Analysis of Granular Flow in a Wedge-Shaped Hopper

RESUMO

We study the velocity and stress distribution for a planar granular flow in a wedge-shaped hopper using Discrete Element Method simulations. Periodic boundary conditions are used in the direction normal to the plane of the flow to simulate a layer system. A parametric study is carried out varying system parameters (orifice width, wedge angle, wall friction and hopper height) and particle properties (particle diameter and particle friction). Scaling relations are obtained for the velocity and stress ratios. The data indicate that the stresses are not dependent on the shear rate, as in the Mohr-Coulomb rheology, however, the friction coefficient varies spatially, and the coaxiality condition is violated in some regions of the flow. A theory based on the scaling relations is presented, which gives good predictions for all the cases studied. Based on the theory, an expression for the mass flow rate, incorporating the effect of system parameters and particle properties is derived, which gives a close match with the computed mass flow rates for all the cases.