A bifurcation analysis of high-temperature ignition of H2−O2 diffusion flames

Abstract

The form of the ignition branch for steady, counterflow, hydrogen-oxygen diffusion flames, with dilution permitted in both streams, is investigated for two-step reduced chemistry by methods of bifurcation theory. Attention is restricted to fuel-stream temperatures less than or equal to the oxidizer-stream temperature T ∞ and to T ∞ larger than or of the order of the crossover temperature T c at which the rates of production and consumption of H atmos are equal. Two types of solutions are identified, a frozen solution that always exists in this kinetic approximation because all rates are proportional to the concentration of the intermediate H atom, and an ignited solution, represented by a branch of the curvev giving the maximum H concentration in terms of a Damköhler number constructed from the strain rate and the rate of the branching step H+O 2 →OH+O. For T ∞ > T c , the latter bifurcates from the frozen solution if the Damköhler number is increased to a critical value. For T ∞ larger than a value T s > T c , the effects of chemical heat release are small, and ignition is always gradual in the sense that the limiting ignited-branch slope is positive (supercritical bifurcation) and there is no S curve. For T ∞ in the range T c < T ∞ < T s , the heat release associated with the radical-consumption step causes the limiting ignition-branch slope to become negative (subcritical bifurcation), producing abrupt ignition which leads to an S curve. For values of T ∞ below crossover, the ignited branch appears as a C-shaped curve unconnected to the frozen solution. The method of analysis introduced here offers a first step toward analytical description of nonpremixed H 2 −O 2 autoignition.