Self-organization of gas flow in the problem of shock wave refraction at the boundary of gases with different heat capacities
https://doi.org/10.18384/2949-5067-2025-3-63-75
Abstract
Aim is to investigate, in a nonlinear formulation, the instability of the boundary of two perfect gases with different heat capacities when an intense shock wave falls on it.
Methodology. Numerical modeling within the Euler equations was applied to use these calculation results with the data obtained within the weakly nonlinear approximation and the experiment.
Results. It is shown that for irregular refraction in the problem, self-organization of the subsonic flow of a perfect gas occurs, which made it possible to obtain a solution without additional measures to determine one of the adiabatic indices. Against the background of small-scale turbulence generated by the Richtmyer – Meshkov instability, explosive instability was detected in the problem.
Research implications. The process of self-organization of gas flow, which allowed the determination of the adiabatic index in one gas, was discovered for the first time in a refraction problem. The results presented in the article explain, at a nonlinear level, the mechanism for the formation of finger-like structures during the interaction of a shock wave with a light-heavy gas boundary, and complement the data obtained experimentally and theoretically within the framework of a weakly nonlinear approach.
About the Author
R. Ya. Tugazakov
Central Aerohydrodynamic Institute
Russian Federation
Russian Federation
Renat Ya. Tugazakov – Dr. Sci. (Phys.–Math.), Leading researcher
Zhukovsky, Moscow Region
References
1. Richtmyer, R. D. (1960). Taylor instability in a shock acceleration of compressible fluids. In: Communications on Pure and Applied Mathematics, 13 (2), 297–319. DOI: 10.1002/cpa.3160130207.
2. Meshkov, E. E. (1969). Instability of the interface of two gases accelerated by a shock wave. In: Fluid Dynamics, 5, 151–158 (in Russ.).
3. Merzhanov, A. G. & Rumanov, E. N. (1987). Nonlinear effects in macroscopic kinetics. In: Soviet Physics Uspekhi, 151 (4), 553–593. DOI: 10.3367/UFNr.0151.198704a.0553 (in Russ.).
4. Kuznetsov, A. P., Kuznetsov, S. P. & Ryskin, N. M. (2002). Nonlinear oscillations. Moscow: Fizmatlit publ. (in Russ.).
5. Henderson, L. F., Colella, P. & Puckett, E. G. (1991). On the refraction of shock waves at slow–fast gas interface. In: Journal of Fluid Mechanics, 224, 1–27. DOI: 10.1017/S0022112091001623.
6. Nevmerzhitskii, N. V., Razin, A. N., Sen’kovskii, E. D., Sotskov, E. A. & Nikulin, A. A. et al. (2015). Experimental and numerical study of turbulent mixing at the contact boundaries of three-dimensional gas systems. In: Journal of Applied Mechanics and Technical Physics, 56 (2), 32–42. DOI: 10.15372/PMTF20150204 (in Russ.).
7. Bulat, P. V. & Volkov, K. N. (2016). Numerical simulation of shock wave refraction on inclined contact discontinuity. In: Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 16 (3), 550–558. DOI: 10.17586/2226-1494-2016-16-3-550-558 (in Russ.).
8. Nourgaliev, R., Sushchikh, S. Dinh, N. T. & Theofanous, T. (2005). Numerical investigation of shock wave refraction patterns at multimaterial interfaces. In: 43rd AIAA Aerospace Sciences Meeting and Exhibit (10–13 January 2005, Reno, Nevada). DOI: 10.2514/6.2005-1292. URL: https://arc.aiaa.org/doi/10.2514/6.2005-1292 (accessed: 25.07.2025).
9. Georgievskii, P. Y., Levin, V. A. & Sutyrin, O. G. (2016). Interaction between a shock wave and a longitudinal low-density gas layer. In: Fluid Dynamics, 5, 125–132. DOI: 10.7868/S056852811605008X (in Russ.).
10. Tugazakov, R. Ya. (2023). Regular and irregular refraction of a shock wave at the boundary of two gases. In: TsAGI Science Journal, 54 (2), 34–42 (in Russ.).
11. Ephraim, L. R. & Burstein, S. Z. (1967). Difference methods for the inviscid and viscous equations of a compressible gas. In: Journal of Computational Physics, 2 (2), 178–196. DOI: 10.1016/0021-9991(67)90033-2.
12. Tugazakov, R. Ya. (2016). On the Theory of Supersonic Inviscid Flow Separation in Gasdynamic Problems. In: Fluid Dynamics, 51 (5), 689–695. DOI: 10.1134/S0015462816050136.
13. Tugazakov, R. Ya. (2024). Numerical and analytical study of turbulence of supersonic viscous gas flow. In: Bulletin of Federal State University of Education. Series: Physics and Mathematics, 1, 68–82. DOI: 10.18384/2949-5067-2024-1-68-82 (in Russ.).
14. Godunov, S. K. (1959). A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics. In: Sbornik: Mathematics, 47 (89), 3, 271–306 (in Russ.).
15. Warner, M. R. E., Craster, R. V. & Matar, O. K. (2004). Fingering phenomena associated with insoluble surfactant spreading on thin liquid films. In: Journal of Fluid Mechanics, 510, 169–200. DOI: 10.1017/S0022112004009437.
16. Marmur, A. & Lelah, M. D. (1981). The spreading of aqueous surfactant solutions on glass. In: Chemical Engineering Communications, 13 (1-3), 133–143. DOI: 10.1080/00986448108910901.
Review
Views:
45
Email this article 