Vibrational favoring effect in DSMC dissociation models

Abstract

Several common models for dissociation reactions in direct simulation Monte Carlo calculations are analyzed quantitatively under general equilibrium and nonequilibrium conditions. The models differ in the degree to which the internal energy of the colliding particles contributes to the probability of dissociation. Test calculations in an equilibrium bath show that the temperature dependence of the predicted equilibrium rate constant, a commonly used measure of accuracy, is dominated by the collision selection algorithm, rather than the details of the dissociation model, and is thus a poor measure of physical validity or accuracy. The distribution of internal energy states of molecules selected for dissociation under the bath conditions, as used for analysis here, is a preferred means to assess accuracy, and is available qualitatively from existing theory. Recent state-specific quasi-classical trajectory calculations allow for quantitative assessment for certain molecules. Certain singularities present in a recent threshold dissociation model [Phys. Fluids 8, 1293 (1996)] are mediated by recourse to the full threshold equations. Sensitivity studies are performed to show the effect of the details of the numerical implementation. A simple generalization of a Weak Vibrational Bias model [Phys. Fluids 6, 3473 (1994)] is suggested to include rotational favoring. The present analysis provides a means to generate quantitatively a two-temperature rate constant, commonly applied in continuum models, for arbitrary conditions. Calibrated simulations which differ only in the dissociation model are performed for the hypersonic stagnation streamline problem to confirm the order of magnitude decrease in dissociation relative to a standard nonfavored model under conditions of large nonequilibrium.

Testing Continuum and Non-Continuum Descriptions in High Speed Flows

“…Dissociation cross sections are based on the Weak Vibrational Bias model [5], as modified in Ref. [2]. The Boltzmann equation represents the behavior of many-particle kinetic system in terms of the evolution equation for the single particle gas distribution function.…”

“…The DSMC code is a modified [2,3] version of that described by Bird [4] suitable for multi-species monatomic and diatomic gas flows. Diatomic molecules are modeled assuming quantized rigid rotor rotational, and anharmonic oscillator vibrational, energy levels.…”

Modeling Dissociation-Vibration Coupling with the Macroscopic Chemistry Method

“…The TLD expressions for P¦ R have singularities at certain energies [6,2,3], giving P¦ R ¢ 1. In such cases, a single dissociation event only is performed in most DSMC codes.…”

“…Distinctly different forms of ε F and dissociation probability P¦ R apply for low and high vibrational levels. Boyd [6] and Wadsworth and Wysong [2] give details of the DSMC implementation of the TLD model. We used Boyd's formulation here.…”

Molecule-based approach for computing chemical-reaction rates in upper atmosphere hypersonic flows.

“…The latter consist of the work by Bird (1994. DSMC chemistry models have been reviewed and comparatively evaluated on many occasions (Dressler 2001, Wadsworth andWysong 1997).…”