Abstract

We study a two-dimensional flow over a cylinder and three ellipses with the aspect ratio \(a / b = 2.04\), \(3.65\), and \(5\) at a Reynolds number \(Re = 100\) based on the inflow velocity and hydraulic diameter using a direct numerical simulation (DNS) and linear stability analysis. The DNS shows that increase in \(a / b\) leads to stabilization of the flow due to decrease in the recirculation zone. The linear stability analysis based on the time-averaged velocity field shows that the modes of interest describe a Karman vortex street. The oscillation frequency reconstructed from the linear stability analysis is in excellent agreement with the DNS. Solving the linearized adjoint equations made it possible to identify the flow area where direct and adjoint modes overlap. These areas of the field \(S_w\), usually called “wavemaker,” change their shape with increase in \(a / b\). Non-zero values of \(S_w\) tend to approach the bottom part of the “tail” of the ellipse due to the asymmetry of the recirculation region, attached to the top side of the ellipse.

中文翻译：

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几何形状对人体低雷诺数层流的直接和伴随线性整体模态的影响

摘要

我们研究了一个圆柱和三个椭圆的二维流，其雷诺数为（Re = 100 \）的纵横比为（a / b = 2.04 \），\（3.65 \）和\（5 \）基于流入速度和水力直径，使用直接数值模拟（DNS）和线性稳定性分析。DNS显示\（a / b \）增加由于再循环区域的减少，导致流量稳定。基于时间平均速度场的线性稳定性分析表明，感兴趣的模式描述了一条卡曼涡街。通过线性稳定性分析重建的振荡频率与DNS非常一致。通过求解线性化的伴随方程，可以确定直接模式和伴随模式重叠的流动区域。字段\（S_w \）的这些区域通常称为“造波器”，其形状随着\（a / b \）的增加而改变。\（S_w \）的非零值趋于接近椭圆的“尾部”的底部，这是由于再循环区域的不对称性（附着在椭圆的顶部）。