Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-05T11:37:05.508Z Has data issue: false hasContentIssue false
  • English
  • Français

The Kelvin impulse: application to cavitation bubble dynamics

Published online by Cambridge University Press:  17 February 2009

J. R. Blake
J. R. Blake
Affiliation:
Department of Mathematics, University of Wollongong, Wollongong, N.S.W. 2500, Australia.
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.

The Kelvin impulse is a particularly valuable dynamical concept in unsteady fluid mechanics, with Benjamin and Ellis [2] appearing to be the first to have realised its value in cavitation bubble dynamics. The Kelvin impulse corresponds to the apparent inertia of the cavitation bubble and, like the linear momentum of a projectile, may be used to determine aspect It is defined as

where ρ is the fluid density, ø is the velocity potential, S is the surface of the cavitation bubble and n is the outward normal to the fluid. Contributions to the Kelvin impulse may come from the presence of nearby boundaries and the ambient velocity and pressure field. With this number of mechanisms contributing to its development, the Kelvin impulse may change sign during the lifetime of the bubble. After collapse of the bubble, it needs to be conserved, usually in the form of a ring vortex. The Kelvin impulse is likely to provide valuable indicators as to the physical properties required of boundaries in order to reduce or eliminate cavitation damage. Comparisons are made against available experimental evidence.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 2 , October 1988 , pp. 127 - 146
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions (Dover, N. Y. 1965).Google Scholar
[2]Benjamin, T. B. and Ellis, A. T., “The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries”, Phil. Trans. R. Soc. London. Ser. A 260 (1966) 221–40.Google Scholar
[3]Blake, J. R. and Cerone, P., “A note on the impulse due to a vapour bubble near a boundary”, J. Aust. Math. Soc. 23 (1982) 383–393.CrossRefGoogle Scholar
[4]Blake, J. R. and Gibson, D. C., “Cavitation bubbles near boundaries”, Ann. Rev. Fluid. Mech. 19 (1987) 99–123.CrossRefGoogle Scholar
[5]Blake, J. R., Taib, B. B. and Doherty, G., “Transient cavities near boundaries. Part 1. Rigid Boundary”, J. Fluid Mech. 170 (1986) 479–497.CrossRefGoogle Scholar
[6]Blake, J. R., Taib, B. B. and Doherty, G., “Transient cavities near boundaries Part 2. Free Surface”, J. Fluid Mech. 181 (1987) 197–212.CrossRefGoogle Scholar
[7]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, Berlin, 1980).Google Scholar
[8]Kucera, A. and Blake, J. R., “Computational modelling of cavitation bubbles near boundaries.” in Commutational Techniques and Applications CTAC-87 (eds. Noye, J. and Fletcher, C.) (North Holland, Amsterdam, 1988) 391–400.Google Scholar
[9]Lamb, H., Hydrodynamics (CUP, Cambridge, 1930).Google Scholar
[10]Lighthill, J., An Informal Introduction to Theoretical Fluid Mechanics (O.U.P. Oxford, 1986).Google Scholar
[11]Prosperetti, A. and Manzi, D., “Mechanism of jet formation for a translating and collapsing bubble”, (submitted 1987).Google Scholar
[12]Shima, A. and Tomita, Y., Private communication (1987).Google Scholar