Deep learning has recently emerged as a successful approach to produce accurate subgrid-scale (SGS) models for Large Eddy Simulations (LES) in combustion. However, the ability of these models to generalize to configurations far from their training distribution is still mainly unexplored, thus impeding their application to practical configurations. In this work, a convolutional neural network (CNN) model for the progress-variable SGS variance field is trained on a canonical premixed turbulent flame and evaluated a priori on a significantly more complex slot burner jet flame. Despite the extensive differences between the two configurations, the CNN generalizes well and outperforms existing algebraic models. Conditions for this successful generalization are discussed, including the effect of the filter size and flame–turbulence interaction parameters. The CNN is then integrated into an analytical reaction rate closure relying on a single-step chemical source term formulation and a presumed beta PDF (probability density function) approach. The proposed closure is able to accurately recover filtered reaction rate values on both training and generalization flames.

Subgrid-scale flame wrinkling is a key unclosed quantity for premixed turbulent combustion models in large eddy simulations. Due to the geometrical and multi-scale nature of flame wrinkling, convolutional neural networks are good candidates for data-driven modeling of flame wrinkling. This chapter presents how a deep convolutional neural network called a U-Net is trained to predict the total flame surface density from the resolved progress variable. Supervised training is performed on a database of filtered and downsampled direct numerical simulation fields. In an a priori evaluation on a slot burner configuration, the network outperforms classical dynamic models. In closing, challenges regarding the ability of deep convolutional networks to generalize to unseen configurations and their practical deployment with fluid solvers are discussed.

No abstract

A probabilistic data-driven approach that models the filtered reaction rate in large-eddy simulation (LES) is investigated. We propose a novel framework that incorporates a conditional generative adversarial network and a Gaussian mixture model to take into account the statistical fluctuations that are present in LES of turbulent reacting flows due to non-resolved subgrid structures, which cannot be predicted by purely deterministic models and machine learning algorithms. The data from a direct numerical simulation of turbulent premixed combustion are spatially filtered using a wide range of filter widths and employed for the training. We extract physically relevant parameters from the database and reduce the input features to the network to the most influential ones based on the result of feature importance analysis. The trained model is then tested on unseen timesteps and untrained LES filter widths, where it is able to accurately predict the distribution of the filtered reaction rate.