The three-dimensional flow around a spherical clean bubble translating steadily in a wall-bounded linear shear flow is studied numerically. The present work is concerned with the drag and lift forces experienced by the bubble over a wide range of Reynolds number ($0.1\le \text{Re}\le {10}^3$, Re being based on the bubble diameter and relative velocity with respect to the ambient fluid), wall distance ($1.5\le L_{\text{R}}\le 8$, $L_{\text{R}}$ being the distance from the bubble center to the wall normalized by the bubble radius), and relative shear rate ($-0.5\le \text{Sr}\le 0.5$, Sr being the ratio between the velocity difference across the bubble and the relative velocity). Based on the above range of parameters, situations where the bubble is repelled from or attracted to the wall are both covered. The flow structure and vorticity field are analyzed to obtain qualitative insight into the interaction mechanisms at work. The drag and lift forces are computed as well. Their variations agree well with theoretical predictions available in the limit of low-but-finite Reynolds number and, when the fluid is at rest, in the potential flow limit. Numerical results and analytical expressions are combined to provide accurate semiempirical expressions for the drag and lift forces at arbitrary Reynolds number and separation distance.

中文翻译：

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在壁边界线性剪切流中平移的清洁球形气泡上的流体动力

数值研究了围绕球形清洁气泡的三维流动，该三维稳定流动在有边界的线性剪切流中平稳地平移。目前的工作涉及气泡在很大范围的雷诺数（$0.1\le \text{回覆}\le {10}^3$，Re是基于气泡直径和相对于环境流体的相对速度），壁距（$1.5\le {\mathrm{大号}}_{\text{[R}}\le 8$， ${\mathrm{大号}}_{\text{[R}}$ 是从气泡中心到壁的距离（通过气泡半径归一化）和相对剪切率（$-0.5\le \text{r}\le 0.5$，Sr是气泡上的速度差与相对速度之间的比率。基于上述参数范围，都涵盖了气泡从壁被排斥或吸引到壁的情况。分析流动结构和涡度场，以定性地了解工作中的相互作用机理。拖动力和举升力也可以计算。它们的变化与在低但有限的雷诺数极限以及在流体静止时在潜在流量极限中可用的理论预测非常吻合。数值结果和解析表达式结合起来，可以为任意雷诺数和分离距离下的阻力和升力提供准确的半经验表达式。