A reactive shock in a polytropic gas

Abstract

We shall consider the progress of a plane-detonation wave in a polytropic gas. Three basic assumptions are made; namely, that the gas is shocked by an infinite piston moving at a constant velocity up, that the shock is sufIicient to start the detonation, and that the detonation iself takes place rapidly throughout a thin but finite-width region, rather than instantaneously across a geometrical surface, as is usually supposed. The main content of the paper centers around this last assumption, which by allowing the energy release to occur in a finite time in a boundary layer, produces a model which is closer to reality. Thus the flow comprises three distinct domains; the unburnt gas ahead of the detonation, the burning zone in the boundary layer, and the burnt gas zone which extends from the back of the boundary layer to the piston. As is usual, the detonation reaction is assumed to transform the undetonated gas into a gas with similar thermodynamical properties, while at the same time releasing a certain amount of heat. The rate at which this heat is released depends on the local thermodynamical conditions and on the progress variable /3 introduced to describe the state of completion of the chemical kinetics of the gas in the burning zone. The equations which will be used to study the burning zone for a