We investigate the flow past circular, square and triangular cylinders embedded on spherical and cylindrical surfaces and quantify the effect of the embedding surface curvature on the flow characteristics. For the circular cylinder, we examine three Reynolds numbers Re = 40, 100, and 1000 based on cylinder diameter (D), and vary the normalized embedding surface curvature values D, where is the maximum principal curvature, from 0 (flat surface) to 1/12. Measures of fluid dynamical quantities of interest: drag coefficient (Cd), lift coefficient (Cl), Strouhal number (St), pressure coefficient (Cp), friction coefficient (Cf ), vorticity magnitude (), street speed (Vst), street wavelength (), length of stationary vortex pair (L), and separation angle (sep) show an insignificant effect of surface curvature. For the range of embedding surface curvature values, we conclude that the dynamics of the flow past a stationary circular cylinder exhibits universality, and essentially independent of the embedding surface curvature. Our conclusion that the flow dynamics is very weakly dependent on the embedding surface curvature is further strengthened when flow past a stationary cylinder with a square or triangular cross-section exhibit similar results.

中文翻译：

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研究流过嵌入在弯曲和平坦表面上的圆柱体的流动

我们研究了流过嵌入在球面和圆柱面上的圆形，方形和三角形圆柱体的流动，并量化了嵌入曲面曲率对流动特性的影响。对于圆柱，我们根据圆柱直径（D）检查三个雷诺数Re = 40、100和1000，然后将归一化的嵌入表面曲率值D（从0（平面）到最大主曲率）更改为1/12。感兴趣的流体动力学量的度量：阻力系数（Cd），升力系数（Cl），斯特劳哈尔数（St），压力系数（Cp），摩擦系数（Cf），涡度大小（），街道速度（Vst），街道波长（），固定涡流对的长度（L）和分离角（sep）对表面曲率的影响很小。对于嵌入表面曲率值的范围，我们得出结论，通过固定圆柱体的流动动力学表现出普遍性，并且基本上与嵌入表面曲率无关。我们的结论是，当流经具有正方形或三角形横截面的固定圆柱体的流量显示出相似的结果时，流动动力学非常弱地取决于嵌入曲面的曲率。