RESUMO
Detailed chemical kinetics typically involve a large number of chemical species and a wide range of time scales. In calculations of chemically reactive flows, dimension-reduction techniques can be used to reduce the computational burden imposed by the direct use of detailed chemistry. In the reduced description, the reactive system is described in terms of a smaller number of reduced composition variables (e.g., some "major" species) instead of the full set of chemical species. Reactive flows exhibiting complex dynamics are especially challenging for dimension-reduction techniques and therefore provide more rigorous validation for such methods. Following the work of Brad et al. [Proc. Combust. Inst. 2007, 31, 455],1 in this paper, we demonstrate the capability of the Invariant Constrained-equilibrium Edge Pre-Image Curve (ICE-PIC) dimension-reduction method [J. Chem. Phys. 2006, 124, Art. No. 114111]2 through calculations of the oxidation of a CO/H2 mixture in a continuously stirred tank reactor (CSTR) at low pressure. The detailed chemical kinetics employed involves 11 species and 33 reactions. The system exhibits complex dynamics such as oscillatory ignition, oscillatory glow, and mixed mode oscillations. It is demonstrated that with five represented species the reduced description provided by the ICE-PIC method is able to quantitatively reproduce the observed complex dynamics. Moreover, the reduced description accurately predicts the boundaries of slow reaction, oscillatory ignition and the steady ignited state.
RESUMO
This work addresses the construction and use of low-dimensional invariant manifolds to simplify complex chemical kinetics. Typically, chemical kinetic systems have a wide range of time scales. As a consequence, reaction trajectories rapidly approach a hierarchy of attracting manifolds of decreasing dimension in the full composition space. In previous research, several different methods have been proposed to identify these low-dimensional attracting manifolds. Here we propose a new method based on an invariant constrained equilibrium edge (ICE) manifold. This manifold (of dimension nr) is generated by the reaction trajectories emanating from its (nr-1)-dimensional edge, on which the composition is in a constrained equilibrium state. A reasonable choice of the nr represented variables (e.g., nr "major" species) ensures that there exists a unique point on the ICE manifold corresponding to each realizable value of the represented variables. The process of identifying this point is referred to as species reconstruction. A second contribution of this work is a local method of species reconstruction, called ICE-PIC, which is based on the ICE manifold and uses preimage curves (PICs). The ICE-PIC method is local in the sense that species reconstruction can be performed without generating the whole of the manifold (or a significant portion thereof). The ICE-PIC method is the first approach that locally determines points on a low-dimensional invariant manifold, and its application to high-dimensional chemical systems is straightforward. The "inputs" to the method are the detailed kinetic mechanism and the chosen reduced representation (e.g., some major species). The ICE-PIC method is illustrated and demonstrated using an idealized H2O system with six chemical species. It is then tested and compared to three other dimension-reduction methods for the test case of a one-dimensional premixed laminar flame of stoichiometric hydrogen/air, which is described by a detailed mechanism containing nine species and 21 reactions. It is shown that the error incurred by the ICE-PIC method with four represented species is small across the whole flame, even in the low temperature region.
