Modelling and simulation of fluid-saturated granular materials with application to sedimentation flows

This PhD thesis is concerned with the continuum modelling of fluid-saturated granular mixtures, with particular emphasis on constant-density stratified flows. It tackles the theoretical description of these mixtures (which are treated as non-Brownian granular suspensions), the development of suitable computational algorithms and the simulation of flows of interest. The first Chapter of this thesis contains a brief introduction to suspension modelling, and delineates its application to a continuum description of sedimentation processes. The motivation for this work is presented and the final objectives are discussed. In the second Chapter, test problems of granular transport are studied with the help of a recently-developed two-phase continuum model. More specifically, this Chapter concerns channel flows over compacted granular beds. The predictive capabilities of the model and its limits are investigated; particular attention is devoted to the evolution equation for the volume fraction, which is of primary importance in the description of sedimentation and erosion phenomena. The third Chapter is concerned with the derivation of a new model for two-phase flows of granular suspensions. This model, which is based on a generalization of the classical theory of irreversible processes, is developed in order to account for a number of physical phenomena that are of particular relevance to granular transport; notably, it accounts for compaction, which has a profound impact on granular rheology. The fourth Chapter presents the application of the newly-derived model to channel flow at low-Reynolds number. This flow is chosen as a benchmark since particle migration plays a crucial role in the definition of its particle-concentration profile. Numerical results are compared with existing experimental measurements and particle-resolved simulations, finding good agreement. Further, the role of intergranular and nonlocal stresses in particle migration is investigated. The fifth Chapter describes the derivation of a general numerical algorithm, based on a two-phase fractional-step projection method, which can be applied to the governing equations of the proposed flow model for the description of unsteady multi-dimensional flows. The specific numerical challenges presented by the new equations are discussed and a suitable treatment is proposed. The sixth Chapter presents numerical results relative to sedimentation processes. First, the sedimentation and settling of a suspension into a granular bed is investigated in order to validate the particle-migration model. Subsequently, computations are presented relative to the collapse of a granular column submerged under water. This flow is used to validate the modelling of suspension rheology, and further to provide insight into a benchmark flow for applications involving granular transport due to gravity.(FSA - Sciences de l'ingénieur) -- UCL, 201