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 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.

翻译：提出了一种基于深度神经网络（DNN）的滤波密度函数（FDF）模型，称为DNN-FDF，用于涉及守恒标量输运的湍流大涡模拟（LES）。本研究的主要目标是开发DNN-FDF模型，并评估其在计算包括非线性源项在内的各种滤波矩时的预测能力。提出了一种系统方法，通过学习曲线选择DNN训练样本大小和架构，以最小化偏差和方差。开发了两个DNN-FDF模型：一个利用常密度时间混合层直接数值模拟（DNS）的FDF数据，另一个利用零维成对混合搅拌反应器模拟数据。后者特别适用于生成DNS数据在计算上不可行的情况。将DNN-FDF模型应用于变密度时间混合层的LES。通过比较预测的滤波标量矩与直接求解矩输运方程的传统LES结果，验证了两种DNN-FDF模型的准确性和一致性。结果表明，DNN-FDF模型优于广泛使用的假定FDF模型，特别是在多模态FDF和高方差值情况下。进一步的结果评估基于DNS和输运FDF方法，后者将LES与蒙特卡洛方法结合用于混合物分数FDF计算。最重要的是，研究表明DNN-FDF模型能够准确滤波变密度流场中的高度非线性函数，凸显了其在湍流反应流模拟中的潜力。总体而言，DNN-FDF方法为描述湍流标量输运提供了一种准确且计算经济的途径。