Treatment of Thermal Non-Equilibrium Dissociation Rates: Application to $\rm H_2$

TL;DR

This paper develops a unified analytical model for the non-equilibrium dissociation rates of $ m H_2$, validated against master equation simulations, and provides fitted rate constants across a wide temperature range based on extensive literature review.

Contribution

It introduces a simple, analytical source term expression for $ m H_2$ dissociation under non-equilibrium conditions, applicable across different regimes, with fitted rate constants from comprehensive literature data.

Findings

The proposed expression accurately reproduces master equation results in most conditions.

A wide-range fit for $k_{d,nr}(T_t)$ is derived from literature, valid from 200 to 20,000 K.

Uncertainty in the fitted rate constants is estimated to be less than a factor of two.

Abstract

This work presents a detailed description of the thermochemical non-equilibrium dissociation of diatomic molecules, and applies this theory to the case of $\rm H_2$ 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, $T_{\rm t}$, and the fraction of dissociation, $\phi_{\rm A}$, is proposed. This expression has two input parameters: the QSS dissociation rate constant in the absence of recombination, $k_{\rm d,nr}(T_{\rm t})$, and a pre-QSS correction factor, $\eta(T_{\rm t})$. The value of $\eta(T_{\rm t})$ 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 $\rm H_2$ dissociation with the third-bodies $\rm H_2$, $\rm H$, and $\rm He$. 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 $k_{\rm d,nr}(T_{\rm t})$ 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 $\rm H_2$, $\rm H$, 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.