Augmenting filtered flame front displacement models for LES using machine learning with a posteriori simulations

The Flame Surface Density (FSD) model is an affordable combustion model that has been widely used in simulating turbulent premixed flames. In Large Eddy Simulations (LES) with FSD, the combined effect of reaction and diffusion is governed by the Filtered Flame Front Displacement (FFFD) term. While the existing modelling approaches for this term are computationally cost-effective, their predictions still show inconsistencies in certain cases. This study aims to address these inconsistencies by generating Machine Learning (ML) models for the FFFD and FSD terms using the DNS data of a turbulent premixed jet flame. With this approach, the relevance of certain input parameters as well as certain modelling assumptions used for the FFFD term are assessed. Overall, it is found that the resolved curvature term is the most important input parameter to consider and that the resolved progress variable should also be considered in the models. It is shown that the ML models perform significantly better than legacy, algebraic formulations using a priori testing. To further assess the performance of ML, one of the ML models is employed in a a posteriori LES and compared against simulations with the algebraic model. The ML simulation is stable and yields encouraging improvements on key physical parameters regarding the flame length and the FFFD distribution.

Novelty and Significance Statement: This research is of importance because it answers fundamental and practical questions related to the use of combustion modelling approaches, specifically the Flame Surface Density (FSD) and the Filtered Flame Front Displacement (FFFD) models, by means of Machine Learning (ML) algorithms. From a fundamental aspect, we show that two features which are typically not considered as inputs in combustion models, i.e., the progress variable and the resolved curvature, are key to consider for improved predictions of the model, more so than features which are typically used in FSD modelling, i.e., $u_{\Delta }^{\prime },\Delta ,$ and $|\nabla \overline{c}|$. From a practical standpoint, we demonstrate a framework to use the developed ML combustion model a posteriori in a LES, without any stability issues. Overall, these findings are key to guide further traditional and ML improvement efforts on combustion models.