Thermodynamically Consistent Vibrational-Electron Energy Exchange and Application to Hypersonic Plasmas

This paper investigates electron heating and cooling in hypersonic plasma flows by utilizing the new thermodynamically consistent vibrational-electron heating model that we recently derived in [F. M. Rodriguez Fuentes and B. Parent, Phys. Fluids 37, 096141 (2025)]. While adhering to this framework, we here introduce new spline fits for the reduced electric field as a function of electron temperature and plasma density for the vibrationally excited states of nitrogen N2(v = 1), N2(v = 2), and N2(v = 3). These fits, constructed via a synthesis of data from swarm experiments and collision cross-sections, reveal that vibrationally excited states enhance electron cooling by up to a factor of 10 in low plasma density regimes. However, this effect diminishes to a factor of 2–3 when the plasma density exceeds 0.01% and becomes negligible when the electron temperature is less than 5000 K. The resulting physical model is validated through numerical simulations of the RAM-C-II and OREX re-entry flight tests. The results demonstrate excellent agreement with experimental flight data regarding plasma density at altitudes between 61 and 81 km. Furthermore, the model accurately predicts the heat flux to the surface at the stagnation point for altitudes as high as 96 km.