Advanced computational tools are applied to simulate a nuclear power plant (NPP) control rod assembly ejection (CRE) accident. The impact of these reactivity-initiated accidents (RIAs) on core reactivity behavior, 3D power distribution and stochastic reactivity estimation are evaluated. The three tools used are: the thermal-hydraulic (TH) RELAP5 (R5) code, the neutronic (NK) PARCS (P3D) code, and the coupled version P3D/R5, with specially developed linkage using the environment code MATLAB. This study considers three different-size cores: NPP1 (2772 MWt); NPP2 (530 MWt); and NPP3 (1061 MWt). The three cores have the same general design and control rod assembly (CRA) positions, and the ejected CRA has similar worth and at the same rod ejection pace. The CRE is assessed under both hot zero power (HZP) and hot full power (HFP) conditions. The analyses indicate that RIA modeling and simulation should be carried out through a systematic coding and configuration approaches, otherwise the results will not capture the true transient behavior of the core under analysis. The simulation of one code depends on the appropriate configuration of parameters generated by the other code and on the correct determination of the TH/NK mapping weight factors for the various mesh regions in each of the models. From the design point of view, the standalone codes predict milder magnitude of power and reactivity increase compared to the coupled P3D/R5 simulation. The magnitudes of reduced peak power and reactivity become larger as the core size shrinks. The HFP simulation shows that the three NPPs have the same transient peak value, but the post-transient steady power is lower for a smaller core. The HZP analysis indicates that the transient peak is lower for the smaller core, but the post-transient power occurs at the same level. The three-dimensional (3D) power distributions are different among the HFP and HZP cases, but do not depend on the size of the core. The results indicate: i) HFP: core power increases in the area surrounding the ejected rod/bank assembly, and this increase becomes lower as the NPPs shrinks however, the power is well-distributed after the transient; and ii) HZP: the area surrounding the CRA stays hotter, but the 3D peak assembly factor becomes lower, during and after the transients, as the NPPs shrinks. These features confirm that the smaller cores yield a safer response to a given inserted reactivity compared to larger cores. A stochastic extended Kalman filter (EKF) algorithm is implemented to estimate the reactivity based on the reactor power profile, after the addition of random noise. The inverse point kinetics (IPK) deterministic method is also implemented and the results of the application of EKF and IPK are compared to the P3D/R5 simulation. The following sophisticated strategies made the EKF algorithm robust and accurate: the system is modeled by a set of continuous time nonlinear stochastic differential equations; the code uses a time step directly based on the power measured and applies that to the model for online discretization and linearization; filter tuning goes automatically up from the first time step; and the state noise covariance matrix is updated online at each time step. It was found that the IPK reactivity has higher noise content compared to the EKF reactivity for all cases. Thus, the EKF presents superior and more accurate results. Furthermore, under a small reactivity insertion, the IPK reactivity varies widely from positive to negative values: this variation is not observed within the EKF. A sensitivity analysis for three distinct standard deviation (SD) noise measurements suggests that EKF is superior to IPK method, independent of the noise load magnitude. As the noise content increases, the error between the IPK and P3D/R5 reactivity also increases. A sensitivity analysis for five distinct carry-over effects of different random noise loads indicates that the random addition of different noise loads to the reactor power does not change the overall performance of both algorithms. / Este trabalho aplica métodos computacionais avançados para simular a ejeção de barras de controle (CRE) em uma planta térmica nuclear (NPP). São avaliados o impacto da ocorrência de acidentes iniciados por reatividade (RIAs) na reatividade total, na distribuição da potência em três dimensões (3D) e na determinação da reatividade. As ferramentas utilizadas são: o código termo-hidráulico (TH) RELAP5 (R5), o código neutrônico (NK) PARCS (P3D), a versão acoplada P3D/R5, e o ambiente computacional MATLAB. Este estudo considera três reatores nucleares de diferentes tamanhos: NPP1 (2772 MWT); NPP2 (530 MWt); e NPP3 (1061 MWt). Os três núcleos possuem projeto similar e idêntica posição dos grupos das barras de controle (CRA), além do mesmo valor de reatividade diferencial das CRA ejetadas e idêntica velocidade de ejeção. A ocorrência da CRE é avaliada sob condições de hot zero power (HZP) e de hot full power (HFP). As análises indicam que a modelagem e a simulação de RIAs devem ser realizadas sistematicamente, caso contrário os resultados não irão refletir o comportamento em regime transitório do núcleo. A simulação de um modelo em um código depende da apropriada configuração de parâmetros gerados pelo outro código e da determinação adequada do mapeamento TH/NK para as várias malhas dos modelos. Do ponto de vista de projeto, a utilização de códigos independentes resulta em cálculos de potência e reatividade conservadores em comparação com os resultados utilizando-se P3D/R5. Os picos de potência e de reatividade são menores à medida que o núcleo encolhe. A simulação em condições de HFP resulta em valores de pico de potência similares durante transitório para as três NPPs, mas a potência de pós-transitórios é menor para o menor núcleo. A análise em condições de HZP também indica que o valor máximo durante o transitório é menor para o menor núcleo, mas o pós-transitórios ocorre aos mesmos níveis de potência das demais NPPS. A distribuição de potência em 3D também apresenta resultados distintos para condições de HFP e HZP, mas tais resultados são independentes do tamanho do núcleo: i) HFP: há um aumento da potência do núcleo em torno da CRE, mas tal comportamento diminui para núcleos menores - no entanto, a potência é bem distribuída após o transitório; e ii) HZP: há aumento de potência na área do CRE, mas o pico de potência em 3D é menor durante e depois dos transitórios para núcleos menores. Tais características indicam que os núcleos menores respondem de forma mais segura quando da inserção de reatividade em comparação a reatores de maiores dimensões. O método estocástico de filtragem de Kalman estendido (EKF) foi codificado para estimar a reatividade com base no perfil de potência da NPP, após a adição de ruído aleatório. O método determinístico da cinética pontual inversa (IPK) também foi implementado e os resultados da aplicação dos algoritmos do EKF e IPK foram comparados com os resultados da simulação do P3D/R5. As seguintes estratégias, implementadas neste trabalho, possibilitaram a aplicação robusta e precisa do EKF: o sistema foi modelado por um conjunto de equações diferenciais não-lineares estocásticas de tempo contínuo; o algoritmo obtém o passo de tempo diretamente da potência medida e aplica-o ao modelo para a discretização e linearização online; o ajuste do filtro ocorre automaticamente a partir do primeiro passo de tempo; e a matriz de covariância do ruído no estado é atualizada online. Verificou-se que a reatividade calculada pelo método IPK possui maior nível de ruído quando comparada ao EKF para todos os casos estudados. Portanto, o EKF apresenta resultados superiores e mais precisos. Além disso, sob uma pequena inserção de reatividade, a reatividade calculada pelo método IPK varia consideravelmente de valores positivos para negativos: esta variação não é observada com o EKF. Uma análise de sensibilidade para três desvios padrão (SD) sugere que o algoritmo EKF é superior ao método IPK, independente da magnitude do ruído. Com o aumento da magnitude do ruído, o erro entre as reatividades calculadas pelo IPK e pelo P3D/R5 aumenta. A análise de sensibilidade para cinco ruídos aleatórios indica que a adição de ruído na potência do reator não altera o desempenho global de ambos os algoritmos.

The Master Thesis performs search concerning advanced small and medium power light-water reactors’ designs, including different possibilities to gain a license for their development and operation. The work covers the principal theory about the area of neutronics calculations, principal equations and simplifications. There are several different methods for solution of neutronics calculations. The thesis gives an overview of two principal groups of codes – deterministic methods and Monte Carlo method. The survey shows computational codes examples based on mentioned methods. The computational code PARCS is chosen for further study, which contained description of the input and output file, process of the model creation and conditions for neutronics calculation the of selected reactor design. Based on these facts, the transient calculation has been prepared within the thesis. Thee analyses are described – reactor emergency shutdown, reactor shutdown with stuck group of control and emergency shutdown rods and reactor shutdown with faulty reaction of emergency shutdown rods.

Ce travail de thèse est consacré à la mise en œuvre d’une méthode de décomposition de domaine appliquée à l’équation du transport. L’objectif de ce travail est l’accès à des solutions déterministes haute-fidélité permettant de correctement traiter les hétérogénéités des réacteurs nucléaires, pour des problèmes dont la taille varie d’un motif d’assemblage en 3 dimensions jusqu’à celle d’un grand cœur complet en 3D. L’algorithme novateur développé au cours de la thèse vise à optimiser l’utilisation du parallélisme et celle de la mémoire. La démarche adoptée a aussi pour but la diminution de l’influence de l’implémentation parallèle sur les performances. Ces objectifs répondent aux besoins du projet APOLLO3, développé au CEA et soutenu par EDF et AREVA, qui se doit d’être un code portable (pas d’optimisation sur une architecture particulière) permettant de réaliser des modélisations haute-fidélité (best estimate) avec des ressources allant des machines de bureau aux calculateurs disponibles dans les laboratoires d’études. L’algorithme que nous proposons est un algorithme de Jacobi Parallèle par Bloc Multigroupe. Chaque sous domaine est un problème multigroupe à sources fixes ayant des sources volumiques (fission) et surfaciques (données par les flux d’interface entre les sous domaines). Le problème multigroupe est résolu dans chaque sous domaine et une seule communication des flux d’interface est requise par itération de puissance. Le rayon spectral de l’algorithme de résolution est rendu comparable à celui de l’algorithme de résolution classique grâce à une méthode d’accélération non linéaire par la diffusion bien connue nommée Coarse Mesh Finite Difference. De cette manière une scalabilité idéale est atteignable lors de la parallélisation. L’organisation de la mémoire, tirant parti du parallélisme à mémoire partagée, permet d’optimiser les ressources en évitant les copies de données redondantes entre les sous domaines. Les architectures de calcul à mémoire distribuée sont rendues accessibles par un parallélisme hybride qui combine le parallélisme à mémoire partagée et à mémoire distribuée. Pour des problèmes de grande taille, ces architectures permettent d’accéder à un plus grand nombre de processeurs et à la quantité de mémoire nécessaire aux modélisations haute-fidélité. Ainsi, nous avons réalisé plusieurs exercices de modélisation afin de démontrer le potentiel de la réalisation : calcul de cœur et de motifs d’assemblages en 2D et 3D prenant en compte les contraintes de discrétisation spatiales et énergétiques attendues. / This thesis is devoted to the implementation of a domain decomposition method applied to the neutron transport equation. The objective of this work is to access high-fidelity deterministic solutions to properly handle heterogeneities located in nuclear reactor cores, for problems’ size ranging from colorsets of assemblies to large reactor cores configurations in 2D and 3D. The innovative algorithm developed during the thesis intends to optimize the use of parallelism and memory. The approach also aims to minimize the influence of the parallel implementation on the performances. These goals match the needs of APOLLO3 project, developed at CEA and supported by EDF and AREVA, which must be a portable code (no optimization on a specific architecture) in order to achieve best estimate modeling with resources ranging from personal computer to compute cluster available for engineers analyses. The proposed algorithm is a Parallel Multigroup-Block Jacobi one. Each subdomain is considered as a multi-group fixed-source problem with volume-sources (fission) and surface-sources (interface flux between the subdomains). The multi-group problem is solved in each subdomain and a single communication of the interface flux is required at each power iteration. The spectral radius of the resolution algorithm is made similar to the one of a classical resolution algorithm with a nonlinear diffusion acceleration method: the well-known Coarse Mesh Finite Difference. In this way an ideal scalability is achievable when the calculation is parallelized. The memory organization, taking advantage of shared memory parallelism, optimizes the resources by avoiding redundant copies of the data shared between the subdomains. Distributed memory architectures are made available by a hybrid parallel method that combines both paradigms of shared memory parallelism and distributed memory parallelism. For large problems, these architectures provide a greater number of processors and the amount of memory required for high-fidelity modeling. Thus, we have completed several modeling exercises to demonstrate the potential of the method: 2D full core calculation of a large pressurized water reactor and 3D colorsets of assemblies taking into account the constraints of space and energy discretization expected for high-fidelity modeling.