Numerical investigation of steady and unsteady state hopper flows

This paper presents a numerical study of the steady and unsteady state granular flows in a cylindrical hopper with flat bottom by means of the discrete element method (DEM). For both flows, the simulations were conducted under comparable conditions so that the similarity and difference between them can be examined. The distributions of the physical properties including velocity, force structure, stress and couple stress for the two hopper flows are investigated. The results suggest that the trends of these distributions for the two hopper flows are similar. In particular, for both cases, the distributions of the normal stresses are related to the normal force structures. Thus, corresponding to the large interaction forces between particles near the bottom corner and in the transitional zone, all the normal stresses are large near the bottom corner, and the radial and circumferential normal stresses are relatively large in the transitional zone. However, there are differences in the magnitudes of some physical properties for the unsteady and steady state flows. Compared with the steady state flow, the unsteady state flow has a narrower velocity distribution, and more particles experience large contact forces. Its radial and circumferential normal stresses in the plug flow and transitional zones are larger. With the decrease of the number of particles or with discharging time, the plug flow and transitional zones reduce, and the differences in the considered properties except wall shear stress and couple stress between the two flows decrease.

The similarity and difference between the steady and unsteady state hopper flows are studied in terms of spatial and statistical distributions of a range of variables under comparable conditions by means of the discrete element method. The results (e.g. Fig. 1) suggest that these distributions for the two flows are qualitatively similar, but may quantitatively differ which should be investigated further.Figure optionsDownload as PowerPoint slideFig. 1 Spatial distributions of stress Tzz (left), couple stress Mrθ (middle), and the radial normal and shear stresses at wall (right) when the discharging time is 120d/g for the steady and unsteady state flows considered (the units for the stresses are πρpdg/6).