Master equation simulation of O₂-N₂ collisions on an ab-initio potential energy surface

Abstract

Simulation of vibrational energy transfer in O2-N2 collisions is conducted using the quasiclassical trajectory method on an accurate potential energy surface. State-resolved rate coefficients are obtained for the O2 and N2 vibrational ladders at temperatures between 8000 and 15,000 K. A system of master equations is constructed using the new dataset in order to simulate nonequilibrium conditions observed in shock flows. The relaxation time derived from a solution of the master equations is in good agreement with the Millikan and White correlation at lower temperatures with an increasing discrepancy toward the translational temperature of 15,000 K. At the same time, the master equation relaxation time is similar to that derived under the assumption of a two-state system. This observation suggests that the multiquantum vibrational energy transfer in O2-N2 may be less efficient compared to that in a chemically reactive molecule-atom system. Nomenclature v, w initial vibrational states of O 2 and N 2 v , w final vibrational states of O 2 and N 2 ∆v = v − v O 2 vibrational quantum jump ∆w = w − w N 2 vibrational quantum jump K rate coefficient of bound-bound transition, cm 3 /s T, T r , T v translational, rotational and vibrational temperatures v, w → v , w transition from O 2 (v) and N 2 (w) to O 2 (v) and N 2 (w) K v→v−1 rate coefficient of O 2 (v) monoquantum deactivation, cm 3 /s pτ 1→0 relaxation time, derived from K 1→0 rate coefficient , atm-s K v,rem removal rate coefficient, K v,rem = v =v K v→v , cm 3 /s

Calculation of Vibrational Relaxation Times Using a Kinetic Theory Approach

“…For molecule–molecule collisions of nitrogen and oxygen, recent QCT simulations show that O 2 –N 2 and N 2 –O 2 collisions are well-described by Millikan–White’s expression for temperatures lower than 9000 K, but at higher temperatures, the Millikan–White formula, even with Park’s correction, underestimates the relaxation times, especially for N 2 –O 2 collisions.…”

On the Vibrational State-Specific Modeling of Radiating Normal Shocks in Air

“…quasi-classical trajectory (QCT) first principles calculations from Ref. [41,42], and experiment of Ref. [43].…”

Kinetic and Continuum Modeling of High-Temperature Oxygen and Nitrogen Binary Mixtures

“…It may rely, however, on empirical models for many thermal and chemical processes [2]. The level of detail in the description of vibrational and chemical relaxation may be much higher when the vibrationally resolved, QCT-based master equation [32] is used; this approach is somewhat cost-prohibitive in 2D flowfields [33], but the ultra-simplified zero-dimensional bath case is well suited for comparing it to other approximations. Recent work [34], however, argues that master equations based purely on vibrational quantum levels which ignore coupling between vibrational and rotational states may have inaccuracies.…”