State-to-state reaction rates in gases with vibration–electronic–dissociation coupling: the influence on a radiative shock heated CO flow

Vibrational energy relaxation in shock-heated CO/N2/Ar mixtures

Experimental and numerical studies were performed on the vibrational energy relaxation in shock-heated CO/N2/Ar mixtures. A laser absorption technique was applied to the time-dependent rovibrational temperature time-history measurements. The vibrational relaxation data of reflected-shock-heated CO were summarized at 1720-3230 K. In shock-tube experiments, the rotational temperature of CO quickly reached equilibrium, whereas a relaxation process was found in the time-dependent vibrational temperature. For the mixture with 1.0% CO and 10.0% N2, the vibrational excitation caused a decrease in the macroscopic thermodynamic temperature of the test gas. In the simulations, the state-to-state (StS) approach was employed, where the vibrational energy levels of CO and N2 are treated as pseudo-species. The vibrational state-specific inelastic rate coefficients of N2-Ar collisions were calculated using the mixed quantum-classical method based on a newly developed three-dimensional potential energy surface. The StS predictions agreed well with the measurements, whereas deviations were found between the Schwartz-Slawsky-Herzfeld formula predictions and the measurements. The Millikan-White vibrational relaxation data of the N2-Ar system were found to have the most significant impact on the model predictions via sensitivity analysis. The vibrational relaxation data of the N2-Ar system were then modified according to the experimental data and StS results, providing an indirect way to optimize the vibrational relaxation data of a specific system. Moreover, the vibrational distribution functions of CO and N2 and the effects of the vibration-vibration-translation energy transfer path on the thermal nonequilibrium behaviors were highlighted.

Quantum-classical rate coefficient datasets of vibrational energy transfer in carbon monoxide based on highly accurate potential energy surface

A merged potential energy surface (PES) is introduced for CO + CO collisions by combining a recent full-dimensional ab initio PES [Chen et al. J. Chem. Phys. 153, 054310 (2020)] and analytical long-range multipolar interactions. This merged PES offers a double advantage: it retains the precision of the ab initio PES in describing the van der Waals well and repulsive short range while providing an accurate physical description of long-range interaction; it significantly reduces the computational time required for trajectory integration since the long-range portion of the ab initio PES (involving numerous neural network fitting parameters) is now replaced by the analytical model potential. Based on the present merged PES, mixed Quantum-Classical (MQC) calculations, which capture quantum effects related to vibrational motion, align with a range of experimental data, including transport properties, vibrational energy transfer between CO and its isotoplogues, as well as rate coefficients for V-V and V-T/R processes. Notably, the original ab initio PES yields V-T/R rate coefficients at low temperatures that are significantly higher than the experimental data due to the artificial contribution of its unphysical long-range potential. In addition to conducting extensive MQC calculations to obtain raw data for V-V and V-T/R rate coefficients, we employ Gaussian process regression to predict processes lacking computed MQC data, thereby completing the considered V-V and V-T/R datasets. These extensive rate coefficient datasets, particularly for V-T/R processes, are unprecedented and reveal the significant role played by V-T/R processes at high temperatures, emphasizing the necessity of incorporating both V-V and V-T/R processes in the applications.

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.

Mutual effect of vibrational relaxation and chemical reactions in viscous multitemperature flows

We study coupling of vibrational relaxation and chemical reactions in nonequilibrium viscous multitemperature flows. A general theoretical model is proposed on the basis of the Chapman-Enskog method modified for strongly nonequilibrium reacting flows; the model differs from models commonly used in computational fluid dynamics since it is able to capture additional cross-coupling terms arising in viscous flow due to compressibility and mutual influence of all nonequilibrium processes occurring in a mixture. The set of fluid dynamic equations is derived starting from the Boltzmann equation; the relaxation terms in these equations are described using the kinetic transport theory formalism. Reaction and relaxation rates depend on the distribution function and thus differ in the zero-order and first-order approximations of the Chapman-Enskog method. An algorithm for the calculation of multitemperature reaction and relaxation rates in both inviscid and viscous flows is proposed for the harmonic oscillator model. This algorithm is applied to estimate the mutual effect of vibrational relaxation and dissociation in binary mixtures of N(2) and N, and O(2) and O, under various nonequilibrium conditions. It is shown that modification of the Landau-Teller expression for the VT relaxation term works rather well in nitrogen, whereas it fails to predict correctly the relaxation rate in oxygen at high temperatures. In oxygen (in contrast to nitrogen), the first-order cross effects of dissociation and VT relaxation are found to be significant. A method for calculation of vibrational relaxation time based on the kinetic theory definition is suggested. Two-temperature dissociation rate coefficients are calculated in the zero- and first-order approximations and compared to other models.

State-specific dissociation modeling with multiquantum vibration-translation transitions

An efficient state-specific model of dissociation using a quadrature approach is proposed by considering multiquantum vibration-translation (VT) transitions (between bound and quasibound vibrational levels) according to the forced harmonic oscillator theory. Application of this model to a pure N₂ gas flow behind a plane shock wave shows that dissociation has a large influence on intermediate and higher vibrational levels and is characterized by state-specific incubation distances, before which VT energy exchanges remain the dominant mechanism just behind the shock.

Simple model for vibration-translation exchange at high temperatures: effects of multiquantum transitions on the relaxation of a N2 gas flow behind a shock

In this paper a simple model is proposed for computation of rate coefficients related to vibration-translation transitions based on the forced harmonic oscillator theory. This model, which is developed by considering a quadrature method, provides rate coefficients that are in very good agreement with those found in the literature for the high temperature regime (≳10,000 K). This model is implemented to study a one-dimensional nonequilibrium inviscid N(2) flow behind a plane shock by considering a state-to-state approach. While the effects of ionization and chemical reactions are neglected in our study, our results show that multiquantum transitions have a great influence on the relaxation of the macroscopic parameters of the gas flow behind the shock, especially on vibrational distributions of high levels. All vibrational states are influenced by multiquantum processes, but the effective number of transitions decreases inversely according to the vibrational quantum number. For the initial conditions considered in this study, excited electronic states are found to be weakly populated and can be neglected in modeling. Moreover, the computing time is considerably reduced with the model described in this paper compared to others found in the literature.