Toward fully-resolved simulations of the bag breakup of a single drop

When an isolated drop is suddenly subjected to a uniform gas stream, the drop will experience deformation and even breakup. When the Weber number based on the drop diameter and free-stream velocity is just above the critical threshold, the drop first deforms into a bag before topology change finally occurs due to the rupture of the bag sheet. The present study aims to demonstrate that 3D simulations are necessary to resolve the turbulent wake, so that the drop acceleration and deformation can be accurately captured, assuming the droplet Reynolds number is high, as in most droplet aerobreakup problems. Since a high mesh resolution is required to resolve the thin bag sheet, it is surprisingly expensive to simulate the bag breakup of a single drop, even with sophisticated numerical techniques, including the Volume-of-Fluid (VOF) method and adaptive mesh refinement. Though disjoining pressure is not included in the Navier-Stokes equation, a numerical cutoff length, larger than the cell size, is introduced in the VOF-based manifold death method to pinch the two interfaces when the thickness is smaller than the cutoff length. The effect of the numerical cutoff length on the bag inflation and breakup dynamics is investigated in detail. Only for tiny droplets with a diameter lower than a hundred microns, the numerical cutoff length can be similar to the physical cutoff length scale that is dictated by disjoining pressure and one can claim that the simulations are close to fully resolving the bag breakup of a single drop. For larger drops, it remains infeasible to fully resolve the bag breakup and subgrid models for thin liquid sheet evolution and breakup are needed.