An Ab Initio Quantum-Chemistry-Based Three-Temperature Approach for Non-Equilibrium Hypersonic Flows: Application to Homogeneous 0-D Chemical Systems

This work presents an ab initio quantum-chemistry-based one-bin, three-temperature (1-bin 3T) model for non-equilibrium thermochemistry of homogeneous chemical systems in their electronic ground state, derived using the multi-group maximum-entropy principle. The proposed framework captures both vibrational and rotational non-equilibrium effects, thereby enabling an accurate representation of thermochemical behavior in high-temperature gases. To account for departures from equilibrium dissociation, a non-equilibrium correction factor derived from ro-vibrational State-to-State (StS) analysis is incorporated into the population distribution. Because this correction is constructed from the quasi-steady-state (QSS) distribution, the resulting model is valid only for systems and conditions under which the QSS assumption holds. The proposed 1-bin 3T model is validated across a broad range of zero-dimensional test cases through comparisons with high-fidelity StS simulations and Direct Molecular Simulations (DMS). The results demonstrate excellent agreement between the reduced-order model and high-fidelity approaches for both dissociating and recombining environments. Overall, the 1-bin 3T model shows strong potential as an efficient and accurate framework for modeling non-equilibrium thermochemical behavior, while keeping computational costs orders of magnitude lower than the high fidelity ro-vibrational StS simulations.