1

0,482

18

4,7

0,449

19

4,2

0,401

20

4,0

0,377

21

3,7

0,354

22

3,3

0,314

23

3,8

0,362

248,9

0,845

26

10,5

1,003

27

6,3

0,598

28

7,5

0,711

29

6,2

0,587

30

4,2

0,404

31

5,0

0,471

32

5,0

0,474

33

3,4

0,328

34

4,9

0,466

35

3,7

0,350

3610,9

1,039

37

9,6

0,912

38

7,5

0,715

39

8,2

0,783

40

7,2

0,685

41

6,3

0,599

42

5,5

0,522

43

5,0

0,478

44

4,6

0,441

45

3,4

0,326

46

3,8

0,363

47

3,8

0,357

4816,2

1,542

50

9,3

0,886

51

8,1

0,766

52

8,9

0,847

53

8,6

0,819

54

6,1

0,581

55

6,3

0,600

56

5,0

0,480

57

3,7

0,350

58

3,6

0,344

59

5,1

0,485

6015,4

1,467

63

12,4

1,175

64

14,2

1,352

65

12,1

1,147

66

9,5

0,902

67

7,1

0,676

68

5,8

0,548

69

5,4

0,518

70

5,2

0,495

71

4,9

0,465

72

3,7

0,355

73

4,1

0,387

7419,0

1,812

76

15,0

1,431

77

19,5

1,858

78

15,9

1,517

79

15,8

1,501

80

10,1

0,963

81

6,5

0,619

82

6,0

0,574

83

6,8

0,644

84

5,5

0,519

85

5,5

0,521

86

3,6

0,346

87

4,2

0,395

8822,9

2,179

90

18,8

1,785

91

20,5

1,949

92

17,5

1,665

93

14,4

1,370

94

10,8

1,031

95

7,9

0,751

96

6,9

0,656

97

6,2

0,592

98

5,6

0,533

99

4,2

0,395

100

4,6

0,435

10135,1

3,337

104

21,2

2,017

105

16,9

1,608

106

18,6

1,766

107

17,8

1,696

108

11,4

1,087

109

10,3

0,983

110

7,5

0,715

111

5,0

0,480

112

4,5

0,432

113

6,5

0,614

11429,9

2,841

116

33,6

3,199

117

22,1

2,103

118

23,1

2,195

119

19,1

1,814

120

15,1

1,432

121

11,4

1,080

122

9,1

0,862

123

7,7

0,736

124

5,4

0,510

125

5,4

0,518

126

5,1

0,489

12732,0

3,041

128

40,5

3,854

129

22,9

2,176

130

18,4

1,753

132

11,1

1,056

133

10,9

1,035

134

9,8

0,933

135

6,2

0,588

136

8,1

0,769

137

5,7

0,545

13821,2

2,015

141

17,1

1,629

142

6,9

0,653

14628,1

2,677

150

24,3

2,313

152

15,0

1,431

153

15,7

1,498

154

8,1

0,767

15616,7

1,587

158

18,9

1,800

159

17,4

1,660

160

14,3

1,359

161

10,4

0,988

162

6,6

0,626

163

0,16

2,968

15

Figure 5.67: Scenario2 with stuck rods in #117&#140, and 12-sector model computed

core BC. Snapshot of COBAYA3/COBRA3 predicted assembly powers at 69s

Assembly #

Relative power, %

Absolute power, MW

95

9,0

0,840

155

23,8

2,225

151

24,2

2,261

149

32,2

3,007

139

26,1

2,436

103

17,6

1,640

89

12,0

1,122

62

12,9

1,204

49

6,8

0,636

16

4,5

0,418

7

3,7

0,348

52,5

0,237

15

2,7

0,249

6

4,5

0,421

2

3,6

0,338

1

4,6

0,431

157

5,6

0,525

148

4,3

0,404

115

3,0

0,282

102

2,7

0,252

75

3,5

0,329

61

3,4

0,316

25

6,6

0,617

147

8,1

0,752

145

10,1

0,940

144

14,2

1,322

143

38,3

3,572

140

26,2

2,441

131

4,5

0,424

3

4,2

0,395

45,7

0,535

8

5,2

0,490

9

6,3

0,588

10

4,5

0,416

11

4,0

0,375

13

5,5

0,509

12

3,7

0,348

146,7

0,622

17

5,0

0,467

18

4,7

0,438

19

4,2

0,393

20

4,0

0,370

21

3,7

0,347

22

3,3

0,307

23

3,8

0,354

248,7

0,808

26

10,2

0,954

27

6,2

0,576

28

7,4

0,694

29

6,2

0,576

30

4,3

0,398

31

4,9

0,462

32

5,0

0,465

33

3,4

0,321

34

4,9

0,455

35

3,7

0,341

3610,9

1,017

37

9,5

0,888

38

7,4

0,692

39

8,2

0,762

40

7,2

0,674

41

6,3

0,590

42

5,5

0,514

43

5,0

0,469

44

4,6

0,431

45

3,4

0,318

46

3,8

0,354

47

3,7

0,347

4816,3

1,518

50

9,4

0,879

51

8,1

0,759

52

8,9

0,835

53

8,7

0,811

54

6,2

0,575

55

6,3

0,590

56

5,0

0,470

57

3,7

0,342

58

3,6

0,334

59

5,0

0,471

6015,9

1,486

63

12,7

1,182

64

14,6

1,360

65

12,4

1,153

66

9,7

0,901

67

7,2

0,672

68

5,8

0,541

69

5,4

0,508

70

5,2

0,483

71

4,8

0,452

72

3,7

0,344

73

4,0

0,375

7420,8

1,946

76

16,2

1,516

77

21,0

1,964

78

17,0

1,588

79

16,6

1,548

80

10,5

0,976

81

6,6

0,616

82

6,0

0,564

83

6,7

0,627

84

5,4

0,503

85

5,4

0,503

86

3,6

0,334

87

4,1

0,380

8824,3

2,269

90

19,8

1,845

91

21,5

2,010

92

18,3

1,710

93

15,0

1,398

94

11,2

1,041

95

7,9

0,741

96

6,8

0,639

97

6,1

0,574

98

5,5

0,516

99

4,1

0,382

100

4,5

0,422

10136,6

3,419

104

22,1

2,066

105

17,6

1,647

106

19,3

1,806

107

18,5

1,729

108

11,4

1,065

109

10,1

0,947

110

7,4

0,688

111

4,9

0,461

112

4,4

0,415

113

6,3

0,592

11431,1

2,904

116

35,0

3,265

117

23,0

2,150

118

24,1

2,248

119

19,9

1,860

120

15,5

1,445

121

11,1

1,032

122

8,8

0,818

123

7,5

0,698

124

5,2

0,486

125

5,3

0,495

126

5,0

0,469

12733,3

3,104

128

42,2

3,937

129

23,9

2,229

130

19,5

1,819

132

10,8

1,008

133

10,5

0,976

134

9,3

0,872

135

5,9

0,551

136

7,8

0,726

137

5,5

0,517

13822,3

2,081

141

18,3

1,711

142

6,5

0,603

14629,7

2,776

150

25,7

2,397

152

14,2

1,328

153

14,5

1,357

154

7,5

0,701

15618,2

1,697

158

20,5

1,918

159

17,1

1,600

160

13,0

1,217

161

9,6

0,897

162

6,1

0,570

163

0,16

2,968

15

Figure 5.68: Scenario2 with stuck rods in #117&#140, and 24-sector model computed

core BC. Snapshot of the COBAYA3/COBRA3 predicted assembly powers at 69s

Assembly #

Relative power, %

Absolute power, MW

96

Chapter 6: Results of Exercise 3

The objective of Exercise 3 is to test the core-vessel-plant coupling in a full plant

simulation. The integrated codes employ improved component and circuit models, already

tested in the V1000CT-2 Benchmark Exercises 1 and 2, and the MCP start up transient of

V1000CT-1 benchmark. A specific objective of this exercise is to test the VVER-1000

secondary circuit model in MSLB calculations.

The results in this Chapter provide a code-to-code comparison of participants‟

solutions. Since the BIPR8/ATHLET plant model of VVER-1000 is well validated, the

BIPR8/ATHLET solution for Scenario 2 serves as a support solution for the secondary

circuit and especially for the controllers. In order to eliminate the uncertainty in modeling

of the SG feed-water flow controllers, an option with ATHLET calculated feed-water

flow boundary conditions is provided in the specification (Kolev et al, 2010a).

In the analysis to follow, we focus on Scenario 2 results. Scenario 1 results are given

in Appendix E and are briefly discussed below.

6.1 Scenario 1 results

The objective is to analyze the impact of the improved vessel thermal-hydraulic

modeling in a core-plant simulation of a coolant transient involving asymmetric loop cool-

down and pump trip. A specific objective is to test the user models of the VVER-1000

secondary circuit in system codes.

The results in Appendix E graphically illustrate the agreement or disagreement of the

solutions in code-to-code comparison. The analysis shows a reasonable qualitative

agreement of the time histories, and unacceptable quantitative differences in important

parameters. As the reactor power is at the decay heat level, the discrepancies are mainly

due to secondary circuit modeling which requires further attention.

Because of an error in the BIPR8/ATHLET user input file, the check valve in the

broken line has been completely closed (actually it allows up to 50 kg/s flow rate in

reverse direction). In consequence, the intact steam generators pressure is incorrect. Please

note that a second MCP trips on secondary circuit pressure signal at ~ 200s, and

comparison with BIPR8/ATHLET results is possible only in the initial part of the

transient.

6.2 Scenario 2 results

For the purposes of this analysis, we consider the MSLB Scenario 2 with stuck rods in

assemblies #117 and #140. This scenario is of special interest because of the return to

power phenomenon enforced by decreasing the tripped rods reactivity worth, which is a

very good test case for the coupled codes.

During the transient, all MCP remain in operation. The control rods in assemblies

#117 and #140 remain stuck out of the core after scram. A return to power occurs,

reaching a maximum of about 50% nominal rated power at about 69 s from the beginning

of the transient.

97

Three participants have submitted integrated code solutions of Exercise 3 - GRS/KI

(BIPR8/ATHLET), VTT (HEXTRAN/SMABRE) and UNIPI (NEM/RELAP3D). The

BIPR8 code has used its native cross-section library. A supplementary CATHARE2

solution with point kinetics is also compared to evaluate the secondary circuit model vs.

the validated BIPR8/ATHLET user model.

The available solutions are insufficient for statistical treatment. In the discussion to

follow, the agreement or disagreement of the results is only graphically illustrated.

We focus on the testing of the secondary circuit and the full plant model. Parameter

distributions have been considered in Exercise 2 and are not analyzed here. The analysis

comprises 39 time histories.

6.3 Time histories

Break flow rate

Figure 6.1 shows the computed total break flow rates. All participants use direct

solution for the break flow with the code thermal-hydraulic model. The significant

difference in maximal values in the first seconds predicted with ATHLET is due to the

specific ATHLET modeling of the liquid fraction of the break flow, based on empirical

information (S. Nikonov, 2004).

Figure 6.2 shows the computed total integrated break flow. The flows computed by

GRS/KI and UNIPI show a relatively good agreement after the initial phase of the

transient where the impact of the liquid break flow is strong.

Figure 6.3 displays a wide spread in the predicted liquid break flows. The

CATHARE2 predicted integrated liquid flow (Kolev et al, 2004), (Kolev et al, 2005) is

22000 kg.

BRU-K and BRU-SN steam dump flows

The modeling of the steam dump flows and MSH pressure are important for the

correct simulation of the MSLB transient.

The results in Figures 6.4 and 6.5 show a generally good agreement between the

ATHLET and CATHARE2 predicted steam dump to condenser (BRU-K) flow rates and

integrated flows. In the CATHARE2 VVER-1000 model, the BRU-K and BRU-SN

controllers are similar to those in the ATHLET input model. The steam dump to house

needs (BRU-SN) model is somewhat simplified, as described in the specification (Kolev

et al, 2010a). Correspondingly, the ATHLET and CATHARE2 predicted MSH pressure

and BRU-SN flows are in generally good agreement.

The results in Figures 6.6 and 6.7 show significant differences in the VTT and UNIPI

computed flow rates of the steam dump to house consumption (BRU-SN), mainly due to

oversimplified controller modeling. In this comparison, the GRS/KI ATHLET solution

serves as reference.

Pressures

Figures 6.8-6.12 show the predicted secondary circuit pressures. Good agreement of

the BIPR8/ATHLET, CATHARE2 and HEXTRAN/SMABRE results is displayed. The

RELAP3D results in Figures 6.8 and 6.9 show a discrepancy due to incorrect modeling of

the MSH pressure controller.

98

Figures 6.13-6.17 show the computed time histories of primary circuit pressures.

There is a spread in the results reflecting the impact of different mixing models and power

dynamics. The significant discrepancy in the VTT results is related with the modeling of

the secondary circuit dynamics, including steam dump controllers (see Figures 6.32-6.39).

Temperatures

Figures 6.18-6.26 show the computed time histories of primary circuit temperatures at

the reactor inlet and outlet nozzles and the core average coolant temperature. The results

of BIPR8/ATHLET and CATHARE2 are in generally good agreement. The discrepancy

in the RELAP3D results reflects the impact of wrong MSH pressure calculation due to the

BRU-K pressure controller modeling, and the use of one-channel upper plenum model

which lumps the flow parameters above the core. The difference in the

HEXTRAN/SMABRE computed temperature in the faulted loop #4 seems to be a

combined effect of the computed pressure and mass inventory in the intact SG.

The differences in the core average coolant density and Doppler temperatures, seen in

Figures 6.27 and 6.29, influence the total power dynamics as shown in Figures 6.30-6.31.

Total power

Figures 6.30 and 6.31 illustrate the time history of the total fission and thermal reactor

power. The predicted maximum total power after scram is smaller than that in Exercise 2

obtained with more conservative vessel thermal hydraulic boundary conditions.

For the considered solutions, the major contributions to the observed differences come

from the modeling of the secondary pressure and steam flow, along with the spatial

coupling and fuel modeling.

99

Figure 6.1: Total break flow rate (Scenario 2)

Figure 6.2: Integrated total break flow rate (Scenario 2)

100

Figure 6.3: Integrated liquid break flow rate (Scenario 2)

Figure 6.4: BRU-K flow rate (Scenario 2)

101

Figure 6.5: Integrated BRU-K flow rate (Scenario 2)

Figure 6.6: BRU-SN total flow rate (Scenario 2)

102

0

20000

40000

60000

80000

100000

0 50 100 150 200 250 300 350 400 450 500

T ime, s

Inte

gra

ted

BR

U-S

N t

ota

l fl

ow

, k

gVT T - HE X T R AN/S MAB R E

G R S /K I - AT HL E T (2B .0)/B IP R

UNIP I - R E L AP 5-3D

INR NE - C AT HAR E 2

Figure 6.7: Integrated total BRU-SN flow (Scenario 2)

Figure 6.8: Main steam header pressure (Scenario 2)

103

Figure 6.9: SG1 pressure (Scenario 2)

Figure 6.10: SG2 pressure (Scenario 2)

104

Figure 6.11: SG3 pressure (Scenario 2)

Figure 6.12: SG4 pressure (Scenario 2)

105

Figure 6.13: Average pressure above the core (Scenario 2)

Figure 6.14: Cold leg 1 pressure (Scenario 2)

106

Figure 6.15: Cold leg 2 pressure (Scenario 2)

Figure 6.16: Cold leg 3 pressure (Scenario 2)

107

Figure 6.17: Cold leg 4 pressure (Scenario 2)

Figure 6.8: Average core coolant temperature (Scenario 2)

108

Figure 6.9: Cold leg 1 temperature (Scenario 2)

Figure 6.10: Cold leg 2 temperature (Scenario 2)

109

Figure 6.11: Cold leg 3 temperature (Scenario 2)

Figure 6.12: Cold leg 4 temperature (Scenario 2)

110

Figure 6.13: Hot leg 1 temperature (Scenario 2)

Figure 6.14: Hot leg 2 temperature (Scenario 2)

111

Figure 6.15: Hot leg 3 temperature (Scenario 2)

Figure 6.16: Hot leg 4 temperature (Scenario 2)

112

Figure 6.17: Core average Doppler temperature (Scenario 2)

Figure 6.18: Maximum nodal fuel temperature (Scenario 2)

113

Figure 6.19: Core average coolant density (Scenario 2)

Figure 6.20: Fission power

114

Figure 6.21: Total core power

Figure 6.22: SG1 mass of fluid (Scenario 2)

115

Figure 6.23: SG2 mass of fluid (Scenario 2)

Figure 6.24: SG3 mass of fluid (Scenario 2)

116

Figure 6.25: SG4 mass of fluid (Scenario 2)

Figure 6.26: SG1 exchanged power (Scenario 2)

117

Figure 6.27: SG2 exchanged power (Scenario 2)

Figure 6.28: SG3 exchanged power (Scenario 2)

118

Figure 6.29: SG4 exchanged power (Scenario 2)

119

Chapter 7: Summary and conclusions

In this volume, the results of the OECD/CEA VVER-1000 MSLB benchmark were

analyzed. The results submitted by the participants were used to make code-to-code

comparisons and subsequent statistical analysis. A coarse-mesh to CFD comparison of

single-phase vessel mixing calculations with MSLB boundary conditions was also

analyzed.

At the start of the VVER-1000 Coolant Transient Benchmarks (V1000CT) the coolant

mixing was an unresolved issue in the analysis of complex plant transients with reactivity

insertion. In order to support the necessary development work, Phase 2 of the benchmarks

(V1000CT-2) was launched. The V1000CT-2 coolant mixing and MSLB benchmark was

designed to provide a validation framework for the new generation best-estimate codes

equipped with 3D neutron kinetics and improved vessel thermal-hydraulic models. A

specific objective was to assess the performance of single-phase vessel mixing models

(CFD and coarse-mesh), and the impact of thermal-hydraulic model refinement. For a

consistent step-by-step validation, the multi-level methodology was employed and three

exercises were defined.

In Exercise 1, which is a pure thermal-hydraulic problem, the participants validated

their CFD or coarse-mesh vessel thermal-hydraulic models against plant data, on different

scales:

separate effects (mixing in the down-comer and lower plenum)

vessel component

plant system (optional)

A validated LES solution with the TRIO_U code served as reference for the separate

effects. The results show that the accuracy attained in both CFD and improved coarse-

mesh thermal-hydraulic models can be acceptable for industrial applications. The codes

still have limitations but the development work for single-phase mixing is on the right

way. The quality of the results depends on the experience of the user and the compliance

with the Best Practice Guidelines.

The mixing models validated in Exercise 1 have been used in the other V1000CT-2

exercises for coupled core-vessel and core-system MSLB simulation to assess the

applicability of best-estimate codes to VVER-1000 MSLB analysis.

In Exercise 2, which is a coupled core-vessel MSLB simulation with imposed vessel

boundary conditions, standalone and coupled codes were tested step-by-step. The

solutions were compared code-to-code and against fine-mesh solutions, where possible.

The results show that:

HZP solutions of COBAYA3, DYN3D, CRONOS and PARCS agree well with

each other and with fine-mesh solutions. The respective nodal solvers yield

converged solutions

the NEM and HEXTRAN solvers need some improvements to produce spatially

converged solutions for large hexagonal nodes and in regions of steep gradients

120

the steady-state core-vessel solutions at HFP with DYN3D/ATHLET,

CRONOS/FLICA, COBAYA/COBRA3, NEM/RELAP3D and HEXTRAN/

SMABRE are in reasonable overall agreement. The observed discrepancies can be

explained with differences in the flux solvers, fuel and hydraulics modeling, and

the spatial coupling

the time histories of total power and reactivity of DYN3D/ATHLET,

COBAYA/COBRA3 and HEXTRAN/SMABRE are in good agreement, despite

some differences in the fuel Doppler temperature, which indicates some

compensation effects due to coarse-mesh N/TH overlays in the radial plane

the transient total power is sensitive to the core inlet distributions and the spatial

coupling, due to local effects and transient 3D flux re-distribution, as illustrated in

Chapter 5

in this type of transient, the refinement of the neutronics model in the radial plane

does not really impact the total power evolution. The neutronics scheme

refinement impacts the local power distributions but not to the extent of the

thermal-hydraulics meshing

the local effects are sensitive to the azimuthal spatial resolution and accuracy of

the core inlet TH conditions, as illustrated by a sensitivity study in Chapter 5. This

sensitivity is stronger in case of steep flux gradients

the axial distributions are sensitive to the core inlet distributions and the decay

heat distribution during the transient, as illustrated in Chapter 5

the vessel thermal-hydraulic models used in this study are applicable to VVER

MSLB analysis. For an acceptable resolution at the core inlet, at least 16 - 24

angular meshes in the vessel are recommended

In Exercise 3, the performance of the integrated codes was evaluated in code-to-code

comparison. It should be noted that the solutions submitted by the participants were „first

calculation‟ results, without feedback and recalculation. Because of this, and of certain

declines from the secondary circuit specification in some user models of the steam dump

controllers and the check valve, a relatively wide scatter of the core-system results is

displayed. The comparison shows that the user models of the secondary circuit of VVER-

1000 require further attention.

In the overall, for the prediction of the system behavior in this benchmark, key

parameters were the SG fluid masses, the break flow rates, the secondary pressure, as well

as the coolant and fuel temperatures, and the powers. Other parameters were important to

analyze because they help to determine what was causing the behavior of the key

parameters. In particular, it was proven that the refinement of the vessel mixing model has

a great effect on the 3D core and core-vessel dynamics.

The following sources of modeling uncertainties were identified:

Thermal-hydraulic modeling issues: vessel mixing modeling; vessel meshing;

turbine bypass controllers modeling; liquid break flow modeling for horizontal

steam generators

Thermal-hydraulic key parameters: core inlet temperatures; core inlet mass flow

rates; core outlet pressure; gas gap conductance

121

Cross-section modeling: spectral history dependencies; instantaneous cross-section

dependences, cross-term effects; ADF modeling; refinement of the cross-section

library

Neutronics and coupling modeling: different flux solvers; spatial N/TH coupling in

terms of the number of thermal-hydraulic channels and spatial mesh overlays at

the core inlet; direct moderator heating; temporal coupling schemes

The comparative study allows a conclusion that the considered vessel mixing models

and coupled codes are applicable to the analysis of asymmetric coolant transients

characterized by sector formation, such as MSLB.

The lessons learned from the VVER vessel mixing and MSLB benchmarks will have a

significant impact on the future coupled code analysis of reactivity transients.

122

References

Bieder, U., S.Betin, G.Fauchet, N.P.Kolev (2004), “Preparation of the V1000CT-2

Exercise 1 thermal-hydraulic benchmark”, 2nd

Workshop on the OECD VVER-1000

Coolant Transient Benchmarks, Sofia, April 5-6

Frisani, A., C.Parisi , F.D‟Auria (2006), “The use of RELAP5-3D code in the

OECD/NEA VVER-1000 CT-1 and CT-2 Benchmark” RELAP5-3D Users Seminar

Holiday Inn Sun-Spree Resort – West Yellowstone, USA, 16-18 August 2006

Hoehne, T. (2007), “CFX-5 calculated transient down-comer core inlet TH parameters for

the OECD VVER-1000 MSLB benchmark”, Invited contribution to the V1000CT-2

benchmark

Ivanov B., K.Ivanov, N.Kolev (2006a), “Cross-section library 2.0 for VVER-1000

MSLB”, Ad-hoc meeting-Workshop on the V1000CT-2 benchmark, Vancouver, Canada,

12 September, 2006

Ivanov, B., S.Aniel, P.Siltanen, E.Royer, K.Ivanov (2006b), “Impact of cross-section

generation procedures on the simulation of the VVER-1000 pump startup experiment in

the OECD/DOE/CEA V1000CT benchmark by coupled 3D N/TH models”, Progress In

Nuclear Energy, Vol.48, No.8, pp. 746-763

Kolev, N.P., D.Popov, S.Aniel, E.Royer (2004), “Specifications of the V1000CT-2

Exercise 1 thermal-hydraulic benchmark”, 2nd

Workshop on the OECD VVER-1000

Coolant Transient Benchmarks, Sofia, April 5-6

Kolev, N.P., N.Petrov, D. Angelova, J.Donov, Y.Dinkov, D.Popov, S.Nikonov (2005),

VVER-1000 Main Steam Line Break Analysis, INRNE Report for CEA, Saclay

Kolev N.P. et al (2009), “VVER-1000 Coolant Transient Benchmark Phase 2 (V1000CT-

2), Volume1: Specifications of the VVER-1000 vessel mixing problem”, NEA/NSC/DOC

(2007)22, OECD/NEA, Paris

Kolev N.P. et al (2010a), “VVER-1000 Coolant Transient Benchmark (V1000CT-2),

Volume 2: Final specifications of the MSLB problem”, NEA/NSC/DOC(2006)6,

OECD/NEA, Paris

Kolev N.P. et al (2010b), “VVER-1000 Coolant Transient Benchmark (V1000CT-2),

Volume 3: Summary results of Exercise 1 on vessel mixing simulation”, NEA/NSC/DOC

(2010)10, OECD/NEA, Paris

Mahaffy, J., B. Chung, F. Dubois, F. Ducros, E. Graffard, M. Heitsch, M. Henriksson, E.

Komen, F. Moretti, T. Morii, P. Mühlbauer, U. Rohde, M. Scheuerer, B. L. Smith, C.

Song, T. Watanabe, G.Zigh (2007), “Best Practice Guidelines for the use of CFD in

Nuclear Reactor Safety Applications”, OECD NEA/CSNI/R (2007)5

Nikonov, S., M.Lizorkin, A.Kotsarev, S.Langenbuch and K.Velkov, “Optimal

Nodalization Schemes of VVER-1000 Reactor Pressure Vessel for the Coupled Code

ATHLET-BIPR8KN”, Proc. 16th AER Symposium on VVER Reactor Physics and

Safety, Bratislava, 25-29 September 2006

Nikonov, S., Private communication, 2004

123

Ts.Topalov, D.Popov (2004), “Overview of the Kozloduy-6 vessel mixing tests”, 2nd

Workshop on the OECD VVER-1000 Coolant Transient Benchmarks, Sofia, April 5-6

Spasov, I., J. Jimenez, J.A. Lozano, J.J. Herrero (2009), “V1000CT2-EXT2 benchmark

solutions with COBAYA3/COBRA3”, Internal Report, Universidad Politecnica de

Madrid

Spasov, I., J. Jimenez, J.A. Lozano, J.J. Herrero, N.P.Kolev, (2010), “COBAYA3 vs.

CRONOS solutions of the V1000-MSLB benchmark”, to appear

U.Bieder, G. Fauchet, S.Betin, N.Kolev and D.Popov (2005), “Calculation of coolant

mixing in VVER-1000”, 11th Int. Conf. on Nuclear Reactor Thermal-Hydraulics

(NURETH-11), Avignon, France, October 2-6, Paper: 201

References (codes)

Aniel S. et al, (2005),”FLICA4: Status of numerical and physical models and overview of

the applications”, Proc. of NURETH11, Avignon, 2-6 October

ANSYS CFX10 Manuals (2006)

Bergeron A., Caruge D., Clement P. (1999), “Assessment of the 3-D Thermal-hydraulic

Nuclear Computer Code FLICA4 on Rod Bundle Experiments”, NURETH-6, San

Francisco, 3-8 October 1999

CEA (2007), CATHARE 2.5 User's Manual

Downar, T., et al (2004), “PARCS v2.6 US NRC Core Neutronics Simulator Theory

Manual”https://engineering.purdue.edu/PARCS/Code/Manual/Theory/PDF/PARCS_Theo

ryManual.pdf (2004)

Grundmann, U. (1999), “HEXNEM: A nodal method for the solution of the neutron

diffusion equation in hexagonal geometry”, Proc. M&C 1999, Madrid, 27-30 September,

pp. 1086-1095

Grundmann, U., F.Holstein (1999), “A 2D intra-nodal flux expansion method for

hexagonal geometry”, Nucl. Sci. Eng., 133, 201-212

Hämäläinen, A. (2004) “Applying thermal hydraulics modeling in coupled processes of

nuclear power plants”, VTT Publication 578

Idaho Nuclear Laboratory (INL) (2001), INEEL-EXT-98-00834, Revision 1.3a, February

2001

Jackson J.W., N.E.Todreas (1981), “COBRA-IIIc/MIT-2: A Computer Program for

Steady State and Transient Thermo-Hydraulic Analysis of Rod Bundle Nuclear Fuel

Elements”, MIT report

Jiménez, J., D. Cuervo, J.M. Aragonés (2007), “Multi-Scale and Multi-Physics Coupling

in COBAYA3”, Proc. NURETH-12, Paper: 48, Pittsburgh, Pennsylvania, Sept 30-Oct 4

Kaloinen, E. et al (1981), “HEXBU-3D: A 3D PWR simulator program for hexagonal fuel

assemblies”, VTT Research report 7/1981, Helsinki

Kyrki-Rajamaki, R. (1991), “HEXTRAN: VVER reactor dynamics code for 3D

transients”, Proc. 1st AER Symp. on VVER reactor physics and safety, Rez, 23-28

September

124

Lautard, J. et al. (1990), “CRONOS – A Modular Computational System for Neutronic

Core Calculation”, Proc. IAEA Meeting, Cadarache, France

Lautard J., D.Schneider, A.M. Baudron (1999), “Mixed dual methods for neutronics

reactor core calculations in the CRONOS system”, Proc. of M&C, Madrid, 27-30

September

Lizorkin, M., S.Nikonov, S.Langenbuch, K.Velkov (2006) “Development and Application

of the Coupled Thermal-Hydraulics and Neutron-Kinetics Code ATHLET/BIPR-VVER

for Safety Analysis”, Proc. EUROSAFE 2006, Paris, 13-14 November

Lozano, J.A., J.Jimenez, N.García-Herranz and J.M.Aragonés (2009), “Development and

performance of the ANDES/COBRAIII coupled system in hexagonal-Z geometry” , Proc.

M&C 2009, Saratoga Springs, NY, May 3-7; Annals of Nuclear Energy, 2010

Magnaud, C. (1999), “Pin-by-pin transport calculation with the CRONOS reactor code”,

Proc. of M&C, Madrid, 27-30 September

Miettinen, J. (1985), “Development and assessment of the SBLOCA code SMABRE”,

Proc. of the Specialists meeting on Small Break LOCA analysis in LWR, Pisa, Italy,

Vol.2, pp. 481-495

Odar, F., C.Murray et al (2003), TRACE V4.0 User‟s Manual, May

Teschendorf, V., H.Austregesilo, G.Lerchl (1996), “Methodology, status and plans for

development and assessment of the code ATHLET“, Proc. of the OECD/CSNI Workshop

on transient thermal-hydraulic and neutronics codes requirements, Annapolis, USA, 5-8

Nov 1996, NUREG/CP-0159, NEA/CSNI/R(97)4

Toumi I., Bergeron A., Gallo D. Royer E., Caruge D. (2000), “FLICA4: A Three-

dimensional Two-phase Flow Computer Code with Advanced Numerical Methods for

Nuclear Applications”, Nuclear Engineering and Design, 200, 139-155

Syrjälahti, E., A. Hämäläinen (2006), “HEXTRAN-SMABRE calculation of the VVER-

1000 coolant transient-1 benchmark”, Progress in Nuclear Energy 48, 849-864

UPM, Madrid (2009), The COBAYA3 neutronic code – “Quick Guide”

125

Appendix A: Two-dimensional radial power

distributions in the steady states

-0,1

0,589

28

0,0

0,791

27

0,0

0,784

18

-0,1

0,585

13

0,1

1,085

26

0,0

0,853

1

0,0

0,935

2

-0,1

1,259

3

-0,2

1,337

4

0,0

1,191

5

0,3

0,805

6

-0,1

0,875

7-0,2

1,205

8

0,0

1,114

9

0,0

1,114

10

0,1

0,946

11

0,1

1,073

120,0

1,115

14

0,0

0,968

15

0,1

0,965

16

0,0

1,198

17-0,1

1,125

19

0,0

1,019

20

0,1

1,063

21

0,0

0,842

220,1

0,983

23

0,0

1,216

24

0,0

0,846

25

-0,1

0,875

7

Figure A.1: HZP state 0. DYN3D computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

0,6

0,593

28

0,6

0,796

27

0,6

0,789

18

0,6

0,589

13

0,0

1,084

26

-0,4

0,850

1

-0,5

0,930

2

0,0

1,261

3

0,1

1,341

4

-0,1

1,191

5

-0,6

0,798

6

0,4

0,879

70,0

1,208

8

-0,3

1,111

9

-0,1

1,113

10

-0,4

0,940

11

0,0

1,072

12-0,3

1,112

14

-0,4

0,964

15

-0,4

0,961

16

0,3

1,202

17-0,1

1,124

19

-0,3

1,016

20

-0,1

1,060

21

0,5

0,846

22-0,4

0,978

23

0,3

1,220

24

0,5

0,851

25

0,4

0,879

7

Figure A.2: HZP state 0. PARCS computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((PARCS - mean)/mean)*100%

Assembly #

Relative power

((DYN3D - mean)/mean)*100%

126

-0,4

0,587

28

-0,4

0,788

27

-0,5

0,780

18

-0,4

0,583

13

-0,2

1,081

26

0,4

0,857

1

0,4

0,938

2

0,2

1,263

3

0,2

1,342

4

0,0

1,192

5

0,3

0,805

6

-0,4

0,872

70,3

1,211

8

0,3

1,117

9

0,2

1,116

10

0,2

0,946

11

-0,2

1,069

120,3

1,119

14

0,3

0,971

15

0,2

0,966

16

-0,3

1,194

170,2

1,128

19

0,1

1,020

20

-0,1

1,061

21

-0,5

0,837

220,2

0,984

23

-0,3

1,212

24

-0,5

0,842

25

-0,4

0,872

7

Figure A.3: HZP state 0. CRONOS computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

-0,1

0,588

28

-0,1

0,790

27

-0,1

0,783

18

-0,1

0,585

13

0,1

1,085

26

0,1

0,854

1

0,0

0,934

2

-0,1

1,259

3

0,0

1,339

4

0,1

1,192

5

0,1

0,803

6

0,0

0,875

7-0,1

1,207

8

0,0

1,114

9

0,0

1,114

10

0,1

0,946

11

0,1

1,073

120,0

1,115

14

0,1

0,968

15

0,1

0,965

16

0,0

1,197

170,0

1,125

19

0,1

1,020

20

0,0

1,062

21

-0,1

0,841

220,1

0,982

23

0,0

1,215

24

-0,1

0,845

25

0,0

0,875

7

Figure A.4: HZP state 0. COBAYA computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((COBAYA - mean)/mean)*100%

Assembly #

Relative power

((CRONOS - mean)/mean)*100%

127

12,8

0,665

28

10,2

0,872

27

10,5

0,866

18

13,1

0,662

13

3,4

1,120

26

-6,5

0,798

1

-6,1

0,877

2

-5,1

1,197

3

-4,2

1,284

4

-2,2

1,166

5

1,6

0,815

6

7,9

0,944

7-5,3

1,144

8

-4,9

1,060

9

-2,6

1,085

10

0,0

0,944

11

3,7

1,111

12-5,0

1,060

14

-2,9

0,939

15

-0,4

0,961

16

3,5

1,240

17-2,7

1,095

19

-0,9

1,010

20

2,7

1,091

21

9,6

0,922

22-0,3

0,979

23

3,3

1,256

24

9,5

0,926

25

7,9

0,944

7

Figure A.5: HZP state 0. NEM computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

15,4

0,680

28

12,2

0,888

27

12,3

0,880

18

15,4

0,676

13

4,8

1,135

26

-11,0

0,759

1

-10,4

0,837

2

-9,1

1,146

3

-6,8

1,248

4

-3,8

1,147

5

0,7

0,808

6

7,8

0,943

7-9,6

1,092

8

-7,8

1,027

9

-5,2

1,057

10

-0,9

0,936

11

4,8

1,123

12-7,8

1,028

14

-5,5

0,915

15

-1,6

0,949

16

3,5

1,240

17-5,1

1,068

19

-1,4

1,005

20

3,4

1,097

21

11,7

0,940

22-0,8

0,973

23

3,5

1,258

24

11,7

0,945

25

7,8

0,943

7

Figure A.6: HZP state 0. HEXTRAN computed assembly powers vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((HEXTRAN-mean)/mean)*100%

Assembly #

Relative power

((NEM - mean)/mean)*100%

128

-0,1

0,882

28

0,0

1,074

27

0,0

1,073

18

-0,2

0,882

13

0,1

1,390

26

-0,1

0,824

1

-0,1

0,848

2

-0,2

1,036

3

0,0

0,768

4

0,0

1,002

5

0,3

0,905

6

-0,1

1,273

7-0,3

0,973

8

-0,1

0,883

9

-0,1

0,901

10

0,4

0,735

11

0,1

1,388

12-0,1

0,883

14

0,1

0,767

15

0,1

0,875

16

0,0

1,343

17-0,1

0,906

19

0,1

0,911

20

0,3

0,824

21

0,0

0,987

220,4

0,750

23

0,0

1,349

24

0,0

0,988

25

-0,1

1,273

7

Figure A.7: HZP state 1a. DYN3D computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results. Blue color marks inserted rods

0,6

0,888

28

0,5

1,080

27

0,5

1,079

18

0,6

0,888

13

-0,1

1,387

26

-0,2

0,823

1

-0,3

0,846

2

0,1

1,039

3

0,0

0,769

4

-0,1

1,001

5

-0,7

0,897

6

0,3

1,279

7-0,1

0,975

8

-0,2

0,882

9

-0,1

0,901

10

-0,6

0,728

11

-0,1

1,386

12-0,2

0,882

14

-0,6

0,761

15

-0,4

0,871

16

0,2

1,346

17-0,1

0,906

19

-0,4

0,907

20

-0,3

0,819

21

0,4

0,992

22-0,6

0,743

23

0,2

1,353

24

0,4

0,993

25

0,3

1,279

7

Figure A.8: HZP state 1a. PARCS computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((PARCS-mean)/mean)*100%

Assembly #

Relative power

((DYN3D-mean)/mean)*100%

129

-0,5

0,879

28

-0,5

1,069

27

-0,5

1,068

18

-0,5

0,879

13

-0,3

1,384

26

1,0

0,833

1

1,0

0,857

2

0,7

1,046

3

0,4

0,771

4

0,1

1,003

5

0,2

0,905

6

-0,4

1,269

70,7

0,982

8

0,7

0,890

9

0,4

0,905

10

0,2

0,734

11

-0,3

1,382

120,7

0,890

14

0,4

0,769

15

0,2

0,877

16

-0,4

1,338

170,4

0,910

19

0,2

0,912

20

-0,1

0,821

21

-0,6

0,982

220,1

0,749

23

-0,3

1,345

24

-0,6

0,983

25

-0,4

1,269

7

Figure A.9: HZP state 1a. CRONOS computed assembly powers vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

0,1

0,884

28

0,1

1,076

27

0,1

1,075

18

0,1

0,884

13

0,3

1,392

26

-0,6

0,820

1

-0,6

0,844

2

-0,6

1,033

3

-0,4

0,765

4

0,0

1,002

5

0,2

0,905

6

0,2

1,277

7-0,3

0,973

8

-0,4

0,880

9

-0,2

0,901

10

0,1

0,733

11

0,3

1,391

12-0,4

0,881

14

0,1

0,767

15

0,1

0,875

16

0,1

1,345

17-0,2

0,905

19

0,1

0,911

20

0,1

0,822

21

0,2

0,989

220,1

0,748

23

0,1

1,351

24

0,2

0,991

25

0,2

1,277

7

Figure A.10: HZP state 1a. COBAYA computed assembly powers vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((COBAYA-mean)/mean)*100%

Assembly #

Relative power

((CRONOS - mean)/mean)*100%

130

12,7

0,996

28

10,4

1,186

27

10,7

1,188

18

13,1

0,999

13

3,7

1,440

26

-9,2

0,749

1

-8,5

0,777

2

-7,2

0,964

3

-6,9

0,715

4

-2,9

0,973

5

2,1

0,921

6

8,0

1,376

7-7,4

0,903

8

-6,5

0,827

9

-3,4

0,871

10

-1,1

0,725

11

4,1

1,443

12-6,6

0,826

14

-3,7

0,738

15

-0,4

0,871

16

4,1

1,398

17-3,6

0,874

19

-0,9

0,902

20

1,9

0,837

21

10,5

1,091

22-1,4

0,737

23

3,8

1,401

24

10,4

1,091

25

8,0

1,376

7

Figure A.11: HZP state 1a. NEM computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

-6,8

0,823

28

-5,6

1,014

27

19,7

1,285

18

30,2

1,150

13

-14,4

1,189

26

-23,8

0,628

1

-16,7

0,707

2

-8,4

0,951

3

3,5

0,795

4

13,4

1,136

5

22,5

1,106

6

30,8

1,667

7-21,2

0,769

8

-12,2

0,776

9

-2,4

0,881

10

6,7

0,782

11

17,6

1,631

12-20,5

0,703

14

-15,2

0,649

15

-3,9

0,840

16

7,1

1,438

17-20,3

0,723

19

-12,9

0,793

20

-3,9

0,790

21

10,4

1,090

22-18,4

0,610

23

-11,0

1,201

24

0,0

0,988

25

30,8

1,667

7

Figure A.12: HZP state 1a. HEXTRAN computed assembly powers vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((HEXTRAN-mean)/mean)*100%

Assembly #

Relative power

((NEM-mean)/mean)*100%

131

-0,5

0,790

28

-0,3

1,092

27

-0,3

1,091

18

-0,5

0,790

13

0,1

0,925

26

0,3

0,751

1

0,1

1,010

2

-0,1

1,328

3

0,2

1,027

4

0,0

1,202

5

0,1

0,824

6

-0,4

1,070

70,1

0,977

8

0,0

1,138

9

0,0

1,071

10

0,3

0,735

11

0,1

0,923

120,0

1,138

14

0,3

0,701

15

0,2

0,666

16

-0,2

1,376

17-0,1

1,074

19

0,2

0,691

20

0,2

0,891

21

-0,2

1,182

220,2

0,750

23

-0,2

1,381

24

-0,2

1,182

25

-0,4

1,070

7

Figure A.13: HZP state 1b. DYN3D computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

0,5

0,798

28

0,4

1,100

27

0,5

1,100

18

0,5

0,798

13

-0,1

0,923

26

-0,3

0,747

1

-0,2

1,007

2

0,2

1,332

3

0,1

1,026

4

-0,1

1,201

5

-0,6

0,818

6

0,3

1,078

70,1

0,977

8

-0,1

1,136

9

0,0

1,071

10

-0,6

0,729

11

-0,1

0,921

12-0,1

1,136

14

-0,5

0,695

15

-0,5

0,661

16

0,2

1,382

170,0

1,075

19

-0,5

0,686

20

-0,3

0,886

21

0,4

1,189

22-0,6

0,744

23

0,2

1,387

24

0,4

1,189

25

0,3

1,078

7

Figure A.14: HZP state 1b. PARCS computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((PARCS-mean)/mean)*100%

Assembly #

Relative power

((DYN3D-mean)/mean)*100%

132

-0,5

0,790

28

-0,6

1,089

27

-0,6

1,088

18

-0,5

0,790

13

-0,3

0,922

26

0,7

0,754

1

0,8

1,017

2

0,5

1,336

3

0,3

1,028

4

0,2

1,204

5

0,3

0,825

6

-0,4

1,071

70,5

0,981

8

0,6

1,144

9

0,4

1,075

10

0,2

0,735

11

-0,3

0,920

120,6

1,144

14

0,5

0,702

15

0,2

0,666

16

-0,4

1,373

170,4

1,079

19

0,2

0,691

20

-0,1

0,888

21

-0,7

1,176

220,2

0,750

23

-0,4

1,378

24

-0,7

1,177

25

-0,4

1,071

7

Figure A.15: HZP state 1b. CRONOS computed assembly powers vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

0,4

0,797

28

0,4

1,100

27

0,4

1,099

18

0,4

0,797

13

0,3

0,927

26

-0,7

0,743

1

-0,7

1,003

2

-0,7

1,320

3

-0,6

1,019

4

-0,1

1,200

5

0,2

0,825

6

0,5

1,080

7-0,8

0,968

8

-0,5

1,132

9

-0,3

1,068

10

0,1

0,734

11

0,3

0,925

12-0,5

1,132

14

-0,3

0,696

15

0,1

0,665

16

0,4

1,384

17-0,3

1,072

19

0,1

0,690

20

0,3

0,892

21

0,5

1,190

220,1

0,749

23

0,3

1,388

24

0,5

1,191

25

0,5

1,080

7

Figure A.16: HZP state 1b. COBAYA computed assembly powers vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((COBAYA-mean)/mean)*100%

Assembly #

Relative power

((CRONOS-mean)/mean)*100%

133

19,9

0,951

28

16,7

1,278

27

17,0

1,281

18

20,3

0,954

13

6,7

0,986

26

-17,4

0,619

1

-15,6

0,851

2

-13,6

1,148

3

-11,7

0,905

4

-5,0

1,141

5

3,4

0,851

6

13,5

1,220

7-15,3

0,827

8

-12,2

0,999

9

-7,0

0,997

10

-0,6

0,729

11

7,1

0,987

12-12,3

0,997

14

-9,1

0,635

15

-1,2

0,657

16

8,6

1,497

17-7,2

0,998

19

-1,7

0,678

20

6,5

0,947

21

16,3

1,377

22-1,0

0,741

23

8,3

1,498

24

16,2

1,377

25

13,5

1,220

7

Figure A.17: HZP state 1b. NEM computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

-42,1

0,460

28

-40,7

0,649

27

-18,0

0,898

18

-1,4

0,783

13

-45,6

0,503

26

33,2

0,997

1

2,7

1,037

2

-1,7

1,307

3

1,7

1,043

4

4,3

1,253

5

8,0

0,889

6

15,5

1,241

7-7,1

0,907

8

-13,0

0,990

9

-13,7

0,925

10

-15,3

0,621

11

-11,9

0,813

12-18,1

0,932

14

-24,9

0,524

15

-28,2

0,477

16

-26,5

1,014

17-30,9

0,743

19

-37,5

0,431

20

-36,1

0,568

21

-27,9

0,854

22-41,4

0,438

23

-42,3

0,798

24

-36,3

0,754

25

15,5

1,241

7

Figure A.18: HZP state 1b. HEXTRAN computed assembly powers vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((HEXTRAN-mean)/mean)*100%

Assembly #

Relative power

((NEM-mean)/mean)*100%

134

0,62

0,421

155

0,12

0,909

151

-0,48

1,288

149

-0,32

2,223

139

-0,49

5,408

103

-0,64

4,336

89

-0,73

2,560

62

-0,54

2,629

49

-0,15

1,242

16

-0,32

0,746

7

0,40

0,400

50,54

0,223

15

0,31

0,264

6

-0,01

0,598

2

-0,32

0,506

1

0,22

0,272

157

0,53

0,344

148

0,89

0,282

115

0,73

0,197

102

0,82

0,190

75

1,07

0,265

61

0,88

0,292

25

0,81

0,322

147

0,78

0,357

145

0,66

0,391

144

0,44

0,526

143

0,02

1,548

140

0,00

1,375

131

0,20

0,565

3

0,35

0,484

4-0,27

0,835

8

0,32

0,584

9

0,14

0,731

10

0,63

0,402

11

0,81

0,321

13

0,42

0,536

12

0,46

0,332

140,20

0,904

17

0,25

0,646

18

0,50

0,475

19

0,50

0,359

20

0,66

0,302

21

0,87

0,283

22

0,88

0,271

23

1,10

0,266

24-0,22

1,662

26

-0,12

1,675

27

0,38

0,734

28

0,21

0,943

29

0,19

0,706

30

0,68

0,375

31

0,45

0,462

32

0,66

0,444

33

1,21

0,232

34

0,98

0,374

35

1,05

0,303

36-0,34

2,210

37

0,12

1,427

38

0,30

0,868

39

0,23

1,029

40

0,36

0,803

41

0,29

0,728

42

0,40

0,577

43

0,68

0,431

44

0,76

0,386

45

1,32

0,200

46

1,46

0,232

47

1,14

0,292

48-0,34

2,945

50

0,17

1,188

51

1,04

0,917

52

0,25

1,110

53

0,09

1,027

54

0,42

0,594

55

0,33

0,637

56

0,71

0,459

57

1,78

0,244

58

1,39

0,197

59

1,14

0,347

60-0,15

2,768

63

0,10

1,801

64

-0,10

1,938

65

0,10

1,481

66

0,25

0,960

67

0,25

0,754

68

0,40

0,567

69

0,67

0,439

70

0,77

0,431

71

0,93

0,347

72

1,40

0,207

73

1,38

0,230

74-0,64

4,843

76

-0,14

3,168

77

-0,20

2,996

78

0,03

1,752

79

-0,12

1,632

80

0,14

0,940

81

0,53

0,516

82

0,45

0,519

83

0,45

0,555

84

0,86

0,365

85

0,91

0,367

86

1,20

0,220

87

0,83

0,265

88-0,31

6,470

90

0,01

2,821

91

-0,20

2,395

92

-0,06

1,685

93

0,14

1,065

94

0,18

0,828

95

0,35

0,615

96

0,58

0,468

97

0,61

0,452

98

0,72

0,358

99

1,29

0,210

100

1,26

0,238

101-0,40

5,902

104

-0,04

2,041

105

0,22

1,238

106

-0,01

1,384

107

-0,05

1,234

108

0,35

0,695

109

0,27

0,726

110

0,51

0,512

111

0,98

0,264

112

1,08

0,204

113

0,90

0,372

114-0,44

4,372

116

0,00

2,674

117

0,04

1,391

118

-0,11

1,465

119

0,15

1,064

120

0,25

0,919

121

0,43

0,700

122

0,60

0,508

123

0,51

0,448

124

0,91

0,236

125

1,14

0,259

126

0,87

0,320

127-0,35

3,103

128

-0,28

2,981

129

0,17

1,168

130

0,11

0,971

132

1,24

0,492

133

0,49

0,574

134

0,53

0,538

135

0,91

0,281

136

0,66

0,436

137

0,75

0,347

1380,05

1,023

141

0,31

0,715

142

0,69

0,338

146-0,46

1,373

150

-0,03

1,087

152

0,48

0,573

153

0,27

0,728

154

0,22

0,419

156-0,53

0,800

158

-0,23

0,907

159

0,00

0,828

160

0,16

0,679

161

0,22

0,543

162

0,09

0,346

163

0,54

0,223

15

Figure A.19: HZP state 3. DYN3D computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((DYN3D -mean)/ mean.)*100%

135

-0,13

0,418

155

-0,20

0,906

151

0,39

1,299

149

0,28

2,236

139

0,50

5,462

103

0,61

4,391

89

0,47

2,591

62

0,48

2,656

49

0,35

1,249

16

0,47

0,752

7

0,50

0,401

50,54

0,223

15

0,58

0,264

6

0,54

0,601

2

0,57

0,511

1

0,59

0,273

157

0,53

0,344

148

0,46

0,281

115

0,52

0,196

102

0,50

0,190

75

0,42

0,263

61

0,47

0,290

25

-0,09

0,319

147

-0,60

0,352

145

-0,57

0,386

144

-0,53

0,521

143

-0,25

1,544

140

-0,17

1,373

131

0,44

0,566

3

0,44

0,484

40,31

0,840

8

-0,13

0,582

9

0,29

0,732

10

-0,28

0,399

11

-0,07

0,318

13

0,31

0,535

12

0,37

0,331

14-0,19

0,900

17

-0,64

0,641

18

-0,60

0,470

19

-0,48

0,356

20

-0,41

0,298

21

-0,48

0,279

22

-0,57

0,268

23

-0,11

0,263

240,29

1,670

26

0,18

1,679

27

-0,63

0,726

28

-0,12

0,940

29

-0,04

0,704

30

-0,44

0,371

31

0,02

0,460

32

0,01

0,441

33

-0,58

0,228

34

0,25

0,371

35

0,35

0,301

360,34

2,225

37

-0,40

1,419

38

-0,60

0,860

39

-0,18

1,025

40

0,06

0,801

41

-0,14

0,725

42

-0,10

0,574

43

0,16

0,428

44

-0,03

0,383

45

-0,56

0,196

46

-0,38

0,227

47

0,35

0,290

480,20

2,960

50

-0,64

1,179

51

-0,82

0,900

52

-0,26

1,104

53

0,15

1,027

54

0,10

0,592

55

0,24

0,636

56

-0,12

0,456

57

-0,65

0,238

58

-0,52

0,193

59

0,21

0,344

60-0,17

2,767

63

-0,70

1,787

64

-0,17

1,937

65

-0,27

1,475

66

0,02

0,958

67

-0,25

0,750

68

-0,22

0,564

69

0,11

0,436

70

-0,12

0,427

71

-0,03

0,344

72

-0,56

0,203

73

-0,17

0,227

740,33

4,891

76

-0,66

3,152

77

-0,19

2,997

78

-0,01

1,751

79

0,10

1,636

80

-0,28

0,936

81

-0,35

0,512

82

-0,21

0,515

83

0,24

0,554

84

0,17

0,362

85

-0,03

0,363

86

-0,60

0,216

87

0,29

0,264

88-0,08

6,486

90

-0,58

2,805

91

-0,18

2,395

92

-0,25

1,682

93

0,01

1,064

94

-0,26

0,825

95

-0,24

0,611

96

0,12

0,466

97

-0,08

0,449

98

0,01

0,356

99

-0,59

0,206

100

-0,14

0,235

1010,23

5,940

104

-0,54

2,031

105

-0,63

1,228

106

-0,23

1,381

107

0,15

1,237

108

0,07

0,693

109

0,21

0,726

110

-0,10

0,509

111

-0,43

0,261

112

-0,46

0,201

113

0,27

0,369

1140,38

4,408

116

-0,40

2,663

117

-0,61

1,382

118

-0,17

1,464

119

0,02

1,062

120

-0,21

0,915

121

-0,19

0,696

122

0,13

0,505

123

0,02

0,445

124

-0,42

0,233

125

-0,30

0,255

126

0,39

0,319

1270,26

3,123

128

0,13

2,993

129

-0,72

1,157

130

-0,13

0,969

132

-0,74

0,482

133

-0,10

0,571

134

-0,03

0,535

135

-0,49

0,277

136

0,29

0,435

137

0,43

0,346

138-0,72

1,016

141

-0,61

0,709

142

-0,60

0,334

1460,23

1,382

150

0,23

1,090

152

-0,36

0,568

153

0,24

0,728

154

0,34

0,419

1560,49

0,808

158

0,47

0,913

159

0,38

0,831

160

0,37

0,680

161

0,44

0,544

162

0,56

0,348

163

0,54

0,223

15

Figure A.20: HZP state 3. PARCS computed assembly powers vs. mean of DYN3D,

CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((PARCS-mean)/mean)*100%

136

0,16

0,419

155

-0,15

0,906

151

-0,55

1,287

149

-0,67

2,215

139

-0,69

5,397

103

-0,62

4,337

89

-0,43

2,568

62

-0,54

2,629

49

-0,57

1,237

16

-0,38

0,746

7

0,05

0,399

50,45

0,223

15

0,24

0,263

6

-0,16

0,597

2

-0,10

0,507

1

0,26

0,272

157

0,21

0,343

148

0,38

0,280

115

0,58

0,196

102

0,61

0,190

75

0,46

0,263

61

0,36

0,290

25

0,44

0,321

147

0,61

0,356

145

0,46

0,390

144

0,32

0,525

143

-0,35

1,542

140

0,09

1,376

131

-0,18

0,563

3

-0,10

0,482

4-0,17

0,836

8

0,06

0,583

9

0,03

0,730

10

0,38

0,401

11

0,43

0,320

13

0,22

0,535

12

0,43

0,332

14-0,18

0,901

17

0,47

0,648

18

0,52

0,475

19

0,64

0,360

20

0,73

0,302

21

0,87

0,283

22

1,07

0,272

23

0,61

0,265

24-0,62

1,655

26

-0,38

1,670

27

0,26

0,733

28

0,29

0,944

29

0,60

0,709

30

0,82

0,375

31

0,91

0,464

32

0,85

0,444

33

1,04

0,232

34

0,55

0,372

35

0,32

0,301

36-0,62

2,204

37

-0,13

1,423

38

0,13

0,867

39

0,32

1,030

40

0,39

0,804

41

0,80

0,732

42

0,97

0,580

43

0,87

0,431

44

1,04

0,387

45

1,06

0,199

46

0,84

0,230

47

0,35

0,290

48-0,39

2,943

50

0,13

1,188

51

0,11

0,909

52

0,51

1,113

53

0,63

1,032

54

0,74

0,596

55

0,95

0,641

56

1,13

0,461

57

0,98

0,242

58

1,08

0,196

59

0,62

0,345

60-0,29

2,764

63

0,11

1,801

64

0,15

1,943

65

0,41

1,485

66

0,45

0,962

67

0,86

0,758

68

1,07

0,571

69

0,96

0,440

70

1,19

0,433

71

1,13

0,348

72

1,15

0,206

73

0,76

0,229

74-0,46

4,852

76

0,14

3,177

77

-0,05

3,001

78

0,09

1,753

79

0,40

1,641

80

0,75

0,945

81

0,82

0,518

82

1,13

0,522

83

1,07

0,559

84

1,02

0,365

85

1,05

0,367

86

1,29

0,220

87

0,68

0,265

88-0,41

6,464

90

0,00

2,821

91

0,11

2,402

92

0,36

1,692

93

0,41

1,068

94

0,81

0,834

95

1,00

0,619

96

0,92

0,469

97

1,17

0,454

98

1,14

0,360

99

1,14

0,210

100

0,71

0,237

101-0,51

5,896

104

-0,01

2,042

105

0,22

1,238

106

0,42

1,390

107

0,50

1,241

108

0,61

0,697

109

0,82

0,730

110

1,06

0,515

111

1,10

0,265

112

1,08

0,204

113

0,54

0,370

114-0,75

4,358

116

-0,26

2,667

117

0,04

1,391

118

0,21

1,470

119

0,28

1,065

120

0,61

0,922

121

0,76

0,702

122

0,68

0,508

123

0,92

0,449

124

0,95

0,236

125

0,75

0,258

126

0,27

0,319

127-0,75

3,091

128

-0,52

2,974

129

0,12

1,167

130

0,38

0,973

132

0,40

0,488

133

0,63

0,575

134

0,64

0,538

135

0,87

0,281

136

0,41

0,435

137

0,17

0,345

1380,30

1,026

141

0,28

0,715

142

0,83

0,338

146-0,35

1,374

150

-0,22

1,085

152

0,11

0,571

153

-0,09

0,725

154

0,20

0,419

156-0,30

0,802

158

-0,38

0,906

159

-0,43

0,824

160

-0,37

0,675

161

-0,24

0,540

162

-0,05

0,346

163

0,45

0,223

15

Figure A.21: HZP state 3. CRONOS computed radial power distribution vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((CRONOS-mean)/mean)*100%

137

-0,65

0,415

155

0,24

0,910

151

0,64

1,302

149

0,72

2,246

139

0,68

5,472

103

0,64

4,392

89

0,69

2,597

62

0,60

2,659

49

0,37

1,249

16

0,23

0,750

7

-0,95

0,395

5-1,53

0,218

15

-1,13

0,260

6

-0,36

0,596

2

-0,14

0,507

1

-1,07

0,268

157

-1,28

0,338

148

-1,73

0,274

115

-1,83

0,192

102

-1,93

0,185

75

-1,95

0,257

61

-1,71

0,284

25

-1,16

0,316

147

-0,80

0,351

145

-0,55

0,386

144

-0,23

0,523

143

0,58

1,556

140

0,08

1,376

131

-0,46

0,561

3

-0,68

0,479

40,13

0,838

8

-0,25

0,581

9

-0,47

0,726

10

-0,73

0,397

11

-1,17

0,315

13

-0,95

0,528

12

-1,26

0,326

140,17

0,904

17

-0,08

0,644

18

-0,43

0,471

19

-0,67

0,355

20

-0,98

0,297

21

-1,27

0,277

22

-1,38

0,265

23

-1,60

0,259

240,55

1,674

26

0,33

1,682

27

-0,01

0,731

28

-0,38

0,937

29

-0,75

0,699

30

-1,06

0,368

31

-1,38

0,454

32

-1,52

0,434

33

-1,67

0,225

34

-1,78

0,363

35

-1,72

0,295

360,62

2,232

37

0,41

1,431

38

0,17

0,867

39

-0,37

1,023

40

-0,81

0,794

41

-0,95

0,719

42

-1,27

0,568

43

-1,71

0,420

44

-1,77

0,376

45

-1,82

0,194

46

-1,92

0,224

47

-1,84

0,283

480,54

2,971

50

0,34

1,190

51

-0,33

0,905

52

-0,50

1,102

53

-0,87

1,017

54

-1,27

0,584

55

-1,52

0,625

56

-1,72

0,448

57

-2,11

0,234

58

-1,96

0,190

59

-1,97

0,337

600,62

2,789

63

0,49

1,808

64

0,12

1,942

65

-0,24

1,476

66

-0,71

0,951

67

-0,86

0,745

68

-1,25

0,558

69

-1,74

0,428

70

-1,85

0,420

71

-2,04

0,337

72

-1,98

0,200

73

-1,97

0,223

740,77

4,912

76

0,65

3,193

77

0,43

3,015

78

-0,11

1,749

79

-0,39

1,628

80

-0,61

0,933

81

-0,99

0,508

82

-1,37

0,509

83

-1,75

0,543

84

-2,05

0,354

85

-1,93

0,356

86

-1,89

0,213

87

-1,80

0,258

880,81

6,543

90

0,57

2,837

91

0,27

2,406

92

-0,06

1,685

93

-0,56

1,058

94

-0,73

0,821

95

-1,11

0,606

96

-1,62

0,458

97

-1,70

0,441

98

-1,87

0,349

99

-1,84

0,204

100

-1,84

0,231

1010,68

5,967

104

0,60

2,055

105

0,18

1,237

106

-0,17

1,382

107

-0,61

1,227

108

-1,03

0,685

109

-1,29

0,715

110

-1,46

0,502

111

-1,65

0,258

112

-1,69

0,199

113

-1,71

0,362

1140,80

4,426

116

0,66

2,691

117

0,54

1,398

118

0,07

1,468

119

-0,45

1,057

120

-0,64

0,911

121

-1,00

0,690

122

-1,42

0,497

123

-1,44

0,439

124

-1,44

0,230

125

-1,59

0,252

126

-1,53

0,313

1270,83

3,140

128

0,67

3,010

129

0,43

1,171

130

-0,36

0,966

132

-0,90

0,481

133

-1,03

0,565

134

-1,14

0,529

135

-1,28

0,275

136

-1,37

0,428

137

-1,34

0,339

1380,37

1,027

141

0,02

0,713

142

-0,92

0,333

1460,58

1,387

150

0,02

1,088

152

-0,22

0,569

153

-0,42

0,723

154

-0,76

0,415

1560,35

0,807

158

0,14

0,910

159

0,05

0,828

160

-0,15

0,677

161

-0,42

0,539

162

-0,60

0,344

163

-1,53

0,218

15

Figure A.22: HZP state 3. COBAYA computed radial power distribution vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((COBAYA-mean)/mean)*100%

138

-5,84

0,394

155

2,41

0,929

151

18,43

1,533

149

15,77

2,582

139

13,04

6,143

103

15,74

5,051

89

17,63

3,034

62

14,78

3,034

49

13,34

1,410

16

15,07

0,861

7

-2,25

0,390

5-6,19

0,208

15

-1,59

0,259

6

4,50

0,625

2

9,91

0,558

1

-0,49

0,270

157

-5,40

0,324

148

-10,34

0,250

115

-8,91

0,178

102

-10,38

0,169

75

-12,85

0,228

61

-10,31

0,259

25

-11,45

0,283

147

-11,58

0,313

145

-9,71

0,350

144

-6,94

0,487

143

6,28

1,645

140

-4,75

1,310

131

1,73

0,573

3

-0,77

0,478

46,87

0,895

8

-2,08

0,570

9

-3,54

0,704

10

-7,64

0,369

11

-11,79

0,281

13

-8,44

0,488

12

-8,97

0,300

143,13

0,930

17

-1,85

0,633

18

-8,28

0,433

19

-11,32

0,317

20

-15,09

0,254

21

-16,74

0,233

22

-16,11

0,226

23

-16,34

0,220

2413,55

1,891

26

5,93

1,776

27

-3,03

0,709

28

-8,61

0,860

29

-12,31

0,618

30

-17,19

0,308

31

-19,24

0,371

32

-20,64

0,350

33

-20,84

0,181

34

-16,85

0,308

35

-11,98

0,264

3614,01

2,528

37

4,97

1,496

38

-2,29

0,846

39

-7,96

0,945

40

-13,84

0,690

41

-16,52

0,606

42

-20,11

0,459

43

-23,27

0,328

44

-22,74

0,296

45

-22,63

0,153

46

-19,47

0,184

47

-12,95

0,251

487,26

3,169

50

-0,04

1,186

51

-7,14

0,843

52

-11,46

0,980

53

-14,82

0,874

54

-19,42

0,476

55

-21,81

0,496

56

-24,18

0,346

57

-25,42

0,178

58

-24,12

0,147

59

-18,70

0,279

606,09

2,941

63

1,00

1,817

64

-2,92

1,884

65

-8,60

1,352

66

-13,42

0,829

67

-16,49

0,628

68

-20,51

0,449

69

-24,26

0,330

70

-25,38

0,319

71

-25,02

0,258

72

-23,79

0,156

73

-19,82

0,182

7411,37

5,429

76

5,08

3,334

77

-0,68

2,982

78

-6,66

1,635

79

-9,77

1,475

80

-13,78

0,809

81

-18,65

0,418

82

-21,88

0,403

83

-24,14

0,419

84

-26,34

0,266

85

-24,55

0,274

86

-20,93

0,172

87

-14,50

0,225

886,46

6,910

90

1,97

2,876

91

-1,98

2,352

92

-7,53

1,559

93

-12,36

0,932

94

-15,31

0,700

95

-19,22

0,495

96

-23,01

0,358

97

-24,27

0,340

98

-24,00

0,270

99

-22,55

0,161

100

-18,38

0,192

1017,21

6,354

104

1,27

2,068

105

-4,88

1,175

106

-9,24

1,256

107

-12,60

1,079

108

-17,16

0,573

109

-19,47

0,583

110

-21,88

0,398

111

-23,11

0,201

112

-21,59

0,158

113

-16,13

0,309

11413,82

4,998

116

6,08

2,836

117

0,72

1,400

118

-4,74

1,397

119

-10,67

0,949

120

-13,43

0,793

121

-16,99

0,579

122

-20,11

0,403

123

-19,43

0,359

124

-19,49

0,188

125

-16,04

0,215

126

-9,57

0,287

12714,89

3,578

128

8,22

3,235

129

0,43

1,171

130

-8,37

0,889

132

-13,41

0,420

133

-15,22

0,484

134

-16,52

0,447

135

-16,74

0,232

136

-12,61

0,379

137

-7,73

0,317

1382,19

1,045

141

-3,96

0,685

142

-10,99

0,299

14610,92

1,529

150

1,45

1,103

152

-2,18

0,558

153

-2,43

0,708

154

-3,03

0,405

15614,69

0,922

158

9,65

0,997

159

7,38

0,889

160

5,50

0,715

161

4,31

0,565

162

5,12

0,364

163

-6,19

0,208

15

Figure A.23: HZP state 3. NEM computed radial power distribution vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((NEM-mean)/mean)*100%

139

0,78

0,321

155

0,20

0,585

151

-0,48

0,746

149

-0,31

1,243

139

-0,59

2,630

103

-0,74

2,561

89

-0,60

4,347

62

-0,44

5,421

49

-0,21

2,225

16

-0,38

1,290

7

0,11

0,542

50,17

0,272

15

-0,01

0,346

6

-0,24

0,907

2

-0,50

0,801

1

0,38

0,223

157

0,68

0,291

148

0,90

0,264

115

0,69

0,190

102

0,69

0,197

75

0,89

0,282

61

0,55

0,344

25

0,98

0,266

147

0,91

0,278

145

0,77

0,292

144

0,55

0,373

143

0,03

0,902

140

0,03

0,939

131

-0,05

0,827

3

0,06

0,678

4-0,39

1,376

8

0,14

0,909

9

-0,06

1,084

10

0,38

0,571

11

0,51

0,421

13

0,14

0,728

12

0,12

0,419

140,12

1,552

17

0,15

1,027

18

0,36

0,704

19

0,32

0,506

20

0,43

0,403

21

0,62

0,363

22

0,60

0,338

23

0,78

0,321

24-0,25

3,106

26

-0,16

2,989

27

0,30

1,193

28

0,12

1,381

29

0,08

0,968

30

0,54

0,486

31

0,27

0,574

32

0,43

0,538

33

0,91

0,276

34

0,68

0,435

35

0,76

0,346

36-0,37

4,378

37

0,10

2,674

38

0,24

1,438

39

0,17

1,476

40

0,30

1,066

41

0,20

0,918

42

0,27

0,698

43

0,52

0,507

44

0,57

0,447

45

1,07

0,228

46

1,21

0,259

47

0,90

0,321

48-0,34

5,902

50

0,12

1,973

51

1,06

1,247

52

0,26

1,387

53

0,06

1,235

54

0,35

0,694

55

0,23

0,725

56

0,58

0,512

57

1,61

0,267

58

1,20

0,212

59

0,93

0,373

60-0,27

6,479

63

0,09

2,773

64

-0,03

2,382

65

0,15

1,684

66

0,27

1,065

67

0,23

0,828

68

0,35

0,615

69

0,58

0,468

70

0,70

0,452

71

0,83

0,360

72

1,27

0,215

73

1,23

0,239

74-0,62

4,849

76

-0,12

3,167

77

-0,17

2,989

78

0,05

1,748

79

-0,09

1,630

80

0,16

0,938

81

0,52

0,516

82

0,43

0,518

83

0,41

0,555

84

0,81

0,364

85

0,83

0,366

86

1,15

0,220

87

0,75

0,265

88-0,17

2,771

90

0,04

1,832

91

-0,23

1,940

92

-0,05

1,476

93

0,16

0,958

94

0,20

0,752

95

0,35

0,566

96

0,57

0,438

97

0,59

0,430

98

0,70

0,345

99

1,22

0,203

100

1,24

0,229

101-0,41

2,953

104

-0,02

1,231

105

0,23

0,910

106

0,00

1,106

107

-0,02

1,024

108

0,38

0,593

109

0,29

0,636

110

0,53

0,458

111

0,98

0,241

112

1,07

0,189

113

0,93

0,345

114-0,43

2,213

116

-0,01

1,429

117

0,04

0,839

118

-0,09

1,022

119

0,19

0,801

120

0,28

0,728

121

0,47

0,578

122

0,64

0,430

123

0,57

0,386

124

1,00

0,207

125

1,24

0,231

126

0,93

0,291

127-0,35

1,663

128

-0,29

1,672

129

0,19

0,718

130

0,17

0,707

132

1,29

0,378

133

0,56

0,461

134

0,60

0,443

135

1,03

0,236

136

0,77

0,374

137

0,84

0,303

1380,09

0,644

141

0,39

0,483

142

0,81

0,271

146-0,41

0,834

150

0,08

0,734

152

0,62

0,404

153

0,41

0,535

154

0,37

0,331

156-0,43

0,506

158

-0,11

0,598

159

0,14

0,566

160

0,32

0,484

161

0,38

0,400

162

0,26

0,264

163

0,17

0,272

15

Figure A.24: HZP state 4. DYN3D computed radial power distribution vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((DYN3D-mean)/mean)*100%

140

-0,04

0,318

155

-0,07

0,583

151

0,53

0,754

149

0,41

1,252

139

0,48

2,658

103

0,46

2,592

89

0,59

4,399

62

0,47

5,471

49

0,24

2,235

16

0,36

1,299

7

0,49

0,544

50,61

0,273

15

0,60

0,348

6

0,48

0,914

2

0,47

0,809

1

0,65

0,223

157

0,58

0,291

148

0,52

0,263

115

0,58

0,190

102

0,59

0,197

75

0,49

0,281

61

0,55

0,344

25

-0,05

0,263

147

-0,51

0,274

145

-0,47

0,288

144

-0,42

0,370

143

-0,13

0,900

140

-0,06

0,938

131

0,40

0,830

3

0,40

0,680

40,20

1,384

8

-0,21

0,906

9

0,23

1,087

10

-0,33

0,567

11

-0,08

0,419

13

0,29

0,730

12

0,41

0,420

14-0,29

1,546

17

-0,73

1,018

18

-0,67

0,696

19

-0,54

0,502

20

-0,44

0,399

21

-0,49

0,359

22

-0,54

0,334

23

-0,07

0,319

240,23

3,121

26

0,09

2,996

27

-0,72

1,181

28

-0,21

1,376

29

-0,12

0,967

30

-0,49

0,481

31

-0,01

0,572

32

0,00

0,536

33

-0,52

0,272

34

0,31

0,433

35

0,44

0,345

360,35

4,410

37

-0,46

2,659

38

-0,66

1,426

39

-0,26

1,470

40

-0,01

1,063

41

-0,19

0,914

42

-0,13

0,695

43

0,16

0,505

44

0,01

0,444

45

-0,49

0,224

46

-0,31

0,255

47

0,40

0,319

480,20

5,934

50

-0,65

1,958

51

-0,92

1,222

52

-0,33

1,379

53

0,11

1,235

54

0,07

0,692

55

0,23

0,725

56

-0,11

0,509

57

-0,60

0,261

58

-0,47

0,209

59

0,28

0,371

60-0,11

6,490

63

-0,67

2,752

64

-0,25

2,377

65

-0,34

1,676

66

-0,03

1,062

67

-0,28

0,824

68

-0,22

0,611

69

0,12

0,466

70

-0,10

0,448

71

-0,01

0,357

72

-0,52

0,211

73

-0,08

0,236

740,32

4,895

76

-0,68

3,149

77

-0,21

2,988

78

-0,03

1,746

79

0,10

1,633

80

-0,29

0,934

81

-0,34

0,511

82

-0,19

0,515

83

0,28

0,554

84

0,20

0,362

85

0,03

0,364

86

-0,55

0,216

87

0,37

0,264

88-0,18

2,771

90

-0,65

1,819

91

-0,14

1,942

92

-0,23

1,474

93

0,05

0,957

94

-0,24

0,749

95

-0,19

0,563

96

0,15

0,436

97

-0,04

0,427

98

0,06

0,343

99

-0,52

0,199

100

-0,09

0,226

1010,21

2,972

104

-0,54

1,224

105

-0,56

0,902

106

-0,16

1,104

107

0,21

1,026

108

0,13

0,591

109

0,27

0,636

110

-0,04

0,455

111

-0,36

0,238

112

-0,43

0,186

113

0,31

0,343

1140,37

2,230

116

-0,35

1,424

117

-0,55

0,834

118

-0,08

1,022

119

0,12

0,800

120

-0,13

0,725

121

-0,11

0,574

122

0,20

0,428

123

0,07

0,384

124

-0,37

0,204

125

-0,25

0,228

126

0,44

0,290

1270,34

1,675

128

0,23

1,680

129

-0,61

0,713

130

-0,01

0,706

132

-0,64

0,371

133

0,01

0,459

134

0,05

0,440

135

-0,43

0,233

136

0,34

0,373

137

0,47

0,302

138-0,58

0,640

141

-0,50

0,479

142

-0,53

0,268

1460,36

0,840

150

0,33

0,736

152

-0,25

0,400

153

0,34

0,535

154

0,43

0,332

1560,61

0,511

158

0,59

0,602

159

0,49

0,568

160

0,46

0,485

161

0,53

0,401

162

0,64

0,265

163

0,61

0,273

15

Figure A.25: HZP state 4. PARCS computed radial power distribution vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((PARCS-mean)/mean)*100%

141

0,43

0,319

155

0,10

0,584

151

-0,33

0,747

149

-0,52

1,240

139

-0,51

2,632

103

-0,41

2,570

89

-0,63

4,345

62

-0,71

5,407

49

-0,73

2,213

16

-0,58

1,287

7

-0,19

0,540

50,28

0,272

15

-0,01

0,346

6

-0,38

0,906

2

-0,31

0,803

1

0,47

0,223

157

0,41

0,291

148

0,52

0,263

115

0,64

0,190

102

0,54

0,197

75

0,38

0,281

61

0,20

0,343

25

0,67

0,265

147

0,87

0,277

145

0,73

0,292

144

0,57

0,373

143

-0,13

0,900

140

0,35

0,942

131

-0,41

0,824

3

-0,34

0,675

4-0,35

1,376

8

-0,17

0,906

9

-0,20

1,082

10

0,15

0,570

11

0,20

0,420

13

-0,02

0,727

12

0,22

0,419

14-0,35

1,545

17

0,23

1,028

18

0,29

0,703

19

0,42

0,507

20

0,51

0,403

21

0,64

0,364

22

0,86

0,339

23

0,43

0,320

24-0,78

3,089

26

-0,55

2,977

27

0,07

1,190

28

0,06

1,380

29

0,39

0,971

30

0,63

0,487

31

0,73

0,577

32

0,68

0,539

33

0,87

0,276

34

0,40

0,434

35

0,17

0,344

36-0,76

4,361

37

-0,27

2,664

38

-0,06

1,434

39

0,12

1,475

40

0,20

1,065

41

0,62

0,922

42

0,82

0,702

43

0,72

0,508

44

0,89

0,448

45

0,93

0,227

46

0,70

0,258

47

0,24

0,319

48-0,55

5,890

50

-0,02

1,970

51

-0,04

1,233

52

0,35

1,388

53

0,48

1,240

54

0,61

0,696

55

0,84

0,730

56

1,03

0,515

57

0,89

0,265

58

1,01

0,212

59

0,53

0,372

60-0,43

6,469

63

-0,01

2,770

64

0,05

2,384

65

0,32

1,687

66

0,37

1,066

67

0,80

0,833

68

1,00

0,619

69

0,92

0,469

70

1,15

0,454

71

1,11

0,361

72

1,13

0,214

73

0,72

0,238

74-0,48

4,856

76

0,14

3,175

77

-0,05

2,993

78

0,11

1,749

79

0,37

1,637

80

0,75

0,944

81

0,83

0,517

82

1,14

0,522

83

1,08

0,559

84

1,03

0,365

85

1,05

0,367

86

1,29

0,220

87

0,67

0,265

88-0,27

2,768

90

0,12

1,833

91

0,22

1,949

92

0,47

1,484

93

0,48

0,961

94

0,90

0,757

95

1,08

0,571

96

1,00

0,440

97

1,25

0,433

98

1,20

0,347

99

1,22

0,203

100

0,79

0,228

101-0,34

2,955

104

0,17

1,233

105

0,39

0,911

106

0,56

1,112

107

0,65

1,031

108

0,75

0,595

109

0,97

0,641

110

1,19

0,461

111

1,24

0,242

112

1,23

0,189

113

0,67

0,344

114-0,59

2,209

116

-0,09

1,428

117

0,26

0,841

118

0,45

1,027

119

0,45

0,803

120

0,81

0,732

121

0,95

0,580

122

0,88

0,431

123

1,11

0,388

124

1,10

0,207

125

0,89

0,230

126

0,41

0,290

127-0,60

1,659

128

-0,32

1,671

129

0,34

0,719

130

0,61

0,710

132

0,62

0,376

133

0,86

0,463

134

0,87

0,444

135

1,07

0,236

136

0,61

0,374

137

0,37

0,301

1380,52

0,647

141

0,54

0,484

142

1,11

0,272

146-0,12

0,836

150

0,07

0,734

152

0,37

0,403

153

0,21

0,534

154

0,46

0,332

156-0,06

0,508

158

-0,13

0,598

159

-0,16

0,564

160

-0,10

0,482

161

0,05

0,399

162

0,26

0,264

163

0,28

0,272

15

Figure A.26: HZP state 4. CRONOS computed radial power distribution vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((CRONOS-mean)/mean)*100%

142

-1,17

0,314

155

-0,23

0,582

151

0,28

0,752

149

0,43

1,252

139

0,61

2,662

103

0,70

2,599

89

0,65

4,401

62

0,68

5,482

49

0,69

2,245

16

0,60

1,302

7

-0,41

0,539

5-1,05

0,269

15

-0,59

0,344

6

0,14

0,911

2

0,34

0,808

1

-1,51

0,219

157

-1,67

0,285

148

-1,93

0,257

115

-1,91

0,185

102

-1,82

0,192

75

-1,76

0,275

61

-1,29

0,338

25

-1,60

0,259

147

-1,27

0,272

145

-1,03

0,287

144

-0,69

0,369

143

0,23

0,904

140

-0,32

0,935

131

0,06

0,827

3

-0,13

0,676

40,54

1,388

8

0,23

0,910

9

0,03

1,085

10

-0,20

0,568

11

-0,63

0,416

13

-0,41

0,724

12

-0,74

0,415

140,53

1,559

17

0,35

1,029

18

0,03

0,701

19

-0,20

0,504

20

-0,49

0,399

21

-0,77

0,358

22

-0,92

0,333

23

-1,14

0,315

240,81

3,139

26

0,63

3,012

27

0,36

1,193

28

0,03

1,380

29

-0,35

0,964

30

-0,68

0,481

31

-0,99

0,567

32

-1,12

0,530

33

-1,25

0,270

34

-1,38

0,426

35

-1,37

0,339

360,79

4,429

37

0,63

2,688

38

0,48

1,442

39

-0,03

1,473

40

-0,48

1,058

41

-0,63

0,910

42

-0,96

0,689

43

-1,40

0,497

44

-1,47

0,438

45

-1,51

0,222

46

-1,60

0,252

47

-1,55

0,313

480,69

5,963

50

0,55

1,981

51

-0,10

1,232

52

-0,28

1,379

53

-0,65

1,226

54

-1,03

0,685

55

-1,29

0,714

56

-1,50

0,502

57

-1,90

0,257

58

-1,75

0,206

59

-1,74

0,363

600,81

6,550

63

0,58

2,787

64

0,24

2,389

65

-0,13

1,679

66

-0,61

1,056

67

-0,76

0,820

68

-1,12

0,606

69

-1,62

0,457

70

-1,75

0,441

71

-1,94

0,350

72

-1,89

0,208

73

-1,86

0,232

740,78

4,917

76

0,66

3,191

77

0,43

3,007

78

-0,13

1,745

79

-0,39

1,625

80

-0,62

0,931

81

-1,00

0,508

82

-1,38

0,509

83

-1,76

0,543

84

-2,04

0,354

85

-1,92

0,356

86

-1,89

0,213

87

-1,80

0,258

880,62

2,793

90

0,48

1,840

91

0,14

1,948

92

-0,19

1,474

93

-0,68

0,950

94

-0,86

0,744

95

-1,24

0,557

96

-1,73

0,428

97

-1,80

0,420

98

-1,96

0,336

99

-1,92

0,196

100

-1,94

0,222

1010,54

2,981

104

0,39

1,236

105

-0,06

0,907

106

-0,40

1,101

107

-0,84

1,016

108

-1,26

0,583

109

-1,52

0,625

110

-1,68

0,448

111

-1,86

0,234

112

-1,87

0,183

113

-1,91

0,336

1140,65

2,236

116

0,46

1,436

117

0,25

0,841

118

-0,27

1,020

119

-0,76

0,793

120

-0,96

0,719

121

-1,31

0,567

122

-1,72

0,420

123

-1,75

0,377

124

-1,73

0,201

125

-1,87

0,224

126

-1,78

0,283

1270,60

1,679

128

0,39

1,683

129

0,08

0,718

130

-0,77

0,700

132

-1,28

0,369

133

-1,43

0,452

134

-1,52

0,434

135

-1,67

0,230

136

-1,73

0,365

137

-1,69

0,295

138-0,03

0,644

141

-0,42

0,479

142

-1,39

0,265

1460,17

0,839

150

-0,48

0,730

152

-0,75

0,398

153

-0,96

0,528

154

-1,26

0,326

156-0,12

0,507

158

-0,36

0,597

159

-0,46

0,562

160

-0,68

0,480

161

-0,95

0,395

162

-1,15

0,260

163

-1,05

0,269

15

Figure A. 27: HZP state 4. COBAYA computed radial power distribution vs. mean

of DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((COBAYA-mean)/mean)*100%

143

-12,39

0,279

155

-3,16

0,565

151

14,13

0,855

149

12,55

1,403

139

14,48

3,028

103

17,64

3,036

89

16,27

5,084

62

13,67

6,190

49

16,37

2,594

16

19,01

1,541

7

3,74

0,561

5-1,50

0,267

15

4,34

0,361

6

10,07

1,001

2

15,20

0,927

1

-6,82

0,207

157

-10,92

0,258

148

-13,40

0,227

115

-11,09

0,168

102

-10,14

0,176

75

-11,65

0,247

61

-6,48

0,320

25

-16,93

0,219

147

-17,34

0,227

145

-15,47

0,245

144

-12,52

0,325

143

2,39

0,923

140

-9,30

0,851

131

7,53

0,889

3

5,22

0,713

411,41

1,538

8

2,85

0,933

9

1,78

1,104

10

-2,18

0,557

11

-6,48

0,392

13

-2,86

0,707

12

-3,85

0,402

146,74

1,655

17

2,61

1,052

18

-3,60

0,676

19

-6,42

0,472

20

-10,24

0,360

21

-12,03

0,318

22

-11,63

0,297

23

-12,29

0,280

2415,55

3,597

26

8,75

3,255

27

0,80

1,199

28

-4,43

1,318

29

-8,14

0,889

30

-13,26

0,420

31

-15,47

0,484

32

-17,00

0,444

33

-17,40

0,226

34

-13,58

0,373

35

-8,91

0,313

3614,50

5,031

37

6,66

2,849

38

0,78

1,446

39

-4,45

1,408

40

-10,46

0,952

41

-13,34

0,794

42

-17,14

0,577

43

-20,49

0,401

44

-20,00

0,355

45

-20,02

0,180

46

-17,14

0,212

47

-10,89

0,283

487,84

6,387

50

2,07

2,011

51

-4,85

1,174

52

-9,11

1,257

53

-12,52

1,080

54

-17,23

0,573

55

-19,78

0,581

56

-22,36

0,395

57

-23,90

0,200

58

-22,79

0,162

59

-17,33

0,306

607,00

6,952

63

2,45

2,838

64

-1,74

2,341

65

-7,45

1,556

66

-12,33

0,931

67

-15,34

0,699

68

-19,43

0,493

69

-23,41

0,356

70

-24,83

0,337

71

-24,72

0,269

72

-23,47

0,162

73

-19,48

0,190

7411,70

5,450

76

5,37

3,341

77

-0,50

2,980

78

-6,60

1,632

79

-9,80

1,471

80

-13,91

0,807

81

-18,88

0,416

82

-22,23

0,401

83

-24,59

0,417

84

-26,88

0,264

85

-25,20

0,272

86

-21,71

0,170

87

-15,41

0,223

886,06

2,944

90

0,93

1,848

91

-2,94

1,887

92

-8,70

1,349

93

-13,64

0,826

94

-16,83

0,624

95

-20,89

0,446

96

-24,65

0,328

97

-25,80

0,317

98

-25,49

0,255

99

-24,32

0,151

100

-20,42

0,180

1016,90

3,170

104

-0,61

1,223

105

-7,15

0,842

106

-11,75

0,976

107

-15,24

0,868

108

-19,86

0,473

109

-22,23

0,493

110

-24,60

0,344

111

-25,73

0,177

112

-24,30

0,141

113

-19,17

0,276

11413,50

2,522

116

4,48

1,493

117

-2,35

0,819

118

-8,43

0,936

119

-14,35

0,684

120

-17,10

0,602

121

-20,63

0,456

122

-23,74

0,326

123

-23,20

0,295

124

-23,39

0,157

125

-19,96

0,183

126

-13,46

0,250

12712,88

1,884

128

5,29

1,765

129

-3,61

0,691

130

-13,04

0,614

132

-17,96

0,306

133

-19,82

0,368

134

-21,18

0,347

135

-21,41

0,184

136

-17,42

0,307

137

-12,52

0,262

138-2,69

0,626

141

-9,21

0,437

142

-16,71

0,224

1465,87

0,887

150

-4,68

0,699

152

-8,57

0,367

153

-9,13

0,484

154

-9,58

0,299

1568,67

0,552

158

3,23

0,618

159

0,61

0,568

160

-1,62

0,475

161

-2,96

0,387

162

-2,24

0,257

163

-1,50

0,267

15

Figure A.28: HZP state 4. NEM computed radial power distribution vs. mean of

DYN3D, CRONOS, COBAYA and PARCS results

Assembly #

Relative power

((NEM-mean)/mean)*100%

144

0,995

1,000

155

1,386

1,397

151

1,260

1,273

149

1,634

1,652

139

1,153

1,165

103

0,790

0,798

89

0,702

0,707

62

0,920

0,926

49

0,830

0,833

16

0,593

0,595

7

0,743

0,743

50,536

0,536

15

0,540

0,539

6

0,766

0,767

2

0,568

0,569

1

0,638

0,642

157

0,849

0,853

148

0,785

0,787

115

0,565

0,566

102

0,551

0,551

75

0,748

0,748

61

0,734

0,733

25

0,912

0,914

147

0,885

0,885

145

0,920

0,921

144

1,045

1,048

143

2,097

2,118

140

1,655

1,661

131

0,820

0,822

3

0,811

0,813

40,831

0,833

8

0,812

0,812

9

1,091

1,092

10

0,793

0,790

11

0,777

0,775

13

1,071

1,070

12

0,771

0,771

140,855

0,856

17

0,725

0,722

18

0,727

0,723

19

0,699

0,695

20

0,714

0,710

21

0,711

0,706

22

0,673

0,669

23

0,769

0,767

240,925

0,931

26

1,202

1,206

27

0,781

0,778

28

1,083

1,079

29

0,978

0,972

30

0,712

0,706

31

0,945

0,938

32

1,011

1,005

33

0,691

0,686

34

1,052

1,050

35

0,798

0,799

360,960

0,967

37

0,914

0,914

38

0,803

0,802

39

1,034

1,029

40

1,010

1,003

41

0,991

0,983

42

0,968

0,959

43

0,949

0,940

44

0,935

0,927

45

0,678

0,673

46

0,779

0,776

47

0,804

0,806

481,295

1,301

50

0,813

0,812

51

0,804

0,800

52

1,056

1,049

53

1,166

1,158

54

0,913

0,904

55

1,106

1,096

56

0,959

0,950

57

0,701

0,695

58

0,711

0,707

59

1,072

1,071

600,995

1,000

63

0,876

0,876

64

1,148

1,145

65

1,121

1,116

66

0,992

0,985

67

0,891

0,883

68

0,860

0,851

69

0,902

0,892

70

0,971

0,962

71

0,957

0,950

72

0,722

0,718

73

0,791

0,790

741,063

1,072

76

0,914

0,915

77

1,327

1,329

78

1,192

1,188

79

1,316

1,310

80

0,953

0,947

81

0,737

0,731

82

0,875

0,867

83

1,136

1,127

84

0,979

0,970

85

1,045

1,040

86

0,698

0,694

87

0,799

0,800

881,140

1,148

90

1,020

1,022

91

1,289

1,289

92

1,246

1,242

93

1,102

1,096

94

0,983

0,976

95

0,932

0,925

96

0,959

0,951

97

1,015

1,007

98

0,986

0,980

99

0,730

0,726

100

0,812

0,812

1011,681

1,696

104

1,094

1,098

105

1,022

1,021

106

1,311

1,308

107

1,412

1,407

108

1,071

1,065

109

1,259

1,252

110

1,065

1,059

111

0,762

0,757

112

0,732

0,729

113

1,131

1,133

1141,360

1,376

116

1,370

1,379

117

1,175

1,179

118

1,470

1,473

119

1,359

1,357

120

1,263

1,260

121

1,175

1,170

122

1,114

1,109

123

1,076

1,072

124

0,790

0,788

125

0,857

0,856

126

0,869

0,873

1271,544

1,564

128

2,148

2,169

129

1,326

1,330

130

1,383

1,384

132

0,937

0,935

133

1,171

1,169

134

1,214

1,214

135

0,825

0,823

136

1,207

1,210

137

0,895

0,900

1381,310

1,315

141

1,161

1,165

142

0,823

0,822

1461,637

1,655

150

1,692

1,706

152

1,135

1,140

153

1,432

1,442

154

0,950

0,956

1561,002

1,012

158

1,236

1,248

159

1,230

1,243

160

1,133

1,144

161

0,987

0,995

162

0,691

0,696

163

0,536

0,536

15

Figure A.29: HZP state 5. COBAYA and CRONOS computed radial power

distribution (XS library for Scenario 2)

Assembly #

COBAYA 6N

CRONOS 6N

145

0,927

0,930

155

1,615

1,628

151

1,668

1,686

149

2,295

2,322

139

1,679

1,697

103

1,070

1,081

89

0,815

0,822

62

1,005

1,012

49

0,772

0,774

16

0,531

0,532

7

0,567

0,565

50,396

0,393

15

0,406

0,404

6

0,624

0,623

2

0,475

0,474

1

0,548

0,550

157

0,709

0,710

148

0,609

0,608

115

0,431

0,430

102

0,410

0,408

75

0,553

0,550

61

0,540

0,537

25

0,782

0,783

147

0,833

0,832

145

0,915

0,916

144

1,114

1,117

143

2,795

2,825

140

1,965

1,974

131

0,653

0,652

3

0,630

0,629

40,720

0,721

8

0,679

0,678

9

0,886

0,884

10

0,627

0,623

11

0,589

0,586

13

0,827

0,823

12

0,576

0,573

140,774

0,774

17

0,632

0,629

18

0,614

0,609

19

0,571

0,566

20

0,565

0,560

21

0,549

0,543

22

0,509

0,504

23

0,571

0,567

240,899

0,905

26

1,137

1,140

27

0,715

0,712

28

0,957

0,952

29

0,837

0,830

30

0,587

0,580

31

0,751

0,743

32

0,782

0,774

33

0,521

0,515

34

0,778

0,774

35

0,587

0,584

360,991

0,999

37

0,916

0,917

38

0,777

0,775

39

0,961

0,956

40

0,906

0,898

41

0,855

0,846

42

0,799

0,790

43

0,756

0,747

44

0,725

0,716

45

0,511

0,506

46

0,577

0,572

47

0,593

0,590

481,384

1,392

50

0,847

0,847

51

0,804

0,800

52

1,006

0,999

53

1,062

1,053

54

0,791

0,781

55

0,915

0,904

56

0,767

0,758

57

0,545

0,538

58

0,537

0,532

59

0,797

0,792

601,141

1,148

63

0,983

0,984

64

1,245

1,243

65

1,157

1,152

66

0,971

0,963

67

0,822

0,814

68

0,746

0,738

69

0,748

0,738

70

0,779

0,769

71

0,746

0,737

72

0,549

0,543

73

0,591

0,588

741,329

1,342

76

1,125

1,128

77

1,566

1,570

78

1,332

1,330

79

1,389

1,384

80

0,950

0,944

81

0,686

0,680

82

0,763

0,755

83

0,946

0,935

84

0,787

0,777

85

0,816

0,809

86

0,533

0,528

87

0,603

0,601

881,555

1,568

90

1,356

1,361

91

1,587

1,589

92

1,418

1,415

93

1,176

1,170

94

0,983

0,977

95

0,867

0,860

96

0,839

0,831

97

0,848

0,840

98

0,794

0,786

99

0,571

0,566

100

0,625

0,622

1012,516

2,541

104

1,566

1,574

105

1,284

1,285

106

1,495

1,493

107

1,500

1,496

108

1,060

1,053

109

1,162

1,154

110

0,934

0,927

111

0,639

0,633

112

0,589

0,585

113

0,888

0,886

1142,130

2,157

116

2,529

2,550

117

1,662

1,669

118

1,808

1,813

119

1,531

1,530

120

1,321

1,318

121

1,139

1,133

122

1,018

1,012

123

0,940

0,934

124

0,660

0,656

125

0,692

0,689

126

0,688

0,689

1272,366

2,397

128

3,114

3,147

129

1,740

1,748

130

1,523

1,524

132

0,956

0,954

133

1,113

1,110

134

1,098

1,096

135

0,712

0,709

136

1,003

1,004

137

0,729

0,730

1381,619

1,626

141

1,324

1,328

142

0,738

0,736

1462,049

2,072

150

1,852

1,867

152

1,171

1,176

153

1,396

1,404

154

0,846

0,850

1561,181

1,193

158

1,381

1,394

159

1,305

1,319

160

1,135

1,146

161

0,946

0,953

162

0,638

0,642

163

0,396

0,393

15

Figure A.30: HZP state 6. COBAYA and CRONOS computed radial power

distribution (XS library for Scenario 2)

Assembly #

COBAYA 6N

CRONOS 6N

146

Appendix B: Initial HFP results of Exercise 2

0,29

0,689

28

0,16

0,892

27

0,16

0,889

18

0,32

0,687

13

-0,03

1,168

26

0,12

0,814

1

0,09

0,866

2

-0,10

1,106

3

-0,17

1,093

4

-0,21

1,127

5

0,32

0,860

6

0,02

0,987

7-0,12

1,085

8

-0,08

0,990

9

-0,09

1,040

10

0,07

0,974

11

-0,02

1,162

12-0,04

0,991

14

0,06

0,926

15

-0,02

0,982

16

-0,08

1,275

17-0,08

1,045

19

-0,06

1,011

20

0,04

1,123

21

0,05

0,942

220,00

0,998

23

-0,12

1,282

24

0,02

0,943

25

0,02

0,987

7

Figure B.1: HFP steady state. DYN3D/ATHLET vs. COBAYA3/COBRA3 computed

assembly powers. COBAYA/COBRA used ATHLET calculated core BCs

-2,55

0,669

28

-0,61

0,886

27

-0,84

0,883

18

-2,65

0,668

13

0,37

1,172

26

-2,00

0,794

1

-1,28

0,850

2

0,11

1,106

3

-1,33

1,079

4

0,70

1,139

5

-0,88

0,851

6

-1,16

0,979

70,13

1,084

8

-0,48

0,983

9

0,18

1,044

10

0,10

0,976

11

0,20

1,167

12-0,49

0,983

14

-0,25

0,923

15

0,62

0,989

16

1,92

1,305

170,41

1,049

19

1,09

1,024

20

1,25

1,138

21

0,05

0,943

220,47

1,003

23

2,17

1,314

24

0,06

0,945

25

-1,16

0,979

7

Figure B.2: HFP steady state. PARCS/TRACE vs. COBAYA3/COBRA3 computed

assembly powers. COBAYA/COBRA used TRACE calculated core BCs

Assembly #

Relative power

((PARCS/TRACE – COBAYA/COBRA)/ COBAYA/COBRA.)*100%

Assembly #

Relative power

((DYN3D/ATHLET – COBAYA/COBRA)/ COBAYA/COBRA.)*100%

147

13,07

0,772

28

9,93

0,974

27

9,99

0,971

18

13,02

0,771

13

2,87

1,195

26

-9,26

0,739

1

-8,72

0,789

2

-7,72

1,021

3

-6,45

1,023

4

-3,69

1,084

5

-0,23

0,853

6

5,55

1,039

7-8,06

0,998

8

-6,90

0,920

9

-4,74

0,989

10

-1,43

0,955

11

2,88

1,190

12-6,87

0,920

14

-4,95

0,876

15

-2,01

0,958

16

2,03

1,296

17-4,71

0,994

19

-1,94

0,988

20

1,83

1,137

21

9,32

1,023

22-1,38

0,979

23

1,94

1,303

24

9,25

1,025

25

5,55

1,039

7

Figure B.3: HFP steady state. HEXTRAN/SMABRE vs. COBAYA3/COBRA3

computed assembly powers. COBAYA/COBRA used SMABRE calculated core BCs

10,21

0,753

28

8,25

0,958

27

8,26

0,955

18

10,13

0,751

13

1,72

1,181

26

-8,71

0,747

1

-7,80

0,800

2

-5,83

1,044

3

-5,00

1,042

4

-3,14

1,092

5

-0,18

0,853

6

5,35

1,036

7-6,28

1,020

8

-5,78

0,934

9

-3,65

1,002

10

-1,58

0,955

11

1,79

1,176

12-5,73

0,934

14

-4,33

0,885

15

-1,86

0,961

16

2,00

1,294

17-3,47

1,008

19

-1,96

0,988

20

1,39

1,132

21

7,48

1,005

22-1,42

0,980

23

2,10

1,303

24

7,58

1,007

25

5,35

1,036

7

Figure B.4: HFP steady state. NEM/RELAP5-3D vs. COBAYA3/COBRA3 computed

assembly powers. COBAYA/COBRA used RELAP5-3D calculated core BCs

Assembly #

Relative power

((NEM/RELAP3D – COBAYA/COBRA)/ COBAYA/COBRA.)*100%

Assembly #

Relative power

((HEXTRAN/SMABRE – COBAYA/COBRA)/ COBAYA/COBRA.)*100%

148

600

700

800

900

1000

1100

0 20 40 60 80 100 120 140 160

Do

pp

ler

tem

pe

ratu

re, K

Assembly #

FZD - ATHLET/DYN3D

INRNE/UPM COBAYA/COBRA - ATHLET BC

Figure B.5: HFP steady state. DYN3D/ATHLET vs. COBAYA3/COBRA3 computed

FA Doppler temperatures. COBAYA/COBRA used ATHLET calculated core BCs

17,7

578,7

28

18,9

657,0

27

18,9

655,8

18

17,7

578,0

13

19,1

758,2

26

18,6

627,6

1

18,9

647,3

2

19,2

736,5

3

18,9

731,7

4

19,1

743,9

5

18,9

645,1

6

19,1

692,6

719,2

728,6

8

19,2

694,0

9

19,2

712,4

10

19,2

687,8

11

19,1

756,2

1219,2

694,1

14

19,1

669,8

15

19,2

690,8

16

18,6

795,9

1719,2

714,2

19

19,2

701,6

20

19,2

742,2

21

19,0

675,4

2219,3

696,8

23

18,6

798,4

24

19,0

676,0

25

19,1

692,6

7

Figure B.6: HFP steady state. DYN3D/ATHLET vs. COBAYA3/COBRA3 computed

FA Doppler temperatures. COBAYA/COBRA used ATHLET calculated core BCs

Assembly #

Doppler temperature

((DYN3D/ATHLET – COBAYA/COBRA/ COBAYA/COBRA.)*100%

149

600

700

800

900

1000

1100

0 20 40 60 80 100 120 140 160

Do

pp

ler

tem

pe

ratu

re, K

Assembly #

VTT - HEXTRAN/SMABRE

INRNE/UPM COBAYA/COBRA - SMABRE BC

Figure B.7: HFP state. HEXTRAN/SMABRE vs. COBAYA3/COBRA3 computed

Doppler temperatures. COBAYA/COBRA used SMABRE calculated core BCs

16,9

573,2

28

5,2

579,4

27

4,1

572,3

18

17,0

573,2

13

-12,9

552,7

26

-3,0

513,0

1

-4,9

517,1

2

-6,1

579,4

3

-5,4

580,5

4

-4,3

596,4

5

-1,2

534,7

6

0,7

584,2

7-16,0

512,6

8

7,4

624,3

9

-5,7

562,0

10

-0,8

571,0

11

-12,7

552,6

12-11,0

517,1

14

-7,9

517,1

15

-0,8

573,2

16

-17,3

552,7

17-4,9

568,4

19

6,6

625,7

20

-17,3

513,0

21

0,1

566,3

2211,9

652,0

23

-16,1

562,8

24

-4,5

540,9

25

0,7

584,2

7

Figure B.8: HFP state. HEXTRAN/SMABRE vs. COBAYA3/COBRA3 computed

FA Doppler temperatures. COBAYA/COBRA used SMABRE calculated core BCs

Assembly #

Doppler temperature

((HEXTRAN/SMABRE – COBAYA/COBRA / COBAYA/COBRA.)*100%

150

600

700

800

900

1000

1100

0 20 40 60 80 100 120 140 160

Do

pp

ler

tem

pe

ratu

re, K

Assembly #

UNIPI - RELAP5-3D

INRNE/UPM COBAYA/COBRA - RELAP5-3D BC

Figure B.9: HFP steady state. NEM/RELAP3D vs. COBAYA3/COBRA3 computed

FA Doppler temperatures. COBAYA/COBRA used RELAP3D calculated core BCs

2,3

503,2

28

3,0

568,5

27

2,9

567,5

18

2,3

502,7

13

1,1

642,5

26

-5,9

500,4

1

-5,4

517,1

2

-3,9

595,9

3

-3,3

596,7

4

-2,2

611,9

5

-1,6

534,2

6

2,1

593,8

7-4,2

587,6

8

-4,1

559,7

9

-2,8

582,0

10

-1,9

566,6

11

-1,4

625,3

12-4,1

559,9

14

-3,5

544,1

15

-2,0

568,5

16

1,9

682,2

17-2,7

583,9

19

-1,9

577,3

20

0,6

625,3

21

3,0

583,9

22-1,7

574,7

23

2,0

685,0

24

3,0

584,5

25

2,1

593,8

7

Figure B.10: HFP steady state. NEM/RELAP3D vs. COBAYA3/COBRA3 computed

FA Doppler temperature. COBAYA/COBRA used RELAP3D calculated core BCs

Assembly #

Doppler temperature

((NEM/RELAP3D – COBAYA/COBRA / COBAYA/COBRA.)*100%

151

559

560

561

562

563

564

565

0 20 40 60 80 100 120 140 160

Te

mp

era

ture

, K

Assemblies

FZD - DYN3D/ATHLETUNIPI - RELAP5-3DVTT - HEXTRAN/SMABREFZK - TRACE/PARCSINRNE/UPM - COBAYA/COBRA

Figure B.11: Assembly-by-assembly core inlet temperature in the initial HFP state

95

97

99

101

103

105

107

109

111

113

115

0 20 40 60 80 100 120 140 160

Ma

ss

flo

w r

ate

, k

g/s

Assemblies

FZD - DYN3D/ATHLET

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZK - TRACE/PARCS

INRNE/UPM - COBAYA/COBRA

Figure B.12: Assembly-by-assembly core inlet mass flow rate in the initial HFP state

152

600

700

800

900

1000

1100

0 20 40 60 80 100 120 140 160

Do

pp

ler

tem

pe

ratu

re, K

Assemblies

FZD - DYN3D/ATHLET

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZK - TRACE/PARCS

INRNE/UPM - COBAYA/COBRA

Figure B.13: Assembly-by-assembly Doppler temperature in the initial HFP state

153

Appendix C: Exercise 2, Scenario 1 results

82,5

84,5

86,5

88,5

90,5

92,5

94,5

96,5

0 20 40 60 80 100 120 140 160

Ma

ss

flo

w r

ate

, k

g/s

Assemblies

FZD - DYN3D/ATHLET

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZK - TRACE/PARCS

Figure C.1: Scenario 1: Assembly-by-assembly core inlet mass flow rates at time of

maximum overcooling (166s)

510

520

530

540

550

560

570

0 20 40 60 80 100 120 140 160

Do

pp

ler

tem

pe

ratu

re, K

Assemblies

FZD - DYN3D/ATHLET

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZK - TRACE/PARCS

Figure C.2: Scenario 1: Assembly-by-assembly Doppler temperatures at time of

maximum overcooling (166s)

154

542,5

543,5

544,5

545,5

546,5

547,5

548,5

0 20 40 60 80 100 120 140 160

Te

mp

era

ture

, K

Assemblies

FZD - DYN3D/ATHLET

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZK - TRACE/PARCS

Figure C.3: Scenario 1: Assembly-by-assembly core inlet temperatures at 600s

155

-40,4

155

-40,5

151

-40,5

149

-42,1

139

-51,3

103

-51,3

89

-51,3

62

-51,3

49

-49,9

16

-49,9

7

-31,9

5

-31,7

15

-31,7

6

-37,1

2

-44,8

1

-40,3

157

-40,3

148

-33,0

115

-32,6

102

-31,8

75

-31,7

61

-31,7

25

-40,3

147

-40,5

145

-40,5

144

-40,5

143

-42,1

140

-40,6

131

-32,8

3

-32,2

4

-44,8

8

-37,6

9

-32,8

10

-32,3

11

-31,7

13

-31,9

12

-31,7

14

-49,8

17

-44,7

18

-38,2

19

-33,2

20

-31,9

21

-31,8

22

-31,8

23

-31,7

24

-51,1

26

-49,8

27

-49,7

28

-44,1

29

-37,3

30

-32,8

31

-31,8

32

-31,8

33

-31,7

34

-31,7

35

-31,7

36

-51,1

37

-51,1

38

-50,3

39

-49,9

40

-45,7

41

-34,1

42

-32,2

43

-31,8

44

-31,7

45

-31,7

46

-31,7

47

-31,7

48

-51,1

50

-51,1

51

-51,0

52

-50,1

53

-42,8

54

-33,1

55

-31,8

56

-31,7

57

-31,7

58

-31,7

59

-31,7

60

-51,3

63

-51,3

64

-51,2

65

-51,1

66

-50,1

67

-36,2

68

-31,8

69

-31,7

70

-31,8

71

-31,8

72

-31,8

73

-33,0

74

-51,3

76

-51,3

77

-51,3

78

-51,3

79

-51,3

80

-49,8

81

-38,8

82

-37,4

83

-32,8

84

-32,6

85

-32,5

86

-32,6

87

-32,5

88

-51,3

90

-47,2

91

-51,0

92

-50,5

93

-48,7

94

-46,0

95

-40,4

96

-39,4

97

-36,8

98

-35,3

99

-33,1

100

-39,1

101

-51,3

104

-51,2

105

-50,6

106

-45,2

107

-41,4

108

-40,5

109

-40,4

110

-39,8

111

-39,0

112

-39,1

113

-39,1

114

-51,2

116

-51,2

117

-47,2

118

-42,2

119

-41,1

120

-40,5

121

-40,5

122

-40,4

123

-40,3

124

-39,8

125

-39,1

126

-39,2

127

-42,0

128

-42,1

129

-42,2

130

-40,5

132

-40,5

133

-40,5

134

-40,4

135

-40,3

136

-40,3

137

-39,2

138

-40,5

141

-40,5

142

-40,4

146

-40,5

150

-40,5

152

-40,5

153

-40,5

154

-40,4

156

-40,5

158

-40,5

159

-40,5

160

-40,5

161

-40,5

162

-40,4

163

Figure C.4: Scenario 1, RELAP3D/NEM results at time of max overcooling (166s):

Core inlet temperature deviations from the initial HFP state

156

Appendix D: Exercise 2, Scenario 2 results

100,5

102,5

104,5

106,5

108,5

110,5

112,5

114,5

116,5

118,5

120,5

0 20 40 60 80 100 120 140 160

Ma

ss

flo

w r

ate

, k

g/s

Assembly #

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

Figure D.1: Scenario 2: Assembly-by-assembly core inlet mass flow rates at time of

maximum overcooling (69s)

450

550

650

750

850

950

1050

1150

1250

0 20 40 60 80 100 120 140 160

Do

pp

ler

tem

pe

ratu

re, K

Assembly #

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

INRNE/UPM - COBAYA/COBRA

Figure D.2: Scenario 2: Assembly-by-assembly Doppler temperatures at time of

maximum overcooling (69s)

157

740

745

750

755

760

765

770

0 20 40 60 80 100 120 140 160

Mo

de

rato

r d

en

sit

y, k

g/m

3

Assembly #

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

INRNE/UPM - COBAYA/COBRA

Figure D.3: Scenario 2: Assembly-by-assembly core outlet coolant density at 200s

540

590

640

690

740

0 20 40 60 80 100 120 140 160

Do

pp

ler

tem

pe

ratu

re, K

Assembly #

UNIPI - RELAP5-3D

VTT - HEXTRAN/SMABRE

FZD - ATHLET/DYN3D

INRNE/UPM - COBAYA/COBRA

Figure D.4: Scenario 2: Assembly-by-assembly Doppler temperatures at 200s

158

0,8

14,223

155

1,3

23,929

151

1,6

28,947

149

2,0

37,343

139

1,6

28,617

103

1,0

18,724

89

0,6

10,167

62

0,6

11,246

49

0,4

7,456

16

0,3

5,138

7

0,2

4,517

50,2

2,968

15

0,2

3,251

6

0,3

5,132

2

0,2

4,113

1

0,4

7,190

157

0,4

8,088

148

0,3

5,558

115

0,2

3,895

102

0,2

3,273

75

0,2

4,129

61

0,2

3,884

25

0,5

8,938

147

0,6

11,378

145

0,7

12,939

144

0,8

15,509

143

2,3

41,590

140

1,4

26,645

131

0,3

5,303

3

0,3

5,091

40,3

6,021

8

0,3

5,231

9

0,4

6,655

10

0,3

4,730

11

0,2

4,248

13

0,3

6,176

12

0,2

4,108

140,4

6,653

17

0,3

4,860

18

0,2

4,423

19

0,2

4,129

20

0,3

4,756

21

0,2

3,824

22

0,2

3,387

23

0,2

3,828

240,5

8,980

26

0,6

10,144

27

0,3

5,808

28

0,4

7,002

29

0,3

5,830

30

0,2

4,060

31

0,3

5,035

32

0,3

5,032

33

0,2

3,335

34

0,3

5,160

35

0,2

4,213

360,6

10,420

37

0,5

8,599

38

0,4

6,755

39

0,4

7,640

40

0,4

6,559

41

0,3

5,859

42

0,3

5,272

43

0,3

4,852

44

0,3

4,662

45

0,2

3,350

46

0,2

3,853

47

0,2

4,312

480,7

13,784

50

0,4

7,951

51

0,4

7,840

52

0,4

8,062

53

0,4

7,817

54

0,3

5,578

55

0,3

6,063

56

0,3

5,027

57

0,2

4,098

58

0,2

3,579

59

0,3

5,430

600,7

12,497

63

0,5

9,860

64

0,6

11,712

65

0,6

10,245

66

0,4

8,222

67

0,4

6,578

68

0,3

5,583

69

0,3

5,245

70

0,3

5,307

71

0,3

5,052

72

0,2

3,725

73

0,2

4,202

740,9

17,248

76

0,7

13,080

77

0,9

16,370

78

0,7

13,113

79

0,7

13,114

80

0,5

8,913

81

0,4

7,104

82

0,3

6,207

83

0,4

7,004

84

0,3

5,619

85

0,3

5,777

86

0,2

3,892

87

0,3

4,765

881,3

23,498

90

1,0

18,340

91

1,0

19,342

92

0,9

16,329

93

0,7

13,656

94

0,6

11,029

95

0,5

8,643

96

0,4

7,229

97

0,4

6,625

98

0,3

5,978

99

0,2

4,358

100

0,3

5,049

1012,1

37,804

104

1,2

21,713

105

0,9

16,741

106

1,0

18,575

107

1,0

18,397

108

0,7

12,130

109

0,7

12,188

110

0,5

8,447

111

0,3

5,422

112

0,3

4,880

113

0,4

7,545

1141,9

35,052

116

2,0

37,080

117

1,3

23,328

118

1,3

24,038

119

1,1

20,027

120

0,9

16,136

121

0,7

13,392

122

0,6

11,333

123

0,5

9,101

124

0,3

6,064

125

0,3

6,325

126

0,4

6,617

1272,1

38,102

128

2,5

45,353

129

1,3

24,477

130

1,1

19,731

132

0,7

13,769

133

0,8

13,985

134

0,7

12,968

135

0,4

7,424

136

0,5

10,066

137

0,4

7,594

1381,3

23,232

141

1,0

18,214

142

0,5

9,513

1461,8

32,573

150

1,5

27,331

152

1,0

17,768

153

1,2

21,507

154

0,7

12,426

1561,1

19,863

158

1,2

22,566

159

1,2

21,595

160

1,0

19,288

161

0,9

16,365

162

0,6

11,281

163

0,16

2,968

15

Figure D.5: Scenario2, stuck rods in #117&#140. HEXTRAN/SMABRE computed

radial power distribution (abs. powers) and ratio of current assembly power/HFP

at 69 s

Assembly #

Absolute power, MW

Ratio of current assembly power to HFP

159

0,5

10,051

155

1,5

28,681

151

1,4

28,234

149

1,9

37,295

139

1,5

29,708

103

1,0

19,964

89

0,7

13,889

62

0,7

12,925

49

0,4

6,855

16

0,2

4,509

7

0,2

3,778

50,1

2,570

15

0,1

2,687

6

0,2

4,599

2

0,2

3,661

1

0,3

5,149

157

0,3

6,247

148

0,2

4,714

115

0,2

3,251

102

0,1

2,821

75

0,2

3,681

61

0,2

3,474

25

0,4

7,160

147

0,5

9,098

145

0,6

11,598

144

0,9

17,896

143

2,3

44,402

140

1,6

30,547

131

0,2

4,647

3

0,2

4,327

40,3

5,759

8

0,3

5,141

9

0,3

6,398

10

0,2

4,369

11

0,2

3,863

13

0,3

5,506

12

0,2

3,737

140,3

6,538

17

0,3

5,033

18

0,2

4,641

19

0,2

4,130

20

0,2

3,867

21

0,2

3,624

22

0,2

3,294

23

0,2

3,667

240,4

8,675

26

0,5

10,260

27

0,3

6,122

28

0,4

7,584

29

0,3

6,309

30

0,2

4,239

31

0,3

5,040

32

0,3

5,077

33

0,2

3,373

34

0,3

4,980

35

0,2

3,789

360,6

10,868

37

0,5

9,355

38

0,4

7,373

39

0,4

8,368

40

0,4

7,350

41

0,3

6,551

42

0,3

5,681

43

0,3

5,075

44

0,2

4,748

45

0,2

3,342

46

0,2

3,740

47

0,2

3,873

480,8

16,284

50

0,5

9,442

51

0,4

8,297

52

0,5

9,296

53

0,5

9,091

54

0,3

6,302

55

0,3

6,613

56

0,3

5,263

57

0,2

3,711

58

0,2

3,549

59

0,3

5,223

600,9

18,063

63

0,7

14,172

64

0,8

14,748

65

0,7

12,708

66

0,5

9,996

67

0,4

7,674

68

0,3

6,164

69

0,3

5,611

70

0,3

5,467

71

0,3

5,072

72

0,2

3,709

73

0,2

4,002

741,2

23,607

76

0,9

18,239

77

1,2

23,346

78

1,0

18,785

79

1,0

18,610

80

0,6

11,904

81

0,4

7,196

82

0,3

6,537

83

0,4

7,215

84

0,3

5,627

85

0,3

5,698

86

0,2

3,742

87

0,2

4,274

881,4

27,379

90

1,1

22,181

91

1,2

24,173

92

1,1

20,663

93

0,9

16,926

94

0,7

12,933

95

0,5

8,894

96

0,4

7,399

97

0,3

6,707

98

0,3

5,954

99

0,2

4,267

100

0,2

4,667

1012,1

41,624

104

1,3

25,010

105

1,0

19,962

106

1,1

22,192

107

1,1

21,662

108

0,7

13,914

109

0,6

11,513

110

0,4

8,208

111

0,3

5,286

112

0,2

4,665

113

0,4

6,877

1141,8

35,591

116

2,1

40,040

117

1,3

26,279

118

1,4

27,705

119

1,2

23,201

120

1,0

18,798

121

0,7

12,715

122

0,5

9,796

123

0,4

8,320

124

0,3

5,552

125

0,3

5,637

126

0,3

5,516

1272,0

38,264

128

2,5

48,542

129

1,4

27,548

130

1,2

23,449

132

0,7

13,732

133

0,6

12,032

134

0,5

10,547

135

0,3

6,430

136

0,4

8,569

137

0,3

6,121

1381,3

26,187

141

1,1

22,052

142

0,4

7,252

1461,8

34,901

150

1,7

32,453

152

1,0

18,701

153

0,9

16,805

154

0,4

8,420

1561,1

21,959

158

1,3

25,653

159

1,2

22,986

160

0,8

15,333

161

0,6

11,102

162

0,4

6,942

163

0,13

2,570

15

Figure D.6: Scenario2, #117&#140. DYN3D/ATHLET computed radial power

distribution (abs. powers) and ratio of current assembly power/HFP at 69 s

Assembly #

Absolute power, MW

Ratio of current assembly power to HFP

160

Appendix E: Exercise 3, Scenario 1 results

Figure E.1: Total break flow rate

Figure E.2: Integrated total break flow rate

161

Figure E.3: Integrated liquid break flow rate

Figure E.4: BRU-SN (steam dump to house needs) total flow rate

162

Figure E.5: BRU-K (steam dump to condenser) total flow rate

Figure E.6: Integrated BRU-SN (steam dump to house needs) total flow rate

163

Figure E.7: Integrated BRU-K (steam dump to condenser) total flow rate

Figure E.8: Average pressure above the core

164

Figure E.9: Hot leg 1 pressure

Figure E.10: Cold leg 1 pressure

165

Figure E.11: Hot leg 2 pressure

Figure E.12: Cold leg 2 pressure

166

Figure E.13: Hot leg 3 pressure

Figure E.14: Cold leg 3 pressure

167

Figure E.15: Hot leg 4 pressure

Figure E.16: Cold leg 4 pressure

168

Figure E.17: SG 1 pressure

Figure E.18: SG 2 pressure

169

Figure E.19: SG3 pressure

Figure E.20: SG4 pressure, MPa

170

Figure E.21: Main steam header pressure

Figure E.22: Average core coolant temperature

171

Figure E.23: Hot leg 1 temperature

Figure E.24: Hot leg 2 temperature

172

Figure E.25: Hot leg 3 temperature

Figure E.26: Hot leg 4 temperature

173

Figure E.27: Cold leg 1 temperature

Figure E.28: Cold leg 2 temperature

174

Figure E.29: Cold leg 3 temperature

Figure E.30: Cold leg 4 temperature

175

Figure E.31: Core average fuel Doppler temperature

Figure E.32: Maximum nodal fuel temperature

176

Figure E.33: SG1 mass of fluid

Figure E.34: SG2 mass of fluid

177

Figure E.35: SG3 mass of fluid

Figure E.36: SG4 mass of fluid

178

Figure E.37: Fission power

Figure E.38: Total core power

179

Figure E.39: Core average coolant density

Figure E.40: SG1 exchanged power

180

Figure E.41: SG2 exchanged power

Figure E.42: SG3 exchanged power

181

Figure E.43: SG 4 exchanged power

182

Appendix F: Description of computer codes used for analysis of

the VVER-1000 MSLB benchmark

CFD CODES

CFX 10 (FZD)

ANSYS CFX software (CFX10 Manuals, 2006) delivers powerful computational fluid

dynamics (CFD) technology for simulations of all levels of complexity.

As one of the many computer-aided engineering (CAE) tools available within the

194HANSYS Workbench platform, ANSYS CFX takes advantage of data and information

common to many simulations. This begins with common geometry: Users can link to

existing native computer-aided design (CAD) packages as well as create and/or modify

CAD models in an intuitive solid modeling environment. Complementing the common

geometry model is a suite of meshing tools, designed to ensure easy generation of the

most appropriate mesh for the given application. ANSYS CFX tools then guide the user

through the setup of operating conditions, selection of materials and definition of models.

The ANSYS CFX solver uses the most modern solution technology with a coupled

algebraic multi-grid solver and extremely efficient parallelization to help ensure that

solutions are ready for analysis quickly and reliably. Solution analysis with the ANSYS

CFX post-processor then gives users the power to extract any desired quantitative data

from the solution; it also provides a comprehensive set of flow visualization options.

Animations of flow simulations can be easily generated and 3D images are directly

created and shared with any colleagues or clients using the 195Hfreely distributable 3D viewer

from ANSYS CFX.

The next-generation physics pre-processor, ANSYS CFX-Pre, allows multiple meshes

to be imported, allowing each section of complex geometries to use the most appropriate

mesh. ANSYS CFX includes the following features:

An advanced coupled solver which is both reliable and robust

Full integration of problem definition, analysis and results presentation

An intuitive and interactive setup process, using menus and advanced graphics

ANSYS CFX is capable of modeling:

Steady-state and transient flows

Laminar and turbulent flows

Subsonic, transonic and supersonic flows

Heat transfer and thermal radiation

Buoyancy

Non-Newtonian flows

Transport of non-reacting scalar components

Multiphase flows

Combustion

Flows in multiple frames of reference

Particle tracking

183

ANSYS Interaction

The coupling of CFX and ANSYS software continues to improve in both user

workflow and simulation capabilities. This release introduces a full two-way Fluid

Structure Interaction capability coupling the ANSYS and CFX solvers, and the ability to

run ANSYS CFX within the Workbench engineering simulation environment is extended

to a number of Unix platforms.

Transient Analysis

Analysis of fully transient situations continues to be a growing trend in CFD

simulation, and ANSYS CFX introduces both new transient physical models (such as

Transient Particle Tracking and Kinetic Theory for Fluidized Beds), as well as algorithmic

and transient efficiency improvements (Adaptive Time-stepping and Extrapolated Initial

Solutions).

Some of the new features of ANSYS CFX 10 are described below:

ANSYS FSI Coupling

ANSYS CFX now has full two-way transient coupling with the ANSYS multi-physics

solver to allow the simulation of Fluid-Structure Interaction. The ANSYS and ANSYS

CFX solvers run simultaneously with Force, Displacement and/or Thermal data shared

implicitly at each time-step. The communication between the solvers uses a native

ANSYS CFX IPC library, and the solvers can be run on the same or different computers,

in serial or parallel.

Porosity

To complement the various momentum porous loss models available in CFX-5.7 and

earlier, ANSYS CFX has added a true volume porosity model. This porous domain model

uses a unique 'double-node' approach at the porous interface, to ensure sharp capture of

the pressure and velocity discontinuities that occur at that location. The interface

treatment conserves total pressure and supports significantly greater pressure losses than

the previous sub-domain based models in previous versions of ANSYS CFX.

Turbulence Modeling

A significant capability in ANSYS CFX is the first-ever commercial release of a

predictive laminar to turbulent transition capability, the Menter-Langtry model. The

transition model in ANSYS CFX has been highly validated and can be used to determine

the location and extent of transition in both aerospace and turbo machinery applications.

The model requires no special provisions for geometry or grid topology. For expert users,

ANSYS CFX also provides user control of turbulent wall functions, including heat

transfer.

Transient Improvements

Computing resources needed for a transient calculation can be optimized through the

use of time step Adaption & Extrapolated Initial Guess for transient calculations in

ANSYS CFX. Time step Adaption allows the solver to automatically adjust the physical

time step in a transient solution based on user-specified criteria including target number of

coefficient loops or Courant Number. The Extrapolated Initial Guess extends the solution

from previous time steps as the initial guess for the current time step, providing a better

184

starting condition and minimizing the required number of coefficient loops to reach time

step convergence. Key numerical transient improvements have also been made, which

makes it possible to achieve 2nd order transient calculation with one iteration per time

step, for time steps in the explicit range.

DESCRIPTION OF SYSTEM CODES

DYN3D/ATHLET (FZD)

DYN3D (Grundmann, 1999), (Grundmann and Holstein, 1999) is a three-dimensional

core model for dynamic and depletion calculations in LWR cores with quadratic or

hexagonal fuel assembly geometry. The neutron-kinetic model is based on the solution of

the three-dimensional, two-group neutron diffusion equations by nodal expansion

methods. Different methods are used for quadratic and hexagonal fuel assembly geometry.

In the case of Cartesian geometry, the three-dimensional diffusion equation of each node

is transformed into three one-dimensional equations for 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 second order and exponential functions are 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 one-

dimensional equation in the axial direction. The two equations are coupled by the

transverse leakage terms that 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 + corner-point values (HEXNEM2) of flux and

current are used for the approximate solution of the diffusion equation.

The thermal-hydraulic system code ATHLET (Teschendorf et al, 1996) was

developed by the Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) for the analysis

of anticipated and abnormal plant transients, small and intermediate leaks as well as large

breaks in light water reactors. It is intended to cover the whole spectrum of design basis

and beyond design basis accidents (without core degradation) for PWRs and BWRs with

only one code. The code features advanced thermal-hydraulics, modular code architecture,

separation between physical models and numerical methods, pre- and post-processing

tools and portability.

The code development is accompanied by a systematic and comprehensive validation

program. A large number of integral experiments and separate effect tests, including the

major International Standard Problems, have been calculated by GRS and by independent

organizations. The range of applicability has been extended to the Russian reactor types

VVER and RBMK in co-operation with foreign partner organizations.

ATHLET is being applied by numerous institutions in Germany and abroad; its

development and validation are sponsored by the German Federal Ministry of Economics

and Labour (BMWA).

185

BIPR8/ATHLET (GRS/KI)

The computer code for 3D neutron kinetics BIPR8-KN (Lisorkin et al, 2006) has been

developed in the Department of Physics in the RRC KI. A two-group, 3D hexagonal

coarse-mesh nodal approximation for neutron flux is applied. The static branch of this

code permits to simulate VVER core burn-up and refueling, including the calculation of

the multiplication factor and reactivity coefficients for different core states. BIPR-8KN

uses its native nuclear data libraries, prepared by a Russian code. The cross-section

libraries include the burn-up dependence and instantaneous dependencies of TH

parameters, as well as Xe and Sm poisoning corrections. Simplified cross-section

corrections are used instead of ADF. The kinetic branch of BIPR-8KN calculates the

transient core power and 3D neutron flux distribution, taking into account two prompt

neutron energy groups and six delayed neutron groups and feedback effects.

The thermal-hydraulic system code ATHLET (Teschendorf et al, 1996) is being

developed by GRS for the analysis of the whole spectrum of leaks and transients in PWR

and BWR. The code is applicable to western LWR designs as well as for Russian VVER

and RBMK reactors. The main code features are the advanced thermal hydraulics, the

modular code architecture, especially the separation between physical models and

numerical methods, the pre- and post-processing tools, and the portability to the prevalent

computer platforms.

The code is based on a five-equation model (mixture momentum equation with drift)

as well as on a six-equation two-fluid model, additionally enabling the simulation of

several non-condensable gases, dissolved nitrogen and boron transport. The piping

network of the reactor coolant system is modeled by connecting basic fluid dynamic

elements, called thermo-fluid objects, allowing for cross flow between parallel channels.

HEXTRAN/SMABRE (VTT)

The 3D core N/TH solution method of the HEXTRAN code (Kyrki-Rajamaki, R., 1991),

is based on coupling and extension of the 3D steady-state hexagonal core simulator

HEXBU-3D (Kaloinen, 1981) and a 1D thermal-hydraulics code.

HEXTRAN solves the two-group neutron diffusion equations by a nodal expansion

method in x-y-z geometry. A basic feature of the method is decoupling of the two-group

equations into separate equations for two spatial modes and reconstruction of group fluxes

from characteristic solutions to these equations. The two solutions are called the

fundamental or asymptotic mode (with a smooth behavior within a homogenized node),

and the transient mode, which deviates significantly from zero only near material

discontinuities. The nodal equations are solved with a two-level iteration scheme where

only one unknown per node - the average of fundamental mode, is determined in inner

iterations. The nodal flux shapes are improved in outer iterations by recalculation of the

coupling coefficients.

The thermal-hydraulic calculation of the reactor core is performed in parallel one-

dimensional hydraulic channels, each channel usually coupled with one fuel assembly.

The channels can be further divided into axial sub-regions. Parallel to the heated channels,

several unheated bypass channels can be modeled. Channel hydraulics is based on

conservation equations for steam and water mass, total enthalpy and total momentum, and

on a selection of optional correlations describing, for example, slip, non-equilibrium

evaporation and condensation and one- and two-phase friction. The phase velocities are

related by an algebraic slip ratio or by the drift flux formalism. The thermal-hydraulic

solution methods are the same as in the one-dimensional code TRAB. During the

186

hydraulic iterations, a one-dimensional heat transfer calculation is made for an average

fuel rod of each assembly. The radial heat conduction of the fuel rod is solved according

to Fourier‟s law. The fission power is divided into prompt and delayed power parts and a

fraction of the power can be dissipated directly in the coolant. Decay heat is included in

the thermal power.

Advanced time integration methods are applied in the dynamic calculation. The

numerical technique can vary between the standard fully implicit theta method and the

central-difference theta method both in the heat conduction calculation for fuel rods and in

the solution of thermal-hydraulic conservation equations for cooling channels.

For the analysis of core-system transients, HEXTRAN is coupled with the SMABRE

system code.

SMABRE (Miettinen, 1985) is a 1D system thermal-hydraulics code, developed by

VTT. The code is able to model 3D thermal hydraulic effects using parallel channels

(multi-1D mode) combined with the turbulent mixing mode. SMABRE contains a five-

equation two-phase thermal hydraulic model, using the drift flux model. The numerical

solution method used in SMABRE is a predictor-corrector type non-iterative solution.

RELAP3D (UNIPI)

NESTLE, the multi-dimensional neutron kinetics model in RELAP5-3D (INL, 2001)

allows the user to model reactor transients where the spatial distribution of the neutron

flux changes with time. The neutron kinetics model uses the Nodal Expansion Method

(NEM) to solve the few-group neutron diffusion equations. The number of energy groups

can be two or four. Up scattering is explicitly taken into account, if desired.

Core geometries modeled include Cartesian and hexagonal. Three-, two- and one-

dimensional models can be utilized. Various core symmetry options are available,

including quarter, half and full core for Cartesian geometry and one-sixth, one-third and

full core for hexagonal geometry. The boundary conditions can be zero flux, non-re-

entrant current, reflective and cyclic. The NEM method uses quartic or quadratic

polynomial expansions for the transverse integrated fluxes in Cartesian or hexagonal

geometries, respectively. Transverse leakage terms are represented by a quadratic

polynomial or constant for Cartesian or hexagonal geometry, respectively. Assembly

discontinuity factors (ADF) are utilized to correct for homogenization errors. The number

of delayed neutron precursor groups is user-specified. The neutron kinetics subroutines

require input regarding the neutron cross-sections in the computational nodes of the

kinetics mesh. A neutron cross-section model is implemented which allows the

instantaneous dependencies of the neutron cross-sections to be parameterized as functions

of heat structure temperatures, fluid void fraction or fluid density, poison concentration

and fluid temperatures.

A flexible coupling scheme between the neutron kinetics mesh and the thermal-

hydraulics mesh is used to minimize the input data needed to specify the neutron cross-

sections in terms of thermal-hydraulic variables. A control rod model has been

implemented so that the effect of the initial position and subsequent movement of the

control rods during transients may be taken into account in the computation of the neutron

cross-sections.

RELAP5-3D (INL, 2001) has a 3D reactor vessel component, which allows coarse-3D

simulation of the vessel thermal hydraulics, coupled to the 3D neutron kinetics.

187

PARCS/TRACE (FZK)

PARCS: The Purdue Advanced Reactor Core Simulator (Downar et al, 2004) is a 3D

neutronic code, which solves the steady state and transient multi-group diffusion and SP3

transport equations in orthogonal and non-orthogonal geometries. The highlights of

PARCS features can be summarized as follows (Downar, 2004):

PARCS has the ability to perform eigenvalue calculations, transient (kinetic)

calculations, xenon transient calculations, decay heat calculations, pin power calculations

and adjoint calculations for LWR

The Triangular Polynomial Expansion (TPEN) method is employed to solve for

the neutron fluxes in the homogenized hexagonal nodes

A transient fixed source problem is solved at each time point of the transient

PARCS is coupled directly (internal coupling) to the thermal-hydraulic system

code TRACE (Odar, 2003) which provides the temperature and flow field information to

PARCS during the transient via the few-group cross sections.

TRACE: The TRAC/RELAP Advanced Computational Engine (Odar et al, 2003) is a

modernized NRC thermal-hydraulic code designed to consolidate and extend the

capabilities of NRC‟s 3 legacy safety codes - TRAC-P, TRAC-B and RELAP. It is able

to analyze large/small break LOCAs and system transients in both pressurized and boiling

reactors. The code was developed by the Los Alamos National Laboratory (LANL), the

Information Systems Laboratory (ISL), and the Penn State University (PSU) for use in

best-estimate analysis of light water reactors and Generation IV systems. To meet these

challenges TRACE uses many new features like multi-dimensional flow modeling and 2D

heat conduction. TRACE is able to use different coolant types like H2O, D2O, He, Na and

PbBi as well. The partial differential equations that describe two-phase flow and heat

transfer are solved with finite-difference numerical methods. This is the NRC flagship

thermal-hydraulic analysis tool.

CATHARE (INRNE)

CATHARE2 (CEA, 2007) is a system thermal-hydraulic code developed by CEA, EDF,

IRSN and AREVA for reactor safety analysis. It is applicable for different types of

reactors – PWR, VVER, BWR and gas-cooled reactors, and covers the domain of

large/small break LOCAs and transients. The code is modular (component modules) and

is based on a six-equation two-fluid model. The current version V2.5_2 includes a 3D

coarse-mesh module. CATHARE provides a set of physical closure laws validated against

a large experimental database.

The code has been tested for VVER in a series of computational benchmarks and

standard problems. The qualification matrix includes experiments relative to VVER such

as horizontal SG, vessel mixing tests, CCFL and re-flooding. All the existing integral test

facilities with horizontal steam generators (PACTEL, PMK and PSB) have been used for

the assessment.

CRONOS/FLICA4 (INRNE/CEA)

CRONOS2 (Lautard et al.,1990), (Lautard et al, 1999), (Magnaud, 1999) is a 3D

neutronics code designed to provide all the computational means needed for diffusion and

transport core calculations, including design, fuel management, operation and accidents. It

allows steady-state, burn-up and kinetic multi-group calculations of power distribution

188

taking into account the thermal-hydraulic feedback effects (performed either by FLICA4

or by a simplified multi-1D model). It has also generalized perturbation theory

capabilities. Either eigenvalue or source calculations can be performed.

CRONOS is coupled with FLICA4 for 3D core dynamics simulation. The mode of

coupling is external.

FLICA4 (Toumi et al, 2000), (Aniel et al, 2005) is a 3D thermal-hydraulic code used for

several reactor types (PWR, VVER, BWR, experimental reactors, gas-cooled reactors).

The two-phase compressible flow is modeled 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 1D thermal module is used to solve the conduction in solids (fuel).

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 (for instance a sub-channel calculation of the hot

assembly). The fully implicit numerical scheme uses the finite volume approximation and

a Roe solver. This kind of method is particularly accurate, with a low numerical diffusion.

For neutronics, coupling with 3D core simulators such as CRONOS2 or internal point

kinetics can be used.

COBAYA/COBRA3 (INRNE/UPM)

COBAYA3 (UPM, 2009; Lozano et al, 2009) is a multi-scale, multi-group 3D neutronics

code for LWR based on the diffusion approximation. The code has a nodal and a pin scale

solver, which can be used separately or together, and both can handle kinetics and

thermal-hydraulic feedbacks for the cross sections libraries.

The nodal solver is called ANDES (Analytical Nodal Diffusion Equation Solver). It

solves the neutron multi-group diffusion equations in 3D geometry and allows calculation

of a variety of cases. The capability to treat nodes with rectangular and triangular-Z

geometry permits the simulation of cores based not only on rectangular fuel assemblies

(PWR, BWR), but also on hexagonal assemblies (VVER, SFR, VHTR).

In both geometries, the code allows transient calculations by coupling the neutronics

code with the COBRA-III and COBRA-TF thermal-hydraulic codes, or using a simplified

model (SIMULA-TH).

The N/TH coupling allows the application of ANDES/COBAYA3 code to a great

variety of steady state and transient problems:

Steady state eigenvalue calculation at any power level.

Steady state calculation with critical boron search at any power level.

Transient calculations (fixed source problem) from an initial steady state

The COBAYA3 lattice solver allows steady state and transient pin-by-pin calculations

in multi-group diffusion approximation, for orthogonal and hexagonal cell geometries.

The orthogonal geometry solver is coupled with the COBRA sub-channel code.

COBRA-III-C/MIT-2 (Jackson, 1981) is a public code for thermal-hydraulics sub-

channel calculations, with implicit cross-flows and homogeneous two-phase flow fluids.

The code is used worldwide for DNBR analysis in PWR sub-channels, and also for 3D

whole core simulation with one or more channels per fuel assembly. COBRA uses direct

189

inversion at each plane of the axial flow equations, with cross flows updated over an outer

iteration loop, for the homogeneous model single-phase coolant , and finite-element direct

solution of the fuel rod radial temperatures.

The 3D core N/TH coupling is internal, through a semi-implicit scheme using a

staggered alternate time mesh.

190

APPENDIX G: Participants’ provided computational details

Organization: FZD (Forchung Zentrum Dresden)

Code: DYN3D/ATHLET

I. Vessel thermal-hydraulic model

1. Type of model

Multi-1D

2. Vessel thermal-hydraulic nodalization. How are the channels/T-H cells

chosen?

3. Vessel mixing model?

An empirical model called SATM (Self Adapting Turbulent Mixing) was developed

and implemented into the interface between ATHLET and DYN3D, which distributes

the enthalpy flow from the single loops between the different fuel assemblies and

simulates the coolant mixing inside the reactor pressure vessel.

This empirical model is based on the following assumptions:

Inside the pressure vessel, there is an azimuthal equalization of the flow rates from

the single loops.

The flow shifts from the loop position to the sector position.

The described sector formation is present in the vessel until the core inlet plane.

At each time step in the coupled code calculation, the position of the sectors and the

fuel assemblies belonging to each of the sectors are recalculated. In this way, the

dynamics of the sector widening and reduction during pump start up and coast –down

as well as the azimuthal moving of the different sectors in the core plane during the

operation of different numbers of MCPs is inherently considered by the model.

Further, in the model a coolant exchange rate between neighboring sectors is

implemented simulating the turbulent mixing in the vessel. Coefficients for the

exchange rate can be input. The exchange is realized on enthalpy flow basis.

4. How are the inlet ring and down-comer modeled?

4 parallel channels

5. How is the lower plenum modeled?

4 thermal hydraulic volumes + above mentioned SATM model

6. How are the upper plenum and upper head modeled?

4 thermal hydraulic volumes; no mixing between them

II. Core thermal-hydraulic model

7. Core thermal hydraulic model (multi-1D, 3D) and nodalization: How are the

channels/TH cells chosen?

Multi-1D; 163 independent thermal hydraulic channels

8. Number of heat structures (fuel rods) modeled?

191

1 average fuel rod per fuel assembly (hydraulic channel), i.e. 163 fuel rods

9. Radial fuel rod nodalization? 5 nodes (equal area)

10. Relation used for Doppler temperature? According to the specification

III. Core neutronics model

11. Number of radial nodes per assembly? one

12. Axial nodalization? 30 nodes in the heated part

13. Radial and axial reflector modeling?

One node for lower and for upper axial reflector; one row of reflector assemblies

around the core (altogether 48)

14. Spatial decay heat distribution modeling?

Distribution is based on infinite operation at the given power level

15. Cross-sections and interpolation procedure used?

Provided cross-section data and interpolation routine

IV. Coupling schemes

16. Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial

and axial plane)?

Both meshes are identical

17. Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and

axial plane)?

Both meshes are identical

18. Heat structure/neutronics spatial mesh overlays (mapping schemes in radial

and axial plane)?

Both meshes are identical

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

Implicit

20. Coupling method – external or internal?

External

21. Coupling design – serial integration or parallel processing?

Serial integration

22. Temporal coupling scheme?

Implicit

V. General

23. Deviations from the specifications? no

24. User assumptions? no

25. Specific features of the used codes?

Dynamic model for determination of gas gap heat transfer coefficients

192

26. Are you using the core outlet pressure boundary conditions? yes

27. Have you used plant specific initial loop flows? yes

28. Neutron kinetics model?

HEXNEM2 option of DYN3D; 2D solution with 12 unknowns in radial plane

(sides and corner points); 1D solution in axial plane; coupling via transverse

leakage

Organization: VTT (Technical Research Centre of Finland)

Code: HEXTRAN/SMABRE

I. Vessel thermal-hydraulic model

1. Type of model

Multi-1D

2. Vessel thermal-hydraulic nodalization. How are the channels/T-H cells

chosen?

6 sectors in the vessel all the way from the inlet to the outlet

3. Vessel mixing model?

Multi-1D model with approximate turbulence modeling

4. How are the inlet ring and down-comer modeled?

6 azimuthal meshes and one axial mesh in the inlet ring

5. How is the lower plenum modeled?

6 azimuthal and 2 axial meshes

6. How are the upper plenum and upper head modeled?

6 azimuthal and 3 axial meshes in the upper plenum

II. Core thermal-hydraulic model

7. Core thermal hydraulic model (multi-1D, 3D) and nodalization: How are the

channels/TH cells chosen?

Multi-1D, 163 channels.

8. Number of heat structures (fuel rods) modeled? 163.

9. Radial fuel rod nodalization? 6 radial meshes.

10. Relation used for Doppler temperature? As provided in the specification.

III. Core neutronics model

11. Number of radial nodes per assembly? One.

Axial nodalization? 30 nodes in the heated part

12. Radial and axial reflector modeling?

One node for each axial reflector and one row of reflector assemblies around the

core.

13. Spatial decay heat distribution modeling?

193

Proportional to the initial 3D power distribution.

14. Cross-sections and interpolation procedure used?

As provided in the specification.

IV. Coupling schemes

15. Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial

and axial plane)?

Both meshes are identical.

16. Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and

axial plane)?

Both meshes are identical.

17. Heat structure/neutronics spatial mesh overlays (mapping schemes in radial

and axial plane)?

Both meshes are identical.

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

Explicit.

19. Coupling method – external or internal?

Internal.

20. Coupling design – serial integration or parallel processing?

Serial integration.

21. Temporal coupling scheme?

V. General

22. Deviations from the specifications? No

23. User assumptions? No

24. Specific features of the used codes?

25. Are you using the core outlet pressure boundary conditions? Yes

26. Have you used plant specific initial loop flows? Yes

27. Neutron kinetics model? Two-group nodal flux solver using modal

representation (asymptotic and transient modes) and high-order polynomial

nodal expansion method

194

Organization: FZK (Forchung Zentrum Karlsruhe)

Code: PARCS V7/TRACE V230

I. Vessel thermal-hydraulic model

1. Type of model: Coarse 3D

2. Vessel thermal-hydraulic nodalization. How are the channels/TH cells chosen?

Six sectors and 5 radial meshes in the radial plane.

3. Vessel mixing model? Coarse 3D without turbulence.

4. How are the inlet ring and down-comer modeled? 3D modeling.

5. How is the lower plenum modeled? 3D modeling.

6. How are the upper plenum and upper head modeled? 3D modeling.

II. Core thermal-hydraulic model

7. Core thermal hydraulic model (multi-1D, 3D) and nodalization: How are the

channels/TH cells chosen?

Coarse 3D with 6 sectors and 3 radial meshes in the radial plane (18 cells).

8. Number of heat structures (fuel rods) modeled? 18

9. Radial fuel rod nodalization? 6 radial meshes

10. Relation used for Doppler temperature? As provided in the specification.

III. Core neutronics model

11. Number of radial nodes per assembly? One

12. Axial nodalization? 30 nodes

13. Radial and axial reflector modeling?

One node for each axial reflector and one row of reflector assemblies around the

core

14. Spatial decay heat distribution modeling?

15. Cross-sections and interpolation procedure used? As provided in the

specification

IV. Coupling schemes

16. Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial

and axial plane)?

Both meshes are identical.

17. Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and

axial plane)?

18 hydraulic cells and 163 neutronics cells in the radial plane.

Identical axial meshes in the heated core.

18. Heat structure/neutronics spatial mesh overlays (mapping schemes in radial

and axial plane)?

195

18 heat structures and 163 neutronics cells in the radial plane.

Identical axial meshes in the heated core.

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

20. Coupling method – external or internal? Internal.

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

22. Temporal coupling scheme? Semi-implicit.

V. General

23. Deviations from the specifications? No

24. User assumptions? No

25. Specific features of the used codes?

26. Are you using the core outlet pressure boundary condition? Yes

27. Have you used plant specific initial loop flows? Yes

28. Neutron kinetics model? Using the TPEN method

Organization: University of Pisa (UNIPI)

Code: NESTLE (NEM) / RELAP5-3D mod3.2.6

I. Vessel thermal-hydraulic model

1. Type of model – Coarse 3D

2. Vessel thermal-hydraulic nodalization. How are the channels/T-H cells

chosen?

60 sectors x 9 radial nodes in the upper part of the lower plenum,

1D upper plenum model (one channel),

6 axial nodes outside the core, in the upward flow part,

30 axial nodes in the heated core

3. Vessel mixing model? Coarse 3D without turbulence.

4. How are the inlet ring and down-comer modeled?

Coarse-3D with 20 azimuth meshes, one radial mesh and 20 axial meshes

5. How is the lower plenum modeled?

Coarse 3D with 4 axial layers:

Number of azimuth nodes: 20, 20, 20, 60.

Number of radial nodes: 4, 4. 8, 9

Number of axial nodes: 1,1,1,1

6. How are the upper plenum and upper head modeled?

1D upper plenum model

II. Core thermal-hydraulic model

7. Core thermal hydraulic model (multi-1D, 3D) and nodalization: How are the

channels/TH cells chosen? 163

8. Number of heat structures (fuel rods) modeled? 163

9. Radial fuel rod nodalization? 6 radial meshes

196

10. Relation used for Doppler temperature? As defined in the specification

III. Core neutronics model

11. Number of radial nodes per assembly? One

12. Axial nodalization? 30 nodes in the active core

13. Radial and axial reflector modeling?

One node for each of the top and bottom reflectors and one additional row of

reflector assemblies for the radial reflector.

14. Spatial decay heat distribution modeling? Proportional to the 3D power

distribution.

15. Cross-sections and interpolation procedure used?

As provided in the specification.

IV. Coupling schemes

16. Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial

and axial plane)?

163 TH channels.

17. Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and

axial plane)?

Both meshes are identical.

18. Heat structure/neutronics spatial mesh overlays (mapping schemes in radial

and axial plane)? N/A

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

20. Coupling method – external or internal? Internal.

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

22. Temporal coupling scheme?

V. General

23. Deviations from the specifications? No

24. User assumptions? No

25. Specific features of the used codes?

26. Are you using the core outlet pressure boundary conditions? Yes

27. Have you used plant specific initial loop flows? Yes

28. Neutron kinetics model? Nodal Expansion Method (NEM)

Organization: INRNE (Institute for Nuclear Research and Nuclear Energy), Sofia

Code: CATHARE 2.5/Point kinetics

I. Vessel thermal-hydraulic model

1. Type of model

Multi-1D

2. Vessel thermal-hydraulic nodalization. How are the channels/T-H cells

chosen?

197

The vessel model is multi-1D with cross-flow, 24 sectors from the vessel inlet to

the core outlet and 12 sectors in the upper plenum.

3. Vessel mixing model?

The model is multi-1D with cross flow governed by local pressure drops. The

cross-flow was modeled with horizontal junctions and vertical (diagonal) junctions

connecting donor cells at a given elevation to receptor cells in the neighboring

sectors, at a higher elevation. Vertical junctions were used to a limited extent, with

small flow area and in the lower and upper plenums only.

4. How are the inlet ring and the down-comer modeled?

Multi-1D modeling without turbulence.

24 volume elements in the inlet ring corresponding to 24 azimuth sectors,

24 volume elements in the upper part of the down-comer,

24 axial elements in the lower down-comer.

5. How is the lower plenum modeled?

2 axial layers of 24 volumes each

6. How are the upper plenum and upper head modeled?

3 axial layers x 12 volumes each in the upper plenum,

12 volumes in the outlet ring

II. Core thermal-hydraulic model

7. Core thermal hydraulic model (multi-1D, 3D) and nodalization: How are the

channels/TH cells chosen?

24 channels and 24 bypass channels

8. Number of heat structures (fuel rods) modeled? 24

9. Radial fuel rod nodalization? 6 radial meshes

10. Relation used for Doppler temperature? As defined in the specification

III. Core neutronics model

Point kinetics with equivalent parameters

11. Spatial decay heat distribution? Uniform

IV. Temporal integration scheme

12. Temporal integration –explicit, semi-implicit or implicit? Implicit

V. General

13. Deviations from the specifications? Point kinetics

14. User assumptions? No

15. Specific features of the used codes? 11-group decay heat model

16. Are you using the core outlet pressure boundary conditions? Yes

17. Have you used plant specific initial loop flows? Yes

18. Neutron kinetics model? Point kinetics model

198

Organization: INRNE/CEA

Code: CRONOS2/FLICA4

I. Core thermal-hydraulics model

1. Core thermal hydraulic model (multi-1D, 3D) and nodalization: How are the

channels/TH cells chosen?

3D FLICA4 model with one point per hexagon in the radial plane,

30 axial nodes in the heated core.

2. Number of heat structures (fuel rods) modeled? 163 x 30

3. Radial fuel rod nodalization? 6 radial meshes

4. Relation used for Doppler temperature? As defined in the specification.

II. Core neutronics model

5. Number of radial nodes per assembly? One

6. Axial nodalization? 30 nodes in the active core.

7. Radial and axial reflector modeling?

One node for each of the top and bottom reflectors and one additional row of

reflector assemblies for the radial reflector.

8. Spatial decay heat distribution modeling? Proportional to the initial 3D power

distribution.

9. Cross-sections and interpolation procedure used? As provided in the

specification.

III. Coupling schemes

10. Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial

and axial plane)?

Both meshes are identical.

11. Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and

axial plane)?

Both meshes are identical.

12. Heat structure/neutronics spatial mesh overlays (mapping schemes in radial

and axial plane)?

Both meshes are identical.

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

14. Coupling method – external or internal? External.

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

16. Temporal coupling scheme? Explicit.

IV. General

17. Deviations from the specifications? No

18. User assumptions? No

19. Specific features of the used codes?

20. Are you using the core outlet pressure boundary conditions? Yes

199

21. Have you used plant specific initial loop flows? Yes

22. Neutron kinetics model? Coarse 3D, CRONOS2 2nd

-order super-convergent

FEM with 6 triangles per hexagon.

Organization: INRNE/UPM

Code: COBAYA3/COBRA3

I. Core thermal-hydraulics model

1. Core thermal hydraulic model (multi-1D, 3D) and nodalization: How are the

channels/TH cells chosen?

Multi-1D COBRA3c model with one point per hexagon in the radial plane.

30 axial nodes in the heated core.

2. Number of heat structures (fuel rods) modeled? 163 x 30

3. Radial fuel rod nodalization? 6 radial meshes

4. Relation used for Doppler temperature? As defined in the specification.

II. Core neutronics model

5. Number of radial nodes per assembly? 6 nodes (triangular-Z prisms).

6. Axial nodalization? 30 nodes in the active core.

7. Radial and axial reflector modeling?

One axial node for each of the top and bottom reflectors and one additional row of

reflector assemblies for the radial reflector.

8. Spatial decay heat distribution modeling? Proportional to the initial 3D power

distribution.

9. Cross-sections and interpolation procedure used? As provided in the

specification.

III. Coupling schemes

10. Hydraulics/heat structure spatial mesh overlays (mapping schemes in radial

and axial plane)?

Both meshes are identical.

11. Hydraulics/neutronics spatial mesh overlays (mapping schemes in radial and

axial plane)?

One hydraulic node/6 neutronic nodes per hexagon in the radial plane.

Identical axial meshes.

12. Heat structure/neutronics spatial mesh overlays (mapping schemes in radial

and axial plane)?

One heat structure/6 neutronic nodes per hexagon in the radial plane.

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

14. Coupling method – external or internal? Internal.

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

16. Temporal coupling scheme? Semi-implicit with staggered mesh.

200

IV. General

17. Deviations from the specifications? No

18. User assumptions? No

19. Specific features of the used codes?

20. Are you using the core outlet pressure boundary conditions? Yes

21. Have you used plant specific initial loop flows? Yes

22. Neutron kinetics model? Coarse 3D, CRONOS2 2nd

-order super-convergent

FEM with 6 triangles per hexagon.