Modeling of Vibration-Vibration Energy Transfer in the DSMC Method

Abstract

Modeling of vibration-vibration (V-V) energy transfer in collisions of diatomic anharmonic oscillators is discussed, applicable for the direct simulation Monte Carlo method. An attempt is made to take into account the fast vibrational relaxation of nitrogen through V-V exchange with oxygen by increasing the vibration-translation relaxation rate by a constant factor. The results have shown that such an approach still significantly overpredicts the available relaxation times. Then, a new approach to account for V-V exchanges is proposed, which incorporates the calculation of near-resonant transitions according to a temperature-dependent probability calibrated with available experimental data. That approach was found to provide quantitative agreement with shock tube measurements of vibrational relaxation in mixtures. While targeting primarily high-temperature air flows, the approach is applicable to any flow where the VV energy transfer needs to be modeled. It provides the benefits of numerical efficiency, simplicity of implementation, and acceptable physical accuracy.