Shock Focusing Effect upon Interaction of a Shock with Low-Density Dust Cloud

  • O. SutyrinEmail author
  • V. Levin
  • P. Georgievskiy
Conference paper


A propagation of Mach 2 and 3 plane shock wave through the air containing cylindrical cloud of low-concentration quartz dust is numerically modeled using Euler’s equations. One-velocity single-temperature model of dust-air mixture is used. A refraction of incident shock and formation and focusing of transversal shocks are described. Two qualitatively different interaction patterns – external and internal – are found to take place for different dust concentration values. A dependence of peak shock focusing point position and relative shock focusing intensity on volume concentration of dust in range from 0.01 to 0.15% is determined. With increase of dust concentration peak focusing point draws near the cloud edge and moves inside the cloud, while focusing intensity non-monotonically rises.


  1. 1.
    V.M. Boiko, V.P. Kiselev, S.P. Kiselev, A.N. Papyrin, S.V. Poplavsky, V.M. Fomin, Shock wave interaction with a cloud of particles. Shock Waves 7(5), 275–285 (1997)CrossRefGoogle Scholar
  2. 2.
    G.B. Jacobs, W.S. Don, T. Dittmann, High-order resolution Eulerian–Lagrangian simulations of particle dispersion in the accelerated flow behind a moving shock. Theor. Comput. Fluid Dyn. 26, 37–50 (2012)CrossRefGoogle Scholar
  3. 3.
    V.P. Kiselev, S.P. Kiselev, E.V. Vorontsov, Interaction of a shock wave with a particle cloud of finite size. Shock Waves 16(1), 53–64 (2006)CrossRefGoogle Scholar
  4. 4.
    K. Benkiewicz, A. Koichi Hayashi, Aluminum dust ignition behind reflected shock wave: Two-dimensional simulations. Fluid Dynamics Research. 30, 269–292 (2002)CrossRefGoogle Scholar
  5. 5.
    P.Y. Georgievskiy, V.A. Levin, O.G. Sutyrin, Shock focusing upon interaction of a shock with a cylindrical dust cloud. Tech. Phys. Lett. 42(9), 936–939 (2016)CrossRefGoogle Scholar
  6. 6.
    R.W. MacCormack, The effect of viscosity in hypervelocity impact cratering, AIAA Paper. No. 69–354 (1969)Google Scholar
  7. 7.
    S.F. Davis, A simplified TVD finite difference scheme via artificial viscosity. SIAM J. Sci. Stat. Comput. 8(1), 1–18 (1987)MathSciNetCrossRefGoogle Scholar
  8. 8.
    J. Ray, R. Samtaney, N.J. Zabusky, Shock interactions with heavy gaseous elliptic cylinders: Two leeward-side shock competition modes and a heuristic model for interfacial circulation deposition at early times. Phys. Fluids 12(3), 707–716 (2000)CrossRefGoogle Scholar
  9. 9.
    P.Y. Georgievskiy, V.A. Levin, O.G. Sutyrin, Interaction of a shock with elliptical gas bubbles. Shock Waves 25(4), 357–369 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Mechanics of Lomonosov Moscow State UniversityMoscowRussia

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