Assessment of species-specific vibrational temperature modelling in hypersonic non-equilibrium flows

A species-specific multi-vibrational model for hypersonic non-equilibrium flows is presented in this work, along with a systematic analysis of its impact across multiple cases, ranging from zero-dimensional adiabatic relaxation to rapid expansion flows and axisymmetric blunt-body configurations. This model assumes a single temperature to characterise both translational and rotational energies, while a separate vibrational temperature is considered for each species. It explicitly accounts for vibrational-translational (V-T) relaxation of individual species and vibrational-vibrational (V-V) relaxation between unlike molecules. The V-V relaxation probabilities for N₂ N 2 - O₂ O 2 and N₂ N 2 -NO collisions are determined by fitting experimental and Schwartz-Slawsky-Herzfeld (SSH) data from the literature, whereas, the probability of O₂ O 2 -NO is assumed to follow the N₂ N 2 -NO system. The proposed model is implemented in an in-house hypersonic computational fluid dynamics (CFD) solver and validated against the numerical simulations for a non-reacting one-dimensional system, and compared with the high-fidelity state-to-state (STS) and direct simulation Monte Carlo (DSMC) approaches for a reacting flow. Further validation is performed against experimental measurements and DSMC for rapid expansion flow and flow over a cylinder. Comparisons with the single-vibrational temperature model reveal noticeable differences in vibrational temperature profiles, shock stand-off distance and vibrational freezing values. The additional computational cost associated with this formulation is also detailed, supporting its applicability as an intermediate-fidelity modelling approach for hypersonic CFD simulations.