Analysis of granular rheology in a quasi-two-dimensional slow flow by means of discrete element method based simulations

Abstract

The steady flow of spherical particles in a rectangular bin is studied using the discrete element method for different flow rates of the particles from the bin in the slow flow regime. The flow has two nonzero velocity components and is more complex than the widely studied unidirectional shear flows. The objective of the study is to characterize, in detail, the local rheology of the flowing material. The flow is shown to be of nearly constant density, with a symmetric stress tensor and the principal directions of the stress and rate of strain tensors being nearly colinear. The local rheology is analyzed using a coordinate transformation which enables direct computation of the viscosity and components of the pressure assuming the granular material to be a generalized Newtonian fluid. The scaled viscosity, fluctuation velocity, and volume fraction are shown to follow power law relations with the inertial number, a scaled shear rate, and data for different flow rates collapse to a single curve in each case. Results for flow of the particles on an inclined surface, presented for comparison, are similar to those for the bin flow but with a lower viscosity and a higher solid fraction due to layering of the particles. The in plane normal stresses are nearly equal and slightly larger than the third component. All three normal stresses correlate well with the corresponding fluctuation velocity components. Based on the empirical correlations obtained, a continuum model is presented for computation of granular flows.