Data-Inspired and Physics-Driven Model Reduction for Dissociation: Application to the O2 + O System

This work presents an in-depth discussion on the nonequilibrium dissociation of O₂ molecules colliding with O atoms, combining quasi-classical trajectory calculations, master equation, and dimensionality reduction. A rovibrationally resolved database for all of the elementary collisional processes is constructed by including all nine adiabatic electronic states of O₃ in the QCT calculations. A detailed analysis of the ab initio data set reveals that for a rovibrational level, the probability of dissociating is mostly dictated by its deficit in internal energy compared to the centrifugal barrier. Because of the assumption of rotational equilibrium, the conventional vibrational-specific calculations fail to characterize such a dependence. Based on this observation, a new physics-based grouping strategy for application to coarse-grained models is proposed. By relying on a hybrid technique made of rovibrationally resolved excitation coupled to coarse-grained dissociation, the new approach is compared to the vibrational-specific model and the direct solution of the rovibrational state-to-state master equation. Simulations are performed in a zero-dimensional isothermal and isochoric chemical reactor for a wide range of temperatures (1500-20,000 K). The study shows that the main contribution to the model inadequacy of vibrational-specific approaches originates from the incapability of characterizing dissociation, rather than the energy transfers. Even when constructed with only twenty groups, the new reduced-order model outperforms the vibrational-specific one in predicting all of the QoIs related to dissociation kinetics. At the highest temperature, the accuracy in the mole fraction is improved by 2000%.

Construction of a coarse-grain quasi-classical trajectory method. I. Theory and application to N2-N2 system

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.

Adaptive coarse graining method for energy transfer and dissociation kinetics of polyatomic species

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 N₂ (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.

Energy transfer models in nitrogen plasmas: analysis of N₂(X¹Σg⁺)-N(⁴S(u))-e⁻ interaction

The relaxation of N₂(X¹Σg⁺) molecules in a background gas composed of N((4)S(u)) atoms and free electrons is studied by using an ideal isochoric and isothermic chemical reactor. A rovibrational state-to-state model is developed to study energy transfer process induced by free electron and atomic collisions. The required cross sections and the corresponding rate coefficients are taken from two well-known kinetic databases: NASA Ames kinetic mechanism for the description of the N₂(X¹Σg⁺)-N((4)S(u)) processes and the Phys4Entry database for the electron driven processes, N₂(X¹Σg⁺)-e(-). 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 10000 to 30,000 K. It was found that the distribution of the rovibrational energy levels of N₂(X¹Σg⁺) is strongly influenced by the electron driven collisional processes, which promote the excitation of the low lying vibrational levels. The macroscopic vibrational energy relaxation is governed by the molecule-atom collisions, when free electrons, initially cold are relaxing to the final heat-bath temperature. Thus, the main role of the free electrons is to ensure the equilibration of vibrational and free electron excitation, thus validating the existence of the local equilibrium T(V)-T(e). However, if electrons and heavy particles are assumed to be in equilibrium at the heat bath temperature, electron driven processes dominate the vibrational relaxation. Finally, we have assessed the validity of the Landau-Teller model for the description of the inelastic energy transfer between molecules and free electrons. In the case of free-electron temperatures lower than 10,000 K, Landau-Teller relaxation model gives an accurate description of the vibrational relaxation, while at higher temperatures the error in the predictions can be significant and the model should not be used.

Nonequilibrium shock-heated nitrogen flows using a rovibrational state-to-state method

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.

Boltzmann rovibrational collisional coarse-grained model for internal energy excitation and dissociation in hypersonic flows

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.