Treatment of Thermal Non-Equilibrium Dissociation Rates: Application to ${\mathrm{H}}_2$

Abstract

This work presents a detailed description of the thermochemical non-equilibrium dissociation of diatomic molecules, and applies this theory to the case of ${\mathrm{H}}_2$ dissociation. The master equations are used to derive corresponding aggregate rate constant expressions that hold for any degree of thermochemical non-equilibrium. These general expressions are analyzed in three key limits/ regimes: the thermal equilibrium limit, the quasi-steady-state (QSS) regime, and the pre-QSS regime. Under several simplifying assumptions, an analytical source term expression that holds in all of these regimes, and is only a function of the translational temperature, $T_{\mathrm{t}}$, and the fraction of dissociation, ${\varphi }_{\mathrm{A}}$, is proposed. This expression has two input parameters: the QSS dissociation rate constant in the absence of recombination, $k_{\mathrm{d},\mathrm{nr}}(T_{\mathrm{t}})$, and a pre-QSS correction factor, $\eta (T_{\mathrm{t}})$. The value of $\eta (T_{\mathrm{t}})$ is evaluated by comparing the predictions of the proposed expression against existing master equation simulations of a 0-D isothermal and isochoric reactor for the case of ${\mathrm{H}}_2$ dissociation with the third-bodies ${\mathrm{H}}_2$, $\mathrm{H}$, and $\mathrm{He}$. Despite its simple functional form, the proposed expression is able to reproduce the master equation results for the majority of the tested conditions. The best fit of $k_{\mathrm{d},\mathrm{nr}}(T_{\mathrm{t}})$ is then evaluated by conducting a detailed literature review. Data from a wide range of experimental and computational studies are considered for the third-bodies ${\mathrm{H}}_2$, $\mathrm{H}$, and inert gases, and fits that are valid from 200 to 20,000 K are proposed. From this review, the uncertainty of the proposed fits are estimated to be less than a factor of two.