Direct numerical simulation and subgrid analysis of a transitional droplet laden mixing layer

Abstract

Direct numerical simulations of a temporally developing, droplet laden mixing layer undergoing transition to mixing turbulence are conducted. The formulation includes complete two-way couplings of mass, momentum, and energy. As many as 18×106 grid points are used to discretize the Eulerian gas phase equations and up to 5.7×106 initially polydisperse evaporating droplets are tracked in the Lagrangian reference frame. The complete transition to mixing turbulence is captured for several of the higher Reynolds number simulations and it is observed that increasing the droplet mass loading ratio results in a more “natural” turbulence characterized by increased rotational energy and less influence of the initial forcing perturbations. An increased mass loading also results in increased droplet organization within the layer. An a priori subgrid analysis is then conducted which shows that neglecting subgrid velocity fluctuations in the context of large eddy simulations may result in significant errors in predicting the droplet drag force for Stokes numbers St∼1 (with the flow time scale based on the mean velocity difference and initial vorticity thickness). Similar possible errors of lesser magnitude are also observed for the droplet heat flux and evaporation rate when thermodynamic subgrid fluctuations are neglected. An extension of the eddy interaction model commonly used in Reynolds-averaged simulations is then proposed in order to account for the missing subgrid information. Probability density functions (PDFs) of the subgrid fluctuations calculated across homogeneous planes are shown to be highly intermittent, particularly near the laminar–turbulent boundaries of the mixing layer. However, the actual subgrid PDFs calculated locally are much less intermittent and may be adequately modeled by the Gaussian distribution throughout the majority of the mixing layer. A scale similarity model is then employed to predict both the velocity and thermodynamic subgrid variances. The similarity model is well correlated with the actual subgrid variances and shows good agreement in predicting the local fluctuation intensities when a filter width-dependent model constant is used. The subgrid fluctuation variances acting on the droplets are then shown to be well modeled if the Eulerian subgrid variance model is interpolated to the droplet locations.