Some Aspects of the Numerical Modeling of Shock Wave–Dense Particle Bed Interaction Using Two-Fluid Approach

  • P. UtkinEmail author
Conference paper


The work is dedicated to the parametric numerical study of the shock wave with the dense particle bed interaction. The problem is solved using two-fluid approach when both gaseous and dispersed phases are considered to be compressible media nonequilibrium on velocities and pressures. The determinative system of equations has the hyperbolic type and is solved using HLL numerical scheme. The statement of the problem corresponds to the natural experiment. The main features of the process are obtained in the calculations, namely, the formation of the transmitted and reflected waves and the motion of the particle cloud with sharp front edge and smearing trailing edge. The comparison of the amplitudes of the reflected and transmitted waves as well as the dynamics of the cloud motion with the experimental data is carried out. The investigation of the influence of the dispersed phase equation of state parameters and some properties of the numerical methods on the process is carried out.


  1. 1.
    T.A. Khmel’, A.V. Fedorov, Combust. Explos. Shock Waves. 50, 2 (2014)Google Scholar
  2. 2.
    T. Khmel, A. Fedorov, J. Loss Prev. Process Ind. 36, 223 (2015)CrossRefGoogle Scholar
  3. 3.
    R.W. Houim, E.S. Oran, J. Fluid Mech. 789, 166 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    T.P. McGrath II, J.G. St Clair, S. Balachandar, J. Appl. Phys. 119, Paper 174903 (2016)Google Scholar
  5. 5.
    M.R. Baer, J.W. Nunziato, Int. J. Multiph. Flow 21, 861 (1986)CrossRefGoogle Scholar
  6. 6.
    D. Gidaspow, Multiphase Flow and Fluidization (Academic Press, 1994)Google Scholar
  7. 7.
    J.D. Regele, J. Rabinovitch, T. Colonius, G. Blanquart, Int. J. Multiph. Flow 61, 1 (2014)CrossRefGoogle Scholar
  8. 8.
    V.M. Boiko, V.P. Kiselev, S.P. Kiselev, A.N. Papyrin, S.V. Poplavsky, V.M. Fomin, Shock Waves 7, 275 (1997)CrossRefGoogle Scholar
  9. 9.
    X. Rogue, G. Rodriguez, J.F. Haas, R. Saurel, Shock Waves 8, 29 (1998)CrossRefGoogle Scholar
  10. 10.
    R. Saurel, R. Abgrall, J. Comp. Phys. 150, 425 (1999)CrossRefGoogle Scholar
  11. 11.
    R. Saurel, O. Lemetayer, J. Fluid Mech. 431, 239 (2001)CrossRefGoogle Scholar
  12. 12.
    R. Abgrall, J. Comp. Phys. 125, 150 (1996)CrossRefGoogle Scholar
  13. 13.
    S. Liang, W. Liu, L. Yuan, Comp. Fluids. 99, 156 (2014)CrossRefGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Computer Aided Design of the Russian Academy of SciencesMoscowRussian Federation
  2. 2.Moscow Institute of Physics and TechnologyMoscow RegionRussian Federation

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