Numerical Study of the Dynamics of Traveling Bubbles around a Body

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We derive the equations of motion for a bubble cluster in an arbitrary potential flow. The physical meaning of the pressure term for the equations is clarified. A numerical method based on the two-dimensional vortex method that combined with the equations of motion for a bubble cluster is proposed to simulate traveling cavitation. The validity of two-dimensional analysis for finite numbers of bubbles is investigated. The method is applied to the cavitation flow around a body. The results show that the bubbles grow and collapse near the body in the early stage of the flow evolution. However, after the vortex cluster is developed behind the body, the bubbles grow around the vortex cluster. It is also shown that the degree of bubble growth is reduced by bubble-bubble interactions. When a particular bubble growa much faster than the other bubbles, the growth rate of the other bubbles is much lower than that predicted using single-bubble theory.The collapse and rebound of two bubbles with different initial radii and those of a bubble near various kinds of walls are studied using the boundary element method in which the dynamics of toroidal bubbles is considered. The results are summarized as follows : (1) The wall pressure depends on the translational motion of bubbles and the formation of a high pressure region due to the penetration of the microjet. (2) The bubble motion is affected by the characteristic of a wall. When the wall is compliant and its natural frequency is close to the driving frequency, the bubble oscillation is reduced significantly.Thermal effects of the internal gas on the motions of nonspherical bubbles are also studied numerically. It is shown that the temperature distribution of the internal gas is much dependent on the initial bubble radius. The thermal damping reduces the bubble oscillations.