Study on free fall surfaces in three-dimensional hopper flows

• DEM simulation of hopper flows were performed on multiple GPUs.
• The free-fall surface in hopper flows were plotted by statistical methods.
• The surface can be fitted into parabolic surface.
• The surface show good consistency in terms of other quantities.

The flow rate of grains discharging from hoppers can be quantified by Beverloo’s law, where the assumption of the free fall arch (FFA) it is very useful in understanding the physical picture of this process but is difficult to be observed directly. Here simulations of 2,000,000 spheres discharging from three-dimensional flat-bottomed hopper with circular outlet were performed on multiple GPUs and the free fall surfaces were explored by statistical analysis. The free fall surfaces in hopper flows were plotted and can be fitted into parabolic surfaces. Other quantities, such as velocity fields and spatial profiles of coordination number, were investigated to support the free fall surfaces we obtained. Although inconsistent with the initial assumption, it is shown that the free fall surfaces can be statistically described and this work provides new insights for understanding the processes of hopper flows.

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