Influence of an inserted bar on the flow regimes in the hopper

We investigated the influence of an inserted bar on the hopper flow experimentally.Three geometrical parameters,size of upper outlet D1,size of lower outlet D0,and the height of bar H,are variables here.With varying H we found three regimes:one transition from clogging to a surface flow and another transition from a surface flow to a dense flow.For the dense flow,the flow rate follows Beverloo’s law and there is a saturation of inclination of free surfaceθ.We plotted the velocity field and there is a uniform linear relation between the particle velocity and depth from the free surface.We also found that the required value of D₁ to guarantee the connectivity of flow is little smaller than D₀.For the transition from a surface flow to a dense flow,there is a jump of flow rate and the minimumθfor flowing is two degrees larger than the repose angle.