Studying the Evolution of Polydisperse Droplet Size Distributions Using Large Eddy Simulations

We develop a Large Eddy Simulation (LES) model that can predict the turbulent transport and evolution of droplet size distributions, for a specific subset of applications in which the dispersed phase can be assumed to consist of spherical droplets, at low volume fraction. We use a population dynamics model for polydisperse droplets specifically adapted to a LES framework including a model for droplet breakup due to turbulence, neglecting coalescence consistent with the assumed small dispersed phase volume fractions. Existing breakup models assume the scale of droplet--eddy collision to be in the inertial range of turbulence. In order to also model smaller droplets comparable to or smaller than the Kolmogorov scale we extend the breakup kernels using a structure function model that smoothly transitions from the inertial to the viscous range. The model includes a dimensionless coefficient that is fitted by comparing predictions in a one-dimensional version of the model with a laboratory experiment of oil droplet breakup below breaking waves. The LES model is applied to a three-dimensional turbulent jet subjected to a uniform crossflow and droplet size distributions downstream of the injection are compared with experimental data with good agreement. The LES results also enable us to quantify size distribution variability. We find that the probability distribution functions of key quantities such as the total surface area and the Sauter mean diameter of oil droplets are highly variable, some displaying strong non-Gaussian intermittent behaviour. Further applications with smaller nozzles require an inlet conditions for coarse LES. We develop a hybrid approach where the inlet condition is prescribed using a one dimensional (1D) parcel model that accounts for the evolution of the dispersed phase along the jet centerline due to the combined effects of advection, radial turbulent transport and droplet breakup. We examine the statistics of the velocity field and the concentration profiles of the polydisperse oil droplet plumes for two droplet Weber numbers. We find that the centerline decay rate of the droplet concentration is modified in the breakup dominated zone. Additionally due to trajectory crossing effects the dispersion of larger droplets is suppressed