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Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary

Published online by Cambridge University Press:  29 March 2006

Milton S. Plesset
Affiliation:
California Institute of Technology
Richard B. Chapman
Affiliation:
California Institute of Technology

Abstract

Vapour bubble collapse problems lacking spherical symmetry are solved here using a numerical method designed especially for these problems. Viscosity and compressibility in the liquid are neglected. Two specific cases of initially spherical bubbles collapsing near a plane solid wall were simulated: a bubble initially in contact with the wall, and a bubble initially half its radius from the wall at the closest point. It is shown that the bubble develops a jet directed towards the wall rather early in the collapse history. Free surface shapes and velocities are presented at various stages in the collapse. Velocities are scaled like (Δp/ρ)½ where ρ is the density of the liquid and Δp is the constant difference between the ambient liquid pressure and the pressure in the cavity. For \[ \Delta p/\rho = 10^6 {\rm cm}^2/\sec^2 \approx 1\, \hbox{atm/density of water} \] the jet had a speed of about 130m/sec in the first case and 170m/sec in the second when it struck the opposite side of the bubble. Such jet velocities are of a magnitude which can explain cavitation damage. The jet develops so early in the bubble collapse history that compressibility effects in the liquid and the vapour are not important.

Type
Research Article
Copyright
© 1971 Cambridge University Press

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References

Benjamin, T. B. & Ellis, A. T. 1966 Phil. Trans. Roy. Soc. A, 260, 221.
Hancox, N. L. & Brunton, J. H. 1966 Phil. Trans. Roy. Soc. A, 260, 121.
Kornfeld, M. & Suvorov, L. 1944 J. Appl. Phys. 15, 495.
Mitchell, T. M., Kling, C. L., Cheesewright, R. & Hammitt, F. G. 1967 U. of Michigan, College of Eng., Rep. 07738-5-T.
Plesset, M. S. 1966 Phil. Trans. Roy. Soc. A, 260, 241.
Plesset, M. S. & Chapman, R. B. 1970 Div. of Eng. and Appl. Science, Calif. Inst. of Tech. Rep. no. 85–49.
Plesset, M. S. & Mitchell, T. P. 1956 Quart. Appl. Math. 13, 419.
Rattray, M. 1951 Ph.D. thesis, California Institute of Technology.
Rayleigh, Lord 1917 Phil. Mag. 34, 94.
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