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A numerical investigation of non-spherical rebounding bubbles

Published online by Cambridge University Press:  26 April 2006

J. P. Best  and
A. Kucera
J. P. Best
Affiliation:
Materials Research Laboratory - DSTO, PO Box 50, Melbourne, 3032. Australia
A. Kucera
Affiliation:
Department of Mathematics, Australian Defence Force Academy, Campbell. ACT, 2600, Australia
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Abstract

The motion of buoyant transient cavities with non-condensible contents is investigated numerically using a boundary-integral method. The bubble contents are described by an adiabatic gas law. Motion is considered in the neighbourhood of a rigid boundary, in an axisymmetric geometry. We investigate whether the non-condensible contents will resist the formation of jets. It is found that jets form upon collapse and, in general, completely penetrate the bubble before it rebounds, but circumstances are identified under which the non-spherical bubble will rebound prior to this occurrence. In these cases the bulk of the jet growth occurs upon rebound. Furthermore, the interaction between the buoyancy force causing jet formation upwards, and the Bjerknes attraction of the rigid boundary causing jet formation towards it, is investigated and general principles discussed which allow the behaviour to be interpreted. The concept of the Kelvin impulse is utilized.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 245 , December 1992 , pp. 137 - 154
Copyright
© 1992 Cambridge University Press

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References

Abramowitz, M. & Stegun I. A. 1965 Handbook of Mathematical Functions, Dover.
Baker, G. R. & Moore D. W. 1989 The rise and distortion of a two-dimensional gas bubble in an inviscid liquid Phys. Fluids A 1, 1451–1459.Google Scholar
Benjamin, T. B. & Ellis A. T. 1966 The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries Phil. Trans. R. Soc. Lond. A 260, 221–240.Google Scholar
Blake J. R. 1988 The Kelvin impulse: Application to cavitation bubble dynamics J. Austral. Math. Soc. B 30, 127–146.Google Scholar
Blake, J. R. & Cerone P. 1982 A note on the impulse due to a vapour bubble near a boundary J. Austral. Math. Soc. B 23, 383–393.Google Scholar
Blake J. R., Taib, B. B. & Doherty G. 1986 Transient cavities near boundaries. Part 1. Rigid boundary. J. Fluid Mech. 170, 479–497.Google Scholar
Blake J. R., Taib, B. B. & Doherty G. 1987 Transient cavities near boundaries. Part 2. Free surface. J. Fluid Mech. 181, 197–212.Google Scholar
Chahine G. L. 1982 Experimental and asymptotic study of non-spherical bubble collapse. Appl. Sci. Res. 38, 187–197.Google Scholar
Chahine G. L. 1990 Numerical modelling of the dynamic behaviour of bubbles in non-uniform flow fields. Proc. ASME 1990 Symp. on Numerical Methods for Multiphase Flows, Toronto.
Chahine, G. L. & Perdue T. O. 1988 Simulation of the three-dimensional behaviour of an unsteady large bubble near a structure. Proc. 3rd Intl Colloq. on Drops and Bubbles, Monterey, California.
Gibson, D. C. & Blake J. R. 1982 The growth and collapse of bubbles near deformable surfaces. Appl. Sci. Res. 38, 215–224.Google Scholar
Guerri L., Lucca, G. & Prosperetti A. 1981 A numerical method for the dynamics of non-spherical cavitation bubbles. Proc. 2nd Intl Colloq. on Drops and Bubbles, Monterey, California. JPL Publication 82–7, pp. 175–181.
Kucera A. 1992 A boundary integral method applied to the growth and collapse of bubbles near a rigid boundary. J. Comput. Phys. (submitted).Google Scholar
Lauterborn, W. & Bolle H. 1975 Experimental investigations of cavitation bubble collapse in the neighbourhood of a solid boundary. J. Fluid Mech. 72, 391–399.Google Scholar
Longuet-Higgins, M. S. & Cokelet E. D. 1976 The deformation of steep surface waves on water. I. A numerical method of computation Proc. R. Soc. Lond. A 350, 1–26.Google Scholar
Lundgren, T. S. & Mansour N. N. 1991 Vortex ring bubbles. J. Fluid Mech. 224, 177–196.Google Scholar
Rayleigh Lord 1917 On the pressure developed in a liquid during the collapse of a spherical void. Phil. Mag. 34, 94–98.Google Scholar
Shiffman, M. & Friedman B. 1944 On the best location of a mine near the sea bed. Underwater Explosion Research, vol. II. Office of Naval Research, Washington. DC.
Taib B. B. 1985 Boundary integral methods applied to cavitation bubble dynamics. Ph.D. thesis, University of Wollongong, Australia.
Tomita, Y. & Shima A. 1986 Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse. J. Fluid Mech. 169, 535–564.Google Scholar
Vogel A., Lauterborn, W. & Timm R. 1989 Optical and acoustic investigations of the dynamics of laser-produced cavitation bubbles near a solid boundary. J. Fluid Mech. 206, 299–338.Google Scholar
Walters, J. K. & Davidson J. F. 1962 The initial motion of a gas bubble formed in an inviscid liquid. Part 1. The two-dimensional bubble. J. Fluid Mech. 12, 408–417.Google Scholar
Wilkerson S. 1989 Boundary integral technique for explosion bubble collapse analysis. ASME Energy-Sources Technol. Conference and Exhibition, Houston, Texas.Google Scholar