Advertisement

To the Complex Approach to the Numerical Investigation of the Shock Wave: Dense Particle Bed Interaction

  • D. Sidorenko
  • P. Utkin
Conference paper

Abstract

The problem of planar shock wave–dense particle cloud interaction is solved using two approaches. In the first one, the two-dimensional gas dynamics modeling of the interaction of the planar shock wave with Mach number 1.67 with the set of cylinders is carried out. The original author’s numerical algorithm of the Cartesian grid method is used. The set of cylinders models the dense particles cloud with the volume fraction 0.15. As a result of interaction, the collective reflected and transmitted waves are formed. In the second approach, the one-dimensional system of equations for the description of the dense two-phase flows is solved. Results of one-dimensional modeling are matched with the cross-section averaged pressure distribution from the two-dimensional calculation. The quantitative agreement is achieved. The specific features of the process are discussed. We formulate the idea of complex approach to the investigation of the shock wave–dense particle cloud interaction that is based on the getting of the drag coefficient of the particles bed from the results of the multidimensional calculations and the comparison of those results with the calculation using the two-phase model.

References

  1. 1.
    J.D. Regele, J. Rabinovitch, T. Colonius, G. Blanquart, Int. J. Multiphase Flow 61, 1 (2014)CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    S.N. Medvedev, S.M. Frolov, B.E. Gel’fand, J. Phys. Eng. 58, 924 (1990)CrossRefGoogle Scholar
  4. 4.
    R.W. Houim, E.S. Oran, J. Fluid Mech. 789, 166 (2016)MathSciNetCrossRefGoogle Scholar
  5. 5.
    T.P. McGrath II, J.G.St. Clair, S. Balachandar, J. Appl. Phys. 119, Paper 174903 (2016)Google Scholar
  6. 6.
    I.A. Bedarev, A.V. Fedorov, V.M. Fomin, Comb., Expl. Shock Waves. 48, 446 (2012)CrossRefGoogle Scholar
  7. 7.
    I.A. Bedarev, A.V. Fedorov, J. Appl. Mech. Tech. Phys. 56, 750 (2015)CrossRefGoogle Scholar
  8. 8.
    M. Berger, C. Helzel, SIAM J. Sci. Comp. 34, A861 (2012)CrossRefGoogle Scholar
  9. 9.
    R. Saurel, R. Abgrall, J. Comput. Phys. 150, 425 (1999)MathSciNetCrossRefGoogle Scholar
  10. 10.
    D.A. Sidorenko, P.S. Utkin, Num. Meth. Programm. 17, 353 (2016)Google Scholar
  11. 11.
    E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, 3rd ed. (Springer, 2009)Google Scholar
  12. 12.
    Y.-X. Ren, Comput. Fluids 32, 1379 (2003)CrossRefGoogle Scholar
  13. 13.
    H.M. Glaz, P. Colella, I.I. Glass, R.L. Deschambault, Proc. Royal Soc. London A. 298, 117 (1985)CrossRefGoogle Scholar
  14. 14.
    K. Takayama, K. Itoh, Proc. 15th Int. Symp. on Shock Waves and Shock Tubes 439 (1985)Google Scholar
  15. 15.
    Y. Tanino, H.M. Nepf, J. Hydraul. Eng. 134, 34 (2008)CrossRefGoogle Scholar
  16. 16.
    S. Ergun, Chem. Eng. Prog. 48, 89 (1952)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • D. Sidorenko
    • 1
    • 2
  • P. Utkin
    • 1
    • 2
  1. 1.Institute for Computer Aided Design of the Russian Academy of SciencesMoscowRussian Federation
  2. 2.Moscow Institute of Physics and TechnologyMoscow RegionRussian Federation

Personalised recommendations