Numerical Investigation of a Planar Shock Wave Interacting with an Acentric Water Ring

  • Gaoming Xiang
  • Bing WangEmail author
Conference paper


The droplet breakup and the bubble collapse are typical flow phenomenon involving complicated pressure and density variation as well as interface evolution. In this paper, the numerical simulation of a planar shock wave interacting with an acentric water ring is studied. In order to simulate the spatiotemporal interface evolution of the water ring impinged by a planar shock wave, a quasi-conservative interface capturing method is employed, in which the governing equations consist of the conservative Euler equations and the scalar transportation equations, together with the stiffened gas equation of state of the two phases. An incremental stencil adapted WENO scheme with fifth order in the smooth regions is employed for the spatial reconstruction. The numerical results show that the bubble collapses under different incident Mach number shock waves due to the strong pressure gradients. The strong transverse jets form because of the Richtmyer-Meshkov instability. The jet tip and its impaction on the downward wall of the cavity are extracted by analyzing the isolines ofγrepresenting the two-phase interface. The jet tip speed and the pressure at the impaction point nonlinearly increase with the incident shock wave strength.


  1. 1.
    E.A. Kush, J.A. Schetz, Liquid jet injection into a supersonic flow. AIAA J. 11(9), 1223–1224 (1973)CrossRefGoogle Scholar
  2. 2.
    C.E. Brennen, Cavitation and bubble dynamics (Cambridge University Press, New York, 2013), pp. 79–107CrossRefGoogle Scholar
  3. 3.
    M. Pilch, C.A. Erdman, Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop. Int. J. Multiphase Flow 13(6) (1987)Google Scholar
  4. 4.
    S. Sembian et al., Plane shock wave interaction with a cylindrical water column. Phys. Fluids. 28, 5 (2016)Google Scholar
  5. 5.
    N.A. Hawker, Y. Ventikos, Interaction of a strong shockwave with a gas bubble in a liquid medium: A numerical study. J. Fluid Mech. 701 (2012)Google Scholar
  6. 6.
    O. Supponen et al., Scaling laws for jets of single cavitation bubbles. J. Fluid Mech. 802 (2016)Google Scholar
  7. 7.
    O. Shpak et al., Acoustic droplet vaporization is initiated by superharmonic focusing. PNAS 111, 5 (2014)CrossRefGoogle Scholar
  8. 8.
    V. Coralic, T. Colonius, Finite-volume WENO scheme for viscous compressible multicomponent flows. J. Comput. Phys. 274 (2014)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Aerospace EngineeringTsinghua UniversityBeijingChina

Personalised recommendations