A theoretical model for compressible bubble dynamics considering phase transition and migration

A novel theoretical model for bubble dynamics is established that simultaneously accounts for the liquid compressibility, phase transition, oscillation, migration, ambient flow field, etc. The bubble dynamics equations are presented in a unified and concise mathematical form, with clear physical meanings and extensibility. The bubble oscillation equation can be simplified to the Keller–Miksis equation by neglecting the effects of phase transition and bubble migration. The present theoretical model effectively captures the experimental results for bubbles generated in free fields, near free surfaces, adjacent to rigid walls, and in the vicinity of other bubbles. Based on the present theory, we explore the effect of the bubble content by changing the vapour proportion inside the cavitation bubble for an initial high-pressure bubble. It is found that the energy loss of the bubble shows a consistent increase with increasing Mach number and initial vapour proportion. However, the radiated pressure peak by the bubble at the collapse stage increases with decreasing Mach number and increasing vapour proportion. The energy analyses of the bubble reveal that the presence of vapour inside the bubble not only directly contributes to the energy loss of the bubble through phase transition but also intensifies the bubble collapse, which leads to greater radiation of energy into the surrounding flow field due to the fluid compressibility.