Bifurcation Structure Of A Periodically Driven Bubble Oscillator Near Blake’s Critical Threshold

Hegedűs, Ferenc and Varga, Roxána and Klapcsik, Kálmán (2015) Bifurcation Structure Of A Periodically Driven Bubble Oscillator Near Blake’s Critical Threshold. In: Proceedings of Conference on Modelling Fluid Flow (CMFF'15). CFD.HU Kft., Budapest, pp. 1-8. ISBN 978-963-313-190-9

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Abstract

It is well-known that gas/vapour bubbles in liquids growth indefinitely if the ambient pressure exceeds Blake’s critical threshold. For several decades of investigations, researchers tried to find numerical evidence for the stabilization of such bubbles by applying a harmonically varying pressure field on the liquid domain (ultrasonic irradiation) in this regime, with only partial success. Since, the applied linearization on the bubble models restricted the findings only for small amplitude radial oscillations. Therefore, the present paper intends to reveal the particularly complex dynamics of a harmonically excited bubble near, but still below Blake’s threshold. The computed solutions with a variety of periodicity, e.g., from period 1 up to period 9, form a well-organised structure with respect to the pressure amplitude of the excitation, provided that the applied frequency is higher than the first subharmonic resonance frequency of the bubble. This predictable behaviour provides a good basis for further investigation to find the relevant stable oscillations beyond Blake’s threshold. Although, the investigated model is the very simple Rayleigh—Plesset equation, the applied numerical technique is free of the restriction of low amplitude oscillations.

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