Numerical Strategies for Detection of Bifurcation Points in the Parametric Continuation of Model Reactors with Detailed Chemical Mechanisms

Limit combustion phenomena, such as ignition, are rather sensitive to chemical kinetics and these properties are therefore used to physically characterize the behaviour of dierent fuels. In the framework of bifurcation theory, ignition and extinction phenomena for combustion correspond to saddle-node bifurcation points and lead to the classical S-shaped steady-state curve. Then, the location of ignition and extinction conditions and their dependence on the main parameters (like pressure, equivalence ratio, residence time or inlet temperature in reactors) can be reformulated as a problem of bifurcation analysis. Even when the reactive mixture is described by a simple fuel surrogate, in conjunction with very complex and detailed chemical mechanism, with several hundreds of species and thousands of chemical reactions, the computation of the bifurcation diagram becomes computationally very demanding. In this work we explore this issue. The several steps required to formulate a complete continuation algorithm are analysed from a computational point of view and convenient formulations or approaches are introduced to make viable this kind of analysis even adopting desktop class computers. It is shown that a proper selection of the algorithms for the computation of the stability properties of the bifurcation points can accelerate the identification of ignition and extinction states. The algorithm is implemented in Matlab coupled with the CANTERA Toolbox for managing of complex chemical kinetic mechanisms and species properties. The algorithm is thus easily applicable to chemical schemes available in the standard CHEMKIN format. To demonstrate the capability of the resulting method, the characteristic S-Shaped curve, including non-stable branches, is computed for different Air-Jet Fuel surrogate mixtures.