Abstracts Category : Other

Dynamical modelling and numerical simulation of grain-fluid mixture flows

by Xiannan Meng

Flows of grain-fluid mixtures are commonly observed in nature and in industry.However, comprehensive understanding of the physics behind them is to date outof reach. This thesis aims to investigate the mechanism underlying flowing grain-fluid mixtures by both analytical and numerical methods.The work of this thesis starts with introducing standard mixture theory to describe the balance equations of mass and momentum for the fluid and the granular phases of grain-fluid mixtures. As the first step, the flowing mixtures are idealized to be saturated media, indicating that the fluid phase fills all the voids between the particles. Accordingly, the granular phase is treated as a frictional Coulomb-like media, while the fluid phase is modelled as a Newtonian fluid. The interaction forces between the two phases include buoyancy force and drag force. Taking into account the flow characteristics that the flow depth is much smaller than the flow length, the thin-layer approximation and the depth-averaged technique are employed to eliminate the dependency of the governing equations on the vertical coordinate, so that a set of depth-averaged equations are derived. The depth-averaged equations are analyzed in terms of steady flows down an inclined plane. It is found that the present model equations can interpret the classical cross-stream profiles of the downslope velocity, the blunt shape of the flowing front, and roll waves. Additionally, the depth-averaged equations are numerically resolved by using a high-resolution scheme with respect to a large-scale unsteady flow, and the numerical results are compared with the experimental data. The comparison demonstrates that this model is capable to describe dynamics of a grain-fluid mixture flow, such as the evolutions of the mixture height and volume fractions.Moreover, unsaturated grain-fluid mixtures are considered, in which the fluid phase cannot fill all interstices of the granular medium. To investigate their dynamic process, it is assumed that the fluid percolates easily down through the interstices of the granular medium and as a result the air is extruded. To describe such a kind of unsaturated mixtures, a two-layer approach is proposed, in which the fluid-saturated granular layer is overlaid by the pure granular material. The upper granular mass is treated as a frictional Coulomb-like medium, and the lower layer is described by the standard mixture theory. The lower and upper layers interact at an interface which is a material surface for the fluid phase, but across which the mass exchange for the granular phase may take place. The proposed model equations are numerically resolved, and the numerical solutions demonstrate that the proposed two-layer model can provide reasonable predictions with respect to dynamic process of unsaturated mixture flows.The last part of this thesis focuses on the improvement of the saturated depth-averaged model, presented in the first part of the thesis, by taking the granular dilatancy into account.The granular dilatancy isAdvisors/Committee Members: Wang, Yongqi (advisor), Oberlack, Martin (advisor).