Analysis and Interpretation of Data-Driven Closure Models for Large Eddy Simulation of Internal Combustion Engine

We present an automatic data-driven machine learning (ML) approach for the development, evaluation and interpretation of deep neural networks (DNNs) for turbulence closures and demonstrate their usage in the context of cold-flow large-eddy simulation (LES) of the four-stroke Darmstadt engine using an open-source compressible multi-dimensional CFD solver OFICE, in a hybrid PDE-ML framework. Rather than explicitly using canonical formulations of closure terms, these DNNs robustly discover the functional relationships between the large-scale features of the resolved flow (cell Re, strain and rotation rate tensors etc.) obtained by solving the Navier Stokes to the small-scale unresolved terms. Experimentally validated high-fidelity LES solutions of the engine at different crank angles are utilized as the ground truth to train the DNN based closure models. Since optimizing these DNNs can be a laborious process for scientific datasets, and often require specialized expertise, we propose a Bayesian optimization framework that automatically determines the best set of network parameters, including the architecture and training hyperparameters - batch size, regularization etc. for optimum performance. We compare and contrast various networks for their effectiveness in an a-priori testing setting. Finally, the best ‘learnt’ network is integrated with the open-source CFD solver (OFICE), and solutions are obtained over several injection cycles. These experiments reveal that the DNN models temporally track resolved scalar variance with a good accuracy. Additionally, we interpret the artificial neural networks with sensitivity analysis to determine the relevant large-scale features for the learning process.