Computationally generated constitutive models for rheology of frictional non-cohesive and cohesive particles in gas-solid flows

Two-Fluid Model and Multi-Phase Particle-In-Cell simulations are commonly used to investigate gas-solid flow behaviors in fluidized beds. Both approaches require constitutive model for particle phase stress. The kinetic theory of granular materials [1-3] is widely used to close the particle phase stress in flowing assemblies of monodisperse non-cohesive frictionless particles. On the basis of Discrete Element Method (DEM) simulation results, ad hoc modifications to the kinetic theory [4-5] have been proposed to improve the accuracy in dense assemblies and to account for inter-particle friction. To account for inter-particle cohesion, several modifications to kinetic theory have been proposed [6-9].
In the present study, we perform CFD-DEM simulations for gas-fluidization of frictional, non-cohesive and cohesive particles in a periodic domain. By analyzing snapshots gathered from the simulation, quantities of interest in formulating a rheological model are determined. These results then guide refinement to the kinetic theory based stress model.

We first show that this approach, when applied to monodisperse non-cohesive particles, leads to results for pressure and shear viscosity that are consistent with the standard kinetic theory [1] coupled with the radial distribution function at contact from Chialvo & Sundaresan [4]. However, bulk viscosity is found to depend on whether the particle phase is in compression or dilation which is not accounted for in the kinetic theory.

For cohesive particles, it is found that inter-particle cohesion does not noticeably affect the particle phase stress except for at high solid volume fractions and low granular temperatures. This observation is consistent with the previous finding [10] based on simple shear simulations of cohesive particles.

This computational approach can be used to formulate simple rheological models for systems with size distribution, as well as particle-particle interactions due to liquid bridge or electrostatic interactions.