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An estimate of the Kelvin impulse of a transient cavity

Published online by Cambridge University Press:  26 April 2006

J. P. Best  and
J. R. Blake
J. P. Best
Affiliation:
Materials Research Laboratory (MRL) – DSTO, PO Box 50, Ascot Vale, Victoria, 3032, Australia
J. R. Blake
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
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Abstract

The Lagally theorem is used to obtain an expression for the Bjerknes force acting on a bubble in terms of the singularities of the fluid velocity potential, defined within the bubble by analytic continuation. This expression is applied to transient cavity collapse in the neighbourhood of boundaries, allowing analytical estimates to be made of the Kelvin impulse of the cavity. The known result for collapse near a horizontal rigid boundary is recovered, and the Kelvin impulse of a cavity collapsing in the neighbourhood of a submerged and partially submerged sphere is estimated. A numerical method is developed to deal with more general body shapes and in particular, bodies of revolution. Noting that the direction of the impulse at the end of the collapse phase generally indicates the direction of the liquid jet that may form, the behaviour of transient cavities in these geometries is predicted. In these examples the concept of a zone of attraction is introduced. This is a region around the body, within which the Kelvin impulse at the time of collapse, and consequent jet formation, is expected to be directed towards the body. Outside this zone the converse is true.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 261 , 25 February 1994 , pp. 75 - 93
Copyright
© 1994 Cambridge University Press

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