Nonequilibrium expansion flows of dissociated oxygen and ionized argon around a corner

Abstract

Detailed studies are presented of nonequilibrium, inviscid, two-dimensional expansion flows of dissociated oxygen and ionized argon around a corner. The numerical-graphical method of characteristics was applied to calculate the flow quantities. The computations were performed on an IBM-7090 computer for a number of cases with different free-stream conditions and wall angles. Of special interest are the flow conditions that will be tested in the UTIAS 4 in. × 7 in. hypersonic shock tube to measure recombination rate constants and other properties of the flow. It was assumed that, for dissociating oxygen, in the temperature range considered here the vibrational excitation was in equilibrium with the translational and rotational modes, except along the wave head and at the very corner, where the degree of dissociation and the vibrational excitation were frozen at their free-stream values. Consequently, it was found that the partially frozen characteristics played the dominant role in the present analysis. For ionizing argon, in the temperature range encountered the electronic excitation was always assumed at its ground state and the electron temperature was assumed to be equal to the atom and ion temperature. As a consequence, it was shown that in this case the frozen characteristics must be used throughout. It was found that, in every case, the flow produced by the corner consisted of seven basic flow areas, some of which were quite complex. In the case of dissociating oxygen, a recombination shock wave was found to exist along the expansion wave tail. However, for ionizing argon, no discontinuous feature was verified to exist, even up to large wall angles and even when using a small characteristic mesh size. The existence of a recombination shock wave in the case of oxygen was found to be the mathematical consequence of the assumed model in which the vibrational mode is instantly de-excited. Had a vibrational rate equation been used for gradual addition of energy it is doubtful if a shock wave would have appeared. Therefore, the term “de-excitation shock wave” would be more appropriate for such a disturbance rather than the term “recombination shock wave”. In every case quasi-similarities in the variations of the flow quantities along the wave head and along the wall surface were found to exist when their appropriately normalized values were plotted as functions of a relevant distance. It is shown that experimentally determined pressure distributions (using piezo gauges) and density distributions (using interferometry) along the wall surface of a corner expansion can be used to evaluate the recombination rate constants.