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Dynamics and surface stability of a cylindrical cavitation bubble in a rectilinear vortex

Published online by Cambridge University Press:  01 March 2019

Yunqiao Liu
Affiliation:
Key Laboratory of Hydrodynamics (Ministry of Education), School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Benlong Wang*
Affiliation:
Key Laboratory of Hydrodynamics (Ministry of Education), School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China
*Corresponding
Email address for correspondence: benlongwang@sjtu.edu.cn

Abstract

In this paper, we formulate the dynamic equations of radial and surface modes for a cylindrical cavitation bubble subject to a prescribed uniform rectilinear vortex flow. The potential flow in the bulk volume of the external flow is modelled using the general mode decomposition approach. The stability of surface modes is investigated under linear analysis. The effects of confinement due to a limited flow domain in a water tunnel and viscosity at the bubble surface are evaluated, which can be fairly neglected for the cylindrical cavitation bubbles discussed. Our model is capable of predicting the developments of surface modes, which agrees well with experimental observations reported in the literature. We derive the Mathieu structure in the dynamic equation of the surface oscillation and the associated instability condition of the surface mode oscillations. The numerical results confirm that the Mathieu-type instability controls the stability diagrams and the emergence of surface modes under specific radial oscillation.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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