Derivation of a consistent multi-internal-temperature model for vibrational energy excitation and dissociation of molecular nitrogen in hypersonic flows

A multi-internal-temperature model has been developed to study vibrational excitation and dissociation processes in nitrogen behind strong shock waves. As a starting point, a vibrational-collisional database has been developed based on the Forced Harmonic Oscillator model for inelastic excitation and dissociation during collisions of ground-state N₂ with N and N₂. The simulation of a strong shock wave condition has put forward that vibration-translation relaxation is dominated by multi-quanta transitions and that the vibrational distribution of N₂ remains relatively close to a Boltzmann distribution during the whole dissociation process behind the shock wave. Then, based on these results, reduced models considering one and two groups of levels with their own internal vibrational temperature have been derived. The results obtained with the different reduced models have been compared against those obtained with the detailed vibrational-collisional model. An excellent agreement with the results of the detailed model has been obtained for a reduced model with only 2 groups of levels with their own internal temperatures.