Path instability of a compressible air bubble rising in quiescent water with consideration of variable thermophysical properties

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 (f_E), the zigzag path (f_p) and vorticity component in X and Y direction accumulated on the bubble surface (f_v) as f_E=2f_p=2f_v.