Velocity profile of granular flows inside silos and hoppers
Velocity profile of granular flows inside silos and hoppers
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DOI：
10.1088/0953-8984/17/24/011
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发表时间：
2005-06-22
影响因子：
2.7
通讯作者：
Bazant, MZ
中科院分区：
文献类型：
--
作者：
Choi, J;Kudrolli, A;Bazant, MZ
我们测量了准二维筒仓排水时散体材料的流动，并将数据与现有的一些模型进行了比较。筒仓内的颗粒在空间和时间上都以前所未有的分辨率被成像和跟踪，以获得它们的速度和扩散特性。通过改变孔板宽度和料斗角度获得的数据使我们能够彻底测试这些几何形状内重力驱动的流动模型。我们测得的所有速度剖面都是光滑的，没有临界状态土力学预测的激波状不连续(‘破裂区’)。另一方面，我们发现，简单的运动学模型虽然不能描述远离孔口的塞状流的快速转变，但它准确地捕捉到了孔口附近的平均速度分布。模型中唯一的自由参数扩散长度b并不像通常假设的那样是恒定的，而是随着孔板上方高度和料斗角度的增大而增大。我们讨论了对模型的改进，以解释这些差异。从我们的数据中，我们还直接测量了颗粒的扩散，发现它明显小于空穴模型的预测，后者提供了经典的运动学模型的微观推导，根据空穴在填料中的扩散。然而，实验数据与最近提出的基于一种简单的合作扩散机制的斑点模型是一致的。最后，我们讨论了流量与孔板宽度和料斗角度的函数关系。我们发现流量与孔板尺寸成1.5次方的关系，这与量纲分析一致。有趣的是，流量随着漏斗角度的增加而增加。
We measure the flow of granular materials inside a quasi-two-dimensional silo as it drains and compare the data with some existing models. The particles inside the silo are imaged and tracked with unprecedented resolution in both space and time to obtain their velocity and diffusion properties. The data obtained by varying the orifice width and the hopper angle allow us to thoroughly test models of gravity driven flows inside these geometries. All of our measured velocity profiles are smooth and free of the shock-like discontinuities ('rupture zones') predicted by critical state soil mechanics. On the other hand, we find that the simple kinematic model accurately captures the mean velocity profile near the orifice, although it fails to describe the rapid transition to plug flow far away from the orifice. The measured diffusion length b, the only free parameter in the model, is not constant as usually assumed, but increases with both the height above the orifice and the angle of the hopper. We discuss improvements to the model to account for the differences. From our data, we also directly measure the diffusion of the particles and find it to be significantly less than predicted by the void model, which provides the classical microscopic derivation of the kinematic model in terms of diffusing voids in the packing. However, the experimental data are consistent with the recently proposed spot model, based on a simple mechanism for cooperative diffusion. Finally, we discuss the flow rate as a function of the orifice width and hopper angles. We find that the flow rate scales with the orifice size to the power of 1.5, consistent with dimensional analysis. Interestingly, the flow rate increases when the funnel angle is increased.