Non-Boltzmann Analysis of Hypersonic Air Re-Entry Flows

Abstract

A vibrational state-specific model is developed to study the energy transfert, dissociation and neutral exchange processes in a high-temperature non-ionized air flow . The gas is described by N2, O2, NO, N, and O species which are assumed to be on their ground electronic state, the molecular species being modeled by a state-to-state approach. The manifold of vibrational levels is given by the solution of the radial Schrodinger equation using an accurate reconstruction of the potential energy curves based on the RKR method. Multiquantum vibration-translation transitions and dissociation processes for diatom-diatom collisions are derived from the Forced Harmonic Oscillator while atom-diatom collisions are described by literature data which is extrapolated to high temperatures and adapted to the current set of vibrational levels. The novel aspect of the proposed kinetic scheme relies in the inclusion of the state-specific Zeldovich processes for NO formation. The system of master equations, coupled to the momentum and energy conservation equations, is solved for the one-dimensional post-shock relaxation system. Conditions from an early trajectory point of the Fire-II flight experiment are considered. The results are interpreted on the basis of the vibrational temperatures evolution, the dynamic of the vibrational distribution functions (VDF) and the behavior of the macroscopic vibrational energy source terms, which are self-consistently derived for each type of kinetic process. A very different behavior is highlighted for N 2 /O 2 molecules and for NO. While the former molecules experience a strong non-equilibrium behavior of their VDF due to multi-quantum VT transitions, the latter is found to closely follow a Boltzmann distribution in the entire relaxation. The existence of level-dependent incubation distance for dissociation is evidenced for molecular oxygen and nitrogen. The analysis of the energetic contribution points out the presence of two overlapping regions respectively governed by excitation and dissociation, the simultaneous action of these two processes leading to the establishment of a non-equilibrium quasi-steady state region characterized by a vibrational temperature undershoot. As far as NO is concerned, the results demonstrates that excitation and, in a least extent, dissociation processes remain negligible with respect to the Zeldovich exchange processes, which are the main kinetic driver toward equilibrium. Moreover, NO is directly formed at the translational temperature and its relaxation toward equilibrium occurs as a succession of Boltzmann distributions. This leads to the conclusion that the vibrational population of NO can be described by Boltzmann equilibrium distribution.