  The present work develops a compressible VOF-LPT coupled solver in OpenFOAM
and utilizes it to simulate a LJICF numerically. This methodology helps
accurately predict a complex primary breakup in the Eulerian framework and the
secondary atomization of spherical droplets using a computationally efficient
LPT method. The coupled solver with AMR is rigorously validated for a liquid
jet in crossflow at varying operating conditions. We have further carried out a
thorough investigation to study the effect of momentum flux ratio and weber
number on the various flow features and liquid jet break-up phenomenon in a
crossflow while identifying the stream-wise location of the liquid jet breakup
region. At low momentum flux ratios in the bag breakup regime, the predictions
reveal that the liquid jet breakup occurs due to the growth of similar
instability as usually observed in the high-speed liquid sheet atomization. The
short wavelength assumption of the inviscid dispersion relation resembles the
Kelvin-Helmholtz type instability observed in this case, as opposed to
Rayleigh-Taylor instability at high momentum flux ratio in the surface breakup
regime. It is also proposed that the shear breakup along the transverse edges
of the liquid column occurs due to the shear layer instability of the air
passing around the liquid column. The simulation wavelength closely matches the
Williamson correlation for shear layer instability around cylinders: a shape
similar to the cross-section of the bottom of the liquid column. The results
show a distinct streamer or bifurcation phenomenon at low momentum flux ratios
and moderate weber numbers. Further investigation suggests that the internal
liquid boundary layer and the three-dimensional flow field behind the liquid
jet are responsible for streamer formation.
