State-specific dissociation in O2–O2 collisions by quasiclassical trajectory method

Experimental and numerical studies on the thermal nonequilibrium behaviors of CO with Ar, He, and H2

The time-dependent rotational and vibrational temperatures were measured to study the shock-heated thermal nonequilibrium behaviors of CO with Ar, He, and H2 as collision partners. Three interference-free transition lines in the fundamental vibrational band of CO were applied to the fast, in situ, and state-specific measurements. Vibrational relaxation times of CO were summarized over a temperature range of 1110-2820 K behind reflected shocks. The measured rotational temperature instantaneously reached an equilibrium state behind shock waves. The measured vibrational temperature experienced a relaxation process before reaching the equilibrium state. The measured vibrational temperature time histories were compared with predictions based on the Landau-Teller model and the state-to-state approach. The state-to-state approach treats the vibrational energy levels of CO as pseudo-species and accurately describes the detailed thermal nonequilibrium processes behind shock waves. The datasets of state-specific inelastic rate coefficients of CO-Ar, CO-He, CO-CO, and CO-H2 collisions were calculated in this study using the mixed quantum-classical method and the semiclassical forced harmonic oscillator model. The predictions based on the state-to-state approach agreed well with the measured data and nonequilibrium (non-Boltzmann) vibrational distributions were found in the post-shock regions, while the Landau-Teller model predicted slower vibrational temperature time histories than the measured data. Modifications were applied to the Millikan-White vibrational relaxation data of the CO-Ar and CO-H2 systems to improve the performance of the Landau-Teller model. In addition, the thermal nonequilibrium processes behind incident shocks, the acceleration effects of H2O on the relaxation process of CO, and the characterization of vibrational temperature were highlighted.

Vibrational non-Boltzmann effects on the dissociation rate of oxygen

Both the internal energy nonequilibrium and the NB effects of the vibrational state distribution influence the calculation of the dissociation rate coefficient. The state-to-state (STS) method gives the exact dissociation rate coefficients under the influence of two nonequilibrium effects, while the single group linear maximum-entropy (SGLM) model only considers the internal energy nonequilibrium effects. Therefore, the ratio ζ of the dissociation rate coefficient calculated by the STS method and the SGLM model is used in this paper to describe the NB effects on the dissociation rate coefficient. The zero-dimensional (0D) heating adiabatic thermochemical nonequilibrium process of oxygen was simulated by the STS method with a post-surge temperature of 7000-11 000 K. The variation regularity of the NB effects in the relaxation process were investigated using ζ, and it was found that the NB effects were mainly affected by temperature. And then the relaxation process after the normal shock with the same post-surge temperature of 7000-11 000 K was simulated. The NB effects in the two non-equilibrium processes were compared, and it was found that although there is a conversion between internal energy and fluid kinetic energy in the latter, the NB effects in both processes have similar change rules with similar temperature change rules. If the specific internal energy is the same, the NB effects in both processes are also quantitatively consistent. This finding provides a basis for the improvement of the nonequilibrium model considering the NB effects.

Rovibrational internal energy transfer and dissociation of high-temperature oxygen mixture

This work constructs a rovibrational state-to-state model for the O₂ + O₂ system leveraging high-fidelity potential energy surfaces and quasi-classical trajectory calculations. The model is used to investigate internal energy transfer and nonequilibrium reactive processes in a dissociating environment using a master equation approach, whereby the kinetics of each internal rovibrational state is explicitly computed. To cope with the exponentially large number of elementary processes that characterize reactive bimolecular collisions, the internal states of the collision partner are assumed to follow a Boltzmann distribution at a prescribed internal temperature. This procedure makes the problem tractable, reducing the computational cost to a comparable scale with the O₂ + O system. The constructed rovibrational-specific kinetic database covers the temperature range of 7500-20 000 K. The reaction rate coefficients included in the database are parameterized in the function of kinetic and internal temperatures. Analysis of the energy transfer and dissociation process in isochoric and isothermal conditions reveals that significant departure from the equilibrium Boltzmann distribution occurs during the energy transfer and dissociation phase. Comparing the population distribution of the O₂ molecules against the O₂ + O case demonstrates a more significant extent of nonequilibrium characterized by a more diffuse distribution whereby the vibrational strands are more clearly identifiable. This is partly due to less efficient mixing of the rovibrational states, which results in more diffuse rovibrational distributions in the quasi-steady-state distribution of O₂ + O₂. A master equation analysis for the combined O₂ + O and O₂ + O₂ system reveals that the O₂ + O₂ system governs the early stage of energy transfer, whereas the O₂ + O system takes control of the dissociation dynamics. The findings of the present work will provide a strong physical foundation that can be exploited to construct an improved reduced-order model for oxygen chemistry.

Potential energy surfaces for high-energy N + O2 collisions

Potential energy surfaces for high-energy collisions between an oxygen molecule and a nitrogen atom are useful for modeling chemical dynamics in shock waves. In the present work, we present doublet, quartet, and sextet potential energy surfaces that are suitable for studying collisions of O₂(³Σ_g ^-) with N(⁴S) in the electronically adiabatic approximation. Two sets of surfaces are developed, one using neural networks (NNs) with permutationally invariant polynomials (PIPs) and one with the least-squares many-body (MB) method, where a two-body part is an accurate diatomic potential and the three-body part is expressed with connected PIPs in mixed-exponential-Gaussian bond order variables (MEGs). We find, using the same dataset for both fits, that the fitting performance of the PIP-NN method is significantly better than that of the MB-PIP-MEG method, even though the MB-PIP-MEG fit uses a higher-order PIP than those used in previous MB-PIP-MEG fits of related systems (such as N₄ and N₂O₂). However, the evaluation of the PIP-NN fit in trajectory calculations requires about 5 times more computer time than is required for the MB-PIP-MEG fit.

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

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.

Dissociation cross section for high energy O2-O2 collisions

Collision-induced dissociation cross section database for high energy O₂-O₂ collisions (up to 30 eV) is generated and published using the quasiclassical trajectory method on the singlet, triplet, and quintet spin ground state O₄ potential energy surfaces. At equilibrium conditions, these cross sections predict reaction rate coefficients that match those obtained experimentally. The main advantage of the cross section database based on ab initio computations is in the study of complex flows with high degree of non-equilibrium. Direct simulation Monte Carlo simulations using the reactive cross section databases are carried out for high enthalpy hypersonic oxygen flow over a cylinder at rarefied ambient conditions. A comparative study with the phenomenological total collision energy chemical model is also undertaken to point out the difference and advantage of the reported ab initio reaction model.

Vibrational energy transfer and dissociation in O2-N2 collisions at hyperthermal temperatures

Simulation of vibrational energy transfer and dissociation in O₂-N₂ collisions is conducted using the quasi-classical trajectory method on an ab initio potential energy surface. Vibrationally resolved rate coefficients are obtained in a high-temperature region between 8000 and 20 000 K by means of the cost-efficient classical trajectory propagation method. A system of master equations is constructed using the new dataset in order to simulate thermal and chemical nonequilibrium observed in shock flows. The O₂ 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 20 000 K. At the same time, the N₂ master equation relaxation time is similar to that derived under the assumption of a two-state system. The effect of vibrational-vibrational energy transfer appears to be crucial for N₂ relaxation and dissociation. Thermal equilibrium and quasi-steady state dissociation rate coefficients in O₂-N₂ heat bath are reported.

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.

Nonequilibrium internal energy distributions during dissociation

In this work, we propose a model for nonequilibrium vibrational and rotational energy distributions in nitrogen using surprisal analysis. The model is constructed by using data from direct molecular simulations (DMSs) of rapidly heated nitrogen gas using an ab initio potential energy surface (PES). The surprisal-based model is able to capture the overpopulation of high internal energy levels during the excitation phase and also the depletion of high internal energy levels during the quasi-steady-state (QSS) dissociation phase. Due to strong coupling between internal energy and dissociation chemistry, such non-Boltzmann effects can influence the overall dissociation rate in the gas. Conditions representative of the flow behind strong shockwaves, relevant to hypersonic flight, are analyzed. The surprisal-based model captures important molecular-level nonequilibrium physics, yet the simple functional form leads to a continuum-level expression that now accounts for the underlying energy distributions and their coupling to dissociation.