O estudo numérico do comportamento estrutural de materiais compostos apresenta-se, desde os últimos anos, como um campo muito fértil de pesquisas, o que justifica o crescimento exponencial de trabalhos científicos nesta área. Atualmente é possível desenhar as propriedades físicas do material adequando-os ao uso que se queira dar a eles. Especificamente quanto às propriedades mecânicas vinculadas a função estrutural que o material em estudo possa ter, estas podem, na atualidade, ser quantificadas, modificadas e otimizadas. No presente trabalho, explora-se um material composto formado por uma matriz polimérica e uma segunda fase particulada com distribuição aleatória. Para realizar esse estudo foi utilizado o método dos elementos discretos e o método dos elementos finitos. No primeiro caso é apresentado um estudo onde se realizam tentativas de determinar o elemento de volume representativo considerando o comportamento do material como não-linear. No segundo caso, aplicando o método dos elementos finitos, realiza-se um estudo considerando a matriz e a fase particulada com comportamento elástico linear, determinando o elemento de volume representativo e comparando os resultados, em termos de constantes elásticas homogeneizadas, com propostas teóricas fornecidas pela micromecânica clássica. Um estudo da convergência da malha e exercícios de otimização foram realizados sobre o composto simulado. Finalmente, realiza-se um estudo não-linear através do método dos elementos finitos, onde a matriz é elástica e a fase particulada hiperelástica, onde se determina o elemento de volume representativo e se faz aplicações para verificação da eficácia dos resultados. / The numerical study of the composite material mechanical behavior has shown lately a fertile field of research, which justifies the exponential growing of scientific works in this area. Nowadays it is possible to design the material properties adapting them to the usage that we want to give them. Specifically, regarding to the mechanical properties, there are methods that allow us to modify them in a rational way to reach different objectives. In the present work, different aspects are analyzed of a composite material built with a polymeric matrix and a second particulate phase with random distribution. The Discrete Element Method (DEM) and the Finite Element Method (FEM) were used to carry out the present work. Firstly, an application of DEM, a study of different alternatives is shown to determine the volume representative element (RVE) considering the non-linear behavior of the studied material. Secondly, an application of FEM, a study considering the matrix and particulate phase, both, with linear elastic behavior. This application consists on computing the RVE and comparing these results with analytical proposals available in the Micromechanics classical bibliography. A mesh convergence study of the FEM models used and simple applications of optimization are also presented. Finally, another application of FEM is presented. In this case a non linear study is shown, where the matrix is considered linear elastic, and the particulate phase is hyperelastic. In this case the RVE was determined and some applications to verify the consistency of the results obtained are presented.

O estudo numérico do comportamento estrutural de materiais compostos apresenta-se, desde os últimos anos, como um campo muito fértil de pesquisas, o que justifica o crescimento exponencial de trabalhos científicos nesta área. Atualmente é possível desenhar as propriedades físicas do material adequando-os ao uso que se queira dar a eles. Especificamente quanto às propriedades mecânicas vinculadas a função estrutural que o material em estudo possa ter, estas podem, na atualidade, ser quantificadas, modificadas e otimizadas. No presente trabalho, explora-se um material composto formado por uma matriz polimérica e uma segunda fase particulada com distribuição aleatória. Para realizar esse estudo foi utilizado o método dos elementos discretos e o método dos elementos finitos. No primeiro caso é apresentado um estudo onde se realizam tentativas de determinar o elemento de volume representativo considerando o comportamento do material como não-linear. No segundo caso, aplicando o método dos elementos finitos, realiza-se um estudo considerando a matriz e a fase particulada com comportamento elástico linear, determinando o elemento de volume representativo e comparando os resultados, em termos de constantes elásticas homogeneizadas, com propostas teóricas fornecidas pela micromecânica clássica. Um estudo da convergência da malha e exercícios de otimização foram realizados sobre o composto simulado. Finalmente, realiza-se um estudo não-linear através do método dos elementos finitos, onde a matriz é elástica e a fase particulada hiperelástica, onde se determina o elemento de volume representativo e se faz aplicações para verificação da eficácia dos resultados. / The numerical study of the composite material mechanical behavior has shown lately a fertile field of research, which justifies the exponential growing of scientific works in this area. Nowadays it is possible to design the material properties adapting them to the usage that we want to give them. Specifically, regarding to the mechanical properties, there are methods that allow us to modify them in a rational way to reach different objectives. In the present work, different aspects are analyzed of a composite material built with a polymeric matrix and a second particulate phase with random distribution. The Discrete Element Method (DEM) and the Finite Element Method (FEM) were used to carry out the present work. Firstly, an application of DEM, a study of different alternatives is shown to determine the volume representative element (RVE) considering the non-linear behavior of the studied material. Secondly, an application of FEM, a study considering the matrix and particulate phase, both, with linear elastic behavior. This application consists on computing the RVE and comparing these results with analytical proposals available in the Micromechanics classical bibliography. A mesh convergence study of the FEM models used and simple applications of optimization are also presented. Finally, another application of FEM is presented. In this case a non linear study is shown, where the matrix is considered linear elastic, and the particulate phase is hyperelastic. In this case the RVE was determined and some applications to verify the consistency of the results obtained are presented.

O estudo numérico do comportamento estrutural de materiais compostos apresenta-se, desde os últimos anos, como um campo muito fértil de pesquisas, o que justifica o crescimento exponencial de trabalhos científicos nesta área. Atualmente é possível desenhar as propriedades físicas do material adequando-os ao uso que se queira dar a eles. Especificamente quanto às propriedades mecânicas vinculadas a função estrutural que o material em estudo possa ter, estas podem, na atualidade, ser quantificadas, modificadas e otimizadas. No presente trabalho, explora-se um material composto formado por uma matriz polimérica e uma segunda fase particulada com distribuição aleatória. Para realizar esse estudo foi utilizado o método dos elementos discretos e o método dos elementos finitos. No primeiro caso é apresentado um estudo onde se realizam tentativas de determinar o elemento de volume representativo considerando o comportamento do material como não-linear. No segundo caso, aplicando o método dos elementos finitos, realiza-se um estudo considerando a matriz e a fase particulada com comportamento elástico linear, determinando o elemento de volume representativo e comparando os resultados, em termos de constantes elásticas homogeneizadas, com propostas teóricas fornecidas pela micromecânica clássica. Um estudo da convergência da malha e exercícios de otimização foram realizados sobre o composto simulado. Finalmente, realiza-se um estudo não-linear através do método dos elementos finitos, onde a matriz é elástica e a fase particulada hiperelástica, onde se determina o elemento de volume representativo e se faz aplicações para verificação da eficácia dos resultados. / The numerical study of the composite material mechanical behavior has shown lately a fertile field of research, which justifies the exponential growing of scientific works in this area. Nowadays it is possible to design the material properties adapting them to the usage that we want to give them. Specifically, regarding to the mechanical properties, there are methods that allow us to modify them in a rational way to reach different objectives. In the present work, different aspects are analyzed of a composite material built with a polymeric matrix and a second particulate phase with random distribution. The Discrete Element Method (DEM) and the Finite Element Method (FEM) were used to carry out the present work. Firstly, an application of DEM, a study of different alternatives is shown to determine the volume representative element (RVE) considering the non-linear behavior of the studied material. Secondly, an application of FEM, a study considering the matrix and particulate phase, both, with linear elastic behavior. This application consists on computing the RVE and comparing these results with analytical proposals available in the Micromechanics classical bibliography. A mesh convergence study of the FEM models used and simple applications of optimization are also presented. Finally, another application of FEM is presented. In this case a non linear study is shown, where the matrix is considered linear elastic, and the particulate phase is hyperelastic. In this case the RVE was determined and some applications to verify the consistency of the results obtained are presented.

In this investigation, a single phase fluid is used to study the coupling between natural convection heat transfer within an enclosure and forced convection through computer covering case to cool the electronic chip. Two working fluids are used (water and air) within a rectangular enclosure and the air flow through the computer case is created by an exhaust fan installed at the back of the computer case. The optimum enclosure size configuration that keeps a maximum temperature of the heat source at a safe temperature level (85°C) is determined. The cooling system is tested for varying values of applied power in the range of 15-40W. The study is based on both numerical models and experimental observations. The numerical work was developed using the commercial software (ANSYS-Icepak) to simulate the flow and temperature fields for the desktop computer and the cooling system. The numerical simulation has the same physical geometry as those used in the experimental investigations. The experimental work was aimed to gather the details for temperature field and use them in the validation of the numerical prediction. The results showed that, the cavity size variations influence both the heat transfer process and the maximum temperature. Furthermore, the experimental results ii compared favourably with those obtained numerically, where the maximum deviation in terms of the maximum system temperature, is within 3.5%. Moreover, it is seen that using water as the working fluid within the enclosure is capable of keeping the maximum temperature under 77°C for a heat source of 40W, which is below the recommended electronic chips temperature of not exceeding 85°C. As a result, the noise and vibration level is reduced. In addition, the proposed cooling system saved about 65% of the CPU fan power.

[pt] Chamas pré-misturadas em escoamentos turbulentos com rotação são encontradas em diversos sistemas de engenharia, como turbinas a gás e motores a jato. Neste trabalho, regimes de chamas característicos de tais sistemas são estudados numericamente num queimador de escala laboratorial. O estado da arte dos estudos numéricos de tais chamas é revisado, com respeito a simulações de grandes escalas, bem como o de modelos computacionais baseados em médias de Reynolds. Um estudo isotérmico é feito no escoamento turbulento, num domínio computacional que consiste de um swirler radial e uma câmara de combustão. O impacto de diferentes modelos de turbulência, níveis de refinamentos de malha e condições de contorno no número de swirl e na estrutura do escoamento é investigado. Os resultados revelam que os três modelos de turbulência propostos resultam em campos de escoamento e número de swirl similares, enquanto o nível de refinamento de malha e a condição de contorno de parede deslizante alteram o número de swirl significativamente. Utilizando as equações de média de Reynolds, com o fechamento do modelo k − E realizável, acoplado a um modelo de duas equações para chamas pré-misturadas de metano e ar, dois regimes de chamas são analisados. Estes regimes correspondem à chama de recirculação externa (chama tipo M) e um regime de instabilidade, que ocorre na transição entre a chama tipo V e chama tornado. A estrutura do escoamento é caracterizada em termos de velocidade e propriedades de turbulência e combustão. Uma comparação entre variáveis de progresso também é feita, utilizando resultados experimentais prévios, levando a boa concordância qualitativa para os dois regimes estudados. / [en] Lean premixed turbulent swirling flames are found in many engineering systems, such as gas turbines and jet engines. This work aims to numerically study flame regimes, representative of such systems, stabilized in a laboratory scale burner. The state of the art of the numerical studies concerning these types of flames is reviewed, with respect to Reynolds-Averaged NavierStokes and Large Eddy Simulations. A turbulent, isothermal flow study is performed within the radial swirler and the combustion chamber. The impact of different turbulence models (realizable k − E, RNG k − E and SST k−W), mesh refinement levels and boundary conditions on the swirl number and overall flow structure is investigated. The results show that the three tested turbulence models yield similar results, with respect to the obtained flow field, whereas the mesh refinement level and slip wall boundary condition alter the swirl number significantly. Using Reynolds-Averaged NavierStokes transport equations, closed by the realizable k − E model, coupled with a two-equation premixed combustion model for methane/air mixtures, two combustion regimes are analyzed. These regimes correspond to the outer recirculation zone flame (M-shaped flame) and an unstable regime, which occurs at the transition between the V-shaped flame and tornado-flame. The flow structure is characterized in terms of velocity fields, turbulence and combustion properties. A reaction progress variable comparison is also performed, using existing experimental results, yielding qualitatively similar results for both studied regimes.

In this investigation, a single phase fluid is used to study the coupling between natural convection heat transfer within an enclosure and forced convection through computer covering case to cool the electronic chip. Two working fluids are used (water and air) within a rectangular enclosure and the air flow through the computer case is created by an exhaust fan installed at the back of the computer case. The optimum enclosure size configuration that keeps a maximum temperature of the heat source at a safe temperature level (85℃) is determined. The cooling system is tested for varying values of applied power in the range of 15−40𝑊. The study is based on both numerical models and experimental observations. The numerical work was developed using the commercial software (ANSYS-Icepak) to simulate the flow and temperature fields for the desktop computer and the cooling system. The numerical simulation has the same physical geometry as those used in the experimental investigations. The experimental work was aimed to gather the details for temperature field and use them in the validation of the numerical prediction. The results showed that, the cavity size variations influence both the heat transfer process and the maximum temperature. Furthermore, the experimental results ii compared favourably with those obtained numerically, where the maximum deviation in terms of the maximum system temperature, is within 3.5%. Moreover, it is seen that using water as the working fluid within the enclosure is capable of keeping the maximum temperature under 77℃ for a heat source of 40𝑊, which is below the recommended electronic chips temperature of not exceeding 85℃. As a result, the noise and vibration level is reduced. In addition, the proposed cooling system saved about 65% of the CPU fan power.

L’objectif de cette thèse est de proposer un modèle d’érosion diffuse qui intègre les principaux processus de ce phénomène (détachement, transport, sédimentation) et qui prend en compte l’interaction des gouttes de pluie avec ces processus. Dans un premier temps, nous avons établi une loi de détachement par la pluie qui inclut l’effet des gouttes et celui de l’épaisseur de la lame d’eau qui couvre la surface du sol. Pour obtenir cette loi, une étude numérique avec le logiciel Gerris a permis de modéliser les cisaillements créés par l’impact des gouttes sur des épaisseurs de lame d’eau variables. Ces cisaillements estiment la quantité de sol détaché par chaque goutte. Nous avons montré, à travers une étude probabiliste, que les gouttes sont quasiment indépendantes lors du détachement. Les détachements de l’ensemble des gouttes sont donc sommés pour établir la loi de détachement pour la pluie. Par ailleurs, l’étude probabiliste a montré la possibilité d’une forte interaction entre les gouttes de pluie et les particules en sédimentation. Par conséquent, pour le processus de transport-sédimentation, nous avons privilégié une approche expérimentale. Cette étude a révélé que l’effet des gouttes de pluie est d’augmenter la vitesse de sédimentation des particules. Enfin, nous avons proposé un nouveau modèle d’érosion qui généralise plusieurs modèles d’érosion de la littérature et décrit l’évolution des concentrations en sédiments avec des effets linéaires et non-linéaires. Selon le choix des paramètres du modèle, celui-ci peut représenter l’érosion diffuse et concentrée à l’échelle du bassin versant, le transport par charriage dans les rivières ou encore le transport chimique. L’intégration du modèle dans le logiciel de ruissellement FullSWOF est aussi réalisée. / The aim of this work is to formulate an interrill erosion model. This model should take into account the main erosion processes (detachment, transport and sedimentation) and the interaction of raindrops during these processes. First we develop a law for rainfall detachment that includes the effects of the raindrops and the water layer thickness at the soil surface. We use the Gerris software to simulate the shear stresses created by the impacts of raindrops at the soil surface. These shear stresses allow to evaluate the quantity of soil detached by each raindrop. We have shown with a probabilistic approach that raindrops are almost independent during soil detachment. Then by summing all the raindrops detachments we obtain the rainfall detachment law. Futhermore the probabilistic study has revealed the possibility of a strong interaction between raindrops and settling particles. So, we used specific laboratory experiments to investigate the particles transport and sedimentation processes. These experiments show that the effect of raindrops is to increase the particles settling velocity. Finally, we propose a new erosion model which encompasses previous literature erosion models and that can describe the behavior of sediments concentrations with linear and non-linear behaviors. The model is able to simulate interrill and rill erosions at the watershed scale, bedload transport in rivers and chemical transfer. The integration of the model in the FullSWOF runoff software is also carried out.

Dans cette thèse, nous étudions différents aspects mathématiques et numériques des équations de Gross-Pitaevskii et de Schrödinger non linéaire. Nous commençons (chapitre 1) par introduire différents modèles à partir des systèmes physiques que sont les condensats de Bose-Einstein et les impulsions lumineuses dans les fibres optiques. Cette modélisation conduit aux équations aux dérivées partielles stochastiques suivantes : l'équation de Gross-Pitaevskii stochastique et l'équation de Schrödinger non linéaire avec dispersion aléatoire. Ensuite, dans le second chapitre, nous nous intéressons au problème de l'existence et l'unicité d'une solution de ces équations. On montre notamment que le problème de Cauchy a une solution pour l'équation de Gross-Pitaevskii stochastique avec rotation grâce à la construction de la solution associée au problème. Nous abordons ensuite dans le troisième chapitre le problème du calcul des états stationnaires pour l'équation de Gross-Pitaevskii. Nous développons une méthode pseudo-spectrale de discrétisation du Continuous Normalized Gradient Flow, associée à une résolution itérative préconditionnée des sous-espaces de Krylov. Le quatrième chapitre concerne l'étude de schémas pseudo-spectraux pour la dynamique de l'équation de Gross-Pitaevskii et de Schrödinger non linéaire. On procède à une étude numérique de ces schémas (schéma de splitting de Lie et de Strang, ainsi qu'un schéma de relaxation). De plus, on analyse le schéma de Lie dans le cadre de l'équation de Schrödinger non linéaire avec dispersion aléatoire. Finalement, nous présentons, dans le cinquième chapitre, une boîte à outils Matlab (GPELab) développée dans le but de fournir les méthodes numériques que nous avons étudiées / The aim of this Thesis is to study various mathematical and numerical aspects related to the Gross-Pitaevskii and nonlinear Schrödinger equations. We begin (chapter 1) by introducing a few models starting from the physics of Bose-Einstein condensates and optical fibers. This naturally leads to introducing a stochastic Gross-Pitaevskii equation and a nonlinear Schrödinger equation with random dispersion. Next, in the second chapter, we analyze the existence and uniqueness problem for these two equations. We prove that the Cauchy problem admits a solution for the stochastic Gross-Pitaevskii equation with a rotational term by constructing the solution associated with the linear. The third chapter is concerned with the computation of stationary states for the Gross-Pitaevskii equation. We develop a pseudo-spectral approximation scheme for the Continuous Normalized Gradient Flow formulation, combined with preconditioned Krylov subspace methods. This original approach leads to the robust and efficient computation of ground states for fast rotations and strong nonlinearities. In the fourth chapter, we consider some pseudo-spectral schemes for computing the dynamics of the Gross-Pitaevskii and nonlinear Schrödinger equations. These schemes (the Lie's and Strang's splitting schemes and the relaxation scheme) are numerically studied. Moreover, we proceed to a rigorous numerical analysis of the Lie scheme for the associated stochastic PDEs. Finally, we present in the fifth chapter a Matlab toolbox (called GPELab) that provides computational solutions based on the schemes previously introduced in the Thesis

La démarche expérimentale menée dans cette thèse CIFRE a eu comme objectif l’étude de la faisabilité de la séparation électrostatique d’une large gamme de mélanges de matériaux granulaires issus de déchets d’équipements électriques et électroniques (conducteur – isolant, conducteur – conducteur et isolant – isolant). Trois mécanismes physiques de charge électriques ont été mis en oeuvre : l’induction électrostatique, la décharge couronne et l’effet triboélectrique. Un dispositif de charge de laboratoire et deux séparateurs électrostatiques industriels ont été conçus et réalisés. Le dispositif de charge à cylindre(s) tournant(s) permet la charge triboélectrique de matériaux plastiques. Le prototype de séparateur industriel a d’abord été réalisé pour le traitement de mélanges granulaires conducteur – isolant puis a été adapté à la séparation isolant – isolant. Les trois mécanismes de charge peuvent y être utilisés. Ce prototype a permis la fabrication du premier séparateur électrostatique de série de la société CITF dédié à la séparation de déchets de câbles électriques. Des mesures de charge et de masse ainsi que des simulations et visualisations des trajectoires des particules par caméra rapide ont facilité l’analyse des phénomènes. La méthode des plans d’expérience a permis d’identifier les facteurs influents sur les processus de séparation et de définir leur point de fonctionnement optimal. L’influence d’une décharge à barrière diélectrique sur la charge triboélectrique et la séparation électrostatique de mélanges plastiques a été étudiée. Les travaux réalisés dans cette thèse ont confirmé la séparabilité électrostatique de mélanges de matériaux granulaires. / The experimental approach used in this thesis was aimed at the study of the feasibility of the electrostatic separation of a wide range of granular mixtures from waste electric and electronic equipment (conductive – insulator, conductive – conductive, insulator – insulator). Three physical mechanisms of electrical charging have been employed: electrostatic induction, corona discharge and triboelectric effect. A tribocharging device and two industrial electrostatic separators have been designed and engineered. The rotating cylinder tribocharging device allows the triboelectric charging of plastics. The industrial separator prototype was firstly built for processing conducting – insulator granular mixtures and then adapted for insulator – insulator separation. This prototype, which enables the use of all three electrical charging mechanisms, served as model for the CITF company first industrial electrostatic separator for the recycling of metals and plastics from electric cable wastes. Charge and mass measurement, as well as modelling and visualization of particle trajectories by a high-speed camera facilitated the investigations. Design of experiments method was used to define the influential factors and find the optimum operating conditions of the separation processes. Dielectric barrier discharge exposure of granular plastics may enhance the efficiency of the triboelectric charging of these materials and hence facilitate their electrostatic separation. These researches have confirmed the feasibility of the electrostatic separation of a wide variety of granular mixtures.

Pour faire face à l’augmentation des émissions de CO2 dans l’atmosphère à cause de la production électrique dans des centrales à charbon, le captage en post-combustion au moyen d’un procédé VSA est une solution envisageable. Les adsorbants utilisés dans notre étude sont la TEPA imprégnée sur SiO2, les oxydes de terre rare et le MOF (Metal Organic Frameworks) SIM-1. Pour chaque adsorbant, une étude du perçage puis de la régénération a été effectuée à partir d’une alimentation composée de 15%vol de CO2 et de N2. De ces essais, les conditions opératoires des cycles VSA ont été établies (durées des phases courtes, pas de circulation de purge). En cycle, les performances sont comparées à celle du procédé d’absorption avec la monoéthénolamine. La pureté du désorbat varie de 89,2%vol à 97,2%vol selon les adsorbants et les conditions opératoires. Elle est inférieure à celle du procédé d’absorption (99%vol) mais est correcte pour le transport et le stockage. Le taux de captage évolue de 87,2% à 94,9% (absorption : 98%). La consommation énergétique est inférieure à celle du procédé avec la MEA (de 1,53 à 3,45 MJ.kgCO2 1 pour notre procédé et 3,7 MJ.kgCO2¬1 pour l’absorption) Enfin la productivité est du même ordre de grandeur que celle d’autres procédés VSA de la littérature. Avec le modèle numérique, une étude locale de l’adsorbeur a été menée. Puis grâce à une étude paramétrique, des conditions optimales en cycle ont été déterminées. Les résultats obtenus ont permis de mettre en évidence des performances comparables avec les autres procédés VSA de la littérature. De plus, notre procédé est beaucoup moins énergivore que le procédé d’absorption mais la pureté du désorbat et le taux de captage en CO2 restent inférieurs. / To deal with the CO2 emissions increase in the atmosphere due to electricity production, CO2 post-combustion capture by VSA process is a promising solution. The adsorbents used in this study are impregnated TEPA on SiO2, lanthanide oxides and the MOF (Metal Organic Frameworks) SIM-1. For each adsorbent, a study of breakthrough and regeneration was carried out from a feed composed of 15%vol CO2 and N2. From these experiments, the cyclic operating conditions of VSA have been established (short duration phases, no purge). Cyclic performances are compared to that of the absorption process with monoethenolamine. The desorbate purity varies from 89.2% to 97.2%vol according to adsorbent and operating conditions. It is less than that obtained with absorption process (99%vol) but it is correct for transport and storage. The recovery varies from 87.2% to 94.2% (absorption: 98%). The energy consumption is less than that the process with the MEA (from 1.53 to 3.45 MJ.kgCO2 1 for our process and 3.7 MJ.kgCO2 1 for absorption). . Finally, the productivity is of the same order of magnitude as that of other VSA processes from literature. With the numerical model, a local study of the adsorber was carried out. Afterwards, through a parametric study, cycle optimal conditions were determined. The cycle results highlighted comparable performances with the other VSA processes from literature. Moreover, our process needs less energy than absorption process but the desorbate purity and CO2 recovery remain lower.