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	The exact solution of a shock wave reflection problem from a wall shielded by a gas suspension layer</div>

Dmitry V. Sadin, Shirokova Elena N.

2023 , VOLUME 23, NUMBER 4 ( july-august )

ISSN 2226-1494 (print), ISSN 2500-0373 (online)

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Nikiforov
Vladimir O.
D.Sc., Prof.

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doi: 10.17586/2226-1494-2023-23-4-843-849

The exact solution of a shock wave reflection problem from a wall shielded by a gas suspension layer

D. V. Sadin, E. N. Shirokova

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Sadin D.V., Shirokova E.N. The exact solution of a shock wave reflection problem from a wall shielded by a gas suspension layer. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2023, vol. 23, no. 4, pp. 843–849 (in Russian). doi: 10.17586/2226-1494-2023-23-4-843-849

Abstract

The paper is devoted to solving the shockwave reflection problem from a wall shielded by a gas suspension layer. The dynamics of the gas suspension are described in a two-speed two-temperature formulation. In contrast to the known approximate models of dusty gas based on the application of classical self-similar solutions by correcting gas dynamic parameters and physical constants, an asymptotically exact solution is obtained. The analytical solution to the problem is constructed in the form of a composition of elementary decays discontinuities. The nonequilibrium solution converges to the exact one with a decrease in the characteristic times of dynamic and thermal relaxation of the carrier gas and suspended particles of arbitrary concentration. Calculations based on the nonequilibrium model are performed by the hybrid large-particle method of the second-order approximation in space and time. Both for the exact and calculate profiles of the relative values of the pressure and density of the mixture, the normalized velocity of the dispersed phase obtained from the nonequilibrium model are given. The influence of the intensity of the incident shock wave, as well as the concentration of particles in the gas suspension layer on the parameters of the impact of the shock wave pulse on the wall, is studied. The presence of a shielding layer leads to an increase in the reflection pressure from the wall compared to the reflection of the shock wave in a pure gas. The analysis of the influence of the relaxation properties of the gas suspension layer with a change in particle sizes from 1 to 8 µm is carried out. For sufficiently small particles of 1 micron and the accepted scales of the problem, the nonequilibrium solution reproduces the shock-wave structure well and corresponds to the asymptotics. With the increase in the size of dispersed inclusions, the spatial relaxation zones, smoothing the profiles of the parameters, increase. The error in calculating the velocity and other parameters for a nonequilibrium gas suspension with particles of 1 µm compared to the exact solution is in the range from 10^–7to 10^–5. The results obtained are of practical importance in substantiating the influence of inert particle impurities on the dynamic loading of structures. The analytical solution to the problem may be in demand when testing various numerical schemes.

Keywords: exact solution, reflection, shock wave, wall, layer of gas suspension

References

Rudinger G. Some properties of shock relaxation in gas flows carrying small particles. Physics of Fluids, 1964, vol. 7, no. 5, pp. 658–663. https://doi.org/10.1063/1.1711265
Sommerfeld M, Selzer M, Grönig H. Shock wave reflections in dusty-gas. Proc 15^th International Symposiumon Shock Waves and Shock Tubes, 1986, pp. 683–689.
Boldyreva O.Y., Gubaidullin A.A., Dudko D.N., Kutushev A.G. Numerical study of the transfer of shock-wave loading to a screened flat wall through a layer of a powdered medium and a subsequent air gap. Combustion, Explosion, and Shock Waves, 2007, vol. 43, no. 1, pp. 114–123. https://doi.org/10.1007/s10573-007-0016-3
Tukmakov D.A. Numerical investigation of the influence of properties of the gas component of a suspension of solid particles on the spreading of a compressed gas-suspension volume in a binary medium. Journal of Engineering Physics and Thermophysics, 2020, vol. 93, no. 2, pp. 291–297. https://doi.org/10.1007/s10891-020-02120-9
Sadin D.V., Davidchuk V.A. Interaction of a plane shock wave with regions of varying shape and density in a finely divided gas suspension. Journal of Engineering Physics and Thermophysics, 2020, vol. 93, no. 2, pp. 474–483. https://doi.org/10.1007/s10891-020-02143-2
Volkov K.N., Emel’yanov V.N., Efremov A.V. Numerical simulation of the interaction of a shock wave with a dense layer of particles. Journal of Engineering Physics and Thermophysics, 2021, vol. 94, no. 3, pp. 638–647. https://doi.org/10.1007/s10891-021-02339-0
Sidorkina S.I. Some aerosol motions. Dokl. Akad. Nauk SSSR, 1957, vol. 112, no. 3, pp. 398–400. (in Russian)
Arutyunyan G.M. Thermohydrodynamic Theory of Heterogeneous Systems. Moscow, Fizmatlit Publ., 1994, 272 p. (in Russian)
Georgievskiy P.Yu., Levin V.A., Sutyrin O.G. Shock focusing upon interaction of a shock with a cylindrical dust cloud. Technical Physics Letters, 2016, vol. 42, no. 9, pp. 936–939. https://doi.org/10.1134/S1063785016090182
Arutyunyan G.M. Conditions of applicability of the results of the hydrodynamics of a perfect gas to disperse media. Fluid Dynamics, 1979, vol. 14, no. 4, pp. 118–121. https://doi.org/10.1007/BF01050823
Ivanov A.S., Kozlov V.V., Sadin D.V. Unsteady flow of a two-phase disperse medium from a cylindrical channel of finite dimensions into the atmosphere. Fluid Dynamics, 1996, vol. 31, no. 3, pp. 386–391. https://doi.org/10.1007/BF02030221
Nigmatulin R.I. Dynamics of Multiphase Media. Vol. 1. New York, USA, Hemisphere Publ. Corp., 1990,507 p.
Ivandaev A.I., Kutushev A.G., Rudakov D.A. Numerical investigation of throwing a powder layer by a compressed gas. Combustion, Explosion, and Shock Waves, 1995, vol. 31, no. 4, pp. 459–465. https://doi.org/10.1007/BF00789367
Sadin D.V. On stiff systems of partial differential equations for motion of heterogeneous media. Matematicheskoe modelirovanie, 2002, vol. 14, no. 11, pp. 43–53. (in Russian)
Roždestvenskii B.L., Janenko N.N. Systems of Quasilinear Equations and Their Applications to Gas Dynamics. American Mathematical Soc., 1983, 676 p.
Sadin D.V. Test problems of gas suspension dynamics using asymptotically exact solutions. Mathematical Models and Computer Simulations, 2023, vol. 15, no. 3, pp. 564–573. https://doi.org/10.1134/S2070048223030158
Sadin D.V. Efficient implementation of the hybrid large particle method. Mathematical Models and Computer Simulations, 2022, vol. 14, no. 6, pp. 946–954. https://doi.org/10.1134/S207004822206014X

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