Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-16T10:52:39.089Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximate methods for modelling cavitation bubbles near boundaries

Published online by Cambridge University Press:  17 April 2009

A. Kucera  and
J.R. Blake
A. Kucera
Affiliation:
Department of Mathematics, La Trobe University, Bundoora Vic 3083, Australia
J.R. Blake
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Edgbaston B15 2TT, United Kingdom
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.

Approximate methods are developed for modelling the growth and collapse of clouds of cavitation bubbles near an infinite and semi-infinite rigid boundary, a cylinder, between two flat plates and in corners and near edges formed by planar boundaries. Where appropriate, comparisons are made between this approximate method and the more accurate boundary integral methods used in earlier calculations. It is found that the influence of nearby bubbles can be more important than the presence of boundaries. In confined geometries, such as a cylinder, or a cloud of bubbles, the effect of the volume change due to growth or collapse of the bubble can be important at much larger distances. The method provides valuable insight into bubble cloud phenomena.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 1 , February 1990 , pp. 1 - 44
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions (Dover, New York, 1965).Google Scholar
[2]Blake, J.R., ‘The Kelvin impulse: applications to cavitation bubble dynamics’, J. Austral. Math. Soc. Ser. B 30 (1988).CrossRefGoogle Scholar
[3]Blake, J.R. and Gibson, D.C., ‘Growth and collapse of a vapour cavity near a free surface’, J. Fluid Mech. 111 (1981), 123–140.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 ner boundaries, Part 1. Rigid Boundary’, J. Fluid Mech. 170 (1986), 479–497.CrossRefGoogle Scholar
[6]Chahine, G.L., ‘Experimental and asymptotic Study of non-spherical bubble collapse’, Appl. Sci. Res. 38 (1982), 187–197.CrossRefGoogle Scholar
[7]Chahine, G.L. and Shen, Y.T., ‘Bubble dynamics and cavitation inception in cavitation susceptibility meters’, Trans ASME 108 (1986), 444–452.Google Scholar
[8]Euler, L., ‘Theorie plus complette des machines qui sont mises en mouvement par la reaction de l'eau’ 10, pp. 227–295.Google Scholar
[9]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
[10]Landweber, L., ‘Axisymmetric potential flow in a circular tube’, J. Hydronautics 8 (1974), 137–145.CrossRefGoogle Scholar
[11]Lighthill, J., An Informal Introduction to Theoretical Fluid Mechanics (Oxford University Press, Oxford, 1986).Google Scholar
[12]Plesset, M.S., ‘The dynamics of cavitation bubbles’, J. Appl. Mech 16 (1949), 277–282.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]Prosperetti, A., ‘Bubble dynamics: a review and some recent results’, Appl. Sci. Res. 38 (1982), 145–164.CrossRefGoogle Scholar
[15]Prosperetti, A., ‘On the dynamics of non-spherical bubbles’, in Cavitation and inhomogeneities in underwater acoustics, Editor Lauterborn, W. (Springer, Berlin, Heidelberg, New York, 1980).Google Scholar
[16]Rayleigh, Lord, ‘On the pressure developed in a liquid during the collapse of a spherical void’, Phil. Mag. 34 (1917), 94–98.CrossRefGoogle Scholar
[17]Reynolds, O., ‘Experiments showing the boiling of water in an open tube at ordinary temperatures’, Brit. Assoc. Adv. Sci. Rep. 564 (1894).Google Scholar
[18]Shima, A. and Nakajima, K., ‘The collapse of a non-hemispherical bubble attached to a solid wall’, J. Fluid Mech. 80 (1978), 369–391.CrossRefGoogle Scholar
[19]Shima, A., Tomita, Y., Gibson, D.C. and Blake, J.R., ‘The growth and collapse of cavitation bubbles near composite surfaces’, J. Fluid Mech. 203 (1989), 199–214.CrossRefGoogle Scholar
[20]Sommerfeld, A., ‘Mathematische Theorie der Diffraction’, Mathematische Annalen 47 (1896), 317–374.CrossRefGoogle Scholar
[21]Tomita, Y. and Shima, A., ‘Mechanisms of impulsive pressure generation and damage pit formation by bubble collapse’, J. Fluid Mech. 169 (1986), 535–564.CrossRefGoogle Scholar