Session: 05-01-02 Applied CFD

Paper Number: 94127

94127 - Free Surface Shape in a Cylinder With a Rotating Bottom 

When a vertical cylinder partly filled with water is set in constant speed rotation, the flow is at rest in the reference frame rotating with the cylinder. In this case, the free surface attains the shape of parabola. On the other hand, in a stationary cylinder with a rotating bottom, stable rotating polygonal free surface patterns were observed experimentally on the bottom. A number of studies were devoted to measuring the flow characteristics and the shape of the free surface depending on the experimental conditions, such as the bottom disc rotating speed and its radius, among others. It was shown that as the rotation speed increases from rest, the free surface shape transforms through a number of stable shapes. The free surface deformation for these cases is rather substantial. Starting from circle, similar to the whole cylinder rotation case, with an increase in the rotation speed, the free surface shape becomes sequentially elliptical, triangular, square, pentagonal and finally hexagonal. Further increasing the cylinder bottom rotating speed results in a visible smearing of the hexagon corners, and polygons are no more recognizable.

Besides experimental observations, a number of theoretical studies were reported in the literature, some being quite successful in predicting the phenomena of polygon formation and transformations in terms of the polygons’ number of corners. Recognizing that the base flow in the case of a stationary cylinder with rotating bottom is of a line vortex type, its instability was numerically demonstrated.

Numerical three-dimensional simulations of the flow in a stationary cylinder with rotating bottom were limited to the case of either flat or slightly deformed free surface. These studies were inherently unable to capture the complicated large free surface deformation associated with polygonal shapes, observed in the experimental studies.

The aim of the present work is to gain knowledge of the detailed flow field, associated with polygon formation on the free surface of the fluid in a stationary cylinder with rotating bottom, by means of a transient three dimensional numerical simulation. The Large Eddy Simulation (LES) with a localized dynamic Subgrid-Scale Stresses (SGS) model, including an energy equation, is employed for turbulence modeling. A volume-of-fluid (VOF) approach has been chosen for free surface resolution, based on its success in capturing the details of the interfaces in similar conditions. Ellipse and triangle shapes, as reported in the literature, are shown and analyzed. Numerical results reported allow for a detailed analysis of the mechanisms and features which accompany the free surface polygonal shapes and their transformations.

Based on the success of numerically obtaining the stably rotating polygonal shapes for the fluid in a stationary cylinder with a rotating bottom, an attempt is made to reproduce numerically the phenomenon of the surface switching of rotating fluid. In this case, the free surface shape demonstrates a high amplitude instability for the constant rotation speed of the cylinder bottom. The free surface periodically exposes the rotating bottom resulting in alternating single and double “touchdown” shapes – periodical transition of single vortex splitting in two vortices. The latter phenomenon resembles the case of twin-tornado event, observed e.g. in Elkhard, Indiana, on Palm Sunday in 1965, see Ward (1972). Like rotating polygons, this phenomenon was also observed experimentally, though attempts of its theoretical explanation and numerical simulation are rather deficient. In this study, we report the first successful simulation of the experiments on a stationary cylinder with rotating bottom resulting in periodical surface switching. The simulations were performed for the well documented experiment from the literature. It is believed that based on the presented results and future simulations, a further insight into the phenomenon of the surface switching would be achieved.

Presenting Author: Alexander Rashkovan NRCN