Integrated Radiation Transport and Nuclear Fuel Performance for Assembly-Level Simulations

The Advanced Multi-Physics (AMP) Nuclear Fuel Performance code (AMPFuel) is focused on predicting the temperature and strain within a nuclear fuel assembly to evaluate the performance and safety of existing and advanced nuclear fuel bundles within existing and advanced nuclear reactors. AMPFuel was extended to include an integrated nuclear fuel assembly capability for (one-way) coupled radiation transport and nuclear fuel assembly thermo-mechanics. This capability is the initial step toward incorporating an improved predictive nuclear fuel assembly modeling capability to accurately account for source-terms and boundary conditions of traditional (single-pin) nuclear fuel performance simulation, such as the neutron flux distribution, coolant conditions, and assembly mechanical stresses. A novel scheme is introduced for transferring the power distribution from the Scale/Denovo (Denovo) radiation transport code (structured, Cartesian mesh with smeared materials within each cell) to AMPFuel (unstructured, hexagonal mesh with a single material within each cell), allowing the use of a relatively coarse spatial mesh (10 million elements) for the radiation transport and a fine spatial mesh (3.3 billion elements) for thermo-mechanics with very little loss of accuracy. In addition, a new nuclear fuel-specific preconditioner was developed to account for the high aspect ratio of each fuel pin (12 feet axially, but 1 4 inches in diameter) with many individual fuel regions (pellets). With this novel capability, AMPFuel was used to model an entire 17 17 pressurized water reactor fuel assembly with many of the features resolved in three dimensions (for thermo-mechanics and/or neutronics), including the fuel, gap, and cladding of each of the 264 fuel pins; the 25 guide tubes; the top and bottom structural regions; and the upper and lower (neutron) reflector regions. The final, full assembly calculation was executed on Jaguar using 40,000 cores in under 10 hours to model over 162 billion degrees of freedom for 10 loading steps. The single radiation transport calculation required about 50% of the time required to solve the thermo-mechanics with a single loading step, which demonstrates that it is feasible to incorporate, in a single code, a high-fidelity radiation transport capability with a high-fidelity nuclear fuel thermo-mechanics capability and anticipate acceptable computational requirements. The results of the full assembly simulation clearly show the axial, radial, and azimuthal variation of the neutron flux, power, temperature, and deformation of the assembly, highlighting behavior that is neglected in traditional axisymmetric fuel performance codes that do not account for assembly features, such as guide tubes and control rods

Neighborhood-corrected interface discontinuity factors for multi-group pin-by-pin diffusion calculations for LWR

Performing three-dimensional pin-by-pin full core calculations based on an improved solution of the multi-group diffusion equation is an affordable option nowadays to compute accurate local safety parameters for light water reactors. Since a transport approximation is solved, appropriate correction factors, such as interface discontinuity factors, are required to nearly reproduce the fully heterogeneous transport solution. Calculating exact pin-by-pin discontinuity factors requires the knowledge of the heterogeneous neutron flux distribution, which depends on the boundary conditions of the pin-cell as well as the local variables along the nuclear reactor operation. As a consequence, it is impractical to compute them for each possible configuration; however, inaccurate correction factors are one major source of error in core analysis when using multi-group diffusion theory. An alternative to generate accurate pin-by-pin interface discontinuity factors is to build a functional-fitting that allows incorporating the environment dependence in the computed values. This paper suggests a methodology to consider the neighborhood effect based on the Analytic Coarse-Mesh Finite Difference method for the multi-group diffusion equation. It has been applied to both definitions of interface discontinuity factors, the one based on the Generalized Equivalence Theory and the one based on Black-Box Homogenization, and for different few energy groups structures. Conclusions are drawn over the optimal functional-fitting and demonstrative results are obtained with the multi-group pin-by-pin diffusion code COBAYA3 for representative PWR configurations

A high-fidelity multiphysics system for neutronic, thermalhydraulic and fuel-performance analysis of Light Water Reactors

Das Verhalten des Kerns in einem Leichtwasserreaktor (LWR) wird von neutronenphysikalischen, thermohydraulischen und thermomechanischen Phänomenen dominiert. Komplexe Rückkopplungsmechanismen verbinden diese physikalischen Bereiche. Einer der aktuellen Tendenzen in der Reaktorphysik ist daher die Implementierung von Multiphysik-Methoden, die diese Wechselwirkungen erfassen, um eine konsistente Beschreibung des Kerns zu liefern. Ein weiterer wichtiger Arbeitsbereich ist die Entwicklung von High-Fidelity-Rechenprogrammen, die die Modellierungsauflösung erhöhen und starke Vereinfachungen eliminieren, die in räumlich homogenisierten Simulationen verwendet werden. Multiphysik- und High-Fidelity-Methoden sind auf die Verfügbarkeit von Hochleistungsrechnern angewiesen, die die Machbarkeit und den Umfang dieser Art von Simulationen begrenzen. Das Ziel dieser Arbeit ist die Entwicklung eines Multiphysik-Simulationssystems, das in der Lage ist, gekoppelte neutronenphysikalische, thermohydraulische und thermomechanische Analysen von LWR-Kernen mit einer High-Fidelity-Methodik durchzuführen. Um dies zu erreichen, wird die Monte-Carlo-Teilchentransportmethode verwendet, um das Verhalten der neutronenphysikalischen Effekte zu simulieren, ohne auf größere physikalische Näherungen zurückzugreifen. Für die Abbrandrechnungen bezüglich des gesamten Kerns, wird eine gebietsbezogene Datenaufteilung der Partikelverfolgung vorgeschlagen und implementiert. Die Kombination der Monte-Carlo-Methode mit der Thermohydraulik auf Unterkanalebene und eine vollständige Analyse des Brennstoffverhaltens aller Brennstäbe beschreibt eine extrem detaillierte Darstellung des Kerns. Die erforderliche Rechenleistung erreicht die Grenzen aktueller Hochleistungsrechner. Auf der Softwareseite wird ein innovativer objektorientierter Kopplungsansatz verwendet, um die Modularität, Flexibilität und Wartbarkeit des Programms zu erhöhen. Die Genauigkeit dieses gekoppelten Systems von drei Programmen wird mit experimentellen Daten von zwei in Betrieb befindlichen Kraftwerken, einem Pre-Konvoi DWR und dem Temelín II WWER-1000 Reaktor, bewertet. Für diese beiden Fälle werden die Ergebnisse der Abbrandrechnung des gesamten Kerns anhand von Messungen der kritischen Borkonzentration und des Brennstabneutronenflusses validiert. Diese Simulationen dienen der Darstellung der hochmodernen Modellierungsfähigkeiten des entwickelten Werkzeugs und zeigen die Durchführbarkeit dieser Methodik für industrielle Anwendungen

정상상태 및 과도상태 해석을 위한 고신뢰도 핵특성 연계 봉단위 열수력 노심 모의 코드 개발

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 에너지시스템공학부, 2021. 2. 주한규.A pin level reactor core thermal-hydraulics (T/H) code capable of massively parallel execution is developed and coupled with a transport direct whole core calculation (DWCC) code and with a pin-by-pin SP3 code for both steady-state and transient neutronics-T/H analyses. The Efficient Simulator of COre Thermal hydraulics (ESCOT) employs the 4-equation drift-flux model for two phase calculations while the numerical solution is obtained by applying the finite volume method and the Semi-Implicit Method for Pressure Linked Equation Consistent (SIMPLEC) algorithm. Important constitutive models to describe key subchannel phenomena, such as turbulent mixing, pressure drops, vapor generation, liquid-vapor interfacial heat transfer and wall heat transfer, are implemented to ensure the validity of subchannel-scale analyses. The ESCOT code solutions are validated through the simulation of various experiments and the comparison between the predicted quantities. The solutions are assessed also by the comparison with the corresponding results of the other subchannel-scale solvers like COBRA-TF, MATRA and/or CUPID. ESCOT has been successfully employed in steady-state transport DWCC analyses by coupling it with the nTRACER code through a wrapping system. The general coupling technique based on the Picard fixed-point iteration (FPI) has low robustness and the application of relaxation factors leaves too much freedom to the user. Thus, the application of the Anderson Acceleration (AA) as an effort to improve the stability of coupled steady-state calculations is analyzed through a series of 3-dimensional problems solved with increasing complexity starting from a single assembly steady-state problem to a full core depletion problem via checker-board (CB) problems. The convergence behavior is examined in terms of true error reduction by comparing the intermediate fission source distributions with the fully converged reference solution obtained by applying a very tight convergence criterion. It turns out that the number of neutronics-T/H iterations is reduced considerably because the oscillatory behaviors of the local solutions noted in the ordinary FPI can be smoothened. Convergence is reached earlier with AA so that the computing times of the coupled calculations can be reduced by about 25% retaining the solution accuracy. In addition, the improvements in both accuracy and details of the time-dependent coupled analyses are shown through the solution of the Main Steam Line Break (MSLB) accident. This scenario involves a considerable reduction of the inlet coolant temperature of one side of the reactor core which results in significant asymmetry in the radial flow characteristics. Because of this asymmetry, the positive reactivity feedback effect introduced by the decrease of the coolant temperature occurs with strong spatial dependence. For sufficient conservatism, a stuck rod in the cold side is assumed during the reactor trip. Thus, employing the pin level solvers increases the fidelity of the calculated results. Despite the increased performances of transport transient solvers, the computing time is still a burden for the calculation of transients lasting longer than 20sec in simulation time. Therefore, ESCOT has been coupled with a pin-by-pin SP3 based code instead of a DWCC code. The analysis of the Nuclear Energy Agency of the Organization for Economic Cooperation and Development MSLB benchmark is performed by solving the Exercise II problem which does not require system modeling since it provides two sets of core flow boundary conditions. It turns out that the better neutronics and T/H nodalization of the core leads to a higher SCRAM worth which implies a lower maximum return-to-power when it is compared with assembly-wise solvers (< 2%). It is noted also that the mixing effect between the hot and cold sides is constrained only to the first assembly row and the size of the mixing region increases with the core axial level. A dominant axial velocity and a CB-like power shape around the separation between the two sides are the primary reasons for the lack of mixing beyond the first assembly row. Moreover, the better T/H nodalization describes more reliably the coolant behavior around the stuck rod. The use of a pin-by-pin solver allows also to capture the high gradient in pin power inside the assemblies close to the stuck rod at the instance of maximum return-to-power, which was not possible with the conventional assembly-wise solvers. The pin-level coupled neutronics-T/H does not increase the computing time noticeably owing to the parallelized execution capability. This study demonstrates the importance of advancing to pin-wise coupled transient analyses in order to fully understand the core power and temperature behaviors in the severe conditions involving highly distorted flow and power distributions.Abstract Contents List of Figures List of Tables Introduction 1 Purpose, Objectives and Scopes of the Research 4 Roadmap of Multiphysics Analyses at SNU Reactor Physics Laboratory 6 Outlines of the Thesis 7 Development of a Pin level Thermal-hydraulics code 9 Four-equation drift-flux model 10 Mixture properties 11 Drift-flux parameters and phasic velocities 12 Balance equations 14 Mixture mass balance 14 Vapor mass balance 14 Mixture momentum balance 14 Mixture energy balance 15 Equations of state 15 Discretization and solution algorithm 16 Description of subchannel-level phenomena 20 Flow regime map 20 Boiling regimes 23 Macro-mesh cell closure laws 25 Micro-mesh cell closure laws 33 Wall temperature calculation 41 Solution of the conduction equation 45 Equations of state for the solid 46 Solution Strategy and Implementation 51 Critical Heat Flux 52 Two phase validation of the ESCOT code 54 RPI Air-water test 55 GE three by three test 58 PSBT Phase I, Exercise Two 62 Parallelization Scheme 67 Analysis of Steady-state Neutronics-Thermal/Hydraulics Coupled Calculations 69 nTRACER/ESCOT coupled system 73 Anderson Acceleration 77 Undamped Anderson Acceleration algorithm 78 Implementation 81 Assessment of the Anderson Acceleration performances 84 Reduced problems 88 Actual core problems 95 Analysis of Transient Neutronics-Thermal/Hydraulics Coupled Calculations 109 Simplified Pthree based neutronics solver 111 Transient neutronics-T/H coupling 113 Analysis of the NEA/OECD MSLB benchmark 115 Description of the scenario 116 Solution of the NEA/OECD MSLB benchmark exercise II 120 Summary and Conclusions 148 Acknowledgements 153 Appendix A Derivation of the Pressure Correction Equation 155 Appendix B Single phase validation 160 Appendix C Decay Heat Model 174 References 177Docto

A High Fidelity Multiphysics Framework for Modeling CRUD Deposition on PWR Fuel Rods.

Corrosion products on the fuel cladding surfaces within pressurized water reactor fuel assemblies have had a significant impact on reactor operation. These types of deposits are referred to as CRUD and can lead to power shifts, as a consequence of the accumulation of solid boron phases on the fuel rod surfaces. Corrosion deposits can also lead to fuel failure resulting from localized corrosion, where the increased thermal resistance of the deposit leads to higher cladding temperatures. The prediction of these occurrences requires a comprehensive model of local thermal hydraulic and chemical processes occurring in close proximity to the cladding surface, as well as their driving factors. Such factors include the rod power distribution, coolant corrosion product concentration, as well as the feedbacks between heat transfer, fluid dynamics, chemistry, and neutronics. To correctly capture the coupled physics and corresponding feedbacks, a high fidelity framework is developed that predicts three-dimensional CRUD deposition on a rod-by-rod basis. Multiphysics boundary conditions resulting from the coupling of heat transfer, fluid dynamics, coolant chemistry, CRUD deposition, neutron transport, and nuclide transmutation inform the CRUD deposition solver. Through systematic parametric sensitivity studies of the CRUD property inputs, coupled boundary conditions, and multiphysics feedback mechanisms, the most important variables of multiphysics CRUD modeling are identified. Moreover, the modeling framework is challenged with a blind comparison of plant data to predictions by a simulation of a sub-assembly within the Seabrook nuclear plant that experienced CRUD induced fuel failures. The physics within the computational framework are loosely coupled via an operator-splitting technique. A control theory approach is adopted to determine the temporal discretization at which to execute a data transfer from one physics to another. The coupled stepsize selection is viewed as a feedback control problem, and a controller of the type integral is utilized. The temporal discretization adapts with the problem solution to maintain a user-prescribed tolerance of specific solution variables. Predictor-corrector algorithms enable convergence error estimates. The highly nonlinear precipitation rate of solid boron phases, and their dependence on the local thermal hydraulic conditions, is the primary motivation for seeking an automated and adaptive stepsize selection algorithm.PhDNuclear Engineering and Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120638/1/djwalter_1.pd

The OpenMOC method of characteristics neutral particle transport code

The method of characteristics (MOC) is a numerical integration technique for partial differential equations, and has seen widespread use for reactor physics lattice calculations. The exponential growth in computing power has finally brought the possibility for high-fidelity full core MOC calculations within reach. The OpenMOC code is being developed at the Massachusetts Institute of Technology to investigate algorithmic acceleration techniques and parallel algorithms for MOC. OpenMOC is a free, open source code written using modern software languages such as C/C++ and CUDA with an emphasis on extensible design principles for code developers and an easy to use Python interface for code users. The present work describes the OpenMOC code and illustrates its ability to model large problems accurately and efficiently.National Science Foundation (U.S.). Graduate Research Fellowship Program ( Grant No. 1122374)United States. Department of Energy. Center for Exascale Simulation of Advanced Reactors (CESAR)United States. Office of the Assistant Secretary for Nuclear Energy (Nuclear Energy University Programs Fellowship)Studsvik Scandpower Graduate FellowUnited States. Department of Energy. Office of Advanced Scientific Computing Research (Contract DE-AC02-06CH11357

Multigroup diffusion preconditioners for multiplying fixed-source transport problems

Several preconditioners based on multigroup di usion are developed for application to multiplying fi xed-source transport problems using the discrete ordinates method. By starting from standard, one-group, diff usion synthetic acceleration (DSA), a multigroup diff usion preconditioner is constructed that shares the same fi ne mesh as the transport problem. As a cheaper but effective alternative, a two-grid, coarse-mesh, multigroup diff usion preconditioner is examined, for which a variety of homogenization schemes are studied to generate the coarse mesh operator. Finally, a transport-corrected diff usion preconditioner based on application of the Newton-Shulz algorithm is developed. The results of several numerical studies indicate the coarse-mesh, diff usion preconditioners work very well. In particular, a coarse-mesh, transport-corrected, diff usion preconditioner reduced the computational time of multigroup GMRES by up to a factor of 17 and outperformed best-case Gauss-Seidel results by over an order of magnitude for all problems studied

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

High-order Spatio-temporal Schemes for Coupled, Multi-physics Reactor Simulations

This report summarizes the work done in the summer of 08 by the Ph.D. student Vijay Mahadevan. The main focus of the work was to coupled 3-D neutron difusion to 3-D heat conduction in parallel with accuracy greater than or equal to 2nd order in space and time. Results show that the goal was attained