Deep learning modeling of the filtered generalized progress variable dissipation rate in turbulent premixed combustion

Abstract

Turbulent combustion models can be made more computationally efficient by projecting the thermochemical state onto a lower-dimensional space. In premixed combustion, a one-dimensional space in generalized progress variable can be utilized, and the thermochemical state can be reconstructed from a set of manifold equations in the generalized progress variable. The generalized progress variable dissipation rate appears as a key parameter in these manifold equations but is extremely challenging to model from a physics-based perspective. To model this generalized progress variable, a data-based perspective is instead pursued, leveraging a machine learning approach using deep neural networks (DNNs). However, the selection of appropriate network architecture and hyperparameters remains a challenge when utilizing a DNN model, so an automated approach that selects the optimal architecture for the DNN would be useful to eliminate ad hoc hand-tuning and ease the integration of DNNs with Computational Fluid Dynamics (CFD) solvers. In this work, four approaches are compared for determining the optimal DNN architecture: (1) a computationally expensive but thorough Grid Search, (2) a Random Search, (3) Bayesian Optimization, and (4) an Adaptive Approach that approximates the model error with a power law fit with respect to the model hyperparameters. Bayesian Optimization tends to provide the best balance between training time and network size (computational cost of DNN evaluation in CFD), but the Adaptive Approach also provides attractive training times, albeit with a bias toward larger networks. A priori evaluations showed that the data-based model is able to capture the physical structure of the turbulent flame and the profiles of key statistics when generalized to new data. An a posteriori evaluation of the data-based model is currently a work in progress as there is difficulty in obtaining a stable simulation of a flame in the baseline case of LES (without the data-based model implemented). Subroutines of the data-based model implemented into NGA are in development but cannot be tested until the baseline case is successful. Future work continuing this study will focus on completing this a posteriori evaluation.