Extrapolation Performance of Convolutional Neural Network-Based Combustion Models for Large-Eddy Simulation: Influence of Reynolds Number, Filter Kernel and Filter Size

Abstract

The extrapolation performance of Convolutional Neural Network (CNN)-based models for Large-Eddy Simulations (LES) has been investigated in the context of turbulent premixed combustion. The study utilises a series of Direct Numerical Simulation (DNS) datasets of turbulent premixed methane/air and hydrogen/air jet flames to train the CNN models. The methane/air flames, which are characterised by increasing Reynolds numbers, are used to model the subgrid-scale flame wrinkling. The hydrogen/air flame, exhibiting complex thermodiffusive instability, is employed to test the ability of the CNN-based combustion models to predict the filtered progress variable source term. This study focuses on the influence of varying training Reynolds numbers, filter sizes, and filter kernels to evaluate the performance of the CNN models to out-of-sample conditions, i.e., not seen during training. The objectives of this study are threefold: (i) analyse the performance of CNN models at different Reynolds numbers compared to the one trained with; (ii) analyse the performance of CNN models at different filter sizes compared to the one trained with; (iii) assess the influence of using different filter kernels (i.e., Gaussian and box filter kernels) between training and testing, to emulate a posteriori applications. The results demonstrate that the CNN models show good extrapolation performance when the training Reynolds number is sufficiently high. Vice versa, when CNN models are trained on low-Reynolds-number flame data, their performance degrades as they are applied to flames with progressively higher Reynolds numbers. When these CNN models are tested on datasets with filter sizes not included in the training process, they exhibit sufficient interpolation capabilities, the extrapolation performance is less precise but still satisfactory overall. This indicates that CNN models can be effectively trained using data filtered with a limited range of filter sizes and then successfully applied across a broader spectrum of filter sizes. Furthermore, when CNNs trained on box-filtered data are applied to Gaussian-filtered data, or vice versa, the models perform well for smaller filter sizes. However, as the filter size increases, the accuracy of the predictions diminishes. Interestingly, increasing the quantity of training data does not significantly enhance model performance. Yet, when training data are distributed with greater weighting towards larger filter sizes, the model’s overall performance improves. This suggests that the strategic selection and weighting of training data can lead to more robust generalization across different filter conditions.