  A population balance model coupled with large eddy simulations (LES) is
adapted and applied to study the evolution of oil droplets in a turbulent jet
including the effects of droplet breakup. A key unknown in simulating secondary
breakup in turbulent multiphase jets is the inflow size distribution generated
within the primary breakup zone near the nozzle exit. A mono-disperse injection
inflow condition is commonly used for simplicity, but this choice is often
unrealistic. In order to provide more realistic inlet conditions for LES, we
develop a one dimensional (1D) parcel model to predict the evolution of the
dispersed phase along the jet centerline due to the combined effects of
advection, radial turbulent transport and droplet breakup due to turbulence in
the regions closer to the jet nozzle that cannot be resolved using coarse LES.
The model is validated with experimental data measured far from the nozzle. The
1D model is also used to generate an initial size distribution for use in a
coarse-resolution LES of a turbulent jet. Number density fields for each bin of
the discretized droplet size distribution are modeled using an Eulerian LES
approach and scalar transport equations are solved for each bin. LES results
are compared to published experimental data, with good agreement and we examine
the statistics of the velocity field and the concentration of the polydisperse
oil droplet plumes for two droplet Weber numbers. We find that the centerline
decay rate of the concentration for different droplet sizes is modified in the
breakup dominated zone. Unlike Reynolds averaged approaches, LES also allows us
to quantify size distribution variability due to turbulence. We quantify the
radial and axial distributions and the variability of key quantities such as
the Sauter mean diameter, total surface area and droplet breakup time-scale and
explore their sensitivity to the Weber number.
