Numerical simulation of cell motility is one of the difficult problems in computational science. It belongs to a class of problems which involve moving interfaces between flowing or deforming media. Different numerical techniques are being developed for different application areas and in this work an attempt is made to apply two popular numerical techniques used in the field of computational multiphase flows to a cell motility problem. An unsteady cell motility problem is considered to simulate numerically based on a two-dimensional mathematical model. Two important numerical methods, the Level set method and the Front tracking methods are applied to the cell motility problem to study several cases and to verify the convergence of the solution. With the assumption of no mechanical or physical obstructions to the cell, the results of the numerical simulations show that the domain shapes converge to a circular shape as they reach the steady state condition. The final steady state velocities with which the domains move and the final steady state area to which they converge are observed to be independent of domain shapes. Moreover all shapes converge to exactly same radius of circle and move with same velocity after reaching steady state condition.

Aluminum and its alloys are used in many aspects of modern life, from soda cans and household foil to the automobiles and aircraft in which we travel. Aluminum alloy systems are characterized by good workability that enables these alloys to be economically rolled, extruded, or forged into useful shapes. Mechanical properties such as strength are altered significantly with cold working, annealing, precipitation-hardening, and/or heat-treatments. Heat-treatable aluminum alloys contain one or more soluble constituents such as copper, lithium, magnesium, silicon and zinc that individually, or with other elements, can form phases that strengthen the alloy. Microstructure development is highly dependent on all of the processing steps the alloy experiences. Ultimately, the macroscopic properties of the alloy depend strongly on the microstructure. Therefore, a quantitative understanding of the microstructural changes that occur during thermal and mechanical processing is fundamental to predicting alloy properties. In particular, the microstructure becomes more homogeneous and secondary phases are dissolved during thermal treatments. Robust physical models for the kinetics of particle dissolution are necessary to predict the most efficient thermal treatment. A general dissolution model for multi-component alloys has been developed using the front-tracking method to study the dissolution of precipitates in an aluminum alloy matrix. This technique is applicable to any alloy system, provided thermodynamic and diffusion data are available. Treatment of the precipitate interface is explored using two techniques: the immersed-boundary method and a new technique, termed here the sharp-interface method. The sharp-interface technique is based on a variation of the ghost fluid method and eliminates the need for corrective source terms in the characteristic equations. In addition, the sharp-interface method is shown to predict the dissolution behavior of precipitates in aluminum alloys when compared with published experimental results. The influence of inter-particle spacing is examined and shown to have a significant effect on dissolution kinetics. Finally, the impact of multiple particles of various sizes interacting in an aluminum matrix is investigated. It is shown that smaller particles dissolve faster, as expected, but influence the dissolution of larger particles through soft-impingement, even after the smaller particles have disappeared.

In this thesis we report the results of investigations on the rheological response of emulsions to the application of the electric field. A front-tracking finite difference scheme is used in conjunction with Taylor-Melcher leaky dielectric theory to study the problem. The numerical results in different regions of the deformation-circulation map show that the structure formation in regions I and III can be hindered by the hydrodynamic effect. This is opposite to what is observed in the perfect dielectric cases and region II of the map. For perfect dielectric systems, where the electrohydrodynamics effects are absent, droplets form chain-like structures spanning the distance between the electrodes after the application of the electric field. Subsequently, the chains interact with each other to form columns comprising two or more chains. Point-dipole approximation is used to analyze the structure formation and it is shown that it is also applicable to region II where the hydrodynamic effect is weak and the behavior of the system is mainly governed by the dielectrophoretic forces. It is shown that the chain formation is not possible in regions I and III due to the competition between the dipolar force and torque on one side and hydrodynamic effect on the other side. In region I, the hydrodynamic torque prevents the chain formation by competing with the dipolar torque, which tends to align the drops with the electric field. On the other hand, in region III, the repulsive nature of the hydrodynamic effect opposes the attractive dipolar force and does not allow the particles to form stable chains.

Le CEA aspire à la création d'un réacteur nucléaire numérique qui nécessite une grande connaissance des écoulements diphasiques. Dans le but d'améliorer notre compréhension des scénarios accidentels, cette thèse s’attache à étudier et à modéliser la dynamique complexe des écoulements à bulles. Les principaux enjeux de la thèse sont d’étudier et de modéliser les forces interfaciales responsables de la migration des bulles ainsi que de proposer un modèle de turbulence à la hauteur de la connaissance actuelle des phénomènes. Afin d'atteindre ces objectifs, une base de données statistique est réalisée à partir d'expériences numériques (simulations numériques directes) d'essaims et de canaux à bulles. Une nouvelle méthode de modélisation des forces interfaciales est développée. Elle révèle une nouvelle force baptisée force de dispersion laminaire qui a un rôle important dans la migration des bulles. Un modèle de cette force est donc proposé. La turbulence dans les écoulements à bulles est constituée de SPT (Single Phase Turbulence), de WIT (Wake Induced Turbulence) et de WIF (Wake Induced Fluctuations). Le SPT est la turbulence issue du cisaillement moyen, le WIT représente les fluctuations temporelles turbulentes issue de la déstabilisation collectives des sillages, et le WIF est fait de fluctuations spatiales engendrées par le sillage moyen. Dans cette thèse, nous proposons une nouvelle forme de modélisation à trois équations de la turbulence, où chaque contribution possède sa propre fermeture. Le modèle à trois équations tensorielles ainsi écrit est complet et peut être dès aujourd'hui utilisé dans un code de calcul moyenné. / The CEA aspires to create a numerical nuclear reactor which requires a great knowledge of two-phase flows. In order to improve our understanding of accidental scenarios, this thesis focuses on studying the complex dynamics of bubbly flows in order to model them. The main challenges of the thesis are to study and model the interfacial forces responsible for the migration of bubbles as well as to propose a model of turbulence in agreement with the current knowledge of the phenomena. In order to achieve these objectives, a statistical database is produced from numerical experiments (direct numerical simulations) of swarms and bubble channels. In this thesis, a new method for interfacial forces modeling is developed. It reveals a new force coined as laminar dispersion force. This force has an important role in bubble migration. It is then modeled and validated on five simulations of bubble channels. Concerning turbulence in bubbly flows, it is comprised of SPT (Single Phase Turbulence), WIT (Wake Induced Turbulence) and WIF (Wake Induced Fluctuations) which characterize distinct phenomena. The SPT is the turbulence produced by the averaged shear, the WIT represent the temporal and turbulent fluctuations due to destabilizations and collective instabilities of wakes, and the WIF reflect the spatial fluctuations generated by the averaged wake and the potential flow around the bubbles. In this thesis, we propose a tensorial three-equations modeling of turbulence, where each contribution has its own closure. The tensorial three-equation model is complete and can be assessed as of now in an averaged calculation code.

Ce travail de thèse est consacré à la modélisation et simulation numérique d'écoulements diphasiques liquide-gaz mettant en jeu des transferts de chaleur. La simulation de configurations où la prise en compte des effets de compressibilité de la phase gazeuse est indispensable (micropompes, microactionneurs, etc...) a nécessité l'utilisation d'un modèle original, considérant le liquide incompressible et le gaz compressible sous l'hypothèse faible Mach. Lors de cette thèse, ce modèle a été implémenté dans un code diphasique prenant en compte l'interface à l'aide d'une méthode de front-tracking. Des cas tests ont été développés spécifiquement afin de vérifier la conservation de l'énergie pour des configurations de complexité croissante. Les résultats des cas tests ont permis de mettre en évidence la difficulté à assurer la conservation de l'énergie lorsque l'interface n'est pas discontinue mais lissée, comme c'est le cas dans la méthode de front-tracking standard. Une méthode de traitement d'interface hybride a été proposée, rétablissant le caractère discontinu de l'interface avec la reconstruction d'une fonction indicatrice de phase échelon, tandis que le déplacement de l'interface est assuré d'un pas de temps à l'autre à l'aide du front-tracking. Les résultats obtenus avec cette nouvelle méthode hybride sont très satisfaisants, la méthode hybride permettant d'assurer la conservation de l'énergie et de la masse avec précision dans les simulations. / This thesis is devoted to the modeling and the numerical simulation of liquid-gas flows in non isothermal micro-cavities or micro-channels. The objective is to describe two-phase flows in which compressibility of the gaseous phase plays a key role (as for instance in micropumps, microactuators, etc...). An original model is developed, considering in the same computational domain, an incompressible liquid and a compressible gas under the low Mach approximation. This model has been implemented in a code using the front-tracking method for the interface description. In order to check the proper satisfaction of the energy balance, specific test cases have been developed considering several configurations of increasing complexity. It has been shown from these test cases that energy conservation can hardly be satisfied when the interface is described by the means of a smooth function, which is done in the front-tracking method. An hybrid method has been proposed, restoring the discontinous nature of the interface. It makes use of a step function combined with the front tracking method. Results obtained with this new hybrid method show that mass conservation and energy balance are very properly enforced during the computations. This thesis is devoted to the modelling and numerical simulation of liqui-gas flow envolving heat transfer. Simulation of configurations where it is essential to take into account the compressibility nature of the gaseous phase(for instance micropumps, microactuators, etc...) require the use of an original model, considering an incompressible liquid and a compressible gas under the low Mach assuption. During this thesis, the model has been implemented in a multiphase flow code using the front-tracking method to handle the interface. Test cases have been developped specifically to check the energy conservation for differents configurations of an increasing complexity. Numerical results highlighted difficulties encountered to ensure the energy conservation while using smooth description of the interface, as it is the case in the standard front-tracking method. An hybrid method has been proposed, restoring the discontinous character of the interface by reconstructing a step maker function, whereas the front displacement from a time step to the next, is still handled with the front-tracking. Results obtained using this new hybride method are very satisfactory, the hybrid method allowing the code to ensure accurately the energy and mass conservation during the computations.

La modélisation des transferts thermiques en écoulements diphasiques est l'une des pierres angulaires de l'étude de la sûreté des réacteurs nucléaires. À l'échelle du réacteur, elle repose sur des corrélations expérimentales. L'utilisation croissante de la mécanique des fluides numérique pour les études de sûreté renforce la demande d'expertise dans les outils de simulation, en particulier du point de vue de la modélisation. En soutien aux modèles moyennés à deux fluides, nous souhaitons apporter des informations de fermetures locales pour considérer la physique des transferts interfaciaux et les effets 3D. Pour cela, comme la résolution directe des équations de bilan locales par SND est trop coûteuse, nous souhaitons développer un outil de SGE diphasique pour modéliser les petites échelles turbulentes et les petites déformations interfaciales. Comme le changement de phase est à l'origine de l'écoulement diphasique pour les applications visées, nous étendons dans ce mémoire le modèle Interfaces and Subgrid-Scales (ISS, Toutant et al., 2009a) aux interfaces avec changement de phase, pour lesquelles l'hypothèse de continuité de la vitesse à l'interface n'est plus valable. Le suivi explicite des interfaces permet d'évaluer précisément les transferts comme le taux de transfert de masse. Dans un premier temps, nous établissons une description mésoscopique du problème où l'interface est diffuse en filtrant les équations locales instantanées et en modélisant les transferts sous-filtres aux interfaces. Les principales difficultés de modélisations proviennent (i) de la détermination de la vitesse de l'interface, (ii) de l'effet de la discontinuité des vitesses sur les modèles sous-maille, (iii) de la discontinuité du flux et (iv) de la condition de saturation de l'interface. Les modèles proposés sont qualifiés a priori en observant leur prédiction par filtrage explicite de solutions de SND. Dans un deuxième temps, nous établissons un système macroscopique discontinu équivalent au problème diffus pour bénéficier de l'expertise acquise pour les méthodes numériques de SND. Aux interfaces, les modèles sous-maille sont concentrés pour modifier les conditions de raccord entre les phases. Les conditions de saut ainsi déterminées montrent que la vitesse de l'interface est affectée par la courbure et par le saut de vitesse. Un saut de vitesse tangentielle est introduit pour modéliser la couche limite dynamique. Sur le plan thermique, nous retrouvons la condition de saturation caractéristique du changement de phase ; le taux de changement de phase ne dépend plus uniquement du saut de flux conductif mais, pour pallier la sous-résolution de la couche limite thermique au voisinage de l'interface, nous proposons de lui ajouter la contribution sous-maille des corrélations vitesse/température. Comme en SGE monophasique, le gain apporté par la modélisation ISS permet d'envisager l'utilisation de simulations fines pour des problèmes appliqués. C'est la première étape d'une démarche multi-échelle pour fournir des fermetures aux modèles moyennés à deux fluides. Nous illustrons son potentiel sur une SND multi-bulles complexe. / Modeling heat and mass transfer in two-phase flows with phase-change is crucial in many industrial studies including nuclear safety. Only averaged two-phase flow models can simulate such complex flows. Their accuracy depends in particular on closure laws for interfacial mass, momentum, and energy transfers that often rely on experimental correlations. Supporting averaged models, the goal of this thesis is to bring local closure information from finer simulations to consider 3D-effects and interfacial transfers more accurately. In this prospect, as direct resolution of the local balance equations is too expensive, we seek for a two-phase equivalent of Large Eddy Simulation (LES) in order to tackle simulations with enough bubbles to extract statistics needed in averaged models. Applying a spatial filter, we aim at modeling subgrid turbulence and interfacial transfers. The largest turbulent scales and interface deformations are captured because the filter size is chosen in-between the Kolmogorov scale and the bubble size. Because of the importance of the phase-change phenomena, this thesis extend the Interfaces and Subgrid Scales (ISS) model proposed by Toutant et al. (2009a) to non-material interfaces, i. e., with phase-change. Explicit interface tracking is valuable to accurately estimate interfacial transfers such as the phase-change rate. In the first part of this document, we establish a smeared-interface description of two-phase flows. Sub-grid transfers and interfacial deformations are modeled using the modified Bardina et al. (1983) scale-similarity hypothesis. Main modeling issues comes from (i) the specific interfacial velocity, (ii) the velocity and the temperature gradient discontinuities at the interface and (iii) the saturation condition of the interface. Models are validated using reference data from DNS. In the second up-scaling step, we transform interfacial subgrid models into source terms in the jump conditions in order to establish an equivalent discontinuous model thus benefitting from the knowledge acquired in DNS numerical methods. Transfers between phases are modified and the interfacial velocity is redefined considering the time evolution of curvature and the velocity jump at the interface. As a result, the normal momentum jump is modified. A tangential velocity jump is also introduced to cancel out the sub-resolution of the boundary layer. From a thermal point of view, the classical saturation condition is recovered ; the phase-change rate not only depends on the conduction heat flux but a contribution from the subgrid velocity and temperature correlations must be added to account for the poor resolution of the thermal boundary layer. As for single-phase LES, ISS modeling enables local-scale simulations of industrial configurations. It is the first step of a multi-scale approach towards turbulent bubbly flows. In this thesis, we illustrates how to bridge the gap between DNS and averaged descriptions from reference results obtained on condensing bubbles in a pseudo-turbulent subcooled liquid. Averaged quantities are compared with correlations for the condensation sink term used in the two-fluid model. We are able to underline the phase-change enhancement with increasing void fraction. It shows that this path could be used to improve the understanding of the strong two-way coupling between flow dynamics and interfacial heat transfers.

"Swirling multiphase flows are found in a wide range of industrial processes. Such flows are used for separation of flows containing phases of different densities and for devices such as the spinning tensiometer. These flows are challenging to predict computationally, due to the presence of a phase boundary and the large pressure gradient generated by the swirl. In the present work the applicability of the front tracking method to swirling multi-phase flows is demonstrated by studying the evolution of a bubble in spinning tensiometer. Previous studies show that the evolution of a bubble in the spinning drop tensiometer can be used to measure the interfacial tension and other rheological properties. The front tracking method is applied to the spinning tensiometer problem to study several cases and verify the convergence of the solutions. The results are validated with other computational methods, theoretical models and experimental results. The length scales obtained from the front tracking method are in agreement with the corresponding values from experiments and other computational studies. The shape of the end of the elongated bubble obtained from the simulations is found to be similar to that suggested by a theoretical expression from previous studies. The simulations predict that the relaxation of bubble radius is exponential with time, at a rate that is found to be slightly greater than that predicted by the theoretical model."

The discontinuities in the solutions of systems of conservation laws are widely considered as one of the difficulties in numerical simulation. A numerical method is proposed for solving these partial differential equations with discontinuities in the solution. The method is able to track these sharp discontinuities or interfaces while still fully maintain the conservation property. The motion of the front is obtained by solving a Riemann problem based on the state values at its both sides which are reconstructed by using weighted essentially non oscillatory (WENO) scheme. The propagation of the front is coupled with the evaluation of "dynamic" numerical fluxes. Some numerical tests in 1D and preliminary results in 2D are presented. / Singapore-MIT Alliance (SMA)

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