Dimensionality Estimate of the Manifold in Chemical Composition Space for a Turbulent Premixed H2+air Flame

The dimensionality (D) of manifolds of active chemical composition space has been measured using three different approaches: the Hausdorff geometrical binning method, Principal Component Analysis, and the Grassberger-Procaccia cumulative distribution method. A series of artificial manifolds is also generated using a Monte Carlo approach to discern the advantages and limitations of the three methods. Dimensionality is quantified for different levels of turbulent intensity in a simulation of the interactions of a 2D premixed hydrogen flame with a localized region of turbulence superimposed over the cold region upstream of the flame front. The simulations are conducted using an adaptive mesh refinement code for low Mach number reacting flows. By treating the N_s species and temperature of the local thermo-chemical state as a point in multidimensional chemical composition space, a snapshot of a flame region is mapped into chemical composition space to generate the manifold associated with the 2-D flame system. An increase in D was observed with increasing turbulent intensity for all three methods. Although each method provides useful information, the Grassberger-Procaccia method is subject to fewer artifacts than the other two thereby providing the most reliable quantification of D.