Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-20T20:52:20.020Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the instantaneous streamlines, pathlines and pressure contours for a cavitation bubble near a boundary

Published online by Cambridge University Press:  17 February 2009

P. Cerone  and
J. R. Blake
P. Cerone
Affiliation:
Department of Mathematics and Operations Research, Footscray Institute of Technology, P.O. Box 64, Footscray, Vic. 3011.
J. R. Blake
Affiliation:
Department of Mathematics, The 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.

Instantaneous streamlines, particle pathlines and pressure contours for a cavitation bubble in the vicinity of a free surface and near a rigid boundary are obtained. During the collapse phase of a bubble near a free surface, the streamlines show the existence of a stagnation point between the bubble and the free surface which occurs at a different location from the point of maximum pressure. This phenomenon exists when the initial distance of the bubble is sufficiently close to the free surface for the bubble and free surface to move in opposite directions during collapse of the bubble. Pressure calculations during the collapse of a cavitation bubble near a rigid boundary show that the maximum pressure is substantially larger than the equivalent Rayleigh bubble of the same volume.

Type
Research Article
Information
The ANZIAM Journal , Volume 26 , Issue 1 , July 1984 , pp. 31 - 44
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Benjamin, T. B. and Ellis, A. T., “The collapse of cavitation bubbles and the pressure thereby produced against solid boundaries”, Phil. Trans. Roy. Soc. London Ser. A 260 (1966), 221–240.Google Scholar
[2]Bevir, M. K. and Fielding, P. J., “Numerical solution of incompressible bubble collapse with jetting”, in Moving boundary problems in hear flow and diffnsion (eds. Ockendon, J. R. and Hodgkins, W. R.), (Clarendon Press, Oxford, 1975), 286–294.Google Scholar
[3]Blake, J. R. and Gibson, D. C., “Growth and collapse of a vapour cavity near a free surface”, J. Fluid Mech. 3 (1981), 123–140.CrossRefGoogle Scholar
[4]Chahine, G. L., “Interaction between an oscillating bubble and a free surface”, Trans. ASME Ser. IJ. Fluids Engng. 99 (1979), 709–716.CrossRefGoogle Scholar
[5]Gibson, D. C., “Cavitation adjacent to plane boundaries”, Proc. 3rd Austral. Hydraulics and Fluid Mech. Conf., Sydney (The Institution of Engineers, Australia, 1968), 210–214.Google Scholar
[6]Gibson, D. C. and Blake, J. R., “Growth and collapse of cavitation bubbles near flexible boundaries”, Proc. 7th Austral. Hydraulics and Fluid Mech. Conf. (1980), 283–286.Google Scholar
[7]Gibson, D. C. and Blake, J. R., “The growth and collapse of bubbles near deformable surfaces”, Appl. Sci. Res. 38 (1982), 215–224.CrossRefGoogle Scholar
[8]Lauterborn, W., “Cavitation bubble dynamics—new tools for an intricate problem”, in Mechanics and physics of bubbles in liquids, (Cd. van Wijngaarden, L.), (Nijhoff, The Hague, 1982), 165–178.CrossRefGoogle Scholar
[9]Longuet-Higgins, M. S., “A technique for time-dependent free-surface flows”, Proc. Roy. Soc. London Ser. A 371 (1980), 441–451.Google Scholar
[10]Longuet-Higgins, M. S., “Bubbles, breaking waves and hyperbolic jets at a free surface”, J. Fluid Mech. 127 (1983), 103–122.CrossRefGoogle Scholar
[11]Mitchell, T.M. and Hammitt, F. G., “Asymmetric cavitation bubble collapse”, Trans. ASME Ser. IJ. Fluids Engng. 95 (1973), 29–37.CrossRefGoogle Scholar
[12]Naudé, C. F. and Ellis, A. T., “On the mechanism of cavitation damage by non-hemispherical cavities collapsing in contact with a solid boundary”, Trans. ASME Ser. D J. Basic Engng. 83 (1961), 648–656.CrossRefGoogle Scholar
[13]Plesset, M. S. and Chapman, R. B., “Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary”, J. Fluid Mech. 47 (1971), 283–290.CrossRefGoogle Scholar
[14]Plesset, M. S. and Mitchell, T. P., “On the stability of the spherical shape of a vapour cavity in a liquid”, Quart. Appl. Math. 13 (1956), 419–430.CrossRefGoogle Scholar
[15]Rayleigh, Lord, “On the pressure developed in a liquid during the collapse of a spherical void”, Phil. Mag. 34 (1917), 94–98.CrossRefGoogle Scholar
[16]Van Dyke, M., An album of fluid mechanics (Parabolic, Stanford, 1982), 108.Google Scholar