Abstract
The growth and collapse of buoyant vapor bubbles close to a free surface in an inviscid incompressible fluid is investigated in this paper. The strong interaction between the deforming bubble and the free surface is simulated numerically by a boundary-integral method (Taib 1985; Blake et al., 1987). Improvements are made in the calculation of the singular integrals, the use of nonuniform boundary elements, and the choice of time-step size. The present numerical results agree better with the experimental observations of Blake and Gibson (1981) than previous numerical predictions for bubbles initiated at one maximum radius from the free surface. There is also concurrence of flow features with the experiments for a bubble initiated as close as half maximum radius from the free surface, where other numerical efforts have failed. The effects of buoyancy on bubbles initiated close to a free surface are also investigated. Vastly different features, depending on the distance of the bubble to the free surface and the buoyancy-force parameter, have been observed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz, M., and Stegun, I.A. (1965). Handbook of Mathematical Functions. Dover, New York.
Akima, H. (1970). A new method of interpolation and smooth curve fitting based on local procedures. J. Assoc. Comput. Mach. 17, 589–602.
Baker, G.R., and Moore, D.W. (1989). The rise and distortion of a two-dimensional gas bubble in an inviscid liquid. Phys. Fluids A 1, 1451.
Baker, G.R., Meiron, D.I., and Orszag, S.A. (1984). Boundary integral methods for axisymmetric and three-dimensional Rayleigh-Taylor instability problems. Phys. D 12, 19–31.
Benjamin, T.B., and Ellis, A.T. (1966). The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries. Philos. Trans. Roy. Soc. London Ser. A 260, 221–240.
Best, J.P., and Kucera, A. (1992). A numerical investigation of non-spherical rebounding bubbles. J. Fluid Mech. 245, 137–154.
Blake, J.R., and Cerone, P. (1982). A note on the impulse due to a vapour bubble near a boundary. J. Austral. Math. Soc. Ser. B 23, 383–393.
Blake, J.R., and Gibson, D.C. (1981). Growth and collapse of a vapour cavity near free surface. J. Fluid Mech. 111, 124–140.
Blake, J.R., Taib, B.B., and Doherty, G. (1986). Transient cavities near boundaries. Part 1. Rigid boundary. J. Fluid Mech. 170, 479–497.
Blake, J.R., Taib, B.B., and Doherty G. (1987). Transient cavities near boundaries. Part 2. Free surface. J. Fluid Mech. 181, 197–212.
Cerone, P., and 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. Ser. B 26, 31–44.
Chahine, G.L. (1977). Interaction between an oscillating bubble and a free surface. Trans. ASME Ser. I J. Fluid Engrg. 99, 709–716.
Chahine, G.L., and Bovis, A.G. (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. Spring-Verlag, New York.
Gibson, D.C. (1968). Cavitation adjacent to plane boundaries. Proc. 3rd Austral. Conf. on Hydraulics and Fluid Mechanics, pp. 210–214. Institution of Engineers, Sydney.
Gibson, D.C., and Blake, J.R. (1980). Growth and collapse of cavitation bubbles near flexible boundaries. Proc. 7th Austral. Conf. on Hydraulics and Fluid Mechanics, pp. 283–286. Institution of Engineers, Brisbane.
Lenoir, M. (1976). Calcul numerique de d'implosion d'une bulle de cavitation au voisinage d'une paroi ou d'une surface libre. J. Méc. 15, 725–751.
Longuet-Higgins, M.S., and Cokelet, E.D. (1976). The deformation of steep surface waves on water. I. A numerical method of computation. Proc. Roy. Soc. London Ser. A 350, 1–26.
Taib, B.B. (1985). Boundary Integral Methods Applied to Cavitation Bubble Dynamics. Ph.D. Thesis, University of Wollongong.
Voinov, O.V., and Voinov, V.V. (1975). Numerical method of calculating non-stationary motions of an ideal incompressible fluid with free surfaces. Soviet Phys. Dokl. 20, 179–180.
Author information
Authors and Affiliations
Additional information
Communicated by M.Y. Hussaini
Rights and permissions
About this article
Cite this article
Wang, Q.X., Yeo, K.S., Khoo, B.C. et al. Strong interaction between a buoyancy bubble and a free surface. Theoret. Comput. Fluid Dynamics 8, 73–88 (1996). https://doi.org/10.1007/BF00312403
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00312403