Shocks generated in a confined gas due to rapid heat addition at the boundary. II. Strong shock waves

Abstract

A study is made of the birth and evolution of a strong shock wave in an inert gas due to rapid energy deposition at a boundary. The gas is confined between infinite parallel planes separated by a distance large compared with the molecular mean free path. Heat flux at the wall rises from zero to a finite constant value during an interval that is a modest multiple of the intermolecular collision time. The thermomechanical response of the gas near the boundary is described by the complete Navier-Stokes equations in a layer with a thickness that is a few molecular mean free paths. Numerical solutions show how a spatial pressure variation is generated adjacent to the boundary, which then propagates away as an almost steady shock wave. If heat addition is continued a thicker high-temperature expanding layer develops in which the pressure remains uniform. This expanding layer acts like a piston, or a contact surface, the speed of which is calculated to leading order. In this way the present theory provides a rational basis for the ad hoc piston analogies used by earlier authors. In particular it shows the importance of power as a crucial factor in the determination of shock strength.