Unsteady Rarefied Gas Flow with Shock Wave in a Channel

Abstract

The two-dimensional time-dependent problem of rarefied gas flow in a plane channel, formed by parallel plates of finite length and closed at one end, is solved on the basis of the kinetic S-model. The flow develops as a result of rupture of a diaphragm which separates the gas at rest in the channel and the gas at rest in a reservoir of infinite volume. The effect of gas deceleration at the channel walls under the conditions of diffuse molecular reflection from the channel walls and end face is studied. Decay of a shock wave and disappearance of a homogeneous flow zone behind the shock wave is traced for three variants of conditions at the channel inlet: (1) gas enters the channel from a reservoir of infinite length and width (as the basic variant), the simultaneous motion in the reservoir and channel being studied; (2) the high-pressure reservoir represents a usual channel section; and (3) the motion of the gas in the reservoir is not considered at all, instead of this, the boundary conditions of the evaporation-condensation type under the conditions of gas at rest in the reservoir are imposed in the inlet cross-section.