State-to-State Internal Energy Relaxation Following the Quantum-Kinetic Model in DSMC

A new model for chemical reactions, the Quantum-Kinetic (Q-K) model of Bird, has recently been introduced that does not depend on macroscopic rate equations or values of local flow field data. Subsequently, the Q-K model has been extended to include reactions involving charged species and electronic energy level transitions. Although this is a phenomenological model, it has been shown to accurately reproduce both equilibrium and non-equilibrium reaction rates. The usefulness of this model becomes clear as local flow conditions either exceed the conditions used to build previous models or when they depart from an equilibrium distribution. Presently, the applicability of the relaxation technique is investigated for the vibrational internal energy mode. The Forced Harmonic Oscillator (FHO) theory for vibrational energy level transitions is combined with the Q-K energy level transition model to accurately reproduce energy level transitions at a reduced computational cost compared to the older FHO models.