Modelling of the Evolution of a Droplet Cloud in a Turbulent Flow

In this work we examine the effect of turbulent mixing on the droplet number density for a cloud of droplets dispersing in a turbulent flow field. The Lagrangian droplets are assumed to be transported and dispersed by the large scale structures of a resolved field. However, turbulent fluctuations not visible to the filtered solution induce unresolved dispersion of droplets within a droplet cloud. The Fully Lagrangian Approach (FLA) is used to model resolved droplet dispersion. A model is presented for the prediction of the unresolved turbulent mixing of the droplet number density for a droplet cloud. This model takes into account the turbulent flux for the droplets permeating the surface of the cloud via turbulent diffusion. Turbulent diffusion is assumed to be driven by the kinetic energy of the droplet fluctuations induced by the turbulent kinetic energy of the carrier phase. This assumption is supported by Direct Numerical Simulations (DNS) of homogeneous and isotropic turbulence. Additionally, DNS of transition of a planar jet to turbulence is used for the assessment of the mixing model which we use. The calculation of the spatial derivatives for the droplet number densities is performed by projecting the FLA solution on the Eulerian mesh, resulting in a hybrid Lagrangian-Eulerian approach to the problem.