Two-parameter continuation algorithms for sensitivity analysis, parametric dependence, reduced mechanisms, and stability criteria of ignition and extinction

A two-parameter continuation algorithm is developed for combustion processes which can calculate exact (within some tolerance) ignition and extinction conditions and provide sensitivity of ignition and extinction; solutions on chemical and transport/fluid mechanics parameters. In addition, two-parameter bifurcation diagrams of ignition and extinction conditions versus any parameter (e.g., pressure) can be computer-generated. The new algorithm surmounts limitations of previous simulations, where approximate critical conditions for flame stability were determined, and extends sensitivity of regular solutions to critical solutions having a singular Jacobian. In conjunction with principal component analysis, this algorithm provides a systematic methodology for mechanism reduction at ignition and extinction. As an example, this methodology is applied to ignition and extinction of hydrogen/air mixtures in a jet-stirred reactor. Important reactions at ignition, extinction, and for flame multiplicity are identified. Two minimal schemes of six reactions are found to lead to flame multiplicity. The validity of quasi-steady-state approximation for all species at ignition and extinction is also examined as a function of pressure. For example, it is shown that on the second branch of the pressure-temperature (P-T) ignition diagram, H, O, and OH are in quasi-steady-state. Predictions from proposed ignition and extinction criteria are in good agreement with detailed kinetics simulations. (C) 1998 by The Combustion Institute.