Reduction of State-to-State Kinetics to Macroscopic Models in Hypersonic Flows

Abstract

The state-to-state chemical kinetic model, which considers a kinetic equation for each vibrational state of diatomic molecules, has been applied to some supersonic flow regimes and in particular in boundary layer, nozzle expansion, and shock wave. Nonequilibrium vibrational distribution obtained in the calculations shows strong departure from equilibrium-inducing non-Arrhenius global chemical rates, which differ substantially from macroscopic rates commonly used in fluid-dynamic codes. The evolution properties of the distribution have been investigated by a zero-dimensional numerical code in controlled conditions. We are trying to obtain from zero-dimensional results the approach to find appropriate macroscopic rate models to be used in fluid-dynamic codes accounting for the vibrational nonequilibrium. A comparison of analytical fitting of the zero-dimensional data and fluid dynamic global rates has been performed. Nomenclature ci = coefficients for the solution of the master equation Ev = energy of the vth vibrational level k = Boltzmann constant k d = dissociation rate constant k p = rates of the process p