Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers
Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers
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DOI：
10.1017/jfm.2017.370
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发表时间：
2017-07
影响因子：
3.7
通讯作者：
J. R. Agudo;C. Illigmann;G. Luzi;A. Laukart;Antonio Delgado;Andreas Wierschem
中科院分区：
文献类型：
--
作者：
J. R. Agudo;C. Illigmann;G. Luzi;A. Laukart;Antonio Delgado;Andreas Wierschem
本文研究了低颗粒雷诺数下规则基底上定常剪切流中单球的初始运动。基底由单层规则排列的固定珠粒组成，其中珠粒之间的间距是变化的，导致颗粒对主流的不同休止角和暴露。流致力和水平的流渗透到基板的数值确定。由于在此范围内的实验表明，临界希尔兹数是独立的惯性，但强烈依赖于基板的几何形状，颗粒雷诺数被固定为0.01的数值研究。数值计算表明，滚动运动总是首选滑动和流动渗透是线性依赖于基板颗粒之间的间距。此外，我们还提出了一个起动的分析模型。该模型是一个扩展的高盛的经典结果为一个单一的球体附近的一个平面，考虑到休止角，流动方向相对于衬底地形和屏蔽的球体的线性剪切流。流动渗透的有效水平是唯一的外部参数。该模型，适用于三角形和二次安排与不同的间距，是能够预测的依赖性的临界屏蔽数的几何形状和基板的取向。该模型与数值计算结果吻合得很好。对于暴露良好的颗粒，我们观察到，对于一定的休止角的最小临界希尔兹数并不敏感地依赖于所考虑的安排。在大的休止角，如预期在完全装甲床，该模型是与实验结果在饱和条件下的可侵蚀床。
We study the incipient motion of single spheres in steady shear flow on regular substrates at low particle Reynolds numbers. The substrate consists of a monolayer of regularly arranged fixed beads, in which the spacing between beads is varied resulting in different angles of repose and exposures of the particle to the main flow. The flow-induced forces and the level of flow penetration into the substrate are determined numerically. Since experiments in this range had shown that the critical Shields number is independent of inertia but strongly dependent on the substrate geometry, the particle Reynolds number was fixed to 0.01 in the numerical study. Numerics indicates that rolling motion is always preferred to sliding and that the flow penetration is linearly dependent on the spacing between the substrate particles. Besides, we propose an analytical model for the incipient motion. The model is an extension of Goldman’s classical result for a single sphere near a plain surface taking into account the angle of repose, flow orientation with respect to substrate topography and shielding of the sphere to the linear shear flow. The effective level of flow penetration is the only external parameter. The model, applied to triangular and quadratic arrangements with different spacings, is able to predict the dependence of the critical Shields number on the geometry and on the orientation of the substrate. The model is in very good agreement with numerical results. For well-exposed particles, we observed that the minimum critical Shields number for a certain angle of repose does not depend sensitively on the considered arrangement. At large angles of repose, as expected in fully armoured beds, the model is consistent with experimental results for erodible beds at saturated conditions.