This work contributes to the structure investigation on the basis of small-angle neutron scattering (SANS). A new analytical scattering function for polydispers precipitates with diffusion zones is presented and used in SANS experiments. For diluted and dense packed systems structure describing parameter values were obtained. These results lead to a deeper understanding of the process of nanocristallization of amorphous alloys. The investigation of SANS on Fe73.5Si15.5B7Cu1Nb3 shows that the Fe3Si type nanocrystals created in the amorphous matrix during annealing are covered by Nb-atoms. The accumulation of Nb-atoms or Nb-B-aggregates acting as inhibitors at the surface of the nanocrystals is assumed to be the basic mechanism controlling the evolution of the precipitates. For the first time this inhibitor-model is shown to be correct without doubts. In the Zr32Ti7.5Al10Cu20Ni8 amorphous alloy the formation of ultrafine nanocystals of about 2-3 nm in diameter was observed. The nanocrystallization starts after ordered clusters achieved particular sizes and a certain packing fraction. This leads to a new model for the microscopic formation procedure of ultrafine nanocrystals in this amorphous alloy. Theoretical models of fractal systems are applied to complicated polydisperse materials. Both the theory for an exact surface fractal of Hermann (1994)and the model for coupled volume and surface fractals in the formulation of Wong (1992) are shown to be applicable. The latter approach is applied to experimental data here for the first time. With computer simulations conditions for scattering experiments were optained therewith predictions about the quality and grade of fractality in real specimens become possible. / Die vorliegende Arbeit ist ein Beitrag zur Strukturaufklärung mittels Neutronen-Kleinwinkel-Streuung (SANS). Es wird eine neu entwickelte analytische Streufunktion für polydisperse Ausscheidungen mit Diffusionszonen genutzt, um SANS Experimente auszuwerten. Sowohl für verdünnte, als auch für dicht gepackte Systeme werden auf diese Weise quantitative Strukturparameter gewonnen. Diese liefern einen Beitrag zum Verständnis des Nanokristallisationsverhaltens amorpher metallischer Gläser. Die Auswertung der Experimente an on Fe73.5Si15.5B7Cu1Nb3 zeigt, dass Fe3Si-artige Nanokristalle, die während der Temperaturbehandlung in der amorphen Matrix entstehen, von Nb-Atomen bedeckt werden. Diese Ansammlung von Nb-Atomen oder von entsprechenden Nb-B-Aggregaten auf der Oberfläche dieser Ausscheidungen hemmt das Größenwachstum der entstehenden Nanokristalle. Dieses Inhibitor-Modell wurde hier erstmals zweifelsfrei bestätigt. In Proben des amorphen metallischen Glases Zr32Ti7.5Al10Cu20Ni8 werden ultrafeine Ausscheidungen mit Durchmessern von 2-3 nm beobachtet. Diese entstehen verzögert nach der Ausprägung dicht gepackter Gebiete mit erhöhter Nahordnungsstruktur. Es wird ein Modell vorgeschlagen, das diesen Prozess erklären kann. Theoretisch diskutierte Modelle für fraktale Systeme werden auf komplizierte polydisperse Materialien angewendet. Sowohl die Formulierung von Hermann (1994) für ein exaktes Oberflächenfraktal, als auch der erstmals auf experimentelle Daten angewendete Ansatz von Wong (1992) für ein gekoppeltes Volumen- und Oberflächenfraktal erweisen sich als praktisch nutzbar. Mittels Computersimulationen wurden Bedingungen abgeleitet, die an Streuexperimente zu stellen sind, damit Aussagen über Qualität und Grad von Fraktalität in realen Proben getroffen werden können.

The thesis involves computer simulation and theoretical studies of phase transition in soft-condensed matter systems and theoretical understanding of enzyme kinetics along with kinetic proofreading of tRNA-aminoacylation in biological systems. Based on the system and phenomena of interest, the work has be classified into the following four major parts: I. Surface phenomena and surface energy of vapor-liquid interface. II. Condensation of vapor in two and three dimensions. III. Liquid-solid phase transition in polydisperse systems. IV. Enzyme catalysis and kinetic proofreading in biosynthesis. Above mentioned four parts have further been divided into thirteen chapters. In the following we provide a brief chapter-wise outline of the thesis. Part I deals with surface tension and interfacial properties of vapor-liquid interface for Lennard-Jones (LJ) fluid in both two and three dimensions. In Chapter 1, we provide a brief overview of vapor-liquid interface and existing theoretical and computer simulation studies of surface/line tension. In this chapter we also discuss about the existing experimental studies. In Chapter 2, we present computer simulation studies of surface tension in two dimensional Lennard-Jones system. The sensitivity of line tension on range (potential cut-off) of interparticle interaction is discussed in this chapter. We present Density Functional Theory (DFT) of line tension of vapor-liquid interface based on Weeks-Chandler-Anderson (WCA) and Barker-Hendersen (BH) perturbation techniques. We compare the DFT prediction with the computer simulation results. In general, WCA approach has been found to be successful for 3D system in predicting the surface tension. In 2D, however, it does not give good agreement either for phase diagram or for the line tension. In fact, BH also does not give accurate values of the coexistence parameters, however, it predicts better line tension compared to WCA. In Chapter 3 we present both theoretical and computer simulation studies of gas-liquid surface tension for three dimensional Lennard-Jones fluid. We perform non-equilibrium computer simulation study following Transition Matrix Monte Carlo (TMMC) method to obtain surface tension for various ranges of potential and introduce a new scaling relation of surface tension in order to capture both the temperature and interparticle interaction range dependence. The scaling shows excellent agreement with the simulation result and it can also predict the critical temperature with sufficient accuracy. The width of the gas-liquid interface is found to be insensitive to the range of the potential, whereas the density separation of the bulk vapor and liquid phases increases with increasing range of potential. Thus, the major contribution comes from the increasing density separation of the bulk vapor and liquid phases. Part II consists of four chapters, where we focus on the age old problem of nucleation, from the perspective of thermodynamics and kinetics. We account for the rich history of the problem in the introductory Chapter 4. In this chapter we describe various types and examples of the nucleation phenomena, and a brief account of the major theoretical approaches used so far. We begin with the most successful Classical Nucleation Theory (CNT), and then move on to more recent applications of Density Functional Theory (DFT) and other mean-field types of models. We present various experimental techniques used in the literature to obtain rate of nucleation. We conclude with a comparison between the experiments, theories and computational studies. In the next chapter (Chapter 5) we attempt to understand the mechanism of the gas-liquid nucleation in three dimension at large metastability from microscopic point of view. Here we study the nature of sequential growth of all liquid-like clusters (not just the largest cluster) at different degrees of metastability. Therefore, we have ordered the clusters according to their decreasing sizes and identified them in terms of kth largest cluster where, k = 1 denotes the largest cluster in the system, k = 2 represents the second largest and k = 3 is the third largest and so on. We have studied both the free energies and the trajectories of the liquid-like clusters in this extended set of order parameters. We further define Fkl(n) as the free energy of the kth largest cluster with size n. Classical nucleation theory provides an expression of unconditional free energy of a single cluster, F (n) (the free energy of formation of a cluster of size n), which is an intensive property of the system. The study of our conditional free energy surfaces, Fkl(n), reveals a more detailed, microscopic picture of the system’s cluster size distribution that is necessary to understand the kinetics of nucleation and growth at large metastability. The rate of nucleation shows a cross over at kinetic spinodal (the limit of metastability, ∆F1 l = 0). Below kinetic spinodal only one (largest) cluster crosses the critical size through activation whereas above this point more than one cluster grow simultaneously through barrierless diffusion. We present a theoretical analysis of the free energy of kth largest cluster based on order statistics. The theoretical predictions are in excellent agreement with computer simulation results for the range of supersaturation we studied. While the previous chapter focuses on relatively well-studied nucleation mechanism in 3dimensional (3D) LJ system at large metastability, in Chapter 6 we present our studies on the characteristics of the nucleation phenomena in two dimensional Lennard-Jones fluid for different ranges of interparticle interaction. Using various Monte Carlo (MC) methods, we calculate the free energy barrier of nucleation and bulk densities of equilibrium liquid and vapor phases, and also investigate the size and shape of the critical nuclei. We find an interesting interplay between the range of interaction potential and the extent of metastability. The free energy barrier of nucleation strongly depends on the range of interaction potential. The study is carried out at an intermediate level of supersaturation (away from the kinetic spinodal limit). A surprisingly large cutoff (rc � 7.0�, where � is the diameter of LJ particles) in the truncation of the LJ potential is required to obtain converged results. A lower cutoff leads to a substantial deviation in the values of the nucleation barrier, and characteristics of the critical cluster (with respect to full range of interaction). We observe that in 2D system CNT fails to provide a reliable estimate of the free energy barrier. While it is known to slightly overestimate the nucleation barrier in 3D, it underestimates the barrier by � 50% at the saturation ratio S =1.1 (defined as S = P/Pc, where Pc is the coexistence pressure) and at the reduced temperature T � =0.427 (defined as T � = kBT/�, where � is the depth of the potential well). The reason for the marked inadequacy of the CNT in 2D can be attributed to the non-circular nature of the critical clusters. Although the shape becomes increasingly circular and the clusters become more compact with increase in cutoff radius, an appreciable non-circular nature remains even for full potential (without truncation) to make the predictions of CNT inaccurate. In Chapter 7 we report the computer simulation study of nucleation in three dimensional LJ system. At a fixed supersaturation the free energy barrier of nucleation increases with increasing range of interparticle interaction. On increasing range of intermolecular interaction, the kinetic spinodal where the mechanism of nucleation changes from activated barrier crossing to barrierless diffusion, shifts towards the deep metastable region. Both the critical cluster size and pre-critical minimum in the free energy surface of kth largest cluster shift towards the smaller size at their respective kinetic spinodal as we increase the range of potential. We find only a weak non-trivial (other than supersaturation and surface tension) contribution to the free energy barrier of nucleation. Part III consists of two chapters and focuses on the liquid-solid phase transition of polydisperse fluid. In Chapter 8 we introduce polydisperse systems and their classification based on different identities. We describe the importance and abundance of polydisperse system in nature. The theoretical modeling of different polydisperse systems and their extent of applicability have also been presented. We have discussed about the various factors which control the phase diagram and various phenomena related to the structure and phase transition. In Chapter 9 we present computer simulation study on freezing/melting of Lennard-Jones (LJ) fluid at different polydispersities. The freezing/melting of polydisperse LJ fluids presents an interesting case study, because, as the polydispersity increases the energy-entropy balance becomes increasingly unfavorable for the solid to exist as a stable phase. The energy of the solid increases due to build up of strain energy because of increasing mismatch in size of the neighbors, while the entropy of the liquid increases. These two factors lead to the existence of a terminal polydispersity. We find beyond the terminal ploydispersity, δ. 0.11system remains in the disorder state even at very high pressure and low temperature. The terminal polydispersity obtained in the present study is close to the experimental value (δt. ≈ 12%). Interestingly, contrary to hard sphere polydisperse fluid, LJ fluid does not exhibit reentrant melting. The last part (Part IV) of the thesis consists of three chapters that deal with the enzyme catalysis and kinetic proofreading of tRNA-aminoacyl synthetases. In Chapter 10 we describe protein synthesis process in biological system and corresponding two processes: aminoacylation of tRNA and translation of amino acid in ribosome. Our interest is to understand the enzyme catalysis involved in aminoacylation of tRNA in the process of protein synthesis. We present the classification of 20 aminoacyl-tRNA synthetases into two classes based on their structure and mode of binding to ATP and tRNA. We discuss all the steps involved in whole tRNA-aminoacylation process. Then we introduce kinetic proofreading during aminoacylation reaction. In Chapter 11 we theoretically analyze the single turn over and steady state reaction mechanism of two classes of aminoacyl-tRNA synthetases. Class I enzymes not only differ in their structure but they also differ with respect to the pre-steady kinetics compared to class II enzymes. We find that the strong binding of product to class I enzymes causes the product release step to be rate limiting step leading to the burst of product formation in pre-steady reaction. On the other hand class II enzymes do not show any burst kinetics. The present study based on time dependent probability statistics is successful in explaining all the experimental results quantitatively. In Chapter 12 we present an augmented kinetic scheme and then employ methods of time dependent probability statistics to understand the mechanism of kinetic proofreading of isoleucyl-tRNA synthetase (IRS) which belongs to class I. We investigate that the enhanced hydrolysis of wrong substrate (Val) enables IRS to discriminate the correct substrate (Ile) and wrong substrate (Val) efficiently. It has been observed that an extra CP1 editing domain serves as an activating domain towards enhanced hydrolysis of Val. The present study is able to explain most of the existing experimental observations. In the concluding note, Chapter 13 lists a few relevant problems that may prove worthwhile to be addressed in future. In the Appendices, we present two of the techniques used in our present computer simulation and theoretical studies. Appendix A describes Grand Canonical Transition Matrix Monte Carlo (GC-TMMC) method which is employed in computer simulation studies of nucleation and surface tension. In Appendix B we present the probabilistic method of waiting time distribution computation used in enzyme catalysis and kinetic proofreading.

En propulsion solide, l'ajout de particules d'aluminium dans le propergol améliore de façon significative les performances du moteur grâce à une augmentation sensible de la température de chambre. La présence de gouttes d'aluminium et de résidus d'alumine de différentes tailles et en quantité importante a un impact notoire sur le fonctionnement du moteur. Dans cette optique, nous souhaitons obtenir une meilleure prévision de la stabilité de fonctionnement en cas de déclenchement d'instabilités d'origine aéroacoustique ou thermoacoustique. Nous visons des calculs plus précis de l'étendue de la zone de combustion, de la chaleur dégagée par la combustion distribuée des gouttes et de la distribution en taille des résidus. Nos efforts ont porté sur la modélisation des échanges entre la phase gazeuse et cette phase dispersée composée de gouttes de nature et de taille très diverses. Le paramètre taille pilotant la dynamique du spray et le couplage avec le gaz, le suivi précis des changements de taille est un enjeu majeur.Dans cette contribution, nous avons choisi une approche cinétique pour la description des sprays polydisperses. L'équation cinétique de Williams-Boltzmann utilisée pour suivre l'évolution des propriétés du spray est résolue par une approche eulérienne. Les méthodes Multi-Fluide (MF) traitent naturellement les changements de taille tels que l'évaporation et la coalescence. Ces méthodes reposent sur une intégration continue de la variable taille sur des intervalles fixes appelés sections sur lesquels nous pouvons dériver des systèmes d'équations de conservation. Chaque système est vu comme un fluide qui est en couplage fort avec la phase gazeuse via des termes sources.Nous avons travaillé sur une méthode MF à deux moments en taille basée sur une famille de fonctions de forme polynomiale pour reconstruire la distribution en taille au sein des sections. Cette approche d'ordre deux en temps et en espace s'avère performante car elle décrit avec précision l'évolution de la distribution avec un nombre modéré de sections. Un travail original a été mené afin d'étendre l'approche MF à des gouttes bicomposants. Cette méthode ouvre la voie à des modèles de combustion des gouttes d'aluminium plus représentatifs. Dans le contexte des simulations instationnaires, nous avons porté une attention particulière à l'emploi d'une stratégie numérique robuste et précise pour le couplage entre les phases modélisées par une approche Euler-Euler. Nous montrons qu'une méthode de splitting séparant le traitement du transport des phases gazeuse/dispersée de celui des termes sources est particulièrement adaptée pour la résolution d'un problème multi-échelle spatial et temporel. Dans la mesure où les conditions de réalisabilité sur les moments en taille des méthodes MF ne sont pas garanties avec des méthodes d'intégration traditionnelles, nous avons développé des schémas innovants pour l'intégration des termes sources. Les travaux proposés dans cette contribution répond à deux exigences : 1- un ratio coût/précision attractif pour des simulations industrielles 2- une facilité d'implémentation des méthodes et une modularité assurant la pérennisation des codes industriels. Ces développements ont d'abord été vérifiés à l'aide d'un code ad hoc ; des cas test d'étude d'acoustique diphasique linéaire ont notamment souligné la pertinence de la technique de splitting pour restituer avec précision les interactions spray-acoustique. Les nouvelles méthodes ont ensuite été implémentées et validées au sein du code multi-physique CEDRE développé à l'ONERA. Des calculs de propulsion solide sur des configurations moteur réalistes ont finalement mis en évidence le niveau de maturité atteint par les méthodes eulériennes pour décrire avec fidélité la dynamique des sprays polydisperses. Les résultats de ces simulations ont mis en avant la sensibilité des niveaux d'instabilités en fonction de la distribution en taille des gouttes d'aluminium et des résidus. / The addition of a significant mass fraction of aluminum particle in the propellant of Solid Rocket Motors improves performance through an increase of the temperature in the combustion chamber. The distributed combustion of aluminum droplets in a portion of the chamber yields a massive amount of disperse aluminum oxide residues with a large size spectrum, called a polydisperse spray, in the entire volume. The spray can have a significant impact on the motor behavior and in particular on the onset/damping of instability. When dealing with aeroacoustical and thermoacoustical instabilities, the faithful prediction of the interactions between the gaseous phase and the spray is a determining step for understanding the physical mechanisms and for future solid rocket motor optimization. In such a harsh environment, experimental measurements have a hard time providing detailed explanation of the physical mechanisms and one has to resort to numerical simulation. For such a purpose, the distributed combustion zone and thermal profile therein, the heat generated by the combustion of the dispersed droplets and the large size distribution of the aluminum oxide residues and its coupling with he gaseous phase hydrodynamic and acoustic fields have to be accurately reproduced through a proper level of modeling and a high fidelity simulation including a precise resolution of size polydispersity, which is a key parameter.In this contribution, we choose a kinetic approach for the description of polydisperse sprays. The Williams-Boltzmann Equation is used to model the disperse phase and we derive a fully Eulerian approach through moment methods. The Multi-Fluid (MF) methods naturally treat droplet size evolution through phenomena such as evaporation and coalescence. These methods rely on the conservation of size moments on fixed intervals called sections and yield systems of conservation laws for a set of "fluids" of droplet of various sizes, which is strongly coupled with the gas phase via source terms. We derive a new optimal and flexible Two Size Moment MF method based on a family of polynomial reconstruction functions to describe the size distribution in the sections, which is second order accurate and particularly efficient at describing accurately the evolution of the size distribution with a moderate number of sections. An original work is also conducted in order to extend this approach to two-component droplets. For size moment MF methods, realizability of the moments is a crucial issue. Thus, we have developed innovative schemes for integrating source terms in moment conservation equations describing transport in phase space. This method enables the use of more representative aluminum droplet combustion models, and leads to more advanced studies of the distributed combustion zone. Moreover, for unsteady two-phase flow simulations, we have developed a robust and accurate coupling strategy between phases that are modeled by a fully Eulerian approach based on operator splitting in order to treat such spatial and temporal very multi-scale problems with reasonable computational time. All the proposed developments have been carried out following two criteria : 1- an attractive cost/accuracy ratio for industrial simulations in the context of high fidelity simulations 2- a preservation of industrial code legacy. Verification of the models and methods have been conducted first using an in-house reseach code and then in the context of a two-phase acoustic study thus emphasizing the relevance of the splitting technique to capture accurately spray-acoustic interactions.

Le modèle multi-fluide permet de décrire par une approche Eulérienne les sprays polydispersés et apparaît donc comme une méthode indiquée pour les applications de combustion diphasique. Sa pertinence pour la simulation à l’échelle d’applications industrielles est évaluée dans ce travail, par sa mise en oeuvre dans des configurations bi-dimensionnelle et tri-dimensionnelle plus représentatives de ce type de simulations. Cette évaluation couple une étude de faisabilité en terme de coût de calcul avec une analyse de la précision obtenue, par des comparaisons avec les résultats de méthodes de références pour la description des sprays. Afin de définir une telle référence, une hiérarchisation des modèles de spray est proposée dans ce travail, soulignant les niveaux de modélisation associée aux diverses méthodes. Une première configuration d’écoulements tourbillonnaires est utilisée pour caractériser la méthode multi-fluide. L’étude de la structure mathématique du système de lois de conservation permet d’analyser la formation de singularités et de fournir les outils permettant d’évaluer leur impact sur la modélisation. Cette étude permet également de dériver un schéma numérique robuste et efficace pour des configurations bi- et tri-dimensionnelle. La description des dynamiques de gouttes conditionnées par la taille est évaluée dans ces configurations tourbillonnaires au moyen de comparaisons quantitatives, sur des champs instantanés, où le multi-fluide est confronté à une méthode Lagrangienne, ainsi qu’à des résultats expérimentaux. Afin d’évaluer le comportement de la méthode multi-fluide dans des configurations plus représentatives des problématiques industrielles, le solveur MUSES3D est développé, permettant, entre autres, une évaluation fine des méthodes de résolution des sprays. Une implémentation originale de la méthode multi-fluide, conciliant généricité et efficacité pour le calcul parallèle, est réalisée. Le couplage de ce solveur avec le code ASPHODELE, développé au CORIA, permet d’effectuer une évaluation opérationnelle des approches Euler/Lagrange et Euler/Euler pour la description des écoulements diphasiques à inclusions dispersées. Finalement, le comportement de la méthode multi-fluide dans des jets bi-dimensionnels et dans une turbulence homogène isotrope tri-dimensionnelle permet de montrer sa précision pour la description de la dynamique de sprays évaporant dans des configurations plus complexes. La résolution de la polydispersion du spray permet de décrire précisément la fraction massique de combustible en phase vapeur, un élément clé pour les applications de combustion. De plus, l’efficacité du calcul parallèle par décomposition de domaine avec la méthode multi-fluide permet d’envisager son utilisation à l’échelle d’applications industrielles. / The multi-fluid model, providing a Eulerian description of polydisperse sprays, appears as an interesting method for two-phase combustion applications. Its relevance as a numerical tool for industrial device simulations is evaluated in this work. This evaluation assesses the feasibility of multi-fluid simulations in terms of computational cost and analyzes their precision through comparisons with reference methods for spray resolution. In order to define such a reference, the link between the available methods for spray resolution is provided, highlighting their corresponding level of modeling. A first framework of 2-D vortical flows is used to assess the mathematical structure of the multi-fluid model governing system of equations. The link between the mathematical peculiarities and the physical modeling is provided, and a robust numerical scheme efficient for 2-D/3-D configurations is designed. This framework is also used to evaluate the multi-fluid description of evaporating spray sizeconditioned dynamics through quantitative, time-resolved, comparisons with a Lagrangian reference and with experimental data. In order to assess the multi-fluid efficiency in configurations more representative of industrial devices, a numerical solver is designed, providing a framework devoted to spray method evaluation. An original implementation of the multifluid method, combining genericity and efficiency in a parallel framework, is achieved. The coupling with a Eulerian/Lagrangian solver for dispersed two-phase flows, developed at CORIA, is conducted. It allows a precise evaluation of Euler/Lagrange versus Euler/Euler approaches, in terms of precision and computational cost. Finally, the behavior of the multi-fluid model is assessed in 2D-jets and 3-D Homogeneous Isotropic Turbulence. It illustrates the ability of the method to capture evaporating spray dynamics in more complex configurations. The method is shown to describe accurately the fuel vapor mass fraction, a key issue for combustion applications. Furthermore, the method is shown to be efficient in domain decomposition parallel computing framework, a key issue for simulations at the scale of industrial devices.

Les gouttes d’oxyde d’aluminium présentes en masse dans l’écoulement interne des moteurs-fusées à propergol solide ont tendance à influerde façon importante sur l’écoulement et sur le fonctionnement du moteur quel que soit le régime. L’objectif de la thèse est d’améliorerles modèles diphasiques eulériens présents dans le code de calcul semi-industriel pour l’énergétique de l’ONERA, CEDRE, en y incluant lapossibilité d’une dispersion locale des particules en vitesse en plus de la dispersion en taille déjà présente dans le code, tout en gardant unestructure mathématique bien posée du système d’équations à résoudre. Cette nouvelle caractéristique rend le modèle capable de traiter lescroisements de trajectoires anisotropes, principale difficulté des modèles eulériens classiques pour les gouttes d’inertie modérément grande.En plus de la conception et de l’analyse détaillée d’une classe de modèles basés sur des méthodes de moments, le travail se concentre sur larésolution des systèmes d’équations obtenus en configurations industrielles. Pour cela, de nouvelles classes de schémas précis et réalisables pourle transport des particules dans l’espace physique et l’espace des phases sont développées. Ces schémas assurent la robustesse de la simulationmalgré différentes singularités (dont des chocs, -chocs, zones de pression nulle et zones de vide...) tout en gardant une convergence d’ordredeux pour les solutions régulières. Ces développements sont conduits en deux et trois dimensions, en plus d’un référentiel bidimensionnelaxisymétrique, dans le cadre de maillages non structurés.La capacité des schémas numériques à maintenir un niveau de précision élevé tout en restant robuste dans toutes les conditions est un pointclé pour les simulations industrielles de l’écoulement interne des moteurs à propergol solide. Pour illustrer cela, le code de recherche SIERRA,originellement conçu durant les année 90 pour les problématiques d’instabilités de fonctionnement en propulsion solide, a été réécrit afin depouvoir comparer deux générations de modèles et de méthodes numériques et servir de banc d’essais avant une intégration dans CEDRE. Lesrésultats obtenus confirment l’efficacité de la stratégie numérique choisie ainsi que le besoin d’introduire, pour les simulations axisymétriques,une condition à la limite spécifique, développée dans le cadre de cette thèse. En particulier, les effets à la fois du modèle et de la méthodenumérique dans le contexte d’une simulation de l’écoulement interne instationnaire dans les moteurs-fusées à propergol solide sont détaillés.Par cette approche, les liens entre des aspects fondamentaux de modélisation et de schémas numériques ainsi que leurs conséquences pour lesapplications sont mis en avant. / The massive amount of aluminum oxide particles carried in the internal flow of solid rocket motors significantly influences their behavior.The objective of this PhD thesis is to improve the two-phase flow Eulerian models available in the semi-industrial CFD code for energeticsCEDRE at ONERA by introducing the possibility of a local velocity dispersion in addition to the size dispersion already taken into accountin the code, while keeping the well-posed characteristics of the system of equations. Such a new feature enables the model to treat anisotropicparticle trajectory crossings, which is a key issue of Eulerian models for droplets of moderately large inertia.In addition to the design and detailed analysis of a class of models based on moment methods, the conducted work focuses on the resolution ofthe system of equations for industrial configurations. To do so, a new class of accurate and realizable numerical schemes for the transport ofthe particles in both the physical and the phase space is proposed. It ensures the robustness of the simulation despite the presence of varioussingularities (including shocks, -shocks, zero pressure area and vacuum...), while keeping a second order accuracy for regular solutions. Thesedevelopments are conducted in two and three dimensions, including the two dimensional axisymmetric framework, in the context of generalunstructured meshes.The ability of the numerical schemes to maintain a high level of accuracy in any condition is a key aspect in an industrial simulation of theinternal flow of solid rocket motors. In order to assess this, the in-house code SIERRA, originally designed at ONERA in the 90’s for solidrocket simulation purpose, has been rewritten, restructured and augmented in order to compare two generations of models and numericalschemes, to provide a basis for the integration of the features developed in CEDRE. The obtained results assess the efficiency of the chosennumerical strategy and confirm the need to introduce a new specific boundary condition in the context of axisymmetric simulations. Inparticular, it is shown that the model and numerical scheme can have an impact in the context of the simulation of the internal flow ofsolid rocket motors and their instabilities. Through our approach, the shed light on the links between fundamental aspects of modeling andnumerical schemes and their consequences on the applications.