Vibrational nonequilibrium in a supersonic expansion with reaction: Application to O2–O

State-to-state study of non-equilibrium recombination of oxygen and nitrogen molecules

Rapidly cooled mixtures are of interest for several applications, including hypersonic flows due to the presence of strong cooling temperature gradients in regions such as hypersonic boundary layers and expanding nozzles. There have been very few studies of rapidly cooled mixtures using the high-fidelity rovibrational databases afforded by ab initio potential energy surfaces. This work makes use of existing rovibrational state-specific databases to study rapidly cooled mixtures. In particular, we seek to understand the importance of thermal non-equilibrium in recombining mixtures using both rovibrational and vibrational state-to-state methods for oxygen and nitrogen molecules. We find that although there is significant non-equilibrium during recombination, it is well captured by the vibrational state-specific approach. Finally, we compare the global recombination rate computed based on the state-specific recombination rate coefficients and the global recombination rate computed based on the time local dissociation rate coefficient, which is reversed using the principle of detailed balance. The local dissociation rate coefficient is computed by weighting the state-specific dissociation rate coefficients with the state-specific distribution of energy states. We find a large difference between these rates, highlighting a potential source of errors in hypersonic flow predictions.

Fokker-Planck equation for Coulomb relaxation and wave-particle diffusion: Spectral solution and the stability of the Kappa distribution to Coulomb collisions

The present paper considers the time evolution of a charged test particle of mass m in a constant temperature heat bath of a second charged particle of mass M. The time dependence of the distribution function of the test particles is given by a Fokker-Planck equation with a diffusion coefficient for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. For the mass ratio m/M→0, the steady distribution is a Kappa distribution which has been employed in space physics to fit observed particle energy spectra. The time dependence of the distribution functions with some initial value is expressed in terms of the eigenvalues and eigenfunctions of the linear Fokker-Planck operator and also interpreted with the transformation to a Schrödinger equation. We also consider the explicit time dependence of the distribution function with a discretization of the Fokker-Planck equation. We study the stability of the Kappa distribution to Coulomb collisions.

The I2 dissociation mechanisms in the chemical oxygen-iodine laser revisited

The recently suggested mechanism of I(2) dissociation in the chemical oxygen-iodine laser (COIL) [K. Waichman, B. D. Barmashenko, and S. Rosenwaks, J. Appl. Phys. 106, 063108 (2009); and J. Chem. Phys. 133, 084301 (2010)] was largely based on the suggestion of V. N. Azyazov, S. Yu. Pichugin, and M. C. Heaven [J. Chem. Phys. 130, 104306 (2009)] that the vibrational population of O(2)(a) produced in the chemical generator is high enough to play an essential role in the dissociation. The results of model calculations based on this mechanism agreed very well with measurements of the small signal gain g, I(2) dissociation fraction F, and temperature T in the COIL. This mechanism is here revisited, following the recent experiments of M. V. Zagidullin [Quantum Electron. 40, 794 (2010)] where the observed low population of O(2)(b, v = 1) led to the conclusion that the vibrational population of O(2)(a) at the outlet of the generator is close to thermal equilibrium value. This value corresponds to a very small probability, ∼0.05, of O(2)(a) energy pooling to the states O(2)(X,a,b, v > 0). We show that the dissociation mechanism can reproduce the experimentally observed values of g, F, and T in the COIL only if most of the energy released in the processes of O(2)(a) energy pooling and O(2)(b) quenching by H(2)O ends up as vibrational energy of the products, O(2)(X,a,b), where the vibrational states v = 2 and 3 are significantly populated. We discuss possible reasons for the differences in the suggested vibrational population and explain how these differences can be reconciled.

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.

Nonequilibrium kinetics of a radiative CO flow behind a shock wave

An investigation is presented of a highly nonequilibrium CO flow with consistently coupled vibrational energy exchanges, chemical reactions, and radiation. A detailed state-to-state model taking into account vibration-vibration, vibration-translation, and vibration-electronic transitions, dissociation-recombination reactions, and radiative transitions between vibrational and electronic states is developed on the basis of kinetic theory methods. A closed set of master equations for vibration-electronic level populations, number densities of atomic species, radiation intensity, temperature, and velocity is derived, and a one-dimensional inviscid carbon monoxide flow behind a plane shock wave is studied numerically. Several models of vibrational transition and dissociation rates in high temperature carbon monoxide are tested, and a model satisfying both accuracy and feasibility requirements is recommended. The role of various energy transfers and chemical reactions in the formation of nonequilibrium vibrational distributions in a shock heated CO flow is studied, and the influence of state-to-state distributions on macroscopic flow parameters and radiation intensity is discussed.