Abstract A numerical study of a compressible air bubble rising in water with variable thermophysical properties is conducted. The coupled level set and volume of fluid method is adopted to track the interface. Empirical correlations in terms of temperature for thermophysical properties and equation of state for air are considered in the simulations. We simulate a compressible 3D static air bubble in water for the first time. The volume change of the bubble and the pressure difference between the inside and outside of the static bubble agree well with the theoretical solutions. We study the zigzag motion of a compressible air bubble considering the temperature difference with respect to the surrounding water. The mechanism of the zigzag motion is clarified by analyzing the shape evolution and the wake structure. The periodic shedding of hairpin vortex with 2R mode is observed during the zigzag motion. There are two periods of the bubble shape oscillation within one zigzag cycle. We obtain the relation between the oscillation frequency of the aspect ratio (fE), the zigzag path (fp) and vorticity component in X and Y direction accumulated on the bubble surface (fv) as f E = 2 f p = 2 f v .

中文翻译：

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考虑可变热物理性质的可压缩气泡在静止水中上升的路径不稳定性

摘要 对在水中上升的具有可变热物理性质的可压缩气泡进行了数值研究。采用液位集与流体体积耦合法跟踪界面。在模拟中考虑了热物理性质的温度和空气状态方程的经验相关性。我们第一次模拟了水中的可压缩 3D 静态气泡。气泡的体积变化和静态气泡内外压差与理论解吻合得很好。我们研究了考虑到与周围水温差的可压缩气泡的曲折运动。通过分析形状演化和尾流结构，阐明了锯齿形运动的机制。在锯齿形运动期间观察到具有 2R 模式的发夹涡旋的周期性脱落。一个之字形周期内有两个气泡形状振荡周期。我们得到纵横比（fE）的振荡频率（fE）、曲折路径（fp）和X和Y方向上累积在气泡表面（fv）上的涡量分量之间的关系为f E = 2 fp = 2 fv 。