Abstract
A mathematical model of mechanics of a two‐velocity two‐temperature mixture of gases is developed. Based on this model, evolution of the mixing layer of two gases with different densities under the action of shock and compression waves is considered by methods of mathematical simulation in the one‐dimensional unsteady approximation. In the asymptotic approximation of the full model, a solution of an initial‐boundary problem is obtained, which describes the formation of a diffusion layer between two gases. Problems of interaction of shock and compression waves with the diffusion layer are solved numerically in the full formulation. It is shown that the layer is compressed as the shock wave traverses it; the magnitude of compression depends on shock‐wave intensity. As the shock wave passes from the heavy gas to the light gas, the mixing layer becomes overcompressed and expands after shock‐wave transition. The wave pattern of the flow is described in detail. The calculated evolution of the mixing‐layer width is in good agreement with experimental data.
Similar content being viewed by others
REFERENCES
S. Chandrasekhar,Hydrodynamics and Hydromagnetic Stability, Oxford Univ., Oxford (1961), pp. 428-436.
B. B. Chakraborty, “Rayleigh-Taylor instability of heavy fluid,”Phys. Fluids 18, No. 8, 1066-1067 (1975).
R. E. Duff, F. H. Harlow, and C. W. Hirt, “Effects of diffusion on interface instability between gases,”Phys. Fluids 5, No. 4, 417-425 (1962).
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).
S. G. Zaitsev, S. N. Titov, and E. I. Chebotareva, “Evolution of the transitional layer separating gases with different densities with a shock wave passing through the layer,”Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 2, 18-26 (1994).
S. G. Zaitsev, I. G. Lebo, V. B. Rozanov, et al., “Hydrodynamic instability of the contact of gas media moving with acceleration,”Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 15-21 (1991).
V. F. Kuropatenko, “Unsteady flow of multispecies media,” in:Numerical Methods of Solving Filtration Problems. Dynamics of Multiphase Media (collected scientific papers) [in Russian], Inst. Theor. Appl. Mech., Sib. Div., Acad. of Sci. of the USSR (1989), pp. 128-155.
D. L. Youngs, “Numerical simulation of turbulent mixing by Rayleigh-Taylor instability,”Phys. D. 12, 32-44 (1984).
S. P. Kiselev, G. A. Ruev, A. P. Trunev, et al.,Shock-Wave Processes in Two-Component and Two-Phase Media [in Russian], Nauka, Novosibirsk (1992).
V. E. Neuvazhaev, “Development of turbulent mixing caused by Richtmyer-Meshkov instability,”Mat. Model. 3, No. 7, 10-28 (1991).
W. K. Anderson, J. L. Thomas, and B. van Leer, “A comparison of finite volume flux vector splitting for the Euler equations,”AIAA J. 24, No. 9, 1453-1460 (1986).
S. R. Chakravarthy and S. Osher, “A new class of high accuracy TVD schemes for hyperbolic conservation laws,” AIAA Paper No. 85-0363 (1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ruev, G.A., Fedorov, A.V. & Fomin, V.M. Evolution of the Diffusion Mixing Layer of Two Gases upon Interaction with Shock Waves. Journal of Applied Mechanics and Technical Physics 45, 328–334 (2004). https://doi.org/10.1023/B:JAMT.0000025013.21719.90
Issue Date:
DOI: https://doi.org/10.1023/B:JAMT.0000025013.21719.90