Two-dimensional flow of a liquid sheet under gravity

Abstract

An iterative FD technique is developed to simulate the free surface flow relative to a two-dimensional gravitational (or vertically falling) liquid sheet. Its features are: it is based on an orthogonal boundary fitted coordinate transformation; a streamfunction-vorticity formulation is adopted; the normal stress boundary condition is employed to update the free interface shape within an iterative process. Inertia, viscous, gravity and surface tension forces are all taken into account in the present model and it is shown that different simplified flow regimes can be conveniently identified according to the values of Reynolds and Stokes numbers. Indeed, the main peculiarity of the present paper just lies in the relatively wider range of simulated Stokes values with respect to previous papers. Computed results (interface profiles, pressure distributions) well agree with available literature data for flows with and without gravity. From one hand the classical die-swell problem phenomenology is recovered, from the other one a discussion about the validity of the Adachi's theoretical model is yielded.