Gopinath A, Trinh E H
Department of Mechanical Engineering, Naval Postgraduate School, Monterey, California 93943, USA.
J Acoust Soc Am. 2000 Oct;108(4):1514-20. doi: 10.1121/1.1289367.
The problem of steady streaming around a rigid isolated sphere in a plane standing acoustic field is considered. Existing results in the literature have been generalized to allow for noncompactness of the sphere, and the influence of fluid compressibility on the streaming behavior has been included. It is found that in the high-frequency limit of interest for which the streaming is strongest, the effective steady slip velocity at the edge of the inner boundary layer region that is responsible for driving the steady streaming in the bulk of the fluid in the outer region, has a complex variation over the surface of the sphere that depends on (i) the sphere position (with respect to the node/antinode of the acoustic field), (ii) the extent of sphere compactness, and (iii) on a well-defined function (representing compressibility effects) of the fluid Prandtl number and its ratio of specific heats. Not surprisingly, the contribution from this function is negligible when the host fluid is a liquid. The steady streaming behavior around the sphere is demonstrated with the help of flow streamlines for various cases in the diffusive limit of weak outer flow for low streaming Reynolds numbers.
研究了平面驻声波场中刚性孤立球体周围的定常流动问题。文献中的现有结果已被推广，以考虑球体的非紧致性，并纳入了流体可压缩性对流动行为的影响。结果发现，在流动最强的高频极限情况下，负责驱动外部区域流体主体中定常流动的内边界层区域边缘处的有效定常滑移速度，在球体表面具有复杂的变化，这取决于：（i）球体位置（相对于声场的节点/波腹），（ii）球体紧致程度，以及（iii）流体普朗特数及其比热比的一个明确定义的函数（代表可压缩性效应）。不出所料，当主体流体为液体时，该函数的贡献可忽略不计。在低流动雷诺数的弱外部流动扩散极限下，通过各种情况下的流线展示了球体周围的定常流动行为。
