Edge flame propagation statistics in igniting monodisperse droplet-laden mixtures

Abstract

The effects of droplet diameter, overall (i.e., liquid+gaseous phases) equivalence ratio, and turbulence intensity on the edge flame propagation statistics for localized forced ignition of uniformly dispersed n-heptane droplet-laden mixtures under homogeneous isotropic decaying turbulence have been analyzed based on direct numerical simulations data. It has been found that the edge flame structure becomes increasingly prominent for large overall equivalence ratios and droplet diameters. Although the mean edge flame speed has been found to be positive and its most probable value remains comparable to the theoretical value for laminar edge flames in purely gaseous mixtures, the mean values have been found to decrease and the probabilities of finding locally negative edge flame speeds have been found to increase with increasing turbulence intensity. The marginal probability density function and curvature and strain rate dependences of the edge flame speed have been found to be principally governed by the displacement speed of the fuel mass fraction isosurface intersecting the stoichiometric mixture fraction isosurface. The displacement speed of the stoichiometric mixture fraction isosurface has also been found to influence the local scalar gradient dependences of the edge flame speed in this configuration, especially for large droplets. The displacement speed of the fuel mass fraction isosurface Sd has been found to be principally governed by leading order contributions of the reaction and molecular diffusion components and the evaporation contribution remains weak in comparison to these leading order contributors. The local edge flame speed exhibits nonlinear curvature and strain rate dependences and its variation with the magnitudes of both fuel mass fraction and mixture fraction gradients has been found to be nonmonotonic for all cases considered here. The correlations of the edge flame speed with curvature, strain rate, and scalar gradient have been found to be qualitatively similar to the corresponding statistics reported in the existing literature for edge flames in purely gaseous mixtures. Additionally, the curvature and tangential strain rate dependences of the edge flame speed have been found to be dependent on the droplet size and overall equivalence ratio, and these dependences become weak for cases with large droplets.