Weak compression waves in relaxing gases

Abstract

Studies have been made of the structure of weak compression (shock) waves in relaxing gases. These studies have been primarily concerned with the development of separate theoretical and experimental techniques. These techniques are not inter-related in general except in the overall context of Vibrational relaxation. The theoretical studies have been concerned with the influence on the structure of weak normal shock waves of translational non-equilibrium. bimodal relaxation and second order unimodal relaxation. The affect of translational nonequilibrium on the relaxation process has been studied by forming an asymptotic expansion in the ratio of the viscous length to the relaxation length. The perturbation scheme was singular and required the application at the method of matched asymptotic expansions. Bimodal relaxation has been studied by forming an asymptotic expansion in the ratio of the energy of the secondary vibrational mode to the total Vibrational energy. The addition of a second order term to the rate equation describing the behaviour of a single vibrational mode has also been studied by forming an asymptotic expansion. In this case. the perturbation parameter was the ratio of the two relaxation times concerned. The experimental studies have been concerned with the production and study or weak normal shock waves in the Cranfield Institute or Technology 2" shock tube. A time resolved quantitative schlieren system has been used for the study of the weak normal shock waves. This particular system had been developed previously for this purpose. and further developments and refinements have been made to it. Experimental studies have been made with the schlieren system of the structure or strong incident shock waves in carbon dioxide. The vibrational relaxation time of carbon dioxide determined in this way for translational temperatures from 300 o K to 1200 o K has been found to be in reasonable agreement with measurements made elsewhere. A technique has been developed for the production of weak incident shock waves in t.i.1e shock tube, which involved the positioning of a perforated plate in the channel of the shock tube. The vibrational relaxation time of carbon dioxide determined in this way for translational o temperatures of approximately 300 K has been found to be in good agreement with measurements made elsewhere. Good agreement has also been obtained between the experimentally measured density gradient profiles and theoretical profiles. The curvature of the shock waves obscured the transition from a fully dispersed to a partly dispersed shook wave. Further improvements and refinements have been made to a technique which had been developed previously for the propagation of weak normal shock waves through the reflected shock region of the shock tube flow. This technique was used to study the behaviour of fully dispersed shock waves at high temperatures. The relaxation time of carbon dioxide determined in this way for temperatures from 300 o K to 600o K has been found to be in good agreement with measurements made elsewhere.