Granular flow in wedge-shaped hoppers using frictional walls: Theory and simulations.*

Granular materials consist of particulate particles found in industries that, behave macroscopically like liquids. A fundamental industrial unit operation is a hopper with a converging channel in which material flows downward under gravity and exits the storage bin through the bottom outlet. The simplest form of the flow is a wedge-shaped, quasi-two-dimensional geometry with frictional walls and radially directed gravitational force toward the apex of the wedge. To test existing theories and calculate stress and velocity fields for the system, we used discrete element method simulation. A parametric analysis is carried out to analyze the rheology by varying the hopper geometry and particle properties. The velocity increases as the flow rate increases but decreases as the wedge angle and friction coefficient increase. We obtained shear stress to be of significant value that showed a linear relationship with radial positions. The fitting function in terms of velocity and the correlation between the mass flow rate are obtained in terms of the system parameters. The studies were performed to examine the transient effects showing significant deviations from mean behaviour having large quasi-periodic oscillations making such deviations observable. The viscosity and volume fraction exhibit correlations with the inertial number showing collapse into a single curve. The results show the utility of the frictional wall hopper flow as a model for the computational evaluation of rheological models.