Log in

Jet formation in shock-heavy gas bubble interaction

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

The influences of the acoustic impedance and shock strength on the jet formation in shock-heavy gas bubble interaction are numerically studied in this work. The process of a shock interacting with a krypton or a SF6 bubble is studied by the numerical method VAS2D. As a validation, the experiments of a SF6 bubble accelerated by a planar shock were performed. The results indicate that, due to the mismatch of acoustic impedance, the way of jet formation in heavy gas bubble with different species is diversified under the same initial condition. With respect to the same bubble, the manner of jet formation is also distinctly different under different shock strengths. The disparities of the acoustic impedance result in different effects of shock focusing in the bubble, and different behaviors of shock wave inside and outside the bubble. The analyses of the wave pattern and the pressure variation indicate that the jet formation is closely associated with the pressure perturbation. Moreover, the analysis of the vorticity deposition, and comparisons of circulation and baroclinic torque show that the baroclinic vorticity also contributes to the jet formation. It is concluded that the pressure perturbation and baroclinic vorticity deposition are the two dominant factors for the jet formation in shock-heavy gas bubble interaction.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Richtmyer, R. D.: Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13, 297–319 (1960)

    Article  MathSciNet  Google Scholar 

  2. Meshkov, E. E.: Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104 (1969)

    Article  MathSciNet  Google Scholar 

  3. Lindl, J. D., Mccrory, R. L., Campbell, E. M.: Progress toward ignition and burn propagation in inertial confinement fusion. Phys. Today 45, 32–40 (1992)

    Article  Google Scholar 

  4. Arnett, W. D., Bahcall, J. N., Kirshner, R. P., et al.: Supernova 1987A. Annu. Rev. Astron. Astrophys. 27, 629–700 (1989)

    Article  Google Scholar 

  5. Yang, J., Kubota, T., Zukoski, E. E.: Applications of shockinduced mixing to supersonic combustion. AIAA J. 35, 854–862 (1993)

    Article  Google Scholar 

  6. Ranjan, D., Oakley, J., Bonazza, R.: Shock-bubble interactions. Annu. Rev. Fluid Mech. 43, 117–140 (2011)

    Article  MathSciNet  Google Scholar 

  7. Rudinger, G., Somers, L. M.: Behaviour of small regions of different gases carried in accelerated gas flows. J. Fluid Mech. 7, 161–176 (1960).

    Article  MATH  Google Scholar 

  8. Haas, J. F., Sturtevan, B.: Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 41–76 (1987).

    Article  Google Scholar 

  9. Layes, G., Jourdan, G., Houas, L.: Distortion of a spherical gaseous interface accelerated by a plane shock wave. Phys. Rev. Lett. 91, 174502 (2003).

    Article  Google Scholar 

  10. Layes, G., Jourdan, G., Houas, L.: Experimental investigation of the shock wave interaction with a spherical gas inhomogeneity. Phys. Fluids. 17, 028103 (2005).

    Article  Google Scholar 

  11. Layes, G., Métayer, O. Le.: Quantitative numerical and experimental studies of the shock accelerated heterogeneous bubbles motion. Phys. Fluids 19, 042105 (2007).

    Article  Google Scholar 

  12. Layes, G., Jourdan, G., Houas, L.: Experimental study on a plane shock wave accelerating a gas bubble. Phys. Fluids 21, 074102 (2009).

    Article  Google Scholar 

  13. Haehn, N., Ranjan, D., Weber, C., et al.: Experimental investigation of a twice-shocked spherical density inhomogeneity. Phys. Scr. T142, 014067 (2010).

    Article  Google Scholar 

  14. Haehn, N., Weber, C., Oakley, J. G., et al.: Experimental investigation of a twice-shocked spherical gas inhomogeneity with particle image velocimetry. Shock Waves 21, 225 (2011).

    Article  Google Scholar 

  15. Winkler, K. H. A, Chalmers, J. W., Hodson, S. W., et al.: A numerical laboratory. Phys. Today 40, 28–37 (1987).

    Article  Google Scholar 

  16. Picone, J. M., Boris, J. P.: Vorticity generation by shock propagation through bubbles in a gas. J. Fluid Mech. 189, 23–51 (1988).

    Article  Google Scholar 

  17. Quirk, J. J., Karni, S.: On the dynamics of a shock-bubble interaction. J. Fluid Mech. 318, 129–163 (1996).

    Article  MATH  Google Scholar 

  18. Cowperthwaite, N.: The interaction of a plane shock and a dense spherical inhomogeneity. Physica D. 37, 264–269 (1989).

    Article  Google Scholar 

  19. Giordano, J., Burtschell, Y.: Richtmyer-Meshkov instability induced by shock-bubble interaction: Numerical and analytical studies with experimental validation. Phys. Fluids 18, 036102 (2006).

    Article  Google Scholar 

  20. Niederhaus, H. J., Greenough, J. A., Oakley, J. G., et al.: A computational parameter study for the three-dimensional shock-bubble interaction. J. Fluid Mech. 594, 85–124 (2008).

    Article  MATH  Google Scholar 

  21. Li, Q. B., Fu, S., Xu, K.: A compressible Navier-Stokes flow solver with scalar transport. J. Comput. Phys. 204, 692–714 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  22. Bai, J. S., Liu, J. H., Wang, T., et al.: Investigation of the Richtmyer-Meshkov instability with double perturbation interface in non-uniform flows. Physical Review E 81, 056302 (2010).

    Article  Google Scholar 

  23. Tian, B. L., Fu, D. X., Ma, Y. W.: Effects of adiabatic exponent on Richtmyer-Meshkov instability. Chin. Phys. Lett. 21, 1770–1772 (2004).

    Article  Google Scholar 

  24. Zhai, Z. G., Si, T., Luo, X. S., et al.: On the evolution of spherical gas interfaces accelerated by a planar shock wave. Phys. Fluids 23, 084104 (2011).

    Article  Google Scholar 

  25. Sun, M., Takayama, K.: Conservative smoothing on an adaptive quadrilateral grid. J. Comput. Phys. 150, 143–180 (1999).

    Article  MATH  Google Scholar 

  26. Sun, M., Takayama, K.: A holographic interferometric study of shock wave focusing in a circular reflector. Shock Waves 6, 323–336 (1996).

    Article  Google Scholar 

  27. Sun, M.: Numerical and Experimental studies of shock wave interaction with bodies. [Ph.D. Thesis], Tohoku University, Sendai, Japan (1998).

    Google Scholar 

  28. Luo, X., Prast, B., van Dongen, M. E. H., et al.: On phase transition in compressible flows: Modelling and validation. J. Fluid Mech. 548, 403–430 (2006).

    Article  MathSciNet  Google Scholar 

  29. Luo, X., Lamanna, G., Holten, A. P. C., et al.: Effects of homogeneous condensation in compressible flows: Ludwieg-tube experiments and simulations. J. Fluid Mech. 572, 339–366 (2007).

    Article  MATH  Google Scholar 

  30. Fan, M. R., Zhai, Z. G., Si, T., et al.: Numerical study on the evolution of the shock-accelerated SF6 interface: Influence of the interface shape. Sci. China Phys. Mech. Astron. 53, 586–597 (2011)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to **-Sheng Luo.

Additional information

The project was supported by the National Natural Science Foundation of China (10972214 and 11172278) and the Fundamental Research Funds for the Central Universities (WK2090050014).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhai, ZG., Si, T., Zou, LY. et al. Jet formation in shock-heavy gas bubble interaction. Acta Mech Sin 29, 24–35 (2013). https://doi.org/10.1007/s10409-013-0003-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-013-0003-8

Keywords

Navigation