Heavy-Impact Vibrational Excitation and Dissociation Processes in CO$_2$

Abstract: A heavy-impact vibrational excitation and dissociation model for CO$2$ 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 CO$_2$ based on First Order Perturbation Theory. The first excited triplet state $^{3}$B${2}$ of CO$_2$, including its vibrational structure, is considered in our model, and a more consistent approach to CO$_2$ dissociation is also proposed. The model is benchmarked against a few academic 0D cases and compared to decomposition time measurements in a shock tube. Our model is shown to have reasonable predictive capabilities, and the CO$_2$ $+$ O $\leftrightarrow$ CO $+$ O$_2$ is found to have a key influence on the dissociation dynamics of CO$_2$ 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 dynamics of CO$_2$, discussing the concept of vibrational chaos and its possible application to CO$_2$. The necessity for further experimental works to calibrate such state-to-state models is also discussed, with a proposed roadmap for novel experiments in shocked flows.