The propagation of a hole in a gravitational liquid sheet (curtain) issuing into a quiescent gaseous environment is numerically investigated in supercritical flow conditions, namely for acurta in Weber number We > 1. The analysis is based on three-dimensional direct numerical simulations carried out by means of the open-source code BASILISK, which implements the volume-of-fluid method to track the gas-liquid interface. For a selected reference configuration, the steady flow solution is first examined. The investigation reveals a triangular shape of the steady curtain, due to the surface tension-induced sheet borders retraction towards its center plane. In addition, capillary waves forming a striped pattern arise at the curtain interface. These waves result from the competition between viscous and surface tension forces, and accordingly vanish when the former become increasingly dominant, namely when the Oh nesorge number (Oh) is relatively high. The unsteady dynamics is then analyzed as the curtain response to a hole perturbation artificially superposed to the steady flow. Several streamwise (xh) and spanwise (zh) hole initial locations are examined, as well as different Weber number values. As major results, it is found that the hole evolution is governed by the interplay between gravity and capillary forces acting on its rims, and by the hole-curtain rims interaction. The hole area undergoes an initial transient growth, it reaches a peak value, and then it decreases, leading to the hole closure or to the hole expulsion at the downstream outflow, respectively for low and high values of xh. Moreover, the effect on the hole amplification of increasing the Weber number at fixed xh is the same of introducing the hole perturbation more upstream (i.e., reducing xh) at fixed,We. The main result found here is that the holeperturbation does not influence the supercritical curtain flow dynamics in the long time limit.
