Vibrationally state-resolved rotational relaxation time

In high-temperature non-equilibrium flows, the traditional Parker rotational relaxation model based on the rigid rotor assumption fails to accurately describe the effects of internal molecular structure on the energy transfer processes, creating a critical bottleneck for precise modeling. This study aims to establish an improved computational framework for rotational relaxation times that incorporates vibrational state-resolved calculations and rovibrational coupling effects to overcome fundamental limitations of existing simplified models. Based on the variable soft sphere molecular model and statistical inelastic cross section theory, an exponential correlation function was introduced to accurately describe transition probabilities between rotational energy levels, establishing a complete state-to-state rotational relaxation time computational model. Through systematic parameter sensitivity analysis, a strict linear relationship between the averaged rotational relaxation time and the model parameter θ' was discovered, significantly streamlining the parameter fitting procedure. For N2-N2, N2-N, O2-O2, and O2-O systems, optimal θ' values were determined with average relative errors below 0.7% when validated against recent theoretical data. Important computational guidelines were established. The improved model provides theoretically accurate and computationally efficient tools for transport coefficient calculations in hypersonic flow numerical simulations, with significant implications for engineering applications such as atmospheric reentry and interplanetary exploration.