Collision cross sections and nonequilibrium viscosity coefficients of N2 and O2 based on molecular dynamics
Tapan K. Mankodi, Upendra Bhandarkar, R.S. Myong
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.