A recombination reaction model for high-temperature chemical kinetics is analytically derived from ab initio simulation data. When atoms recombine, the kinetic rate model shows that product molecules favor high vibrational energy states. In this manner, recombination repopulates high vibrational energy states depleted by dissociation, in a high-temperature reacting gas. Coupling of internal energy relaxation, dissociation, and recombination results in depleted or overpopulated (relative to a corresponding Boltzmann distribution) vibrational energy distributions. Through a simple model, we show that non-Boltzmann behavior, in other words, depletion or overpopulation of highenergy states, is not only linked to thermal nonequilibrium but also chemical nonequilibrium. The mathematical derivation also indicates that the conventional approach for modeling recombination rates, where shock-tube dissociation rate measurements are combined with the principle of detailed balance, is incorrect. The complete analytical dissociation/recombination model embeds all relevant kinetic processes, including specific terms for translation/rotation/vibration/chemistry coupling, anharmonic and quasi-bound effects, and non-Boltzmann depletion and overpopulation effects. The model is a multitemperature model that can be used within computational fluid dynamics simulations with no appreciable increase in computational expense. Finally, because the model is analytical, containing separate terms for various physical effects, further model simplification could be performed depending on the flow conditions of interest.
Bibliographical noteFunding Information:
This work was supported by U.S. Air Force Office of Scientific Research Grant through grant number FA9550-19-1-0219 and NASA grant number 80NSSC20K1061. Narendra Singh was partially supported by Doctoral Dissertation Fellowship at the University of Minnesota.
© 2022 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.