Dynamics of a Vapour Bubble inside a Vertical Rigid Cylinder in the Absence of Buoyancy Forces

In this paper, growth and collapse of a vapour bubble generated due to a local energy input inside a rigid cylinder and in the absence of buoyancy forces is investigated using Boundary Integral Equation Method and Finite Difference Method .The fluid is treated as potential flow and Boundary Integral Equation Method is used to solve Laplace-s equation for velocity potential. Different ratios of the diameter of the rigid cylinder to the maximum radius of the bubble are considered. Results show that during the collapse phase of the bubble inside a vertical rigid cylinder, two liquid micro jets are developed on the top and bottom sides of the vapour bubble and are directed inward. It is found that by increasing the ratio of the cylinder diameter to the maximum radius of the bubble, the rate of the growth and collapse phases of the bubble increases and the life time of the bubble decreases.

Authors:

• S. Mehran
• S. Rouhi
• F.Rouzbahani
• E. Haghgoo

Keywords:

• Vapour bubble
• Vertical rigid cylinder
• Boundaryelement method
• Finite difference method
• Buoyancy forces.

References:

[1] Li, S. C. 2000. "Cavitations of hydraulic machinery," Imperial College
Press. pp. 464.
[2] Blake, J. R., Taib, B. B. and Doherty, G. (1986), " Transient cavities
near boundaries; Part 1. Rigid boundary", J. Fluid Mech., Vol. 170, pp.
479-497.
[3] Blake, J. R. and Gibson, D. C. (1987), " Cavitation bubbles near
boundaries", Ann. Rev. Fluid Mech., Vol. 19, pp. 99-123.
[4] Soh, W. K. and Shervani-Tabar, M. T. (1994), " Computer model for a
pulsating bubble near a rigid surface", Computational Fluid Dynamics
JOURNAL, Vol. 3, No. 1, pp. 223-236.
[5] Blake, J. R., Taib, B. B. and Doherty, G. (1986), " Transient cavities
near boundaries; Part 2. Free surface", J. Fluid Mech., Vol. 181, pp. 197-
212.
[6] Blake, J. R. and Gibson, D. C. (1981), " Growth and collapse of a
vapour cavity bubble near a free surface", J. Fluid Mech., Vol. 111, pp.
123-140.
[7] Shervani-Tbar, M. T. (1995), " Computer study of a cavity bubble near a
rigid boundary, a free surface, and a compliant wall", PhD Thesis,
University of Wollongong, Wollongong, Australia.
[8] Lauterborn, W. (1980), " Cavitation and coherent optics", Cavitation and
Inhomogenities in Underwater Acoustics, Proceedings of the First
International Conference, , Fed. Rep. of Germany, Lauterborn (Ed.),
Springer-Verlag, pp. 3-12.
[9] Rayleigh, Lord (1917), "On the pressure developed in a liquid during
collapse of a spherical void", Phil. Mag., Vol. 34, pp. 94-98.
[10] Best, J. P. (1991), "The dynamics of underwater explosions", PhD
Thesis, University of Wollongong, Wollongong, Australia.
[11] Shervani-Tabar, M. T., Abdullah, A. and Shabgard, M. R. (2006), "
Numerical study on the dynamics of an electrical discharge generated
bubble in EDM", Engineering Analysis with Boundary Elements, Vol.
30, pp. 503-514.