Wavelet-spectral analysis and large-eddy simulation using neural networks of droplet-laden decaying isotropic turbulence

Abstract

In this work, we propose new methods for both the analysis and simulation of droplet-laden isotropic turbulence. First, we suggest using the wavelet energy spectrum to study multiphase turbulent flows to overcome the challenges of applying the Fourier energy spectrum to velocity fields with sharp velocity gradients. Also, we propose a new decomposition of the wavelet energy spectrum into three contributions corresponding to the carrier phase, droplets, and interaction between the two. We apply these new wavelet-decomposition tools in analyzing the direct numerical simulation (DNS) data of droplet-laden decaying isotropic turbulence of Dodd & Ferrante (2016, J. Fluid Mech. 806:356–412). Our results show that, in comparison to the spectrum of the single-phase case, the droplets (i) do not affect the carrier-phase energy spectrum at high wavenumbers (kₘ/kₘᵢₙ ≥ 128), (ii) increase the energy spectrum at high wavenumbers (kₘ/kₘᵢₙ ≥ 256) by increasing the interaction energy spectrum at these wavenumbers, and (iii) decrease the energy at low wavenumbers (kₘ/kₘᵢₙ ≤ 16) by increasing the dissipation rate at these wavenumbers. Then, 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 of Dodd & Ferrante, we analyze these terms a priori to show that they are all significant to warrant modeling. Then, we propose a new modeling approach that we call mixed-ANN (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 (ANNs) 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 with our wavelet analysis of the DNS data. 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.