Three-dimensional analytic probabilities of coupled vibrational-rotational-translational energy transfer for DSMC modeling of nonequilibrium flows

Abstract

A three-dimensional, nonperturbative, semiclassical analytic model of vibrational energy transfer in collisions between a rotating diatomic molecule and an atom, and between two rotating diatomic molecules (Forced Harmonic Oscillator-Free Rotation model) has been extended to incorporate rotational relaxation and coupling between vibrational, translational, and rotational energy transfer. The model is based on analysis of semiclassical trajectories of rotating molecules interacting by a repulsive exponential atom-to-atom potential. The model predictions are compared with the results of three-dimensional close-coupled semiclassical trajectory calculations using the same potential energy surface. The comparison demonstrates good agreement between analytic and numerical probabilities of rotational and vibrational energy transfer processes, over a wide range of total collision energies, rotational energies, and impact parameter. The model predicts probabilities of single-quantum and multi-quantum vibrational-rotational transitions and is applicable up to very high collision energies and quantum numbers. Closed-form analytic expressions for these transition probabilities lend themselves to straightforward incorporation into DSMC nonequilibrium flow codes. C 2014 AIP Publishing LLC.

Atomic and molecular data for spacecraft re-entry plasmas

“…However, when dealing with the application into detailed models, normally reactive and non-reactive processes as well as dissociation/recombination have to be considered from and to the whole sets of molecular rovibrational states for both reactants and products, possibly on more than one PES, in quite large collision energy ranges. In this context it is obvious to use more approximate methods, such as Schwartz-Slawsky-Herzfeld (SSH) theory [202,52,203], forced harmonic oscillator [204,205], and QCT, in order to use reasonable amounts of computational resources. QM methods can be used to assess the validity of a limited number of transitions treated with more approximate methods.…”

Application of the 3D Forced Harmonic Oscillator Model in the DSMC Method

“…The FHO-FR [35,36] is a three-dimensional nonperturbative, semiclassical analytic model of vibrational energy transfer in collisions between a rotating diatomic molecule and an atom, as well as between two rotating diatomic molecules. In its most general form [18], it incorporates rotational relaxation and coupling between vibrational, translational, and rotational energy transfer. An analysis of semiclassical trajectories of rotating molecules interacting by a repulsive exponential atom-to-atom potential resulted in closed-form analytic expressions of VT and VV transition probabilities as functions of rotational and relative translational energies of colliding particles.…”

“…Accurate ab initio modeling of the collisional process in the DSMC method allows detailed analysis of the gas relaxation in spatially homogeneous or one-dimensional flows, but it becomes prohibitively time consuming for multidimensional problems, especially in the near-continuum flow regime. An alternative is to simplify the transition probability in the first approximation, presenting it [18] as the product of the vibration-translation (VT) and rotation-translation (RT) transition probabilities. In this case, the RT process may be modeled separately using the Jeans relaxation equation and a temperature-dependent RT relaxation rate in the solution of the Navier-Stokes equations, or its equivalent based on the Larsen-Borgnakke [19] approach in the DSMC method.…”

“…Most of those may be classified into one of the two groups: the first-order perturbation theory (FOPT) methods [25] and methods based on the nonperturbative semiclassical forced harmonic oscillator (FHO) theory [26,27]. The FOPT methods neglect a sequential mechanism of single-quantum transition steps in a single collision, and they are known to underpredict semiclassical calculations by orders of magnitude [18]. On the other hand, the FHO theory, based on that sequential mechanism, was shown to provide very good agreement with such calculations [18].…”

“…The FOPT methods neglect a sequential mechanism of single-quantum transition steps in a single collision, and they are known to underpredict semiclassical calculations by orders of magnitude [18]. On the other hand, the FHO theory, based on that sequential mechanism, was shown to provide very good agreement with such calculations [18]. Although previous studies of nonequilibrium flows have included FHO expressions for resonant VVexchanges, comparison cases for a single-species gases both with and without a resonant VV process show, not surprisingly, little effect (see, for example, [22]).…”