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CLOUD CAVITATION DYNAMICS

Part of: Two-phase and multiphase flows

Published online by Cambridge University Press:  01 October 2008

MILES WILSON ,
JOHN R. BLAKE  and
PETER M. HAESE
MILES WILSON
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK (email: [email protected])
JOHN R. BLAKE*
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK (email: [email protected])
PETER M. HAESE
Affiliation:
School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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An analysis is developed for the behaviour of a cloud of cavitation bubbles during both the growth and collapse phases. The theory is based on a multipole method exploiting a modified variational principle developed by Miles [“Nonlinear surface waves in closed basins”, J. Fluid Mech.75 (1976) 418–448] for water waves. Calculations record that bubbles grow approximately spherically, but that a staggered collapse ensues, with the outermost bubbles in the cloud collapsing first of all, leading to a cascade of bubble collapses with very high pressures developed near the cloud centroid. A more complex phenomenon occurs for bubbles of variable radius with local zones of collapse, with a complex frequency spectrum associated with each individual bubble, leading to both local and global collective behaviour.

Keywords

bubblesmultipolescloudsclusterscavitation

MSC classification

Secondary: 76T10: Liquid-gas two-phase flows, bubbly flows
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 2 , October 2008 , pp. 199 - 208
Copyright
Copyright © Australian Mathematical Society 2009

References

[1]Best, J. P. and Blake, J. R., “An estimate of the Kelvin impulse of a transient cavity”, J. Fluid Mech. 261 (1994) 75–93.CrossRefGoogle Scholar
[2]Blake, J. R., Keen, G. S., Tong, R. P. and Wilson, M., “Acoustic cavitation: the fluid dynamics of non-spherical bubbles”, Philos. Trans. R. Soc. A357 (1999) 251–267.CrossRefGoogle Scholar
[3]Chahine, G. L. and Duraiswami, R., “Dynamical interactions in a multi-bubble cloud”, J. Fluids Engrg. 114 (1992) 680–687.CrossRefGoogle Scholar
[4]Hanson, I., Kendrinskii, V. K. and Mørch, K. A., “On the dynamics of cavity clusters”, J. Appl. Phys. 15 (1981) 1725–1734.Google Scholar
[5]Hobson, E. W., The theory of spherical and ellipsoidal harmonics (Cambridge University Press, Cambridge, 1931).Google Scholar
[6]Kucera, A. and Blake, J. R., “Approximate methods for modelling the growth and collapse of cavitation bubbles near boundaries”, Bull. Aust. Math. Soc. 41 (1990) 1–44.CrossRefGoogle Scholar
[7]Landweber, L. and Miloh, T., “Unsteady Lagally theorem for multipoles and deformable bodies”, J. Fluid Mech. 96 (1980) 33–46.CrossRefGoogle Scholar
[8]Landweber, L. and Miloh, T., “Unsteady Lagally theorem for multipoles and deformable bodies. Corrigendum”, J. Fluid Mech. 112 (1981) 502.Google Scholar
[9]Landweber, L. and Yih, C. S., “Forces, moments, and added masses for Rankine bodies”, J. Fluid Mech. 1 (1956) 319–336.CrossRefGoogle Scholar
[10]Luke, J. C., “A variational principle for a fluid with a free surface”, J. Fluid Mech. 27 (1967) 395–397.CrossRefGoogle Scholar
[11]Miles, J. W., “Nonlinear surface waves in closed basins”, J. Fluid Mech. 75 (1976) 418–448.CrossRefGoogle Scholar
[12]Sangani, A. S. and Yao, C., “Bulk thermal conductivity of composites with spherical inclusions”, J. Appl. Phys. 63 (1988) 1334–1341.CrossRefGoogle Scholar
[13]Taylor, G. I., “The energy of a body moving in an infinite fluid, with application to airships”, Proc. R. Soc. Lond. Ser. A 120 (1928) 13–21.Google Scholar
[14]Wilson, M., Mathematical modelling of bubble-vortex interactions, Ph. D. Thesis, University of Birmingham, 1997.Google Scholar
[15]Wilson, M., Blake, J. R. and Haese, P. M., “A potential multipole theory for the hydrodynamics of bubble clouds”, IMA J. Appl. Math. 73 (2008) 556–577.CrossRefGoogle Scholar