  The secondary atomization of liquid droplets is a common physical phenomenon
in many industrial and engineering applications. Atomization in high speed
compressible flows is less well understood than its more frequently studied low
Mach number counterpart. The key to understanding the mechanisms of secondary
atomization is examination of the breakup characteristics and droplet
trajectories across a range of physical conditions. In this study, a planar
shock wave impacting a cylindrical water column ($\rho_l=1000 \rm~kg/m^3$) is
simulated for a range of Weber numbers ranging three orders of magnitude ($\sim
10^0-10^3$). Four different incident shock speeds are simulated ($M_s=1.47, 2,
2.5, 3$) which induce subsonic, transonic, and supersonic crossflow across the
column. The flowfield is solved using a compressible multicomponent
Navier-Stokes solver with capillary forces. Fluid immiscibility is maintained
with an interface sharpening scheme. Overall, a diverse range of complex
interface dynamics are captured across the range of physical conditions
studied. Additionally, while the unsteady drag coefficient of the liquid column
shows a dependence on the Weber number using the undeformed diameter,
calculations using the deformed diameter significantly reduce the dependence,
particularly for the supersonic cases, with implications for subgrid droplet
modeling in atomization simulations. A preliminary under-resolved
three-dimensional simulation of droplet breakup shows reasonable agreement with
experimental data, indicating the potential of the numerical approach for
future investigations.

Fluid Dynamics