A major drawback in the operation of mechanical heart valve prostheses is thrombus formation in the near valve region potentially due to the high shear stresses present in the leakage jet flows through small gaps between leaflets and the valve housing. Detailed flow analysis in this region during the valve closure phase is of interest in understanding the relationship between shear stress and platelet activation. An efficient Cartesian grid method is developed for the simulation of incompressible flows around stationary and moving three-dimensional immersed solid bodies as well as fluid-fluid interfaces. The embedded boundaries are represented using Levelsets and treated in a sharp manner without the use of source terms to represent boundary effects. The resulting algorithm is implemented in a straightforward manner in three dimensions and retains global second-order accuracy. When dealing with problems of disparate length scales encountered in many applications, it is necessary to resolve the physically important length scales adequately to ensure accuracy of the solution. Fixed grid methods often have the disadvantage of heavy mesh requirement for well resolved calculations. A quadtree based adaptive local mesh refinement scheme is developed to complement the sharp interface Cartesian grid method scheme for efficient and optimized calculations. Detailed timing and accuracy data is presented for a variety of benchmark problems involving moving boundaries. The above method is then applied to modeling heart valve closure and predicting thrombus formation. Leaflet motion is calculated dynamically based on the fluid forces acting on it employing a fluid-structure interaction algorithm. Platelets are modeled and tracked as point particles by a Lagrangian particle tracking method which incorporates the hemodynamic forces on the particles. Leaflet closure dynamics including rebound is analyzed and validated against previous studies. Vortex shedding and formation of recirculation regions are observed downstream of the valve, particularly in the gap between the valve and the housing. Particle exposure to high shear and entrapment in recirculation regions with high residence time in the vicinity of the valve are observed corresponding to regions prone to thrombus formation.

We studied the effect of a first order irreversible chemical reaction on mass transfer for two-phase flow systems in which the continuous phase is a fluid and the dispersed phase consists in catalystspherical particles. The reactive solute is transported by the fluid flow and penetrates through the particle surface by diffusion. The chemical reaction takes place within the bulk of the particle. Wehandle the problem by coupling mass balance equations for internal-external transfer with two boundary conditions: continuity of concentration and mass flux at the particle surface. We start with the case of a single isolated sphere. We propose a model to predict mass transfer coefficient (`reactive' Sherwood number) accounting for the external convection-diffusion along with internal diffusion-reaction. We validate the model through comparison with fully resolved Direct Numerical Simulations (DNS) performed by means of a boundary-fitted mesh method. For the simulation of multi-particle systems, we implemented a Sharp Interface Method to handle strong concentration gradients. We validate the implementation of the method thoroughly thanks to comparison with existing analytical solutions in case of diffusion, diffusion-reaction and by comparison with previously established correlations for convection-diffusion mass transfer. In case of convectiondiffusion- reaction, we validate the method and we evaluate its accuracy through comparisons with single particle simulations based on the boundary-fitted method. Later, we study the problem of three aligned-interacting spheres with internal chemical reaction. We propose a `reactive' Sherwood number model based on a known non-reactive prediction of mass transfer for each sphere. We validate the model by comparison with direct numerical simulations for a wide range of dimensionless parameters. Then, we study the configuration of a fixed bed of catalyst particles. We model the cup-mixing concentration profile, accounting for chemical reaction within the bed, and the mean surface and volume concentration profiles of the particles. We introduce a model for `reactive' Sherwood number that accounts for the solid volume fraction, in addition to the aforementioned effects. We compare the model to numerical simulations to evaluate its limitations

Two immersed boundary methods (IBM) for the simulation of conjugate heat transfer problems with complex geometries are introduced: a finite element (IFEM) and a finite volume (IFVM) immersed boundary methods are discussed. In the IFEM a projection approach is presented for the coupled system of time-dependent incompressible Navier-Stokes equations (NSEs) and energy equation in conjunction with the immersed boundary method for solving fluid flow and heat transfer problems in the presence of rigid objects not represented by the underlying mesh. The IBM allows solving the flow for geometries with complex objects without the need of generating a body-fitted mesh. Dirichlet boundary constraints are satisfied applying a boundary force at the immersed body surface. Using projection and interpolation operators from the fluid volume mesh to the solid surface mesh (i.e., the “immersed” boundary) and vice versa, it is possible to impose the extra constraint to the NSEs as a Lagrange multiplier in a fashion very similar to the effect pressure has on the momentum equations to satisfy the divergence-free constraint. The IFEM approach presented shows third order accuracy in space and second order accuracy in time when the simulation results for the Taylor-Green decaying vortex are compared to the analytical solution. For the IFVM a ghost-cell approach with sharp interface scheme is used to enforce the boundary condition at the fluid/solid interface. The interpolation procedure at the immersed boundary preserves the overall second order accuracy of the base solver. The developed ghost-cell method is applied on a staggered configuration with the Semi-Implicit Method for Pressure-Linked Equations Revised algorithm. Second order accuracy in space and first order accuracy in time are obtained when the Taylor-Green decaying vortex test case is compared to the IFVM analytical solution. Computations were performed using the IFEM and IFVM approaches for the two-dimensional flow over a backward-facing step, two-dimensional flow past a stationary circular cylinder, three-dimensional flow past a sphere and two and three-dimensional natural convection in an enclosure with/without immersed body. The numerical results obtained with the discussed IFEM and IFVM were compared against other IBMs available in literature and simulations performed with the commercial computational fluid dynamics code STAR-CCM+/V7.04.006. The benchmark test cases showed that the numerical results obtained with the implemented immersed boundary methods are in good agreement with the predictions from STAR-CCM+ and the numerical data from the other IBMs. The immersed boundary method based of finite element approach is numerically more accurate than the IBM based on finite volume discretization. In contrast, the latter is computationally more efficient than the former.

Nous avons étudié l'effet d'une réaction chimique sur le transfert de matière pour des systèmes à deux phases sous écoulement. La phase continue est une phase fluide et la phase dispersée est constituée de particules de catalyseur au sein desquelles une réaction chimique irréversible de premier ordre a lieu. Le soluté réactif est transporté par l'écoulement externe de fluide et pénètre dans la particule par diffusion, il se produit alors une réaction chimique qui consomme cette espèce. Nous modélisons le problème par un couplage interne-externe des équations de bilan et au moyen de deux conditions limites de raccordement: continuité de la concentration et équilibre des flux de masse à la surface des particules. Le cas d'une seule sphère isolée est traitée en premier lieu de manière théorique et numérique. Nous proposons un modèle pour prédire le coefficient de transfert de masse (nombre de Sherwood «réactif») en tenant compte de la convection-diffusion externes et du couplage diffusion-réaction internes. Nous validons le modèle en le comparant à des simulations numériques directes pleinement résolues (DNS boundaryfitted) sur un maillage adapté à la géométrie des particules. Pour la simulation de systèmes multiparticules, nous mettons en œuvre une méthode d'interface «Sharp» pour traiter les fronts raides de concentration. Nous validons la mise en œuvre de la méthode sur des solutions analytiques existantes en cas de diffusion, de diffusion-réaction et par comparaison avec des corrélations de convection-diffusion disponibles dans la littérature. Dans le cas d'une réaction chimique en présence de convection-diffusion, nous validons la méthode et nous évaluons sa précision en comparant avec les simulations pleinement résolues de référence. Ensuite, nous étudions le problème de l'écoulement et du transfert autour de trois sphères alignées soumis à une réaction chimique interne. Nous proposons un modèle de nombre de Sherwood «réactif» en complément d'une prédiction de transfert pour chaque sphère disponible dans la littérature. Nous validons le modèle par comparaison avec des simulations numériques directes pour une large gamme de paramètres adimensionels. Ensuite, nous étudions la configuration du lit fixe de particules de catalyseur. Nous modélisons le profil de concentration moyenne, en tenant compte de la réaction chimique dans le lit et les profils de concentration moyenne surfacique et volumique des particules. Nous introduisons un modèle pour le nombre de Sherwood «réactif» qui est comparé à des simulations numériques pour en évaluer les limites de validité / We studied the effect of a first order irreversible chemical reaction on mass transfer for two-phase flow systems in which the continuous phase is a fluid and the dispersed phase consists in catalystspherical particles. The reactive solute is transported by the fluid flow and penetrates through the particle surface by diffusion. The chemical reaction takes place within the bulk of the particle. Wehandle the problem by coupling mass balance equations for internal-external transfer with two boundary conditions: continuity of concentration and mass flux at the particle surface. We start with the case of a single isolated sphere. We propose a model to predict mass transfer coefficient (`reactive' Sherwood number) accounting for the external convection-diffusion along with internal diffusion-reaction. We validate the model through comparison with fully resolved Direct Numerical Simulations (DNS) performed by means of a boundary-fitted mesh method. For the simulation of multi-particle systems, we implemented a Sharp Interface Method to handle strong concentration gradients. We validate the implementation of the method thoroughly thanks to comparison with existing analytical solutions in case of diffusion, diffusion-reaction and by comparison with previously established correlations for convection-diffusion mass transfer. In case of convectiondiffusion- reaction, we validate the method and we evaluate its accuracy through comparisons with single particle simulations based on the boundary-fitted method. Later, we study the problem of three aligned-interacting spheres with internal chemical reaction. We propose a `reactive' Sherwood number model based on a known non-reactive prediction of mass transfer for each sphere. We validate the model by comparison with direct numerical simulations for a wide range of dimensionless parameters. Then, we study the configuration of a fixed bed of catalyst particles. We model the cup-mixing concentration profile, accounting for chemical reaction within the bed, and the mean surface and volume concentration profiles of the particles. We introduce a model for `reactive' Sherwood number that accounts for the solid volume fraction, in addition to the aforementioned effects. We compare the model to numerical simulations to evaluate its limitations

In meshfree methods, partial differential equations are solved on an unstructured cloud of points distributed throughout the computational domain. In collocated meshfree methods, the differential operators are directly approximated at each grid point based on a local cloud of neighboring points. The set of neighboring nodes used to construct the local approximation is determined using a variable search radius. The variable search radius establishes an implicit nodal connectivity and hence a mesh is not required. As a result, meshfree methods have the potential flexibility to handle problem sets where the computational grid may undergo large deformations as well as where the grid may need to undergo adaptive refinement. In this work we develop the sharp interface formulation of the immersed boundary method for collocated meshfree approximations. We use the framework to implement three meshfree methods: General Finite Differences (GFD), Smoothed Particle Hydrodynamics (SPH), and Moving Least Squares (MLS). We evaluate the numerical accuracy and convergence rate of these methods by solving the 2D Poisson equation. We demonstrate that GFD is computationally more efficient than MLS and show that its accuracy is superior to a popular corrected form of SPH and comparable to MLS. We then use GFD to solve several canonic steady state fluid flow problems on meshfree grids generated using uniform and variable radii Poisson disk algorithm.

A complete two-phase numerical model of film condensation from a mixture of a vapour and a non-condensing gas that is based on the two-dimensional elliptic governing equations with variable physical properties is presented. The model predicts the full viscous flow and heat and mass transfer for the mixture around the tube and in the entire liquid film from the top of the tube to the falling film below the tube. A finite volume method is used with a segregated solution approach and a dynamically moving computational grid that tracks the phase interface sharply. Fundamental balances of mass, energy, and force are enforced accurately at the phase interface. The model was developed in steps and validated against various experimental and theoretical works in the literature for different two-phase flows. The validation tests included stratified flow of liquid and gas in a horizontal channel, falling liquid film over a vertical wall, and condensation of steam from a steam-air mixture in a vertical channel. The model was used to simulate laminar film condensation from a downward flowing steam-air mixture over an isothermal horizontal tube. The validity of this new model is demonstrated by comparisons with previous theoretical and experimental studies. New results are presented on the effects of free-stream-to-tube temperature difference, upstream Reynolds number, free-stream gas mass fraction, and free-stream pressure on the condensate film development, the local and average heat transfer coefficients, and the total condensate mass flow rate. It was found that the temperature difference had the greatest effect on the condensation rate and film thickness. The presence of non-condensing gas in the vapour has a strong negative impact on the condensation process. For the pure steam case, moderate changes in the upstream Reynolds number showed slight increases in condensate mass flow rate with increased Reynolds number. For the mixture case, however, moderate increase in upstream Reynolds number increases significantly the condensate mass flow rate and film thickness. This trend becomes more noticeable as the free-steam gas mass fraction increases. Changing the free-stream pressure demonstrated that property variation had a relatively smaller effect than temperature difference and gas mass fraction changes. / February 2017

Immersed boundary (IB) methods are attractive due to their ability to simulate flow over complex geometries on a simple Cartesian mesh. Unlike conformal grid formulation, the mesh does not need to conform to the shape and orientation of the boundary. This eliminates the need for complex mesh and/or re-meshing in simulations with moving/morphing boundaries, which can be cumbersome and computationally expensive. However, the imposition of boundary conditions in IB methods is not straightforward and numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In a nutshell, IB methods in the literature often suffer from numerical oscillations, implementation complexity, time-step restriction, burred interface, and lack of generality. This limits their ability to mimic conformal grid results and enforce Neumann boundary conditions. In addition, there is no generic IB capable of solving flow with multiple potentials, closely/loosely packed structures as well as IBs of infinitesimal thickness. This dissertation describes a novel 2$ ^{\text{nd}} $ order direct forcing immersed boundary method designed for simulation of two- and three-dimensional incompressible flow problems with complex immersed boundaries. In this formulation, each cell cut by the IB is reshaped to conform to the shape of the IB. IBs are modeled as a series of 2D planes in 3D space that connect seamlessly at the edges of the cut cells, in a way that mimics conformal grid. IBs are represented in a continuous and consistent fashion from one cell to another, thus eliminating spatial pressure oscillations originating from inconsistent description of the IB as well as the traditional stair-step problem, leading to a more accurate resolution of the boundary layer. Boundary conditions are enforced at the exact location of the IB devoid of interpolation, which guarantees sound simulations even on grids with high aspect ratio, and enables simulations of flow packed with multiple IBs in close proximity. Boundary conditions for each phase across the IB are enforced independently, yielding a unique capability to solve flows with zero-thickness IBs. Simulations of a large number of 2D and 3D test cases confirm the prowess of the devised immersed boundary method in solving flows over multiple loosely/closely-packed IBs; stationary, moving and highly morphing IBs; as well as IBs with zero-thickness. Extension of the proposed scheme to solve flow with multiple potentials is demonstrated by simulating transfer and transport of a passive scalar from an array of side-by-side and tandem cylinders in cross-flow. Aquatic vegetation represented by a colony of circular cylinders with low to high solid fraction is simulated to showcase the prowess of the current numerical technique in solving flow with closely packed structures. Aquatic vegetation studies are extended to a colony of flat plates with different orientations to show the capability of the developed method in modeling zero-thickness structures.

The photoactive component of a polymeric organic solar cell can be produced by drying a mixture consisting of a volatile solvent and non-volatile polymers. As the solvent evaporates, the polymers demix and self-assemble into microscale structures, the morphology of which plays a pivotal role in determining the efficiency of the resulting device. Thus, a detailed understanding of the physical mechanisms that drive and influence structure formation in evaporating solvent-polymer mixtures is of high scientific and industrial value. This thesis explores several problems that aim to produce novel insights into the dynamics of evaporating solvent-polymer mixtures. First, the role of compositional Marangoni instabilities in slowly evaporating binary mixtures is studied using the framework of linear stability theory. The analysis is non-trivial because evaporative mass loss naturally leads to a time-dependent base state. In the limit of slow evaporation compared to diffusion, a separation of time scales emerges in the linear stability problem, allowing asymptotic methods to be applied. In particular, an asymptotic solution to linear stability problems that have slowly evolving base states is derived. Using this solution, regions of parameter space where an oscillatory instability occurs are identified and used to formulate appropriate conditions for observing this phenomenon in future experiments. The second topic of this thesis is the use of multiphase fluid models to study the dynamics of evaporating solvent-polymer mixtures. A two-phase model is used to assess the role of compositional buoyancy and to examine the formation of a polymer-rich skin at the free surface. Then, a three-phase model is used to conduct a preliminary investigation of the link between evaporation and phase separation. Finally, this thesis explores the dynamics of a binary mixture that is confined between two horizontal walls using a diffusive phase-field model and its sharp-interface and thin-film approximations. We first determine the conditions under which a homogeneous mixture undergoes phase separation to form a metastable bilayer. We then present a novel mechanism for generating a repeating lateral sequence of alternating A-rich and B-rich domains from this bilayer.

No description available.

Dans cette thèse, on utilise des outils mathématiques et numériques pour modéliser les écoulements tridimensionnels incompressibles à surface libre instationnaires. L'application industrielle visée est l'étude de la phase de remplissage des moules dans une fonderie. On développe un algorithme pour le transport de l'interface par la vitesse du fluide pour un fluide diphasique incompressible visqueux non-miscible de rapport de densité important en utilisant la méthode de caractéristiques pour traiter le problème de convection. Il y a des défis majeurs dans le contexte de la modélisation des fluides diphasiques. Tout d'abord, on doit prendre en considération l'évolution de l'interface et de ses changements topologiques. Deuxièmement, on doit traiter la non-linéarité convective de l'interface et de l'écoulement. Troisièmement, les équations de Navier-Stokes et du transport doivent être munies des conditions aux bords appropriées. En outre, il faut traiter soigneusement les singularités géométriques et topologiques à travers l'interface en particulier dans le cas de rapport de densité et viscosité important. On doit également maintenir la résolution d'une interface d'épaisseur nulle durant les cas du pliage, la rupture et la fusion de l'interface. Quatrièmement, on doit respecter les propriétés physiques telles que la conservation de la masse pour tout écoulement d'un fluide incompressible. Cinquièmement, il faut toujours penser aux limitations du temps de calcul et de mémoire pour résoudre ce genre de problème dans les cas pratiques. Notre but est de trouver un schéma fiable capable de modéliser le remplissage des moules tridimensionnelles industrielles. La première partie de cette thèse est dédiée à la description mathématique du schéma de transport de l'interface par la vitesse du fluide. Le mouvement des fluides est décrit par les équations de Navier-Stokes. L'interface est capturée par la fonction Level-Set. Le problème est discrétisée en espace par la méthode des éléments finis et en temps par la méthode de caractéristiques.Des conditions aux bords appropriées pour le problème du remplissage d'un moule sont introduites et un algorithme de calcul de la solution est présentée. Finalement,des résultats numériques montrent et valident l'efficacité duschéma proposé. Dans la deuxième partie de cette thèse, on introduit une méthode de décomposition de domaine qui correspond à la discrétisation par la méthode des caractéristiques dans le but d'améliorer la performance de l'algorithme proposé lors de la modélisation du remplissage des moules industrielles à moyennes séries. Des résultats numériques de comparaison valident la précision du code parallèle. / In this thesis, we use mathematical and numerical tools to model three dimensional incompressible laminar flows with free surface. The described industrial application is the study of the mould filling phase in a foundry. We develop an algorithm for the transport of the interface by the fluid velocity for a viscous incompressible immiscible fluids of high density ratio in two-phase flow using the method of characteristics for the convection problem.There are, however, major challenges in the context of two-phase flow modeling.First, we have to take into account the evolution of the interface and its topological changes. Second, we have to deal with the non-linearity for the convection of the flow and the interface. Third, we must assign appropriate boundary conditions to the flow and transport equations.In addition, care must be taken in treating the geometrical and topological singularities across the interface.We also have to maintain a sharp interface resolution, including the cases of interface folding, breaking and merging.Furthermore, we should respect the physical properties such as the mass conservation for any incompressible fluid flows.Finally, we have to keep in mind the limitations in the time of computation and memory to solve this kind of problem in practical cases. Our purpose is to find a reliable scheme able to model the filling of three dimensional industrial moulds.The first part of the thesis is devoted to the mathematical description of the interface transport scheme by the fluid velocity. The fluids motion is described by the Navier-Stokes equations. The interface is captured by the Level-Set function. The problem isdiscretized by the characteristics method in time and finiteelements method in space. The interface is captured by the Level-Setfunction. Appropriate boundary conditions for the problem ofmould filling are investigated, a new natural boundary conditionunder pressure effect for the transport equation is proposed andan algorithm for computing the solution is presented. Finally,numerical experiments show and validate the effectiveness of theproposed scheme.In the second part of the thesis, we introduce a domain decomposition method that suits the discretization by the method of characteristics in order to improve the performance of the proposed algorithm to model the filling phase for moulds of medium series. Numerical results of comparison validate the precision of the parallel code.