Introducing surface corrugations to alter the boundary layer flow is a proven way to reduce the fluid drag on a surface. In this study, we examine the effect of periodic, infinitely long spanwise grooves on the laminar boundary layer over a plate for global Reynolds numbers $\left(\mathrm{R}{\mathrm{e}}_L\right)$ between 1000 and 25 000. By employing numerical simulations in two-dimensional domains, we investigate the flow and pressure evolution over surfaces containing rectangular grooves that are perpendicular to the flow and infinitely long in the spanwise direction, and compare them to a flat plate. We characterize the flow interactions near the grooves based on their width-to-depth aspect ratio (AR). Below a certain aspect ratio, a primary vortex fills the space inside each groove. These vortices allow the free stream to “slip over” the grooved regions and result in less skin friction on the wall. However, the interaction between the flow and the grooves’ vertical walls leads to a pressure drag. We study the behavior of the individual drag components over a wide range of aspect ratios (0.2 < AR < 200) and compare the total drag reduction in each case. Based on the simulation results, the transverse grooves in the laminar regime can reduce the total drag up to 10% in comparison to a flat plate, despite increasing the wetted surface area of the plate. Conversely, at some aspect ratios the grooves cause a total drag increase of more than 200%. We observe that by increasing the aspect ratio, the free stream bends more toward the grooves; ultimately at a certain aspect ratio, denoted by $\mathrm{A}{\mathrm{R}}^{*}$, the flow breaks apart the underlying circulation and reaches the bottom of the grooves. When this happens, the flow shear on the grooves’ bottom walls combined with the high-pressure drag exerted on the vertical walls can lead to a net increase in the drag. Therefore, the aspect ratio of the grooves is a critical parameter in optimizing drag reduction in transverse geometries.

中文翻译：

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使用不可压缩粘性层流的周期性展向槽减少阻力的研究

引入表面波纹以改变边界层流量是减少表面上流体阻力的一种行之有效的方法。在这项研究中，我们针对整体雷诺数检验了板的层流边界层上周期性无限长的展向凹槽的影响$（\mathrm{[R}{\mathrm{Ë}}_{\mathrm{大号}}）$介于1000到25000之间。通过在二维域中使用数值模拟，我们研究了包含垂直于流动且在展向方向上无限长的矩形凹槽的表面上的流动和压力演变，并将它们与平板进行比较。我们根据凹槽的宽度与深度的长宽比（AR）表征凹槽附近的流动相互作用。在一定的纵横比以下，主旋涡填充每个凹槽内的空间。这些涡流使自由流“滑过”带凹槽的区域，并减少了壁上的皮肤摩擦。然而，流与凹槽的垂直壁之间的相互作用导致压力拖曳。我们研究了宽高比（0.2 <AR < 200），并比较每种情况下的总阻力减少情况。根据模拟结果，尽管增加了平板的湿润表面积，但与平板相比，层流状态下的横向沟槽可以将总阻力降低多达10％。相反，在某些纵横比下，凹槽会导致总阻力增加超过200％。我们观察到，通过增加长宽比，自由流会更多地向凹槽弯曲。最终以一定的长宽比表示 自由流更向凹槽弯曲；最终以特定的长宽比表示 自由流更向凹槽弯曲；最终以一定的长宽比表示$\mathrm{一种}{\mathrm{[R}}^{*}$，气流破坏了下面的循环并到达了凹槽的底部。发生这种情况时，凹槽底壁上的流动剪切力加上施加在垂直壁上的高压阻力会导致阻力净增加。因此，凹槽的纵横比是优化横向几何形状的减阻的关键参数。