VVER-1000 MOX Core Computational Benchmark

Transcription

1 Nuclear Science ISBN NEA/NSC/DOC(2005)17 VVER-1000 MOX Core Computational Benchmark Specification and Results Expert Group on Reactor-based Plutonium Disposition Eugeny Gomin, Mikhail Kalugin, Dmitry Oleynik Russian Research Centre, Kurchatov Institute OECD 2006 NEA No NUCLEAR ENERGY AGENCY ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT

2 ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT The OECD is a unique forum where the governments of 30 democracies work together to address the economic, social and environmental challenges of globalisation. The OECD is also at the forefront of efforts to understand and to help governments respond to new developments and concerns, such as corporate governance, the information economy and the challenges of an ageing population. The Organisation provides a setting where governments can compare policy experiences, seek answers to common problems, identify good practice and work to co-ordinate domestic and international policies. The OECD member countries are: Australia, Austria, Belgium, Canada, the Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Korea, Luxembourg, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal, the Slovak Republic, Spain, Sweden, Switzerland, Turkey, the United Kingdom and the United States. The Commission of the European Communities takes part in the work of the OECD. OECD Publishing disseminates widely the results of the Organisation s statistics gathering and research on economic, social and environmental issues, as well as the conventions, guidelines and standards agreed by its members. * * * This work is published on the responsibility of the Secretary-General of the OECD. The opinions expressed and arguments employed herein do not necessarily reflect the official views of the Organisation or of the governments of its member countries. NUCLEAR ENERGY AGENCY The OECD Nuclear Energy Agency (NEA) was established on 1 st February 1958 under the name of the OEEC European Nuclear Energy Agency. It received its present designation on 20 th April 1972, when Japan became its first non-european full member. NEA membership today consists of 28 OECD member countries: Australia, Austria, Belgium, Canada, the Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Luxembourg, Mexico, the Netherlands, Norway, Portugal, Republic of Korea, the Slovak Republic, Spain, Sweden, Switzerland, Turkey, the United Kingdom and the United States. The Commission of the European Communities also takes part in the work of the Agency. The mission of the NEA is: to assist its member countries in maintaining and further developing, through international co-operation, the scientific, technological and legal bases required for a safe, environmentally friendly and economical use of nuclear energy for peaceful purposes, as well as to provide authoritative assessments and to forge common understandings on key issues, as input to government decisions on nuclear energy policy and to broader OECD policy analyses in areas such as energy and sustainable development. Specific areas of competence of the NEA include safety and regulation of nuclear activities, radioactive waste management, radiological protection, nuclear science, economic and technical analyses of the nuclear fuel cycle, nuclear law and liability, and public information. The NEA Data Bank provides nuclear data and computer program services for participating countries. In these and related tasks, the NEA works in close collaboration with the International Atomic Energy Agency in Vienna, with which it has a Co-operation Agreement, as well as with other international organisations in the nuclear field. OECD 2006 No reproduction, copy, transmission or translation of this publication may be made without written permission. Applications should be sent to OECD Publishing: rights@oecd.org or by fax (+33-1) Permission to photocopy a portion of this work should be addressed to the Centre Français d exploitation du droit de Copie, 20 rue des Grands Augustins, Paris, France (contact@cfcopies.com).

3 FOREWORD The NEA Nuclear Science Committee has established an Expert Group that deals with the status and trends of reactor physics, fuel performance and fuel cycle issues related to disposing of weapons-grade plutonium in mixed-oxide fuel. The objectives of the group are to provide NEA member countries with up-to-date information on, and to develop consensus regarding, core and fuel cycle issues associated with burning weapons-grade plutonium in thermal water reactors (PWR, BWR, VVER-1000, CANDU) and fast reactors (BN-600). These issues concern core physics, fuel performance and reliability, and the capability and flexibility of thermal water reactors and fast reactors to dispose of weapons-grade plutonium in standard fuel cycles. The activities of the NEA Expert Group on Reactor-based Plutonium Disposition are carried out in close co-operation (jointly, in most cases) with the NEA Working Party on Scientific Issues in Reactor Systems (WPRS). A prominent part of these activities include benchmark studies. At the time of preparation of this report, the following benchmarks were completed or in progress: x VENUS-2 MOX Core Benchmarks: carried out jointly with the WPRS (formerly the WPPR) (completed); x VVER-1000 LEU and MOX Benchmark (completed); x KRITZ-2 Benchmarks: carried out jointly with the WPRS (formerly the WPPR) (completed); x Hollow and Solid MOX Fuel Behaviour Benchmark (completed); x PRIMO MOX Fuel Performance Benchmark (ongoing); x VENUS-2 MOX-fuelled Reactor Dosimetry Calculation (ongoing); x VVER-1000 In-core Self-powered Neutron Detector Calculational Benchmark (started); x MOX Fuel Rod Behaviour in Fast Power Pulse Conditions (started); x Benchmark on the VENUS Plutonium Recycling Experiments Configuration 7 (started). This report describes the detailed results of the benchmark investigating the physics of a whole VVER-1000 reactor core using two-thirds low-enriched uranium (LEU) and one-third MOX fuel. It contributes to the computer code certification process and to the verification of calculation methods used in the Russian Federation. 3

4 DEDICATION Lev Vasilievich Mayorov 18 July February 2005 We wish to dedicate this report to the memory of Lev Mayorov, for his exceptional contribution to the development and application of the Monte Carlo method. His insight into both physical and mathematical aspects of problem solving led him to the development of the MCU computer code system. He strongly supported and encouraged the work of the OECD/NEA Expert Group on Reactor-based Plutonium Disposition and participated in several meetings. His contributions and comments were always of the highest relevance and quality. The Expert Group and his colleagues will miss him. 4

5 CONTRIBUTORS Text E. Gomin RRC-KI Russian Federation M.A. Kalugin RRC-KI Russian Federation D. Oleynik RRC-KI Russian Federation Text Review J. Gehin ORNL United States E. Sartori OECD/NEA Russian Federation Text Processing/Outlay A. Griffin-Chahid OECD/NEA Specification P.A. Bolobov RRC-KI Russian Federation S.N. Bolshagin RRC-KI Russian Federation S.A. Bychkov RRC-KI Russian Federation M.A. Kalugin RRC-KI Russian Federation A.I. Pavlovichev RRC-KI Russian Federation Y.A. Styrine RRC-KI Russian Federation Participants M.A. Kalugin RRC-KI Russian Federation S.N. Bolshagin RRC-KI Russian Federation W. Zwermann GRS Germany S. Langenbuch GRS Germany W. Bernnat IKE Germany ABSTRACT This report presents the VVER MOX Core Computational Benchmark Specification and Results, which was proposed as a benchmark within the OECD/NEA Expert Group on Reactor-based Plutonium Disposition (TFRPD). Benchmark results, obtained using three computer codes, are presented. The codes include: the MCU Monte Carlo code (Kurchatov Institute, Russian Federation), RADAR (Kurchatov Institute, Russian Federation), and the MCNP Monte Carlo code (GRS, Germany). The codes use different methods and different nuclear data. A comparison of the results shows good agreement among the various codes. 5

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7 TABLE OF CONTENTS Foreword... 3 Contributors... 5 Chapter 1. Introduction... 9 Chapter 2. Benchmark model Chapter 3. Participants, codes and data Chapter 4. Results of the benchmark calculations K eff for separate states Assembly-by-assembly fission rate distributions Pin-by-pin fission rate distributions Problems connected with Monte Carlo modelling of large systems Chapter 5. Conclusion References Appendix. VVER MOX core benchmark specification List of tables Table 2.1. Reactor state descriptions Table 3.1. Participants, basic library and computer codes used Table 1. Monte Carlo calculation parameters Table 2. K eff for states S1-S Table 3. Assembly average fission rate distribution State S Table 4. Assembly average fission rate distribution State S Table 5. Assembly average fission rate distribution State S Table 6. Assembly average fission rate distribution State S Table 7. Assembly average fission rate distribution State S Table 8. Assembly average fission rate distribution State S Table 9. Estimated statistical uncertainty of assembly average fission rates Table 10. Maximum deviation of MCNP and RADAR from MCU in the central part of the core and on the core periphery Table 11. Pin-by-pin fission rate distribution Assembly N: Table 12. Pin-by-pin fission rate distribution Assembly N: Table 13. Pin-by-pin fission rate distribution Assembly N:

8 Table A.1. Dimensions of the cell zones Table A.2. Material names used in the fuel assemblies Table A.3. Isotopic composition of fuel U_4.2, atoms/barn*cm Table A.4. Isotopic composition of fuel TVEG_ Table A.5. Isotopic composition of fuel U_ Table A.6. Isotopic composition of fuel PU_ Table A.7. Isotopic composition of fuel TVEG_ Table A.8. Isotopic composition of fuel PU_ Table A.9. Isotopic composition of fuel PU_ Table A.10. Isotopic composition of the structural materials Table A.11. Moderator and water in reflector materials Table A.12. Reactor state descriptions List of figures Figure 2.1. Pattern of the VVER core with 30% MOX-fuel loading Figure 2.2. Pattern of graded UOX assembly Figure 2.3. Pattern of graded MOX assembly Figure 1. Assembly average fission rate distribution State S Figure 2. Assembly average fission rate distribution State S Figure 3. Assembly average fission rate distribution State S Figure 4. Assembly average fission rate distribution State S Figure 5. Assembly average fission rate distribution State S Figure 6. Assembly average fission rate distribution State S Figure 7. State S1 Deviations of MCNP and RADAR from MCU Figure 8. Pin-by-pin fission rate distribution Assembly N: Figure 9. Pin-by-pin fission rate distribution Assembly N: Figure 10. Pin-by-pin fission rate distribution Assembly N: Figure A.1. Pattern of the VVER core with 30% MOX-fuel loading Figure A.2. Location of different elements in the VVER-1000 core model 60q angle Figure A.3. Water gap of 3 mm between FA and steel buffer Figure A.4. Cell numbers in the fuel assembly Figure A.5. Fuel assembly cell types Figure A.6. Pattern of graded UOX assembly Figure A.7. Pattern of graded MOX assembly

9 Chapter 1 INTRODUCTION Future MOX fuel utilisation in VVER-1000 reactors requires certification of corresponding calculational codes. This is due to essential differences between MOX and standard LEU fuel that are listed below: x x x x x x Reduced worth of the control rods, boric acid and burnable poisons. Reduced effective fraction of delayed neutrons. Reduced moderator temperature reactivity coefficient at the end of the fuel cycle. Increased pin power peaking factor at the boundary between MOX and UOX FAs, which makes it necessary to use fuel rods with different contents of plutonium in the fuel assembly. Increased quantity of fission neutrons. Increased neutron flux sensitivity to local changes of moderator/fuel ratio. Certification according to the Russian Federation (RF) licensing rules should be based mainly on the comparison of benchmark calculations performed by Russian design and different reference codes, including international ones. Within the USA/RF joint work, a calculational benchmark was formulated by staff of the Kurchatov Institute [1,2]. In this work, only part of the benchmarks reported in Ref. [1] is considered. This is a standard problem for VVER-1000 core physics. The 2-D core configuration consists of the heterogeneous 30% MOX-fuel loading of the VVER-1000 core with a reflector described in detail. The model is described in 2-D geometry. This benchmark was proposed to the OECD/NEA in 2002 by the participants in the Task Force on Reactor-based Plutonium Disposition (TFRPD). This benchmark may be considered as Phase 2 of the benchmarking efforts with orientation on the verification of the Russian whole-code package for VVER calculations. Phase 1, A VVER-1000 LEU and MOX Assembly Computational Benchmark, was successfully completed within the TFRPD activity. An OECD report was issued in 2002 [NEA/NSC/DOC (2002)10]. A further phase has recently been started and concerns a VVER-1000 In-core Self-powered Neutron Detector Calculational Benchmark. 9

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11 Chapter 2 BENCHMARK MODEL The benchmark model consists of a full-size 2-D VVER-1000 core with heterogeneous 30% MOX-fuel loading. A 2-D model of the VVER-1000 core with reflector will be described in detail. The core with 30% MOX-fuel loading consists of fresh and burned fuel assemblies (FA) of the following types: x x Graded UOX FA with U-Gd burnable absorber (BA) rods. Graded, profiled MOX FA with U-Gd BA rods. Twenty-eight (28) assemblies in 60q rotation symmetry angles are considered. The system has an infinite axial dimension and vacuum condition on the side surface. A pattern of the core is shown in Figure 2.1. There are three numbers in each assembly: 1. N is the number of the assembly; N = 1, Type of assembly; type = 1 for UOX and type = 2 for MOX fuel assembly. 3. The numbers at the bottom indicate the burn-up value in MWd/kg. For example, 20/2 and 17 means that assembly number 20 of type 2 (MOX) has a burn-up of 17 MWd/kg. The UOX and MOX FA configurations are shown in Figures 2.2 and 2.3. The eight rows of FA s are surrounded by a reflector. A reflector consists of the following elements ordered from centre to periphery: water gap, steel buffer with water holes, steel barrel, downcomer (water) and steel vessel. The water gap (width of 3 mm) is located between fuel assemblies and steel buffer. The width of the water gap is equal to 3 mm. The pattern of the reflector and water hole diameters are provided in the benchmark specification in the Appendix. The fuel assembly consists of 331 elementary hexagonal cells and a moderator. Cell numbers in the FA are presented in the Appendix. The pitch of the assembly s lattice is equal to 23.6 cm. There are three main types of the elementary cells: fuel cells, central tube cell/guide tube cell and guide tube with absorber rod cell. The pitch of the cell s lattice is equal to cm. All the materials have special names, for example U_4.2 means UOX fuel with enrichment 4.2%. UOX assemblies consist of pins with fuels U_4.2, TVEG_5 and U_3.7, while MOX assemblies consist of pins with fuels PU_3.6, TVEG_4, PU_2.7 and PU_2.4. Note that these fuel materials have isotopic composition according to assembly burn-up. All this information is provided in the Appendix. 11

12 Isotopic compositions of the fuel cladding, central and guide tubes, absorber cladding, absorber rod, steel buffer, steel barrel and steel vessel are presented in the Appendix. Six different state calculations were performed. The reactor state is described by material temperatures and the presence in the core of absorber rods. These states are described in Table 2.1. There is only one state, S6, with absorber rods inserted. The following functionals were provided by participants for each of the six states: x K eff. x Assembly average fission reaction rate distribution for the 28 assemblies in the core. x Only for state S1 cell average fission reaction rate distribution within several assemblies (N:3, N:21, N:27, see Figure 2.1) for 331 cells per each of the three assemblies. State State name Table 2.1. Reactor state descriptions Fuel T, K Moderator in FA T, K Moderator in FA material Reflector T, K Water gap, water hole, downcomer material Absorber rod S1 Working state M575B M560B1.3 S2 State with constant temperature M575B M560B1.3 S3 Cold state with high boron M300B M300B2.8 content S4 Working state without boron M575B0 560 M560B0 S5 State with constant temperature M575B0 560 M560B0 without boron S6 State with control rods inserted M553B0 553 M553B0 Inserted Figure 2.1. Pattern of the VVER core with 30% MOX-fuel loading N:/type burnup UOX assembly Type 1 Assembly with absorber rod inserted 17/1 0 23/ /1 0 MOX assembly Type 2 12/ / /1 0 8/ / / /1 15 5/2 33 9/ / / /1 0 3/2 0 6/ / / /1 0 28/1 40 1/1 40 2/1 32 4/2 17 7/2 0 11/ /2 0 22/

13 Figure 2.2. Pattern of graded UOX assembly Cell number Cell type 1 Central tube cell 2 Fuel cell with fuel U_4.2 3 Guide tube cell 4 Fuel cell with U-Gd, fuel TVEG_5 5 Fuel cell with fuel U_3.7 7 Cells with moderator 13

14 Figure 2.3. Pattern of graded MOX assembly Cell number Cell type 1 Central tube cell 2 Fuel cell with fuel PU_3.6 3 Guide tube cell 4 Fuel cell with U-Gd, fuel TVEG_4 5 Fuel cell with fuel PU_2.7 6 Fuel cell with fuel PU_2.4 7 Cells with moderator 14

15 Chapter 3 PARTICIPANTS, CODES AND DATA A total of three solutions were submitted from two countries with each participant using different methods and data combinations. Two of the solutions are based on continuous energy Monte Carlo methods, while the other solution is based on collision probability (or similar) methods. The submitted solutions cover several data libraries. The complete list of participants, basic libraries and codes used are presented below and summarised in Table RRC-KI, Russian Federation Participants: M. Kalugin Basic library: MCUDAT-2.1 Code: MCU Remarks: MCU is a continuous energy Monte Carlo code 2. RRC-KI, Russian Federation Participants: S. Bolshagin Basic library: MCUDAT-2.1 Code: RADAR Remarks: same basic library as MCU, calculation method similar to collision probability one 3. GRS, Germany IKE, Universität Stuttgart, Germany Participants: Winfried Zwermann a, Siegfried Langenbuch a, Wolfgang Bernnat b a) Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) mbh Forschungsinstitute, Garching, Germany b) IKE, Universität Stuttgart Pfaffenwaldring 31, Stuttgart, Germany Basic library: point data generated by IKE Stuttgart mainly from JEF 2.2 Code: MCNP-4C Table 3.1. Participants, basic library and computer codes used Institution Library used Codes used RRC-KI (RF) Mikhail Kalugin MCUDAT-2.2 MCU Monte Carlo code RRC-KI (RF) Sergey Bolshagin 63-group library with 40 thermal groups (with RADAR design code for VVER GRS (Germany) Winfried Zwermann Siegfried Langenbuch IKE Stuttgart (Germany) Wolfgang Bernnat boundary energy of 1.0 ev). Point data generated by IKE Stuttgart mainly from JEF 2.2 calculations MCNP-4C Monte Carlo code 15

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17 Chapter 4 RESULTS OF THE BENCHMARK CALCULATIONS In summary, the following can be found in Chapter 4: Participants results and their comparison are presented in Tables 1-13 and Figures The statistical uncertainties for MCU and MCNP as well as for the other Monte Carlo calculational parameters are shown in Table 1. The k eff values for different states are presented in Table 2. The assembly-by-assembly fission rate distributions are presented in Tables 3-8 and in Figures 1-6. Pin-by-pin fission rate distributions are presented in Tables and in Figures K eff for separate states The k eff values obtained by means of three codes for states S1-S6 are presented in Table 2. The RADAR results for state S6 are not available. The results show generally good agreement, but it should be noted that: For all the states, MCNP systematically overestimates k eff in comparison with MCU. The differences between codes are equal to ~0.4% in k eff. Such a systematic discrepancy may be explained by the use of different data libraries. The situation with RADAR is very similar to that with MCNP. For all the states, except S3, RADAR systematically overestimates k eff in comparison with MCU. The differences between codes are equal to ~ % in k eff. The MCNP and RADAR codes give very similar results. The differences between codes are equal to ~0.2% in k eff. Such good agreement between the MCNP and MCU Monte Carlo codes and design code RADAR is impressive Assembly-by-assembly fission rate distributions The results of comparison of assembly-by-assembly fission rate distributions computed by the codes are shown in Figures 1-6 and Tables

18 The number of neutron histories used for modelling with MCNP and MCU as well as other Monte Carlo calculation parameters are presented in Table 1. The estimated relative statistical uncertainty (1 sigma) of the assembly average fission rates are presented in Table 9. It should be noted that the statistical uncertainty of the assembly average fission rates estimated by MCU exceeds the one estimated by MCNP several times. One of the possible reasons for it is that MCNP estimates an apparent variance instead of the real one. For all the states the codes show very good agreement. The one exception is state S4 working state without boron. For this state, assembly average fission rate in the central assembly obtained by MCU differs from the one obtained by MCNP by 4%. Taking into account that the estimated real variance is equal to 2%, this discrepancy is acceptable. The maximum deviation in the central part of the core and on the core periphery of the MCNP and RADAR results from those of MCU are shown in Table 10. The meaning of this table is illustrated in Figure 7, where numbers from Table 10 are shown in italics and underlined Pin-by-pin fission rate distributions For state S1, pin-by-pin fission reaction rate distributions within several assemblies (N:3, N:21, N:27) were calculated. In order to achieve an acceptable statistical uncertainty in the pin-by-pin fission rates, 240 u 10 6 histories in total were modelled by MCU. The estimated relative statistical uncertainty (1 sigma) obtained by MCNP and MCU are equal to 1%. The results of comparing the computed pin-by-pin fission rate distributions are shown in Tables For all the assemblies, the codes show very good agreement. The deviation between the results obtained with the computer codes for the pin-by-pin fission rate calculations is equal to 2-3% and does not exceed the statistical uncertainty. It should be noted that the statistical uncertainty of the pin-by-pin fission rates estimated by MCU and MCNP are practically the same Problems connected with Monte Carlo modelling of large systems Monte Carlo modelling of large systems has some well-known problems, especially for neutron flux functionals, such as assembly-by-assembly or pin-by-pin fission rate distributions. The problems to be solved are as follows: 1. Correct choice regarding the number of particles in one generation: too small a size of the generation may cause a biased result. 2. Correct choice regarding the number of the initial generations to be skipped for the purpose of eliminating the initial neutron source dependence. 18

19 3. Correct estimation of the functional variance/statistical uncertainty. The problem is that many sequential (consecutive) generations are dependent and the correlation coefficient should be taken into account. The MCU code has special tools that are used to prove the reliability of the results obtained. These tools are completely automated, and for all the systems in the post-calculation stage they are applied for the analysis of the results: The real variance is estimated in contrast to the apparent one. The number of skipped generations is estimated. For the real variance estimation, the MacMillan method is used taking into account the correlation between batches. The number of generations in the batch as well as the number of the skipped generations is estimated automatically. The details are described in the book, The Estimation of Criticality Parameters by Monte Carlo Method, by L. Mayorov and V. Zolotukhin [Energoatomizdat, Moscow, p. 91, 1984 (in Russian)]. 19

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21 Chapter 5 CONCLUSION The results from the VVER MOX Core Calculational Benchmark were analysed. Three participants submitted results. The codes use different methods and different nuclear data. A comparison of the results shows rather good agreement among the various codes. All codes give very similar values of k eff, but the MCU code has a tendency to slightly underestimate the k eff value relative to the other two codes. Assembly-by-assembly fission rate distribution calculations show very good agreement. Except for the S4 state, the discrepancy does not exceed 2-3%. For the state S4 assembly, the average fission rate in the central assembly obtained via MCU differs from the one obtained via MCNP by 4%. Taking into account that the estimated real variance equals 2%, this discrepancy is acceptable. Large discrepancies are observed for the estimated statistical uncertainty of the assembly average fission rates obtained by MCU and MCNP. One possible reason may be the different methods used in MCNP and MCU for estimating the statistical uncertainty. The state S1 pin-by-pin fission reaction rate distributions within several assemblies (N:3, N:21, N:27) were calculated by MCU and MCNP. The estimated relative statistical uncertainty (1 sigma) obtained by MCNP and MCU is equal to 1%. For all the assemblies, the codes show very good agreement. The difference between codes does not exceed the statistical uncertainty. It should be emphasised here that verification on the basis of calculational benchmarks does not eliminate the necessity of comparing against the results obtained at MOX fuelled experimental facilities. REFERENCES [1] Alyoshin, S.S., P.A. Bolobov, S.N. Bolshagin, S.A. Bychkov, M.A. Kalugin, L.V. Maiorov, A.M. Pavlovichev, Y.A. Styrine, A.G. Kalashnikov, A.A. Tsyboulia, Core Benchmarks for Verification of Production Neutronic Codes as Applied to VVER-1000 with MOX Fuel Plutonium from Surplus Russian Nuclear Weapons, PHYSOR 2002, Seoul, Korea, 7-10 October [2] Bolobov, P.A., S.N. Bolshagin, S.A. Bychkov, A.G. Kalashnikov, M.A. Kalugin, A.I. Pavlovichev, Y.A. Styrine, Core Benchmarks Description Report, Prepared by RRC-KI, Published by ORNL, ORNL/SUB/00-85B99398V-6, May

22 Table 1. Monte Carlo calculation parameters State MCNP MCU N, 10 6 M NG NS N, 10 6 M NG NS S S S S S S N neutron histories M neutrons per generation NG active neutron generations NS skipped generations Table 2. K eff for states S1-S6 State MCNP Sigma % MCU Sigma % RADAR MCNP- MCU % RADAR- MCU % S S S S S S N/A 0.44 N/A 22

23 Figure 1. Assembly average fission rate distribution State S1 23

24 Figure 2. Assembly average fission rate distribution State S2 24

25 Figure 3. Assembly average fission rate distribution State S3 25

26 Figure 4. Assembly average fission rate distribution State S4 26

27 Figure 5. Assembly average fission rate distribution State S5 27

28 Figure 6. Assembly average fission rate distribution State S6 28

29 Table 3. Assembly average fission rate distribution State S1 N MCNP MCU RADAR (MCNP MCU) / MCU, % (RADAR MCU) / MCU, %

30 Table 4. Assembly average fission rate distribution State S2 N MCNP MCU RADAR (MCNP MCU) / MCU, % (RADAR MCU) / MCU, %

31 Table 5. Assembly average fission rate distribution State S3 N MCNP MCU RADAR (MCNP MCU) / MCU, % (RADAR MCU) / MCU, %

32 Table 6. Assembly average fission rate distribution State S4 N MCNP MCU RADAR (MCNP MCU) / MCU, % (RADAR MCU) / MCU, %

33 Table 7. Assembly average fission rate distribution State S5 N MCNP MCU RADAR (MCNP MCU) / MCU, % (RADAR MCU) / MCU, %

34 Table 8. Assembly average fission rate distribution State S6 N MCNP MCU (MCNP MCU) / MCU, %

35 Table 9. Estimated statistical uncertainty of assembly average fission rates State MCNP, V, % MCU, V, % S S S S S S6 V statistical uncertainty, % Table 10. Maximum deviation of MCNP and RADAR from MCU in the central part of the core and on the core periphery (MCNP MCU) max % (RADAR MCU) max % State Core Core Core centre Core centre periphery periphery S S S S S S6 1-1 N/A N/A Figure 7. State S1 Deviations of MCNP and RADAR from MCU (MCNP MCU) / MCU in 1% (RADAR MCU) / MCU in 1% 35

36 36 MCU FISSION RATES*100 MCNP FISSION RATES*100 Figure 8. Pin-by-pin fission rate distribution Assembly N:3

37 Figure 8. Pin-by-pin fission rate distribution Assembly N:3 (cont d) MCU STAT. ERROR in 0.1% (MCNP MCU) / MCU in % 37

38 Figure 9. Pin-by-pin fission rate distribution Assembly N:21 MCU FISSION RATE*100 MCNP FISSION RATE*100 38

39 Figure 9. Pin-by-pin fission rate distribution Assembly N:21 (cont d) MCU STAT. ERROR in 0.1% (MCNP MCU) / MCU in % 39

40 40 MCU FISSION RATES*100 MCNP FISSION RATES*100 Figure 10. Pin-by-pin fission rate distribution Assembly N:27

41 41 MCU STAT. ERROR in 0.1% (MCNP MCU) / MCU in % Figure 10. Pin-by-pin fission rate distribution Assembly N:27 (cont d)

42 Table 11. Pin-by-pin fission rate distribution Assembly N:3 Cell MCU MCNP (MCNP MCU) / MCU, %

43 Table 11. Pin-by-pin fission rate distribution Assembly N:3 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

44 Table 11. Pin-by-pin fission rate distribution Assembly N:3 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

45 Table 11. Pin-by-pin fission rate distribution Assembly N:3 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

46 Table 11. Pin-by-pin fission rate distribution Assembly N:3 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

47 Table 11. Pin-by-pin fission rate distribution Assembly N:3 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

48 Table 11. Pin-by-pin fission rate distribution Assembly N:3 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

49 Table 11. Pin-by-pin fission rate distribution Assembly N:3 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

50 Table 11. Pin-by-pin fission rate distribution Assembly N:3 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

51 Table 12. Pin-by-pin fission rate distribution Assembly N:21 Cell MCU MCNP (MCNP MCU) / MCU, %

52 Table 12. Pin-by-pin fission rate distribution Assembly N:21 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

53 Table 12. Pin-by-pin fission rate distribution Assembly N:21 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

54 Table 12. Pin-by-pin fission rate distribution Assembly N:21 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

55 Table 12. Pin-by-pin fission rate distribution Assembly N:21 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

56 Table 12. Pin-by-pin fission rate distribution Assembly N:21 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

57 Table 12. Pin-by-pin fission rate distribution Assembly N:21 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %

58 Table 12. Pin-by-pin fission rate distribution Assembly N:21 (con t) Cell MCU MCNP (MCNP MCU) / MCU, %