Nonlinear non-spherical oscillations of gas bubble under a periodic variation of ambient liquid pressure
A.A. Aganin1, M.A. Ilgamov2, L.A. Kosolapova3, V.G. Malakhov4
1 Institute of Mechanics and Engineering, Kazan Scientific Center of RAS, Kazan, Russia Institute of Mechanics USC, Ufa, Russia, aganin@kfti.knc.ru
2 Institute of Mechanics and Engineering, Kazan Scientific Center of RAS, Kazan, Russia Institute of Mechanics USC, Ufa, Russia
3 Institute of Mechanics and Engineering, Kazan Scientific Center of RAS, Kazan, Russia Institute of Mechanics USC, Ufa, Russia
4 Institute of Mechanics and Engineering, Kazan Scientific Center of RAS, Kazan, Russia Institute of Mechanics USC, Ufa, Russia
Keywords: gas bubble, nonlinear oscillations, potential flow
Pages: 491-502
Abstract
A mathematical model is constructed for the bubble dynamics, in which the interphase surface variation is presented in the form of a series in spherical harmonics, and the equations are written with the accuracy up to the squared amplitude of the distortion of the spherical shape of the bubble. In the oscillation regimes close to periodic sonoluminescence of a single bubble in a standing acoustic wave, the character of air bubble oscillations in water was studied depending on the bubble initial radius and the amplitude of the liquid pressure variation. It was found that non-spherical oscillations of bounded amplitude can take place outside the region of linearly stable spherical oscillations. Both the oscillations with a period equal to one or several periods of the liquid pressure variation and aperiodic oscillations are observed. It is shown that neglecting the distortions in the form of spherical harmonics with large numbers (i > 3) may lead to a change of oscillation regimes. The influence of distortions on the bubble surface shape for the harmonics with i > 8 is insignificant.
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