Le contexte général de cette thèse est la simulation numérique de l’injection de carburant dans un moteur à combustion interne, afin d’améliorer son rendement et de limiter la production de polluants. Intrinsèquement, il est possible de simuler l’ensemble de l’écoulement avec les équations classiques de la dynamique des fluides sans avoir recours à des outils de modélisation supplémentaires liés au caractère diphasique. Mais, les tailles des structures générées pendant l’injection (gouttes de diamètre < à 10 μm) conduisent à des temps de calculs prohibitifs pour une application industrielle. C’est pourquoi il est nécessaire d’introduire une modélisation diphasique. C’est dans ce contexte que deux régions sont formellement distinguées: le cœur liquide dense proche de l’injecteur, appelé écoulement à phases séparées, et le spray constitué d’une population de gouttes polydisperse générées après le processus d’atomisation en aval de l’injecteur. Ce travail de thèse étudie les modèles Eulériens pour la description de spray évaporants et polydisperses, en vue d’applications industrielles. Ils représentent une alternative potentielle aux modèles Lagrangiens qui sont majoritairement utilisés en industrie mais présentant des inconvénients majeurs. Ainsi, le modèle multi-fluide est étudié dans un premier temps. Bien que prometteur, deux difficultés sont soulignées: le coût requis pour une description précise de la polydispersion, et son incapacité à décrire les croisements de gouttes (particle trajectory crossing, PTC). La thèse propose des solutions à ces deux limitations. Elles reposent sur des méthodes de moments. Premièrement, le modèle appelé Eulerian Size Multi Size Moment (EMSM) permet de résoudre des sprays évaporants et polydisperses de manière bien plus efficace que le modèle multi-fluide. Des outils mathématiques sont utilisés pour fermer le système d’équations associé au modèle, et combinés à des schémas de types volumes finis appelés schémas cinétiques, afin de préserver la réalisabilité du vecteur de moments, pour le transport et l’évaporation. Une réponse à la seconde limitation est apportée avec le modèle appelé Eulerian Multi Velocity Moment (EMVM) basé sur le transport de moments en vitesse d’ordre élevé. Une distribution bimodale peut être localement reconstruite à partir des moments en utilisant une méthode de quadrature de moments ( QMOM) en une ou plusieurs dimensions d’espace. De la même manière, l’utilisation de schémas cinétiques permet de préserver la réalisabilité du vecteur de moment. De plus, une étude mathématique approfondie de la dynamique du système en une dimension d’espace en révèle toute la complexité et représente une étape indispensable en vue de l’élaboration de schémas de transport d’ordre élevé (supérieur ou égal à 2).Afin de les tester, ces deux modèles ainsi que les outils numériques associés sont implémentés dans MUSES3D, un code académique de simulation numérique directe (DNS) dédié à l’évaluation des modèles de spray. Des résultats de grande qualité démontrent le potentiel des modèles. L’extension du modèle EMSM dans un contexte industriel est ensuite considérée, avec son implémentation dans IFP-C3D, un code résolvant des écoulements réactifs sur des maillages non structurés et mobiles dans un formalisme RANS (Reynolds Averaged Navier Stokes) en présence de sprays. Le formalisme ALE (Arbitrary Lagrangian Eulerian) est utilisé et le modèle EMSM réécrit dans ce formalisme afin de mener des calculs en maillage mobile. De plus, une étude numérique a permis d’étendre les propriétés de précision et de stabilité obtenues en maillage fixe. La robustesse du modèle EMSM est alors démontrée avec succès dans IFP-C3D sur un cas impliquant un mouvement de piston, ainsi que dans le cadre d’une comparaison avec le code MUSES3D. Enfin, des résultats très encourageants prouvent la faisabilité d’un calcul d’injection dans une chambre de combustion d’un spray polydisperse avec le modèle EMSM. / The general context of the PhD is the simulation of fuel injection in an internal combustion engine, in order to improve its thermal and ecological efficiency. This work more generally concerns any industrial device involving a multiphase flow made of liquid fuel injected in a chamber filled with gaz: automotive or aircraft engines, or turbo machines. In and of itself, it is possible to simulate this flow without any modeling. However the small structures created during injection (droplets of diameter until 10 μm or less) lead to a prohibitive computational cost for any industrial application. Therefore modeling is necessary. In this context, two areas are formally distinguished: the dense liquid core close to the injector called separate-phase flow, and the spray made of a polydisperse droplet population (i.e. droplets with different sizes) generated after the atomization processes downstream of the injector. This PhD work investigates Eulerian models for the description of polydisperse evaporating sprays, for industrial computations. They represent a potential alternative to Lagrangian models, widely used at present, yet suffering from major drawbacks. Thus, the Multi-Fluid model is assessed. Although it is very promising, two difficulties are highlighted: its cost for a precise description of polydispersity, and its inability to describe particle trajectory crossing (PTC). Solutions to these two limitations are considered. Both rely on high order moment methods. First, the Eulerian Multi Size Moment (EMSM) proposes a much more efficient resolution of polydisperse evaporating sprays than the Multi-Fluid model does. Mathematical tools are used to close the model and combined with original finite volume kinetic-based schemes in order to preserve the moment-set integrity, for evaporation and advection. An answer to the second limitation is provided with the Eulerian Multi Velocity Moment (EMVM) based on high order velocity moments. A bimodal velocity distribution can be locally reconstructed for the moments using the quadrature method of moments (QMOM), in one or multi-dimensions. Here also, finite volume kinetic-based schemes are studied in order to preserve the moment set integrity. Moreover, a mathematical study of the one-dimensional dynamic system highlights its peculiarity and constitutes a necessary basis for the design of high order numerical schemes. In order to assess them, both the models and their numerical tools are implemented in the MUSES3D code, an academic DNS solver that provides a framework devoted to spray method evaluation. Achievements of the EMSM and the EMVM models are presented. The extension of the EMSM model to an industrial context is then considered, with its implementation in the IFP-C3D code, a 3D unstructured reactive flow solver with spray. In order to perform computations within a moving domain (due to the piston movement) the Arbitrary Lagrangian Eulerian (ALE) formalism is used. A numerical study has been achieved, in order to extent to this formalism the properties of accuracy and stability of the EMSM model, which already induces strong stability condition in an Eulerian approach. The robustness of the EMSM model in the IFP-C3D code has been successfully demonstrated on a case involving a moving piston, and also on a comparison with the MUSES3D code. Moreover, very encouraging results demonstrate the feasibility of the EMSM model for spray injection.

A distribuição do tamanho de bolhas é uma importante característica em sistemas bifásicos. A área interfacial de bolhas está fortemente relacionada às taxas de reações químicas e de transferência de massa em aplicações industriais como colunas de destilação e fermentação, sistemas biológicos, oxidação, hidrogenação, tratamento de água, e em processos naturais, como dinâmicas de aerossóis e transferência de gás oceano-atmosfera. Pontas de provas intrusivas são largamente usadas para determinar a distribuição do tamanho de bolhas em colunas de borbulhamento bifásicas. Embora o tamanho de bolhas não possa ser obtido diretamente pelo uso de uma simples ponta de prova porque estas medem somente comprimentos perfurados em bolhas, é possível relacionar distribuições de cordas à distribuição de tamanho de bolhas usando análises estatísticas. Este trabalho apresenta a implementação de um sistema capaz de medir distribuição de tamanho de bolhas em uma coluna de borbulhamento composta por água e ar através de uma ponta de prova condutiva. Imagens obtidas por uma câmera de vídeo CCD (Charge-Coupled Devices) monocromática são usadas para validar e calibrar o sistema. / The distribution of bubble sizes is a critical feature in two–phase systems. The interfacial area of bubbles is strongly related to chemical reaction and mass transfer rates in industrial applications such as distillation and fermentation columns, biological systems, oxidation, hydrogenation, waste water treatment and in natural processes such as aerosol dynamics and air-sea gas transfer. Intrusive probes are widely used to determine bubble size distribution in two-phase bubble columns. Although bubble size cannot be obtained by a simple probe because it measures only the pierced length of the bubbles, it is possible to relate chord distributions to bubble size distribution by the use of statistical analysis. This work proposes a system implementation which is able to determine bubble size distribution in a water-air bubble column using an intrusive conductance probe. Images obtained by a monochromatic video camera CCD (Charge-Coupled Devices) are used to validate and calibrate the system.

En fonction de la configuration avion, de son altitude du vol, du type de carburant, différents phénomènes physiques modifient les caractéristiques de l'alimentation du moteur en carburant. En effet, il se produit principalement un phénomène de dégazage qui pourrai être couplé à de la cavitation. Les écoulements diphasiques ainsi obtenus contiennent des microbulles, des bulles ou des poches de gaz qui risquent d'induire des dysfonctionnements du moteur. Ces dysfonctionnements se traduisent par des fluctuations de poussée pouvant conduire à une perte de contrôle de l’appareil. De cette problématique industrielle découlent de nombreux verrous scientifiques encore mal connus. Dans le cadre de cette thèse des travaux sur la modélisation numérique et la caractérisation expérimentale du couplage entre la cavitation et le dégazage. Pour cela deux bancs d’essai et un code propre capable d'étudier la problématique scientifique retenue ont été développés et exploités. Trois régimes de cavitation pure et trois autres de cavitation aérée sur une géométrie de venturi 8° symétrique ont été étudiés." / Depending on the configuration of the plane, its flight altitude, the type of fuel, different physical phenomena significantly change the characteristics of the fuel supply to the engine. Indeed, it primarily occurs a fuel degassing phenomenon that could be coupled to the cavitation phenomenon. As a result, the thus obtained multiphase flows contain micro bubbles, larger bubbles or vapor pockets which might induce engines malfunctions. The latter result in thrust fluctuations which can lead to a loss of power. The scientific context of the industrial problem lies in the development of a numerical and experimental representation of the cavitation and degassing phenomena on a smaller scale. As a result, it is of primary importance for one to understand the mechanisms of occurrence of gas and cavitation in the given industrial configuration. In order to deal with those issues, two test benches have been developed, as well as an in-house numerical code capable of simulating aerated cavitation phenomenon. Therefore, three different pure cavitation regimes and three other aerated cavitation are shown, as a result of the experimental work. The multiphase flow observations are based on a statistical post-processing of images taken by a high-speed camera. Moreover, two 2D aerated cavitation numerical simulations, as well as the first 3D pure cavitation simulation have been shown.

Slush is a two phase flow of solid particles (crystals) and liquid at the triple point temperature, and constitutes an appealing alternative to liquid propellants for space launchers. The crystals give to the mixture higher density and lower specific enthalpy than liquid, enabling reduced tank volume storage and larger fuel holding time. However, the presence of solid crystals significantly modifies the thermo-hydraulics of the fuel transport, and requires novel predictive tools and diagnostic techniques for efficiently exploiting slush propellants. This thesis contributes to both aspects. In particular, this work studied the flow pressure losses and the heat transfer of solid-liquid mixtures in pipelines, combining experimental and numerical methods. Hydraulic and thermal flow features were analyzed separately with substitute mixtures chosen to mimic the behavior of slush flows in engine fuel feed systems. A dedicated facility was designed and built. The pipeline mounted conventional probes for pressure, temperature and mass flow rate measurements. Moreover, a capacitance-based density meter was developed and validated to measure the mixture's solid content. Optical flow visualization and image processing routines were combined to retrieve particulate phase distribution and velocity fields. The experimental work was complemented with 3D Unsteady Reynolds Averaged Navier Stokes simulations in OpenFOAM. The simulations coupled the Euler-Euler approach with the granular kinetic theory for the treatment of the solid dispersed phase. The model was validated with the experimental results on the pressure drop, heat transfer and solid volume fraction.The resulting physical insights and the proposed empirical correlations on the pressure drop and heat transfer in solid-liquid flows contribute to move a step forward towards slush propelled space launchers. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Consider a bottom-hinged Oscillating Wave Surge Converter (OWSC): This device oscillates due to the hydrodynamic forces applied on it by the action of ocean waves. The focus of this thesis is to build upon the in-house multi-block generalized coordinate finite volume solver GenIDLEST using a collocated grid arrangement within the framework of the fractional-step method to make it compatible to simulate such systems. The first step in this process is to deploy a convection scheme which differentiates between air and water. This process is further complicated by the 1:1000 density and 1:100 viscosity ratio between the two fluids. For this purpose, a phase field method is chosen for its ease of implementation and proven boundedness and conservativeness properties. Extensive validation and verification using standard test cases, such as droplet in shear flow, Rayleigh Taylor instability, and the Dam Break Problem is carried out. This development is then coupled with the present Immersed Boundary Module which is used to simulate the presence of moving bodies and again verified against test cases, such as the Dam Break problem with a vertical obstacle and heave decay of a partially submerged buoyant cylinder. Finally, a relaxation zone technique is used to generate waves and a numerical beach technique is used to absorb them. These are then used to simulate the Oscillating Surge Wave Converter. / Master of Science / An Oscillating Wave Surge Converter can be best described as a rectangular flap, hinged at the bottom, rotating under the influence of ocean waves from which energy is harvested. The singular aim of this thesis is to model this device using Computational Fluid Dynamics (CFD). More specifically, the aim is to model this dynamic device with the full Navier Stokes Equations, which include inertial forces, arising due to the motion of the fluid, viscous forces which dissipate energy, and body forces such as gravity. This involves three key steps: 1. Modelling the air-water interface using a convection scheme. A phase field method is used to differentiate between the two fluids. This task is made more challenging because of the very large density and viscosity differences between air and water. 2. Model dynamic moving geometries in a time-dependent framework. For this, we rely on the Immersed Boundary Method. 3. Develop a numerical apparatus to generate and absorb ocean waves. For this, we rely on the Relaxation Zone and Numerical Beach Method. These developments are validated in different canonical problems and finally applied to a two-dimensional oscillating surge wave energy converter.

Kinematic simulation (KS) is a means of generating a turbulent-like velocity field, in a manner that enforces an input Eulerian energy spectrum. Such models have also been applied in particle-laden flows, due to their ability to enforce spatial organization of the fluid velocity field when simulating the trajectories of individual particles. A critical evaluation of KS is presented; in particular, its ability to reproduce single-particle Lagrangian statistics is examined. Also the ability of KS to reproduce the preferential concentration of inertial particles is explored. Some numerical results are presented, in which fluid tracers and inertial particles are transported alternatively by (1) simulated turbulence generated by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations, and (2) KS. The effect of unsteadiness formulation in particular is examined. It is found that even steady KS qualitatively reproduces the continuity effect, clustering of inertial particles, elevated dispersion of inertial particles and the intermittent turbulence velocity signal. A novel method is then motivated and formulated, in which, for input RANS parameters, a simulated spectrum is used to generate a KS field which enforces a target Lagrangian timescale. This method is then tested against an existing experimental benchmark, and good agreement is obtained. / Thesis / Doctor of Philosophy (PhD) / Turbulence arises in an immense variety of industrial and scientific applications; from weather to automotive design; from medicine to nuclear engineering. Because turbulence is chaotic, it is difficult to make accurate predictions of how a turbulent flow will behave in a given scenario. The objective of my research is to find easier ways of accurately modelling turbulence in a certain class of particle-laden flows.

Nanoparticle-based technologies are an emerging field with the promise to impact a wide range of application areas. However, that potential is somewhat married to a host of research questions that remain to be answered. This work explores the surface modification of magnetic nanoparticles in a controlled fashion to produce hybrid nanoparticle (metal/polymer) systems with different morphologies, understand in-situ behavior of stimuli-responsive polymers grafted to a substrate, and obtain better computational methods for particle-tracking and -deposition. Nanoparticle surface modification was performed using ATRP, obtaining homo-, block-co-, and ‘twoaced/biphasic’ polymer structures on the nanoparticle surfaces. Biphasic Janus nanoparticles (JPs) were formed using a magnetic nanoparticle core and an innovative technique combining non-covalent solid protection with sequential controlled radical polymerization to form the two surface-grafted polymer phases. Surface-confined polymerizations were conducted using pH- and thermo-responsive materials. Poly(methacrylic acid) (PMAA) and a series of (aminoalkyl) methacrylate polymers were used as pH responsive polymers. Additionally, poly(N-isopropylacrylamide) (PNIPAM) was selected as the thermo-responsive material for this study. In-situ characterization techniques, including atomic force microscopy (AFM), dynamic light scattering (DLS), and ellipsometry, were used to evaluate the thermo- and pH-responsiveness of these stimuli responsive materials. A new general-oscillator (GENOSC) model was used to determine swelling ratio, thickness, and optical constant changes in the polymer brush as pH was changed in-situ. AFM was used to study morphological changes due to changes in pH and temperature. Nanoparticle temperature responsiveness was investigated using DLS. A related effort involved the use of computational fluid dynamic (CFD) methods to track (micron-sized) particles in certain geometries, including a human lung morphology. Predicted particle transport and deposition was compared to Lagrangian computational approaches and available experimental data. The Eulerian particle phase modeling method developed resulted in the accurate prediction of both near-wall particle tracking and wall deposition. This Eulerian-Eulerian model is a new tool that has potential for particle tracking in physiological morphologies. This combination of experimental and computational research has led to new nano- and micro-particle surface modification methods and particle transport modeling.

Cette thèse est consacrée au développement et à la comparaison des méthodes de suivi d'interface pour les écoulements diphasiques incompressibles. Elle s'intéresse à la sélection de méthodes robustes de suivi d'interface, puis à leur couplage avec le solveur des équations de Navier-Stokes. La méthode level-set est en premier lieu étudiée, en particulier l'influence du schéma d'advection et de l'étape de réinitialisation sur la qualité des résultats du suivi d'interface. Il a été montré que la méthode de réinitialisation avec contrainte de volume est robuste et précise en combinaison avec des schémas conservatifs WENO d'ordre 5 pour l'advection. Il a été constaté que les erreurs du suivi d'interface augmentent de manière abrupte lorsque la condition CFL est trop petite. Comme remède, la réinitialisation du champ level-set effectuée moins souvent réduit la diffusion numérique et le déplacement non-physique de l'interface. La conservation de la masse n'est pas assurée avec les méthodes level-set. Les méthodes VOF (volume-of-fluid) qui conservent naturellement la masse du fluide de référence sont alors étudiées. Une résolution géométrique avec un schéma consistent et conservatif est alors adoptée, ainsi qu'une autre technique alternative plus aisément extensible en 3D. Il a été trouvé que ces deux dernières méthodes donnent des résultats très proches. La méthode MOF (moment-of-fluid), qui reconstruit l'interface en utilisant le centre de masse du fluide de référence, est plus précise que les méthodes VOF. Différentes méthodes couplées entre level-set et VOF sont alors étudiées, notamment: CLSVOF, MCLS, VOSET et CLSMOF. Il a été observé que la méthode level-set tend à épaissir les filaments minces, tandis que VOF et les méthodes couplées les fragmentent en petites particules. Finalement, on a couplé les méthodes level-set et VOF avec le solveur incompressible des équations de Navier-Stokes. On a comparé différentes manières de prise en compte des conditions de saut à l'interface (lisse et raide). Il a été montré que les méthodes VOF sont plus robustes, et donnent d'excellents résultats pour quasiment toutes les simulations. Deux méthodes level-set donnant de très bons résultats, comparables à ceux de VOF, sont aussi identifiées. / This thesis is devoted to the development and comparison of interface methods for incompressible two-phase flows. It focuses on the selection of robust interface capturing methods, then on the manner of their coupling with the Navier-stokes solver. The level-set method is first investigated, in particular the influence of the advection scheme and the reinitialization step on the accuracy of the interface capturing. It is shown that the volume constraint method for reinitialization is robust and accurate in combination with the conservative fifth-order WENO schemes for the advection. It is found that interface errors increase drastically when the CFL number is very small. As a remedy, reinitializing the level-set field less often reduces the amount of numerical diffusion and non-physical interface displacement. Mass conservation is, however, not guaranteed with the level-set methods. The volume-of-fluid (VOF) method is then investigated, which naturally conserves the mass of the reference fluid. A geometrical consistent and conservative scheme is adopted, then an alternative technique more easily extended to 3D. It is found that both methods give very similar results. The moment-of-fluid (MOF) method, which reconstructs the interface using the reference fluid centroid, is found to be more accurate than the VOF methods. Different coupled level-set and VOF methods are then investigated, namely: CLSVOF, MCLS, VOSET and CLSMOF. It is observed that the level-set method tends to thicken thin filaments, whereas the VOF and coupled methods break up thin structures in small fluid particles. Finally, we coupled the level-set and volume-of-fluid methods with the incompressible Navier-Stokes solver. We compared different manners (sharp and smoothed) of treating the interface jump conditions. It is shown that the VOF methods are more robust, and provide excellent results for almost all the performed simulations. Two level-set methods are also identified that give very good results, comparable to those obtained with the VOF methods.

La conception d'un statoréacteur bénificie aujourd'hui des progrès divers des outils numériques permettant par la même occasion d'alléger les différentes étapes préliminaires de tests en géométrie réelle nécessaires au développement de telle configuration. L'objectif de cette thèse est de développer une méthodologie s'appuyant sur la Simulation aux Grandes Echelles (SGE) afin de contribuer à la validation de ce nouvel outil numérique pour la simulation de statoréacteur et ainsi de contribuer à la compréhension des phénomènes mis en jeu dans ces chambres de combustion. L'outil numérique est tout d'abord adapté pour la simulation des écoulements réactifs fortement turbulents avec un accent mis sur la gestion des chocs avec des schémas centrés et la discrétisation de la convection pour la simulation Eulérienne de la phase dispersée. La configuration cible est le "Statoréacteur de Recherche'' étudié expérimentalement par l'ONERA. Sa simulation est réalisée de manière graduelle. Tout d'abord, il est montré que la simulation de la totalité de la configuration, y compris les diffuseurs d'entrée où se positionne un réseau de choc, est essentielle afin de considérer une géométrie acoustiquement close pour reproduire correctement les modes d'oscillation du statoréacteur. La pertinence du schéma cinétique est aussi étudiée et il est montré l'importance de bien reproduire l'évolution de la vitesse de flamme adiabatique pour une plage de richesse grande, en raison du régime de combustion partiellement prémélangé. Finalement, trois cas à richesse différente sont simulés et un excellent accord est trouvé avec l'expérience. La phénoménologie et les mécanismes pilotant la combustion sont alors étudiés pour ces trois cas. / Design of ramjets benefits today from the progress of numerical tools which relieve the various test stages of real engines that remain necessary for the development of such a kind of configuration. The objective of this dissertation is to develop a methodology based on the Large Eddy Simulation (LES) to contribute to the validation of this new type of advanced numerical tool for the simulation of ramjets and improve the understanding of combustion in these devices. The numerical tool is first adapted for the simulation of highly turbulent reacting flows with emphases on the management of shocks with centered schemes and the discretization of convection for the Eulerian simulation of the dispersed phase. The target configuration is the “Research ramjet” experimentally studied by ONERA. Simulation is carried out gradually. First, it is shown that the simulation of the entire configuration, including diffusers at the inlets where shocks appear is essential to consider an acoustically close geometry to properly reproduce the oscillation modes of combustion. The relevance of the kinetic scheme is also studied. It is shown that reproducing the evolution of the adiabatic flame speed for a wide range of equivalence ratio is critical because of the partially premixed combustion regime involved in this configuration. Finally, three different cases are simulated and excellent agreement is found with experimental data. The phenomenology and the different mechanisms governing combustion are studied for these three cases.

La simulation des écoulements diphasiques rencontrés dans les moteurs à combustion interne (MCI) est de grande importance pour la prédiction de la performance des moteurs et des émissions polluantes. L’injection directe du carburant liquide à l’intérieur de la chambre de combustion génère loin de l’injecteur un brouillard de gouttes polydisperses, communément appelé spray. Du point de vue de la modélisation, l’émergence des méthodes Eulériennes pour la description du spray est considérée prometteuse par la communauté scientifique. De plus, la prise en compte de la distribution en taille des gouttes par les approches Eulériennes, de manière peu coûteuse en temps de calcul, n’est plus considérée comme un verrou depuis le développement de la méthode Eulerian Multi Size Moment (EMSM). Afin d’envisager la simulation de configurations réalistes de MCI, ce travail de thèse propose de modéliser les interactions turbulentes two-way entre le spray polydisperse évaporant et la phase gazeuse environnante par la méthode EMSM. Dans le contexte du formalisme Arbitrary Lagrangian Eulerian (ALE) dédiée au traitement du maillage mobile, les termes sources présents dans le modèle diphasique sont traités séparément des autres contributions. Le système d’équations est fermé à l’aide d’une technique de reconstruction par maximisation d’entropie (ME), originellement introduite pour EMSM. Une nouvelle stratégie de résolution a été développée pour garantir la stabilité numérique aux échelles de temps très rapides introduites par les transferts de masse, quantité de mouvement et énergie, tout en respectant la condition de réalisabilité associée à la préservation de l’espace des moments d’ordre ´élevé. A l’aide des simulations académiques, la stabilité et la précision de la méthode ont été étudiées aussi bien pour des lois d’évaporation constantes que dépendantes du temps. Tous ces développements ont été intégrés dans le code industriel IFP-C3D dédié aux écoulements compressibles et réactifs. Dans le contexte de la simulation en 2-D de l’injection directe, les résultats se sont avérés très encourageants comme en témoignent les comparaisons qualitatives et quantitatives de la méthode Eulerienne à la simulation Lagrangienne de référence des gouttes. De plus, les simulations en 3-D effectuées dans une configuration typique de chambre de combustion et des conditions d’injection réalistes ont donné lieu à des résultats qualitativement très satisfaisants. Afin de prendre en compte la modélisation de la turbulence, une extension moyennée, au sens de Reynolds, des équations du modèle diphasique two-way est dérivée, un soin particulier étant apporté aux fermetures des corrélations turbulentes. La répartition de l’énergie dans le spray ainsi que les interactions turbulentes entre les phases ont été étudiées dans des cas tests homogènes. Ces derniers donnent un aperçu intéressant sur la physique sous-jacente dans les MCI. Cette nouvelle approche RANS diphasique est maintenant prête à être employée pour les simulations d’application de MCI. / The ability to simulate two-phase flows is of crucial importance for the prediction of internal combustion engine (ICE) performance and pollutant emissions. The direct injection of the liquid fuel inside the combustion chamber generates a cloud of polydisperse droplets, called spray, far downstream of the injector. From the modeling point of view, the emergence of Eulerian techniques for the spray description is considered promising by the scientific community. Moreover, the bottleneck issue for Eulerian methods of capturing the droplet size distribution with a reasonable computational cost, has been successfully tackled through the development of Eulerian Multi Size Moment (EMSM) method. Towards realistic ICE applications, the present PhD work addresses the modeling of two-way turbulent interactions between the polydisperse spray and its surrounding gas-phase through EMSM method. Following to the moving mesh formalism ArbitraryLagrangian Eulerian (ALE), the source terms arising in the two-phase model have been treated separately from other contributions. The equation system is closed through the maximum entropy (ME) reconstruction technique originally introduced for EMSM. A new resolution strategy is developed in order to guarantee the numerical stability under veryfast time scales related to mass, momentum and energy transfers, while preserving the realizability condition associated to the set of high order moments. From the academic point of view, both the accuracy and the stability have been deeply investigated under both constant and time dependent evaporation laws. All these developments have beenintegrated in the industrial software IFP-C3D dedicated to compressible reactive flows. In the context of 2-D injection simulations, very encouraging quantitative and qualitative results have been obtained as compared to the reference Lagrangian simulation of droplets. Moreover, simulations conducted under a typical 3-D configuration of a combustion chamber and realistic injection conditions have given rise to fruitful achievements. Within the framework of industrial turbulence modeling, a Reynolds averaged (RA) extension of the two-way coupling equations is derived, providing appropriate closures for turbulent correlations. The correct energy partitions inside the spray and turbulent interactions between phases have been demonstrated through homogeneous test-cases. The latter cases gave also some significant insights on underlying physics in ICE. This new RA approach is now ready for ICE application simulations.