# Isothermal Interpretations of Oscillatory Ignition During Hydrogen Oxidation in an Open System. II. Numerical Analysis

Katherine Chinnick, C. Gibson, J. F. Griffiths

## Abstract

Numerical methods are used to simulate oscillatory ignition under conditions resembling those associated with the second ignition limit for equimolar hydrogen and oxygen mixtures flowing through a well stirred reactor. The starting point is a scheme comprising 17 elementary reactions coupled to heat release and dissipation. The system of equations is then simplified without loss of the major qualitative features of the predicted time-dependent phenomena, first by eliminating the temperature change, so yielding an isothermal branching system, and then by reducing the kinetic scheme to seven elementary steps as follows: $H_2 + O_2 \rightarrow \text{radicals},\\OH + H_2 \rightarrow H_2O + H,\\ H + O_2 \rightarrow OH + O,\\ O + H_2 \rightarrow OH + H,\\ H + O_2 + M \rightarrow HO_2 + M,\\ HO_2 + H \rightarrow H_2O + O,\\ HO_2 \rightarrow \text{inert}.$ This scheme constitutes the minimum viable kinetic foundation from which isothermal chain-branching oscillations are predicted in H$_2$ + O$_2$ under flowing conditions. Its features are analysed and the role of each reaction explained. The change in overall third-body efficiency of M leading to HO$_2$ formation, as the composition within the reactor varies under flowing conditions, is a key kinetic prerequisite to oscillations. The interaction between H and HO$_2$ that follows is an essential additional feature. The overall third-body efficiency is highest immediately after ignition, when the concentration of water is highest. The displacement of water by inflowing hydrogen and oxygen reduces the overall efficiency, and hence the effective rate constant of the termolecular step relative to that for the branching reactions. This condition is in complete accord with the analytical prediction of periodicity presented in the previous paper.