State-to-state approach in hypersonic thermochemical nonequilibrium flow simulations: a review

Thermochemical nonequilibrium flows play a critical role in shaping the aerothermal environment of hypersonic vehicles and therefore strongly influence the analysis and design of thermal protection systems (TPS). Traditional multi-temperature models often fail to accurately represent non-Boltzmann population distributions and detailed vibration-dissociation coupling, whereas state-to-state (StS) models provide a more physically rigorous description by directly resolving transitions between internal energy levels. This review summarizes recent advances in StS modeling for hypersonic thermochemical nonequilibrium flows, including elementary rate-coefficient determination, benchmark applications in canonical nonequilibrium flows, and current extension strategies based on reduced-order modeling, coarse graining, and machine-learning-assisted acceleration. The reviewed literature shows that the reliability of StS predictions depends strongly on the availability, accuracy, and consistency of elementary kinetic data, while their broader engineering use remains limited by the enormous number of internal states and elementary processes, severe equation stiffness, incomplete kinetic databases, and insufficient experimental data for robust validation. Overall, this review clarifies the recent progress, key bottlenecks, and promising future directions of StS modeling in hypersonic nonequilibrium flows.