Strong oblique shock waves in granular free-surface flows
Strong oblique shock waves in granular free-surface flows
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DOI：
10.1063/5.0057700
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发表时间：
2021-08
影响因子：
4.6
通讯作者：
X. Cui
中科院分区：
文献类型：
--
作者：
X. Cui
颗粒流的强斜激波是当颗粒自由表面流以超临界速度绕楔形障碍物偏转时形成的稳态解，但它们通常不会发生，因为它们的形成需要满足激波下游的特定条件。本文讨论了在实验室和数值模拟中产生强斜激波的方法。实验是在与水平面成一定角度倾斜的有机玻璃溜槽上进行的，其中干燥的颗粒材料从溜槽顶部的料斗释放，以形成通过下坡位置处的楔形物的通道化流。为了产生强烈的斜激波，在楔形体下游建立第二道闸门，控制物料只在设计的时间和高度流出。采用深度平均颗粒流模型模拟了这种颗粒流动过程，其中上述双闸门系统分别反映到入口和出口边界。通过流场的瞬态解研究了强斜激波的形成，实验与数值模拟结果吻合较好。在此基础上，对弱、强斜激波相互作用的稳态解进行了实验和数值分析。这一结果可以看作是颗粒冲击的第三解，因为它可以通过改变第二闸门的开启时间来形成。当流体厚度和速度在强斜激波上发生剧烈变化时，用来定量描述颗粒流变关系的体惯性数变得非常小，但它似乎并不影响本文所讨论的流动行为。
Strong oblique shock waves of granular flow are a steady-state solution formed when a granular free-surface flow deflects around a wedge-shaped obstacle at a supercritical speed, but they do not usually occur because their formation requires specific conditions to be satisfied downstream of the shock wave. This paper discusses the method of generating the strong oblique shock wave in a laboratory experiment and numerical simulation. The experiment is conducted on a plexiglass chute inclined at an angle to the horizontal, in which a dry granular material is released from a hopper at the top of the chute to form a channelized flow that passes a wedge at a downslope location. In order to generate a strong oblique shock wave, a second gate is established at the downstream of the wedge to control the material to flow out only at the designed time and height. Such a granular flowing process is simulated with a depth-averaged granular flow model, where the above two-gate system is mirrored into the inlet and outlet boundaries, respectively. The formation of the strong oblique shock is investigated through the transient solution of the flow field, and a good agreement is observed between the experiment and the simulation. Then, the steady-state solution of the interaction between the weak and strong oblique shocks is analyzed in the experiment and simulation. This result can be regarded as the third solution of granular shock because it can be formed by just changing the opening time of the second gate. With the dramatic change in flow thickness and velocity across the strong oblique shock, the bulk inertial number, used to quantify the rheological relation of granular materials, becomes extremely small, but it does not seem to affect the behavior of the flow discussed in this paper.