Higher criteria for the regularity of a one-dimensional local field

Abstract

A coupled problem of gasdynamics, vibrational relaxation, and dissociation in the flow of oxygen behind reflected shock waves is studied. The detailed state-to-state kinetic approach is used, which is based on a coupled solution of the momentum and energy conservation equations with the balance equations for molecular vibrational state populations and concentrations of oxygen atoms. Initial conditions corresponding to recent experiments in shock tubes are considered. For different models of physicochemical processes, a comparison is made with experimental data; varying the model parameters yields satisfactory agreement of all gas-dynamic parameters with the measured ones. The key feature of the proposed approach is the allowance for partial vibrational-chemical relaxation in the time interval between the incident and reflected shock waves. When relaxation between the shocks is not frozen, the reflected shock wave propagates through a vibrationally nonequilibrium gas, which significantly affects kinetics and gas dynamics. Accounting for partial relaxation ensures good agreement between the pressure calculated behind the front of the reflected shock wave and the pressure measured in the experiment. On the other hand, comparison with the vibrational temperature calculated indirectly from spectroscopic experimental data under the assumption of frozen relaxation shows noticeable differences near the shock wave front. We conclude that the technique for extracting gas-dynamic parameters fromspectroscopic data has to be improved by taking into account vibrational excitation before the reflected shock wave.