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.
Similar content being viewed by others
References
Richtmyer, R. D.: Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13, 297–319 (1960)
Meshkov, E. E.: Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 4, 101–104 (1969)
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)
Arnett, W. D., Bahcall, J. N., Kirshner, R. P., et al.: Supernova 1987A. Annu. Rev. Astron. Astrophys. 27, 629–700 (1989)
Yang, J., Kubota, T., Zukoski, E. E.: Applications of shockinduced mixing to supersonic combustion. AIAA J. 35, 854–862 (1993)
Ranjan, D., Oakley, J., Bonazza, R.: Shock-bubble interactions. Annu. Rev. Fluid Mech. 43, 117–140 (2011)
Rudinger, G., Somers, L. M.: Behaviour of small regions of different gases carried in accelerated gas flows. J. Fluid Mech. 7, 161–176 (1960).
Haas, J. F., Sturtevan, B.: Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 41–76 (1987).
Layes, G., Jourdan, G., Houas, L.: Distortion of a spherical gaseous interface accelerated by a plane shock wave. Phys. Rev. Lett. 91, 174502 (2003).
Layes, G., Jourdan, G., Houas, L.: Experimental investigation of the shock wave interaction with a spherical gas inhomogeneity. Phys. Fluids. 17, 028103 (2005).
Layes, G., Métayer, O. Le.: Quantitative numerical and experimental studies of the shock accelerated heterogeneous bubbles motion. Phys. Fluids 19, 042105 (2007).
Layes, G., Jourdan, G., Houas, L.: Experimental study on a plane shock wave accelerating a gas bubble. Phys. Fluids 21, 074102 (2009).
Haehn, N., Ranjan, D., Weber, C., et al.: Experimental investigation of a twice-shocked spherical density inhomogeneity. Phys. Scr. T142, 014067 (2010).
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).
Winkler, K. H. A, Chalmers, J. W., Hodson, S. W., et al.: A numerical laboratory. Phys. Today 40, 28–37 (1987).
Picone, J. M., Boris, J. P.: Vorticity generation by shock propagation through bubbles in a gas. J. Fluid Mech. 189, 23–51 (1988).
Quirk, J. J., Karni, S.: On the dynamics of a shock-bubble interaction. J. Fluid Mech. 318, 129–163 (1996).
Cowperthwaite, N.: The interaction of a plane shock and a dense spherical inhomogeneity. Physica D. 37, 264–269 (1989).
Giordano, J., Burtschell, Y.: Richtmyer-Meshkov instability induced by shock-bubble interaction: Numerical and analytical studies with experimental validation. Phys. Fluids 18, 036102 (2006).
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).
Li, Q. B., Fu, S., Xu, K.: A compressible Navier-Stokes flow solver with scalar transport. J. Comput. Phys. 204, 692–714 (2005).
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).
Tian, B. L., Fu, D. X., Ma, Y. W.: Effects of adiabatic exponent on Richtmyer-Meshkov instability. Chin. Phys. Lett. 21, 1770–1772 (2004).
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).
Sun, M., Takayama, K.: Conservative smoothing on an adaptive quadrilateral grid. J. Comput. Phys. 150, 143–180 (1999).
Sun, M., Takayama, K.: A holographic interferometric study of shock wave focusing in a circular reflector. Shock Waves 6, 323–336 (1996).
Sun, M.: Numerical and Experimental studies of shock wave interaction with bodies. [Ph.D. Thesis], Tohoku University, Sendai, Japan (1998).
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).
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).
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)
Author information
Authors and Affiliations
Corresponding author
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
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-013-0003-8