Minimization of drainage time of filled PET bottle with initial rotation

Abstract

The drainage time of liquid-filled PET bottles can be greatly reduced by pre-rotating the bottle with a certain angular velocity. Depending on the magnitude of the angular velocity, up to four different flow regimes can be distinguished during the emptying of a bottle: bubble regime, transition regime, vortex
regime and the swirl regime. At zero or low pre-rotation, the flow is in the so-called bubble regime in which the intermittent downward liquid flow is accompanied by an upward motion of irregularly shaped air bubbles into the bottle. At sufficiently high pre-rotation, the picture is completely different. After
initial transient behaviour in which the flow is first in the bubble regime, the flow undergoes transition towards a so-called vortex regime. This is characterized by regular downward motion of liquid along the bottle wall in a free-surface vortex and accompanying upward motion of air through the nozzle core. Finally, close to the end of the drainage process another transition towards a so-called swirl regime takes place, in which the last bit of liquid swirls around in the bottle before being slowed down sufficiently to exit the bottle through the nozzle opening. Dimensional analysis indicates that for a specific bottle geometry the non-dimensional total drainage time td/td,0, where td,0 is a characteristic drainage time scale for stationary low-viscosity fluids in the bubble regime, depends primarily on 3 non-dimensional numbers: (1) the rotation number, Π (2) the Morton number, Mo, and (3) the E¨otvos number, Eo. The former represents the characteristic ratio of centrifugal to hydrostatic forces inside the liquid phase. The objective of this study is to determine the relationship between the non-dimensional drainage time and Π and gain insight in the influence of E¨otvos and Morton onto this. To this purpose, a parametric CFD study of a model PET bottle has been conducted and the results have been compared with previous preliminary experiments performed in our group. The numerical study is divided into three categories, each discussing the influence of one of the dimensionless parameters. The influence of the Π-number was studied by altering the initial rotational velocity of the bottle. It was found that at some critical Π-number, the drainage time was minimal. A further increase beyond the critical Π-number resulted in a longer drainage time, due to the stronger centrifugal force acting on the liquid layer. It was found through an analytical solution and verified with the numerical results that the rate at which the Π-number grows in relation to the dimensionless drainage time is to the power 3 for the laminar case and to the power 3/2 for the turbulent case. Below the critical value, the flow is expected to remain in the so-called bubble regime, also increasing the drainage time. Furthermore, the onset of the vortex regime was expected to occur at a constant value of Π. This was also verified with the numerical results and a strong correlation was found between the onset and the corresponding local Π-number. The influence of the Morton number is also discussed, where an increase in the Morton number was realized with an increase in viscosity. It was found that the drainage time got substantially reduced with an increase in viscosity. The effects of viscous dissipation resulted in a bigger effective area and higher axial downward flow velocity. However, increasing the Morton number excessively would result in the flow regime remaining in the bubble regime. Therefore, the critical Πnumber shifts depending on the different fluid compositions. When varying the E¨otvos number, by both changing the viscosity and the surface tension, it was found that the latter had negligible effect on the generation of the air-core or the drainage time.