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Transient cavities near boundaries Part 2. Free surface

Published online by Cambridge University Press:  21 April 2006

J. R. Blake ,
B. B. Taib  and
G. Doherty
J. R. Blake
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, New South Wales, 2500 Australia
B. B. Taib
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, New South Wales, 2500 Australia
G. Doherty
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, New South Wales, 2500 Australia
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Abstract

Calculations of the growth and collapse of transient vapour cavities near a free surface when buoyancy forces may be important are made using the boundary-integral method described in Part 1. Bubble shapes, particle paths, pressure contours and centroid motion are used to illustrate the calculations. In the absence of buoyancy forces the bubble migrates away from the free surface during the collapse phase, yielding a liquid jet directed away from the free surface. When the bubble is sufficiently close to the free surface, the nonlinear response of the free surface produces a high-speed jet (‘spike’) that moves in the opposite direction to the liquid jet and, in so doing, produces a stagnation point in the fluid between the bubble and the free surface. For sufficiently large bubbles, buoyancy forces may be dominant, so that the bubble migrates towards the free surface with the resulting liquid jet in the same direction. The Kelvin impulse provides a reasonable estimate of the physical parameter space that determines the migratory behaviour of the collapsing bubbles.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 181 , August 1987 , pp. 197 - 212
Copyright
© 1987 Cambridge University Press

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References

Blake, J. R. 1983 The Kelvin impulse: application to bubble dynamics. In Proc. 8th Austral. Fluid Mech. Conf., vol. 2, pp. 10B.1–10B.4. Newcastle, Australia: Institution of Engineers.
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., Cerone, P. & Gibson, D. C. 1984 A note on the growth and collapse of buoyant vapour bubbles near a free surface. Preprint No. 9/84, Department of Mathematics. University of Wollongong.
Blake, J. R. & Gibson, D. C. 1981 Growth and collapse of a vapour cavity near a free surface. J. Fluid Mech. 111, 123–140.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
Cerone, P. & Blake, J. R. 1984 A note on the instantaneous streamlines, pathlines and pressure contours for a cavitation bubble near a boundary. J. Austral. Math. Soc. B 26, 31–44.Google Scholar
Chahine, G. L. 1977 Interaction between an oscillating bubble and a free surface. Trans. ASME I: J. Fluids Engng 99, 709–716Google Scholar
Chahine, G. L. & Bovis, A. 1980 Oscillation and collapse of a cavitation bubble in the vicinity of a two-liquid interface. In Cavitation and Inhomogeneities in Underwater Acoustics (ed. W. Lauterborn), pp. 23–29. Springer.
Gibson, D. C. 1968 Cavitation adjacent to plane boundaries. In Proc. 3rd Austral. Conf. on Hydraulics and Fluid Mech., pp. 210–214. Sydney, Australia: Institution of Engineers.
Gibson, D. C. & Blake, J. R. 1980 Growth and collapse of cavitation bubbles near flexible boundaries. In Proc. 7th Aust. Conf. on Hydraulics and Fluid Mech., pp. 283–286. Brisbane, Australia: Institution of Engineers.
Gibson, D. C. & Blake, J. R. 1982 The growth and collapse of bubbles near deformable surfaces. Appl. Sci. Res. 9, 215–224.Google Scholar
Holt, M. 1977 Underwater explosions. Ann. Rev. Fluid Mech. 9, 187–214.Google Scholar
Lenoir, M. 1976 Calcul numérique de d'implosion d'une bulle de cavitation au voisinage d'une paroi ou d'une surface libre. J. Méc. 15, 725–751.Google Scholar
Longuet-Higgins, M. S. & Cokelet, E. D. 1976 The deformation of steep surface waves on water. 1. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1–26.Google Scholar
Taib, B. B. 1985 Boundary integral methods applied to cavitation bubble dynamics. Ph.D. thesis, University of Wollongong.
Taib, B. B., Doherty, G. & Blake, J. R. 1984 Boundary integral methods applied to cavitation bubble dynamics. In Proc. Centre Math. Anal. Workshop (ed. S. A. Gustafson & R. S. Womersley), vol. 6, pp. 166–186.