  We study the dispersion characteristics of slightly buoyant droplets in a
turbulent jet using large eddy simulations (LES). The droplet number density
fields are represented using an Eulerian approach with the dispersed phase
modelled using the Fast-Eulerian method (Ferry & Balachandar 2001) that
includes the droplet rise velocity. Radial concentration profiles and turbulent
concentration fluxes for droplets of different sizes are analyzed to quantify
the "trajectory crossing effect", when relative motions between particles and
turbulent eddies tend to reduce turbulent diffusion. For finer LES grid
resolutions, the model captures the differential, size based dispersion
characteristics of the droplets with the transverse dispersion of the larger
droplet sizes suppressed, since trajectory crossing effects are explicitly
resolved in LES. We examine a similarity solution model for the size dependent
radial concentration profiles based on a modified Schmidt number derived from
the theory of turbulent diffusion of particles in the atmosphere proposed by
Csanady 1963. The results are validated with the high resolution LES data and
show good agreement. Then, the size dependent Schmidt number model is
reformulated as a model for unresolved subgrid-scale trajectory crossing
effects and used to calculate the subgrid concentration flux in a coarse LES of
a turbulent jet, with slightly buoyant droplets injected at the centerline in
the self-similar region of the jet. The results are compared to a simulation
with higher grid resolution and a coarse simulation with a constant Schmidt
number SGS model. We find that the subgrid model enhances the prediction
accuracy of the concentration profiles and turbulent concentration flux for the
coarse LES.
