The high degree of vibrational excitation of O 2 ground state molecules recently observed in inductively coupled plasma discharges is investigated experimentally in more detail and interpreted using a detailed self-consistent 0D global kinetic model for oxygen plasmas. Additional experimental results are presented and used to validate the model. The vibrational kinetics considers vibrational levels up to v=41 and accounts for electron impact excitation and de-excitation (e-V), vibration-to-translation relaxation (V-T) in collisions with O 2 molecules and O atoms, vibration-to-vibration energy exchanges (V-V), excitation of electronically excited states, dissociative electron attachment, and electron impact dissociation. Measurements were performed at pressures of 10-80 mTorr (1.33 and 10.67 Pa) and radio frequency (13.56 MHz) powers up to 500 W. The simulation results are compared with the absolute densities in each O 2 vibrational level obtained by high sensitivity absorption spectroscopy measurements of the Schumann-Runge bands for O 2 (X, v=4-18), O( 3 P) atom density measurements by two-photon absorption laser induced fluorescence (TALIF) calibrated against Xe, and laser photodetachment measurements of the O − negative ions. The highly excited O 2 (X, v) distribution exhibits a shape similar to a Treanor-Gordiets distribution, but its origin lies in electron impact e-V collisions and not in V-V up-pumping, in contrast to what happens in all other molecular gases known to date. The relaxation of vibrational quanta is mainly due to V-T energy-transfer collisions with O atoms and to electron impact dissociation of vibrationally excited molecules, e+O 2 (X, v)→O( 3 P)+O( 3 P).
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.
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%.
A heavy particle impact vibrational excitation and dissociation model for CO2 is presented. This state-to-state model is based on the forced harmonic oscillator (FHO) theory, which is more accurate than current state-of-the-art kinetic models of CO2 based on first-order perturbation theory. The first excited triplet state 3B2 of CO2, including its vibrational structure, is considered in our model, and a more consistent approach to CO2 dissociation is also proposed. The model is benchmarked against a few academic zero-dimensional (0D) cases and compared to decomposition time measurements in a shock tube. Our model is shown to have reasonable predictive capabilities, and the CO2 + O ↔ CO + O2 reaction is found to have a key influence on the dissociation dynamics of CO2 shocked flows, warranting further theoretical studies. We conclude this study with a discussion on the theoretical improvements that are still required for a more consistent analysis of the vibrational/dissociation dynamics of CO2.
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