Large-eddy simulation of droplet-laden decaying isotropic turbulence using artificial neural networks

Abstract

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.