Acceleration of turbulent combustion simulation through principal components transport and machine learning

The dimensionality reduction of the combustion thermochemical state space using principal component analysis (PCA) can yield a significant reduction in the variables of this space. In this study, we investigate the potential of accelerating direct numerical simulations (DNS) in turbulent combustion by the solution of transport equations for the principal components (PCs) of the combustion state space and machine learning to evaluate their chemical source terms and transport coefficients. A reduced set of transport equations for these PCs is used instead of the transport equations for the thermo-chemical scalers (species and energy) as in a traditional DNS. The data needed for the determination of the PCs and their chemical and transport terms is based on a lower-dimensional and smaller domain DNS data spanning the desired composition space. PCA is performed on this data and the desired number of PCs is determined. Moreover, this data is used to determine the chemical source terms and the PCs diffusion coefficients. These quantities are modeled in terms of the transported PCs using artificial neural networks (ANN). The formulation is implemented for a premixed methane-air flame in a three- dimensional slot- bunsen burner. Fluid flow and premixed combustion statistics of DNS based on the PC transport show an agreement with the statistics of DNS of the full thermo-chemical state. Moreover, the results show a two order reduction in the computational cost of the simulation, thus enabling the extension of the simulation to a larger computational domain with complex reaction mechanisms.