Chemical reaction rates and non-equilibrium pressure of reacting gas mixtures in the state-to-state approach

- State-to-state approach for coupled vibrational relaxation and chemical reactions.
- Self-consistent model for rates of non-equilibrium reactions and energy transitions.
- In viscous flows mass action law is violated.
- Cross coupling between reaction rates and non-equilibrium pressure in viscous flow.
- Results allow implementing the state-to-state approach for viscous flow simulations.

Viscous gas flows with vibrational relaxation and chemical reactions in the state-to-state approach are analyzed. A modified Chapman-Enskog method is used for the determination of chemical reaction and vibrational transition rates and non-equilibrium pressure. Constitutive equations depend on the thermodynamic forces: velocity divergence and chemical reaction/transition affinity. As an application, N2 flow with vibrational relaxation across a shock wave is investigated. Two distinct processes occur behind the shock: for small values of the distance the affinity is large and vibrational relaxation is in its initial stage; for large distances the affinity is small and the chemical reaction is in its final stage. The affinity contributes more to the transition rate than the velocity divergence and the effect of these two contributions are more important for small distances from the shock front. For the non-equilibrium pressure, the term associated with the bulk viscosity increases by a small amount the hydrostatic pressure.