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.

中文翻译：

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筒仓内致密颗粒流的全局自相似性：筒仓宽度的作用


通过实验和模拟研究了二维筒仓宽度对密粒流的影响。尽管对于较大的筒仓宽度，流量保持稳定，但筒仓宽度的轻微减小会导致对于较小的筒仓宽度，流量显着增加。 Beverloo 和 Janda 的公式都准确地捕捉了流量和出口尺寸之间的关系。出口附近区域的流动特性表现出局部自相似性，支持 Beverloo 和 Janda 的原理。此外，还分析了全局自相似性，表现为流动状态从远离出口区域的质量流到靠近出口的漏斗流的转变。这种转变的较早发生有利于提高颗粒速度，从而增加密流率。提出了指数缩放定律来描述流量、颗粒速度和过渡高度对筒仓宽度的依赖性。