Hydrodynamic slip is known to suppress vorticity production at the solid-fluid boundary in bluff body flows. This suppression combined with the enhanced vorticity convection results in a substantial reduction in the unsteady vortex shedding and the hydrodynamic loads experienced by the bluff body. Here, using combined theoretical and computational techniques, we investigate the effect of slip on three-dimensional wake dynamics and convective scalar transport from a circular cylinder placed in the uniform cross-flow of a Newtonian incompressible fluid over Reynolds numbers ranging from 0.1 to 1000. We find the wake patterns to be strongly influenced by the degree of the slip, quantified through the non-dimensional slip length in the Naiver slip model, with the asymptotic slip lengths of zero and infinity characterizing no-slip and no-shear boundaries, respectively. With increasing slip length, the wake three-dimensionality, that is observed in the case of a no-slip surface for Re > 190, is gradually suppressed and eventually eliminated completely. For each Reynolds number, we identify the critical slip length beyond which the three-dimensionality is completely suppressed and the wake becomes two-dimensional, on the basis of the total transverse entropy present in the flow field. Over the Reynolds number range considered in this work, we find the critical slip length to be an increasing function of Reynolds number. For sufficiently large slip lengths, we observe suppression of two-dimensional vortex shedding leading to formation of a steady separated wake. Further increments in slip length lead to reduction in the intensity and size of the recirculating eddy pair eventually resulting in its complete disappearance for a no-shear surface for which the flow remains attached all along the cylinder boundary. Next, we quantify the effect of hydrodynamic slip on convective transport from an isothermal circular cylinder placed in the uniform cross flow of an incompressible fluid at a lower temperature. For low Reynolds and high P´eclet numbers, theoretical analysis based on Oseen and thermal boundary layer equations allows us to obtain explicit relationships for the dependence of transport rate on the prescribed slip length. We observe that the non-dimensional transport coefficients follow a power law scaling with respect to the P´eclet number, with the scaling exponent increasing gradually from the lower asymptotic limit of 1/3 for the no-slip surface to 1/2 for a no-shear boundary. Results from our simulations at finite Reynolds number indicate that the local time-averaged transport rates for a no-shear surface exceed the one for the no-slip surface all along the cylinder except in the neighbourhood of the rear stagnation region, where flow separation and reversal augment the transport rates substantially.

This dissertation focuses on the effects of heating on superhydrophobic (SHPo) surfaces. The work is divided into two main categories: heat transfer without mass transfer and heat transfer in conjunction with mass transfer. Numerical methods are used to explore the prior while experimental methods are utilized for the latter. The numerical work explores convective heat transfer in SHPo parallel plate microchannels and is separated into two stand-alone chapters that have been published archivally. The first considers surfaces with a rib/cavity structure and the second considers surfaces patterned with a square lattice of square posts. Laminar, fully developed, steady flow with constant fluid properties is considered where the tops of the ribs and posts are maintained at a constant heat flux boundary condition and the gas/liquid interfaces are assumed to be adiabatic. For both surface configurations the overall convective heat transfer is reduced. Results are presented in the form of average Nusselt number as well as apparent temperature jump length (thermal slip length). The heat transfer reduction is magnified by increasing cavity fraction, decreasing Peclet number, and decreasing channel size relative to the micro-structure spacing. Axial fluid conduction is found to be substantial at high Peclet numbers where it is classically neglected. The parameter regimes where prior analytical works found in the literature are valid are delineated. The experimental work is divided into two stand-alone chapters with one considering channel flow and the other a pool scenario. The channel work considers high aspect ratio microchannels with one heated SHPo wall. If water saturated with dissolved air is used, the air-filled cavities of SHPo surfaces act as nucleation sites for mass transfer. As the water heats it becomes supersaturated and air can effervesce onto the SHPo surface forming bubbles that align to the underlying micro-structure if the cavities are comprised of closed cells. The large bubbles increase drag in the channel and reduce heat transfer. Once the bubbles grow large enough, they are expelled from the channel and the nucleation and growth cycle begins again. The pool work considers submerged, heated SHPo surfaces such that the nucleation behavior can be explored in the absence of forced fluid flow. The surface is maintained at a constant temperature and a range of temperatures (40 - 90 °C) are explored. Similar nucleation behavior to that of the microchannels is observed, however, the bubbles are not expelled. Natural convection coefficients are computed. The surfaces with the greatest amount of nucleation show a significant reduction in convection coefficient, relative to a smooth hydrophilic surface, due to the insulating bubble layer.

Ce travail de thèse a pour objectif de simuler numériquement des écoulements de gaz dans des matrices poreuses dont les pores sont de taille micrométrique. On étudie l'influence des phénomènes de glissement hydrodynamique qui apparaissent lorsque la dimension caractéristique de micro- conduites est caractérisée par des nombres de Knudsen compris entre Kn = 0,01 et Kn = 0,1.Le mémoire de thèse est composé de cinq chapitres suivis d'une conclusion dans laquelle nous présentons quelques perspectives pour une suite de ce travail. Le chapitre I constitue le travail préliminaire de thèse qui s'est ensuite orienté vers des approches complémentaires. Le principe des méthodes d'homogénéisation périodique est d'abord exposé. Suit une présentation de deux méthodes de résolution dans l'espace de Fourier : l'approche en déformation et l'approche en contrainte. L'extension de ces méthodes à la résolution d'écoulements régis par l'équation de Stokes est ensuite décrite. Des applications aux cas d'écoulements à travers des réseaux de cylindres, avec condition d'adhérence ou avec condition de glissement, sont ensuite discutées. Deux techniques de modélisation des phénomènes de transport dans des milieux poreux saturés par un fluide monoconstituant sont présentées dans le second chapitre. La première est basée sur la méthode des développements asymptotiques, appelée aussi méthode d'homogénéisation. On explique que le processus consiste en trois étapes : description locale, localisation et description macroscopique. La seconde technique s'appuie sur la méthode de calcul de moyennes à l'échelle d'un VER. Le point de départ de cette méthode est basé sur des théorèmes donnant les expressions des moyennes de tous les opérateurs intervenant dans une équation de transport. Après une brève présentation du logiciel commercialisé que nous avons utilisé, nous exposons les études de convergence spatiale que nous avons effectuées et nous comparons nos solutions avec des résultats de la littérature dans le chapitre III. Diverses géométries sont considérées (allant de géométries planes à des empilements 3D de cubes ou de sphères).L'effet du glissement sur la perméabilité de milieux microporeux est abordé dans le chapitre IV. Le formalisme résultant de l'homogénéisation de structures périodiques est utilisé pour simuler numériquement des écoulements isothermes de gaz dans divers empilements de complexités croissantes. Les perméabilités sont déterminées en calculant les moyennes spatiales des champs de vitesses, solutions des équations de Stokes. Les valeurs obtenues en imposant des conditions d'adhérence sont comparées à celles obtenues avec des conditions de glissement du premier ordre. Dans le chapitre V, nous présentons des solutions pour des écoulements anisothermes et étudions l'effet du glissement sur la conductivité effective de milieux microporeux 2D et 3D. Dans ce chapitre, nous résolvons les équations de Navier-Stokes et de l'énergie en imposant des conditions de symétries dans une ou deux directions. A partir des solutions locales, sont calculées les moyennes intrinsèques des champs de vitesse et de température. Nous considérons des cas pour lesquels la condition d'équilibre thermique local peut être considérée comme satisfaite et d'autres correspondant à un non-équilibre thermique (NTLE). On détermine les conductivités de dispersion en fonction du nombre du Péclet et on montre l'influence du glissement sur les composantes longitudinales et transverses pour différentes porosités et longueur de glissement. Dans les cas NLTE, le coefficient macroscopique de transfert fluide-solide est aussi calculé / This thesis aims at numerically simulating gas flows in porous matrices with micro-sized pores. We study the influence of hydrodynamic slip phenomena that appear when the characteristic dimension of micro pores is characterized by Knudsen numbers between Kn = 0.01 and Kn = 0.1.The thesis consists of five chapters followed by a conclusion in which we present some perspectives for further studies. Chapter I is the preliminary work of thesis that turned into complementary approaches. The principle of periodic homogenization methods is first exposed. We present then two methods in the Fourier space: the stress approach and the strain approach. The extension of these methods for solving flows governed by the Stokes equation is described in what follows. Applications to flows through networks of cylinders, subjected to no slip or slip condition, are then discussed. Two techniques for modeling transport phenomena in porous media saturated by a mono-component fluid are presented in the second chapter. The first is based on the method of asymptotic expansions, also known as homogenization method, based on the concept of separation of scales. It is explained that the process consists of three steps: local description, localization and macroscopic description. The second technique is based on the method of averaging at the level of a representative elementary volume (REV). The starting point of this method is based on the equations of Continuum Mechanics and theorems giving the averaged expressions of all operators involved in a transport equation. We show that it extends easily to gas flows in micro porous media. After a short presentation of the commercial software used, we present the spatial convergence studies carried out and we compare our solutions with the results of the literature in Chapter III. Various geometries are considered (plane to 3D geometries made of cubes or spheres), but these comparisons are limited to isothermal flows. The effect of slip on the permeability in micro porous media is discussed in Chapter IV. The resulting formalism of the periodic homogenization structures is used for numerical simulation of isothermal gas in various geometries of increasing complexity. The permeabilities are determined by calculating the spatial averages of velocity fields, solutions of the Stokes equations. The values obtained by imposing no slip conditions are compared with first order slip conditions. We discuss the relative increase in permeability due to slip according to the geometry of the pores. In Chapter V, we present the solutions for anisothermal flows and we study the effect of slip on the effective conductivity in 2D and 3D microporous media. In this chapter, we solve the Navier-Stokes and energy equations by imposing symmetry conditions in one or two directions. The intrinsic mean velocity and temperature fields are calculated from these local solutions. We consider cases where the local thermal equilibrium condition can be considered as satisfied and other corresponding to a non-local thermal equilibrium (NLTE). We determine the dispersion conductivity based on the Péclet number and show the influence of velocity slip on longitudinal and transverse components for various porosities and slip lengths. In NLTE cases, the macroscopic fluid-to-solid heat transfer coefficient is also calculated