Document Type : Original Article

Author

Department of Mechanical Engineering, Bu-Ali Sina University, Hamedan

Abstract

 In this paper, growth and collapse of a cavitation bubble inside a rigid cylinder with a compliant coating (a model of human’s vessels) are studied using Boundary Integral Equation and Finite Difference Methods. The fluid flow is treated as a potential flow and Boundary Integral Equation Method is used to solve Laplace’s equation for velocity potential. The compliant coating is modeled as a membrane with a spring foundation. At the interface between the fluid and the membrane, the pressure and normal velocity in the flow are matched to the pressure and normal velocity of the membrane using linearized condition. The effects of the parameters describing the flow (the fluid density, the initial cavity size and its position) and the parameter describing the compliant coating (membrane tension) on the interaction between the fluid and the cylindrical compliant coating are shown throughout the numerical results. It is shown that the bubble life time slightly decreases by increasing membrane tension.

Keywords

Article Title [فارسی]

GROWTH AND COLLAPSE OF A CAVITATION BUBBLE INSIDE A RIGID CYLINDER: EFFECT OF MEMBRANE TENSION

Author [فارسی]

  • Amireh Norbaskhsh

Department of Mechanical Engineering, Bu-Ali Sina University, Hamedan

Abstract [فارسی]

 In this paper, growth and collapse of a cavitation bubble inside a rigid cylinder with a compliant coating (a model of human’s vessels) are studied using Boundary Integral Equation and Finite Difference Methods. The fluid flow is treated as a potential flow and Boundary Integral Equation Method is used to solve Laplace’s equation for velocity potential. The compliant coating is modeled as a membrane with a spring foundation. At the interface between the fluid and the membrane, the pressure and normal velocity in the flow are matched to the pressure and normal velocity of the membrane using linearized condition. The effects of the parameters describing the flow (the fluid density, the initial cavity size and its position) and the parameter describing the compliant coating (membrane tension) on the interaction between the fluid and the cylindrical compliant coating are shown throughout the numerical results. It is shown that the bubble life time slightly decreases by increasing membrane tension.

Keywords [فارسی]

  • bubble
  • collapse
  • membrane tension
  • Boundary element method
  1. Blake, J. R., Taib, B. B., and Doherty, G. Transient cavities near boundaries; Part 1. Rigid boundary. J. Fluid Mech, Vol. 170 (1986), 479.
  2. Blake, J. R., Gibson, D. C. Cavitation bubbles near boundaries. Ann. Rev. Fluid Mech, Vol. 19 (1987) 99- 123.
  3. Soh, W. K., Shervani-Tabar, M. T. Computer model for a pulsating bubble near a rigid surface. Computational Fluid Dynamics Journal. Vol. 3, 1 (1994) 223-236.
  4. Blake, J. R., Taib, B. B., and Doherty, G. Transient cavities near boundaries; Part 2. Free surface. J. Fluid Mech, Vol. 181 (1986) 197-212.
  5. Blake, J. R., Gibson, D. C. Growth and collapse of a vapour cavity bubble near a free surface. J. Fluid Mech, Vol. 111 (1981) 123-140.
  6. Shervani-Tbar, M. T. Computer study of a cavity bubble near a rigid boundary, a free surface, and a compliant wall. PhD Thesis, University of Wollongong, Wollongong, Australia (1995).
  7. Lauterborn, W. Cavitation and coherent optics. Cavitation and Inhomogenities in Underwater Acoustics, Proceedings of the First International

Conference, , Fed. Rep. of Germany, Lauterborn (Ed.),

Springer-Verlag, (1980) 3-12.

  1. Rheingans, W. J. Resistance of various materials to cavitation damage. Report of 1956 Cavitation symposium, published by Am. Soc. Mechanical. Engrs (1956).
  2. Lichtman, J. Z., Kallas, D. H., Chatten, C. K, and Cochran, E. P. Study of corrosion and cavitation erosion damage. Transactions, Am. Soc. Mechanical. Engrs (1958).
  3. Gibson, D. C., and Blake, J. R. The growth and Collapse of Cavitation Bubble near Deformable Surfaces. appl. sci. res, Vol. 38 (1982) 215-224.
  4. Shima, A., Tomita, Y., Gibson, D. C., and Blake, J. R. The growth and collapse of cavitation bubbles near composite surface. J. Fluid Mech, Vol. 203 (1989) 199- 214.
  5. Tomita, Y., and Shima, A. Destructive action of cavitation bubbles collapsing near boundaries. Shock focussing effect in medical science and sonoluminescence (2003) 73- 109.
  6. Duncan, J. H., and Zhang, S. On the interaction of a collapsing cavity and a compliant wall. J. Fluid Mech, Vol. 226 (1991) 401-423.
  7. Wolfrum, B. Cavitation and shock wave effects on biological systems. PhD Thesis, Department of Physic, University of Gottingen (2004).
  8. Shervani-Tabar, M. T., Rezaee-Barmi, A., and Mahmoudi, S. M. Velocity field and pressure distribution around two parts of a cavitation bubble after its Splitting near a rigid boundary. Fifth international Symposium on cavitation (Cav 2003), November 1-4, Osaka, Japan. Cav03-GS-2-008.
  9. Shervani-Tabar, M. T., Rezaee-Barmi, A., and Mahmoudi, S. M. Velocity field and pressure distribution around a collapsing cavitation near a rigid boundary during the Necking phenomenon. Fifth international Symposium on cavitation (Cav 2003), November 1-4, Osaka, Japan. Cav03-GS-2-007.
  10. LeClair ML, Barros EF, Guvench MG. Cavitation and the Future of Nanotechnology. Ninth Foresight Conference on molecular nanotechnology (2005).
  11. Patek, S. N., and Caldwell, R. L. Extreme impact and cavitation forces of a biological hammer: Strike forces of the peacock mantis shrimp Odontodactylus scyllarus. Journal of Experimental Biology, Vol. 208 (2005) 3655- 3664.
  12. Rayleigh, L. On the pressure developed in a liquid during collapse of a spherical void. Phil. Mag, Vol. 34 (1917) 94-98.
  13. Best, J. P. The Dynamics of Underwater Explosions. PhD Thesis, Department of Mathematics, University of

Wollongong (1991) 1-48.