Submitted by Mery Piedad Zamudio Igami (mery@ipen.br) on 2017-03-10T16:45:35Z No. of bitstreams: 0 / Made available in DSpace on 2017-03-10T16:45:35Z (GMT). No. of bitstreams: 0 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / O presente estudo foi realizado para verificar a possibilidade de redução do núcleo do reator IEA-R1 do IPEN/CNEN-SP. Cálculos neutrônicos foram desenvolvidos para um conjunto de novas configurações para que, a posteriori, a análise termo-hidráulica e de segurança pudessem ser realizadas. As novas configurações analisadas são menores por diversos motivos, como obter uma melhor utilização do combustível, melhor distribuição dos fluxos de nêutrons, dentre outros. Para que se possa atingir tais configurações, a densidade de Urânio no combustível deve ser aumentada. Neste estudo, combustíveis de U3Si2-Al com 4,8gU/cm3 foram testados e novos núcleos para o reator IEA-R1 foram propostos e discutidos. A análise neutrônica não impõe restrições aos núcleos estudados. A análise termohidráulica mostrou que as margens de segurança e os perfis de temperatura ao longo das placas combustíveis não excedem os limites de projeto. Os coeficientes de temperatura obtidos para os novos núcleos, no caso isotérmico, são todos negativos, conforme desejado. A queima mostrou que núcleos supercompactos não apresentam excesso de reatividade suficiente para o funcionamento dos mesmo, ao se utilizar combustíveis com 4,8gU/cm3. Um APR (Acidente de Perda de Refrigerante) foi simulado para os núcleos remanescentes. A ruptura da fronteira do primário se mostrou o acidente mais crítico, devido ao curto tempo para o esvaziamento completo da piscina do reator. As temperaturas atingidas após o descobrimento foram calculadas e não excedem aquelas cujos valores propiciam empolamento nas placas combustíveis (475 °! a 550 °!), uma vez que se obedeça os tempos de esvaziamento seguro da piscina para as novas configurações. / Tese (Doutorado em Tecnologia Nuclear ) / IPEN/D / Instituto de Pesquisas Energéticas e Nucleares - IPEN-CNEN/SP / FAPESP: 11/17090-7

This thesis is a blend of neutron transport theory and numerical analysis. We start with the study of the problem of the Mika/Case eigenexpansion used in the solution process of the homogeneous one-speed Boltzmann neutron transport equation with anisotropic scattering for plane symmetry. The anisotropic scattering is expressed as a finite Legendre series in which the coefficients are the ``scattering coefficients'. This eigenexpansion consists of a discrete spectrum of eigenvalues with its corresponding eigenfunctions and the continuous spectrum [-1,+1] with its corresponding eigendistributions. In the general case where the anisotropic scattering can be of any (finite) order, multiple discrete eigenvalues exist and these have to be located to have the complete spectrum. We have devised a stable and robust method that locates all these discrete eigenvalues. The method is a two-step process: first the number of discrete eigenvalues is calculated and this is followed by the calculation of the discrete eigenvalues themselves, now being able to count them down and make sure none are forgotten. <p><p>During our numerical experiments, we came across what we called near-singular eigenvalues: discrete eigenvalues that are located extremely close to the continuum and hence lead to near-singular behaviour in the eigenfunction. Our solution method has been adapted and allows for the automatic detection of such a near-singular eigenvalue. <p><p>For the elements of the continuous spectrum [-1,+1], there is no non-zero function satisfying the associated eigenequation but there is a non-zero distribution that does satisfy it. It is not feasible to compute a distribution as such but one can evaluate integrals in which this distribution appears. The continuum part of the eigenexpansion can hence only be characterised by its (angular) moments. Accurate and fast numerical quadrature is needed to evaluate these integrals. Several quadrature methods have been evaluated on a representative test function. <p><p><p>The eigenexpansion was proved to be orthogonal and complete and hence can be used to represent the infinite medium Green's function. The latter is the building block of the Boundary Sources Method, an integral solution method for the neutron transport equation. Using angular and angular/spatial moments of the Green's function, it is possible to solve with high accuracy slab problems. We have written a one-dimensional slab code implementing this Boundary Sources Method allowing for media with arbitrary order anisotropic scattering. Our results are very good and the code can be considered as a benchmark code for others. <p><p><p>As a final application, we have used our code to study the discrete spectrum of a well-known scattering kernel in radiative transfer, the Henyey-Greenstein kernel. This kernel has one free parameter which is used to fit the kernel to experimental data. Since the kernel is a continuous function, a finite Legendre approximation needs to be adopted. Depending on the free parameter, the approximation order and the number of secondaries per collision, the number of discrete eigenvalues ranges from two to thirty and even more. Bounds for the minimum approximation order are derived for different requirements on the approximation: non-negativity, an absolute and relative error tolerance. <p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

L’un des principaux objectifs de la physique des réacteurs nucléaires est de caractériser la répartition aléatoire de la population de neutrons au sein d’un réacteur. Les fluctuations de cette population sont liées à la nature stochastique des interactions des neutrons avec les noyaux fissiles du milieu : diffusion, capture stérile, ou encore émission de plusieurs neutrons lors de la fission d’un noyau. L’ensemble de ces mécanismes physiques confère une structure aléatoire branchante à la trajectoire des neutrons, alors modélisée par des marches aléatoires. Avec environs 10⁸ neutrons par centimètre cube dans un réacteur de type REP à pleine puissance en conditions stationnaires, les grandeurs physiques du système (flux, taux de réaction, énergie déposée) sont, en première approximation, bien représentées par leurs valeurs moyennes respectives. Ces observables physiques moyennes obéissent alors à l’équation de transport linéaire de Boltzmann. Au cours de ma thèse, je me suis penchée sur deux aspects du transport qui ne sont pas décrits par cette équation, et pour lesquels je me suis appuyée sur des outils issus de la théorie des marches aléatoires. Tout d’abord, grâce au formalisme de Feynman-Kac, j’ai étudié les fluctuations statistiques de la population de neutrons, et plus particulièrement le phénomène de « clustering neutronique », qui a été mis en évidence numériquement pour de faibles densités de neutrons (typiquement un réacteur au démarrage). Je me suis ensuite intéressée à différentes propriétés de la statistique d’occupation des neutrons effectuant un transport anormal (càd non-exponentiel). Ce type de transport permet de modéliser le transport dans des matériaux fortement hétérogènes et désordonnés, tel que les réacteurs à lit de boulets. L’un des aspects novateurs de ce travail est la prise en compte de la présence de bords. En effet, bien que les systèmes réels soient de taille finie, la plupart des résultats théoriques pré-existants sur ces thématiques ont été obtenus sur des systèmes de taille infinie. / One of the key goals of nuclear reactor physics is to determine the distribution of the neutron population within a reactor core. This population indeed fluctuates due to the stochastic nature of the interactions of the neutrons with the nuclei of the surrounding medium: scattering, emission of neutrons from fission events and capture by nuclear absorption. Due to these physical mechanisms, the stochastic process performed by neutrons is a branching random walk. For most applications, the neutron population considered is very large, and all physical observables related to its behaviour, such as the heat production due to fissions, are well characterised by their average values. Generally, these mean quantities are governed by the classical neutron transport equation, called linear Boltzmann equation. During my PhD, using tools from branching random walks and anomalous diffusion, I have tackled two aspects of neutron transport that cannot be approached by the linear Boltzmann equation. First, thanks to the Feynman-Kac backward formalism, I have characterised the phenomenon of “neutron clustering” that has been highlighted for low-density configuration of neutrons and results from strong fluctuations in space and time of the neutron population. Then, I focused on several properties of anomalous (non-exponential) transport, that can model neutron transport in strongly heterogeneous and disordered media, such as pebble-bed reactors. One of the novel aspects of this work is that problems are treated in the presence of boundaries. Indeed, even though real systems are finite (confined geometries), most of previously existing results were obtained for infinite systems.