This study utilizes computations based on a soft-particle discrete element method for investigating the scaling of velocity in the region of orifice influence situated directly above and in proximity to the outlet in a two-dimensional silo. The velocity at the exit scales with the outlet size ($D$), in striking agreement with the earlier studies. However, the scaling of velocity upstream of the outlet with $D$ as the length scale does not exist. Consequently, we present a scaling with a length parameter $h_e$ being the height of an equi-inertial curve, which is defined to be a curve on which the inertial number is constant, thereby consolidating the coexisting different flow regimes in a discharging silo. The velocity corresponding to an equi-inertial curve, when measured relative to the velocity at the outlet, scales very well with $h_e$ for low inertial numbers belonging to the dense flow regime. However, such scaling does not hold for high inertial numbers corresponding to the rapid flow regime in the region located closer to the orifice. We tie this scaling breakdown to the velocity fluctuations in light of the similarity between the profiles of scaled relative velocity and the scaled kinetic pressure, suggesting $h_e$ to be a promising candidate for unifying the kinematics of granular flow near the outlet in the silo.

中文翻译：

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孔口区域的速度缩放对重力作用下筒仓排水的影响

这项研究利用基于软粒子离散元方法的计算方法，来研究位于二维筒仓中出口上方和附近的孔口影响区域中速度的缩放比例。出口处的速度与出口尺寸成正比（$d$），并与早期的研究达成了一致。但是，出口上游速度的比例随$d$因为长度刻度不存在。因此，我们提出一个带有长度参数的缩放$H_{Ë}$是等惯性曲线的高度，它定义为惯性数恒定的曲线，从而巩固了排放筒仓中并存的不同流态。当相对于出口处的速度进行测量时，与等惯性曲线相对应的速度与$H_{Ë}$属于稠密流动状态的低惯性数。然而，这种缩放不适用于与位于靠近孔口的区域中的快速流动状态相对应的高惯性数。根据缩放后的相对速度和缩放后的动压之间的相似性，我们将此缩放分解与速度波动相关联，表明$H_{Ë}$ 成为统一筒仓出口附近的颗粒流动运动学的有希望的候选人。