Discharge rate characterization for submerged grains flowing through a hopper using DEM-LBM simulations

Submerged granular flows through an orifice were investigated numerically in the context of sinkhole occurrences during a flood due to the presence of underground conduits. To account for fluid-solid interaction at the pore-scale, we use a numerical modelling that combines the Discrete Element Method (DEM) for the solid particles with the Lattice Boltzmann Method (LBM) for the fluid dynamics. The numerical setup studied is a submerged granular discharge from a hopper, which is shown to be particularly sensitive to hydraulic boundary conditions. With a given choice of configuration, we performed a parametric study by varying particle diameters, fluid viscosity and hopper orifice size, enabling the exploration of the Archimedes number over five orders of magnitude. The solid discharge rates are shown to have self-similar temporal evolutions and the grains at the orifice display self-similar velocity profiles, normalized by the maximum velocity reached at the center of the orifice. In this paper, we finally propose an extension of the classical Beverloo law that takes into account the effect of fluid entrainment by the downward granular flow.