On the passage of a shock wave through a dusty-gas layer

Abstract

The flow resulting from the passage of a shock wave through a dusty-gas layer is studied theoretically. On the basis of an idealized equilibrium-gas approximation, the criteria for the wave reflexion at the contact surface separating the pure gas from the dusty-gas layer are obtained in terms of the properties of the gas and the dusty gas. For the cases treated here, a shock wave is reflected at the first contact surface and a shock wave stronger than the incident one is transmitted into the dusty-air layer. Subsequently, a rarefaction wave is reflected at the second contact surface and the shock wave transmitted into the free air is weakened by this nonlinear interaction. The induced rarefaction wave reflects later at the first contact surface as a compression wave, which runs through the layer to overtake the transmitted shock wave in air. The final emergent shock wave from the dusty air has almost the same strength as the original shock wave entering the layer. The time-dependent transition properties through the shock waves, contact surfaces and rarefaction waves are found by solving the equations of motion numerically by a modified random-choice method with an operator-splitting technique.