The unsteady wake of a rotating and translating sphere is experimentally investigated at Reynolds numbers (Re) ranging from 115 to 550 for two rotational speeds. Non-dimensional rotational speed, $$\Omega^{ * }$$ Ω ∗ , is defined as the ratio of the maximum azimuthal speed of the sphere and the speed of translation. Motion of the sphere is generated using a specially designed mechanism in a channel, and its wake has been visualized using fluorescent dye. Unlike the steady flow past a stationary sphere where the limiting Reynolds number is 270, the flow becomes unsteady when sufficient rotation rate is introduced at much lower Reynolds number ( $${\text{Re}} = 115,\Omega^{ * } = 0.375$$ Re = 115 , Ω ∗ = 0.375 ). The transition from one-sided to double-sided hairpin vortex occurs at one critical Re for a given rotational speed, and it switches back to one-sided hairpin vortex shedding at another critical Re. Particle image velocimetry results demonstrate the vorticity distribution in the wake and the variation of the wake width with axial distance. At very low Re, velocity profiles in the wake are nearly self-similar. The strength of the vortex rings weakens in the far wake. The decay of centerline velocity in axial direction confirms the dissipation of the vorticity in the far wake. In this unsteady flow, the time-averaged value of the separation angle is higher than that of the steady flow on the advancing side due to enhanced adverse pressure gradient. The Strouhal number calculated from the dye visualization in this range of $$\Omega^{ * }$$ Ω ∗ and Re varies from 0.175 to 0.25, a clear increasing trend both with increasing Re and $$\Omega^{ * }$$ Ω ∗ . The coefficient of drag evaluated at the center plane remains constant at 0.94 for the present investigation up to $${\text{Re}} = 550$$ Re = 550 . The wavelength of the unstable hairpin vortices is found to scale inversely with the translational velocity of the sphere.

中文翻译：

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低雷诺数下静止水中横向旋转平移球体的尾流

在雷诺数 (Re) 范围从 115 到 550 的两种旋转速度下，对旋转和平移球体的不稳定尾流进行了实验研究。无量纲旋转速度 $$\Omega^{ * }$$ Ω ∗ 定义为球体的最大方位角速度与平移速度的比值。球体的运动是在通道中使用专门设计的机制生成的，其尾迹已使用荧光染料进行可视化。与通过静止球体的稳定流不同，其中限制雷诺数为 270，当在低得多的雷诺数下引入足够的旋转速率时，流动变得不稳定（$${\text{Re}} = 115,\Omega^{ * } = 0.375$$ Re = 115 ，Ω ∗ = 0.375 ）。对于给定的转速，从一侧到双侧发夹涡的过渡发生在一个临界 Re 处，它在另一个关键 Re 处切换回单侧发夹涡旋脱落。粒子图像测速结果表明尾流中的涡度分布和尾流宽度随轴向距离的变化。在非常低的 Re 下，尾流中的速度剖面几乎自相似。涡环的强度在遥远的尾流减弱。轴向中心线速度的衰减证实了远尾涡流的消散。在这种非定常流动中，由于逆压力梯度增强，分离角的时均值高于前进侧的稳定流动。在 $$\Omega^{ * }$$ Ω ∗ 和 Re 范围内从染料可视化计算的 Strouhal 数从 0.175 到 0.25，随着 Re 和 $$\Omega^{ * }$ 的增加，呈现明显的增加趋势$Ω*。在当前调查中，在中心平面评估的阻力系数保持恒定为 0.94，直至 $${\text{Re}} = 550$$ Re = 550 。发现不稳定的发夹涡旋的波长与球体的平移速度成反比。