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

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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 10–7 to 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.

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