Advertisement

Journal of Engineering Physics and Thermophysics

, Volume 83, Issue 6, pp 1210–1217 | Cite as

Mathematical modeling of instabilities in the interaction of wave processes with the contact discontinuities between gases of different densities

  • A. V. Fedorov
  • V. M. Fomin
  • G. A. Ruev
Article
  • 40 Downloads

Works performed in the field of mathematical modeling of the process of mixing of gases of different densities on the interface between them under the action of transmitted and reflected shock waves and compression and rarefaction waves are reviewed. A mathematical model of two-velocity, two-temperature gases, which has been derived from the basic principles, is proposed for this modeling. A number of examples on the interaction of the above wave processes with the interfaces in helium–xenon and helium–argon mixtures are given; the appearing Richtmyer–Meshkov instability and the distinctive features of the wave dynamics of flow of a mixture are described. The performed comparison of the time dependence of the mixing-zone breadth and other dependences has shown that the description of the phenomenon within the framework of the proposed approach is satisfactory.

Keywords

mixing of gases of different densities laser thermonuclear fusion contact discontinuity shock waves compression waves 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. E. Neuvazhaev, Mathematical Simulation of Turbulent Mixing [in Russian], Izd. RFYaTs–VNIITF, Snezhinsk (2007).Google Scholar
  2. 2.
    N. A. Inogamov, A. Yu. Dem’yanov, and É. E. Son, Hydrodynamics of Mixing [in Russian], Izd. MFTI, Moscow (1999).Google Scholar
  3. 3.
    O. Belotserkovskii, Turbulence and Instabilities [in Russian], MZ-Press, Moscow (2003).Google Scholar
  4. 4.
    E. E. Meshkov, Investigation of Hydrodynamic Instabilities under Laboratory Conditions [in Russian], FGUP "RFYaTs–VNIIIÉF," Sarov (2006).Google Scholar
  5. 5.
    D. L. Youngs, Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities, Laser and Particle Beams, 12, No. 4, 725–750 (1994).CrossRefGoogle Scholar
  6. 6.
    S. P. Kiselev, G. A. Ruev, A. P. Trunev, V. M. Fomin, and M. Sh. Shavaliev, Shock-Wave Process in Two-Component and Two-Phase Media [in Russian], Nauka, Novosibirsk (1992).Google Scholar
  7. 7.
    G. A. Ruev, A. V. Fedorov, and V. M. Fomin, Evolution of the diffusion layer of mixing of two gases in its interaction with shock waves, Prikl. Mekh. Tekh. Fiz., 45, No. 3, 24–31 (2004).MATHGoogle Scholar
  8. 8.
    G. A. Ruev, A. V. Fedorov, and V. M. Fomin, Interaction of shock waves with mixing layer of two gases with widely differing masses of molecules, in: Proc. 12th Int. Conf. Methods of Aerophysical Research (ICMAR 2004), Vol. 1, ITAM, Novosibirsk (2004), pp. 194–197.Google Scholar
  9. 9.
    G. A. Ruev, A. V. Fedorov, and V. M. Fomin, Development of the Richtmyer–Meshkov instability due to the interaction of a diffusion mixing layer with shock waves, Prikl. Mekh. Tekh. Fiz., 46, No. 3, 3–11 (2005).MATHGoogle Scholar
  10. 10.
    G. A. Ruev, A. V. Fedorov, and V. M. Fomin, Development of the Richtmyer–Meshkov instability due to the interaction of a diffusion layer of mixing of two gases with transmitted and reflected shock waves, Dokl. Ross. Akad. Nauk, 427, No. 4, 489–491 (2009).Google Scholar
  11. 11.
    G. A. Ruev, A. V. Fedorov, and V. M. Fomin, Development of the Rayleigh–Taylor instability due to interaction of a diffusion mixing layer of two gases with compression waves, Shock Waves, 16, No. 1, 65–74 (2006).MATHCrossRefGoogle Scholar
  12. 12.
    G. A. Ruev, A. V. Fedorov, and V. M. Fomin, Evolution of diffusion mixing layer of two gases at its interaction with compression waves, in: AIP Conference Proceedings, 849, 311–316 (2006).Google Scholar
  13. 13.
    G. A. Ruev, A. V. Fedorov, and V. M. Fomin, Modeling of the development of Rayleigh–Taylor and Richtmyer–Meshkov instabilities on the basis of the multivelocity multitemperature gasdynamics of mixtures, in: IX Zababakhin Scientific Lectures, Abstracts of papers submitted to the Int. Conf. on the Physics of High Energy Densities, 10–14 September 2007, RFYaTs–VNIITF, Snezhinsk (2007), pp. 149–150.Google Scholar
  14. 14.
    G. A. Ruev, A. V. Fedorov, and V. M. Fomin, Description of the anomalous Rayleigh–Taylor instability on the basis of the model of the three-velocity and three-temperature dynamics of mixtures, Prikl. Mekh. Tekh. Fiz., 50, No. 1, 58–67 (2009).MathSciNetGoogle Scholar
  15. 15.
    S. G. Zaitsev, S. N. Titov, and E. I. Chebotarev, Evolution of the transition layer separating different-density gases with the shock wave transmitted by it, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 18–26 (1994).Google Scholar
  16. 16.
    I. G. Lebo, V. V. Nikishin, V. B. Rozanov, and V. F. Tishkin, On the effect of boundary conditions on the instability growth at a contact surface in passage of a shock wave, Bull. Lebedev Phys. Inst., No. 1, 40–47 (1997).Google Scholar
  17. 17.
    W. K. Anderson, J. L. Thomas, and B. Van Leer, Comparison of finite volume flux vector splitting for the Euler equations, J. AIAA, 24, No. 9, 1453–1460 (1986).CrossRefGoogle Scholar
  18. 18.
    G. A. Ruev, A. V. Fedorov, and V. M. Fomin, Development of the Richtmyer–Meshkov instability in interaction of a diffusion layer of mixing of two gases with transmitted and reflected shock waves, Prikl. Mekh. Tekh. Fiz., 51, No. 3 (2010) (in press).Google Scholar
  19. 19.
    M. Brouillette and B. Sturtevant, Growth induced by multiple shock waves normally incident on plane gaseous interfaces, Phys. D, 37, Nos. 1–3, 248–263 (1989).CrossRefGoogle Scholar
  20. 20.
    M. Brouillette and B. Sturtevant, Experiments on the Richtmyer–Meshkov instability: single-scale perturbations on a continuous interface, J. Fluid Mech., 263, 271–292 (1994).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of SciencesNovosibirskRussia

Personalised recommendations