Effect of particle shape on the flow of an hourglass

Bo Fan, Tivadar Pongó, Raúl Cruz Hidalgo, Tamás Börzsönyi
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Abstract

The flow rate of a granulate out of a cylindrical container is studied as a function of particle shape for flat and elongated ellipsoids experimentally and numerically. We find a nonmonotonic dependence of the flow rate on the grain aspect ratio a/b. Starting from spheres the flow rate grows and has two maxima around the aspect ratios of a/b = 0.6 (lentil-like ellipsoids) and a/b = 1.5 (rice-like ellipsoids) reaching a flow rate increase of about 15% for lentils compared to spheres. For even more anisometric shapes (a/b = 0.25 and a/b = 4) the flow rate drops. Our results reveal two contributing factors to the nonmonotonic nature of the flow rate: both the packing fraction and the particle velocity through the orifice are nonmonotonic functions of the grain shape. Thus, particles with slightly non-spherical shapes not only form a better packing in the silo but also move faster through the orifice than spheres. We also show that the resistance of the granulate against shearing increases with aspect ratio for both elongated and flat particles, thus change in the effective friction of the granulate due to changing particle shape does not coincide with the trend in the flow rate.
颗粒形状对沙漏流动的影响
通过实验和数值计算,研究了扁平椭圆体和拉长椭圆体颗粒从圆柱形容器中流出的流速与颗粒形状的函数关系。我们发现流速与颗粒长宽比 a/b 存在非单调关系。从球形开始,流速不断增加,在长宽比 a/b = 0.6(扁豆状椭圆体)和 a/b = 1.5(大米状椭圆体)附近有两个最大值,扁豆的流速比球形增加了约 15%。对于更多的异形(a/b = 0.25 和 a/b = 4),流速则会下降。我们的结果揭示了导致流速非单调性的两个因素:堆积分数和颗粒通过孔口的速度都是颗粒形状的非单调函数。因此,略呈非球形的颗粒不仅能在筒仓中形成更好的堆积,而且通过孔口的速度也比球形颗粒快。我们还发现,无论是细长颗粒还是扁平颗粒,颗粒对剪切的阻力都会随长径比的增加而增加,因此颗粒形状的变化导致颗粒有效摩擦力的变化与流速的变化趋势并不一致。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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