Free response of a gravitational liquid sheet by means of three-dimensional Volume-of-Fluid simulations

The volume-of-fluid (VOF) method is employed to simulate the dynamics of gravitational liquid sheets (curtains) issuing into an initially quiescent gaseous environment. The flow behaviour is investigated by varying two governing parameters, namely the sheet aspect ratio, (formula presented), and the Weber number, (formula presented), where (formula presented) and (formula presented) are the curtain inlet thickness and width, respectively, (formula presented) the inlet mean liquid velocity, l and σ the liquid density and surface tension coefficient. For a reference Weber number greater than one, three different aspect ratio values are considered, namely AR = 40, 25 and 10, and it is found that a varicose mode progressively arises as AR decreases, dramatically affecting the flow at AR = 10. The analysis performed by varying We reveals that a stable liquid sheet can be obtained in both supercritical (We > 1) and subcritical (We < 1) regimes, down to We = 0:8, where rupture mechanisms (holes formation and their amplification) start to occur. Linear stability analysis predictions of the sheet oscillation frequency based on a simplified linear low-dimensional model of the flow system are found to be in good agreement with corresponding values arising from the three-dimensional simulations.