Data-driven Learning of Unsteady Flamelet Progress Variable Manifolds via Hierarchical Clustering and Grouped Multi-Target Artificial Neural Networks

In this work, a data-driven framework is presented with the goal of replacing tabulation of multidimensional unsteady flamelet progress variable (UFPV) manifolds with deep learning models for computational fluid dynamics (CFD) simulations of turbulent reacting flows. Tabulated flamelet combustion models require accessing lookup tables and performing interpolation for online retrieval of quantities of interest (thermochemical scalars, PV source term, etc.), at the cost of high memory footprint. The data-driven approach is divided into two parts: a) grouping together strongly correlated chemical species using hierarchical clustering, and b) training a separate artificial neural network (ANN) to infer species mass fractions within each cluster. A separate ANN is trained for predicting the PV source term. For a priori demonstration of the proposed approach, a 4D UFPV lookup table (containing 25 species) generated from methane/air counterflow flame simulations at constant pressure is employed. Sensitivity studies are carried out with respect to the number of clusters, wherein the impact of clustering on the predictive accuracy of ANNs is evaluated against a baseline case with no clustering for species. Additionally, with regard to the prediction of species mass fractions within individual clusters, hyperparameter tuning indicates that having a separate hidden layer for each species before the output layer improves ANN accuracy.