Abstract
Vortex methods for domains bounded by closed surfaces such as bubbles must be modified to account for the changes in the enclosed volume. In the past, this has been accomplished by placing a source of unknown strength inside the bubble. Here, a new vortex method capable of simulating problems of this nature is developed. The volume changes of the domain are handled by introducing a uniform source distribution at the surface. Examples of the application of this technique are drawn from the area of bubble dynamics. A vapor bubble collapsing under hydrostatic pressure is studied as a test case. The results agree very well with the available boundary integral calculations in the literature. As an example of importance to bubble dynamics,the shape and volume oscillations of two bubbles in an acoustic field are also examined and several intriguing results are found.
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References
G.R. Baker, D.I. Meiron, and S.A. Orszag. Generalized vortex methods for free-surface flow problems. J. Fluid Mech. ,123:477–501, 1980.
G.R. Baker, D.I. Meiron, and S.A. Orszag. Boundary integral methods for axisymmetric and three-dimensional Rayleigh-Taylor instability problems. Physica ,12D: 19–31, 1984.
J.P. Best. The formation of toroidal bubbles upon the collapse of transient cavities. J. Fluid Mech. ,251:79–107, 1993.
J.R. Blake, B.B. Taib, and G. Doherty. Transient cavities near boundaries. Part 1. Rigid boundary. J. Fluid. Mech. ,170:479–497, 1986.
J.R. Blake, B.B. Taib, and G. Doherty. Transient cavities near boundaries. Part 2. Free surface. J. Fluid Mech. ,181:197–212, 1987.
K.W. Commander and A. Prosperetti. Linear pressure waves in bubbly liquids: Comparison between theory and experiments. J. Acoust. Soc. Am. ,85:732–46, 1989.
D.G. Dommermuth and D.K.P. Yue. Numerical simulations of nonlinear axisymmetric flows with a free surface. J. Fluid Mech. ,178:195–219, 1987.
D.G. Dommermuth, D.K.P Yue, W.M. Lin, R.J. Rapp, E.S. Chan, and W.K. Melville. Deepwater plunging breakers: a comparison between potential theory and experiments. J. Fluid Mech. ,189:423–442, 1988.
L. Guerri, G. Lucca, and A. Prosperetti. A numerical method for the dynamics of non-spherical cavitation of bubbles. In Le Croissette, editor, Proceedings of the Second International Colloquium on Drops and Bubbles ,pages 175–181, Jet Propulsion Laboratory, Pasadena, 1982.
A. Kucera and J.P. Best. A numerical investigation of non-spherical rebounding bubbles. J. Fluid Mech. ,245:137–154, 1992.
M.S. Longuet-Higgins. Monopole emission of sound by asymmetric bubble oscillations: I normal modes. J. Fluid Mech. ,201:525–541, 1989.
M.S. Longuet-Higgins. Monopole emission of sound by asymmetric bubble oscillations: II an initial value problem. J. Fluid Mech. ,201:543–565, 1989.
M.S. Longuet-Higgins and E.D. Cokelet. The deformation of steep surface waves on water. i.numerical method of computation. Proc. R. Soc. Lond. ,A350:l–26, 1976.
T.S. Lundgren and N.N. Mansour. Oscillations of drops in zero gravity with weak viscous effects. J. Fluid Mech. ,194:479–510, 1988.
H.N. Oguz, A.M. Lezzi, and A. Prosperetti. Examples of air-entraining flows. Phys. Fluids, 4:649–651, 1992.
H.N. Oguz and A. Prosperetti. Surface-tension effects in the contact of liquid surfaces. J. Fluid Mech. ,203:149–171, 1989.
H.N. Oguz and A. Prosperetti. Bubble entrainment by the impact of drops on liquid surfaces. J. Fluid Mech. ,219:143–179, 1990.
H.N. Oguz and A. Prosperetti. Numerical calculation of the underwater noise of rain. J. Fluid Mech. ,228:417–442, 1991.
H.N. Oguz and A. Prosperetti. Dynamics of bubble growth and detachment from a needle. J. Fluid Mech. ,257:11–145, 1993.
A. Prosperetti. The thermal behaviour of oscillating gas bubbles. J. Fluid Mech. ,222:587–616, 1991.
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© 1994 Springer Science+Business Media Dordrecht
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Oğuz, H.N. (1994). Vortex simulations of bubble oscillations. In: Blake, J.R., Boulton-Stone, J.M., Thomas, N.H. (eds) Bubble Dynamics and Interface Phenomena. Fluid Mechanics and Its Applications, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0938-3_6
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DOI: https://doi.org/10.1007/978-94-011-0938-3_6
Publisher Name: Springer, Dordrecht
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