A large spherical bubble rising in quiescent liquid generally leads to the formation of a toroidal bubble (central breakup). In this paper, we investigate the bubble dynamics during the central breakup process using the three dimensional Volume of Fluid method implemented in OpenFOAM. The potential energy of the large bubble is converted into the kinetic energy of the liquid jet, resulting in the formation of the toroidal bubble. Before the central breakup of the bubble, a high pressure zone is formed on the top of the bubble due to the collision of the liquid jet with the top of the bubble. We report for the first time that a protrusion is formed on the top of the toroidal bubble for a large spherical bubble rising in quiescent liquid. The velocity of the gas inside the toroidal bubble around the liquid jet is much faster than that in other places after the central breakup, which leads to the formation of the protrusion against the restriction of the surface tension force. We find that the bubble size, liquid viscosity, and density can influence the formation of the toroidal bubble, while the influence of surface tension is negligible. We summarize the above influencing factors into two dimensionless numbers: Galilei (Ga) number and Eotvos number (Eo). In the end, we discover a simple linear relation between the jet Reynolds number and the Ga number by analyzing all numerical experiments.

中文翻译：

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液体射流引起大气泡中心破裂的数值研究

在静止液体中上升的大球形气泡通常会导致形成环形气泡（中心破裂）。在本文中，我们使用在 OpenFOAM 中实施的三维流体体积方法研究中心破裂过程中的气泡动力学。大气泡的势能转化为液体射流的动能，从而形成环形气泡。在气泡中心破裂之前，由于液体射流与气泡顶部的碰撞，在气泡顶部形成了高压区。我们首次报告了在静止液体中上升的大球形气泡在环形气泡顶部形成突起。围绕液体射流的环形气泡内部的气体速度在中心破裂后比其他地方快得多，这导致形成突起以抵抗表面张力的限制。我们发现气泡大小、液体粘度和密度会影响环形气泡的形成，而表面张力的影响可以忽略不计。我们将上述影响因素归纳为两个无量纲数：伽利略(Ga)数和Eotvos数(Eo)。最后，我们通过对所有数值实验的分析，发现了射流雷诺数和 Ga 数之间的简单线性关系。密度会影响环形气泡的形成，而表面张力的影响可以忽略不计。我们将上述影响因素归纳为两个无量纲数：伽利略(Ga)数和Eotvos数(Eo)。最后，我们通过对所有数值实验的分析，发现了射流雷诺数和 Ga 数之间的简单线性关系。密度会影响环形气泡的形成，而表面张力的影响可以忽略不计。我们将上述影响因素归纳为两个无量纲数：伽利略(Ga)数和Eotvos数(Eo)。最后，我们通过对所有数值实验的分析，发现了射流雷诺数和 Ga 数之间的简单线性关系。