Cover
Vol. 7 No. 1 (2007)

Published: June 30, 2007

Pages: 44-56

Original Article

Liquid Temperature Dependent Behaviour of a Cavitation Bubble in Acoustic Field

Abbas Z. AL-Asady 1
1 Mechanical Engineering Department, Engineering College, Basrah University, Iraq
History
  • Received: March 30, 2007
  • Available Online: June 30, 2007
DOI

https://doi.org/10.33971/bjes.7.1.5

Abstract

A new model of bubble dynamics is constructed using linear wave equation, including effects of variation of the gas temperature inside the bubble and the liquid temperature near the bubble, and effects of evaporation-condensation of the liquid vapour at the bubble wall. The liquid is assumed water and the gas inside the bubble is only vapour (neglecting non-condensable gas). The temperature inside the bubble and the liquid temperature are numerically calculated by solving the energy equation both inside (vapour-phase) and outside (liquid-phase) the bubble (using finite difference method). The pressure inside the bubble is obtained numerically without assuming that it follows any assuming relation. The results reveal that the bubble radius, the liquid temperature, and the pressure and temperature inside the bubble change with time periodically. Both the pressure and temperature become higher when the radius becomes minimum. The present theoretical result is compared with data from other reference and with another theoretical model to check the validity of the present model. The calculated result approximately fits with the data of the previous studies.

Keywords

References

  1. M. Fanelli, A. Prosperetti and M. Real, "Radial oscillations of gas-vapour bubbles in liquid, Part I: Mathematical Formulation", Vol. 47, No. 4, 1981.
  2. M. S. Plesset and A. Prosperetti, " Bubble dynamics and cavitation", Ann. Rev. Fluid Mech., 1977.
  3. E. A. Neppiras, "Acoustic Cavitation", Physics Reports, 61, 3, 1980.
  4. B. E. Noltingk and E. A. Neppiras," Cavitation produced by ultrasonics", Proc. Phys. Soc. London Sec. B 63, 1950.
  5. H. Poritsky," The collapse or growth of a spherical bubble or cavity in a viscous fluid", in proceedings of the First U.S. National Congress on Applied Mechanics, edited by E. Sternberg (Am. Soc. Mech. Eng., New York, 1952).
  6. W. Lauterborn, "Numerical investigation of nonlinear oscillations of gas bubbles in liquids", J. Acoust. Soc. Am. 59, 1976.
  7. J. B. Keller and I. I. Kolodner," Damping of underwater explosion bubble oscillations", J. Appl. Phys. 27, 1956.
  8. V. Kamath, A. Prosperetti and F. N. Egolfopoulos, " A theoretical study of sonoluminescence", J. Acoust. Soc. Am. 94, 1993.
  9. S. Fujikawa and T. Akamatsu," Effects of the non-equilibrium condensation of vapour on the pressure wave produced by the collapse of a bubble in a liquid", J. Fluid Mech. 97, 1980.
  10. B. P. Barber, C. C. Wu, R. Lofted, R. H. Roberts and S. J. Putterman", Sensitivity of sonoluminescence to experimental parameters", Phys. Rev. Lett. 72, 1994.
  11. L. A. Crum, T. J. Mason, J. L. Reisse and K. S. Suslick," Sonochemistry and Sonoluminescence", Kluwer Academic Publishers. Printed in the Netherlands, (1999).
  12. A. Prosperetti and A. Lezzi, "Bubble dynamics in a compressible liquid. Part 1. First-order theory", J. Fluid Mech., Vol. 168, 1986.
  13. S. Sochard, A. M. Wilhelm and H. Delmas, "Gas-vapour bubble dynamics and homogeneous sonochemistry", Chem. Eng. Vol. 53, 1997.
  14. A. Z. AL-Asady, "Modeling oscillation of an acoustic bubble using nonlinear wave equation", Ph.D. Thesis, Engineering College, Basrah University Iraq, 2002.
  15. K. Yasui, "Variation of liquid temperature at bubble wall near the sonoluminescence threshold", J. Phys. Soc. Japan, Vol. 65, No.9. Sep. 1996.
  16. R. I. Nigmatulin, N. S. Khabeev and F. B. Nagiev, Dynamics, heat and mass transfer of vapour-gas bubbles in a liquid Int. J. Heat Mass Transfer, Vol. 24, No. 6, 1981.
  17. K. Yasui, "Effect of non-equilibrium evaporation and condensation on bubble dynamics near the sonoluminescence threshold", Ultrasonic 36, 1998.
  18. A. Prosperetti, L. A. Crum and K. W. Commander, "Nonlinear bubble dynamics", J. Accost. Soc. Am. 83, 1988.
  19. V. Kamath and A. Prosperetti, "Numerical integration methods in gas-bubble dynamics", J. Acoust. Soc. Am. 85, 1989.
  20. A. Prosperetti, "The thermal behavior of oscillating gas bubbles", J. Fluid Mech. 222, 1991.
  21. A. Prosperetti and Y. Hao, "Modelling of spherical gas bubble oscillations and sonoluminescence", Phil. Trans. R. Soc. London A. 357, 1999.
  22. K. Yasui, "Effect of surfactants on single-bubble sonoluminescence", Physical Review E, Vol. 4, No. 4, Oct. 1998.
  23. G. J. Lastman and R. A. Wentzell, "Equations of radial motion of a cavitating spherical bubble in an inviscid compressible liquid, with variable speed of sound", Acoustica, vol. 49, 1981.