A rovibrational collisional model is developed to study energy transfer and dissociation of N(2)((1)Σ(g)(+)) molecules interacting with N((4)S(u)) atoms in an ideal isochoric and isothermal chemical reactor. The system examined is a mixture of molecular nitrogen and a small amount of atomic nitrogen. This mixture, initially at room temperature, is heated by several thousands of degrees Kelvin, driving the system toward a strong non-equilibrium condition. The evolution of the population densities of each individual rovibrational level is explicitly determined via the numerical solution of the master equation for temperatures ranging from 5000 to 50,000 K. The reaction rate coefficients are taken from an ab initio database developed at NASA Ames Research Center. The macroscopic relaxation times, energy transfer rates, and dissociation rate coefficients are extracted from the solution of the master equation. The computed rotational-translational (RT) and vibrational-translational (VT) relaxation times are different at low heat bath temperatures (e.g., RT is about two orders of magnitude faster than VT at T = 5000 K), but they converge to a common limiting value at high temperature. This is contrary to the conventional interpretation of thermal relaxation in which translational and rotational relaxation timescales are assumed comparable with vibrational relaxation being considerable slower. Thus, this assumption is questionable under high temperature non-equilibrium conditions. The exchange reaction plays a very significant role in determining the dynamics of the population densities. The macroscopic energy transfer and dissociation rates are found to be slower when exchange processes are neglected. A macroscopic dissociation rate coefficient based on the quasi-stationary distribution, exhibits excellent agreement with experimental data of Appleton et al. [J. Chem. Phys. 48, 599-608 (1968)]. However, at higher temperatures, only about 50% of dissociation is found to take place under quasi-stationary state conditions. This suggest the necessity of explicitly including some rovibrational levels, when solving a global kinetic rate equation.

No abstract

A rovibrational collisional model is developed to study the internal energy excitation and dissociation processes behind a strong shock wave in a nitrogen flow. The reaction rate coefficients are obtained from the ab initio database of the NASA Ames Research Center. The master equation is coupled with a one-dimensional flow solver to study the nonequilibrium phenomena encountered in the gas during a hyperbolic reentry into Earth's atmosphere. The analysis of the populations of the rovibrational levels demonstrates how rotational and vibrational relaxation proceed at the same rate. This contrasts with the common misconception that translational and rotational relaxation occur concurrently. A significant part of the relaxation process occurs in non-quasi-steady-state conditions. Exchange processes are found to have a significant impact on the relaxation of the gas, while predissociation has a negligible effect. The results obtained by means of the full rovibrational collisional model are used to assess the validity of reduced order models (vibrational collisional and multitemperature) which are based on the same kinetic database. It is found that thermalization and dissociation are drastically overestimated by the reduced order models. The reasons of the failure differ in the two cases. In the vibrational collisional model the overestimation of the dissociation is a consequence of the assumption of equilibrium between the rotational energy and the translational energy. The multitemperature model fails to predict the correct thermochemical relaxation due to the failure of the quasi-steady-state assumption, used to derive the phenomenological rate coefficient for dissociation.

No abstract

A novel reduced-order method is presented for modeling reacting flows characterized by strong non-equilibrium of the internal energy level distribution of chemical species in the gas. The approach seeks for a reduced-order representation of the distribution function by grouping individual energy states into macroscopic bins, and then reconstructing state population using the maximum entropy principle. This work introduces an adaptive grouping methodology to identify and lump together groups of states that are likely to equilibrate faster with respect to each other. To this aim, two algorithms have been considered: the modified island algorithm and the spectral clustering method. Both methods require a measure of dissimilarity between internal energy states. This is achieved by defining "metrics" based on the strength of the elementary rate coefficients included in the state-specific kinetic mechanism. Penalty terms are used to avoid grouping together states characterized by distinctively different energies. The two methods are used to investigate excitation and dissociation of N (Σg+1) molecules due to interaction with N(Su4) atoms in an ideal chemical reactor. The results are compared with a direct numerical simulation of the state-specific kinetics obtained by solving the master equations for the complete set of energy levels. It is found that adaptive grouping techniques outperform the more conventional uniform energy grouping algorithm by providing a more accurate description of the distribution function, mole fraction and energy profiles during non-equilibrium relaxation.

A Boltzmann rovibrational collisional coarse-grained model is proposed to reduce a detailed kinetic mechanism database developed at NASA Ames Research Center for internal energy transfer and dissociation in N(2)-N interactions. The coarse-grained model is constructed by lumping the rovibrational energy levels of the N(2) molecule into energy bins. The population of the levels within each bin is assumed to follow a Boltzmann distribution at the local translational temperature. Excitation and dissociation rate coefficients for the energy bins are obtained by averaging the elementary rate coefficients. The energy bins are treated as separate species, thus allowing for non-Boltzmann distributions of their populations. The proposed coarse-grained model is applied to the study of nonequilibrium flows behind normal shock waves and within converging-diverging nozzles. In both cases, the flow is assumed inviscid and steady. Computational results are compared with those obtained by direct solution of the master equation for the rovibrational collisional model and a more conventional multitemperature model. It is found that the proposed coarse-grained model is able to accurately resolve the nonequilibrium dynamics of internal energy excitation and dissociation-recombination processes with only 20 energy bins. Furthermore, the proposed coarse-grained model provides a superior description of the nonequilibrium phenomena occurring in shock heated and nozzle flows when compared with the conventional multitemperature models.

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 introduces a novel methodology for the quantification of uncertainties associated with potential energy surfaces (PESs) computed from first-principles quantum mechanical calculations. The methodology relies on Bayesian inference and machine learning techniques to construct a stochastic PES and to express the inadequacies associated with the ab initio data points and their fit. By combining high fidelity calculations and reduced-order modeling, the resulting stochastic surface is efficiently forward propagated via quasi-classical trajectory and master equation calculations. In this way, the PES contribution to the uncertainty on predefined quantities of interest (QoIs) is explicitly determined. This study is done at both microscopic (e.g., rovibrational-specific rate coefficients) and macroscopic (e.g., thermal and chemical relaxation properties) levels. A correlation analysis is finally applied to identify the PES regions that require further refinement, based on their effects on the QoI reliability. The methodology is applied to the study of singlet (11A′) and quintet (25A′) PESs describing the interaction between O2 molecules and O atoms in their ground electronic state. The investigation of the singlet surface reveals a negligible uncertainty on the kinetic properties and relaxation times, which are found to be in excellent agreement with the ones previously published in the literature. On the other hand, the methodology demonstrated significant uncertainty on the quintet surface, due to inaccuracies in the description of the exchange barrier and the repulsive wall. When forward propagated, this uncertainty is responsible for the variability of 1 order of magnitude in the vibrational relaxation time and of factor four in the exchange reaction rate coefficient, both at 2500 K.