Bifurcation analysis of perfectly stirred reactors with large reaction mechanisms

An accurate characterization of new generation fuels gets through a definition of the ignition and extinction conditions. According to the terminology of non-linear analysis the ignition and extinction conditions (critical conditions) are defined as the turning-points on the S-curve and are uniquely identified by two saddle-node bifurcations. The exact location of the critical points that mark the ignition and extinction conditions, the onset of instabilities, as well as the dependence of the location on parameter values, cannot be obtained easily using temporal simulations tools. For a systematic and accurate analysis, the bifurcation analysis and the parametric continuation technique are the tools of choice. Even when the reactive mixture is described by a simple surrogate, but in conjunction with very complex and detailed chemical mechanism, the computation of the critical conditions become computationally very demanding. Usually, these difficulties are overcome by using reduced schemes and allowing simplifications in the model, like constant averaged thermodynamic properties. In this work we explore these issues. Particularly, we show that the adoption of a Broyden type corrector in the continuation algorithm leads to performances that made affordable the computations even with desktop computers. Consequently, we introduce a suitable algorithm to investigate ignition, extinction and linear stability of the air-fuel mixtures in a Perfectly Stirred Reactor (PSR). The algorithm is based on the well-known Keller pseudo-arclength continuation method in order to compute steady state solution curves. The solutions stability and then ignition and extinction states are identified by test functions based on the numerical eigenvalues of the Jacobian of the governing system of equations. The algorithm is implemented in the numerical computing environment Matlab coupled with the CANTERA Toolbox for managing of complex chemical kinetic mechanisms. The algorithm is thus easily applicable to chemical schemes available in the standard ChemKin format. To illustrate the capability of the resulting method, the characteristic S-Shaped curve, including non-stable branches, for several air-hydrocarbon mixtures have been computed.