Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T18:25:57.347Z Has data issue: false hasContentIssue false

A note on the impulse due to a vapour bubble near a boundary

Published online by Cambridge University Press:  17 February 2009

J. R. Blake
Affiliation:
Department of Mathematics, University of Wollongong, P. O. Box 1144, Wollongong, N.S.W. 2500
P. Cerone
Affiliation:
Department of Mathematics, University of Wollongong, P. O. Box 1144, Wollongong, N.S.W. 2500
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An expression for the impluse due to a vapour (cavitation) bubble is obtained in terms of an integral over a nearby boundary. Examples for a point source near a free surface, rigid boundary, inertial boundary and a fluid of different density are considered. It appears that the sign of the impluse determines the direction a cavitation bubble will migrate and the direction of the high speed liquid jet during the collapse phase. The theory may explain recent observations on buoyant bubbles near an interface between two fluids of different densities.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Abramowitz, M. and Stegun, I. A. (eds.), Handbook of mathematical functions (Dover, New York, 1965).Google Scholar
[2]Batchelor, G. K., An introduction to fluid dynamics (C.U.P., Cambridge, 1967).Google Scholar
[3]Benjamin, T. B. and Ellis, A. T., “The collapse of cavitation bubbles and the pressures thereby produced against solid bodies”, Phil. Trans. Roy. Soc. (London) A260 (1966), 221240.Google Scholar
[4]Birkhoff, G. and Zarantonello, E. H., Jets, wakes and cavities (Academic Press, New York, 1957).Google Scholar
[5]Blake, J. R. and Gibson, D. C., “Growth and collapse of a vapour cavity near a free surface”, J. Fluid Mech. 111 (1981), 123140.CrossRefGoogle Scholar
[6]Chahine, G. L. and Bovis, A., “Oscillations and collapse of a cavitation bubble in the vicinity of a two-liquid interface”, in Cavitation and inhomogeneities in underwater acoustics (ed. Lauterborn, W.) (Springer, 1980).Google Scholar
[7]Fenton, J. D. and Mills, D. A., “Shoaling waves: numerical solution of exact equations” in Waves on water of variable depth (eds. Provis, D. G. and Radok, R.), Lecture Notes in Physics 64 (Springer, 1976).Google Scholar
[8]Gibson, D. C., “Cavitation adjacent to plane boundaries”, Proc. 3rd Aust. Hyd. and Fluid Mech. Conf. Sydney (1968), 210214.Google Scholar
[9]Gibson, D. C. and Blake, J. R., “Growth and collapse of vapour bubbles near flexible boundaries”, Proc. 7th Aust. Hyd. and Fluid Mech. Conf. Brisbane (1980), 283286.Google Scholar
[10]Keane, A., Integral transforms (Science Press, Sydney, 1965).Google Scholar
[11]Landau, L. D. and Lifshitz, E. M., Fluid mechanics (Pergamon, Oxford, 1975).Google Scholar
[12]Longuet-Higgins, M. S. and Cokelet, E. D., “The deformation of steep surface waves on water. I A numerical method of computation”, Proc. Roy. Soc. A350 (1976), 126.Google Scholar
[13]Saffman, P. G., “The self-propulsion of a deformable body in a perfect fluid”, J. Fluid Mech. 28 (1967), 385389.CrossRefGoogle Scholar
[14]Wu, T. Y., “The momentum theorem for a deformable body in a perfect fluid”, Schiffstechnik 23 (1976), 229232.Google Scholar