Les moteurs diesel sont largement utilisés pour la propulsion automobile, grâce à leur rendement élevé. Les émissions polluantes les plus importantes des moteurs diesel sont les NOx et les particules (en combustion Dieselconventionnelle). Il est difficile de réduire et contrôler ces émissions parce que la diminution d’un polluant entraine l’augmentation de l’autre. Une voie est la combustion Diesel LTC (Combustion à basse température) qui peut réduireces deux polluants, mais d’autres polluants apparaissent alors, comme CO et HC. Une façon d’arriver à desconditions LTC est l’utilisation de l’injection multiple (pilote/main, split injection, etc.). La caractérisation de cesinjections multiples est particulièrement complexe, en raison des interactions entre les différentes injections.Cette thèse a pour but de réaliser un modèle 1D de spray qui peut simuler l’injection multiple et la combustioncorrespondante dans un moteur diesel de type automobile, suite à la thèse de G. Ma soutenue au LHEEA en 2013,qui a développé un modèle de combustion basé sur le modèle de spray 1D eulérien de Musculus et Kattke (sprayinerte). Une comparaison de ce modèle avec un modèle lagrangien (Hiroyasu, Poetsch), qui a un traitement pseudo2D pour le spray de carburant, est menée pour évaluer les différences entre les approches et déterminer l’approche lamieux adaptée aux cas envisagés.L’interaction du spray avec une paroi, essentielle pour modéliser les conditions dans un moteur automobile faitégalement l’objet d’une étude bibliographique et de premières tentatives de modélisation. Une modélisation pseudo-2D pour le modèle Eulérien est faite pour améliorer le calcul du dégagement de chaleur et de délai d’inflammation. Lavalidation de ces différentes évolutions est faite en confrontant les résultats du modèle avec des résultatsexpérimentaux obtenus sur la base de données de l’ECN (Engine Combustion Network), mais aussi avec des relevéseffectués par des autres auteurs. Des développements spécifiques sont également introduits pour traiter le casd’injection multiple et l’injection dans une chambre de combustion à géométrie variable (le système piston-cylindre). / Diesel engines are largely used in automotive propulsion due to their elevated efficiency. The most important pollutant emissions of diesel engines are NOx and particulate matter (in the case of conventional Diesel combustion). It is difficult to reduce and control these emissions because reducing one pollutant emission increases the other one. One way to try to achieve reduction in both pollutant emissions is called LTC (Low Temperature Combustion), which can reduce these two pollutants, but other pollutant emissions appear, as CO and HC. One way to achieve LTC conditions is using multiple injections (pilot/main, split injection, etc.). Modeling these injections is particularly complex, mainly due to their interactions.The objective of this thesis is to make a 1D spray model that can simulate multiple injections and the correspondingcombustion in an automobile diesel engine, continuing the work of G. Ma in his thesis defended at LHEEA in 2013,which developed a combustion model based in the 1D Eulerian spray of Musculus and Kattke (inert spray). Acomparison is made of this model and a Lagrangian model (Hiroyasu, Poetsch), which has a pseudo-2D treatment ofthe fuel spray, to evaluate the differences between the approaches and determine the best one suited for the foreseencases.The spray-wall interaction, essential to model the conditions inside an automotive engine, is subject to a bibliographyreview and coarse modeling. A pseudo-2D modeling for the Eulerian model is made, to improve the heat release rateand ignition delay calculation. The validation of these different evolutions is made by comparing the model results withexperimental results obtained from the ECN (Engine Combustion Network) data base, and also with data obtainedfrom the TSM test engines. Specific developments are also introduced to treat the multiple injection case and injectionin a variable geometry combustion chamber (the piston-cylinder system).

Ce travail porte sur le couplage des déformations d'une bulle avec son sillage et sa trajectoire dans plusieurs configurations. Un formalisme de type eulérien-lagrangien permet d'écrire le problème sur un domaine mouvant faiblement déformé par rapport à la configuration de référence. Grâce à cette approche, il est possible d'étudier dans un cadre linéaire le couplage entre les déformations d'une bulle et les effets hydrodynamiques. En appliquant ce formalisme, on peut dans un premier temps calculer l'écoulement de base autour de la bulle et sa géométrie d'équilibre, et dans un second temps développer une approche de stabilité globale prédisant les seuils d'instabilité et les propriétés des modes d'oscillation. Afin de développer cette méthode, des résultats sur les oscillations linéaires de bulles et de gouttes dans un fluide au repos et sans influence de la gravité sont tout d'abord présentés et comparés à des résultats théoriques existants. Puis, le principe du formalisme eulérien-lagrangien est illustré en prenant pour problème modèle l'équation de la chaleur formulée sur un domaine arbitrairement déformé. Ce principe est ensuite appliqué aux équations de Navier-Stokes, aboutissant à une version linéarisée autour d'un domaine de référence incluant de manière complète les couplages entre déformations de la géométrie et perturbations de l'écoulement. On met en oeuvre sur le système obtenu une méthode itérative de Newton donnant accès à l'état de base, c'est-à-dire à l'écoulement stationnaire autour de la bulle et à sa forme d'équilibre. Ce même système permet par la suite d'effectuer une analyse de stabilité globale de l'écoulement autour d'une bulle qui se déforme. L'algorithme développé est d'abord appliqué au cas d'une bulle piégée dans un écoulement d'étirement, permettant de décrire des formes d'équilibre dans des régimes stables et instables. Le cas de la bulle en ascension dans un fluide pur est ensuite abordé. Une étude paramétrique est conduite, couvrant une vaste gamme de liquides allant de l'eau pure à des huiles de silicone très visqueuses. Les états de base calculés par la méthode de Newton ainsi que les seuils d'instabilité des sillages sont en bon accord avec les résultats expérimentaux. Dans les cas des liquides très peu visqueux, notre approche décrit de manière plus précise les effets visqueux dans les couches limites et donne des résultats plus satisfaisants que les approches numériques existantes. Elle confirme par ailleurs que la déformation de la bulle joue un rôle mineur dans ces gammes de paramètres. Pour les liquides plus visqueux en revanche, on observe un couplage plus fort entre déformation et sillage. / This works deals with the coupling between time-dependent deformation, wake dynamics and path characteristics of a gas bubble in different configurations. An Eulerian-Lagrangian formalism is sought to formulate this problem in a moving domain having a small deformation compared to the reference configuration. This approach allows us to study the linear coupling between bubble deformations and hydrodynamic effects. This formalism makes it possible to first compute the base flow around a bubble and the corresponding steady shape, then to develop a global stability approach aimed at predicting the threshold of path instability and the properties of bubble oscillation modes. To develop this method, we first compute the linear oscillations of bubbles and drops in a quiescent fluid without gravity and compare them to existing theory. Then, the premise of the Eulerian-Lagrangian formalism is illustrated using a model equation, namely the heat equation written in an arbitrarily deformed domain. The same formalism is applied to the NavierStokes equations, yielding a linearized version of these equations in the neighbourhood of a reference domain, including the two-way coupling between shape deformations and perturbations of the base flow. With this system of equations at hand, we implement a Newton method that provides the steady state, i.e. the base flow around the bubble and its geometry. The same system allows us to carry out a global stability analysis of the flow past a deformable bubble. We first consider the situation where the bubble is trapped in a straining flow, for which we compute stable and unstable equilibrium shapes. We finally tackle the case of a buoyancy-driven bubble rising in a pure liquid. A parametric study is carried out over a wide range of liquids, from pure water to high-viscosity silicon oils. Steady states computed with the Newton method and instability thresholds are found to be in good agreement with experimental observations. For low-viscosity fluids, our approach captures the viscous effects that take place in the boundary layer better than existing computational approaches, yielding predictions for the onset of path instability in better agreemnt with observations. Furthermore, it confirms that time-dependent bubble deformations play a minor part for such liquids. In contrast, a stronger coupling between shape and path instabilities is observed in high-viscosity fluids

This thesis investigates whether a game world based solely on fluid dynamics could be an interesting alternative to one based on rigid bodies by presenting a prototype to players where they can control the movement of a fluid. The players evaluate the prototype’s responsiveness, intuitiveness, visual appeal, immersion, and how well they think the fluid could represent ghosts, flocks, magic, and a platformer avatar by rating them vocally while playing. The fluid physics engine prototype is a simple grid-based one that utilizes the ideal gas law and pressure gradient force to calculate the flow between its cells. It is unstable and thus cannot handle too large time-steps. Therefore, simulating many cells (more than 10000 for two fluids) at the same is a slow process, and the prototype can only present a pixelated result. If a highresolution game is in general preferred by players, a computationally efficient solution could consist of utilizing shaders for cell blending. In the experiments, all categories except the platform avatar received positive evaluations despite the prototype’s early stage, which according to theories presented within Swink’s Game Feel (Swink, 2009) and the MDA framework (Hunicke et al., 2004) may indicate that a game based on a fluid physics engine like this one could be entertaining. The simulation could possibly be run as a separate system to add game mechanics to a game based on rigid bodies as well.

Le contexte général de cette thèse s'inscrit dans le cadre de la modélisation eulérienne instationnaire des écoulements turbulents anisothermes gaz - particules. La modélisation de ces écoulements est cruciale pour de nombreuses applications industrielles et pour la prédiction de certains phénomènes naturels. Par exemple, la combustion diphasique dans les moteurs automobiles et aéronautiques est précédée par l'injection et la dispersion de carburant liquide dans la chambre de combustion. Les phénomènes mis en jeu exigent alors une prédiction locale tenant compte du caractère instationnaire de l'écoulement turbulent et de la présence de géométries complexes. De plus, de nombreuses études expérimentales et numériques récentes ont mis en évidence le rôle prépondérant de l'inertie des particules sur les mécanismes de dispersion et de concentration préférentielle en écoulement turbulent. Ceci rend donc indispensable la prise en compte de ces mécanismes dans la modélisation diphasique. Au cours de ce travail de thèse, une approche eulérienne locale et instantanée a été développée pour prédire les écoulements gaz-particules anisothermes et turbulents. Elle est basée sur l'approche statistique du Formalisme Eulérien Mésoscopique (MEF) introduite par Février et al. (JFM, 2005). Cette approche a été ici étendue aux variables thermiques pour la prise en compte du caractère anisotherme de l'écoulement. Cette approche a été ensuite utilisée dans le cadre de la méthode des moments (Kaufmann et al., JCP, 2008), et un système d'équations locales et instantanées pour la phase dispersée a été proposé. La modélisation au premier ordre exige la fermeture des moments de second ordre apparaissant dans les équations de la quantité de mouvement et de l'énergie. La proposition de telles relations constitutives fait l'objet d'une partie de la thèse. Afin de fournir une méthode capable de prédire le comportement local, instantané et anisotherme de la phase dispersée dans des configurations `a une échelle réaliste, les équations pour la phase dispersée ont été filtrées et une modélisation aux grandes échelles (LES) est effectuée. Cette modélisation étends, par la prise en compte des variables thermiques, le travail de Moreau et al. (FtaC, 2010) sur l'approche LES Euler-Euler en conditions isothermes. L'approche complète est enfin appliquée aux résultats de simulation numérique d'un jet plan turbulent gazeux froid, chargé en particules, dans une turbulence homogène isotrope chaude monophasique. / The aim of this thesis is to provide an Eulerian modeling for the dispersed phase interacting with unsteady non-isothermal turbulent flows. The modeling of these flows is crucial for several industrial applications and for predictions of natural events. Examples are the combustion chambers of areo engines where the combustion is preceded by the injection and dispersion of liquid fuel. The prediction of such phenomena involves a local modeling of the mixture for taking into account the unsteady behavior of the turbulent flow and the presence of complex geometries. Moreover, many experimental and numerical studies have recently highlighted the significant role of the particle inertia on the mechanisms of dispersion and preferential concentration. Accounting for such mechanisms is therefore essential for modeling the particle-laden turbulent flows. In this thesis, a local and instantaneous Eulerian approach able to describe and to predict the local behavior of inertial particles interacting with non-isothermal turbulent flows has been developed. It is based on the statistical approach known as Mesoscopic Eulerian formalism (MEF) introduced by Février et al. (JFM, 2005). The statistical approach has been extended to the thermal quantities in order to account for the non-isothermal conditions into the modeling. This formalism is then used in the framework of the moment approach (Kaufmann et al., JCP, 2008) and a system of local and instantaneous equations for the non-isothermal dispersed phase has been suggested. The first order modeling requires to close second-order moments appearing in momentum and energy equations. The proposal of such constitutive relations makes the object of a part of this study. In order to provide an Eulerian approach usable in real configurations at industrial scale, the equations of the dispersed phase are filtered and the approach developed in the framework of the Large-Eddy Simulations. From the work of Moreau et al. (FTaC, 2010), the Eulerian-Eulerian LES approach is then extended to non-isothermal conditions. The whole modeling is then a priori tested against numerical simulations of a cold planar turbulent particle-laden jet crossing a homogeneous isotropic decaying hot turbulence.

O estudo do transporte de partículas tem uma importância fundamental em diversas áreas de pesquisas como, por exemplo, na formação de gelo em uma aeronave pois pode afetar a sua sustentação e estabilidade. Tamanha é a preocupação com a segurança de vôo que diversos estudos têm sido realizados, resultando em códigos computacionais como o LEWICE nos Estados Unidos, TRAJICE no Reino Unido, ONERA na França e CANICE no Canadá. No Brasil, um dos estudo é feito pela EMBRAER em parceria com algumas instituições. O objetivo deste trabalho é desenvolver um algoritmo que possa ser empregado na trajetória das partículas, utilizando uma formulação euleriana que elimina a dificuldade da semeadura de partículas específica da formulação lagrangiana na determinação da fração de volume da partícula. O método empregado é dos volumes finitos em malhas não-estruturadas cuja principal chave está na reconstrução mínimos quadrados de alta ordem com restrição nos contornos. O desenvolvimento do trabalho engloba 3 etapas: definição da geometria e geração das malhas; utilização de um solver para o tratamento do escoamento do ar e obtenção do campo de velocidade; implementação e utilização do esquema numérico com reconstrução mínimos quadrados de alta ordem para simular o cálculo da fração de volume com imposição de condições limites apropriadas no contorno do corpo. Os resultados dos testes realizados mostram que o esquema numérico com reconstrução mínimos quadrados pode ser empregado na resolução de equações que apresentam uma região de descontinuidade, como é o caso da região de sombra, reduzindo a largura da banda de difusão numérica e overshoots. / The particle transport study has a fundamental importance in diverse research area like in the icing accretion on an aircraft because that can affect its sustentation and stability. The concern is so big that many researches have been carried through, resulting in computational codes like the LEWICE in the United States, TRAJICE in the United Kingdom, ONERA in France and CANICE in Canada. In Brazil, one of the study has been made by the EMBRAER with some institutes. The goal of this work is to develop an algorithm that can be used in the particles trajectory study, using an Eulerian method that eliminates the difficulty particle sowing, particular of the Lagrangian method, in the determination of the droplet fraction volume. This is made by the finite volume method on unstructured meshes whose main key is the high order reconstruction with restriction on the boundary. The development of the work involves 3 stages: geometry definition and mesh generation; using code for the treatment of the air flow and obtained flow velocity; use of the high order numerical scheme least square reconstruction to simulate the droplet fraction volume result with imposition of appropriate limit conditions in the body contour. The realized simulations shown that Least Square method can be used in problem resolution that present descontinuos region like is shadow region reducing numerical diffusion and overshoots.

O estudo do transporte de partículas tem uma importância fundamental em diversas áreas de pesquisas como, por exemplo, na formação de gelo em uma aeronave pois pode afetar a sua sustentação e estabilidade. Tamanha é a preocupação com a segurança de vôo que diversos estudos têm sido realizados, resultando em códigos computacionais como o LEWICE nos Estados Unidos, TRAJICE no Reino Unido, ONERA na França e CANICE no Canadá. No Brasil, um dos estudo é feito pela EMBRAER em parceria com algumas instituições. O objetivo deste trabalho é desenvolver um algoritmo que possa ser empregado na trajetória das partículas, utilizando uma formulação euleriana que elimina a dificuldade da semeadura de partículas específica da formulação lagrangiana na determinação da fração de volume da partícula. O método empregado é dos volumes finitos em malhas não-estruturadas cuja principal chave está na reconstrução mínimos quadrados de alta ordem com restrição nos contornos. O desenvolvimento do trabalho engloba 3 etapas: definição da geometria e geração das malhas; utilização de um solver para o tratamento do escoamento do ar e obtenção do campo de velocidade; implementação e utilização do esquema numérico com reconstrução mínimos quadrados de alta ordem para simular o cálculo da fração de volume com imposição de condições limites apropriadas no contorno do corpo. Os resultados dos testes realizados mostram que o esquema numérico com reconstrução mínimos quadrados pode ser empregado na resolução de equações que apresentam uma região de descontinuidade, como é o caso da região de sombra, reduzindo a largura da banda de difusão numérica e overshoots. / The particle transport study has a fundamental importance in diverse research area like in the icing accretion on an aircraft because that can affect its sustentation and stability. The concern is so big that many researches have been carried through, resulting in computational codes like the LEWICE in the United States, TRAJICE in the United Kingdom, ONERA in France and CANICE in Canada. In Brazil, one of the study has been made by the EMBRAER with some institutes. The goal of this work is to develop an algorithm that can be used in the particles trajectory study, using an Eulerian method that eliminates the difficulty particle sowing, particular of the Lagrangian method, in the determination of the droplet fraction volume. This is made by the finite volume method on unstructured meshes whose main key is the high order reconstruction with restriction on the boundary. The development of the work involves 3 stages: geometry definition and mesh generation; using code for the treatment of the air flow and obtained flow velocity; use of the high order numerical scheme least square reconstruction to simulate the droplet fraction volume result with imposition of appropriate limit conditions in the body contour. The realized simulations shown that Least Square method can be used in problem resolution that present descontinuos region like is shadow region reducing numerical diffusion and overshoots.

Cette thèse s'inscrit dans un projet de modélisation numérique de la dispersion atmosphérique de polluants à travers le code de mécanique des fluides numérique Code_Saturne. L'objectif est de pouvoir simuler la dispersion atmosphérique de polluants en environnement complexe, c'est-à-dire autour de centrales, sites industriels ou en milieu urbain. Dans ce contexte, nous nous concentrons sur la modélisation de la dispersion des polluants à micro-échelle, c'est-à-dire pour des distances de l'ordre de quelques mètres à quelques kilomètres et correspondant à des échelles de temps de l'ordre de quelques dizaines de secondes à quelques dizaines de minutes : on parle de modélisation en champ proche. L’approche suivie dans ces travaux de recherche suit une formulation hybride eulérienne/lagrangienne, où les champs dynamiques moyens relatifs au fluide porteur (pression, vitesse, température, turbulence) sont calculés via une approche eulérienne et sont ensuite fournis au solveur lagrangien. Ce type de formulation est couramment utilisé dans la littérature atmosphérique pour son efficacité numérique. Le modèle lagrangien stochastique considéré dans nos travaux est le Simplified Langevin Model (SLM), développé par Pope (1985,2000). Ce modèle appartient aux méthodes communément appelées méthodes PDF (Probability Density Function), et, à notre connaissance, n'a pas été exploité auparavant dans le contexte de la dispersion atmosphérique. Premièrement, nous montrons que le SLM respecte le critère dit de mélange homogène (Thomson, 1987). Ce critère, essentiel pour juger de la bonne qualité d'un modèle lagrangien stochastique, correspond au fait que si des particules sont initialement uniformément réparties dans un fluide incompressible, alors elles doivent le rester. Nous vérifions le bon respect du critère de mélange homogène pour trois cas de turbulence inhomogène représentatifs d'une large gamme d'applications pratiques : une couche de mélange, un canal plan infini, ainsi qu'un cas de type atmosphérique mettant en jeu un obstacle au sein d'une couche limite neutre. Nous montrons que le bon respect du critère de mélange homogène réside simplement en la bonne introduction du terme de gradient de pression en tant que terme de dérive moyen dans le modèle de Langevin (Pope, 1987; Minier et al., 2014; Bahlali et al., 2018c). Nous discutons parallèlement de l'importance de la consistance entre champs eulériens et lagrangiens dans le cadre de telles formulations hybrides eulériennes/lagrangiennes. Ensuite, nous validons le modèle dans le cas d'un rejet de polluant ponctuel et continu, en conditions de vent uniforme et turbulence homogène. Dans ces conditions, nous disposons en effet d'une solution analytique nous permettant une vérification précise. Nous observons que dans ce cas, le modèle lagrangien discrimine bien les deux différents régimes de diffusion de champ proche et champ lointain, ce qui n'est pas le cas d'un modèle eulérien à viscosité turbulente (Bahlali et al., 2018b).Enfin, nous travaillons sur la validation du modèle sur plusieurs campagnes expérimentales en atmosphère réelle, en tenant compte de la stratification thermique de l'atmosphère et de la présence de bâtiments. Le premier programme expérimental considéré dans nos travaux concerne le site du SIRTA (Site Instrumental de Recherche par Télédétection Atmosphérique), dans la banlieue sud de Paris, et met en jeu une stratification stable de la couche limite atmosphérique. La seconde campagne étudiée est l'expérience MUST (Mock Urban Setting Test). Réalisée aux Etats-Unis, dans le désert de l'Utah, cette expérience a pour but de représenter une ville idéalisée, au travers d'un ensemble de lignées de conteneurs. Deux rejets ont été simulés et analysés, respectivement en conditions d'atmosphère neutre et stable (Bahlali et al., 2018a) / This Ph.D. thesis is part of a project that aims at modeling pollutant atmospheric dispersion with the Computational Fluid Dynamics code Code_Saturne. The objective is to simulate atmospheric dispersion of pollutants in a complex environment, that is to say around power plants, industrial sites or in urban areas. In this context, the focus is on modeling the dispersion at micro-scale, that is for distances of the order of a few meters to a few kilometers and corresponding to time scales of the order of a few tens of seconds to a few tens of minutes: this is also called the near field area. The approach followed in this thesis follows a hybrid Eulerian/Lagrangian formulation, where the mean dynamical fields relative to the carrier fluid (pressure, velocity, temperature, turbulence) are calculated through an Eulerian approach and are then provided to the Lagrangian solver. This type of formulation is commonly used in the atmospheric literature for its numerical efficiency. The Lagrangian stochastic model considered in our work is the Simplified Langevin Model (SLM), developed by Pope (1985,2000). This model belongs to the methods commonly referred to as PDF (Probability Density Function) methods, and, to our knowledge, has not been used before in the context of atmospheric dispersion. First, we show that the SLM meets the so-called well-mixed criterion (Thomson, 1987). This criterion, essential for any Lagrangian stochastic model to be regarded as acceptable, corresponds to the fact that if particles are initially uniformly distributed in an incompressible fluid, then they must remain so. We check the good respect of the well-mixed criterion for three cases of inhomogeneous turbulence representative of a wide range of practical applications: a mixing layer, an infinite plane channel, and an atmospheric-like case involving an obstacle within a neutral boundary layer. We show that the good respect of the well-mixed criterion lies simply in the good introduction of the pressure gradient term as the mean drift term in the Langevin model (Pope, 1987; Minier et al., 2014; Bahlali et al., 2018c). Also, we discuss the importance of consistency between Eulerian and Lagrangian fields in the framework of such Eulerian/Lagrangian hybrid formulations. Then, we validate the model in the case of continuous point source pollutant dispersion, under uniform wind and homogeneous turbulence. In these conditions, there is an analytical solution allowing a precise verification. We observe that in this case, the Lagrangian model discriminates well the two different near- and far-field diffusion regimes, which is not the case for an Eulerian model based on the eddy-viscosity hypothesis (Bahlali et al., 2018b).Finally, we work on the validation of the model on several experimental campaigns in real atmosphere, taking into account atmospheric thermal stratification and the presence of buildings. The first experimental program considered in our work has been conducted on the `SIRTA' site (Site Instrumental de Recherche par Télédétection Atmosphérique), in the southern suburb of Paris, and involves a stably stratified surface layer. The second campaign studied is the MUST (Mock Urban Setting Test) experiment. Conducted in the United States, in Utah's desert, this experiment aims at representing an idealized city, through several ranges of containers. Two cases are simulated and analyzed, respectively corresponding to neutral and stable atmospheric stratifications (Bahlali et al., 2018a)

Les objectifs ambitieux, fixés aux acteurs du secteur automobile par les pouvoirs publics, en matière d'émission de polluants et de gaz à effet de serre rendent aujourd'hui indispensable une compréhension plus fine de la combustion dans les moteurs. La simulation 3D aux grandes échelles (LES) représente une voie prometteuse pour répondre à ces enjeux. Elle permet l'étude de phénomènes transitoires complexes inaccessibles avec des moyens expérimentaux ou des méthodes de calculs traditionnelles de type RANS. Ce travail de thèse est une première étape vers la simulation LES de l'injection de carburant liquide dans les moteurs à piston. Il a consisté à adapter le code de calcul aux particularités physiques de l'injection directe, technologie qui se généralise actuellement à tous les types de moteurs à piston. Dans un premier temps, et afin de s'affranchir du calcul 3D complexe en sortie d'injecteur, une méthodologie originale, consistant à initier le calcul en aval de l'injecteur, est proposée et validée sur différents cas. Pour la simulation 3D, l'approche Eulérienne mésoscopique, à laquelle est ajouté un modèle d'interaction particules-particules, est utilisée pour simuler le spray. Les simulations ont été premièrement validées par comparaison expérimentale dans des conditions proches de l'injection Diesel. De plus, une étude sur la dynamique du spray a permis de mieux comprendre son évolution et de dégager des points communs avec un jet de gaz turbulent. Des simulations complémentaires ont également montré la prédictivité de la LES sur des injections Diesel réalistes. Enfin, un premier calcul moteur à injection directe a été réalisé et a permis de valider les développements réalisés dans le cadre de cette thèse. / Car manufacturers are facing increasingly severe regulations on pollutant emissions and fuel consumption. To respect these regulations, a better understanding of combustion processes is needed. Large Eddy Simulation (LES) is becoming a promising tool for such issues as it allows the study of complex unsteady phenomena which can not be analysed with RANS simulations or experiments. The present work is a step towards the LES of liquid injection in piston engines. The numerical code has been adapted to the specifications of Direct Injection which is more and more used in industry. Firstly, in order to avoid the difficulties linked to the 3D simulation of cavitation, primary break-up and turbulence in the near-nozzle region, an original methodology, based on an injector model, has been proposed. The idea is to initiate the spray physics downstream to the injector exit. Then LES 3D simulations of spray have been conducted using the Eulerian Mesoscopic approach extended to dense dispersed sprays by the addition of a particle-particle interactions model. The simulation results have been validated by comparison with experimental data in Diesel conditions with a low injection pressure. Furthermore a study on the spray dynamics has permitted to better understand its development and to find similarities with a turbulent gaseous jet. Additional simulations on realistic Diesel injection conditions have shown the good predictivity of LES in such cases. Finally, a first simulation of a Direct Injection Engine has been been carried out to assess the developments achieved in this work.

O fenômeno de molhamento, estudo de como um líquido se deposita em um sólido, apresenta problemas ainda em aberto, dos pontos de vista da modelagem física e da simulação numérica. O maior interesse acadêmico neste tipo de escoamento é a linha tríplice (ou linha de contato) formada da interação sólido-líquido-gás. A condição de contorno clássica de não escorregamento na interface líquido-sólido leva a uma singularidade no tensor de tensões nesta linha. Além disso, ainda não está estabelecido qual o melhor modelo para descrever o ângulo de contato formado entre a superfície livre e o substrato (o sólido). Neste trabalho, são discutidos métodos numéricos para a simulação de linhas de contato dinâmicas. Os efeitos da tensão superficial são estudados com a abordagem do princípio do trabalho virtual, o qual leva o problema à equações na formulação variacional, linguagem natural para o tratamento numérico com o método dos elementos finitos (FEM). O domínio é discretizado por uma malha não-estruturada de forma que as interfaces separadoras são explicitamente representadas pela malha. As derivadas temporais são tratadas em uma abordagem Lagrangeana-Euleriana arbitrária (ALE). Finalmente, são apresentados os resultados numéricos obtidos com o método ALE-FEM, discutindo alguns aspectos da sua convergência temporal e espacial. / Wetting phenomena, study of how of a liquid spreads out on a solid substrate, presents challenges both in physical modeling and in numerical simulation. The triple line (or contact line) formed by the solid-liquid-gas interaction has increasingly attracted the attention of the fluid dynamic community. The classical no-slip boundary condition on the liquid-solid interface leads to a singularity in the stress tensor at contact lines. Furthermore, there is no consensus on what the best model to describe the dynamics of the contact angle formed by the solid substrate and free surface. In this work, numerical methods for simulating dynamic contact lines are considered. The capillarity effects are studied in the approach of the virtual-work principle, which describes the problem in the variational formulation, natural language for numerical treatment with the finite element method (FEM). The domain is discretized by a dynamic unstructured mesh, where the separating interfaces are explicit represented by the mesh. Time derivatives present in the governing equations are treated with the arbitrary Lagrangian-Eulerian (ALE) framework. Finally, we discuss some temporal and spatial convergence issues ofthe ALE-FEM method.

In its theoretical part, this thesis sums up the basic knowledge concerning permutations. Besides the representation of permutations and determination of their fundamental characteristics, the theoretical part is, first of all, aimed at results concerning the decomposition of permutations into disjoint cycles and at finding the number of permutations with a certain characteristic. We introduce the fundamental bijection that is useful for solving many problems concerning the permutations. Further on, we focus on the number of permutations without a fixed point, Eulerian numbers expressing the number of permutations with a given number of descents, and the number of permutations with a given number of excedances, Stirling numbers of the first kind expressing the number of permutations with a given number of cycles, and Catalan numbers representing the number of permutations avoiding a chosen pattern of length three. Attention is also paid to the Gilbreath permutations and their characteristics. The practical part consists of 14 solved problems. The solutions rely on the results presented in the theoretical part, and there are deduced some further interesting results concerning random permutations.