An equivalent air model for vibrational non-equilibrium flows

Non-equilibrium real gas effects significantly impact the aerothermodynamic characteristics of hypersonic vehicles, and gases with different compositions could show distinct non-equilibrium behaviors. This paper studies the vibrational non-equilibrium of air, a N 2 -O 2 mixture, by introducing a model which treats air as an equivalent pure diatomic gas. Molecular parameters of the equivalent air are derived based on principle of energy conservation, and a piecewise vibrational relaxation rate is proposed, informed by a detailed analysis on the two-stage relaxation process of air. Relaxations of nitrogen and oxygen components are out of sync, and the competition between two components, as well as among different energy modes, plays a critical role in distinguishing air from a pure diatomic gas. Nonetheless, as long as the equivalent air model is employed, non-equilibrium flow and heat transfer features of the gas mixture, including those with component ratios beyond real air, can be predicted within a unified theoretical framework originally developed for the pure diatomic gas. The theoretical analyses are calibrated and validated against results from the direct simulation Monte Carlo method. The equivalent air model reveals a generalized similarity across non-equilibrium flows of different gases, offering valuable implications for ground-to-flight extrapolation and rapid estimation in engineering practice.