A Bifurcation Analysis of High-temperature Ignition of H2-02 Diffusion Flames

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 Tx and to T„ larger than or of the order of the crossover temperature Tc at which the rates of production and consumption of H atoms 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 intermedíate H atom, and an ignited solution, represented by a branch of the curve giving the máximum H concentration in terms of a Damkohler number constructed from the strain rate and the rate of the branching step H + Os -• OH + O. For T„ > T„ the latter bifurcates from the frozen solution if the Damkohler number is increased to a critical valué. For T„ larger than a valué Ts > Tc, the effeets of chemical heat reléase 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 Tc< T„ < T„ the heat reléase 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 valúes of Tx 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 H2-02 autoignition.