Collision cross sections and nonequilibrium viscosity coefficients of N2 and O2 based on molecular dynamics

Abstract

This study examines the collision dynamics of atom–atom, atom–molecule, and molecule–molecule interactions for O–O, N–N, O2–O, N2–N, O2–N, N2–O, O2–O2, N2–N2, and N2–O2 systems under thermal nonequilibrium conditions. Investigations are conducted from a molecular perspective using accurate O4, N4, and N2O2 ab initio potential energy surfaces and by performing Molecular Dynamics (MD) simulations. The scattering angle and collision cross sections for these systems are determined, forming the basis for better collision simulations. For molecular interactions, the effect of the vibrational energy on the collision cross section is shown to be significant, which in turn has a profound effect on nonequilibrium flows. In contrast, the effect of the rotational energy of the molecule is shown to have a negligible effect on the cross section. These MD-based cross sections provide a theoretically sound alternative to the existing collision models, which only consider the relative translational energy. The collision cross sections reported herein are used to calculate various transport properties, such as the viscosity coefficient, heat conductivity, and diffusion coefficients. The effect of internal energy on the collision cross sections reflects the dependence of these transport properties on the nonequilibrium degree. The Chapman–Enskog formulation is modified to calculate the transport properties as a function of the trans-rotational and vibrational temperatures, resulting in a two-temperature nonequilibrium model. The reported work is important for studying highly nonequilibrium flows, particularly hypersonic re-entry flows, using either particle methods or techniques based on the conservation laws.

First-principles predictions for shear viscosity of air components at high temperature

“…Similar to atomic nitrogen, the DMS shear viscosity data for O + O interactions are generally larger than the corresponding results from QCT, 21 as shown in Fig. 6(a).…”

“…DMS shear viscosity predictions for nitrogen and oxygen are also compared with the QCT data of Mankodi et al 21 For N + N and N 2 + N 2 interactions, both sets of results are obtained from precisely the same PES. However, for O 2 + O 2 , the QCT results were obtained on the triplet surface only, 11 which constitutes one of the three possible spin couplings.…”

“…, ground-state O 2 + O 2 ), interactions occur on the relevant set of PESs with the appropriate statistical weights related to the overall spin couplings. We point out that the results presented by Mankodi et al 21 for molecular oxygen were obtained from trajectories on the triplet ground-state O 2 + O 2 surface only. Finally, we estimate the shear viscosity of the gas by using the known analytic solution for the flow.…”

“…Only recently, studies have been conducted to obtain transport phenomena from first-principles potential surfaces. Although shear viscosity has received some particular attention, 21–24 we devised a novel approach using the direct molecular simulation (DMS) method to estimate thermal conductivity from ab initio PESs. 25…”

“…33 For diatom–diatom systems, because of the high dimensionality of the reactants’ configuration space, several simplifying assumption must be used to make the calculations computationally tractable. For example, Mankodi et al 21 present QCT-obtained data for shear viscosity of molecular nitrogen and oxygen, but they consider reactant molecules in the ground rotational state only and having different vibrational states. Previously, we found very good agreement between DMS predictions for molecular nitrogen shear viscosity 30 and the data presented by Mankodi et al , 21 where both sets of results were based upon the same potential energy surface of Paukku et al 8,9 However, this conclusion cannot be extended in general.…”