Modelling of laminar multiphase flow is extremely important in a wide range of engineering and scientific applications. The particle phases are often difficult to model, especially when particles display a range of sizes and velocities at each location in space. Lagrangian methods can be too expensive and many Eulerian methods, though often computationally more affordable, suffer from model deficiencies and mathematical artifacts that lead to non-physical results. For example, efficient Eulerian models that can accurately predict the crossing of multiple streams of non-interacting particles in laminar flow have traditionally been lacking. The predictive capabilities of modern techniques from the kinetic theory of gases to the treatment of disperse multiphase flows are investigated. In particular, several moment-methods, including a recently proposed fourteen-moment approximation to the underlying kinetic equation describing particle motion, are considered and their abilities to predict particle-stream crossing are assessed. Furthermore, a new polydisperse model has been proposed for treatment of flows that display a range of particles sizes. The proposed model is an extension of the well-known maximum-entropy ten-moment model from rarefied gas dynamics with an addition for the treatment of a range of particle diameters. This model allows for anisotropic variance of particle velocities in phase space and directly treats correlations between particle diameter and velocity. The derivation and mathematical structure, of the proposed models are presented. A fine-volume discretization solution procedure for the resulting moment equations is described and used for performing numerical experiments. Results for flow problems that are designed to demonstrate the fundamental behaviour of each model are presented. It is shown that the new models offer clear advantages in terms of accuracy as compared to traditional Eulerian models for multiphase flows.

Die Charakterisierung von Nanopartikeln erfordert eine Messung des Dispersitätszustandes bei allen Schritten der Herstellung - von der Synthese bis zum fertigen Produkt. Dafür ist eine leistungsfähige Partikelmesstechnik notwendig, deren Methoden bei der Beschreibung des komplexen Materialverhaltens helfen können. Die Ultraschalldämpfungsspektroskopie ist eine Messmethode, die zur prozessbegleitenden Charakterisierung hochdisperser Pulver und Suspensionen geeignet ist. Mit Vergleichen von Messungen und Modellrechungen wurde festgestellt, dass für die Ultraschalldämpfungs-Modellierung in Dispersionen homogener Partikel ein auf dem Phänomen der elastischen Streuung basierendes Modell praktisch relevant ist. Dies betrifft sowohl die Anwendung zur Messung in Suspensionen als auch in Emulsionen homogener Partikel. Bei einem Vergleich von Modellrechungen und Messungen für ein System poröser Partikel bzw. Aggregate wurde das Modell der Streuung an poroelastischen Kugeln als geeignet zur Beschreibung der Dämpfung disperser Systeme identifiziert. Bei Vorhandensein grober Partikel in Suspensionen nanoskaliger Systeme ist somit eine korrekte Auswertung der Partikelgröße möglich; der bislang übliche Messbereich wurde erweitert. Sekundärer Schwerpunkt der Arbeit ist die Diskussion der numerischen Modellanwendung. Es werden weiterhin Lösungsmöglichkeiten zur Dämpfungsberechnung und zur Berechnung der Größenverteilungen beschrieben. Des Weiteren wurden Anregungen für Entwickler von Ultraschallspektrometern abgeleitet.

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.

Une étude expérimentale sur le transfert des particules en suspension dans les milieux poreux est menée au laboratoire sur des colonnes remplies de sable en utilisant des techniques de traçage. Les effets du milieu poreux, de la taille des particules et de la polydispersivité de ces particules sur leur transport et dépôt sont étudiés. Des injections impulsion et des injections en continue de particules en suspension monodisperses (Latex) et polydisperses (Kaolinite) à différentes vitesses d’écoulement ont été réalisées. Deux milieux poreux de granulométries serrées et un troisième milieu poreux constitué du mélange des deux précédents sont utilisés. Par ailleurs, pour étudier l’effet de la taille et de de la polydispersivité des particules injectées, trois populations monodisperses de particules de latex ainsi que trois mélanges de ces dernières ont été utilisés. Les paramètres caractérisant le transport et le dépôt des particules en suspension sont déterminés en utilisant la solution analytique de l’équation convection-dispersion avec une cinétique de dépôt de premier ordre. L’effet de sélection de taille est étudié à partir des analyses granulométriques des particules prélevées dans les effluents à différents moments de la restitution et des particules déposées à différents horizons dans le milieu poreux. Les résultats ont montré que la vitesse d’écoulement, la distribution granulométrique du milieu poreux, la taille et la polydispersivité des particules en suspension jouent un rôle important dans le transport et le dépôt dans les milieux poreux. / An experimental study on the transfer of suspended particles in porous media is conducted in laboratory columns filled with sand using tracing techniques. The effects of the porous medium, the particle size and the polydispersity of the particles on their transport and deposition are investigated. Pulse injections and continuous injections of monodisperse suspended particles (latex) and polydisperse (kaolinite) under different flow velocities were performed. To study the effect of porous media grain size distribution on the transport and deposition of polydisperse suspended particles, three sands filled columns were used : Fine sand, Coarse sand, and a third sand obtained by mixing the two last sands in equal weight proportion. Furthermore, to investigate the effects of size and polydispersivity of the suspended particles, three populations of monodisperse latex particles and a forth population obtained by mixing the last three populations in equal volume proportion were used. The transport and deposition parameters of suspended particles were determined using the analytical solution of convection-dispersion equation with a first order deposition kinetics. The size selection effect is analyzed using particle-size analysis of the recovered particles in the effluent at different time intervals of injection and the deposited particles in the porous medium. The results showed that the flow velocity, porous media grain size distribution, the size and the polydispersity of the suspended particles play an important role in the transport and the deposition in porous media.

Modelling multiphase flow, more specifically particle-laden flow, poses multiple challenges. These difficulties are heightened when the particles are differentiated by a set of “internal” variables, such as size or temperature. Traditional treatments of such flows can be classified in two main categories, Lagrangian and Eulerian methods. The former approaches are highly accurate but can also lead to extremely expensive computations and challenges to load balancing on parallel machines. In contrast, the Eulerian models offer the promise of less expensive computations but often introduce modelling artifacts and can become more complicated and expensive when a large number of internal variables are treated. Recently, a new model was proposed to treat such situations. It extends the ten-moment Gaussian model for viscous gases to the treatment of a dilute particle phase with an arbitrary number of internal variables. In its initial application, the only internal variable chosen for the particle phase was the particle diameter. This new polydisperse Gaussian model (PGM) comprises 15 equations, has an eigensystem that can be expressed in closed form and also possesses a convex entropy. Previously, this model has been tested in one dimension. The PGM was developed with the detonation of radiological dispersal devices (RDD) as an immediate application. The detonation of RDDs poses many numerical challenges, namely the wide range of spatial and temporal scales as well as the high computational costs to accurately resolve solutions. In order to address these issues, the goal of this current project is to develop a block-based adaptive mesh refinement (AMR) implementation that can be used in conjunction with a parallel computer. Another goal of this project is to obtain the first three-dimensional results for the PGM. In this thesis, the kinetic theory of gases underlying the development of the PGM is studied. Different numerical schemes and adaptive mesh refinement methods are described. The new block-based adaptive mesh refinement algorithm is presented. Finally, results for different flow problems using the new AMR algorithm are shown, as well as the first three-dimensional results for the PGM.

No description available.

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.

Die Charakterisierung von Nanopartikeln erfordert eine Messung des Dispersitätszustandes bei allen Schritten der Herstellung - von der Synthese bis zum fertigen Produkt. Dafür ist eine leistungsfähige Partikelmesstechnik notwendig, deren Methoden bei der Beschreibung des komplexen Materialverhaltens helfen können. Die Ultraschalldämpfungsspektroskopie ist eine Messmethode, die zur prozessbegleitenden Charakterisierung hochdisperser Pulver und Suspensionen geeignet ist. Mit Vergleichen von Messungen und Modellrechungen wurde festgestellt, dass für die Ultraschalldämpfungs-Modellierung in Dispersionen homogener Partikel ein auf dem Phänomen der elastischen Streuung basierendes Modell praktisch relevant ist. Dies betrifft sowohl die Anwendung zur Messung in Suspensionen als auch in Emulsionen homogener Partikel. Bei einem Vergleich von Modellrechungen und Messungen für ein System poröser Partikel bzw. Aggregate wurde das Modell der Streuung an poroelastischen Kugeln als geeignet zur Beschreibung der Dämpfung disperser Systeme identifiziert. Bei Vorhandensein grober Partikel in Suspensionen nanoskaliger Systeme ist somit eine korrekte Auswertung der Partikelgröße möglich; der bislang übliche Messbereich wurde erweitert. Sekundärer Schwerpunkt der Arbeit ist die Diskussion der numerischen Modellanwendung. Es werden weiterhin Lösungsmöglichkeiten zur Dämpfungsberechnung und zur Berechnung der Größenverteilungen beschrieben. Des Weiteren wurden Anregungen für Entwickler von Ultraschallspektrometern abgeleitet.

The thesis involves computer simulation and theoretical studies of dynamics of water under confinement and structural transformation in different complex systems. Based on the systems and phenomena of interest, the work has been classified in to three major parts: I. Dynamics of water under confinement II. Dynamics of water in presence of amphiphilic solutes III. Structural transformation in complex systems The three parts have further been divided into nine chapters. Brief chapter wise outline of the thesis is discussed below. Part I deals with the dynamics of water in confined systems. In Chapter I.1, we provide a brief introduction of water dynamics inc on fined systems. We also give a brief outline of relevant experimental and theoretical techniques used to study the water dynamics under confinement. Chapter I.2 describes a model based analytical study of dynamical correlation in confined systems. Here, we introduce a novel one dimensional Ising model to investigate the propagation and annihilation of dynamical correlations in confined systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles (RMs).In our model, the two spins located at the two end cells are oriented in the opposite directions to mimic the surface effects present in the real systems. These produce opposing polarizations which propagate from the surface to the center, thus producing bulk like condition at the center. This model can be solved analytically for short chains. For long chains, we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm).We show that the model satisfactorily reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is non-exponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of the relaxation of spins undergoes a change with the emergence of homogeneous dynamics, where the decay is predominantly exponential. In Chapter I.3, layer-wise distance dependent orientation relaxation of water confined in reverse micelle s(RM)is studied using theoretical and computational tools. We use both a newly constructed spins on a ring (SOR) Ising-type model with modified Shore-Zwanzig rotational dynamics and atomistic simulations with explicit water. Our study explores the size effect of RMs and the role of intermolecular correlations, compromised by the presence of a highly polar surface, on the distance (from the surface) dependence of water relaxation. The SOR model can capture some aspects of distance dependent orientation relaxation, such as acceleration of orientation relaxation at intermediate layers. In atomistic simulations, layer-wise decomposition of hydrogen bond (H-bond) formation pattern clearly reveal that the H-bond arrangement of water at a certain distance away from the surface can remain frustrated due to interaction with the polar surface head groups. We show that this layer-wise analysis also reveals the presence of a non-monotonic, slow relaxation component which can be attributed to the frustration effect and is accentuated in small to intermediate size RMs. For larger RMs, the long-time component decreases monotonically from the interface to the interior of the RMs with slowest relaxation observed at the interface. In ChapterI.4, we present theoretical two dimensional infrared spectroscopic (2D-IR) studies of water confined within RMs of various sizes. Here we focus again mainly on the altered dynamics of confined water by performing a layer-wise decomposition of water. We aim to quantify the relative contributions to the calculated 2D-IR spectra by water molecules located in different layers. The spectra of 0-1 transition clearly show substantial elongation along the diagonal, due to in homogeneous broadening and incomplete spectral diffusion, in the surface water layer of different size of RMs studied in this work. Our study reveals that the motion of the surface water molecules is sub-diffusive, establishing the constrained nature of their dynamics. This is further supported by the two peak nature of the angular analogue of the van Hove correlation function. With increasing system size the motion of water molecules becomes more diffusive in nature and the structural diffusion is observed to be almost completed in the central layer of larger RMs. Comparisons between experiment and simulation help establishing the correspondence between the spectral decomposition available in experimental 2D-IR with the spatial decomposition of simulated 2D-IR. Simulations also allow a quantitative exploration of the relative role of water, sodium ions and sulfonate head groups in irrational dephasing. Interestingly, the negative cross correlation between forces on oxygen and hydrogen of O-H bond in bulk water significantly decreases in the surface layer of different RMs. This negative cross correlation gradually increases in the central layer with increasing size of the RMs and this is found to be partly responsible for the faster relaxation rate of water in the central layer. Part II consists of two chapters and focuses on the dynamics of water in presence of amphiphilic solutes. In Chapter II.1, we present a brief introduction of water – DMSO binary mixture and various anomalous properties of the same. In Chapter II.2, we present theoretical IR study of water dynamics in water–DMSO binary mixtures of different compositions. We show that with increasing DMSO concentration, the IR absorption peak maxima show the presence of structural transformation in similar concentration range, observed in earlier studies. Analysis of H-bonded network near hydrophilic and hydrophobic part of DMSO also suggests that average number of hydrogen bonds near the hydrophobic parts possess maxima at the same concentration range. We also show that with increasing DMSO concentration water dynamics becomes very slow. This has been supported by the diagonal elongation of the 2D-IR spectra and also the slow decay of frequency fluctuation correlation n function (FFCF) and the orientation time correlation function (OTCF). The decoupling of the OTCF establishes that water-DMSOH-bond is much stronger than that of water-water. The last part (Part III) consists of three chapters that deal with structural transformation in various complex systems. In Chapter III.1, we introduce polydisperse systems and present existing theoretical, computer simulation and experimental studies. It also contains the importance and diversity of polydisperse system in nature. In Chapter III.2, we present computer simulation study of melting of polydisperse Lennard-Jones (LJ) system with Gaussian polydispersity in size. The phase diagram reproduces the existence of an early temperature in variant terminal polydispersity (δt0.11), with no signature of re-entrant melting. The absence of re-entrant melting can be attributed to the influence of attractive part of the potential on melting. We find that at terminal polydispersity the fractional density change approaches zero that seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction system undergoes a sharp transition from crystalline solid to disordered state with increasing polydispersity. This has been quantified by second and third order rotational invariant bond orientational orders as well as by the average inherent structure energy. The translational order parameter also indicates similar structural change The free energy calculation further supports the nature of the transition. The third order bond orientational order shows that with increasing polydispersity, local cluster favors more icosahedral-like arrangements and thus the system loses its crystalline symmetry. In Chapter III.3, we present study of phase transition and effect of confinement on it in SOR model. This system is similar to our SOR model discussed in Chapter I.3. The spins execute continuous rotation under a modified XY Hamiltonian. In order to understand the nature of phase transition in such confined spin systems we have performed extensive Monte Carlo simulations. The system size dependence of Binders cumulant, specific heat, order parameter and finite size scaling of order parameter universally suggest the existence of a phase transition. The absence of hysteresis and Scaling of Binders energy cumulant minimum confirm the continuous nature of the transition. The finite size scaling analyses give rise to the mean field nature of the transition. Plausible applications of the proposed model in modeling dipolar liquids in confined systems are also discussed. In Appendix A, we discuss a preliminary study of front propagation in a non-equilibrium system. The model system analogous to the super cooled liquid shows non-Avrami domain growth during rejuvenation. The origin of the non-Avrami nature of the domain growth and the presence of cross over are also discussed. In Appendix B, we discuss umbrella a sampling technique and WHAM analysis which is used in ChapterIII.2 to get the free energy of polydisperse LJ system.

L’injection directe à haute pression du carburant dans les moteurs à combustion interne permet une atomisation compacte et efficace. Dans ce contexte, la simulation numérique de l’injection est devenue un outil fondamental pour la conception industrielle. Cependant,l’écoulement du carburant liquide dans une chambre occupée initialement par l’air est un écoulement diphasique très complexe ; elle implique une très large gamme d’échelles. L’objectif de cette thèse est d’apporter de nouveaux éléments de modélisation et de simulation afin d’envisager une simulation prédictive de ce type d’écoulement avec un coût de calcul abordable dans un contexte industriel. En effet, au vu du coût de calcul prohibitif de la simulation directe de l’ensemble des échelles spatiales et temporelles, nous devons concevoir une gamme de modèles d’ordre réduit prédictifs. En outre, des méthodes numériques robustes, précises et adaptées au calcul de haute performance sont primordiales pour des simulations complexes.Cette thèse est dédiée au développement d’un modèle d’ordre réduit Eulérien capable de capter tant la polydispersiond’un brouillard de goutte dans la zone dispersée,que la dynamique de l’interface dans le régime de phases séparées. En s’appuyant sur une extension des méthodes de moments d’ordre élevé à des moments fractionnaires qui représentent des quantités géométriques de l’interface, et sur l’utilisation de variables géométrique sen sous-échelle dans la zone où l’interface gaz-liquide ne peut plus être complètement résolue, nous proposons une approche unifiée où un ensemble de variables géométriques sont transportées et valides dans les deux régimes d’écoulement [...]. / Direct fuel injection systems are widely used in combustionengines to better atomize and mix the fuel withthe air. The design of new and efficient injectors needsto be assisted with predictive simulations. The fuel injectionprocess involves different two-phase flow regimesthat imply a large range of scales. In the context of thisPhD, two areas of the flow are formally distinguished:the dense liquid core called separated phases and thepolydisperse spray obtained after the atomization. Themain challenge consists in simulating the combinationof these regimes with an acceptable computational cost.Direct Numerical Simulations, where all the scales needto be solved, lead to a high computational cost for industrialapplications. Therefore, modeling is necessaryto develop a reduced order model that can describe allregimes of the flow. This also requires major breakthroughin terms of numerical methods and High PerformanceComputing (HPC).This PhD investigates Eulerian reduced order models todescribe the polydispersion in the disperse phase andthe gas-liquid interface in the separated phases. First,we rely on the moment method to model the polydispersionin the downstream region of the flow. Then,we propose a new description of the interface by usinggeometrical variables. These variables can provide complementaryinformation on the interface geometry withrespect to a two-fluid model to simulate the primary atomization.The major contribution of this work consistsin using a unified set of variables to describe the tworegions: disperse and separated phases. In the case ofspherical droplets, we show that this new geometricalapproach can degenerate to a moment model similar toEulerian Multi-Size Model (EMSM). However, the newmodel involves fractional moments, which require somespecific treatments. This model has the same capacityto describe the polydispersion as the previous Eulerianmoment models: the EMSM and the multi-fluid model.But, it also enables a geometrical description of the interface...].