Shock-wave stratification in inhomogeneous media

Abstract

The analysis of phenomena associated with shock-wave propagation in inhomogeneous media is needed for the solution of a large number of problems of explosion physics, relaxation gasdynamics of supersonic flows, and astrophysics. A number of theoretical and experimental papers (1-7) are devoted to different aspects of shock interaction with gases in which signif- icant temperature and density gradients exist. Curving of the shock front and attenuation of its intensity in a heated layer above a plate surface were observed in (i, 2). The re- sults of experiments (i) were compared with a computation based on a one-dimensional model of the decay of a discontinuity, developed for the average parameters of the heated layer. The possibility is indicated of shock front blurring if the velocity of its propagation in the unperturbed domain is less than the speed of sound within the thermal inhomogeneity. Features of shock propagation in mixtures of unmixed or partially mixed gases with dif- ferent thermophysical properties were studied in (3, 4, 6, 7). The good agreement between flow patterns under normal shock incidence on the boundary of preliminarily unmixed gases obtained by using two-dimensional computations and the results of experiments is shown in (7). Reports have recently appeared about the anomalous phenomena during shock propagation in substantially inhomogeneous and nonequilibrium media (gas glow discharge plasmm (8-ii), or the plasma being formed because of optical or microwave-breakdown in air (12-14)). A considerable increase in the shock velocity, its damping, the formation of a jet, and deforma- tion and dissipation of the wave front have b~en noticed. The correct theoretical treatment of the roles of the thermal, relaxation, and gasdynamic effects in these cases requires a detailed examination of the substantially inhomogeneous and nonstationary flow pattern. By using two-dimensional computations shock propagation (with Mach number M) is inves- tigated in a plane channel in this paper, which contains a domain of temperature stratifica- tion of the gas (Fig. I, I and II). The problem is characterized by the geometric dimen- sions: h is the hot gas domain with temperature T 2 > Ti, where T i is the cold gas tempera- ture (Fig. i, I), and H is the channel transverse dimension. The pressure ahead of the wave is constant and equal to Pi. The gas is characterized by a constant ratio between the speci- fic heats 7. The wave is propagated along the coordinate X and at time t = 0 the wave front coincides with the axis OY. Computations were performed in Euler coordinates according to the Maccormac monotonized scheme (15).