Granular flow in a quasi-two-dimensional wedge-shaped hopper: experiments and simulations

We carry out an experimental study of granular flow in a quasi-two-dimensional wedge-shaped hopper, with glass front and back walls, using videography, along with image analysis and particle tracking. Results are presented for different orifice sizes and roughnesses of the sidewalls for nearly spherical glass and steel particles of different sizes. The data for the radial velocity in the hopper (wedge angle $2\theta _w$ ) are well described by $v_r(r,\theta )=v_{r0}(r)[1-F(r)(\theta /\theta _w)^2],$ in cylindrical coordinates $(r,\theta )$ , with the origin at the apex of the wedge. The centreline velocity is given by $v_{r0}=(a_0/r+a_1)$ , and the effective wall friction by $F=(b_0+b_1r)$ , where $a_0$ and $a_1$ increase with orifice width, while $b_0$ increases with roughness. For the smooth wall system, we obtain $F\in (0,1)$ , however, for the rough walls $F\gt 1$ for most cases, with the velocity at the wall being zero, and a few layers of slow-moving particles adjacent to the wall. The mass flow rate scaled by the particle density and the radial velocity profile are independent of the particle density, for a threefold increase in the density, implying insignificant inertial effects. Discrete element method simulations are carried out using glass particles for a system of the same size as the experimental hopper, with the simulation parameters calibrated to closely match the experimental results. The simulation results indicate that the variation in the direction normal to the plane of the flow is small and the radial velocity profiles without the front and back walls are similar to the experimental profiles.