Luận án: Độ nhạy và bất định dữ liệu hạt nhân trong phân tích lò phản ứng hạt nhân Đà Lạt

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY VIETNAM ATOMIC ENERGY INSTITUTE DAU DUC TU STUDY ON SENSITIVITY AND UNCERTAINTY OF NUCLEAR DATA IN KINETIC PARAMETERS AND CRITICALITY ANALYSES FOR A CORE CONFIGURATION WITH 92 LOW ENRICHED FUEL BUNDLES OF THE DALAT NUCLEAR RESEARCH REACTOR DISSERTATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHYSICS HANOI - 2026 BỘ GIÁO DỤC VÀ ĐÀO TẠO BỘ KHOA HỌC VÀ CÔNG NGHỆ VIỆN NĂNG LƯỢNG NGUYÊN TỬ VIỆT NAM ĐẬU ĐỨC TỪ NGHIÊN CỨU ĐỘ NHẠY VÀ ĐỘ BẤT ĐỊNH SỐ LIỆU HẠT NHÂN TRONG PHÂN TÍCH THÔNG SỐ ĐỘNG HỌC VÀ TỚI HẠN CHO VÙNG HOẠT 92 BÓ NHIÊN LIỆU ĐỘ GIÀU THẤP CỦA LÒ PHẢN ỨNG HẠT NHÂN ĐÀ LẠT LUẬN ÁN TIẾN SĨ VẬT LÝ Chuyên ngành: Vật lý Nguyên tử và Hạt nhân Mã số: 9.06 Giáo viên hướng dẫn: o 1. TRẦN HOÀI NAM 2. NGUYỄN NHỊ ĐIỀN HÀ NỘI - 2026 MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY VIETNAM ATOMIC ENERGY INSTITUTE DAU DUC TU STUDY ON SENSITIVITY AND UNCERTAINTY OF NUCLEAR DATA IN KINETIC PARAMETERS AND CRITICALITY ANALYSES FOR A CORE CONFIGURATION WITH 92 LOW ENRICHED FUEL BUNDLES OF THE DALAT NUCLEAR RESEARCH REACTOR DISSERTATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHYSICS Major: Nuclear and Atomic Physics Code: 9. TRAN HOAI NAM 2.

NGUYEN NHI DIEN HANOI - 2026 Declaration I certify that this dissertation, entitled "Study on sensitivity and un- certainty of nuclear data in kinetic parameters and criticality analyses for a core configuration with 92 low enriched fuel bundles of the Dalat nuclear research reactor" is my original work, except where otherwise clearly indi- cated. I confirm that the dissertation submitted to the Nuclear Training Center, Vietnam Atomic Energy Institute, was primarily completed during my candidacy for a PhD degree under the supervision of Prof. Tran Hoai Nam and Assoc. Nguyen Nhi Dien.

DAU DUC TU Acknowledgements First of all, I would like to express my heartfelt gratitude to my su- pervisors, Prof. Tran Hoai Nam and Assoc. Nguyen Nhi Dien, for their invaluable support and encouragement throughout my research. I would like to extend my sincere gratitude to Dalat Nuclear Research Institute and Nuclear Training Centre of Vietnam Atomic Energy Institute for permitting me to conduct this research.

I sincerely thank the leadership of the Reactor Center at the Dalat Nuclear Research Institute and all my colleagues for their generous assistance during my research and for allowing me to use experimental data from 30 crit- ical configurations, which served as an important benchmark for validating this research’s results. Finally, I want to express my gratitude to my family, who have con- sistently given me the confidence and motivation to complete my thesis. Contents List of Tables. vii List of Figures.

1 Chapter 1: GENERAL OVERVIEW. The role of nuclear data libraries. Reactor core analysis and uncertainty sources. Uncertainty and sensitivity analysis.

Brief overview of the Dalat nuclear research reactor. Objectives of this Dissertation. 20 Chapter 2: METHODS AND MODELLING.1 The Dalat nuclear research reactor with low enriched uranium fuel .1 The reactor core .2 The fuel bundles .2 Code and reactor model .2 The reactor model .3 Nuclear data libraries .1 Evaluated Nuclear Data File (ENDF) .2 Joint Evaluated Fission and Fusion Nuclear Data Li- brary (JEFF) .3 Japanese Evaluated Nuclear Data Library (JENDL) .4 Chinese Evaluated Nuclear Data Library (CENDL) .4 Methods for sensitivity/uncertainty analysis .1 Sensitivity/uncertainty theory .2 Direct perturbation sensitivity analysis .3 Forward sensitivity analysis .4 Adjoint sensitivity analysis .5 Sensitivity and uncertainty analysis methods .5 Estimation of the effective multiplication factor .6 Methods for kinetic parameter evaluation .1 Effectively delayed neutron fraction .2 Neutron generation and prompt neutron lifetime. 55 Chapter 3: RESULTS AND DISCUSSION .1 Criticality, sensitivity and uncertainty analysis .1 Criticality calculations and comparison with measure- ments .2 Sensitivity analysis of the effective multiplication factor 63 iii 3.3 Uncertainty analysis of the effective multiplication factor 69 3.2 Evaluation of kinetic parameters .1 Influence of operational parameters on kinetic parameters 72 3.2 Dependence of kinetic parameters on fuel bur- nup using ENDF/B-VIII.3 Kinetic parameters versus control rod posi- tions using ENDF/B-VIII.4 Dependence of kinetic parameters on fuel tem- perature using ENDF/B-VIII.5 Dependence of kinetic parameters on burnup using JENDL-5 .2 Sensitivity analysis of the effectively delayed neutron fraction .3 Uncertainty analysis of the effectively delayed neutron fraction.

95 CONCLUSIONS, NEW CONTRIBUTIONS AND FUTURE WORKS. 101 Papers published during the dissertation. 118 Appendix A: Evaluation of kinetic parameters of the DNRR using Serpent 2 code .1 Meulekamp-Spriggs method .3 Nauchi and Kameyama method .4 Iterated Fission Probability (IFP) method .2 Results and discussion. 122 Appendix B: Covariance data.

125 Appendix C: Neutron spectrum. 132 iv List of symbols and abbreviations AR Automatic Regulating rod ASA Adjoint sensitivity analysis BOC Beginning of cycle BROND Russian Evaluated Nuclear Data Library CENDL Chinese Evaluated Nuclear Data Library CIELO Coordination International Evaluation Library Organization CNDC China Nuclear Data Center CNDCN Chinese Nuclear Data Cooperation Network CRPs Coordinated Research Projects CSEWG Cross Section Evaluation Working Group DNRR Dalat Nuclear Research Reactor DPSA Direct perturbation sensitivity analysis ENDF Evaluated Nuclear Data File EOC End of cycle FBR Fast Breeder Reactor FSA Forward sensitivity analysis HEU High Enriched Uranium IAEA International Atomic Energy Agency INDEN International Nuclear Data Evaluator Network JEFF Joint Evaluated Fission and Fusion File JENDL Japanese Evaluated Nuclear Data Library JNDC Japanese Nuclear Data Committee LEU Low Enriched Uranium LWR Light Water Reactor NAA Neutron Activation Analysis NDS Nuclear Data Section NEA Nuclear Energy Agency NDM Nuclear Data Measurement NNDC National Nuclear Data Center NPS Nuclear Physics Studies NRDC Nuclear Reaction Data Centres NSDD Nuclear Structure and Decay Data OECD Organization for Economic Cooperation and Development PCM Per Cent Mille (10−5 ) PGNAA Prompt Gamma Neutron Activation Analysis PT Perturbation Theory R&T Research and Training RI Radioisotope SA Sensitivity Analysis ShR Shim Rods SR Safety Rods S/U Sensitivity and Uncertainty TENDL TALYS based Evaluated Nuclear Data Library TRIGA Training, Research, Isotopes, General Atomics UA Uncertainty Analysis WPEC Working Party on International Nuclear Data Evaluation Cooperation Be S(α, β) Thermal scattering data for beryllium C-nat S(α, β) Thermal scattering data for natural carbon βeff Effective delayed neutron fraction Λ Neutron generation time λ Decay constant of delayed neutron precursors lp Prompt neutron lifetime Lwtr S(α, β) Thermal scattering data for hydrogen bound in light water keff Effective multiplication factor ρ Reactivity ρex Excess reactivity vi List of Tables 1.1 Design specifications of the DNRR with LEU fuel.2 Physical characteristics of irradiation facilities in the DNRR.1 Design parameters of the VVR-M2 LEU fuel bundle.2 Overview of ENDF versions and formats.3 Characteristics of the JENDL nuclear data library.4 Summary of the CENDL nuclear data library versions.1 Control rod position corresponding to the criticality condi- tions of the DNRR with LEU fuel established experimentally [101, 102] .2 The keff of the DNRR core with 92 LEU fuel bundles at critical, supercritical and subcritical conditions calculated using the MCNP6 code and the four data libraries.3 Criticality analysis of the DNRR with 92 LEU fuel bundles using the MCNP6 code and the four data libraries.4 Positive sensitivities of the keff , listed in descending order of magnitude according to the ENDF/B-VIII.5 Negative sensitivities of the keff , listed in descending order of magnitude according to the ENDF/B-VIII.6 The keff relative uncertainties for the reactions of the pri- mary isotopes are listed in order of decreasing magnitude based on the ENDF/B-VIII.7 Comparison of the βeff calculated by the adjoint weighted method and prompt method.8 Comparison of the kinetic parameters calculated by the ad- joint weighted and the 1/v absorber insertion method.9 Group delayed neutron fractions (βi ) and decay constants (λi ) calculated using the adjoint weighted method.10 Comparison of kinetic parameters derived from MCNP6 with those obtained from the Serpent 2 code∗∗ using ENDF/B- VIII.11 Summary of the kinetic parameters of the DNRR with 92 LEU fuel bundles.12 The βeff calculated by the adjoint weighted method and the prompt method.13 The Λ and lp calculated by the adjoint weighted and the 1/v insertion methods.14 Positive sensitivities of the βeff , listed in descending order of magnitude according to the ENDF/B-VIII.15 Negative sensitivities of the βeff , listed in descending order of magnitude according to the ENDF/B-VIII.16 The βeff relative uncertainties for the reactions of the pri- mary isotopes are listed in order of decreasing magnitude based on the ENDF/B-VIII.1 Delayed neutron parameters group using Meulekamp, Nauchi, and IFP methods.2 Comparison of kinetic parameters obtained through different methods. 123 viii List of Figures 1.1 The concept of safety margins as defined by the IAEA [4].2 Vertical section view of the DNRR.3 Horizontal cross section view of the DNRR pool tank.1 Configuration of the reactor core with 92 LEU fuel bundles.2 Cross sectional views and dimensional parameters of the Russian VVR-M2 type LEU fuel bundle.3 The control rods of the DNRR.4 The random walks of the different particles [66].5 The format of the MCNP6 input file [66].6 The vertical views of the DNRR model using the MCNP6.7 The horizontal views of the DNRR model using the MCNP6.8 The progression of the JEFF project.1 The keff values of 30 critical conditions of the DNRR with 92 LEU fuel bundles obtained with the four nuclear data libraries.2 Energy dependent sensitivities of the keff to U-235, H-1, and C-nat in the increasing direction.3 Energy dependent sensitivities of the keff to Lwtr S(α, β), O-16, Be-9, and Al-27 in the increasing direction.4 Energy dependent sensitivities of the keff to H-1, U-235, Al- 27, and U-238 in the decreasing direction.5 Energy dependent sensitivities of the keff to B-10, Be S(α, β), and Be-9 in the decreasing direction.6 Comparison of kinetic parameters calculated using MCNP6 with various methods in the Serpent 2 code.7 Variation of the kinetic parameters as functions of burnup.8 Variation of the kinetic parameters with respect to control rod positions.9 Variation of the kinetic parameters with respect to the change of fuel temperature.10 Variation of the kinetic parameters as functions of burnup.11 The lp as a function of B-10 concentration at the BOC and the EOC obtained from the 1/v absorber insertion method.12 Energy dependent sensitivities of the βeff of U-235, Lwtr S(α, β), Al-27, and C-nat S(α, β) .13 Energy dependent sensitivities of the βeff of Al-27, Be S(α, β), Fe-56, and U-235.14 Energy dependent sensitivities of the βeff of U-235, H-1, and O-16.15 Energy dependent sensitivities of the βeff of O-16, Be S(α, β), and Be-9.1 Covariance data of U-235 (n,fission) taken from the ENDF/B- VIII.3 and JENDL-5 libraries.2 Covariance data of H-1 (n,γ) taken from the ENDF/B-VIII.3 and JENDL-5 libraries.3 Covariance data of H-1 (n,elastic) taken from the ENDF/B- VIII.3 and JENDL-5 libraries.4 Covariance data plot for Al-27 (n,elastic).5 Covariance data plot for H-1 (n,elastic).6 Covariance data plot for Bo-10 (n,γ).7 Covariance data plot for O-16 (n,elastic).1 The neutron spectrum was calculated at the neutron trap using 44 energy groups and the ENDF/B-VIII.2 The neutron spectrum was calculated at the fuel rod using 44 energy groups and the ENDF/B-VIII. 132 x PREFACE The safe and efficient utilization of nuclear reactors requires accurate knowledge of reactor behavior under both normal operating conditions and anticipated operational occurrences.

Over the past decades, remarkable ad- vances in computational methods and computer technology have transformed reactor physics analyses, making numerical simulation an indispensable com- ponent of reactor design, operation, and safety assessment. Modern com- putational tools enable detailed investigations of neutron transport, reactor criticality, fuel management, burnup evolution, and reactor kinetics, thereby reducing reliance on costly and time consuming experiments. The reliability of reactor physics calculations depends strongly on the quality of the nuclear data employed in neutron transport simulations. Evalu- ated nuclear data libraries provide fundamental information describing neu- tron interactions with reactor materials, including reaction cross sections, fission yields, decay data, and thermal scattering laws.

These data con- stitute the foundation of all neutronic calculations.