A non-equilibrium dissociation and vibrational relaxation model for computational fluid dynamics simulations of flows with shock waves

Gasdynamic equations describing a vibrationally non-equilibrium flow of a chemically reacting binary mixture A(2)/A are derived within the previously proposed general approach of solving the Boltzmann equation. The obtained equations differ from the traditional ones in their expressions for the reaction and relaxation rates. Aiming to obtain analytical expressions for these rates, a cutoff harmonic oscillator model for the vibrational spectrum of A(2) molecules and dissociation from the highest vibrational level are assumed. The equation for the dissociation rate describes two different dissociation regimes, determined by the dissociation rate constant at low temperatures and by the vibrational energy exchange rate constants at high temperatures, since it is limited by the vibrational energy delivery to the highest vibrational levels. A parameter for determining the appropriate regime is proposed. The derived expressions for the reaction and relaxation rates are used in computations of O-2/O and N-2/N mixture flows. A comparison of our results with the numerical and experimental data of other authors shows that the model used for the reaction and relaxation rates calculation should be refined, at least by considering anharmonicity effects.

Automated summary

Gasdynamic equations describing a vibrationally non-equilibrium flow of a chemically reacting binary mixture A(2)/A are derived within the previously proposed general approach of solving the Boltzmann equation. The obtained equations differ from the traditional ones in their expressions for the reaction and relaxation rates. A cutoff harmonic oscillator model for the vibrational spectrum of A(2) molecules is assumed to obtain analytical expressions for reaction and relaxation rates, with two different dissociation regimes described by the dissociation rate constant at low temperatures and by the vibrational energy exchange rate constants at high temperatures.