Non-equilibrium flow of an ideal dissociating gas

Abstract

The theory of an ‘ideal dissociating’ gas developed by Lighthill (1957) for conditions of thermodynamic equilibrium is extended to non-equilibrium conditions by postulating a simple rate equation for the dissociation process (including the effects of recombination). This equation contains the ‘equilibrium’ parameter of the Lighthill theory plus a further ‘non-equilibrium’ parameter which determines the time scale of the dissociation phenomena.The behaviour of this gas is investigated in flow through a strong normal shock wave and past a bluff body. The assumption is made that the gas receives complete excitation of its rotational and vibrational degrees of freedom in an infinitesimally thin region according to the familiar Rankine-Hugoniot shock wave relations before dissociation begins. The variation of the relevant thermodynamic variables downstream of this region is then computed in a few particular cases. The method used in the latter case is an extension of the ‘Newtonian’ theory of hypersonic inviscid flow. In particular, the case of a sphere is treated in some detail. The variation of the shock shape and the ‘stand-off’ distance with the coefficient Λ, which is the ratio of the sphere diameter to the length scale of the dissociation process, is exhibited for conditions extending from completely undissociated flow to dissociated flow in thermal equilibrium. Results would indicate that significant and observable changes from the undissociated values occur, although values for the non-equilibrium parameter are not, at present, available.