A combined stability‐sensitivity analysis of weak and strong reactions of hydrogen/oxygen mixtures

Stability and sensitivity analysis are used to examine the ignition/reaction characteristics of dilute hydrogen‐oxygen mixtures. The analysis confirms the existence of two distinct regions of ignition and fast reaction previously labeled “weak” and “strong” ignition, both of which are located in the explosive pressure‐temperature domain and separated by a region related to the “extended” classical second limit. The stability analysis is based on an eigenanalysis of the Green's function matrix of the governing kinetic equations. The magnitudes of the largest (and system controlling) eigenvalue allow the strengths of the two processes to be quantified, giving a clear definition to the terms “weak” and “strong.” The sensitivities of the largest eigenvalue to the reaction rate constants of the mechanism pinpoint the elementary steps controlling the two ignition processes and the subsequent reaction. The associated eigenvectors yield the direction of change in species concentrations and temperature during the course of reaction. These vectors are found to be nearly constant during the induction period of both “weak” and “strong.” ignition, thus producing constant overall stoichiometric reactions. The subsequent reaction of major reactants associated with “weak” ignition also has a constant overall reaction vector, although, different than that during the induction period. However, the vector describing the reaction of major reactants associated with “strong.” ignition is found never to be constant, but continuously changing beyond the induction period.