  In the context of many applications of turbulent multi-phase flows, knowledge
of the dispersed phase size distribution and its evolution is critical to
predicting important macroscopic features. We use a population dynamics model
for polydisperse droplet distributions specifically adapted to a LES framework
including a model for droplet breakup due to turbulence, neglecting
coalescence. Following earlier methods used in the Reynolds averaged
Navier--Stokes framework, the droplet breakup due to turbulent fluctuations is
modelled by treating droplet-eddy collisions as in kinetic theory of gases. 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. After initial comparisons of the
one-dimensional model to measurements of oil droplets in an axisymmetric jet,
it is then applied in a three-dimensional LES of a jet in crossflow with large
oil droplets of a single size being released at the source of the jet. We model
the concentration fields using $N_d =15$ bins of discrete droplet sizes and
solve scalar transport equations for each bin. The resulting droplet size
distributions are compared with published experimental data, and good agreement
for the relative size distribution is obtained. 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 behavior.
