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The statistical behaviors of the magnitude of the reaction progress variable gradient (alternatively known as the Surface Density Function (SDF)) and the strain rates, which affect the SDF evolution, have been analyzed using three-dimensional Direct Numerical Simulations (DNS) of spherically expanding flames in globally stoichiometric initially mono-sized droplet-laden mixtures for different initial turbulence intensities and droplet diameters. It has been found that gaseous phase combustion predominantly takes place under fuel–lean mode and this tendency strengthens for large droplets and high turbulence intensities. The mean values of flame displacement speed, dilatation rate and normal strain rate decrease with increasing turbulence intensity and droplet diameter. By contrast, the mean tangential strain rate increases with increasing turbulence intensity for all droplet diameters. The mean normal strain rate induced by flame propagation remains negative but its magnitude decreases with increasing droplet size and turbulence intensity. The mean tangential strain rate induced by flame propagation (alternatively curvature stretch rate) assumes negative values except for the laminar flame with small droplets. The mean effective normal strain rate has been found to assume predominantly positive values and increases with increasing turbulence intensity for the droplet cases considered here. The mean effective tangential strain rate (alternatively stretch rate) is found to assume mostly negative values except for the laminar case with small droplets. The mean effective tangential strain rate decreases with increasing droplet size, which leads to a smaller extent of flame surface area generation for flames with larger droplets.

Surface Density Function Evolution in Spherically Expanding Flames in Globally Stoichiometric Droplet-laden Mixtures