This thesis presents a two-phase liquid-solid numerical model using Smoothed Particle Hydrodynamics (SPH). The scheme is developed for multi-phase flows in industrial tanks containing sediment used in the nuclear industry for decommissioning. These two-phase liquid-sediments flows feature a changing interfacial profile, large deformations and fragmentation of the interface with internal jets generating resuspension of the solid phase. SPH is a meshless Lagrangian discretization scheme whose major advantage is the absence of a mesh making the method ideal for interfacial and highly non-linear flows with fragmentation and resuspension. Emphasis has been given to the yield profile and rheological characteristics of the sediment solid phase using a yielding, shear and suspension layer which is needed to predict accurately the erosion phenomena. The numerical SPH scheme is based on the explicit treatment of both phases using Newtonian and non-Newtonian Bingham-type constitutive models. This is supplemented by a yield criterion to predict the onset of yielding of the sediment surface and a suspension model at low volumetric concentrations of sediment solid. The multi-phase model has been compared with experimental and 2-D reference numerical models for scour following a dry-bed dam break yielding satisfactory results and improvements over well-known SPH multi-phase models. A 3-D case using more than 4 million particles, that is to the author’s best knowledge one of the largest liquid-sediment SPH simulations, is presented for the first time. The numerical model is accelerated with the use of Graphic Processing Units (GPUs), with massively parallel capabilities. With the adoption of a multi-phase model the computational requirements increase due to extra arithmetic operations required to resolve both phases and the additional memory requirements for storing a second phase in the device memory. The open source weakly compressible SPH solver DualSPHysics was chosen as the platform for both CPU and GPU implementations. The implementation and optimisation of the multi-phase GPU code achieved a speed up of over 50 compared to a single thread serial code. Prior to this thesis, large resolution liquid-solid simulations were prohibitive and 3-D simulations with millions of particles were unfeasible unless variable particle resolution was employed. Finally, the thesis addresses the challenging problem of enforcing wall boundary conditions in SPH with a novel extension of an existing Modified Virtual Boundary Particle (MVBP) technique. In contrast to the MVBP method, the extended MVBP (eMVBP) boundary condition guarantees that arbitrarily complex domains can be readily discretized ensuring approximate zeroth and first order consistency for all particles whose smoothing kernel support overlaps the boundary. The 2-D eMVBP method has also been extended to 3-D using boundary surfaces discretized into sets of triangular planes to represent the solid wall. Boundary particles are then obtained by translating a full uniform stencil according to the fluid particle position and applying an efficient ray casting algorithm to select particles inside the fluid domain. No special treatment for corners and low computational cost make the method ideal for GPU parallelization. The models are validated for a number of 2-D and 3-D cases, where significantly improved behaviour is obtained in comparison with the conventional boundary techniques. Finally the capability of the numerical scheme to simulate a dam break simulation is also shown in 2-D and 3-D.

Le titre de ma thèse de doctorat est "Equations de Stokes et de Navier-Stokes avec la con- dition de Navier", où j’ai considéré l’écoulement d’un fluide newtonien visqueux, incompressible dans un domaine borné de R3. L’écoulement du fluide est décrit par les équations bien connues de Navier-Stokes, données par le système suivant ∂t − ∆u + (u • ∇)u + ∇π = 0, div u = 0 dans Ω × (0, T )u • n = 0, 2[(Du)n]τ + αuτ = 0 sur Γ × (0, T )u(0) = u0 dans Ω (0.1) dans un domaine borné Ω ⊂ R3 de frontière Γ, éventuellement non simplement connexe, de classe C1,1. La vitesse initiale u0 et le coefficient de friction α, scalaire, sont des fonctions don- nées. Les vecteurs unitaires normal extérieur et tangents à Γ sont notés n et τ respectivement et Du = 1 (∇u + ∇uT ) est le tenseur des déformations. Les fonctions u et π décrivent respective- ment les champs de vitesses et de pression du fluide dans Ω satisfaisant la condition aux limites (0.1.2).Cette condition aux limites, proposée par H. Navier en 1823, a été abondamment étudiée ces dernières années, qui pour de nombreuses raisons convient parfois mieux que la condition aux limites de Dirichlet sans glissement : elle offre plus de liberté et est susceptible de fournir une solution physiquement acceptable au moins pour certains des phénomènes paradoxaux résultant de la condition de non-glissement, comme par exemple le paradoxe de D’Alembert ou le paradoxe de non-collision.Ma thèse comporte trois parties. Dans la première, je cherche à savoir si le problème (0.1) est bien posé en théorie Lp, en particulier l’existence, l’unicité de solutions faibles, fortes dans W 1,p(Ω) et W 2,p(Ω) pour tout p ∈ (1, ∞), en considérant la régularité minimale du coefficient de friction α. Ici α est une fonction, pas simplement une constante qui reflète les diverses propriétés du fluide et/ou de la frontière, ce qui nous permet d’analyser le comportement de la solution par rapport au coefficient de frottement.Utilisant le fait que les solutions sont bornées indépendamment de α, on montre que la solution des équations de Navier-Stokes avec la condition de Navier converge fortement vers une solution des équations de Navier-Stokes avec la condition de Dirichlet, correspondant à la même donnée initiale dans l’espace d’énergie lorsque α → ∞. Des résultats similaires ont été obtenus pour le cas stationnaire.Le dernier chapitre concerne les estimations pour le problème de Robin pour le laplacien : l’opérateur elliptique de second ordre suivant, sous forme divergentielle dans un domaine bornéΩ ⊂ Rn de classe C1, avec la condition aux limites de Robin a été considéré div(A∇)u = divf + F dans Ω, ∂u+ αu = f n + g sur Γ.∂n (0.2) Les coefficients de la matrice symétrique A sont supposés appartenir à l’espace V MO(R3). Aussi α est une fonction appartenant à un certain espace Lq . En plus de prouver l’existence, l’unicité de solutions faibles et fortes, nous obtenons une borne sur u, uniforme par rapport à α pour α suffisamment large, en norme Lp. Pour plus de clarté, nous avons étudié séparément les deux cas: l’estimation intérieure et l’estimation au bord. / My PhD thesis title is "Navier-Stokes equations with Navier boundary condition" where I have considered the motion of an incompressible, viscous, Newtonian fluid in a bounded do- main in R3. The fluid flow is described by the well-known Navier-Stokes equations, given by thefollowing system 1 )t − L1u + (u ⋅ ∇)u + ∇n = 0, div u = 01u ⋅ n = 0, 2[(IDu)n]r + aur = 0 in Q × (0, T )on Γ × (0, T ) (0.1) 11lu(0) = u0 in Qin a bounded domain Q ⊂ R3 with boundary Γ, possibly not connected, of class C1,1. The initialvelocity u0 and the (scalar) friction coefficient a are given functions. The unit outward normal and tangent vectors on Γ are denoted by n and r respectively and IDu = 1 (∇u + ∇uT ) is the rate of strain tensor. The functions u and n describe respectively the velocity2 and the pressure of a fluid in Q satisfying the boundary condition (0.1.2).This boundary condition, first proposed by H. Navier in 1823, has been studied extensively in recent years, among many reasons due to its contrast with the no-slip Dirichlet boundary condition: it offers more freedom and are likely to provide a physically acceptable solution at least to some of the paradoxical phenomenons, resulting from the no-slip condition, for example, D’Alembert’s paradox or no-collision paradox.My PhD work consists of three parts. primarily I have discussed the Lp -theory of well-posedness of the problem (0.1), in particular existence, uniqueness of weak and strong solutions in W 1,p (Q) and W 2,p (Q) for all p ∈ (1, ∞) considering minimal regularity on the friction coefficienta. Here a is a function, not merely a constant which reflects various properties of the fluid and/or of the boundary. Moreover, I have deduced estimates showing explicitly the dependence of u on a which enables us to analyze the behavior of the solution with respect to the friction coefficient.Using this fact that the solutions are bounded with respect to a, we have shown the solution of the Navier-Stokes equations with Navier boundary condition converges strongly to a solution of the Navier-Stokes equations with Dirichlet boundary condition corresponding to the sameinitial data in the energy space as a → ∞. The similar results have also been deduced for thestationary case.The last chapter is concerned with estimates for a Laplace-Robin problem: the following second order elliptic operator in divergence form in a bounded domain Q ⊂ Rn of class C1, withthe Robin boundary condition has been considered1div(A∇)u = divf + F in Q, 11 )u + u = f ⋅ n + g on Γ. (0.2) 2The coefficient matrix A is symmetric and belongs to V MO(R3). Also a is a function belonging to some Lq -space. Apart from proving existence, uniqueness of weak and strong solutions, we obtain the bound on u, uniform in a for a sufficiently large, in the Lp -norm. We have separately studied the two cases: the interior estimate and the boundary estimate to make the main idea clear in the simple set up.

Les systèmes de combustion sont sujets aux instabilités de combustion (IC). Elles résultent d'un couplage constructif entre le taux de dégagement de chaleur instationnaire et des modes acoustiques du système. Les IC peuvent mettre en danger la performance et l'intégrité des systèmes de combustion. Même si ces phénomènes sont connus depuis plus d'un siècle, éviter quelles aient lieux dans les chambres de combustions industrielles reste difficile. Les objectifs de cette thèse sont les suivants : (1) étudier la dynamique des modes acoustiques, (2) analyser la réponse de flamme d'un moteur de fusée à propergol liquide H2/O2 (appelé "BKD"), sujet aux IC, à l'aide de la Simulation aux Grandes Echelles (SGE) et (3) dériver, utiliser et étudier des conditions limites permettant d'imposer des impédances acoustiques complexes en SGE. / Combustion devices are prone to combustion instabilities. They arise from a constructive coupling between the unsteady heat release rate of the flame and the resonant acoustic modes of the entire system. The occurence of such instabilities can pose a threat to both performance and integrity of combustion systems. Although these phenomena have been known for more than a century, avoiding their appearance in industrial engines is still challenging. The objective of this thesis is threefold: (1) study the dynamics of the resonant acoustic modes, (2) investigate the flame response of a liquid rocket engine under unstable conditions using Large Eddy Simulation(LES) and (3) derive, use and study Time Domain Impedance Boundary Conditions (TDIBCs), i.e. boundary conditions modeling complex acoustic impedances.

Orientador: Marcelo Cristianini / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia de Alimentos / Made available in DSpace on 2018-08-13T10:42:20Z (GMT). No. of bitstreams: 1 Augusto_PedroEstevesDuarte_M.pdf: 2374617 bytes, checksum: 51b7576f4277bc0fdae47e5122fc60fd (MD5) Previous issue date: 2009 / Resumo: A crescente busca por alimentos mais seguros e de melhor qualidade nutricional e sensorial cria a necessidade de melhor entendimento dos processos envolvidos na produção dos mesmos. O tratamento térmico é um dos métodos mais utilizados na conservação de alimentos, sendo o processamento dentro da embalagem um dos mais seguros. A utilização de modelamento matemático da transferência de calor na avaliação de tratamentos térmicos vem se mostrando uma poderosa ferramenta na garantia da segurança sem comprometimento da qualidade nutricional e sensorial dos alimentos. A fluidodinâmica computacional (CFD) vem sendo utilizada em diversos trabalhos para melhor entendimento de processos térmicos de alimentos líquidos. Entretanto, a falta de consistência e uniformidade nas modelagens, aliadas as raras avaliações experimentais das simulações, criam a necessidade de avaliações entre metodologias utilizadas e validações criteriosas. O presente trabalho estudou a transferência de calor durante tratamentos térmicos de alimentos líquidos embalados em garrafas comerciais através de modelagem matemática por CFD. Determinou-se o coeficiente convectivo de transferência de calor (h) para duas garrafas comerciais em um sistema de aquecimento e um de resfriamento em imersão em água. Observou-se que mesmo pequenas diferenças entre geometrias de embalagens resultaram em considerável diferença nos valores de h entre embalagens e sistemas, reforçando a necessidade de avaliação dessa propriedade para cada processo real estudado. Avaliou-se quatro metodologias utilizadas nos trabalhos de CFD para determinação das condições de contorno das simulações, observando-se que as que consideram perfis de temperatura superestimam o fluxo de calor trocado com o produto, podendo comprometer a segurança e conservação do mesmo. A metodologia que considera o fluxo de calor decorrente das condições de contorno h e perfil térmico do meio de aquecimento apresentaram boa concordância com os perfis térmicos experimentais, mostrando-se adequados à modelagem de processos térmicos de alimentos. Caracterizou-se reologicamente um alimento líquido modelo, podendo ser utilizado para simulação de sucos de frutas, assim como a inativação térmica de um microrganismo modelo em processos de pasteurização (Lactobacillus plantarum). Analisou-se as características do tratamento térmico de alimentos líquidos em duas embalagens comerciais, através de perfis de temperatura, velocidade, característica da região de aquecimento mais lento (RAML) e inativação microbiana. Os perfis de temperatura e velocidade obtidos nas simulações de CFD do processo térmico do alimento modelo utilizado se mostraram semelhantes aos reportados na literatura, sendo descritas as características do processo. A análise dos perfis de temperatura obtidos experimentalmente e através do modelo indicaram boa correlação das simulações de CFD, sugerindo a possibilidade de utilização dessa ferramenta para avaliação de perfis térmicos em processos térmicos de alimentos embalados. Entretanto, a análise de validação microbiológica indicou grande desvio entre os valores experimentais e obtidos pelo modelo, atribuído a baixa resistência térmica do microrganismo alvo utilizado nas condições de processo. Nesse caso, mesmo pequenos desvios entre as temperaturas experimentais e obtidas por CFD podem resultar em grande desvio na inativação microbiana final, sugerindo que a utilização de CFD na avaliação de tratamentos térmicos deve ser vista com cautela. Os resultados obtidos comprovam a necessidade de validação dos modelos obtidos através de avaliação de perfil térmico e inativação microbiológica / Abstract: The growing demand for safer and high-quality food products creates the need for better knowledge of the processes involved in food production. Thermal process is one of the safest and most frequently used methods for food preservation, in special when performed in the package. The mathematical modelling of heat transfer is a useful tool for designing safety process while minimizing nutritional and sensory drops. The computational fluid dynamics (CFD) have been widely used for better understand of liquid food thermal process. However, no consistency in the mathematical models built is observed, and just a very few works compare the CFD data with experimental ones. There is a need for the evaluation of the use of CFD for thermal process design. The present work has evaluated the heat transfer in in-package liquid food during thermal process, using mathematical modelling by CFD. The convective heat transfer coefficient (h) among two commercial bottles and a heat and a cooling system were determinated. It was observed that even small differences among packages and heat transfer system result in distinct coefficient and that it must be measured for the exact heat transfer system. Four methodologies were evaluated for the boundary conditions definition of the CFD simulations, based on the previous CFD works. The models that considered the temperature profiles as boundary condition, showed faster heating. By over-estimating the product heating rate, those models are not appropriated for the mathematical modelling of heat process, as it compromises the safety and preservation of food products. The model that considered the measured value of h and temperature profile of the water bath as boundary condition showed good agreement with experimental values, being appropriated for thermal process modelling. The rheological characteristics of a model liquid food was determinated, and the thermal resistance of Lactobacillus plantarum, a target microorganism in pasteurization processes, was evaluated in this model, which can be used as a fruit juice simulator. The thermal process of liquid foods was evaluated in two commercial bottles, using temperature, velocity, slowest heating zone (SHZ) and microbiological inactivation profiles. The temperature and velocity profiles were compatible with those described in CFD works. The thermal profile obtained by CFD shown good correlation with experimental values, suggesting that CFD can be used in thermal process temperature profiles evaluation. Although, the microbiological validation shown large deviation between the experimental values and obtained by the model, probably due the low thermal resistance of the studied microorganism. These results indicate that the CFD utilization in thermal process evaluation might be carefully seen, in especial when the microorganism thermal resistance is low in process conditions. In these situations, even small differences between CFD and experimental temperatures results in considerable microbial inactivation divergence. The results obtained in this work show the need for CFD models evaluation by thermal profile and microbiological inactivation / Mestrado / Mestre em Tecnologia de Alimentos

A model for stress and strain accumulation in strike slip earthquake faults is presented in which a finite width cuboidal fault region is embedded between two cuboidal tectonic plates. Elasto-plastic continuum constitutive equations model the gouge in the fault and the tectonic plates are linear elastic solids obeying the generalised Hooke's law. The model predicts a velocity field which is comparable to surface deformations. The plastic behaviour of the fault material allows the velocities in the tectonic plate to increase to values which are independent of the distance from the fault. Both of the non-trivial stress and strain components accumulate most significantly in the vicinity of the fault. The release of these strains during a dynamic earthquake event would produce the most severe deformations at the fault which is consistent with observations and the notion of an epicenter. The accumulations in the model, however, are at depths larger than would be expected. Plastic strains build up most significantly at the base of the fault which is in yield for the longest length of time but additionally is subject to larger temperatures which makes the material more ductile. The speed of propagation of the elasto-plastic boundary is calculated and its acceleration towards the surface of the fault may be indicative of a dynamic earthquake type event.

En se basant sur un niveau océanique constant, les études des nappes côtières ne considèrent généralement pas l'impact des forçages océaniques. Notre approche combine le suivi à long terme de la « Nappe des Sables » de l'Ermitage (en arrière d'un récif frangeant, La Réunion) avec la réalisation de modèles numériques dans le but de tester l'influence des de ces forçages sur l'évolution de la piézométrie, du front dispersif et des flux transitant le long de la limite océanique. En mettant en parallèle le comportement de la nappe et du domaine océanique (récif), ces travaux présentent l'étude comparative la plus complète d'un système côtier, basée sur un enregistrement en continu d'environ 600 jours. Il apparaît que la géométrie du modèle et les paramètres hydrodynamiques choisis, associés à différents types de forçages océaniques, ont des conséquences variables sur la piézométrie, le front dispersif et les flux. Ainsi, les différentes définitions de limite océanique testées sur des simulations reproduisant la période de suivi montrent que la prise en compte d'une limite océanique complexe en régime transitoire sur cette période génère une meilleure reproductibilité des signaux enregistrés (piézométriques et salinité) que lorsque l'on utilise un niveau océanique moyen constant dans les modèles. Ces résultats mettent en évidence qu'une bonne compréhension des mécanismes hydrodynamiques au sein des nappes côtières implique la mise en place d'un suivi à long terme des phénomènes de forçage océanique qui agissent directement sur la nappe. La caractérisation des différents forçages océaniques nécessite de décomposer le signal global, dont l'analyse en harmonique permet d'identifier les contributions respectives des oscillations périodiques et homogènes de marée et des oscillations brusques et ponctuelles liées à la houle. La modélisation met ici en évidence qu'il est indispensable que la complexité du système naturel soit reproduite de manière réaliste dans les futures études des nappes côtières. Dans cette optique, la combinaison des données hydrogéologiques et océanographiques dans des environnements côtiers où ces approches n'ont, jusqu'à présent, jamais été couplées, permettra de quantifier l'impact des forçages océaniques sur ces milieux. / Studies of coastal aquifers based on a constant mean sea level generally not consider the impact of oceanic oscillations. Our approach combines a long-term recording of “La Nappe des Sables” (adjacent to the fringing reef system of l'Ermitage, La Reunion) with numerical models in order to investigate the influence of these oceanic seasonal oscillations on groundwater hydrodynamics, seawater intrusions and submarine groundwater discharges. Analyzing both the behavior of the aquifer and the oceanic domain (reef), this study integrates a continuous recording of 600 days. It shows that the geometry and the hydrodynamic parameters chosen in the model, correlated to three types of oceanic oscillations, have variable consequences on the hydraulic head, the dispersive front and submarine groundwater discharges. Moreover, taking into account different complex oceanic boundaries in transient simulations over this 600 days period generates a better reproducibility of recorded signals (hydraulic head and salinity). These results underline that a long-term recording of oceanic oscillations is necessary for a good understanding of hydrodynamic mechanisms within coastal aquifers. The global signal must be decomposed with a harmonic analysis in order to identify the respective contributions of wave set up and tidal pumping to this signal. Our models reveal that the complexity of the natural system must be accounted for realistically in future numerical studies. The combination of hydrogeological and oceanographical data will allow the quantification of the impact of oceanic seasonal oscillations on such environments.

No description available.

Cette thèse est consacrée à l'étude des équations du Darcy Brinkman Forchheimer (DBF) avec des conditions aux limites non standards. Nous montrons d'abord l'existence de différents type de solutions (faible, forte) correspondant au problème DBF stationnaire dans un domaine simplement connexe avec des conditions portants sur la composante normale du champ de vitesse et la composante tangentielle du tourbillon. Ensuite, nous considérons le système Brinkman Forchheimer (BF) avec des conditions sur la pression dans un domaine non simplement connexe. Nous prouvons que ce problème est bien posé ainsi que l'existence de la solution forte. Nous établissons la régularité de la solution dans les espaces L^p pour p >= 2.L'étude et l'approximation du problème DBF non stationnaire est basée sur une approche pseudo-compressibilité. Une estimation d'erreur d'ordre deux est établie dans le cas o\`u les conditions aux limites sont de types Dirichlet ou Navier.Enfin, une méthode d'éléments finis Galerkin Discontinue est proposée et la convergence établie concernant le problème DBF linéarisé et le système DBF non linéaire avec des conditions aux limites non standard. / This thesis is devoted to Darcy Brinkman Forchheimer (DBF) equations with a non standard boundary conditions. We prove first the existence of different type of solutions (weak, strong) of the stationary DBF problem in a simply connected domain with boundary conditions on the normal component of the velocity field and the tangential component of the vorticity. Next, we consider Brinkman Forchheimer (BF) system with boundary conditions on the pressure in a non simply connected domain. We prove the well-posedness and the existence of a strong solution of this problem. We establish the regularity of the solution in the L^p spaces, for p >= 2.The approximation of the non stationary DBF problem is based on the pseudo-compressibility approach. The second order's error estimate is established in the case where the boundary conditions are of type Dirichlet or Navier. Finally, the finite elements Galerkin Discontinuous method is proposed and the convergence is settled concerning the linearized DBF problem and the non linear DBF system with a non standard boundary conditions.

Establishing dynamic characteristics of structures is a challenging area of research. The dynamic characteristics of structures, such as natural frequencies, modeshapes, response levels and damping characteristics play an important role in identifying the condition of the structures. The assumed modes method is a particular analytical method used to estimate the dynamic characteristics of a structure. However, the eigenfunctions used in the assumed mode method often led to ill-conditioning due to the presence of hyperbolic functions. Furthermore, a change in the boundary conditions of the system usually necessitates a change in the choice of assumed mode. In this thesis, a set of Alternative Admissible Functions (AAF), along with penalty functions, are used to obtain closed form solutions for an Euler-Bernoulli beam with various boundary conditions. A key advantage of the proposed approach is that the choice of AAF does not depend on the boundary conditions since the boundary conditions are modelled via penalty functions. The mathematical formulation is validated with different boundary conditions, Clamped-Free (CF), Simply-Supported (SS), and Clamped-Clamped (CC). A specific relation between the penalty function and the system parameters are established for CF, SS and CC boundary conditions to obtain appropriate values of penalties. Validation of results with the reported literature indicates excellent agreement when compared with closed-form Euler-Bernoulli beam values. The AAF approach with penalties is extended to a beam with a shallow crack to estimate the dynamic characteristics. The crack is modelled as a penalty function via a massless rotational spring. This model has the advantage of simplifying parametric studies, because of its discrete nature, allowing easy modification in the crack position and depth of the crack. Therefore, once the model is established, various practical applications may be performed without reformulation of the problem. Validation of results with the reported literature on beams with shallow cracks indicates the suitability of the proposed approach.

京都大学 / 0048 / 新制・論文博士 / 博士(農学) / 乙第13021号 / 論農博第2831号 / 新制||農||1042(附属図書館) / 学位論文||H28||N4967(農学部図書室) / 32949 / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 藤原 正幸, 教授 村上 章, 准教授 宇波 耕一 / 学位規則第4条第2項該当 / Doctor of Agricultural Science / Kyoto University / DFAM