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Flow dynamics of spherical grains through conical cardboard hoppers

机译：球形颗粒通过锥形纸板漏斗的流动动力学

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The gravity-driven flow of monodisperse spherical grains of different nature and diameter d, through conical cardboard hoppers, has been studied as function of the orifice diameter D for different values of the aperture angle (similar to 3 degrees divided by 15 degrees) at large grains conditions (D10d). The mass flow rate trend function has displayed, at the lowest angles, a series of linear tracts, with increasing slope, delimited by approximately odd integers of the grains diameter. The linear tracts have been associated to different flow rate regimes, governed by the formation, at the bottom of the granular column, of short-lived arches of quantized size (similar to 5d, similar to 7d, similar to 9d, ...), acting as brakes to flow, by their detachment and ejection from the hopper. This mechanism of events should give rise to a modulation of the flow whose frequency was effectively measured, for the arches of similar to 5d size, by analyzing the signal produced by the falling grains on a microphone. The data of mass flow rate W, as function of the orifice diameter D, have shown, on average, a growth following the 5/2 power-law function, as foreseen by the well-known Beverloo law. Here we analyze the simplified expression of the mass flow rate with the dimension of the square root of the acceleration of gravity, which shows only a slight dependence on the aperture angle of the hopper. The jamming of grains at the outlet opening has been also investigated throughout the transition region at D similar to 3d divided by 4d, which characterizes the passage from the blocked to the continuous flow for few tens thousand grains, by an optical method and by measuring the frequency of the clogging events.
机译：研究了不同性质和直径d的单分散球形颗粒通过圆锥形纸板料斗的重力驱动流，其对于大孔径角（近似于3度除以15度）的不同值与孔直径D的关系。谷物条件（D10d）。质量流率趋势函数已在最低角度显示了一系列线性区域，这些线性区域的斜率不断增加，并由晶粒直径的近似奇数定界。线性束已与不同的流量模式相关联，这取决于颗粒大小的底部（尺寸近似于5d，类似于7d，类似于9d等）的短寿命拱门的形成。通过从料斗中分离和弹出，起到制动的作用。通过分析传声器上掉落的谷物所产生的信号，这种事件机制应该引起流量的调制，对于类似于5d尺寸的拱形，可以有效测量其频率。质量流量W的数据，作为孔直径D的函数，平均显示出遵循5/2幂律函数的增长，这是众所周知的贝弗洛定律所预见的。在这里，我们用重力加速度平方根的大小来分析质量流率的简化表达式，该表达式仅显示出与料斗孔径角的微小关系。还通过D的过渡区域（类似于3d除以4d）研究了谷物在出口处的堵塞，这是通过光学方法并通过测量3万个谷物从阻塞流向连续流的通道来表征的。堵塞事件的发生频率。

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