Made available in DSpace on 2014-06-11T19:23:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-09-08Bitstream added on 2014-06-13T19:09:39Z : No. of bitstreams: 1 lacerda_jf_me_ilha.pdf: 4631781 bytes, checksum: cad33ad7c5cac9de6cec08fd94b419e7 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Nesse trabalho resolve-se numericamente o escoamento em difusores radiais, os quais têm sido utilizados como modelo para o estudo do escoamento em válvulas automáticas de compressores de refrigeração. As equações governantes do escoamento, escritas no sistema de coordenadas cilíndricas, são resolvidas utilizando um código numérico baseado no Método dos Volumes Finitos. O Método da Fronteira Imersa, em conjunto com o Modelo Físico Virtual, foi implementado no código numérico e utilizado para representar a região sólida imersa no escoamento. Inicialmente, o código numérico foi utilizado para resolver o problema do escoamento em torno de um cilindro de base quadrada, como parte do processo de validação do código. O confronto dos resultados numéricos com dados da literatura indicou a validação parcial do código. Posteriormente, realizou-se um estudo preliminar do comportamento da solução do escoamento no difusor radial em relação a diversos parâmetros geométricos e de simulação numérica, com o objetivo de identificar a configuração numérica capaz de fornecer, simultaneamente, resultados satisfatórios com o menor custo computacional. Usando esta configuração, o código numérico foi validado através da comparação dos resultados da distribuição de pressão sobre o disco frontal (palheta) do difusor com dados experimentais da literatura, para duas distâncias entre disco frontal e disco inferior (assento), s=0,02 e 0,025 cm, e números de Reynolds variando entre 1500 e 2500. As comparações entre esses resultados mostraram que a metodologia utilizada é adequada para estudar o problema. Finalmente, a geometria do disco inferior foi modificada através da inserção de um chanfro com três ângulos de inclinação (30, 45 e 60º), com o objetivo de avaliar sua influência sobre o comportamento da distribuição de pressão sobre o disco frontal... / In this work the flow in radial diffusers, which have been used as a model to study the flow in refrigeration compressors valves, is solved numerically. The governing equations, written in cylindrical coordinates, are solved using a numerical code based on the Finite Volume Method. The Immersed Boundary Method, with the Virtual Physical Method, was implemented in the numerical code and used to represent the solid region immersed in the flow. Initially, the numerical code was used to solve the flow around a square base cylinder, as part of the code validation. The comparison of the numerical results with literature data indicated the partial validation of the code. Afterwards it was performed a preliminary study of the behavior of the flow solution in the radial diffuser relating to several geometrical and numerical parameters, with the objective of identifying a configuration capable of providing, simultaneously, satisfactory results with the smaller computational cost. Using this configuration, the numerical code was validated through the comparison with experimental pressure distribution on the frontal disk (reed) for two gaps between the frontal disk and inferior disk (seat), s=0.020 and 0.025 cm, and Reynolds numbers varying between 1500 and 2500. These comparisons have shown that the implemented methodology is suitable to study this problem. Finally, the inferior disk geometry was modified by inserting a chamfer with three inclination angles (30, 45 e 60º), with the objective of evaluating its influence on the pressure distribution on the frontal disk. The decreasing of the total pressure gradient through the flow for increasing inclination angles indicates less amount of energy to drive the flow. This is an important result that can be used to design refrigeration compressors with lower compression power

Orientador: José Luiz Gasche / Banca: Sérgio Said Mansur / Banca: Aristeu da Silveira Neto / Resumo: Nesse trabalho resolve-se numericamente o escoamento em difusores radiais, os quais têm sido utilizados como modelo para o estudo do escoamento em válvulas automáticas de compressores de refrigeração. As equações governantes do escoamento, escritas no sistema de coordenadas cilíndricas, são resolvidas utilizando um código numérico baseado no Método dos Volumes Finitos. O Método da Fronteira Imersa, em conjunto com o Modelo Físico Virtual, foi implementado no código numérico e utilizado para representar a região sólida imersa no escoamento. Inicialmente, o código numérico foi utilizado para resolver o problema do escoamento em torno de um cilindro de base quadrada, como parte do processo de validação do código. O confronto dos resultados numéricos com dados da literatura indicou a validação parcial do código. Posteriormente, realizou-se um estudo preliminar do comportamento da solução do escoamento no difusor radial em relação a diversos parâmetros geométricos e de simulação numérica, com o objetivo de identificar a configuração numérica capaz de fornecer, simultaneamente, resultados satisfatórios com o menor custo computacional. Usando esta configuração, o código numérico foi validado através da comparação dos resultados da distribuição de pressão sobre o disco frontal (palheta) do difusor com dados experimentais da literatura, para duas distâncias entre disco frontal e disco inferior (assento), s=0,02 e 0,025 cm, e números de Reynolds variando entre 1500 e 2500. As comparações entre esses resultados mostraram que a metodologia utilizada é adequada para estudar o problema. Finalmente, a geometria do disco inferior foi modificada através da inserção de um chanfro com três ângulos de inclinação (30, 45 e 60º), com o objetivo de avaliar sua influência sobre o comportamento da distribuição de pressão sobre o disco frontal... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In this work the flow in radial diffusers, which have been used as a model to study the flow in refrigeration compressors valves, is solved numerically. The governing equations, written in cylindrical coordinates, are solved using a numerical code based on the Finite Volume Method. The Immersed Boundary Method, with the Virtual Physical Method, was implemented in the numerical code and used to represent the solid region immersed in the flow. Initially, the numerical code was used to solve the flow around a square base cylinder, as part of the code validation. The comparison of the numerical results with literature data indicated the partial validation of the code. Afterwards it was performed a preliminary study of the behavior of the flow solution in the radial diffuser relating to several geometrical and numerical parameters, with the objective of identifying a configuration capable of providing, simultaneously, satisfactory results with the smaller computational cost. Using this configuration, the numerical code was validated through the comparison with experimental pressure distribution on the frontal disk (reed) for two gaps between the frontal disk and inferior disk (seat), s=0.020 and 0.025 cm, and Reynolds numbers varying between 1500 and 2500. These comparisons have shown that the implemented methodology is suitable to study this problem. Finally, the inferior disk geometry was modified by inserting a chamfer with three inclination angles (30, 45 e 60º), with the objective of evaluating its influence on the pressure distribution on the frontal disk. The decreasing of the total pressure gradient through the flow for increasing inclination angles indicates less amount of energy to drive the flow. This is an important result that can be used to design refrigeration compressors with lower compression power / Mestre

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho apresenta um estudo teórico e numérico sobre os erros que ocorrem nos cálculos de gradientes em malhas não estruturadas constituídas pelo diagrama de Voronoi, malhas estas, formadas também pela triangulação de Delaunay. As malhas adotadas, no trabalho, foram as malhas cartesianas e as malhas triangulares, esta última é gerada pela divisão de um quadrado em dois ou quatro triângulos iguais. Para tal análise, adotamos a escolha de três metodologias distintas para o cálculo dos gradientes: método de Green Gauss, método do Mínimo Resíduo Quadrático e método da Média do Gradiente Projetado Corrigido. O texto se baseia em dois enfoques principais: mostrar que as equações de erros dadas pelos gradientes podem ser semelhantes, porém com sinais opostos, para pontos de cálculos em volumes vizinhos e que a ordem do erro das equações analíticas pode ser melhorada em malhas uniformes quando comparada as não uniformes, nos casos unidimensionais, e quando analisada na face de tais volumes vizinhos nos casos bidimensionais. / This work presents a theoretical and numerical study on the errors that occur in the calculation of gradients on unstructured meshes Voronoi type, these meshes, also formed by Delaunay triangulation. The meshes adopted in the work were cartesian and triangular meshes, the latter is formed by dividing a square in two or four equal triangles. For this analysis, we adopt the choice of three different methodologies for the calculation of gradients: Green Gauss method, weighted least-squares method and mean value of the projected gradients method. The text is based on two main approaches: to show that the equations of errors given by the gradients may be similar, but with opposite signs, for calculation point in opposite volumes. And show that the order of the error of the analytical equations can be improved in uniform mesh when compared to not uniform, the one-dimensional case, and when viewed from the opposite face of such volumes for the two-dimensional case.

L’objet de cette thèse est l’étude de la séparation membranaire de l’air appliquée à la réduction desémissions d’oxyde d’azote (NOx) des moteurs Diesel. Il a en effet été démontré précédemment quel’utilisation d’air dopé en azote pour la combustion Diesel entrainait une diminution des émissions deNOx. Les travaux présentés ici ont consisté à produire des outils de modélisation d’un module deséparation membranaire des gaz de type fibres creuses et à valider expérimentalement ces outils.Deux approches de modélisation ont été retenues, une approche génie chimique a conduit à unmodèle monodimensionnel applicable en régime stationnaire ; une approche dynamique des fluidesa permis de développer un modèle bidimensionnel valable en régime transitoire. Le premier modèlea été utilisé pour le dimensionnement de modules, le second pour simuler les performances deséparation de ces modules. Par ailleurs, l’influence du taux de dopage en azote de l’air sur la quantitéde NOx émis a été numériquement étudiée à l’aide d’un outil commercial. Enfin, la possibilitéd’implanter un tel module sur un moteur Diesel de série et les paramètres limitants ont été étudiés àl’aide d’un code commercial et d’un modèle développé par Renault. / The purpose of this work is the study of the air membrane separation applied to the reduction ofnitrogen oxides (NOx) emissions of Diesel engines. As a matter of fact, previous works proved thatusing nitrogen-doped air in Diesel combustion led to lower NOx emissions. The study presentedherein consisted in developing a set of modeling tools simulating a gas separation hollow fibersmembrane module and in experimentally validating these tools. A chemical engineering approachresulted in a monodimensional model suitable for stationary regime; a flow dynamic approach led toa bidimensional model dedicated to transitory regime. The first model was used to design modulessize, the second one to simulate separation performances of these modules. Beside, the impact ofnitrogen doping on NOx emissions was numerically studied with a commercial software. Finally, thefeasibility of the introduction of such a module in a mass-produced Diesel engine was investigatedwith a model developed at Renault on a commercial software.

The consumption of energy is a main factor that determines the viability of any industrial process. Thermal dehydration is responsible for a high consumption of energy. In developed countries, 9 to 25% of the energy consumption of the national industry is attached to thermal dehydration. Thus, studying the dehydration process shows itself very promisor. In biological products, dehydration has a specific importance, the product conservation. The organic matter of the product and its water create a propitious medium for microorganisms proliferation that will deteriorate the product, making the product inappropriate for consumption. In this work, the modeling and simulation of a convective dehydration process using a diffusive-convective differential model solved by the finite volumes numeric method for predicting the behavior of the mean moisture content during the dehydration, defining molecular mass transfer and convective coefficients, and drawing moisture profiles of the interior of the solid. To evaluate the influence of internal and external resistances, the mass transfer Biot number was obtained. The implementation of the models of this work were made in Python using its scientific models for solving differential equations. This tool has been utilized because it is open source, has simple implementation when compared to other programming languages and has performance when performing simulations. As study of cases, experimental data of assisted convective dehydration by ultrasound of apple (Malus domestica L. var Royal Gala) cubes with 8 mm under the following operation conditions: 1, 2, 3 and 5 m/s for dehydration velocities, air flow temperature of 45ÂC and 60ÂC, presence and absence of ultrasound during the dehydration process and presence and absence of the pre-treatment with ultrasounds. The apple cubes of the experiments have 25 Â1g of mass. The dehydration has been performed until the removal of 80% of the initial mass of the cubes. The parameters, diffusivity and mass transfer coefficient, have been adjusted by Levenberg-Marquardt non-linear regression method. The results obtained in the simulations showed that the implemented model is very promisor, because it represents accurately the process. The values for diffusivity and mass transfer coefficient herein obtained were plausible. The influence of the air flow velocity, temperature and ultrasounds assistance and ultrasounds pre-treatments have been analyzed. / O consumo de energia à um fator determinante na viabilidade de qualquer processo industrial. A desidrataÃÃo tÃrmica à responsÃvel por um alto consumo de energia tÃrmica. Em paÃses desenvolvidos, o consumo da energia da indÃstria nacional à atribuÃdo, em mÃdia, entre 9-25% a desidrataÃÃo tÃrmica. Assim, o estudo do processo de secagem se mostra bastante promissor. Em produtos biolÃgicos, a secagem tem uma importÃncia especÃfica, a conservaÃÃo do produto, pois a matÃria orgÃnica do produto e a Ãgua presente nele torna este um local propÃcio para a proliferaÃÃo de micro-organismos que irÃo deteriorar o produto, tornando-o inapropriado para consumo. Neste trabalho, realizou-se a modelagem e simulaÃÃo do processo de secagem convectiva utilizando modelo diferencial difusivo-convectivo resolvido pelo mÃtodo numÃrico dos volumes finitos para predizer o comportamento do conteÃdo de umidade mÃdio durante a secagem de cubos, definir os coeficientes de transferÃncia de massa molecular e convectivo e encontrar os perfis do conteÃdo de umidade no interior do sÃlido. Para avaliar a influÃncia das resistÃncias interna e externa, o nÃmero de Biot de Massa foi obtido. A implementaÃÃo dos modelos deste trabalho foi realizada na ferramenta livre Python utilizando seus mÃdulos cientÃficos de resoluÃÃo de equaÃÃes diferenciais. Esta ferramenta foi utilizada porque à livre, implementaÃÃo simples, quando comparada com outras linguagens e possui alta performance nas simulaÃÃes. Como estudos de caso, utilizaram-se dados experimentais da secagem convectiva assistida por ultrassom de cubos de maÃà (Malus domestica L. var Royal Gala) com 8 mm de aresta nas seguintes condiÃÃes operacionais: velocidades de secagem: 1, 2, 3 e 5 m/s; temperatura do ar de secagem: 45 ÂC e 60 ÂC; presenÃa e ausÃncia de ultrassom durante a secagem; presenÃa e ausÃncia de etapa de prÃ-tratamento com ultrassom. Os cubos de maÃà dos experimentos tinham, em mÃdia, 25Â1 g. A secagem foi realizada atà que as amostras perdessem 80% da massa inicial. Os parÃmetros, difusividade e coeficiente de transferÃncia de massa, foram ajustados por regressÃo nÃo linear pelo mÃtodo de Levenberg-Marquardt. Os resultados obtidos nas simulaÃÃes mostraram que o modelo implementado à promissor, pois representa bem o processo. Os valores obtidos da difusividade e coeficiente de transferÃncia de massa foram plausÃveis. Analisou-se a influÃncia da velocidade do ar de secagem, da temperatura, da assistÃncia do ultrassom no processo e da utilizaÃÃo de uma etapa de prÃ-tratamento com ultrassom no processo de secagem.

Orientador: Milton Mori, Marcos A. d'Avila / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-06T05:47:36Z (GMT). No. of bitstreams: 1 Santos_CelsoMurilodos_M.pdf: 3396606 bytes, checksum: 6f04eb0860468401aa6369dba2b5c839 (MD5) Previous issue date: 2005 / Resumo: Colunas de bolhas são equipamentos de simples operação, mas que apresentam uma fluidodinâmica complexa. Seu funcionamento básico é dado pela injeção de um gás (fase dispersa) na base da coluna em um meio líquido (fase contínua). Elas são empregadas nas mais diversas áreas industriais, como processos de química fina, reações de oxidação, reações de alquilação, síntese de Fischer-Tropsch, tratamento de efluentes, reações de fermentação e produção de proteínas, e mais recentemente, em cultura de células. Neste trabalho foram realizadas simulações tridimensionais do escoamento transiente em coluna de bolhas utilizando o pacote computacional de CFD CFX® 5.7 (ANSYS®). Este pacote utiliza o método dos volumes finitos para solucionar as equações governantes de transporte em escoamento multifásico, utilizando a abordagem Euleriana-Euleriana, que mostrou-se adequada para este estudo. Os estudos de casos foram feitos para verificar a influência das propriedades da fase contínua (viscosidade e tensão superficial), da fase dispersa (diâmetro das bolhas) e dos modelos de arraste ... Observação: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital / Abstract: Bubble columns are equipments of simple operation, but presents a complex fluidodynamic. Its basic operation consists of the injection of a gas (disperses phase) in the bottom of the column in a liquid medium (continuous phase). As reactors, they are used in a variety of chemical processes, such as Fischer-Tropsch synthesis, oxidation reactions, alkylation reactions, effluent treatment, fermentation, reactions, protein production, and more recently, in cell cultures. In this work, three-dimensional simulations of the transient flow in bubble columns was performed using the computational package CFD CFX® 5.7 (ANSYS®). This package uses the finite volumes method to solve the governing equations of transport in multiphase flow using the Eulerian-Eulerian approach, which showed to be adequate for this study. The case studies were carried out in order to verify the influence of the properties of the continuous phase (viscosity and superficial tension), the dispersed phase (diameter of the bubbles) and the drag models ... Note: The complete abstract is available with the full electronic digital thesis or dissertations / Mestrado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química

Dans les installations nucléaires, les explosions, qu’elles soient d’origine interne ou externe, peuvent entrainer la rupture du confinement et le rejet de matières radioactives dans l’environnement. Il est donc fondamental, dans un cadre de sûreté de modéliser ce phénomène. L’objectif de cette thèse est de contribuer à l’élaboration de schémas numériques performants pour résoudre ces modèles complexes. Les travaux présentés s’articule autour de deux axes majeurs : le développement de schémas volumes finis consistants pour les équations d’Euler compressible qui modélise les ondes de choc et celui de schémas performants pour la propagation d’interfaces comme le front de flamme lors d'une déflagration. La discrétisation spatiale est de type mailles décalées pour tous les schémas développés. Les schémas pour les équations d'Euler se basent sur une formulation en énergie interne qui permet de préserver sa positivité ainsi que celle de la masse volumique. Un bilan d'énergie cinétique discret peut être obtenu et permet de retrouver un bilan d'énergie totale par l'ajout d'un terme de correction dans le bilan d'énergie interne. Le schéma ainsi construit est consistant au sens de Lax avec les solutions faibles entropiques des équations continues. On utilise les propriétés des équations de type Hamilton-Jacobi pour construire une classe de schémas volumes finis performants sur une large variété de maillages modélisant la propagation du front de flamme. Ces schémas garantissent un principe du maximum et possèdent des propriétés importantes de monotonie et consistance qui permettent d'obtenir un résultat de convergence. / In nuclear facilities, internal or external explosions can cause confinement breaches and radioactive materials release in the environment. Hence, modeling such phenomena is crucial for safety matters. The purpose of this thesis is to contribute to the creation of efficient numerical schemes to solve these complex models. The work presented here focuses on two major aspects: first, the development of consistent schemes for the Euler equations which model the blast waves, then the buildup of reliable schemes for the front propagation, like the flame front during the deflagration phenomenon. Staggered discretization is used in space for all the schemes. It is based on the internal energy formulation of the Euler system, which insures its positivity and the positivity of the density. A discrete kinetic energy balance is derived from the scheme and a source term is added in the discrete internal energy balance equation to preserve the exact total energy balance. High order, MUSCL-like interpolators are used in the discrete momentum operators. The resulting scheme is consistent (in the sense of Lax) with the weak entropic solutions of the continuous problem. We use the properties of Hamilton-Jacobi equations to build a class of finite volume schemes compatible with a large number of meshes to model the flame front propagation. These schemes satisfy a maximum principle and have important consistency and monotonicity properties. These latters allows to derive a convergence result for the schemes based on Cartesian grids.

On s'intéresse dans ce document à la modélisation d'écoulements compressibles en conduite unidimensionnelle (1D) à section variable et dans des domaines bi ou tridimensionnelles encombrés d'obstacles. Le travail est motivé par la modélisation d'écoulements dans les circuits de refroidissement de réacteurs à eau pressurisée (REP). Ainsi ce travail a pour objectif de proposer une nouvelle formulation pour de tels écoulements. L'idée de base consiste a utiliser une formulation intégrale sur la base des équations aux dérivées partielles. Le système de lois de conservation associé aux équations d'Euler (masse, dynamique et énergie) est examiné.Le premier chapitre examine le cas de conduite 1D à section continue ou discontinue. La formulation intégrale est présentée et les résultats numériques sont comparés avec (i) l'approche Well-Balanced et (ii) la solution de référence obtenue sur maillage très fin.Les second et troisième chapitres examinent la modélisation d'écoulements compressibles dans des domaines contenant de nombreux tubes. La formulation intégrale est donnée, et les schémas numériques présentés, afin de gérer les interfaces fluide/fluide et les parois. Les schémas peuvent être explicites (chapitre 2), ou implicites (chapitre 3). Quelques cas tests analytiques sont présentés. On se concentre sur l'écoulement d'un fluide abordant une zone de tubes alignés de petite taille. Ici encore, la comparaison est faite avec la référence fluide; les résultats sont également comparés avec ceux issus de l'approche équilibre classique, et ceux associés à la formulation intégrale unidimensionnelle présentée dans le premier chapitre. / This document focuses on the modeling of compressible flows in one-dimensional (1D) pipes with variable cross-section, and in two or three-dimensional domains containing many small obstacles. The basic motivation is urged by the modeling of flows in the coolant circuit of pressurised water reactors (PWR). Thus this work aims at providing a new formulation for such a variety of flows. The basic idea consists in using an integral approach that is applied to the governing set of partial differential equations. Here the keystone is the conservative Euler set of equations, including mass, momentum and energy balance for any equation of state.Hence, the first chapter investigates the case of one-dimensional pipes with continuous or discontinuous cross-section. Once the 1D+ integral formulation has been presented, numerical results are compared with : (i) the classical Well-Balanced (WB) approach, and (ii) the reference solution obtained with a multi-dimensional code with huge mesh refinement.The second and third chapters provide some new insight on the numerical modeling of compressible flows in domains obstructed with many tubes. The integral formulation is derived, and numerical schemes are detailed, in order to handle fluid/fluid interfaces and wall boundaries. Schemes may be explicit (chapter 2), or implicit (chapter 3). A few analytic test cases are investigated. Focus is made on the flow incoming a region containing many tiny and aligned tubes. Here again, a comparison with the reference "fluid" solution is achieved; results are also compared with those arising from the WB approach, and with those coming from the 1D+ integral approach proposed in the first chapter.

Cette thèse a pour objectif la construction de schémas d’ordre élevé et peu diffusifs pour le transport d’un scalaire dans les écoulements à surface libre, en deux ou trois dimensions. On souhaite en particulier obtenir des schémas robustes, qui gardent au niveau discret les propriétés mathématiques de l’équation de transport avec une faible diffusion numérique, et les utiliser sur des cas industriels. Dans ce travail deux méthodes numériques sont envisagées : une méthode aux volumes finis (VF) et une méthode aux résidus distribués (RD). Dans les deux cas, l’équation de transport est résolue avec une approche découplée, qui est la solution la plus avantageuse en termes de précision et de coûts de calcul. Pour ce qui concerne la méthode aux volumes finis, les équations de Saint-Venant couplées à l’équation du transport sont d’abord résolues avec un schéma dit vertex-centred où le flux numérique est approximé avec un solveur de Riemann appelé Harten-Lax-Van Leer-Contact [135]. A partir de cette approche, une formulation découplée est proposée. Cette dernière permet de résoudre l’équation du transport avec un pas de temps plus grand que celui de la formulation couplée. Cette idée a été d’abord proposée pour d’autres schémas dans [13]. Pour augmenter l’ordre de précision en espace, la technique MUSCL [89] est utilisée en combinaison avec l’approche découplée. Finalement, la problématique des zones sèches est abordée. Dans le cas de la méthode aux résidus distribués, les équations de Saint-Venant sont résolues avec une méthode éléments finis, et la méthode RD est utilisée seulement pour discrétiser l’équation du transport, en focalisant l’attention sur les problèmes non stationnaires. L’équation de continuité du fluide discrétisée est employée pour garantir la conservation de la masse et le principe du maximum. Pour obtenir des schémas d’ordre deux dans les problèmes non stationnaires, un schéma prédicteur-correcteur [112] est utilisé, en l’adaptant au cas de concentration moyennée sur la verticale. Une version d’ordre 1 mais peu diffusive, est aussi présentée dans ce travail. De plus, un schéma localement implicite, complètement nouveau, est aussi formulé pour pouvoir traiter le problème des bancs découvrant. Les deux techniques sont validées d’abord sur des cas simples, pour évaluer l’ordre de précision des schémas et ensuite sur des cas plus complexes pour vérifier aussi les autres propriétés numériques. Les résultats montrent que les nouveaux schémas sont à la fois précis et conservatifs, tout en gardant la monotonie comme le prévoient les démonstrations. Un cas d’application industriel est aussi présenté en conclusion. Le schéma prédicteur-correcteur RD est adapté aussi au cas 3D, sans aucun problème théorique nouveau, par rapport au cas 2D. Les propriétés de base des schémas sont validées sur des cas test préliminaires / The purpose of this thesis is to build higher order and less diffusive schemes for pollutant transport in shallow water flows or 3D free surface flows. We want robust schemes which respect the main mathematical properties of the advection equation with relatively low numerical diffusion and apply them to environmental industrial applications. Two techniques are tested in this work: a classical finite volume method and a residual distribution technique combined with a finite element method. For both methods we propose a decoupled approach since it is the most advantageous in terms of accuracy and CPU time. Concerning the first technique, a vertex-centred finite volume method is used to solve the augmented shallow water system where the numerical flux is computed through an Harten-Lax-Van Leer-Contact Riemannsolver [135]. Starting from this solution, a decoupled approach is formulated and is preferred since it allows to compute with a larger time step the advection of a tracer. This idea was inspired by [13]. The Monotonic Upwind Scheme for Conservation Law [89], combined with the decoupled approach, is then used for the second order extension in space. The wetting and drying problem is also analysed and a possible solution is presented. In the second case, the shallow water system is entirely solved using the finite element technique and the residual distribution method is applied to the solution of the tracer equation, focusing on the case of time-dependent problems. However, for consistency reasons the resolution of the continuity equation must be considered in the numerical discretization of the tracer. In order to get second order schemes for unsteady cases a predictor-corrector scheme [112] is used in this work. A first order but less diffusive version of the predictor-corrector scheme is also introduced. Moreover, we also present a new locally semi-implicit version of the residual distribution method which, in addition to good properties in terms of accuracy and stability, has the advantage to cope with dry zones. The two methods are first validated on academical test cases with analytical solution in order to assess the order of the schemes. Then more complex cases are addressed to test the robustness of the schemes and their performance under different flow conditions. Finally a real test case for which real data are available is carried out. An extension of the predictor-corrector residual distribution schemes to the 3D case is presented as final contribution. Even in this case the RD technique is completely compatible with the finite element framework used for the Navier-Stokes equations, thus its extension to the 3D case does not present any extra theoretical problem. The method is tested on preliminary cases

Dans le cadre du stockage de Gaz Naturel Liquéfié (GNL) dans des réservoirs flottants, tels que les méthaniers, les contraintes imposées à la cuve par le ballotement de la cargaison doivent être quantifiées. La plupart des études expérimentales ou numériques actuelles ne prennent pas en compte la possibilité de changement de phase entre le GNL et sa vapeur lors d'un impact du liquide sur la paroi. L'objectif de cette thèse est l'ajout de ce phénomène physique dans un code de mécanique des fluides numérique pour la simulation de l'impact d'une vague déferlante sur une paroi.Dans ce but, un état de l'art des différentes modélisations possibles du changement de phase en mécanique des fluides est présenté. Il a été choisi de modéliser le changement de phase entre le liquide et le gaz à une interface franche sans hypothèse d'équilibre thermodynamique à l'interface. Un système hyperbolique de lois de conservation incluant le changement de phase interfacial hors-équilibre est présenté.Deux approches sont utilisées pour la résolution numérique de ce système. La première utilise un modèle de mélange pour décrire les mailles contenant l'interface liquide-vapeur. Dans la seconde méthode, l'interface est reconstruite et évolue de manière lagrangienne. Les deux approches sont basées sur un schéma volume fini de type Roe.L'enjeu de la simulation numérique du changement de phase interfacial est la capacité du code à gérer un rapport de densité loin de 1 et une chaleur latente élevée, qui entrainent respectivement de fortes variations de pression et de température à l'interface. L'aspect thermique est le phénomène limitant dans le cadre de la simulation d'impacts de vagues avec changement de phase. Seule une fine couche limite thermique autour de l'interface tend à revenir à l'équilibre thermodynamique liquide vapeur, ce qui limite l'effet quantitatif du changement de phase. / In the context of Liquefied Natural Gas (LNG) transportation in floating tanks, such as in LNG carriers, the constraints imposed by the sloshing of the liquid cargo on the tank have to be estimated. Most experimental and numerical studies until now do not take into account the possibility of phase change between the LNG and its vapor during the impact of liquid on the wall. The goal of this thesis is to include this physical phenomenon into a CFD code for the simulation of a breaking wave impact on a wall.A state of the art of the different modelisations of phase change in fluid mechanics is thus presented. This work focus on the modeling of phase change between the liquid and the gas at a sharp interface, without any equilibrium hypothesis. An hyperbolic system of balance laws including non-equilibrium interfacial phase change is presented.Two approaches are used to solve numerically this system. The first one relies on a mixture model for the description of the finite volume cells containing the interface, whereas in the second approach the interface is reconstructed and evolves in a lagrangian way. Both methods are based on a Roe-type finite volume scheme.The challenge of the numerical simulation of interfacial phase change is the capacity of the code to deal with density ratio far from 1 and high latent heat, as the lead to high temperature and pressure variations at the interface. The thermal aspect is the limiting phenomenon in the frame of wave impact simulation with phase change. Only a thin boundary layer around the interface tends to return to thermodynamical equilibrium, thus limiting the quantitative effect of phase change.