Investigation of deep learning-based filtered density function for large eddy simulation of turbulent scalar mixing

A filtered density function (FDF) model based on deep neural network (DNN), termed DNN-FDF, is introduced for large eddy simulation (LES) of turbulent flows involving conserved scalar transport. The primary objectives of this study are to develop the DNN-FDF models and evaluate their predictive capability in accounting for various filtered moments, including that of non-linear source terms. A systematic approach is proposed to select the DNN training sample size and architecture via learning curves to minimize bias and variance. Two DNN-FDF models are developed, one utilizing FDF data from direct numerical simulations (DNS) of constant-density temporal mixing layer and the other from zero-dimensional pairwise mixing stirred reactor simulations. The latter is particularly intended for cases where generating DNS data is computationally infeasible. DNN-FDF models are applied for LES of a variable-density temporal mixing layer. The accuracy and consistency of both DNN-FDF models are established by comparing their predicted filtered scalar moments with those of conventional LES, where moment transport equations are directly solved. The DNN-FDF models are shown to outperform a widely used presumed-FDF model, especially for multi-modal FDFs and higher variance values. Results are further assessed against DNS and the transported FDF method. The latter couples LES with Monte Carlo for mixture fraction FDF computation. Most importantly, the study shows that DNN-FDF models can accurately filter highly non-linear functions within variable-density flows, highlighting their potential for turbulent reacting flow simulations. Overall, the DNN-FDF approach is shown to offer an accurate yet computationally economical approach for describing turbulent scalar transport.