Unsteady Dynamics of Free-Interface Gravitational Liquid Sheet Flows

Abstract

Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, are performed through Volume-of-Fluid (VOF) technique. The global unsteady dynamics of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively very small amplitude, thereby exciting sinuous modes. Thanks to the development of a theoretical linear one-dimensional model, more physical insights are gained on the flow system. It is found that surface tension plays a stabilizing role for the gravitational sheet, and for relatively high values of density ratio r ρ of gaseous-to-liquid phases it becomes unstable. An analogy is shown between the global unstable behavior exhibited by the liquid sheet as r ρ increases, and the shear-induced global instability found by Tammisola et al. ["Surface tension-induced global instability of planar jets and wakes", J. Fluid Mech. 713, 632-658 (2012)] for planar jet and wake flows of two immiscible fluids in the presence of surface tension.