Identification and Parameterization of Low-Dimensional Manifolds in Turbulent Flames

Novel methodology based on Principal Component Analysis (PCA) was developed for the identification of the low-dimensional manifold of a chemical reacting system, the determination of its dimensionality and the selection of optimal reaction variables. Results are presented for a simple CO/H2 jet flame and for a CH4 piloted flame (TNF Flame F). Results of the global PCA analysis (GPCA) on the whole data sets show that, in all cases, the number of modes required to reproduce the different state variables is a strong function of the physical processes by which the variables themselves are affected. As a result, a greater dimensionality is observed for the piloted flame, characterized by significant extinction. A local PCA (LPCA) algorithm, VQPCA, was also employed to reduce the effect of non-linear dependencies among state variables on the manifold dimension determination. By applying VQPCA, the data were divided into separated clusters, by using an unsupervised partitioning algorithm based on reconstruction error minimization. Also, results from VQPCA were compared with those obtained with an approach based on mixture fraction conditioning (FPCA). Both approaches are comparable for the CO/H2/N2 flame, while VQPCA performances are superior to FPCA for the CH4 flame, due to its higher complexity.