The free surface flow field relative to a two-dimensional gravitational liquid sheet (or vertically falling jet) has been numerically solved by means of a CFD technique based on an orthogonal boundary fitted coordinate transformation. An iterative process minimizing the imbalance between the total normal stress and the surface tension contribution at the sheet free interface has been employed. Inertia, viscous stress, gravity and surface tension forces are all included in the present model, it is shown, however, that different simplified jet flow regimes can be conveniently identified according to the values of Reynolds and Stokes non-dimensional numbers, the capillary number being considered as an additional governing parameter. It should be remarked that in previous similar papers dealing with die-swell or fluid extrusion phenomena, gravity very often was ignored. On the contrary, the peculiarity of the present work lies just in the relatively wider range of simulated Stokes numbers values. The particular case of gravity regime has been computed as a test case to validate the numerical code effectiveness: the accuracy of present results has been found to lie to within a less than 3% discrepancy, in term of free boundary profile, pressure and jet contraction ratio data of literature. More properly gravitational regimes have been computed and compared with the theoretical predictions as taken from Adachi. The very close agreement found in the far downstream inertia-gravity region might represent the final confirmation of the validity of the Adachi's model intrinsic inadequacy there. Regimes approaching the classical inviscid solution have been also examined: they can be characterized by a pair of Re, St numbers both greater than about 50. Surface tension, when gravity in important, seems to be less relevant with respect to the no gravity situation in reducing both swelling and contraction. Its effect is more evident at low Re numbers.
Numerical solution of a two-dimensional gravitational free-surface liquid sheet
Costa M
1994
Abstract
The free surface flow field relative to a two-dimensional gravitational liquid sheet (or vertically falling jet) has been numerically solved by means of a CFD technique based on an orthogonal boundary fitted coordinate transformation. An iterative process minimizing the imbalance between the total normal stress and the surface tension contribution at the sheet free interface has been employed. Inertia, viscous stress, gravity and surface tension forces are all included in the present model, it is shown, however, that different simplified jet flow regimes can be conveniently identified according to the values of Reynolds and Stokes non-dimensional numbers, the capillary number being considered as an additional governing parameter. It should be remarked that in previous similar papers dealing with die-swell or fluid extrusion phenomena, gravity very often was ignored. On the contrary, the peculiarity of the present work lies just in the relatively wider range of simulated Stokes numbers values. The particular case of gravity regime has been computed as a test case to validate the numerical code effectiveness: the accuracy of present results has been found to lie to within a less than 3% discrepancy, in term of free boundary profile, pressure and jet contraction ratio data of literature. More properly gravitational regimes have been computed and compared with the theoretical predictions as taken from Adachi. The very close agreement found in the far downstream inertia-gravity region might represent the final confirmation of the validity of the Adachi's model intrinsic inadequacy there. Regimes approaching the classical inviscid solution have been also examined: they can be characterized by a pair of Re, St numbers both greater than about 50. Surface tension, when gravity in important, seems to be less relevant with respect to the no gravity situation in reducing both swelling and contraction. Its effect is more evident at low Re numbers.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
