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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 Open the ORCID record for Yunqiao Liu [Opens in a new window]  and
Benlong Wang Open the ORCID record for Benlong Wang [Opens in a new window]
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
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Cavitation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 963 - 992
Copyright
© 2019 Cambridge University Press 

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