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The Kelvin impulse: application to cavitation bubble dynamics

  • J. R. Blake (a1)
Abstract

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.

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References
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[1]Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions (Dover, N. Y. 1965).
[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.
[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) 383393.
[4]Blake, J. R. and Gibson, D. C., “Cavitation bubbles near boundaries”, Ann. Rev. Fluid. Mech. 19 (1987) 99123.
[5]Blake, J. R., Taib, B. B. and Doherty, G., “Transient cavities near boundaries. Part 1. Rigid Boundary”, J. Fluid Mech. 170 (1986) 479497.
[6]Blake, J. R., Taib, B. B. and Doherty, G., “Transient cavities near boundaries Part 2. Free Surface”, J. Fluid Mech. 181 (1987) 197212.
[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).
[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) 391400.
[9]Lamb, H., Hydrodynamics (CUP, Cambridge, 1930).
[10]Lighthill, J., An Informal Introduction to Theoretical Fluid Mechanics (O.U.P. Oxford, 1986).
[11]Prosperetti, A. and Manzi, D., “Mechanism of jet formation for a translating and collapsing bubble”, (submitted 1987).
[12]Shima, A. and Tomita, Y., Private communication (1987).
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The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
  • URL: /core/journals/anziam-journal
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