Oscillating viscous flow past a streamwise linear array of circular cylinders
Oscillating viscous flow past a streamwise linear array of circular cylinders
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DOI：
10.1017/jfm.2023.178
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发表时间：
2023-03-24
影响因子：
3.7
通讯作者：
Sanchez, A. L.
中科院分区：
文献类型：
--
作者：
Alaminos-Quesada, J.;Lawrence, J. J.;Sanchez, A. L.
本文研究了速度随时间周期性振荡的不可压缩流体绕一列等间距完全相同的圆柱体发展的粘性流动。分析的重点是行程长度等于或小于圆柱体半径的简谐振荡流动，使流动保持二维、时间周期和相对于中心线的对称性。具体考虑了渐近小冲程长度的极限，其中流动是先导阶谐和的，一阶修正显示了定常流动分量，它与伴随的斯托克斯漂移一起在这里计算。与常见的单缸振荡流动情况一样，对于小冲程，由定常流动分量和Stokes漂移分量之和给出的时间平均拉格朗日速度场显示出循环涡，循环涡是根据两个相关控制参数的不同值而量化的，这两个控制参数即沃默斯利数和缸间距与缸半径之比。与直接数值模拟结果的比较表明，即使在冲程长度与气缸半径相当的情况下，对于无限小的冲程长度，拉格朗日平均流动的描述仍然相当准确。数值积分也被用来量化在周期性周围运动由非简谐压力梯度驱动的情况下，由圆柱体阵列的存在所引起的流向流速，这是与沿椎管的神经根周围的脑脊液振荡流动有关的一个有趣的问题。
This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.