Species reconstruction using pre-image curves

All chemistry dimension-reduction methodologies, such as quasi-steady-state approximation (QSSA), rate-controlled constrained equilibrium (RCCE), and intrinsic low-dimensional manifolds (ILDM), either implicitly or explicitly, provide a means of species reconstruction. Given a reduced description of the chemical composition (e.g., in terms of some ‘‘major’’ species), species reconstruction is a procedure to estimate the full composition. In this paper, we develop and demonstrate a new species reconstruction methodology, which is based on a pre-image curve of the reaction mapping. By definition, in the composition space, if a reaction trajectory is followed from any point on the pre-image curve, then at some time the reduced composition on the trajectory intersects the given reduced composition. The reconstructed composition is taken to be the full composition on the reaction trajectory at this intersection. The method is tested for a case of methane autoignition in which the detailed mechanism has 27 degrees of freedom, and two reduced descriptions are considered with 4 and 6 degrees of freedom. It is shown that the normalized reconstruction errors are very small; they are two orders of magnitude smaller than those in RCCE; and with 6 degrees of freedom they are smaller than those in QSSA with 12 degrees of freedom. The reconstructed compositions (for all reduced compositions) form the reconstructed manifold. It is shown that, to an excellent approximation, this manifold is inertial (i.e., it is composed of reaction trajectories). In comparison to other dimension-reduction methodologies, this is the first approach which determines, locally, points on a low-dimensional inertial manifold. The combination of in situ adaptive tabulation and species reconstruction can be used to reduce substantially the computational cost of applying detailed chemistry to turbulent combustion calculations. 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.