Three-dimensional dynamics of a pair of deformable bubbles rising initially in line. Part 1. Moderately inertial regimes

Three-dimensional dynamics of a pair of deformable bubbles rising initially in line. Part 1. Moderately inertial regimes
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一对最初排成一行的可变形气泡的三维动力学。

DOI:
10.1017/jfm.2021.429
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发表时间:
2020-12
影响因子:
3.7
通讯作者:
Magnaudet Jacques
Magnaudet Jacques
中科院分区:
工程技术2区
文献类型:
--
作者:
Zhang Jie;Ni Ming-Jiu;Magnaudet Jacques

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摘要利用高分辨率模拟研究了静止液体中两个相同气泡的浮力驱动运动,重点是中等惯性状态下孤立气泡的路径是垂直的。假设第一个轴对称的演变,平衡配置的气泡对被确定为一个函数的浮力,粘性和浮力,毛细作用力比定义的伽利略($Ga$)和债券($BO$)的系统,分别。三维解表明,这种轴对称平衡实际上永远不会达到。相反,提供$Bo$站在一个关键的$Ga$依赖的阈值确定合并的开始,两个明显不同的演变观察。在探索的$(Ga,Bo)$范围的低端,串联遵循起草接吻翻滚的情况下,最终产生一个平面并排运动。对于较大的$Ga$,尾随的气泡横向漂移,并得到了领先的气泡的尾流,几乎没有改变后者的路径。在第二种情况下,后期配置的特征是串联相对于垂直方向的显著倾斜,范围为30 - 40美元。气泡变形对系统的演化有重要影响。它控制着尾流中的旋涡效应的大小,从而控制着作用在尾流气泡上的吸引力的强度。它还控制着作用在这个气泡上的横向力的强度甚至符号,当串联以小的角度偏差释放时,这是一种特别重要的机制。
Abstract The buoyancy-driven motion of two identical gas bubbles released in line in a liquid at rest is examined with the help of highly resolved simulations, focusing on moderately inertial regimes in which the path of an isolated bubble is vertical. Assuming first an axisymmetric evolution, equilibrium configurations of the bubble pair are determined as a function of the buoyancy-to-viscous and buoyancy-to-capillary force ratios which define the Galilei ($Ga$) and Bond ($Bo$) numbers of the system, respectively. The three-dimensional solutions reveal that this axisymmetric equilibrium is actually never reached. Instead, provided $Bo$ stands below a critical $Ga$-dependent threshold determining the onset of coalescence, two markedly different evolutions are observed. At the lower end of the explored $(Ga, Bo)$-range, the tandem follows a drafting–kissing–tumbling scenario, which eventually yields a planar side-by-side motion. For larger $Ga$, the trailing bubble drifts laterally and gets out of the wake of the leading bubble, barely altering the path of the latter. In this second scenario, the late configuration is characterized by a significant inclination of the tandem ranging from $30^\circ$ to $40^\circ$ with respect to the vertical. Bubble deformation has a major influence on the evolution of the system. It controls the magnitude of vortical effects in the wake of the leading bubble, hence the strength of the attractive force acting on the trailing bubble. It also governs the strength and even the sign of the lateral force acting on this bubble, a mechanism of particular importance when the tandem is released with a small angular deviation.
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