No abstract

This work aims to construct a reduced order model for energy transfer and dissociation in non-equilibrium nitrogen mixtures. The objective is twofold: to present the Coarse-Grain Quasi-Classical Trajectory (CG-QCT) method, a novel framework for constructing a reduced order model for diatom-diatom systems; and to analyze the physics of non-equilibrium relaxation of the nitrogen molecules undergoing dissociation in an ideal chemical reactor. The CG-QCT method couples the construction of the reduced order model under the coarse-grain model framework with the quasi-classical trajectory calculations to directly construct the reduced model without the need for computing the individual rovibrational specific kinetic data. In the coarse-grain model, the energy states are lumped together into groups containing states with similar properties, and the distribution of states within each of these groups is prescribed by a Boltzmann distribution at the local translational temperature. The required grouped kinetic properties are obtained directly by the QCT calculations. Two grouping strategies are considered: energy-based grouping, in which states of similar internal energy are lumped together, and vibrational grouping, in which states with the same vibrational quantum number are grouped together. A zero-dimensional chemical reactor simulation, in which the molecules are instantaneously heated, forcing the system into strong non-equilibrium, is used to study the differences between the two grouping strategies. The comparison of the numerical results against available experimental data demonstrates that the energy-based grouping is more suitable to capture dissociation, while the energy transfer process is better described with a vibrational grouping scheme. The dissociation process is found to be strongly dependent on the behavior of the high energy states, which contribute up to 50% of the dissociating molecules. Furthermore, up to 40% of the energy required to dissociate the molecules comes from the rotational mode, underscoring the importance of accounting for this mode when constructing non-equilibrium kinetic models. In contrast, the relaxation process is governed primarily by low energy states, which exhibit significantly slower transitions in the vibrational binning model due to the prevalence of mode separation in these states.

This work presents the analysis of non-equilibrium energy transfer and dissociation of nitrogen molecules (N(Σg+1)) using two different approaches: the direct molecular simulation (DMS) method and the coarse-grain quasi-classical trajectory (CG-QCT) method. The two methods are used to study thermochemical relaxation in a zero-dimensional isochoric and isothermal reactor in which the nitrogen molecules are heated to several thousand degrees Kelvin, forcing the system into strong non-equilibrium. The analysis considers thermochemical relaxation for temperatures ranging from 10 000 to 25 000 K. Both methods make use of the same potential energy surface for the N(Σg+1)-N(Σg+1) system taken from the NASA Ames quantum chemistry database. Within the CG-QCT method, the rovibrational energy levels of the electronic ground state of the nitrogen molecule are lumped into a reduced number of bins. Two different grouping strategies are used: the more conventional vibrational-based grouping, widely used in the literature, and energy-based grouping. The analysis of both the internal state populations and concentration profiles show excellent agreement between the energy-based grouping and the DMS solutions. During the energy transfer process, discrepancies arise between the energy-based grouping and DMS solution due to the increased importance of mode separation for low energy states. By contrast, the vibrational grouping, traditionally considered state-of-the-art, captures well the behavior of the energy relaxation but fails to consistently predict the dissociation process. The deficiency of the vibrational grouping model is due to the assumption of strict mode separation and equilibrium of rotational energy states. These assumptions result in errors predicting the energy contribution to dissociation from the rotational and vibrational modes, with rotational energy actually contributing 30%-40% of the energy required to dissociate a molecule. This work confirms the findings discussed in Paper I [R. L. Macdonald et al., J. Chem. Phys. 148, 054309 (2018)], which underlines the importance of rotational energy to the dissociation process, and demonstrates that an accurate non-equilibrium chemistry model must accurately predict the deviation of rovibrational distribution from equilibrium.

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.

No abstract