The harmonic oscillator rigid-rotator model has been used to calculate the relaxation region behind a shock wave in carbon dioxide. Finite relaxation rates for the three different vibrational modes and two dissociation reactions are included. Models for the coupling between the vibrational relaxation and the dissociation process are based on the assumption that dissociation can proceed from any vibrational level with equal probability. Two different models for the vibrational excitation have been examined. Solutions have been obtained for the interdependent fluid-flow, chemical rate, and vibrational relaxation-rate equations incorporating estimated rate coefficients. Results are presented in the form of flow-field profiles for density, pressure, translational and vibrational temperatures, and species concentrations. The effects of vibrational excitation, vibration-dissociation coupling, and energy exchange between the vibrational modes are investigated. The effect of vibrational relaxation and vibration-dissociation coupling is much stronger in CO2 with three different vibrational modes than in diatomic gases with only a single mode. The results of this study show that the effect of coupled vibrational relaxation and dissociation can sometimes alter the flow-field profiles by a factor of 2 compared to similar calculations without such coupling. For vibrational relaxation the results indicate that the shock-wave profiles depend primarily on the rate at which the translational energy is fed into internal modes and not so strongly on the energy distribution among the modes.

The coupling between vibrational relaxation and dissociation is discussed. A model for computations of dissociation behind strong shock waves is presented. It is shown that the loss of vibrational energy during dissociation introduces an inverse temperature dependence into the observed dissociation rate of O2 between 4000 and 8000K. Changing the model so that dissociation from higher vibrational levels is enhanced results in a dissociation-incubation time immediately behind the shock. The vibrational-energy distribution behind the shock is calculated, and shown to depart considerably from a Boltzmann distribution. The molecular model, which uses a Boltzmann distribution, is shown to give the same result as the non-Boltzmann model for both the nonequilibrium dissociation rate and the dissociation incubation time. (Author).