La méthode Smoothed Particle Hydrodynamics (SPH) est une méthode lagrangienne, sans maillage développée initialement pour des simulations de phénomènes astrophysiques. Depuis, elle a connu de nombreuses applications, notamment pour la simulation des écoulements des fluides. Contrairement aux méthodes utilisant un maillage, la méthode SPH peut gérer de manière naturelle et sans traitement spécifique les simulations des écoulements à sur- face libre et multiphasiques avec interface subissant de grandes déformations. Dans cette thèse, une modélisation SPH des écoulements des fluides multiphasiques a été réalisée en tenant compte de différentes complexités (écoulements à surface libre et multiphasiques interfacials) et de natures d'écoulement (si- mulation des fluides, des sols et les deux en interactions). Un modèle SPH faiblement compressible (WCSPH) a été proposé pour simuler les écoulements des fluides multiphasiques avec interface comprenant plus de deux phases de fluide. Ce modèle inclut le développement d’une nouvelle formulation de force de tension de surface en utilisant un opérateur SPH consistant de premier ordre. Une modification de condition généralisée aux parois solides a été apportée pour qu’elle soit appliquée sur les écoulements des fluides multiphasiques avec des rapports de densité et de viscosité élevés. Une nouvelle loi de comportement dépendant de la pression nommée RBMC-αμ ( Regularized Bingham Mohr Coulomb où αμ est un paramètre libre) a également été développée. Cette loi peut simuler les fluides (Newtonien, Binghamien), les sols (cohésif, frictionnel) et les deux en interactions. La loi précédente étant sensible à la pression, une extension du terme diffusif δ-SPH a été faite pour le cas des écoulements des fluides multiphasiques afin de réduire les oscillations de pression à haute fréquence qui sont dues à l’utilisation d’une équation d’état. La validation et l’application des modèles développés dans cette thèse sont montrées à travers plusieurs cas tests de difficulté croissante. / Smoothed Particle Hydrodynamics (SPH) is a Lagrangian gridless method developed initially to simulate astrophysical phenomena, and since it has been known for a large number of applications, especially for fluid flow simulations. Contrary to the grid-based method, the SPH method can handle free surface and interfacial fluid flow simulation including large deformations naturally and without the need for any specific treatment. In this thesis a SPH modeling of multiphase fluid flows has been achieved with consideration of different complexities ( free surface and interfacial fluid flows) and natures (simulation of fluids, soil and both in interactions). A consistent weakly compressible SPH model (WCSPH) has been proposed to simulate interfacial multiphase fluid flows with more than two fluid phases. This model includes a new expression of the surface tension force using a first order consistency SPH operator. A modification to the well known generalized wall boundary condition have been brought in order to be applied to multiphase fluid flow with large density and viscosity ratios. A new pressure-based constitutive law named RBMC-αμ (Regularized Bingham Mohr Coulomb with αμ is free parameter) has been developed in this thesis. This model can simulate fluids (Newtonian, Binghamton), soils (cohesive, frictional) and both in interactions. Because the previous model is pressure sensitive, an extension of δ-SPH diffusive term has been proposed for multiphase fluid flows to overcome the hight frequency pressure oscillations due to the determination of pressure from an equation of state. The validation and application of the developed models have been shown in this thesis through several test-cases of increasing difficulty.

In this thesis, a numerical method is developed for simulating non-isothermal multiphase flows, which are important in many technical applications such as crystal growth and welding. The method is based on the arbitrary Lagrangian Eulerian method of Li (2013). The interface is represented explicitly by mesh lines, and is tracked by an adaptive moving unstructured mesh. The $P2-P1d$ finite element method (FEM) is used for discretisation and the incompressible Navier-Stokes equations are solved by the uzawa method. Firstly, a thorough study is presented on the method's capability in numerically representing the force balance condition on the interface. An inaccurate representation of this condition induces the non-physical spurious currents, which degrade the simulation accuracy especially when the viscous damping is weak (small Ohnesorge number, $Oh$). For the example of a circular/spherical droplet, the interfacial tension and the associated pressure jump are exactly balanced numerically and thus the static Laplace solution exists in our method. The stability of this solution is examined numerically. The amplitude of the dimensionless spurious currents is found to be around $10^{−15}$ for $Oh \geq 10^{−3} $. Another benchmark test is the axisymmetric oscillation of a freesurface droplet/bubble. The simulation results are in good agreement with the analytical solution for $Oh = 10^{−3}$. This is by far the first successful simulation of droplet/bubble oscillation with such weak viscous damping and it demonstrates the ability of our method in simulating flows with strong capillary forces. Secondly, a numerical treatment of interface topology changes is incorporated into our method for studying problems with interface breakup. Thanks to the adaptive mesh generator, the thin region between the interface boundary and another boundary consists of one layer of elements. The interface topology change is performed once the minimum distance between the two boundaries falls below a pre-set scale $l_{breakup}$ . The numerical implementation is verified through two different examples: dripping faucet and droplet coalescence. Remarkably good agreement has been obtained with the experimental results. The simulation of the low Oh dripping problem shows both the accuracy and robustness of our method. The simulation of droplet coalescence demonstrates the great advantage of our method in solving problems with a large disparity in length scales. Finally, an FEM solver for temperature is developed and the non-isothermal effects are included in our method for the purpose of simulating non-isothermal multiphase flows. The modified method is validated to be accurate through three benchmark examples: natural convection in a cavity, thermocapillary convection of two layers, and droplet migration subject to a temperature gradient. Our method is then applied to investigate the liquid bridge breakup with thermocapillary effect. The non-isothermal liquid bridge breakup in the viscous and inertial regimes are studied. It has been found that the inertial regime breakup exhibits different pinchoff shapes as the Capillary number increases, and that the viscous regime breakup is accelerated by the thermocapillary motion.

L’étude des Réacteurs à Lit Bouillonnant (RLB) est à l’origine de ce projet de thèse. Ce type de réacteur chimique est très étudié en génie des procédés, en raison notamment de son utilisation pour l’hydrocraquage des charges lourdes. Des phénomènes complexes ont lieu dans un RLB, ce qui rend leur design et leur optimisation difficiles. Certains des mécanismes physiques prenant place dans les RLBs sont également des champs de recherche actifs en mécanique des fluides. Par conséquent, cette étude se concentre sur des mécanismes locaux participant à l’hydrodynamique des RLBs avec des catalyseurs cylindriques. Dans un premier temps, l’impact de l’anisotropie du catalyseur sur sa chute est étudié. Nous réalisons une étude expérimentale de la chute libre d’un cylindre en fluide au repos, afin de déterminer l’effet de l’anisotropie du corps sur sa dynamique. Les paramètres d’intérêt du problème sont le nombre d’Archimède du cylindre (Ar) et son rapport d’élongation (L/d). Les expériences sont menées avec deux caméras orthogonales, et des techniques de traitement d’images avancées sont développées pour parvenir à une mesure précise de la position et de l’orientation du corps en 3D. Pour (200 < Ar < 1100, 2 < L/d < 20), les cylindres adoptent différents types de trajectoire. Les deux principaux sont la chute rectiligne, durant laquelle l’axe du cylindre reste horizontal, et un mouvement de fluttering, qui est analysé en détail. D’autres types de mouvement plus complexes sont observés et discutés. De surcroît, le sillage du cylindre est analysé et caractérisé. De nombreuses particules sont présentes dans un RLB (40% de fraction massique environ). Les interactions entre ces corps multiples ont un impact fort sur le mouvement de chacun d’entre eux, mais sont très complexes. En première approximation, nous rendons compte de la présence de multiples particules en introduisant un milieu confiné. Nous étudions expérimentalement la chute d’un seul cylindre dans une cellule confinée verticale, dans laquelle le cylindre n’est libre de se mouvoir que dans deux directions. Le rapport d’élongation du cylindre (3<L/d<40) et son rapport de densité ( c / f = 1,16, 2,70, 4,50) sont les deux paramètres d’intérêt. Le nombre d’Archimède du cylindre se trouve entre les mêmes bornes qu’en milieu non confiné, et les deux modes principaux de mouvement sont aussi la chute rectiligne et le fluttering. Cependant, pour des paramètres (Ar,L/d) comparables, il existe des différences importantes dans le déplacement du cylindre comparé au cas non confiné. Nous avons également étudié l’interaction entre un cylindre en chute libre et un nuage de bullesascendantes. Cette étude a été menée expérimentalement dans la cellule confinée utilisée pour la seconde partie de la thèse. Des cylindres de plusieurs rapports de densité ( c / f = 1,16, 2,70, 4,50) and rapports d’élongation (3<L/d<20) ont été lâchés dans un nuage de bulles de fraction volumique de gaz comprise entre 2% et 5%. Plusieurs mécanismes d’interaction entre le cylindre et les bulles ont été identifiés (contact direct, interaction avec des perturbations du fluide. . .), et leur effet a été caractérisé. Nous avons effectué une étude statistique du mouvement du cylindre dans le nuage de bulles, et nous l’avons comparée aux résultats obtenus en milieu confiné et en fluide au repos. Les rapports de densité et d’élongation du cylindre jouent tous deux un rôle important dans son mouvement au sein du nuage de bulles. Des statistiques conditionnelles nous permettent d’approfondir notre analyse du contact entre le cylindre et les bulles, ainsi que du rôle de l’orientation du cylindre. Enfin, la dispersion du mouvement du cylindre dans le nuage est caractérisée. Un des principaux effets du nuage de bulles est d’accroître, via les contacts bulle cylindre, l’orientation du cylindre jusqu’à-ce qu’il soit presque vertical, ce qui a un effet très fort sur sa cinématique en comparaison avec le fluide au repos / The origin of this PhD thesis lies in the study of Ebullated Bed Reactors (EBRs). These chemical reactors are very active research topics in chemical processes, notably thanks to their usage in heavy oil processing. Many complex phenomena take place within EBRs, and make their design and optimization difficult. In fluid mechanics, a lot of physical mechanisms present in EBRs are active fields of study (three-phase flow, fluid-body interaction...). Hence, in the present work, a study of the mechanisms participating in the hydrodynamics of an EBR with cylindrical catalysts is performed. In a first part, the impact of the catalyst anisotropy on its fall is investigated. In order to gain insight on the effect of the body anisotropy on its fall dynamics, we investigate experimentally the free fall of a solid cylinder in a fluid at rest. The sensitivity to two dimensionless parameters, the Archimedes number (Ar) and the aspect ratio of the cylinder (L/d) is examined. Experiments are conducted with two orthogonal cameras, and advanced image processing techniques are developed in order to measure the position and orientation of the cylinder in 3D. Within the range of parameters studied (200 < Ar < 1100, 2 < L/d < 20), the cylinders adopt different types of falling motion. Two main types of paths are observed, the first one is a rectilinear fall of the cylinder that keeps its axis horizontal, and the second one is a fluttering oscillatory motion. Other more complex types of motion are observed and discussed. The fluttering motion of the cylinder is analyzed in details. On top of the study of the body motion, the cylinder wake is also visualized and characterized. A large number of particles are present at the same time inside an EBRs (about 40% of the mass). Interactions between multiple objects have a strong impact on the motion of each individual particle, but are very complex. In a first approximation, we take into account the presence of numerous particles by introducing a confined medium. We study experimentally the fall of a single cylinder in a confined vertical thin-gap cell, where the cylinders are free to move in only two directions. The cylinder elongation ratio (3<L/d<40) and density ratio ( c / f = 1.16, 2.70, 4.50) are the two parameters of interest. The Archimedes number of the cylinder lies within the same range as in the unconfined medium, and the two main modes of motion of the cylinder are a rectilinear motion, and a fluttering one. However, for the same parameters (Ar,L/d), the motion of the cylinder in the confined cell is strongly different in form to that in the unconfined medium. We also studied the interaction between a freely falling cylinder and a rising swarm of bubbles. This investigation was performed experimentally, in the confined cell used in the second part. Cylinders of various density ratio ( c / f = 1.16, 2.70, 4.50) and elongation ratio (3<L/d<20) are released in a bubble swarm of gas volume fraction between 2% and 5%. The cylinder motion is greatly modified by the bubble swarm. Several mechanisms of interaction between the cylinder and the bubbles are identified (direct contact, interactions with fluid perturbations...), and their effect is characterized. We perform a statistical analysis of the cylinder motion in the swarm, and compare it to results in the confined fluid at rest. The cylinder density ratio and elongation ratio both play an important role in its motion in the bubble swarm. Conditional statistics allow us to further investigate the effect of the contact between the cylinder and a bubble, and of the cylinder orientation in the swarm. Finally, the dispersion of the cylinder motion in the swarm is characterized. A major effect of the bubble swarm is to increase, through bubble-cylinder contacts, the probability of the cylinder to be in nearly vertical orientations. This drastically changes the kinematics of the cylinder as compared to its motion in the fluid at rest

This thesis reports an experimental investigation of low Reynolds number particle-laden turbulent flows in a horizontal plane channel. Experiments were conducted over a smooth wall and over two rough surfaces made from sand grain and gravel of relative roughness k/h ≈ 0.08 and 0.25, respectively, where k is the roughness height and h is the channel half-height. The flow was loaded with small solid particles with diameters less than 1/10 of the length scale of the energy-containing eddies, and whose concentrations decreased with time due to sedimentation. A novel particle image velocimetry (PIV) method that employed colour filtering for phase discrimination was used to measure the velocities of the fluid and solid particles. Over the smooth wall, the particles mean velocity, turbulence intensities and Reynolds shear stress matched those of the unladen flow very well. There were substantial differences between particle and fluid profiles over the rough wall, which include more rapid reduction in the particle mean velocity and significantly larger turbulence intensities and Reynolds shear stress compared to the unladen flow values. Stratification of the particle concentration led to attenuation of the fluid wall-normal turbulence intensity. This effect was nullified by the roughness perturbation leading to collapse of the wall-normal turbulence intensities over the rough wall. The streamwise turbulence intensity also collapsed over the rough wall but it was found that particles augmented the fluid Reynolds shear stress due to enhanced correlation between the rough wall streamwise and wall-normal velocity fluctuations. A quadrant decomposition of the fluid Reynolds shear stress also revealed corresponding enhancements in ejections and sweeps, the dominant contributors to the Reynolds shear stress, over the rough wall. Based on two-point correlations between the velocity fluctuations and between the velocity fluctuations and swirling strength, it was concluded that both wall roughness and particles modified the turbulence structure by increasing the size of the larger-scale structures. The idea of eddies growing from the wall, thereby enhancing communication between the inner layer and outer parts of the flow, has implications for wall-layer models that assume that the outer layer is detached from the turbulence in the inner region.

Cette travail de thèse est lié au besoin de modélisation des écoulements diphasiques en générateurs de vapeur (entrée liquide et sortie vapeur). La démarche proposée consiste à faire le choix d'une modélisation hybride de l'écoulement, en scindant la phase gaz en deux champs, modélisés de manières différentes. Ainsi, les petites bulles sphériques sont modélisées avec une approche dispersée classique avec le modèle eulérien à deux fluides, et les bulles déformées sont simulées à l'aide d'une méthode de localisation d'interface.Le travail effectué porte sur la mise en place, la vérification et la validation du modèle dédié aux larges bulles déformées, ainsi que le couplage entre les deux approches pour le gaz gaz, permettant des premiers calculs de démonstration utilisant l'approche hybride complète. / The present study is related to the need of modeling the two-phase flows occuring in a steam generator (liquid at inlet and vapour at outlet). The choice is made to investigate a hybrid modeling of the flow, considering the gas phase as two separated fields, each one being modeled with different closure laws. In so doing, the small and spherical bubbles are modeled through a dispersed approach within the two-fluid model, and the distorted bubbles are simulated with an interface locating method.The main outcome is about the implementation, the verification and the validation of the model dedicated to the large and distorted bubbles, as well as the coupling of the two approaches for the gas, allowing the presentation of demonstration calculations using the so-called hybrid approach.

abstract: Many physical phenomena and industrial applications involve multiphase fluid flows and hence it is of high importance to be able to simulate various aspects of these flows accurately. The Dynamic Contact Angles (DCA) and the contact lines at the wall boundaries are a couple of such important aspects. In the past few decades, many mathematical models were developed for predicting the contact angles of the inter-face with the wall boundary under various flow conditions. These models are used to incorporate the physics of DCA and contact line motion in numerical simulations using various interface capturing/tracking techniques. In the current thesis, a simple approach to incorporate the static and dynamic contact angle boundary conditions using the level set method is developed and implemented in multiphase CFD codes, LIT (Level set Interface Tracking) (Herrmann (2008)) and NGA (flow solver) (Desjardins et al (2008)). Various DCA models and associated boundary conditions are reviewed. In addition, numerical aspects such as the occurrence of a stress singularity at the contact lines and grid convergence of macroscopic interface shape are dealt with in the context of the level set approach. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2015

abstract: The atomization of a liquid jet by a high speed cross-flowing gas has many applications such as gas turbines and augmentors. The mechanisms by which the liquid jet initially breaks up, however, are not well understood. Experimental studies suggest the dependence of spray properties on operating conditions and nozzle geom- etry. Detailed numerical simulations can offer better understanding of the underlying physical mechanisms that lead to the breakup of the injected liquid jet. In this work, detailed numerical simulation results of turbulent liquid jets injected into turbulent gaseous cross flows for different density ratios is presented. A finite volume, balanced force fractional step flow solver to solve the Navier-Stokes equations is employed and coupled to a Refined Level Set Grid method to follow the phase interface. To enable the simulation of atomization of high density ratio fluids, we ensure discrete consistency between the solution of the conservative momentum equation and the level set based continuity equation by employing the Consistent Rescaled Momentum Transport (CRMT) method. The impact of different inflow jet boundary conditions on different jet properties including jet penetration is analyzed and results are compared to those obtained experimentally by Brown & McDonell(2006). In addition, instability analysis is performed to find the most dominant insta- bility mechanism that causes the liquid jet to breakup. Linear instability analysis is achieved using linear theories for Rayleigh-Taylor and Kelvin- Helmholtz instabilities and non-linear analysis is performed using our flow solver with different inflow jet boundary conditions. / Dissertation/Thesis / Ph.D. Mechanical Engineering 2013

Simulações de escoamentos multifásicos são de grande interesse em aplicações práticas na indústria, em particular na indústria petrolífera, entre outras. Vários processos dependem do entendimento físico de escoamentos envolvendo iteração com partículas, sedimentação e separação de fluidos. Dos muitos métodos existentes para a simulação dos processos acima descritos, há um crescente interesse no aumento de precisão, o que levou ao desenvolvimento de estratégias que utilizam esquemas de elementos finitos discretizados em malhas dinâmicas e adaptativas, usando uma formulação ALE (do inglês, Arbitrary Lagrangian-Eulerian), juntamente com uma representação geométrica da interface. Neste sentido, este trabalho tem o objetivo de estudar e implementar estratégias robustas de controle e adaptação de malhas, em situações onde a malha dinâmica é sujeita a grandes deformações. Uma biblioteca de algoritmos e rotinas foi então desenvolvida para este fim, implementando técnicas de controle e otimização da qualidade dos elementos da malha, técnicas de adaptação da interface entre fluidos com esquemas de conservação de massa, técnicas de mudanças topológicas e preservação de propriedades materiais, além de uma comunicação facilitada destas rotinas com códigos de simulação numérica de escoamentos multifásicos existentes / Multiphase flow simulations are of great interest in practical applications, particularly in the oil industry. Several processes depend on understanding physical aspects of flows with particle interaction, sedimentation and fluid separation. Among the several existing methods to simulate the processes described above, theres a growing interest in achieving higher precision, which led to the development of strategies that use finite element discretization in adaptive, dynamic meshes, using the ALE formatulation along with a geometrical representation of the interface. In this context, this thesis aims to study and implement robust strategies for mesh adaptation, for cases where the dynamic mesh is subject to large deformations. A library of routines and algorithms was developed, implementing mesh elements control and quality optimization techniques, fluid interface adaptation techniques with a mass conservation scheme, topological modifications and material properties preservation techniques, and also a decoupled, simplified communication between these routines with existing multiphase flow numerical simulation code

L'objectif de ces travaux est de déterminer l'atténuation des effets d'une explosion sous-marine par un rideau de bulles. Dans ce cadre, une modélisation de la propagation d'un chocdans les liquides à bulles a été développée, basée sur une technique de transition d'échelles.Cette méthode permet la formulation de modèles continus de liquides aérés, dont la mise enoeuvre est aisée et rapide. Nous avons d'abord développé une modélisation pour des liquidesdiphasiques au sein desquels les bulles sont régulièrement réparties dans l'espace, avant deproposer une extension de ce modèle au cas des liquides à bulles présentant des hétérogénéitésde porosité sous la forme d'amas sphériques de bulles. Un modèle de fragmentation des bulleslors du passage du choc a également été développé, basé sur une analyse linéaire de stabilitédes bulles. L'étude a permis d'établir un critère prédictif de fission et de déterminer le nombrede fragments associés. L'ensemble des modélisations proposées a fait l'objet de comparaisonsavec des résultats expérimentaux issus de la littérature. La concordance entre résultats d'essaiset résultats issus de la modélisation démontre les capacités prédictives de l'approche proposée.Cette modélisation a enfin été appliquée au cas de rideaux de bulles soumis à une explosionsous-marine. Une étude de sensibilité sur les paramètres physiques du rideau a été menée, eta permis de confirmer les tendances expérimentales : sous certaines conditions, la dispositiond'un rideau de bulles sous l'eau permet de diminuer de façon très conséquente l'énergie duchoc transmis en aval du rideau. / The present work deals with the modelling of shock wave propagation in bubbly liquids, inorder to assess the damping of underwater explosion by bubble curtains. The modelling is basedon a scale transition technique, which allows to formulate efficient continuum models of bubblyliquids. A modelling of homogeneous bubbly liquids has first been proposed, then extended tothe case of liquids with spherical bubble clusters. A modelling of bubble fragmentation duringshock propagation has also been developed, based on a stability analysis of the bubbles. Thisstudy enables us to establish a criterion for bubble fission and to determine the numberof fragments. The accuracy of the proposed models has been assessed through comparisonwith experimental data of the literature. The agreement between numerical and experimentalresults proves the predictive capabilities of the whole approach. The modelling has then beenapplied to the mitigation of UNDEX-induced shock wave by bubble curtain. A sensitive studyabout physical parameters of the curtain has been performed, and confirms the experimentaltendencies : the use of a bubble curtain can dissipate a significant part of the shock energy.

Flash boiling may be defined as the finite-rate mechanism that governs phase change in a high temperature liquid that is depressurized below its vapor pressure. This is a transient and complicated phenomenon which has applications in many industries. The main focus of the current work is on modeling flash boiling in injectors used in engines operating on the principle of gasoline direct injection (GDI). These engines are prone to flash boiling due to the transfer of thermal energy to the fuel, combined with the sub-atmospheric pressures present in the cylinder during injection. Unlike cavitation, there is little tendency for the fuel vapor to condense as it moves downstream because the fuel vapor pressure exceeds the downstream cylinder pressure, especially in the homogeneous charge mode. In the current work, a pseudo-fluid approach is employed to model the flow, and the non-equilibrium nature of flash boiling is captured through the use of an empirical time scale. This time scale represents the deviation from thermal equilibrium conditions. The fuel composition plays an important role in flash boiling and hence, any modeling of this phenomenon must account for the type of fuel being used. In the current work, standard, NIST codes are used to model single component fluids like n-octane, n-hexane, and water, and a multi-component surrogate for JP8. Additionally, gasoline-ethanol blends are also considered. These mixtures are azeotropic in nature, generating vapor pressures that are higher than those of either pure component. To obtain the properties of these fuels, two mixing models are proposed that capture this non-ideal behavior. Flash boiling simulations in a number of two and three dimensional nozzles are presented, and the flow behavior and phase change inside the nozzles is analyzed in detail. Comparison with experimental data is performed in cases where data are available. The results of these studies indicate that flash boiling significantly affects the characteristics of the nozzle spray, like the spray cone angle and liquid penetration into the cylinder. A parametric study is also presented that can help understand how the two different time scales, namely the residence time in the nozzle and the vaporization time scale, interact and affect the phenomenon of flash boiling.