Simulations of BEAVRS Benchmark Cycle 2 Depletion with MCS/CTF Coupling System

The quarter-core simulation of BEAVRS Cycle 2 depletion benchmark has been conducted using the MCS/CTF coupling system. MCS/CTF is a cycle-wise Picard iteration based inner-coupling code system, which couples sub-channel T/H (thermal/hydraulic) code CTF as a T/H solver in Monte Carlo neutron transport code MCS. This coupling code system has been previously applied in the BEAVRS benchmark Cycle 1 full-core simulation. The Cycle 2 depletion has been performed with T/H feedback based on the spent fuel materials composition pre-generated by the Cycle 1 depletion simulation using refueling capability of MCS code. Meanwhile, the MCS internal one-dimension T/H solver (MCS/TH1D) has been also applied in the simulation as the reference. In this paper, an analysis of the detailed criticality boron concentration and the axially integrated assembly-wise detector signals will be presented and compared with measured data based on the real operating physical conditions. Moreover, the MCS/CTF simulated results for neutronics and T/H parameters will be also compared to MCS/TH1D to figure out their difference, which proves the practical application of MCS into the BEAVRS benchmark two-cycle depletion simulations. (C) 2019 Korean Nuclear Society, Published by Elsevier Korea LLC

A Multi-Physics Adaptive Time Step Coupling Algorithm for Light-Water Reactor Core Transient and Accident Simulation

A new reactor core multi-physics system addresses the pellet-to-cladding heat transfer modeling to improve full-core operational transient and accident simulation used for assessment of reactor core nuclear safety. The rigorous modeling of the heat transfer phenomena involves strong interaction between neutron kinetics, thermal-hydraulics and nuclear fuel performance, as well as consideration of the pellet-to-cladding mechanical contact leading to dramatic increase in the gap thermal conductance coefficient. In contrast to core depletion where parameters smoothly depend on fuel burn-up, the core transient is driven by stiff equation associated with rapid variation in the solution and vulnerable to numerical instability for large time step sizes. Therefore, the coupling algorithm dedicated for multi-physics transient must implement adaptive time step and restart capability to achieve prescribed tolerance and to maintain stability of numerical simulation. This requirement is met in the MPCORE (Multi-Physics Core) multi-physics system employing external loose coupling approach to facilitate the coupling procedure due to little modification of constituent modules and due to high transparency of coupling interfaces. The paper investigates the coupling algorithm performance and evaluates the pellet-to-cladding heat transfer effect for the rod ejection accident of a light water reactor core benchmark

Overcoming the challenges of Monte Carlo depletion: Application to a material-testing reactor with the MCS code

The theoretical aspects behind the reactor depletion capability of the Monte Carlo code MCS developed at the Ulsan National Institute of Science and Technology (UNIST) and practical results of this depletion feature for a Material-Testing Reactor (MTR) with plate-type fuel are described in this paper. A verification of MCS results is first performed against MCNP6 to confirm the suitability of MCS for the criticality and depletion analysis of the MTR. Then, the dependence of the effective neutron multiplication factor to the number of axial and radial depletion cells adopted in the fuel plates is performed with MCS in order to determine the minimum spatial segmentation of the fuel plates. Monte Carlo depletion results with 37,800 depletion cells are provided by MCS within acceptable calculation time and memory usage. The results show that at least 7 axial meshes per fuel plate are required to reach the same precision as the reference calculation whereas no significant differences are observed when modeling 1 or 10 radial meshes per fuel plate. This study demonstrates that MCS can address the need for Monte Carlo codes capable of providing reference solutions to complex reactor depletion problems with refined meshes for fuel management and research reactor applications. (c) 2020 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Analysis of VVER-1000 mock-up criticality experiments with nuclear data library ENDF/B-VIII.0 and Monte Carlo code MCS

The criticality analysis of VVER-1000 mock-up benchmark experiments from the LR-0 research reactor operated by the Research Center Rez in the Czech Republic has been conducted with the MCS Monte Carlo code developed at the Computational Reactor Physics and Experiment laboratory of the Ulsan National Institute of Science and Technology. The main purpose of this work is to evaluate the newest ENDF/B-VIII.0 nuclear data library against the VVER-1000 mock-up integral experiments and to validate the criticality analysis capability of MCS for light water reactors with hexagonal fuel lattices. A preliminary code/code comparison between MCS and MCNP6 is first conducted to verify the suitability of MCS for the benchmark interpretation, then the validation against experimental data is performed with both ENDF/B-VII.1 and ENDF/B-VIII.0 libraries. The investigated experimental data comprises six experimental critical configurations and four experimental pin-by-pin power maps. The MCS and MCNP6 inputs used for the criticality analysis of the VVER-1000 mock-up are available as supplementary material of this article

Verification and validation of monte carlo code MCS for the multi-physics high-fidelity analysis of OPR-1000 multi-cycle operation

Department of Nuclear EngineeringWorldwide demand for high-fidelity simulation tools for large scale power reactor analysis resulted in the coupling of neutronics, thermal hydraulics, and fuel mechanics in nuclear reactor cores. The Computational Reactor Physics and Experiment (CORE) laboratory at Ulsan National Institute of Science and Technology (UNIST) has developed an inhouse Monte Carlo code MCS coupled with multi-physics (MP) tools such as a one-dimensional (1D) single-phase closed-channel thermal-hydraulic code (TH1D), a sub-channel two-phase thermal-hydraulic code (CTF) and a fuel performance code (FRAPCON) to provide thermal-hydraulic and fuel behavior feedbacks for realistic applications. This thesis describes the 3D whole-core analysis with pin-wise resolution in which neutron transport, depletion, thermal-hydraulic, and fuel behavior calculations are performed using the coupled MCS/TH1D, MCS/CTF, and MCS/FRAPCON tools. The OPR-1000 PWR core operated for 2 consecutive cycles is selected as a target for MP coupling analysis, including verification and validation. The OPR-1000 PWR is a Generation II nuclear reactor in South Korea with 2815 MW thermal power modeled explicitly in MCS. The MCS simulation of OPR core during the zero-power physics testing was evaluated for critical boron concentration (CBC) and control rod worth, and the results show good agreement with the references. The verification and validation of MCS MP coupling were conducted at hot full power conditions along with various feedback required for reactor power simulation such as depletion, equilibrium xenon update, CBC search, and on-the-fly cross-section reconstruction. The influence on other parameters, including CBC, axial shape index, pin- and assembly-wise radial/axial power profiles, fuel temperatures, and moderator temperatures/densities, were investigated. The MCS MP coupled results were also compared against the experimental data for validation. Additional comparisons were made with the data from the plant???s nuclear design report and result from the deterministic two-step code STREAM/RASTK 2.0 (ST/R2) and 3D Method of Characteristic (MOC) direct neutron transport code STREAM. For the MCS MP coupling tool with thermal-hydraulic and fuel performance feedback, excellent agreement is observed with the measured values with a root mean square (RMS) error of 26 ppm for CBC and 1.8% for assembly power. Compared to other codes, MCS MP coupling results have an RMS error of 16 ppm for CBC and 1.8% for assembly power. Larger discrepancies in relative assembly power between MCS based MP tool and measured data occur in the core-periphery where the power is relatively low, while at the end of cycles, the discrepancies are still within 1 standard deviation of about 2.4%. This study demonstrates MCS???s capability to perform high-fidelity simulation of a practical light water reactor core.clos

MCS based neutronics/thermal-hydraulics/fuel-performance coupling with CTF and FRAPCON

A Monte-Carlo neutronics/thermal-hydraulics/fuel-performance (N/TH/FP) multi-physics coupling system has been developed based on the MCS code recently for the purpose of large-scale high-fidelity analysis of light water reactors (LWRs). The full N/TH/FP coupling overcomes the drawbacks of the previous N/TH (MCS/CTF) and N/FP (MCS/FRAPCON) coupling systems, which suffered respectively from the approximations in CTF on the fuel thermal conductivity and gap conductance, and from the approximations due to the single closed channel enthalpy model in FRAPCON. Thus, compared to the previous coupling systems, the new full coupling system benefits from the transverse cross flow between neighboring sub-channels in CTF, the burnup-dependent fuel thermal conductivity formulation in FRAPCON, and the iteratively determined fuel pellet-cladding gap thermal conductance in FRAPCON. Two applications of the full coupling systems are presented. First, a single fuel rod case is tested to verify the accuracy and efficiency of the new coupled system. Then, the simulation of the BEAVRS whole core model with three-dimensional (3D) pin-by-pin power density and T/H feedbacks exchange between different solvers is performed using the MCS based multi-physics coupling system. The obtained results demonstrate the practical capability of the Monte Carlo based steady-state multi-physics coupling code system for large-scale high-fidelity LWR analysis

VVER을 포함한 광범위 적용을 위한 고신뢰도 다물리 해석의 최적화 및 안정화

학위논문(박사) -- 서울대학교대학원 : 공과대학 에너지시스템공학부, 2023. 2. 심형진.The capability of the nTRACER direct whole core calculation code coupled with the ESCOT pin-level core thermal-hydraulics (T/H) code is extended and stabilized for extended applications including the high-fidelity multiphysics analysis of VVER cores. First of all, the calculation feature of ESCOT is extended to handle the hexagonal geometry cores of VVERs and its performance is assessed by a code-to-code comparison with COBRA-TF (CTF). The coupling of ESCOT with the nTRACER direct whole core calculation code is then enhanced to deal with the VVER cores. Secondly, the stability of the nTRACER calculation involving strong nonlinear feedback such as xenon and Doppler is stabilized by imposing the Anderson Acceleration (AA) to the neutron flux after Fourier analysis of the feedback effects. In ESCOT, the lateral momentum terms, the turbulent mixing coefficient values, the fuel conduction solution and the parallelization algorithms are modified for the handling of hexagonal geometry. The newly implemented ESCOT features are verified by comparing the solution of the single assembly, minicore and full core steady-state standalone and coupled problems for the VVER-1000 benchmark X-2 with the CTF results. ESCOT and CTF results show differences within an acceptable range in both standalone and coupled calculations. The computing time superiority due to the use of the drift flux model (DFM) of ESCOT over the CTF two-fluid model is confirmed with a speed-up factor of 1.35. The use of the DFM together with the axial-radial parallelization capability of ESCOT makes ESCOT an ideal alternative to replace the simplified built-in T/H solver in nTRACER as the coupled simulation results demonstrate. It is shown that the xenon feedback in nTRACER sometimes reveals a non-convergent oscillatory behavior, particularly in depletion calculations as the fissile material becomes scarce. A Fourier analysis is performed to a simplified 1G 1D problem with periodic boundary condition and variable cross sections to obtain an analytical expression relating the convergence degree of the Power Iteration (PI) that yields the smallest spectral radius for different feedback coefficients. Increasing problem complexity to a non-homogeneous problem makes it not feasible to obtain an analytical expression for realistic problems. Consequently, the AA is retrieved, modified and analyzed for multiphysics problems. By systematically studying the sequential addition of xenon and boron to the neutronics-T/H 1G 1D problem, it is demonstrated that if the original fixed-point map of the AA applied only to the T/H variables is extended to include other physics by applying the AA to neutron flux, the oscillatory behavior is greatly suppressed. It turned out that the AA applied on the condensed two-group flux instead of on the original 47-group works well so that the increase in memory is trivial. The necessary average number of Fixed-Point Iterations (FPI) is reduced from about 15 to less than 10. The eigenvalue yielded also an error reduction from about 5 pcm to less than 0.5 pcm and it is highlighted that the AA applied to flux can achieve a convergence behavior similar to the quasi-optimal point. The application of these findings to nTRACER solved the non-convergence issues in the depletion calculations for cores such as the APR1400 and the BEAVRS benchmark. In addition, the revision of the convergence criterion for the CMFD calculation is improved by adding the residual check to the original criterion of the residual ratio. This improvement saves the computing time by about an 11.5 % for the APR1400 quarter core depletion calculation. Finally, a depletion calculation for the modified X-2 VVER benchmark is performed with nTRACER/ESCOT. The result show that the direct whole core depletion can be finished in 14 hours, among which only 11 % is spent for the ESCOT calculation and only 5 FPIs per depletion step are needed. This calculation demonstrates that stable high-fidelity depletion calculation for hexagonal geometry cores is possible in a competitive time span.봉단위 노심 열수력 해석 부수로 코드인 ESCOT을 확장하여 육각 기하 노심 처리능을 탑재하고, 특히 VVER 노심을 해석할 수 있도록 하였다. ESCOT의 전처리기는 육각 기하구조에서의 부수로-간극-연료봉의 관계식을 생산할 수 있도록 개선하였. 해당 코드의 알고리즘은 새로운 기하 구조에 대해 맞게 조정하였다. 구체적으로는 측면 운동량의 반경방향 항을 제거하고, 난류 혼합 계수의 고정값을 재계산하고, 중공 연료봉 형태의 계산을 위한 핵연료봉 열전도 풀이법을 조정하였다. 축방향의 압력 강하, 열전달 계수의 개선, 난류 혼합 증가에 대한 지지격자의 효과를 고려하기 위한 보다 정교한 상관관계 모델이 적용하였다. 고스트 셀의 정의와 문제 단위 프로세스 할당으로 병렬 처리를 위한 두 방향의 영역분할 기법 또한 조정하였다. ESCOT 코드는 전노심 직접해석 코드인 nTRACER의 육각 기하 솔버와 연계시켰다. 독립 계산과 연계 계산 모두 CTF 결과와 비교하여검증하였다. 참조해는 PSI에서 개발한 nTRACER/CTF 코드 연계 시스템으로부터 확보하였다. 독립계산 결과는 참조해와 비슷한 결과를 보였고, CTF 코드와 비교하여 1.35배 빠른 것으로 나타났다. 연계 계산 또한 서로잘 일치하는 결과를 보여준다. 전노심 계산의 경우 wrapper 기반 병렬화를 통한 ESCOT과 연계 시 CTF 코드 연계와 비교해 7배 가량 더 빠른 결과를 보여주었다. 이후 열수력 궤환 효과와 제논 궤환 효과가 혼합된 연소계산에서 나타나는 수렴 불안정성을 해결하기 위한 연구를 수행하였다. 먼저 단일군-일차원으로 단순화된 문제를 통해 열수력 관련 변수들 외에 제논 및 붕산농도의 궤환효과등의 확장된 물리현상을 고려하는 고정점 반복 연계 체계에 대해 분석하였다. Power iteration의 최적의 수렴을 위한 인자를 찾기 위해 해석적인 식을 정의하는 것은 실용적이지 않기 때문에, 기존의 Anderson 가속법을 수정하여 수렴성을 개선시켰다. 해당 기법을 열수력 관련 변수들에 적용하는 대신 중성자속 변수에 적용함으로써 과도하게 진동하는 수렴거동을 효과적으로 완화할 수 있었고, 결과적으로 고정점 반복 계산의 수렴거동이 눈에 띄게 개선되는 것을 확인하였다. 고정점 반복 계산 방법의 변화는 반복 계산의 횟수를 1.5배 가량 줄이는 효과를 보였다. 수정된 Anderson 가속법은 nTRACER에도 적용시켜 연소 계산을 안정시키는 성능을 확인했다. nTRACER에서의 power iteration 동안의 불필요한 CMFD 반복계산을 피하기 위한 수렴 조건을 평가하였고, 잔차절대값에대한수렴조건을추가함으로써총 계산 시간을 11.5 % 가량 줄일 수 있었다. 마지막으로, 연구성과 및 계산성능 개선효과 등을 보여주기 위해 nTRACER/ESCOT 연계 체계를 통한 VVER 노심의 연소 계산을 수행하였다. 이 연구에 제시한 방법과 개발한 코드 모듈을 통해 육각 기하노심에 대한 봉단위 열수력 연계 고신뢰도 직접 전노심 연소 계산이 현 실적인 시간안에 안정적으로 수행이 가능함을 입증하였다.Chapter 1. Introduction 14 1.1. Purpose and Scope of the Research 18 1.2. Outline of the Thesis 20 Chapter 2. Description of the Pinwise Core Thermal-Hydraulics Code ESCOT 22 2.1. Mixture Properties 23 2.2. Field Equations of the Four-Equation Drift-Flux Model 24 2.2.1. Mixture mass conservation equation 24 2.2.2. Vapor mass conservation equation 24 2.2.3. Mixture momentum conservation equation 25 2.2.4. Mixture energy conservation equation 25 2.3. Constitutive Relations for Subchannel-Scale Analysis 25 2.3.1. Equation of state 26 2.3.2. Drift-flux parameters 26 2.3.3. Pressure drop model 28 2.3.4. Turbulent mixing model 29 2.3.5. Vapor generation model 32 2.4. Numerical Solution Method 32 2.4.1. Discretization 33 2.4.2. The pressure correction equation and solution with SIMPLE algorithm 35 2.5. Solution of the Conduction Equation 41 2.5.1. The conduction equation 41 2.5.2. The solution strategy and implementation 42 2.6. Hexagonal Geometry Extension 44 2.6.1. Lateral momentum equation modifications 44 2.6.2. Turbulent mixing coefficient in hexagonal problems 47 2.6.3. Fuel conduction in hollow pins 50 2.7. Hexagonal Geometry Radial Domain Decomposition 52 2.8. Code-to-Code ESCOT Hexagonal Verification with CTF 54 2.8.1. Solution accuracy assessment with single assembly problem 54 2.8.2. Drift-flux model time performance assessment with full core problem 57 2.8.3. Parallelization assessment with minicore problem 58 2.9. Spacer Grids Models in ESCOT 60 2.9.1. Spacer grid form loss coefficient for pressure drop 61 2.9.2. Spacer grid HTC enhancement 64 2.9.3. Spacer grid turbulent mixing enhancement 68 Chapter 3. nTRACER/ESCOT Coupled Calculations for Hexagonal Geometry 70 3.1. nTRACER/ESCOT Coupling Strategy 70 3.1.1. nTRACER/CTF coupling characteristics 73 3.2. X-2 benchmark modeling 75 3.3. ESCOT-CTF coupled case comparison 79 3.3.1. Single assembly calculations 79 3.3.2. Minicore calculation 84 3.3.3. Full core calculation 88 Chapter 4. Study and Optimization of the Multiphysics Calculation 94 4.1. Fourier Analysis of the Multiphysics Problem 95 4.1.1. Review of the Fixed-Point Iteration 95 4.1.2. Problem description and cross sections change functionalization 97 4.1.3. Fourier analysis of the multiphysics homogeneous problem 101 4.1.4. Fourier analysis of the multiphysics non-homogeneous problem 108 4.2. Numerical Analysis of the Anderson Acceleration for Multiphysics Problems 110 4.2.1. Review of the Anderson Acceleration 110 4.2.2. The physical model 112 4.2.3. Problem specifications 117 4.2.4. Numerical analysis of neutronics-T/H problems 118 4.2.5. Numerical analysis of neutronics-T/H-xenon problems 128 4.2.6. Numerical analysis of neutronics-T/H-xenon-boron problems 137 Chapter 5. Anderson Acceleration in nTRACER 147 5.1. Checkerboard Calculations 148 5.1.1. Checkerboard steady state calculations 148 5.1.2. Checkerboard depletion calculations 152 5.2. Optimization of the Core Depletion 157 5.2.1. Core depletion calculation 158 5.2.2. Study of the power iteration convergence criteria in nTRACER 159 5.3. nTRACER/ESCOT VVER Depletion Calculation 166 5.3.1. Core model simplification 167 5.3.2. Depletion calculation results 168 Chapter 6. Summary and Conclusions 170 Acknowledgements 175 References 176 APPENDIX A. Conservation Equations in Discretized Form 181 APPENDIX B. Coupled Linear System of Scalar Equations 185박

Development of Reactor Multiphysics framework to analyze the effect of crossflow and dynamic gHTC for Depletion and REA transient

Department of Nuclear EngineeringThe aim of this research is to create a Multiphysics coupling framework called MPCORE (Multi-Physics CORE) to analyze the behavior of nuclear reactors. This framework couples fuel performance (FP) with neutron kinetics (NK) and thermal hydraulics (TH) modules for depletion and transient analysis. Coupling the FP code allows for accurate modeling of dynamic gap heat transfer for each pin. Converging all modules together provides a more meaningful insight into the variation of reactor parameters. Depletion studies with Multiphysics parameters are essential to understand safety parameters throughout a nuclear reactor's life. The study investigates the passive response of the reactor core to reactivity insertions caused by rod ejection accidents (REA). Most coupling frameworks only couple NK with TH, but this research also includes FP and uses two-way coupling between TH and FP modules to examine the impact on critical safety parameters. The adaptive time-step feature of MPCORE reduces execution time, and the framework performs in-memory data transfer between modules. Verification and validation work for MPCORE coupled modules (RAST-K for NK, CTH1D/CTF for TH, and FRAPI for FP) has been performed for single assembly, 3x3 mini-core, and whole-core problems. The performance of the TH module is evaluated with and without crossflow for transient calculations in whole-core problems. The effect of dynamic and static gap heat transfer coefficient models on the FP module is quantified for assembly, mini-core, and whole-core transient problems. Difference between one-way and two-way coupling between FP and TH modules is quantified for whole-core depletion problems. The study compares safety parameters such as departure from nucleate boiling ratio, linear power, fuel enthalpy, fuel centerline temperature, cladding outer surface temperature, coolant temperature, and cladding hydrogen concentration for different models. A best-estimate coupling framework has been developed and tested for uncertainty quantification (UQ) studies for assembly and mini-core problems. Random sampling and Latin hypercube sampling options are available for UQ studies in MPCORE. Standard deviation of different parameters in case of dynamic gap conductance has increased due to the difference of gap heat transfer in different cases.clos