A priori subgrid analysis of temporal mixing layers with evaporating droplets

Abstract

Subgrid analysis of a transitional temporal mixing layer with evaporating droplets has been performed using three sets of results from a direct numerical simulation (DNS) database, with Reynolds numbers (based on initial vorticity thickness) as large as 600 and with droplet mass loadings as large as 0.5. In the DNS, the gas phase is computed using an Eulerian formulation, with Lagrangian droplet tracking. The large eddy simulation (LES) equations corresponding to the DNS are first derived, and key assumptions in deriving them are first confirmed by using the DNS database. Since LES of this flow requires the computation of droplet source terms, it is essential to obtain the unfiltered gas-phase variables at droplet locations from filtered gas-phase variables at the grid points. This paper proposes to model these unfiltered gas-phase variables at the drop locations by assuming the gas-phase variables to be the sum of the filtered variables and a correction based on the filtered standard deviation; this correction is then computed from the subgrid scale (SGS) standard deviation. This model predicts the unfiltered variables at droplet locations considerably better than simply interpolating the filtered variables. Three methods are investigated for modeling the SGS standard deviation: the Smagorinsky approach, the gradient model and the scale-similarity formulation. When the proportionality constant inherent in the SGS models is properly calculated, the gradient and scale-similarity methods give results in excellent agreement with the DNS.