State-to-State Master Equation and Direct Molecular Simulation Study of Energy Transfer and Dissociation for the N₂–N System

Abstract

We present a detailed comparison of two high-fidelity approaches for simulating non-equilibrium chemical processes in gases: the state-to-state master equation (StS-ME) and the direct molecular simulation (DMS) methods. The former is a deterministic method, which relies on the pre-computed kinetic database for the N2–N system based on the NASA Ames ab initio potential energy surface (PES) to describe the evolution of the molecules’ internal energy states through a system of master equations. The latter is a stochastic interpretation of molecular dynamics relying exclusively on the same ab initio PES. It directly tracks the microscopic gas state through a particle ensemble undergoing a sequence of collisions. We study a mixture of nitrogen molecules and atoms forced into strong thermochemical non-equilibrium by sudden exposure of rovibrationally cold gas to a high-temperature heat bath. We observe excellent agreement between the DMS and StS-ME predictions for the transfer rates of translational into rotational and vibrational energy, as well as of dissociation rates across a wide range of temperatures. Both methods agree down to the microscopic scale, where they predict the same non-Boltzmann population distributions during quasi-steady-state dissociation. Beyond establishing the equivalence of both methods, this cross-validation helped in reinterpreting the NASA Ames kinetic database and resolve discrepancies observed in prior studies. The close agreement found between the StS-ME and DMS methods, whose sole model inputs are the PESs, lends confidence to their use as benchmark tools for studying high-temperature air chemistry.

Rovibrational-Specific QCT and Master Equation Study on N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) Systems in High-Energy Collisions

“…Figure compares the present dissociation rate coefficients with the existing data. ,,,,,− For both chemical systems, the QSS rate coefficients have slightly lower values than the equilibrium ones, which is consistent with the results obtained for the N 2 + N , and O 2 + O systems. For the N 2 + O system, the measured N 2 + N dissociation rate coefficients − are employed in the comparison due to the lack of experimental data for the N 2 + O system.…”

“…The present calculations predict lower values than the measured ones for both QSS and equilibrium. Interestingly, the present QSS dissociation rate coefficients in N 2 + O interactions are close to those for N 2 + N. , This seems to confirm the possible similarity in physical behavior among different chemical systems that have been discussed in detail in Sections and 3.2. In Figure S8, the PES cuts for N 2 O and N 3 are provided around one of the local minima locations of N 2 O 3 A′.…”

“…Comparisons of the dissociation rate coefficients with the existing experimental ,− and theoretical ,,,,, data: (a) N 2 + O → 2N + O and (b) NO + N → 2N + O.…”

Rovibrational Internal Energy Transfer and Dissociation of High-Temperature Oxygen Mixture

“…The present average rotational energy profile shows a larger discrepancy from the DMS result than the vibration during the non-equilibrium energy transfer. According to the previous studies by Venturi et al 2 and Macdonald et al 32 , it was demonstrated that the StS master equation approach yields very similar results with those from the DMS provided that the identical PES is adopted.…”

Computational analysis of experiments on shock detachment in hypersonic flow of nitrogen and carbon dioxide over a wedge

“…Gordon & McBride (1994), the rates of vibrational excitation and dissociation have required complex measurements in shock tubes and other devices, although recent developments employing sophisticated theoretical methods to obtain the relevant data have been quite successful, see e.g. Macdonald et al (2020) and Chaudry et al (2020). Nevertheless, the uncertainties associated with dissociation rates remain so high that they are usually quoted as error margins of ±0.2 or so in the power of 10.…”