(144f) Continuum Simulations of Granular Flow Near the Maximum Packing Limit Using a Novel Solution Approach to Address Realizability

The hydrodynamics and rheology of powder flow are critical in many industrial processes such as pharmaceutical and agricultural production, and petrochemical refining. Continuum simulations solve the averaged equations for conservation of mass and momentum by treating the granular medium as a continuum to predict granular hydrodynamics. A comparison of continuum simulations of silo discharge (Vidyapati et al. 2013) with experimental data and discrete element model simulations indicates that the simulations are limited in their accuracy of predicted discharge rates by the constitutive model for granular stress. One of the challenges in incorporating newly proposed constitutive models for the granular stress in continuum simulations, which account for intermediate regime behavior (Chialvo et al. 2012, Sun et al. 2011, Vidyapati et al. 2016), is ensuring their realizable behavior near the maximum packing limit. Realizability in this context means guaranteeing that the solid volume fraction is always non-negative and does not exceed its theoretical maximum value without ad hoc modifications.

The behavior of continuum solvers near the packing limit depends on the constitutive model for the granular pressure as a function of solid volume fraction. As the solid volume fraction approaches the maximum packing limit, there is a threshold above which the granular material behaves like an incompressible fluid, resulting in high granular pressures. High pressures generate a moving shock that requires special numerical treatment including (1) formulation of the governing equations in terms of conserved variables, and (2) a flux-splitting scheme which is monotone and total-variation-diminishing (TVD) in order to capture the propagating shock waves. This solution method gives accurate results without any ad hoc modifications, even when the pressure versus volume fraction curve does not have a steep slope as the volume fraction approaches the maximum packing limit.

The newly developed computational scheme is implemented in OpenFOAM. We report solutions to a three-dimensional (3-D) granular flow problem illustrating the transition from variable density to incompressible regime at the maximum packing limit by extending the previously reported 1-D canonical problem when a sphere consisting of granular particles is compressed isotropically. We verify the solution method using the well-known Sedov Point Blast problem to establish accuracy. Continuum simulations of silo discharge using the novel numerical approach have been compared to experimental data and discrete element model simulations to validate the results, and good agreement is observed.