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Transient cavities near boundaries. Part 1. Rigid boundary

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. Current address: Mathematics Department, Universiti Pertanian Malaysia, Serdang, Selangor, Malaysia.
G. Doherty
Affiliation:
Department of Mathematics, The University of Wollongong, Wollongong, New South Wales, 2500 Australia.
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Abstract

The growth and collapse of transient vapour cavities near a rigid boundary in the presence of buoyancy forces and an incident stagnation-point flow are modelled via a boundary-integral method. Bubble shapes, particle pathlines and pressure contours are used to illustrate the results of the numerical solutions. Migration of the collapsing bubble, and subsequent jet formation, may be directed either towards or away from the rigid boundary, depending on the relative magnitude of the physical parameters. For appropriate parameter ranges in stagnation-point flow, unusual ‘hour-glass’ shaped bubbles are formed towards the end of the collapse of the bubble. It is postulated that the final collapsed state of the bubble may be two toroidal bubbles/ring vortices of opposite circulation. For buoyant vapour cavities the Kelvin impulse is used to obtain criteria which determine the direction of migration and subsequent jet formation in the collapsing bubble.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 170 , September 1986 , pp. 479 - 497
Copyright
© 1986 Cambridge University Press

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References

Abramowitz, M. & Stegun I. A.1965 Handbook of Mathematical Functions. Dover.
Arndt R. E. A.1981 Recent advances in cavitation research. Adv. Hydrosci. 12, 1–78.Google Scholar
Batchelor G. K.1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Benjamin T. B.1984 Impulse, flow force and variational principles. IMA J. Appl. Maths. 32, 3–68.Google Scholar
Benjamin, T. B. & Ellis A. T.1966 The collapse of cavitation bubbles and the pressures thereby produced against solid boundaries Phil. Trans. R. Soc. Lond. A 260, 221–240.Google Scholar
Birkhoff, G. & Zarantonello E. H.1957 Jets, Wakes and Cavities. Academic Press.
Blake J. R.1983 The Kelvin impulse: application to bubble dynamics. Proc. 8th Aust. Fluid Mech. Conf. Newcastle. pp. 10B.1–10.B.4.
Blake, J. R. & Cerone P.1982 A note on the impulse due to a vapour bubble near a boundary J. Aust. Math. Soc. B 23, 383–393.Google Scholar
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
Cerone, P & Blake J. R.1984 A note on the instantaneous streamlines, pathlines and pressure contours for a cavitation bubble near a boundary J. Aust. Math. Soc. B 26, 31–44.Google Scholar
Chahine G. L.1982 Experimental and asymptotic study of non-spherical bubble collapse. Appl. Sci. Res. 38, 187–198.Google Scholar
Chahine, G. L. & Bovis A. G.1983 Pressure field generated by non spherical bubble collapse. Trans. ASME 105, 356–363.Google Scholar
Ellis A. T.1956 Techniques for pressure pulse measurements and high speed photography in ultrasonic cavitation. Cavitation in Hydrodynamics, Paper 8, pp. 1–32. HMSO, London.
Gibson D. C.1968 Cavitation adjacent to plane boundaries. Proc. 3rd Aust. Conf. on Hydraulic and Fluid Mechanics, pp. 210–214. Institution of Engineers, Sydney, Australia.
Gibson, D. C. & Blake J. R.1982 The growth and collapse of bubbles near deformable surfaces. Appl. Sci. Res. 38, 215–224.Google Scholar
Guerri L., Lucca, G. & Prosperetti A.1981 A numerical method for the dynamics of non-spherical cavitation bubbles. Proc. 2nd Int. Collog. on drops and bubbles, California, pp. 175–181.
Hammitt F. G.1980 Cavitation and Multiphase Flow Phenomena. McGraw-Hill.
Knapp R. T., Daily, J. W. & Hammitt F. G.1970 Cavitation, McGraw-Hill.
Lamb H.1932 Hydrodynamics. Cambridge University Press.
Landweber, L. & Miloh T.1980 Unsteady Lagally theorem for multipoles and deformable bodies. J. Fluid Mech. 96, 33–46.Google Scholar
Lauterborn W.1982 Cavitation bubble dynamics - new tools for an intricate problem. Appl. Sci. Res. 38, 165–178.Google Scholar
Lauterborn, W. & Bolle H.1975 Experimental investigations of cavitation bubble collapse in the neighbourhood of a solid boundary. J. Fluid Mech. 72, 391–399.Google Scholar
Lauterborn, W. & Hentschel W.1985 Cavitation bubble dynamics studied by high speed photography and holography. Part I. Ultrasonics (in press).
Lauterborn, W. & Vogel A.1984 Modern optical techniques in fluid mechanics. Ann. Rev. Fluid Mech. 16, 223–244.Google Scholar
Lenoir M.1976 Calculations numerique le l'implosion d'une bulle de cavitation au voisinage d'une paroi ou d'une surface libre. J. Mech. 15, 725–751.Google Scholar
Mcintyre M. E.1981 On the ‘wave momentum’ myth. J. Fluid Mech. 106, 331–347.Google Scholar
Miksis M. J., Vanden-Broeck, J. M. & Keller J. B.1982 Rising bubbles. J. Fluid Mech. 123, 31–42.Google Scholar
Pinczewski W. W.1981 The formation and growth of bubbles at a submerged orifice. Chem. Engng. Sci. 36, 405–411.Google Scholar
Plesset, M. S. & Chapman R. B.1971 Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary. J. Fluid Mech. 47, 283–290.Google Scholar
Prosperetti A.1982 Bubble dynamics: a review and some recent results. Appl. Sci. Res. 38, 145–164.Google Scholar
Rayleigh Lord1917 On the pressure developed in a liquid during the collapse of a spherical void. Phil. Mag. 34, 94–98.Google Scholar
Ryskin, G. & Leal L. G.1984 Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent fluid. J. Fluid Mech. 148, 19–36.Google Scholar
Saffman P. G.1967 The self propulsion of a deformable body in a perfect fluid. J. Fluid Mech. 28, 385–389.Google Scholar
Stroud, A. H. & Secrest D.1966 Gaussian Quadrature Formulas. Prentice Hall.
Taib B. B.1985 Boundary integrals methods applied to cavitation bubble dynamics. PhD thesis, University of Wollongong.
Taib B. B., Doherty, G. & Blake J. R.1984 Boundary integral methods applied to cavitation bubble dynamics. Mathematical Programming and Numerical Analysis Workshop (eds. S. A. Gustafson & R. S. Womersley,), vol. 6, pp. 166–186. Centre for Math. Anal. A.N.U.
Wu T. Y.1976 The momentum theorem for a deformable body in a perfect fluid. Schiffstechnik 23, 229–232.Google Scholar