(143d) Implementation of a Non-Local Granular Fluidity Model in Openfoam for Simulation in Arbitrary 3D Geometries

Unlike simple liquids and gases, the bulk flow and transport of granular materials remain poorly understood by physicists and pose many problems for engineers. Discrete element methods (DEM) are currently considered the state-of-the-art for simulating the flow of granular materials, but DEM is limited in system size to about a few million particles due to high computational costs, even when run on current high-performance computing architectures. This limitation prevents the simulation of flows in industrial-scale vessels and equipment, e.g., grain silos and coal-ash disposal piles, where particle counts can easily approach 100 million to a billion. There are several notable and ongoing efforts to develop continuum constitutive models to describe the emergent dynamic behavior of deforming granular materials, including the so-called inertial rheology model [Nature, 441(7094), 727–730]. Many of these models are unable to reproduce nonlocal behavior that arise when granular phenomena occur on length scales that are near the scale of the system geometry, e.g., jamming of hopper outlets. More recently, an extension to the inertial rheology model has been proposed, called the nonlocal granular fluidity (NLGF) model, that is able to quantitatively reproduce flow phenomena that depend on system length scales [PNAS, 110(17), 6730–6735]. While inertial-rheology models have been implemented and demonstrated in volume-of-fluid (VOF) CFD solvers, according to our knowledge the NLGF model has been so far only solved analytically for simple cases and implemented for defined strains in FEM software. In this work, we implement the NLGF model in a VOF solver developed on the OpenFOAM CFD framework. An evolution equation for a scalar fluidity variable is solved along with the Navier-Stokes equations for each volume element and at each time increment, where the viscosity is a function of the fluidity and pressure. A regularization of the viscosity is required due to yield-stress behavior that would otherwise result in infinite viscosity values. Our new NLGF-VOF solver is demonstrated for a few simple flow geometries, including flow down an incline and out of a silo, and the simulation results are compared to those found in the literature.