An analysis of the explosion limits of hydrogen/oxygen mixtures with nonlinear chain reactions

The ignition boundary of hydrogen/oxygen mixtures is a Z-shaped curve in the pressure-temperature space, demonstrating the existence of three explosion limits. In this study, a general analysis governing all the three explosion limits in an isothermal environment is performed by considering both linear chain reactions (reactant-radical reactions) and nonlinear chain reactions (radical-radical reactions), in addition to the zeroth-order reactant-reactant reactions. For the nonlinear reactions, it is further shown that the linear-nonlinear coupling has the major influence, while the effect of nonlinear-nonlinear coupling is negligible. Phenomenologically, at low pressures, the competition between linear branching and linear termination as well as wall destruction determines the first and second explosion limits, while the nonlinear chain reactions are unimportant because of the small radical concentrations under these conditions. However, at higher pressures, both linear and nonlinear chain reactions are needed to accurately describe the third limit, which would be underpredicted by considering the linear chain reactions alone. For intermediate and high pressures, the dominant species are HO₂ and H₂O₂, respectively. Mechanistically, the concentration of HO₂ becomes higher at higher pressures due to the three-body recombination reaction, H + O₂ + M → HO₂ + M, such that the radical-radical reactions involving HO₂ become important, while the reaction HO₂ + HO₂ → H₂O₂ + O₂ renders HO₂ nonessential at the third limit, with the H₂O₂ radical generated by the nonlinear chain reactions becoming the controlling species.