Investigation of Deep Learning-Based Filtered Density Function for Large Eddy Simulation of Turbulent Scalar Mixing

The present investigation focuses on the application of deep neural network (DNN) models to predict the filtered density function (FDF) of mixture fraction in large eddy simulation (LES) of variable density mixing layers with conserved scalar mixing. A systematic training method is proposed to select the DNN-FDF model training sample size and architecture via learning curves, thereby reducing bias and variance. Two DNN-FDF models are developed: one trained on the FDFs generated from direct numerical simulation (DNS), and another trained with low-fidelity simulations in a zero-dimensional pairwise mixing stirred reactor (PMSR). The accuracy and consistency of both DNN-FDF models are established by comparing their predicted scalar filtered moments with those of conventional LES, in which the transport equations corresponding to these moments are directly solved. Further, DNN-FDF approach is shown to perform better than the widely used $\beta$-FDF method, particularly for multi-modal FDF shapes and higher variances. Additionally, DNN-FDF results are also assessed via comparison with data obtained by DNS and the transported FDF method. The latter involves LES simulations coupled with the Monte Carlo (MC) methods which directly account for the mixture fraction FDF. The DNN-FDF results compare favorably with those of DNS and transported FDF method. Furthermore, DNN-FDF models exhibit good predictive capabilities compared to filtered DNS for filtering of highly non-linear functions, highlighting their potential for applications in turbulent reacting flow simulations. Overall, the DNN-FDF approach offers a more accurate alternative to the conventional presumed FDF method for describing turbulent scalar transport in a cost-effective manner.