Skip to main content
SpringerLink
Log in

Shock wave propagation in bubbly liquids at small gas volume fractions

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

It is well known that shock wave propagation in liquid media is strongly affected by the presence of gas bubbles that interact with the shock and in turn affect the gas bubbles. An explicit form of a wave equation was obtained from a set of equations for wave propagation in bubbly liquid (Caflisch et al., 1985a) in this study. Shock wave propagation in bubbly mixtures was considered with the solution for the obtained wave equation, of which homogeneous and particular solutions provide the pressure field due to the shock profile and bubble- bubble interaction, respectively. The gas behavior inside a spherical bubble under the shock wave was obtained by a set of homologous solutions for the mass and momentum conservation equations. The energy equation for the gas inside the bubble was solved analytically with help of the homologous solutions. The bubble wall motion in compressible medium was obtained from the Keller-Miksis equation. The heat transfer from/to the bubble was obtained by solving the energy equation for the gas inside the bubble and for the liquid outside the bubble wall. The relaxation oscillations behind the shock front, which were calculated using the Keller-Miksis equation with the solutions of the obtained wave equation, are in close agreement with those obtained in shock tube experiments for a uniform bubbly flow by Kameda et al. (1998). Heat exchange between the gas bubbles and the liquid and the interaction between bubbles were found to be very important factors to affect the relaxation oscillations in the shock front.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. Noordzij and L. van Wijngaarden, Relaxation effects, caused by relative motion, on shock waves in gasbubble/ liquid mixtures, J. Fluid Mech., 66 (1974) 115–143.

    Article  MATH  Google Scholar 

  2. A. E. Beylich and A. Guelhan, On the structure of nonlinear waves in liquids with gas bubbles, Phys. Fluids A, 2 (1990) 1412–1428.

    Article  MATH  Google Scholar 

  3. M. Kameda and Y. Matsumoto, Shock waves in a liquid containing small gas bubbles, Phys. Fluids, 8 (1996) 322–335.

    Article  MathSciNet  Google Scholar 

  4. M. Kameda, N. Shimaura, F. Higashino and Y. Matsumoto, Shock waves in a uniform bubbly flow, Phys. Fluids, 10 (1998) 2661–2668.

    Article  Google Scholar 

  5. Y. Matsumoto and M. Kameda, Propagation os shock waves in dilute bubbly liquids, JSME Int. J., 39 (1996) 264–272.

    Article  Google Scholar 

  6. A. T. Preston, T. Colonius and C. E. Brennen, A reducedorder model of diffusive effects on the dynamics of bubbles, Phys. Fluids, 19 (2007) 123302.

    Article  MATH  Google Scholar 

  7. A. Prosperetti, L. Crum and C. E. Commander, Nonlinear bubble dynamics, J. Acoust. Soc. Am., 83 (1988) 502–514.

    Article  Google Scholar 

  8. R. E. Caflisch, M. J. Miksis, G. C. Papanicolaou and L. Ting, Wave propagation in bubbly liquids at inite volume fraction, J. Fluid Mech., 160 (1985b) 1–14.

    Article  MATH  Google Scholar 

  9. J. Rubinstein, Bubble interaction effects on waves in bubbly liquids, J. Acoust. Soc. Am., 77 (1985) 2061–2066.

    Article  MATH  Google Scholar 

  10. J. H. Seo, S. K. Lele and G. Tryggvason, Investigation and modeling of bubble-bubble interaction effect in homogeneous flow, Phys. Fluids, 22 (2010) 063302.

    Article  MATH  Google Scholar 

  11. H. Grandjean, N. Jacques and S. Zaleski, Shock propagation in liquids containing bubbly clusters: A continum approach, J. Fluid Mech., 701 (2012) 304–332.

    Article  MATH  Google Scholar 

  12. R. E. Caflisch, M. J. Miksis, G. C. Papanicolaou and L. Ting, Effective equations for wave propagation in bubbly liquids, J. Fluid Mech., 153 (1985a) 259–273.

    Article  MATH  Google Scholar 

  13. J. B. Keller and M. Miksis, Bubble oscillations of large amplitude, J. Acoust. Soc. Am., 68 (1980) 628–633.

    Article  MATH  Google Scholar 

  14. H. Kwak and H. Yang, An aspect of sonoluminescence fro hydrodynamic theory, J. Phys. Soc. Jap., 64 (1995) 1980–1992.

    Article  Google Scholar 

  15. H. Kwak and J. Na, Hydrodynamic solutions for a sonoluminescing gas bubble, Phys. Rev. Lett., 77 (1996) 4454–4457.

    Article  Google Scholar 

  16. H. Kwak and J. Na, Physical processes for single bubble sonoluminescence, J. Phys. Soc. Jap., 66 (1997) 3074–3083.

    Article  Google Scholar 

  17. H. Kwak, S. Oh and C. Park, Bubble dynamics on the evolving bubble formed from the droplet at the superheat limit, Int. J. Heat Mass Trans., 38 (1995) 1709–1718.

    Article  MATH  Google Scholar 

  18. R. T. Lahey Jr., R. P. Taleyarkhan, R. L. Nigmatulin and I. S. Akhatov, Sonolumineacence and the search for sonofusion, Advances in Heat Transfer, 39 (2006) 1–168.

    Article  Google Scholar 

  19. S. Mahmood, Y. Yoo, J. Oh and H. Kwak, Hydrodynamic approach to multibubble sonoluminescence, Ultrasonic Sonochem., 21 (2014) 1512–1518.

    Article  Google Scholar 

  20. C. C. Wu and P. H. Roberts, Shock-wave propagation in a sonoluminescing gas bubble, Phys. Rev. Lett., 70 (1993) 3424–3427.

    Article  Google Scholar 

  21. M.-C. Chu, The homologous contraction of a sonoluminescing bubble, Phys. Rev. Lett., 76 (1996) 4632–4635.

    Article  Google Scholar 

  22. H. Lin, B. D. Storey and A. J. Szeri, Intially riven inhomogeneities in violently collapsing bubble: The validity of the Rayleigh-Plesset equation, J. Fluid Mech., 452 (2002) 145–162.

    Article  MathSciNet  MATH  Google Scholar 

  23. K. Kim, H. Kwak and J. H. Kim, Moleculr dynamis simulation of collapsing phase for a sonoluminescing gas buble in sulfuric acid solutions: A comparative study with theoretical results, J. Phys. Soc. Jap., 76 (2007) 024301.

    Article  Google Scholar 

  24. J.-W. Jun and H. Kwak, Gravitational collapse of Newtonian stars, Int. J. Modern Phys., 9 (2000) 35–42.

    Google Scholar 

  25. K. Kim, C. Lim, H. Kwak and J. H. Kim, Validation of a molecular dynamics for a collapsing proces of sonoluminescing gas bubbles, Mol. Phys., 106 (2008) 967–975.

    Article  Google Scholar 

  26. W. G. Vincenti and C. H. Kruger, Introduction to Physical Gas Dynamics, Robert E. Krieger Publishing Co., New York, USA (1965).

    Google Scholar 

  27. T. Theofanous, L. Biasi and H. S. Isbin, A theoretical study on bubble growth in constant and time-dependant pressure fields, Chem. Eng. Sci., 24 (1969) 885–897.

    Article  Google Scholar 

  28. S. W. Karng and H. Kwak, Relaxation behavior of microbubbles in ultrasonic field, Jap. J. Appl. Phys., 45 (2006) 317–322.

    Article  Google Scholar 

  29. H. Kwak, J. Oh, Y. Yoo and S. Mahmood, Bubble formation on the surface of laser-irradiated mnanosized particles, J. Heat Trans., 136 (2014) 081501.

    Article  Google Scholar 

  30. J. Lighthill, Waves in Fluids, Cambridge University Press, Cambridge, UK (1978).

    MATH  Google Scholar 

  31. A. Kuboda, H. Kato and H. Yamaguchi, A new modeling of cavitating flows: A numerical study of unsteady cavitation on a hydrofoil section, J. Fluid Mech., 240 (1992) 59–96.

    Article  Google Scholar 

  32. K. Yasui, Y. Iida, T. Tuziuti, T. Kozuka and A. Towata, Strongly interacting bubbles under ultrasonic horn, Phys. Rev. E., 77 (2008) 016609.

    Article  Google Scholar 

  33. Y. An, Formulation of multibubble cavitation, Phys. Rev. E., 83 (2011) 066313.

    Article  Google Scholar 

  34. D. T. Blackstock, Fundamentals of Physical Acoustics, John Wiley & Sons, Inc., New York, USA (2000).

    Google Scholar 

  35. C. E. Brennen, Cavitation and Bubble Dyanmics, Oxford University Press, UK (1995).

    Google Scholar 

  36. S. Mahmood and H. Kwak, Pressure waves in bubbly liquids, J. Mech. Sci. Tech., 30 (2016) 3935–3943.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mechanical Design Engineering, Kangwon National University, Samcheok-si, 25913, Korea

    Samsun Seung

  2. Mechanical Engineering Department, Chung-Ang University, Seoul, 06974, Korea

    Ho-Young Kwak

Authors
  1. Samsun Seung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ho-Young Kwak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ho-Young Kwak.

Additional information

Recommended by Associate Editor Kyu Hong Kim

Samsun Seung received B.S. from Chung-Ang University in 1981 and M.A. and Ph.D. in mechanical engineering from the Chung-Ang University, Korea in 1983 and 1991, respectively. He joined MDE Faculty, Kangwon National University, Korea in 1996 and is currently Professor there. His research interests are in fluid flow phenomena, and heat transfer.

Ho-Young Kwak received B.S. from Seoul National University in 1971 and M.A. in plasma physics and Ph.D. in mechanical engineering from the University of Texas at Austin, USA in 1977 and 1981, respectively. He joined M.E. Faculty, Chung-Ang University, Korea in 1981 and served 35 years and is currently Emeritus Professor there. His research interests are in bubble nucleation and dynamics, sonoluminescence phenomena, and exergy and thermoeconomic analysis for thermal systems. He is a member of Korean Academy of Science and Technology.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Seung, S., Kwak, HY. Shock wave propagation in bubbly liquids at small gas volume fractions. J Mech Sci Technol 31, 1223–1231 (2017). https://doi.org/10.1007/s12206-017-0221-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-017-0221-2

Keywords

Search

Navigation