Stability of the flow during sedimentation in inclined channels
Stability of the flow during sedimentation in inclined channels
复制标题
倾斜渠道沉积过程中的水流稳定性
DOI：
10.1063/1.864408
复制
发表时间：
1983
影响因子：
4.6
通讯作者：
E. Herbolzheimer
中科院分区：
文献类型：
--
作者：
E. Herbolzheimer
本文采用线性稳定性分析方法，在大的Grashof数和雷诺数为O（1）的条件下，研究了倾斜渠道中波浪在沉积过程中的形成和发展条件。长波的渐近解表明，临界雷诺数正比于通道倾角的正切乘以通道下表面下方形成的薄纯流体层的厚度与通道宽度之比。因此，临界雷诺数非常小，除非通道非常长和窄。然而，数值计算表明，最大放大率往往是如此之小，扰动可能会对流的通道之前，他们达到一个可观察的大小。这一结论与我们实验室的实验结果相一致，并且观测到的波起始点和计算出的最大放大率对倾角和悬浮液浓度的依赖关系非常相似。
The conditions for wave formation and growth during sedimentation in inclined channels is investigated using a linear stability analysis in the limit of large sedimentation Grashof number with the Reynolds number remaining O(1). An asymptotic solution for long waves reveals that the critical Reynolds number is proportional to the tangent of the angle of inclination of the channel times the ratio of the thickness of the thin pure‐fluid layer, which forms beneath the downward‐facing surface of the channel, to the width of the channel. Hence, the critical Reynolds number is very small unless the channel is extremely long and narrow. Numerical calculations indicate, however, that the maximum amplification rates are often so small that the disturbances may be convected out of the channel before they reach an observable size. This conclusion is consistent with experiments performed in our laboratory, and the observed wave inception point and the calculated maximum amplification rates exhibit remarkably similar dependence on the angle of inclination and the suspension concentration.