Constitutive model development for flows of granular materials

Abstract

Granular flows are ubiquitous in both natural and industrial processes. When com- posed of dry, noncohesive particles, they manifest three different flow regimes -- commonly referred to as the quasistatic, inertial, and intermediate regimes -- each of which exhibits its own dependences on solids volume fraction, shear rate, and particle-level properties. The differences in these regimes can be attributed to mi- croscale phenomena, with quasistatic flows being dominated by enduring, frictional contacts between grains, inertial flows by grain collisions, and intermediate flows by a combination of the two. Existing constitutive models for the solids-phase stress tend to focus on one or two regimes at a time, with a limited degree of success; the same is true of models for wall-boundary conditions for granular flows. Moreover, these models tend not to be based on detailed particle-level flow data, either from experiment or simulation. Clearly, a comprehensive modeling framework is lacking. The work in this thesis aims to address these issues by proposing continuum models constructed on the basis of discrete element method (DEM) simulations of granular shear flows. Specifically, we propose (a) a constitutive stress model that bridges the three dense flow regimes, (b) an modified kinetic-theory model that covers both the dense and dilute ends of the inertial regime, and (c) a boundary-condition model for dense, wall-bounded flows. These models facilitate the modeling of a wide range of flow systems of practical interest and provide ideas for further model development and refinement.