On the Approach to Chemical and Vibrational Equilibrium Behind a Strong Normal Shock Wave

Summary The concurrent approach to chemical and vibrational equilib­ rium of a pure diatomic gas passing through a strong normal shock wave is investigated. It is demonstrated that the equilib­ rium degree of dissociation behind the shock front, and hence the density, for the case where the vibrational degrees of freedom are frozen out can exceed the degree of dissociation, and hence the density, for the case where all degrees of freedom are in equilib­ rium. Thus the necessary condition for a maximum of the density between the shock front and the position of full equilib­ rium flow downstream of the shock front is established. The sufficient condition that such a maximum be observable is shown to be that the approach to equilibrium of the vibrational degrees of freedom (or any other internal degrees of freedom) must lag the approach to dissociation equilibrium by a significant amount; that is, there must be at least an order of magnitude difference in the respective relaxation times before such a maximum might be observed. An example calculation for a Mach 13 strong shock wave in oxygen illustrates the appearance of such a maximum of the density and its dependency upon the relative values of the vibration and dissociation relaxation times.