Population Balance Modeling to study evolution of jet with polydisperse oil droplets in a Large Eddy Simulation framework*

In the context of oil spills, knowledge of the dispersed phase droplet size distribution and its evolution is critical to predict many macroscopic features. We adopt a population dynamics model for polydisperse droplet size distributions in a Large Eddy Simulation framework. This allows us to study the evolution of the number density of droplets due to convection, breakup and coalescence. Modeling breakup based on turbulent fluctuations and collisions is a major mechanism that has been adopted in the literature, in which the breakup occurs primarily due to the bombardment of droplets by turbulent eddies. Existing models assume the scale of droplet-eddy collision to be in the inertial scale of turbulence. In this work we extend the breakup kernels to the entire spectrum of turbulence using generalized structure functions. As a flow application for LES we consider a jet in crossflow with oil being released at the source of the jet. We model the concentration fields of the droplets using an Eulerian approach. We compare the droplet size distribution obtained from our simulations with published experimental data.