Effect of oxygen recombination on one-dimensional flow at high Mach numbers

Steve P. Heims
naca-tn-4144
Jan 1958


A theoretical analysis of air flow in a channel in which oxygen dissociation and recombination occur has been made. The channel is viewed as a streamtube in the flow around a blunt body. The analysis is begun with the writing of the differential equation which gives the concentration of atomic oxygen as a function of distance along the channel. The differential equation involves the reaction rate constant for the oxygen recombination reaction. This rate constant is evaluated theoretically from a formula due to Wigner, which yields a different result from simple collision theory. The equation for the atomic oxygen concentration thus obtained is solved together with the flow equations. The equations may be solved by ordinary hand-computation procedures. An example is worked out to show the variation of the flow in a certain streamtube and its dependence on whether the oxygen is frozen, in local equilibrium, or proceeding at the finite rate indicated by the theory. The concept of a local relaxation length is employed. From inspection of the flow equations and the behavior of the cumulative lag of the chemical reaction it is possible to judge without detailed numerical calculations whether changing one of the flow parameters brings the system closer to the chemical equilibrium or frozen reaction limit. An investigation is made of the comparative relaxation times of the oxygen dissociation-recombination reaction in relation to molecular vibrations. A reason for interest in this is that it has usually been assumed that vibrational relaxation occurs fast relative to chemical relaxation and therefore may be regarded as being in equilibrium. The present analysis indicates that it is not generally true that the vibrational relaxation times are short compared to the time characteristic of the chemical reaction. In this connection, the generalization of the concept of chemical equilibrium constant is introduced for the case that the molecular vibrations are not in equilibrium. Some values of the relaxation times are calculated and presented. A method is given to estimate the effect of vibrational lag when the vibrational relaxation times are relatively long.

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