Path instability of a millimetric spheroidal bubble in quiescent fluid and in isotropic turbulence is investigated by direct numerical simulation. An immersed boundary method along with a new formulation of the equation of bubble motion is utilized to impose the no-slip condition on the surface of an air bubble in fixed shape with the equivalent diameter of $1.0\sim 4.0\text{mm}$ in contaminated water. The range of Galilei number defined as the ratio of the gravitational force to the kinematic viscosity considered in this study is 100 $\sim$ 800. In still fluid, as the bubble size grows, the frequency of the zigzagging motion of the bubble increases while the range in the orientation angle variation of the bubble is hardly affected. The effect of background turbulence on path instability of a rising bubble, which typically shows zigzag pattern in still fluid, is investigated at three different Reynolds numbers, ${\text{Re}}_{\lambda }$, of 26, 45, and 73, or equivalently, for the ratio of fluid root-mean-square velocity to the bubble rise velocity $u^{\prime }/V_T$ ranging 0.030 $\sim$ 0.671. When a bubble rises in isotropic turbulence, the terminal rise velocity of the bubble does not show a noticeable difference. However, the pathways are significantly distorted by turbulence. Furthermore, the magnitude of zigzagging frequency and the degree of obliquity of the bubble become enhanced with ${\text{Re}}_{\lambda }$. We also observed wakes behind the bubble to find that the rear tails become weaker and tangled due to turbulence.

中文翻译：

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各向同性湍流中无滑移球体气泡的路径不稳定性

通过直接数值模拟研究了静止流体和各向同性湍流中毫米球体气泡的路径不稳定性。利用浸入边界法和气泡运动方程的新公式，对等效直径为 的固定形状气泡表面施加无滑移条件。$1.0～4.0\text{毫米}$在受污染的水中。伽利略数的范围定义为重力与本研究中考虑的运动粘度之比为 100$～$800. 在静止流体中，随着气泡尺寸的增大，气泡曲折运动的频率增加，而气泡的方位角变化范围几乎不受影响。在三个不同的雷诺数下研究了背景湍流对上升气泡路径不稳定性的影响，通常在静止流体中显示锯齿形图案，${\text{关于}}_{\lambda }$, 26, 45, 和 73, 或等效地, 流体均方根速度与气泡上升速度的比值 ${你}^{\prime }/{伏}_{吨}$ 范围 0.030 $～$0.671。当气泡在各向同性湍流中上升时，气泡的终端上升速度没有显着差异。然而，这些路径因湍流而显着扭曲。此外，锯齿形频率的大小和气泡的倾斜度随着${\text{关于}}_{\lambda }$. 我们还观察了气泡后面的尾流，发现由于湍流，尾部尾部变得更弱并缠结在一起。