Droplet-laden isotropic turbulence: from DNS to MANN-LES
The interaction of liquid droplets with turbulence is relevant to both environmental flows and engineering applications, e.g., rain formation and spray combustion. In this colloquium, I will present how we proceeded from studying the physical mechanisms of droplet/turbulence interaction via direct numerical simulation (DNS) to modeling such flow by creating the mixed artificial neural network (MANN) approach for large-eddy simulation (LES).
First, in order to perform DNS of droplet-laden decaying isotropic turbulence, we developed a new pressure-correction method, FastP*, for simulating incompressible two-fluid flows with large density and viscosity ratios between the two phases, coupled with a novel volume-of-fluid (VoF) method. Then, we performed DNS of finite-size droplets of diameter approximately equal to the Taylor length-scale of turbulence in decaying isotropic turbulence. We derived the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. This allowed us to explain the pathways for TKE exchange between the carrier turbulent flow and the flow inside the droplet. Next, we developed a new methodology for the spectral analysis of multiphase flows using wavelets. We proposed a decomposition of the wavelet energy spectrum into three contributions corresponding to the regions where the wavelet is entirely contained in the carrier phase, entirely contained in a droplet, or partially contained in both carrier and droplet fluids. Finally, via analysis of the DNS results both in physical and spectral space, the physical mechanisms we revealed helped us to propose a model for large-eddy simulation (LES) of such flow. The main challenge in creating LES models for this flow is that the presence of the droplets introduces additional subgrid-scale (SGS) closure terms to the filtered governing equations of motion. The results of a priori analysis showed that they are all significant enough to warrant modeling. Thus, we proposed a new modeling approach that we called mixed artificial neural network (MANN) LES because it is a mixed LES model that uses the standard Smagorinsky SGS stress model in the carrier flow, and artificial neural networks to predict the SGS closure terms at the interface. Furthermore, we have performed the first a posteriori analysis of such flow for droplets of different Weber numbers, and the results will be presented. Finally, the MANN LES approach could be applied to a variety of multiphase turbulent flows due to its ease of implementation, adaptability, and performance.
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 Baraldi A., Dodd M. & Ferrante A., "A mass-conserving volume-of-fluid method: volume tracking and droplet surface-tension in isotropic turbulence", Computers and Fluids, Vol. 96, pp. 322-337 (2014)
 Dodd M. & Ferrante A., "On the interaction of Taylor lengthscale size droplets and isotropic turbulence"
Journal of Fluid Mechanics, Vol. 806, pp. 356-412 (2016)
 Freund A. & Ferrante A., "Wavelet-spectral analysis of droplet-laden isotropic turbulence", Journal of Fluid Mechanics, Vol. 875, pp. 914-928 (2019)
 Freund A. & Ferrante A., "Large-eddy simulation of droplet-laden decaying isotropic turbulence using artificial neural networks", International Journal of Multiphase Flows, Vol. 142, pp. 1-25 (2021)