Ce travail de recherche est dédié à la compréhension des mécanismes physiques de l’érosion de cavitation dans un fluide compressible à l’échelle fondamentale de l’implosion d’une bulle de cavitation. Suite à l’implosion d’une bulle de vapeur à proximité d’une surface solide, des très hautes pressions sont générées. Ces pressions sont considérées responsables de l’endommagement (érosion) des surfaces solides observé dans la plupart des applications. Notre approche numérique démarre avec le développement d’un solveur compressible capable de résoudre les bulles de cavitation au sein du code volumes finis YALES2 en utilisant un simple modèle de mélange homogène des phases fluides. Le solveur est étendu à une approche ALE (Arbitraire Lagrangien Eulérien) dans le but de mener des simulations d’interaction fluide-structure sur un maillage mobile. La réponse du matériau solide est calculée avec le code de calcul éléments finis Cast3M, et nous a permis de mener des simulation avec un couplage d’abord monodirectionnel, ensuite bidirectionnel, entre le fluide et le solide. On compare des résultats obtenus à deux dimensions, puis à trois, avec des observations expérimentales. On discute les chargements de pression estimés, et les réponses de différents matériaux pour des implosions de bulle à des différentes distances de la surface. Enfin, à travers l’utilisation de simulations avec couplage bidirectionnel entre fluide et solide, on identifie l’amortissement des chargements de pression pour les différents matériaux. / This research is devoted to understanding the physical mechanism of cavitation erosion in compressible liquid flows on the fundamental scale of cavitation bubble collapse. As a consequence of collapsing bubbles near solid wall, high pressure impact loads are generated. These pressure loads are believed to be responsible for the erosive damages on solid surface observed in most applications. Our numerical approach begins with the development of a compressible solver capable of resolving the cavitation bubbles in the finite-volume solver YALES2 employing a simplified homogenous mixture model. The solver is extended to Arbitrary Lagrangian-Eulerian formulation to perform fluid structure interaction simulation with moving mesh capabilities. The material response is resolved with the finite element solver Cast3M, which allowed us to perform one-way and two-way coupled simulations between the fluid and solid domains. In the end, we draw comparisons between 2D and 3D vapor bubble collapse dynamics and compare them with experimental observations. The estimated pressure loads on the solid wall and different responses of materials for attached and detached bubble collapses are discussed. Finally, the damping of pressure loads by different materials is identified with two-way coupled fluid-structure interaction.

Les réseaux de tuyauterie industriels sont le siège de niveaux importants de vibrations induites par l’écoulement qui peuvent mener à la rupture par fatigue des installations. La présente étude se concentre sur l’analyse et modélisation simplifiée de la source vibratoire associée au passage d’un écoulement liquide turbulent par un coude à 90°. Une approche combinant expériences et simulation a été conduite. Une boucle de circulation d’eau munie d’un coude transparent a été conçue afin de permettre des me-sures de vitesse à l’intérieur du coude. Pour cette finalité, les techniques de Vélocimétrie par Imagerie de Particules (PIV) plane et stéréoscopique ont été utilisées. La pression pariétale et les vibrations du banc d’essais ont été mesurées simultanément. Plusieurs configurations d’écoulement ont été testées afin d’obtenir une riche base de données couplées reliant l’écoulement fluide à l’excitation dynamique des parois et, finalement, à la réponse vibratoire de la structure. En parallèle, l’écoulement instationnaire d’eau dans le coude a été simulé au moyen d’une approche du type Simulation des Grandes Echelles (LES). La simulation fluide a permis d’étudier en détails la topologie de l’écoulement turbulent au passage du coude ainsi que le champ instationnaire de pression fluctuante induit sur la paroi. Finale-ment, un ensemble d’outils statistiques a été appliqué aux données expérimentales et numériques afin de proposer un modèle simplifié des transferts qui relient l’écoulement turbulent à la sollicitation dynamique de la structure contenant le coude. / The flow of dense fluids within thin-walled piping systems may lead to significant levels of Flow-Induced Vibration, mainly in the vicinities of singularities such as obstacles inserted into the flow, sudden changes of cross-sectional area or flow direction. This study focuses on the analysis and reduced-order modelling of the vibrational source associated with the turbulent flow of liquids through a 90° elbow.A mixed experimental-computational approach is undertaken. A closed water loop containing a transparent elbow was designed in order to allow for fluid velocity measurements inside the singularity. To this purpose, planar and stereoscopic Particle Image Velocimetry (PIV) were employed. Wall pressure fluctuations and structural vibrations were measured simultaneously. Several flow configurations were tested in order to obtain a large coupled database linking the flow to the dynamic excitation, and then to the vibration response of the structure.In parallel, the unsteady water flow through the elbow was computed using Large-Eddy Simulation (LES). The fluid simulation allowed for a detailed study of the turbulent flow through the singularity and the unsteady pressure field induced on the piping walls. Finally, a set of statistical tools was applied to both experimental and computational data in order to propose a reduced-order model of the transfer function that links the tur-bulent flow to the dynamic excitation of the elbowed piping structure.

Pour améliorer la conception des turbomachines, les industriels doivent appréhender des phénomènes aéroélastiques complexes présents dans les compresseurs comme les cycles limites d’interaction fluide-structure des fans. La compréhension et la modélisation de ces phénomènes impliquent de développer des modèles numériques complexes intégrant des phénomènes multi-physique et de valider ces modèles à l’aide de bancs d’essais. Le banc d’essai du compresseur CREATE est instrumenté pour étudier des instabilités aérodynamiques couplées à des vibrations, notamment sur le rotor du premier étage, et permet de valider des modèles numériques. La modélisation de l’écoulement en amont du premier étage du compresseur à l’aide du logiciel Turb’Flow, développé pour l’étude des écoulements dans les compresseurs aéronautiques, a permis de mettre en évidence l’importance des conditions limites d’entrée pour l’obtention de résultats précis. En particulier, il a été possible de modéliser correctement l’ingestion d’une alimentation non-homogène en entrée de la roue directrice d’entrée. Ce phénomène peut se produire en amont des fans et interagir avec un mode de la structure. Une stratégie de couplage partitionné fort explicite dans le domaine temporel a été introduite dans le logiciel Turb’Flow. Comme cette méthode présente un risque de décalage temporel à l’interface fluide-structure, une attention particulière a été portée à la modélisation de la conservation de l’énergie à cette interface. La conservation de l’énergie à l’interface est cruciale quand les déplacements sont importants et quand un comportement non-linéaire fort apparaît entre le fluide et la structure (onde de choc et amortissement structurel nonlinéaire). Parallèlement au développement du module aéroélastique, le schéma implicite de Runge- Kutta d’ordre 3 en temps (RKI-3) a été développé et évalué sur un cas de dynamique (vibration d’une aube de turbine transsonique) et sur un cas de propagation d’onde de choc. L’utilisation du schéma RKI-3 permet d’augmenter, à iso-précision, d’un ordre le pas de temps par rapport aux schémas de Gear et de Newmark. S’il apporte un gain en temps CPU pour l’étude de la dynamique des structures, il est pénalisant dans le cadre de simulation URANS. Cependant, le schéma RKI-3 est utilisable dans le cadre de simulations couplées fluide-structure. / To increase turbomachinery design, manufacturers have to comprehend complex aeroelastic phenomena involving compressors like fluid-structure interaction limit cycles of fans. The understanding and the modeling of these phenomena involve developing complex solvers coupling techniques and validating these techniques with bench tests. The bench test of the CREATE compressor is instrumented to study the coupling between aerodynamic instabilities and structure vibration, in particular on the first stage rotor, and allows to validate numerical techniques. The flow modeling upstream to the first stage with the Turb’Flow flow solver (targeting turbomachinery applications) shows that, to have accurate results, inlet limit conditions must take into account. The ingestion of non-homogeneous flow upstream to the inlet guide vane is accurately modeled. This phenomenon can appear upstream to fans and interact with structure Eigen-modes. Explicit partitioned strong coupling considered in time domain was implemented in a Turb’Flow flow solver. As there is a risk of time shift at the fluid-structure interface, careful attention should be paid to energy conservation at the interface. This conservation is crucial when displacements are large and when strong non-linear behaviors occur in both fluid and structure domains, namely shock waves, flow separations and non-linear structural damping. In parallel with coupling technique development, the three-order implicit Runge-Kutta scheme (RKI-3) was implemented and validated on a structure dynamic case (transonic turbine blade vibration) and on a case of shock waves propagation. The RKI-3 scheme allows increasing the time step of one order of magnitude with the same accuracy. There is a CPU time gain for structure dynamics simulations, but no for URANS simulations. However, the RKI-3 scheme can be to use for fluid-structure coupling simulations. The coupling technique was validated on a test case involving tube in which the shock wave impinges on a cross flow flexible panel, initially at rest. This case allows modeling an interaction between sonic flow and a panel movement with a tip clearance. Some numerical simulations were carried out with different temporal schemes. The RKI-3 scheme has no influence on results (compared with Gear and/or Newmark scheme) on the energy conservation at the fluid-structure interface. Compared to experimental results, pressure is in fairly good ix Liste des publications agreement. The analysis of numerical results highlighted that a vertical shock tube with up and down waves creates pressure fluctuation. Frequency is under predicted and amplitude is not in fairly good agreement. The panel root modeling might be questionable.

Le palier hydrodynamique est une solution de guidage en rotation particulièrement appréciée pour ses caractéristiques d’amortissement à hautes vitesses de rotation. Cependant les performances des machines tournantes lubrifiées par un film fluide sont impactées par des effets non linéaires difficiles à analyser. La prédiction du comportement du système par la simulation nécessite une modélisation avancée de l’écoulement de lubrifiant dans le palier hydrodynamique. Enfin, l’état de surface semble avoir un impact important sur l’écoulement du fluide lubrifiant, lui-même agissant sur les caractéristiques statiques et dynamiques des parties tournantes. Cette étude vise à améliorer les modèles numériques liés à l’impact de l’état de surface des paliers hydrodynamiques sur la dynamique de ligne d’arbre. La méthode d’homogénéisation multi-échelles a été utilisée à cet effet dans un algorithme multi-physiques pour décrire l’interaction entre la structure flexible en rotation et les films fluides des supports de lubrification. Différents modèles ont été utilisés pour prendre en compte la présence de zone de rupture de film lubrifiant. Des méthodologies non-linéaires fréquentielles ont été mises en place afin de permettre l’étude paramétrique des solutions périodiques d’un tel système et de leur stabilité. Afin de confronter ce modèle complexe à la réalité, un banc d’essai miniature a également été conçu. Différents échantillons présentant des états de surface modifiés par ablation à l’aide de LASER femto-seconde ont été testés. L’étude expérimentale a permis de vérifier certaines tendances prévues par la simulation. Des améliorations des performances des paliers hydrodynamiques par rapport aux vibrations auto-entretenues du système ont été démontrées pour certaines textures. En revanche toutes les améliorations ne sont pas prédites par les algorithmes d’homogénéisation multi-échelles. La présence de recirculation dans les aspérités du motif a été mise en évidence à partir de la résolution locale des équations de Navier-Stokes. Ce résultat participe à la remise en question des hypothèses classiques utilisées en texturation, et peut justifier les améliorations obtenues expérimentalement avec les paliers texturés. / The hydrodynamic bearing provides good damping properties in rotating machineries. However, the performances of rotor-bearings systems are highly impacted by nonlinear effects that are difficult to analyze. The rotordynamics prediction requires advanced models for the flow in the bearings. The surface of the bearings seems to have a strong impact on the lubricant flow, acting on the static and dynamic properties of the rotating parts. This study aims to enhance the simulation of the bearings’ surface state effect on the motion of the rotating shaft. The flexible shaft interacts with textured hydrodynamic bearings. Multi-scales homogenization is used in a multi-physics algorithm in order to describe the fluid-structure interaction. Different models are used to account for the cavitation phenomenon in the bearings. Nonlinear harmonic methods allow efficient parametric studies of periodic solutions as well as their stability. Moreover, a test rig has been designed to compare predictions to real measurements. Several textured shaft samples modified with femto-seconds LASER surface texturing are tested. In most cases the experimental study showed similar results than the simulation. Enhancements of the vibration behaviors of the rotor-bearing system have been revealed for certain texturing patterns. The self-excited vibration, also known as "oil whirl" phenomenon, is stabilized on a wide rotating frequency range. However, the simulation tool does not predict well the enhancements that are observed. Vortices in surface texturing patterns have been revealed numerically with Navier-Stokes equation resolution. These results are opposed to the classical lubrication hypothesis. It is also a possible explanation of the enhancements that are experimentally measured with textured bearings.

Esta investigación busca evaluar la Interacción entre el Suelo y la Estructura (ISE) en reservorios elevados tipo INTZE de tres diferentes capacidades, cimentados en diferentes tipos de suelos, ubicados en la zona con más peligro sísmico en el Perú. Para esto se planteó realizar una muestra de 27 configuraciones estructurales, con variaciones de altura y diámetro del fuste, y diámetro de losa de cimentación, las cuales están cimentadas en cuatro tipos de suelos de acuerdo con la norma Sismorresistente E.030-16. Se evaluará la influencia de la carga sísmica, mediante un análisis dinámico espectral definido por los lineamientos de las normas nacionales E.030-16 y complementariamente por códigos y estándares internacionales como el ACI 350.3-06. Para el dimensionamiento de los reservorios se aplicó el criterio de Otto Intze, análisis estático de esfuerzos y criterios del código ACI 350.3-06 y ACI 307-48. Estos reservorios fueron modelados en el software SAP2000, contando con 216 simulaciones en total. Se aplicó el modelo de Housner (1963) para la Interacción Fluido-Estructura y para la ISE se aplicó el modelo recomendado por el código FEMA P-750. Para analizar los resultados de interés, como las fuerzas internas en el fuste, la cortante basal, momento de volteo, desplazamientos y periodos, se aplicó la prueba de normalidad de Shapiro Wilk para la variación porcentual que se genera al evaluar la ISE, con el fin de determinar intervalos de variación con una probabilidad del 95%. Además, se aplicó la prueba de independencia Chi-Cuadrado para determinar cuantitativamente si la ISE influye en la reducción de las respuestas de interés. Se concluye de la prueba de independencia que, para un nivel de significancia de 15% la ISE influye en la reducción de la fuerza cortante basal y momento de volteo. Así mismo, para un nivel de significancia de 5% la ISE influye en la reducción de las fuerzas internas locales de fuste. / This research seeks to evaluate the soil structure interaction (SSI) in elevated water tanks of three different capacities, founded on different types of soil, all located in the most seismic hazard zone in Peru. Twenty-seven models were evaluated, all with different structural adjustments, including variations in the capacity, height, and diameter of the foundation slab, which are founded on four types of soil, according to the Peruvian Code for Earthquake Resistant Design E.030-16. We are going to analyze the seismic load influence through a spectral dynamic analysis, according to the Peruvian Code E.030-16, and the ACI 350.3-06 code for elevated tanks. For the sizing of the elevated tanks, the Otto Intze criterion, the static stress analysis, the ACI 350.3-06 and the ACI 307-48 code were applied. These elevated water tanks were modeled in the SAP2000 software, with 216 simulations. The Housner model (1963) was applied for the Fluid Structure Interaction, and for the Soil-Structure Interaction (SSI), we applied the model recommended by the FEMA P-750 code. To analyze the results of interest, such as internal forces in the shaft, base shear, rocking moment, displacements and periods, we applied the Shapiro Wilk normality test for the percentage variation that is generated when we evaluate the SSI, in order to determinate variations intervals with a probability of 95%. Also, we applied the Chi-Square test of independence to determinate, quantitatively, if the results are influenced by the SSI. We concluded, from the independence test that, for a significance level of 15%, the SSI influences the reduction of the basal shear force and the rocking moment. Likewise, for a significance of 5%, the SSI influences the reduction of the internal shaft forces. / Tesis

Um dos grandes desafios da engenharia atualmente é viabilizar soluções computacionais que reduzam o tempo de processamento e forneçam respostas ainda mais precisas. Frequentemente surgem propostas com as mais diversas abordagens que exploram novas formas de resolver tais problemas ou tentam, ainda, melhorar as soluções existentes. Uma das áreas que se dedica a propor tais melhorias é a computação paralela e de alto desempenho - HPC (High Performance Computing). Técnicas que otimizem o tempo de processamento, algoritmos mais eficientes e computadores mais rápidos abrem novos horizontes possibilitando realizar tarefas que antes eram inviáveis ou levariam muito tempo para serem concluídas. Neste projeto propõe-se a implementação computacional de uma arquitetura de computação paralela com o intuito de resolver, de forma mais eficiente, em comparação com a arquitetura sequencial, problemas de Dinâmica dos Fluidos e Interação Fluido-Estrutura e que também seja possível estender esta arquitetura para a resolução de outros problemas relacionados com o Método dos Elementos Finitos. O objetivo deste trabalho é desenvolver um algoritmo computacional eficiente em linguagem de programação científica C++ e CUDA - de propriedade da NVIDIAr - tendo como base trabalhos anteriores desenvolvidos no LMC (Laboratório de Mecânica Computacional) e, posteriormente, com a arquitetura desenvolvida, executar e investigar problemas de Dinâmica dos Fluidos e Interação Fluido-Estrutura (aplicando o método dos Elementos Finitos com Fronteiras Imersas e a solução direta do sistema de equações lineares com PARDISO) com o auxílio dos computadores do LMC. Uma análise de sensibilidade para cada problema é realizada de forma a encontrar a melhor combinação entre o número de elementos da malha de elementos finitos e o speedup, e posteriormente é feita uma análise comparativa de desempenho entre a arquitetura paralela a sequencial. Com uma única GPU conseguiu-se uma considerável redução no tempo para o assembly das matrizes globais e no tempo total da simulação. / One of the biggest challenges of engineering is enable computational solutions that reduce processing time and provide more accurate numerical solutions. Proposals with several approaches that explore new ways of solving such problems or improve existing solutions emerge. One of the biggest areas dedicated to propose such improvements is the parallel and high performance computing. Techniques that improve the processing time, more efficient algorithms and faster computers open up new horizons allowing to perform tasks that were previously unfeasible or would take too long to complete. We can point out, among several areas of interest, Fluid Dynamics and Interaction Fluid-Structure. In this work it is developed a parallel computing architecture in order to solve numerical problems more efficiently, compared to sequential architecture (e.g. Fluid Dynamics and Fluid-Structure Interaction problems) and it is also possible to extend this architecture to solve different problems (e.g. Structural problems). The objective is to develop an efficient computational algorithm in scientific programming language C ++, based on previous work carried out in Computational Mechanics Laboratory (CML) at Polytechnic School at University of São Paulo, and later with the developed architecture, execute and investigate Fluid Dynamics and Fluid-Structure Interaction problems with the aid of CML computers. A sensitivity analysis is executed for different problems in order to assess the best combination of elements quantity and speedup, and then a perfomance comparison. Using only one GPU, we could get a 10 times speedup compared to a sequential software, using the Finite Element with Immersed Boundary Method and a direct solver (PARDISO).

O fenômeno de vibração induzida por vórtices (VIV) é um problema fundamental dentro da Mecânica dos Fluidos e um exemplo importante de interação fluido-estrutura. Esta tese investiga fenômeno de VIV quando um cilindro rígido, submetido a escoamento uniforme, está livre para oscilar na direção transversal e alinhada com a corrente incidente. A tese foi estruturada ao redor de sete perguntas relacionadas ao fenômeno de VIV: 1) O fenômeno e os resultados experimentais são repetitivos? 2) Como ocorre a transição entre ramos de resposta? 3) Qual é o papel da inércia da estrutura oscilante? 4) Qual é o papel de sua rigidez? 5) Quais são as frequências naturais mais importantes da estrutura? 6) Quais padrões de esteira se desenvolvem para VIV com dois graus de liberdade? 7) Quais são os efeitos do movimento na direção alinhada com a corrente no processo de formação e desprendimento de vórtices? O fenômeno de VIV é estudado de maneira experimental em uma base elástica pendular capaz de oscilar com o mesmo momento de inércia e frequência natural nas duas direções. Os experimentos de VIV foram realizados em canal de água recirculante e com diferentes condições de inércia e rigidez. A técnica de velocimetria por imagem de partículas foi usada e permitiu identificar diferentes padrões de esteira de vórtices. Verificou-se que o VIV é repetitivo a nível de amplitudes médias e frequências dominantes. A transição dos ramos pode ocorrer de maneira intermitente ou com histerese. Os parâmetros de inércia e rigidez da estrutura são capazes de mudar o regime de oscilação e, para algumas condições, suprimir as vibrações alinhadas com a corrente. Dentre os padrões de esteira observados, um deles não havia sido relatado na literatura e é definido nesta tese. O novo modo de emissão apresenta dois vórtices com circulação oposta e elevada intensidade emitidos por ciclo. A influência da direção alinhada com o escoamento está relacionada a dois efeitos: a velocidade relativa entre o cilindro e o fluido, responsável pelo aumento da circulação dos vórtices na esteira, e o ângulo de fase do movimento nas direções alinhada e transversal, capaz de mudar o processo de formação dos vórtices. / Vortex-induced vibration (VIV) phenomenon is a fundamental problem of Fluid Mechanics and a typical example of fluid-structure interaction. This thesis explores the VIV phenomenon for a rigid circular cylinder immersed in a uniform fluid current. The cylinder is free to oscillate in two degrees of freedom (2dof): in-line and cross flow. The thesis was structured in order to answer seven questions regarding VIV: 1) Are the phenomenon and its experimental results repetitive? 2) How do the branches transition occur? 3) What is the role played by the inertia of the oscillating structure? 4) What is the role of its stiffness? 5) Which are the most relevant natural frequencies of the structure? 6) Which are the vortex wake patterns developed in VIV 2dof? 7) What are the influences of the in-line movement to the process of vortex formation and shedding? The phenomenon is experimentally investigated using an elastic base similar to a pendulum and able to oscillate with the same moment of inertia and natural frequencies in both directions. All the experiments were conducted in a recirculating water channel facility and with several combinations of moment of inertia and stiffness of the structure. Particle image velocimetry provided visualization of different vortex wake patterns. The phenomenon is repetitive in terms of its mean amplitudes and dominant frequencies. The transitions between dfferent branches can be hysteretic or intermittent. It is shown that both the moment of inertia and the stiffness of the structure are able to change the regime of oscillations and, for some cases, suppress the in-line movement. Among the different vortex wake patterns observed, one has not been reported previously in the literature. The new wake pattern shows two large vortices with high and opposite circulations shed per cycle. The influence of the displacement in the current direction is related to two different effects: the relative velocity between the incoming flow and the structure motion, responsible for the increase in the net circulation shed in the vortex wake, and the influence of the phase angle between the displacement in the in-line and cross-flow directions, capable of changing the vortex formation process.

Este trabalho pode ser dividido em três etapas principais. Inicialmente é proposta uma formulação estabilizada do método dos elementos finitos (MEF) para solução de problemas de escoamento incompressível governado pela equação de Navier-Stokes. Esta formulação foi implementada em um código computacional e testada através de diversos exemplos numéricos. Alguns elementos finitos com diferentes pares de função de interpolação da velocidade e pressão, consagrados na literatura, e também elementos finitos menos populares, foram investigados e seus resultados e performance comparados. A segunda etapa consiste na formulação do problema estrutural. Buscou-se por uma formulação dinâmica, não linear, capaz de simular movimentos complexos de estruturas sujeitas a grandes deslocamentos e grandes deformações durante longos intervalos de tempo. A etapa final deste trabalho é a proposição de um método para solução de problemas de Interação Fluido Estrutura (IFE) que utiliza o conceito de fronteiras imersas como alternativa a abordagens ALE (Arbitrary Lagrangian Eulerian) clássicas. Elementos Finitos Generalizados, juntamente com Multiplicadores de Lagrange, são utilizados para prover descontinuidade nos campos de velocidade e pressão do fluido ao longo da interface com a estrutura. O acoplamento dos dois problemas é realizado utilizando um método implícito e alternado (staggered scheme), que possui a vantagem de permitir, facilmente, a implementação de códigos computacionais desenvolvidos para resolver isoladamente o problema fluido e/ou estrutural. / This work is divided in three parts. Initially, it is presented a stabilized Finite Element Method formulation to solve fluid flow problems governed by the incompressible Navier-Stokes Equations. This formulation was implemented in a computer code and validated throughout several numeric simulations. Some well-known finite elements with different pairs of velocity/pressure approximations, as well as some other less popular elements, were investigated and their performance compared. The second part describes the Structural Problem formulation. This formulation is able to simulate nonlinear dynamic problems involving large displacements and finite strains during long period of time. In the final part of this work, it is proposed a Fluid-Structure Interaction method based on an immersed interface approach in opposition to classical ALE (Arbitrary Lagrangian Eulerian) approaches. Generalized Finite Elements, together with Lagrange Multipliers, are used to provide velocity and pressure discontinuities on the fluid domain across the immersed interface. To couple both fluid and structural problems, an implicit staggered scheme is adopted, which allows the easy implementation of already developed black box computer codes.

Several nuclear research reactors use or are planned with cores containing flat-plate- type fuel elements. The nuclear fuel is contained in parallel plates that are separated by narrow channels through which the fluid flows to remove the heat generated by fission reactions. One of the problems of this fuel element design is the mechanical stability of the fuel plates. High-velocity coolant flowing through the channels can cause large deflections of these plates leading to local overheating, structural failure or plate collapse. As a consequence, the safe operation of the reactor may be affected. In this work, a numerical fluid-structure interaction study was conducted for evaluating the mechanical stability of nuclear fuel plates under axial flow conditions. Five different cases were analyzed. In all cases, the system consisted of two fuel plates bounded by fluid channels but, in case 5, a support comb at the leading edge of the plates was inserted. The pressure loadings caused by the fluid flow were calculated using a Computational Fluid Dynamics model created with ANSYS CFX. The structural response was determined by means of a Finite Element Analysis model generated with ANSYS Mechanical. Both models were coupled using the two-way fluid-structure interaction approach. The results from Case 1 allowed proposing a methodology to predict the critical velocity of the assembly without an inlet support comb. The maximum deflection of the plates was detected at their leading edges. It was detected that, for flow rates in the channels less than a certain value, the maximum deflection increased linearly with the square of the coolant velocity. In contrast, for greater flow rates, a nonlinear behavior was observed. Therefore, that fluid velocity was identified as the critical velocity of the system. Besides, above the critical velocity, an extra deflection peak was observed near the trailing edge of the plates. In cases 2, 3 and 4, the influence of manufacturing deviations and the change of materials properties due to the increment of temperature on the critical velocity was investigated. With these conditions, the critical velocity of the system was found at lower values. Lastly, in Case 5, the effectiveness of using a support comb at the leading edge of the plates was investigated. The results showed that the static divergence at the inlet end is effectively eliminated with the installation of the comb. In addition, the flow-induced deflections along the length of the plates were significantly diminished with the comb. / Muitos reatores nucleares de pesquisa usam ou são planejados com elementos combustíveis tipo placas planas. O combustível nuclear está contido em placas paralelas que são separadas por canais estreitos através dos quais o fluido refrigerante passa para remover o calor gerado pelas reações de fissão. Um dos problemas deste tipo de elemento combustível é a estabilidade mecânica das placas de combustível. O líquido refrigerante a alta velocidade pode causar deflexões excessivas dessas placas, bloqueando o canal de escoamento e levar ao superaquecimento nas placas, falha estrutural ou colapso da placa. Como consequência, a operação segura do reator pode ser afetada. Neste trabalho, foi realizado um estudo numérico de interação fluido-estrutura para avaliar a estabilidade mecânica de placas de combustível nuclear sob condições de fluxo axial. Cinco diferentes casos foram analisados. Em todos os casos, o sistema consistiu em duas placas de combustível delimitadas por canais de fluido, mas, no caso 5, um pente de suporte na borda de ataque das placas foi inserido. As cargas de pressão causadas pela vazão foram calculadas usando um modelo de Dinâmica dos Fluidos Computacional, criado com ANSYS CFX. A resposta estrutural foi determinada por meio de um modelo de elementos finitos, gerado com ANSYS Mechanical. Os modelos foram acoplados usando a abordagem de interação fluido-estrutura bidirecional. Os resultados do Caso 1 permitiram propor uma metodologia para prever a velocidade crítica do sistema sem o pente de suporte. A deflexão máxima das placas foi observada em suas bordas de ataque. Foi detectado que, para velocidades nos canais inferiores a um determinado valor, a deflexão máxima aumentava linearmente com o quadrado da velocidade do líquido refrigerante. Em contraste, para maiores vazões, um comportamento não linear foi observado. Portanto, essa velocidade do fluido foi identificada como a velocidade crítica. Além disso, acima da velocidade crítica, um pico extra de deflexão foi observado próximo à borda de saída das placas. Nos casos 2, 3 e 4, a influência dos desvios de fabricação e da alteração das propriedades dos materiais devido ao incremento de temperatura na velocidade crítica foi investigada. Sob essas condições, a velocidade crítica foi encontrada a valores mais baixos. Por fim, no Caso 5, a eficácia do uso do pente de suporte na borda de entrada das placas foi estudada. Os resultados mostraram que a divergência estática na extremidade de entrada foi efetivamente eliminada com a instalação do pente. Além disso, as deflexões induzidas pelo fluido ao longo do comprimento das placas foram significativamente diminuídas com o pente.

Cette thèse vise à obtenir et à développer des modèles mathématiques pour comprendre certains aspects de la dynamique des fluides granulaires hétérogènes. Plus précisément, le résultat attendu consiste à développer trois modèles. Nous supposons dans un premier temps que la dynamique du matériau granulaire est modélisée à l’aide d’une approche fondée sur la théorie du mélange. D’autre part, pour les deux modèles restant, nous considérons que le fluide granulaire est modélisé à l’aide d’une approche multiphase associant des structures et des fluides rigides. Plus exactement : • Dans le premier modèle, nous avons obtenu un ensemble d’équations basées sur la théorie du mélange en utilisant des outils d’homogénéisation et une procédure thermodynamique. Ces équations reflètent deux propriétés essentielles des fluides granulaires : la nature visqueuse du fluide interstitiel et un comportement de type Coulomb de la composante granulaire. Avec nos équations, nous étudions le problème de Couette entre deux cylindres infinis d’un écoulement hétérogène granulaire dense, composé d’un fluide newtonien et d’une composante solide. • Dans le deuxième modèle, nous considérons le mouvement d’un corps rigide dans un matériau viscoplastique. Les équations 3D de Bingham modélisent ce matériau et les lois de Newton régissent le déplacement du corps rigide. Notre résultat principal est d’établir l’existence d’une solution faible pour le système correspondant. • Dans le troisième modèle, nous considérons le mouvement d’un corps rigide conducteur thermique parfait dans un fluide newtonien conducteur de la chaleur. Les équations 3D de Fourier-Navier-Stokes modélisent le fluide, tandis que les lois de Newton et l’équilibre de l’énergie interne modélisent le déplacement du corps rigide. Notre principal objectif dans cette partie est de prouver l’existence d’une solution faible pour le système correspondant. La formulation faible est composée de l’équilibre entre la quantité du mouvement et l’équation de l’énergie totale, qui inclut la pression du fluide, et implique une limite libre due au mouvement du corps rigide. Pour obtenir une pression intégrable, nous considérons une condition au limite de glissement de Navier pour la limite extérieure et l’interface mutuelle / This Ph.D. thesis aims to obtain and to develop some mathematical models to understand some aspects of the dynamics of heterogeneous granular fluids. More precisely, the expected result is to develop three models, one where the dynamics of the granular material is modeled using a mixture theory approach, and the other two, where we consider the granular fluid is modeled using a multiphase approach involving rigid structures and fluids. More precisely : • In the first model, we obtained a set of equations based on the mixture theory using homogenization tools and a thermodynamic procedure. These equations reflect two essential properties of granular fluids : the viscous nature of the interstitial fluid and a Coulomb-type of behavior of the granular component. With our equations, we study the problem of a dense granular heterogeneous flow, composed by a Newtonian fluid and a solid component in the setting of the Couette flow between two infinite cylinders. • In the second model, we consider the motion of a rigid body in a viscoplastic material. The 3D Bingham equations model this material, and the Newton laws govern the displacement of the rigid body. Our main result is the existence of a weak solution for the corresponding system. • In the third model, we consider the motion of a perfect heat conductor rigid body in a heat conducting Newtonian fluid. The 3D Fourier-Navier-Stokes equations model the fluid, and the Newton laws and the balance of internal energy model the rigid body. Our main result is the existence of a weak solution for the corresponding system. The weak formulation is composed by the balance of momentum and the balance of total energy equation which includes the pressure of the fluid, and it involves a free boundary (due to the motion of the rigid body). To obtain an integrable pressure, we consider a Navier slip boundary condition for the outer boundary and the mutual interface