Reduced-order PCA models for chemical reacting flows

One of the most challenging aspects of turbulent combustion research is the development of reduced-order combustion models which can accurately reproduce the physics of the real system. The identification and utilization of the low dimensional manifolds in these system is paramount to understand and develop robust models which can account for turbulence-chemistry interactions. Recently, principal components analysis (PCA) has been given notable attention in its analysis of reacting systems, and its potential in reducing the number of dimensions with minimum reconstruction error. The present work provides a methodology which has the ability of exploiting the information obtained from PCA. Two formulations of the approach are shown: Manifold Generated from PCA (MG-PCA), based on a global analysis, and Manifold Generated from Local PCA (MG-L-PCA), based on performing the PCA analysis locally. The models are created using the co-variance matrix of a data-set which is representative of the system of interest. The reduced models are then used as a predictive tool for the reacting system of interest by transporting only a subset of the original state-space variables on the computational grid and using the PCA basis to reconstruct the non-transported variables. The present study first looks into the optimal selection of the subset of transported variables and analyzes the effect of this selection on the approximation of the state space and chemical species source terms. Then, a demonstration of various a posteriori cases is presented.