Advanced modeling of non-equilibrium flows using a maximum entropy quadratic formulation

This paper presents a study of an advanced non-equilibrium model for state-specific chemical kinetics based on a moment method combined with an energy state grouping strategy. The paper focuses on the rovibrational chemical kinetics of the N₂(¹Σ⁺_g)-N(⁴S_u) system. Internal excitation, dissociation, recombination and energy transfer reactions, which are important processes in aerothermodynamics, are studied. The kinetic and ther-modynamic data is obtained from abinitio calculations performed at NASA Ames Research Center. Previous analysis of the population distribution revealed that the population of the low lying energy levels of nitrogen molecules strongly deviate from a Boltzmann distribution, and the non-equilibrium distribution exhibits significant curvature. By invoking the maximum entropy principle subject to a series of constraints, the logarithm of distribution function is reconstructed using quadratic functions in the internal energy space of the molecular species. The results of the numerical simulations for an ideal chemical reactor show that the quadratic model captures the excitation and dissociation profiles accurately by using only three to seven groups thereby reducing the computational costs for non-equilibrium flow simulations significantly.