Vibrational relaxation time at high temperatures and its effect on heat exchange

Hypersonic flow around a solid moving along a gliding trajectory of re-entry into the earth's atmosphere is considered. The Lifshits equation and the reciprocal frequency formula with the effective cross section of molecular collisions are used for approximating the vibrational relaxation time at $T > 8000$ K. A comparison of the calculation results based on these expressions is provided for different values of the effective collision cross section. The effect of various approximations on the thermal flux, the temperature, and the density profiles is demonstrated.