We propose a model for large-eddy simulation (LES) of decaying isotropic turbulence laden with droplets with diameter of Taylor length-scale. The main challenge in creating LES models for such flow is that the presence of the droplets introduces additional subgrid-scale (SGS) closure terms to the filtered governing equations of motion of the flow. By processing available DNS data (Dodd & Ferrante, J. Fluid Mech. 806:356–412, 2016), we analyze these terms a priori to show that they are all significant enough to warrant modeling. Then, we propose a new modeling approach that we call mixed artificial neural network (MANN) LES because it is a mixed LES model that uses the standard Smagorinsky SGS stress model in the carrier fluid, and artificial neural networks to predict the SGS closure terms at the interface. Such an approach is justified because the SGS energy in the carrier flow away from the droplet interface is practically unaffected by the droplets, as we have previously shown using wavelet analysis of the DNS data (Freund & Ferrante, J. Fluid Mech. 875:914–928, 2019). Furthermore, we have performed the first a posteriori analysis of such flow for droplets of different Weber numbers, and show that our LES method closely reproduces the temporal decay of the filtered-velocity turbulence kinetic energy as well its p.d.f. of the filtered DNS, show that the modeling of the SGS terms at the interface is necessary for reproducing the results of the filtered DNS, and provide both physical- and spectral-space analysis of the LES results. Finally, the MANN LES approach could be applied to a variety of multiphase turbulent flows due to its ease of implementation, adaptability, and performance.

我们提出了一个大涡模拟 (LES) 模型，用于衰减各向同性湍流，该湍流带有泰勒长度尺度直径的液滴。为这种流动创建 LES 模型的主要挑战是，液滴的存在将额外的亚网格尺度 (SGS) 闭合项引入到过滤后的流动运动控制方程中。通过处理可用的 DNS 数据 (Dodd & Ferrante, J. Fluid Mech.  806:356–412, 2016)，我们先验地分析这些术语表明它们都足够重要以保证建模。然后，我们提出了一种新的建模方法，我们称之为混合人工神经网络 (MANN) LES，因为它是一种混合 LES 模型，它使用载液中的标准 Smagorinsky SGS 应力模型和人工神经网络来预测在界面。这种方法是合理的，因为远离液滴界面的载流子中的 SGS 能量实际上不受液滴的影响，正如我们之前使用 DNS 数据的小波分析所示 (Freund & Ferrante, J. Fluid Mech.  875:914 –928, 2019)。此外，我们已经执行了第一个后验对不同韦伯数液滴的这种流动的分析，并表明我们的 LES 方法密切地再现了过滤速度湍流动能的时间衰减及其过滤 DNS 的 pdf，表明界面处的 SGS 项的建模是重现过滤后 DNS 的结果所必需的，并提供 LES 结果的物理和频谱空间分析。最后，由于其易于实施、适应性和性能，MANN LES 方法可应用于各种多相湍流。