Direct numerical simulation is performed for flow past an isolated cylinder at Re=1,000. The corners of the cylinder are rounded at different radii, with the non-dimensional radius of curvature varying from R+=R/D=0.000 (square cylinder with sharp corners) to 0.500 (circular cylinder), in which R is the corner radius and D is the cylinder diameter. Our objective is to investigate the effect of the rounded corners on the development of the separated and transitional flow past the cylinder in terms of time-averaged statistics, time-dependent behavior, turbulent statistics and three-dimensional flow patterns. Numerical results reveal that the rounding of the corners significantly reduces the time-averaged drag and the force fluctuations. The wake flow downstream of the square cylinder recovers the slowest and has the largest wake width. However, the statistical quantities do not monotonically vary with the corner radius, but exhibit drastic variations between the cases of square cylinder and partially rounded cylinders, and between the latter and the circular cylinder. The free shear layer separated from the R+=0.125 cylinder is the most stable in which the first roll up of the wake vortex occurs furthest from the cylinder and results in the largest recirculation bubble, whose size reduces as R+ further increases. The coherent and incoherent Reynolds stresses are most pronounced in the near-wake close to the reattachment point, while also being noticeable in the shear layer for the square and R+=0.125 cylinders. The wake vortices translate in the streamwise direction with a convection velocity that is almost constant at approximately 80% of the incoming flow velocity. These vortices exhibit nearly the same trajectory for the rounded cylinders and are furthest away from the wake centerline for the square one. The flow past the square cylinder is strongly three-dimensional as indicated by the significant primary and secondary enstrophy, while it is dominated by the primary enstrophy (View the MathML source) for the rounded cylinders.
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机译：在Re = 1,000处对通过隔离气瓶的流量进行直接数值模拟。圆柱体的拐角以不同的半径倒圆，无量纲曲率半径从R + = R / D = 0.000（带有尖角的正方形圆柱体）到0.500（圆形圆柱体）不等，其中R是拐角半径， D是圆柱直径。我们的目的是根据时间平均统计量，时间相关行为，湍流统计量和三维流动模式，研究圆角对经过圆柱体的分离流动和过渡流动的影响。数值结果表明，圆角的倒圆大大减少了时间平均阻力和力的波动。方筒下游的尾流恢复最慢，尾流宽度最大。但是，统计量不会随拐角半径而单调变化，而是在方形圆柱体和部分圆角圆柱体的情况之间以及圆角圆柱体和圆柱体之间呈现出急剧的变化。与R + = 0.125圆柱体分离的自由剪切层是最稳定的，在该自由剪切层中，尾流涡旋的第一次卷起发生在离圆柱体最远的地方，并导致最大的循环气泡，随着R +的进一步增大，其再循环气泡的大小减小。相干和不相干的雷诺应力在接近重附着点的近尾流中最为明显，而在方形和R + = 0.125圆柱体的剪切层中也很明显。尾流涡流在对流方向上以对流速度平移，该对流速度几乎恒定为传入流速的大约80％。对于圆形圆柱体，这些涡流具有几乎相同的轨迹，并且对于正方形的涡流而言离涡流中心线最远。通过方形圆柱体的流动具有强烈的三维性，如明显的一次和二次涡旋所表明的那样，而对于圆形圆柱体来说，则主要由一次涡旋所主导。
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