A detailed multiscale study of rotational-translational relaxation process of diatomic molecules

摘要

This article continues our cycle devoted to comprehensive investigation of the diatomic molecule collision process. In this paper, we focus particularly on the in-depth study of the rotational-translational (R-T) energy exchange process and Borgnakke-Larsen (BL) energy exchange model used in the direct simulation Monte Carlo method. The present study, which was performed on several levels of description (molecular, microscopic, and macroscopic), is based mainly on the highly detailed dataset (around 10~(11) configurations) of binary N_2-N_2 collisions, obtained via the classical trajectory calculation (CTC) method. This dataset, along with the explicit mathematical representation of the Borgnakke-Larsen model derived in the present paper, allowed us to obtain new results regarding the R-T energy exchange process: (1) we present an ab initio method to derive physically accurate expressions for inelastic collision probability pr in the BL model directly from CTC data; (2) we present a new two-parametric model for p_r and compared it to the previously known models, including the recent nonequilibrium-direction-dependent model of Zhang et al. "Nonequilibrium-direction-dependent rotational energy model for use in continuum and stochastic molecular simulation," AIAA J. 52(3), 604 (2014); (3) it showed that apart from the well-known dependence of the rotational relaxation rate on "direction to equilibrium" (ratio between translational and rotational temperatures), on molecular scale, rotationally over-excited molecule pairs demonstrate almost zero energy transfer to the translational energy mode (even in the case of very significant discrepancies between translational and rotational energies); (4) it was also shown that the Borgnakke-Larsen approach itself may require reassessment since it fails to give a proper description of distribution of postcollision energies. Throughout this paper, we also tried to put together and analyze the existing works studying the rotationa