Ce travail de thèse concerne la modélisation numérique fine des processus locaux dans le transport sédimentaire, à l'échelle d'un à plusieurs centaines de grains. Une méthode aux éléments discrets (DEM) basée sur la méthode dite des sphères molles et prenant en compte les contacts entre les grains a été développée et couplée à une méthode de frontière immergée (IBM) qui calcule l'écoulement autour d'objets solides mobiles dans un fluide Newtonien incompressible. Dans ce couplage, une force de lubrification est incluse pour représenter les interactions entre le fluide et les particules proches d'un contact. Il est montré que la méthode numérique reproduit de manière satisfaisante le coefficient de restitution effective mesuré dans des expériences de rebonds normal et oblique d'un grain sur un plan, ainsi que de rebond entre deux grains dans un fluide visqueux. Deux modèles analytiques associés au phénomène de rebond sont proposés et montrent l'importance de la rugosité de surface du grain et du nombre de Stokes sur le phénomène. La méthode numérique est ensuite utilisée pour simuler deux configurations tridimensionnelles d'écoulements granulaires pilotés par la gravité en milieu fluide : l'avalanche de grains sur un plan incliné rugueux et l'effondrement d'une colonne de grains. Dans le premier cas, les résultats permettent de caractériser les différents régimes d'écoulement granulaires (visqueux, inertiel et sec) observés dans les expériences en fonction du rapport de masse volumique grain-fluide et du nombre de Stokes. En particulier, les simulations apportent des informations originales quant aux profils de vitesse de grains et du fluide ainsi qu'aux forces prédominantes dans chacun des régimes. Dans le second cas, les résultats sont en bon accord avec les expériences et le mécanisme dit de « pore pressure feedback », qui dépend de la compacité initiale de la colonne, est pour la première fois observé dans des simulations numériques directes. / This work deals with direct numerical simulations of sediment transport at the scale of O(103) grains. A soft-sphere discrete element method (DEM) taking into account grain contacts is developed and coupled to an immersed boundary method (IBM) which computes the flow around moving solid objects in an incompressible Newtonian fluid. A lubrication force is added for representing fluid-particles interaction near contact. The numerical method is shown to adequately reproduce the effective coefficient of restitution measured in experiments of the normal and oblique rebound of a grain on a plane and the rebound between two grains in a viscous fluid. Two analytical models are proposed and highlight the importance of the grain roughness and Stokes number on the rebound phenomenon. This numerical method is then used for simulating two three-dimensional configurations of gravity-driven dense granular flow in a fluid, namely the granular avalanche on a rough inclined plane and the collapse of a granular column. In the first case, results allow to characterize the granular flow regimes (viscous, inertial and dry) observed in experiments as a function of the grain-to-fluid density ratio and the Stokes number. In particular, the simulations provide insight on the grain and fluid velocity profiles and force balance in each regime. In the second case, results agree well with experiments and in particular the pore pressure feedback, which depends on the initial volume fraction of the column, is observed for the first time in direct numerical simulations.

Sedimenting suspensions exist in a varity of natural phenomena and industrial applications. It is already observed in experiments that the dilute fibre suspensions experience a hydrodynamics instability under gravity at low Reynolds numbers. Initially well-mixed suspensions become inhomogeneous and anisotropic due to this instability.The main goal of this work is to understand the instability in a dilute fibre suspension by means of an Eulerian approach which is based on the Navier-Stokes equations coupled to Fokker-Planck equation for the PDF of fibres.Using a linear stability analysis, we show that inertia and hydrodynamic translational diffusion damp perturbations at long wavelengths and short wavelengths, respectively, leading to a wavenumber selection. For small, but finite Reynolds number of the fluid bulk motion, the most unstable wavenumber is a finite value which increases with Reynolds number, and where the diffusion narrows the range of unstable wavenumbers. With periodic boundary conditions, numerical simulations of the full non-linear evolution in time of a normal mode perturbation show that the induced flow may either die or saturate on a finite amplitude. The character of this long time behaviour is dictated by the wavenumber and the presence or absence of the translational and rotational diffusivities.In a simulation domain confined by vertical walls, a series of alternating structures of risers and streamers emerge continuously from the walls until they meet in the middle of the domain. For moderate times, this agrees qualitatively with experimental and theoretical results. Moreover, our simulation in a vessel of infinite height obtained an increasing wavelength evolution due to the congregation of the streamers or risers. In the end, there is constantly only one streamer left, and it drifts randomly to one side of the container until the evolution reaches a steady state. It is also found that the perturbations added to the initial conditions can induce more high density regions whose sizes and velocities are strongly linked to the initial perturbations of the number density or the flow field. In addition, the maximum number of streamers increases with Reynolds number, volume fraction and channel width. / QC 20120625