Global self-similarity of dense granular flow in silo: The role of silo width

The influence of silo width on dense granular flow in a two-dimensional silo is investigated through experiments and simulations. Though the flow rate remains stable for larger silo widths, a slight reduction in silo width results in a significant increase in flow rate for smaller silo widths. Both Beverloo's and Janda's formula accurately capture the relationship between the flow rate and outlet size. Flow characteristics in the regions near the outlet exhibit local self-similarity, supporting Beverloo and Janda's principles. Moreover, global self-similarity is analyzed, indicated by the transition in flow state from mass flow in regions far from the outlet to funnel flow near the outlet. The earlier occurrence of this transition favors to enhance the grain velocity and consequently increases the dense flow rate. An exponential scaling law is proposed to describe the dependencies of flow rate, grain velocity, and transition height on silo width.