Porous media flows are encountered in many natural and man-made systems such as gas adsorption, filtration, heat exchangers, combustion, catalytic reactors and groundwater hydrology. This study experimentally investigates these flows as function of pore Reynolds number, Re[subscript pore]. The pore Reynolds number is based on the porous bed hydraulic diameter, D[subscript H] =φD[subscript Β]/(1−φ) where φ is bed porosity and D[subscript B] is solid phase bead diameter and average bed interstitial velocity, V[subscript int]= V[subscript Darcy]/φ, where VDarcy= Q/A[subscript bed], with Q being the volumetric flow rate and A[subscript bed] the bed cross section normal to the flow. The flow characteristics are studied through application of a particle displacement technique called particle image velocimetry, PIV. In the case of PIV, flow fields are estimated by seeding the flow with tracer particles and then evaluating their displacements. Application of quantitative imaging technique such as PIV to a complex flow domain like porous bed requires matching refractive index of liquid phase to that of the solid phase. Firstly, the effect of slight index mismatch, due to experimental uncertainties, on obtaining highly accurate PIV measurements as expressed as an experimental uncertainty was explored. Mismatch of refractive indices leads to error in estimation of particle positions and their displacements due to refraction at solid-liquid interfaces. Slight mismatch, in order of 10⁻³, in refractive indices also leads to reduction in particle density, particle signal peak intensity and degrade the particle image. These effects on velocity field estimation using PIV is studied experimentally and numerically. The numerical model, after validating against experimental results, is used to generate an expression for the error in PIV measurements as a function of refractive index mismatch for a range of bead diameters, bed widths, bed porosity, and optical magnification. After refractive index matching, planar PIV measurements were taken at discrete locations throughout a randomly packed bed with aspect ratio (bed width to bead diameter) of 4.67 for steady, low pore Reynolds number flows, Re[subscript pore] ~ 6, intermediate Re[subscript pore] of 54 and unsteady flow with high Re[subscript pore] ranging from 400-4000. Details of the measurement uncertainties as well as methods to determine local magnification and determination of the dynamic velocity range are presented. The data are analyzed using the PIV correlation averaging method for steady flows and multigrid and multipass correlation methods for unsteady turbulent flows with the largest velocity uncertainties arising from in plane image loss and out of plane motion. Results for low Re[subscript pore] flows show the correspondence of the geometric and velocity correlation functions across the bed, and that the centerline of the bed shows a random-like distribution of velocity with an integral length scale on the order of one hydraulic diameter (or 0.38 bead diameters based on the porosity for this bed). The velocity variance is shown to increase by a factor of 1.8 when comparing the center plane data versus using data across the entire bed. It is shown that the large velocity variance contributes strongly to increased dispersion estimates, and that based on the center plane data of the variance and integral length scales, the dispersion coefficient matches well with that measured in high aspect ratio beds using global data. For unsteady and turbulent flow, velocity data were used to determine the following turbulence measures: (i) turbulent kinetic energy components, (ii) turbulent shear production rate, (iii) integral Eulerian length and time scales, and (iv) energy spectra all for a range of pore Reynolds numbers, Re[subscript pore], from 418 to 3964. These measures, when scaled with the bed hydraulic diameter, DH, and average interstitial velocity, V[subscript int], all collapse for Re[subscript pore], beyond approximately 2800, except that the integral scales collapse at a lower value near 1300-1800. The results show that the pore turbulence characteristics are remarkably similar from pore to pore and that scaling based on bed averaged variables like D[subscript H] and V[subscript int] characterizes their magnitudes despite very different local mean flow conditions. In the case of high Re[subscript pore] flows, large scale structures such as stationary and convected vortices and structures resembling jets were also identified. These structures were analyzed in detail using decomposition techniques like Large Eddy Scale decomposition and critical point analysis like swirl strength analysis. Direct velocity measurements were used to estimate Lagrangian statistics through Eulerian measures and then estimate contribution of flow structures to turbulent mechanical dispersion. Results agree well with those in the literature obtained using global measurements in very high aspect ratio, long test beds. Stationary vortical or recirculation regions were seen to play a dominant role in contributing to overall dispersion in porous beds. / Graduation date: 2013

Je reporte ici une étude expérimentale sur la réorganisation inertielle de liquide dans un microcanal, constitutif des mousses liquides, appelé le bord de Plateau qui est soutenu par trois films de savon. Deux perturbations sont appliquées sur un bord de Plateau. Premièrement, une goutte y est ajoutée. La viscosité du liquide et taille initiale du bord de Plateau et de la goutte sont variés. La redistribution du liquide ajouté est pilotée par les forces capillaires. On observe un régime inertiel où un ressaut hydraulique capillaire se déplace à vitesse et géométrie constantes dans le bord de Plateau. Ce régime est décrit théoriquement et révèle le rôle majeur joué par les films de savon. On observe aussi un régime dominé par les effets visqueux où le liquide ajouté est redistribué selon une dynamique de type diffusive. La transition entre les deux régimes dépend des paramètres de contrôle du système et est caractérisée. La seconde perturbation est acoustique. Une plaque vibrante perturbe le bord de Plateau et les films. La taille du bord de Plateau, la fréquence et l’amplitude de forçage sont variées. Une onde de flexion se propage dans les films qui ont le bord de Plateau pour condition limite fixe ou libre selon sa masse. A haute amplitude, un régime non linéaire apparaît et le liquide dans le bord de Plateau se réorganise en trois zones de taille et d’amplitude d’oscillation très contrastées. Dans chacune des zones, le déphasage entre l’onde dans le film et l’onde dans le bord de Plateau est différent. Le système couplé du film et du bord de Plateau est modélisé par un oscillateur forcé dont la fréquence propre dépend de la fréquence de forçage. / I report an experimental study of inertial liquid reorganization into a liquid foam microchannel, also called a Plateau border supported by three soap films. Two perturbations are applied on the Plateau border. Firstly, a liquid drop is injected. Liquid viscosity, drop size and Plateau border size are changed. The liquid redistribution is drived by capillary forces. We observe an inertial regime where a capillary hydraulic jump move on the Plateau border with a constant shape and a constant velocity. This regime is modeled and shows the importance of soap films. We also observe a viscous-dominated regime where the added liquid is redistributed with a diffusive-like dynamic. The transition between the two regimes is investigated and qualitatively accounted for. Secondly, the Plateau border and the three films are vibrated by a plate. A bending wave is shown to propagate in the soap films with the Plateau border for free or fixed limit conditions according to its mass. For high amplitudes, a non linear regime appears and the liquid inside the Plateau border is redistributed along three zones of very contrasted size and oscillation amplitudes. In each zone, the phase difference between the wave in soap films and the wave in Plateau border is different. The system composed of films and the Plateau border is modelled by a forced oscillator with a resonance frequency which depends on the forced frequency.

Les aquifères fissurés de type karst contiennent d'importantes ressources en eau. Ces aquifères sont complexes et hétérogènes sur une gamme d'échelles importantes. Leur gestion nécessite l'utilisation d'outils et de méthodologies adaptés. Dans le cadre de cette étude, différents outils et méthodologies numériques d'étude ont été développés pour la modélisation des aquifères karstiques, et plus généralement, des milieux poreux très fissurés 2D et 3D - en mettant l'accent sur la morphologie et sur le comportement hydrodynamique du milieu à travers la notion de changement d'échelle ("second changement d'échelle", reposant sur un modèle d'écoulement local de type Darcy et/ou Poiseuille avec quelques généralisations). Plusieurs axes sont explorés concernant la morphologie du milieu poreux fissuré (milieux aléatoires, milieux booléens avec réseaux statistiques de fissures, mais aussi, modèles morphogénétiques). L'étude du changement d'échelle hydrodynamique tourne autour du concept de macro perméabilité. Dans un premier temps, l'étude porte sur un modèle de perte de charge linéaire darcien. Les perméabilités effectives sont calculées numériquement en termes des fractions volumiques de fissures et du contraste de perméabilité matrice/fissures. Elles sont analysées et comparées à des modèles théoriques (analytiques). Une étude particulière des effets de quasi-percolation pour les grands contrastes aboutit à la définition de trois fractions critiques liées à des seuils de percolation. Pour tenir compte des effets inertiels dans les fissures, l'étude est étendue au cas d'une loi locale comprenant un terme quadratique en vitesse (Darcy/Ward-Forchheimer). Une perméabilité macroscopique équivalente non linéaire est définie et analysée à l'aide d'un modèle inertiel généralisé (linéaire/puissance). Enfin, l'anisotropie hydraulique à grande échelle du milieu fissuré est étudiée, en termes de perméabilités directionnelles, à l'aide d'une méthode numérique d'immersion. / Karstic aquifers contain large subsurface water resources. These aquifers are complex and heterogeneous on a large range of scales. Their management requires appropriate numerical tools and approaches. Various tools and numerical methodologies have been developed to characterize andmodel the geometry and hydraulic properties of karstic aquifers, more generally, of highly fissured 2D and 3D porous media. In this study, we emphasize morphological characterization, and we analyze hydrodynamic behavior through the concept of upscaling ("second upscaling"). Concerning the morphology of fissured porous media, several axes are explored : random media, composite random Boolean media with statistical properties, and morphogenetic models. Hydrodynamic upscaling is developed using the macro-permeability concept. This upscaling method is based on either Darcy's linear law, or on a linear/quadratic combination of Darcy's and Ward-Forchheimer's quadratic law (inertial effects). First, the study focuses on Darcy's linear head loss law, and Darcian effective permeabilities are calculated numerically in terms of volume fractions of fissures and "fissure/matrix" permeability contrasts. The results are analysed and compared with analytical results and bounds. A special study of percolation and quasi-percolation effects, for high contrasts, leads to defined three critical fractions. These critical fractions are "connected" to percolation thresholds. Secondly, in order to consider inertial effect in fissures, the study is extended to a local law with a quadratic velocity term (Darcy/Ward-Forchheimer). Then, an equivalent nonlinear macroscopic permeability is defined and analysed using a generalized inertial model (linear/power). Finally, the large scale hydraulic anisotropy of fissured medium is studied, in terms of directional permeabilities, using an "immersion" numerical method.

Ce travail de thèse concerne les écoulements de fluides à seuil de contrainte autour d‘un obstacle cylindrique en milieu confiné avec une configuration d‘écoulement de Poiseuille.Expérimentalement, un banc d‘essai permettant d‘obtenir un écoulement en continu dans un circuit fermé a été mis en place. Les régimes d‘écoulement rampant, recirculant et instationnaire périodique ont été étudiés. De nouveaux résultats ont été obtenus avec un fluide newtonien et des solutions de Carbopol, polymère permettant de réaliser des fluides à seuil modèles utilisés en recherche et développement et dans l‘industrie. Une caméra rapide et un éclairage plan laser a servi pour l‘établissement d‘images qui ont ensuite été traitées par PIV. Les champs de vitesses cinématiques, les morphologies d‘écoulement et les paramètres critiques de transitions de régimes ont été déterminés.Numériquement, un modèle viscoplastique basé sur la loi de Herschel-Bulkley régularisée a été utilisé. Des résultats comme les morphologies d‘écoulement, la localisation des zones rigides, les champs de vitesses ont été obtenus. Ceci a permis de comparer les différences entre les effets liés à la nature des gels de Carbopol et la modélisation viscoplastiques. Une étude spécifique sur le glissement à l‘interface fluide-structure a également été réalisée avec l‘utilisation d‘un modèle de lubrification élasto-hydrodynamique. / The flow of yield stress fluids around a circular cylinder in a confined geometry has been investigated with a Poiseuille flow configuration.Experimentally, a test set-up was built which provides a continuous flow in a closed loop. We studied creeping, recirculating and vortex shedding flow regimes. New results has been realised with a Newtonian fluid and Carbopol solutions, models for yield stress behaviour in laboratory experiments and in industry. A high speed camera and a laser sheet have been used to perform images which are treated by PIV. Kinematic fields, flow morphologies and critical transition parameters have been determined.Numerically, a viscoplastic model based on the regularised Herschel-Bulkley law has been used. Results as flow morphologies, rigid areas and local flow parameters fields have been performed. That allowed us to compare the intrinsic effects of Carbopol solutions and the viscoplastic numerical model. A specific study on the wall slip has also been considered with an elasto-hydrodynamic lubrication model.