Hydrodynamics of oscillating cylinders and disks at low Keulegan-Carpenter numbers.

Abstract

Resonant vertical excitation of a Tension Leg Platform (TLP) is typically of high frequency and small amplitude. The hydrodynamic damping of structural members of a TLP in this mode of oscillation is studied in this thesis. Experimental flow visualization studies were conducted on oscillating cylinders and disks of different thickness. The Keulegan-Carpenter (KC) number was varied from 0.2-0.5, and frequency parameter $(\beta)$ in the range 2500-12500. A double-exposure variant of the Digital Particle Image Velocimetry technique was developed to obtain velocity and vorticity information of the flow. It was found that thin disks of finite edge thickness generated a flow that remained symmetric with respect to the mean position of oscillation. For disks of infinitesimal edge thickness, the initial start-up condition determined the emerging vortex shedding pattern. The relative effects of convection and viscous diffusion were dependent on a KC number based on disk thickness. Drag force measurements were conducted on an axially oscillating cylinder of 0.457 m (1.5 ft) diameter and 1.219 m (4.0 ft) draft, at zero and small forward speeds. Experiments were conducted at KC numbers in the range of 0.1-1.0, and $\beta$ in 89236-191700. From these experiments, a definite nonlinear trend was observed between the drag force and velocity. The drag coefficient $(C\sb{d})$ was approximately doubled upon addition of a disk to the bottom of the cylinder. Effects of forward speed were significant at low values of KC, but were diminished at larger values. The damping coefficients of individual structural components of a TLP follow different scaling laws. Rules are presented for scaling friction and form drag components from model to full scale. Results from experiments are used to obtain a scaling law for vertical columns of a TLP. Previously published results are used for horizontal pontoons. An example TLP calculation shows that the equivalent linear damping ratio of horizontal cylinders is approximately 0.049-0.078%, depending upon cylinder shape, and that for vertical cylinders is in the range 0.025-0.394%, depending upon KC and the size of the disk used.