Formulation and numerical analysis of vibrationally coupled recombination of monatomic molecules using Boltzmann kinetic equation

Monatomic molecular recombination is formulated using the Boltzmann kinetic equation. The recombination is coupled to the diatomic molecular vibrational states using the truncated harmonic oscillator model. The obtained recombination rate is equal to the modified Arrhenius rate, which is independent of the dissociation (activation) energy, when the temperature defined in the gain term on the basis of the intermediate's collisions is much lower than that of the dissociation. The formulated model is numerically analyzed by solving the hypersonic shock layer problem with dissociation-recombination reactions. The obtained numerical results indicate that dissociated monatomic molecules behind a shock wave recombine into diatomic molecules owing to the decrease in the temperature near the wall.