RESPONSE OF A CYLINDER IN OSCILLATORY FLOW

The two-dimensional response of a flexibly mounted rigid cylinder in o scillatory flow is studied in this paper. Both measurements of cylinde r response obtained in a U-tube and mathematical modelling of this pro blem are considered. Trajectories of the cylinder response are obtaine d experimentally for ranges of Keulegan-Carpenter numbers from 2 to 60 and the ratio of the natural frequency of the cylinder in water to th e frequency of oscillation of the U-tube from 1 to 9. It is found that the cylinder responds in a strongly two-dimensional fashion for parti cular combinations of these parameters. Regions of repeatable two-dime nsional response are identified. These are separated by transition reg ions characterized by poor synchronization between the vortex shedding and the motion of the cylinder, with resulting three-dimensional resp onse. The ability of the cylinder to respond both in-line and transver se to the flow has a significant influence on the resulting response. In order to analyse this fluid-structure interaction problem, three si mple mathematical models are formulated which attempt to predict this two-dimensional response. The first two models use the relative veloci ty formulation of the Morison equation for the force in-line with the flow, but with different expressions for the transverse force. The equ ations of motion for these models are uncoupled. In contrast, the thir d model considers drag and lift force components in directions paralle l and perpendicular to the direction of instantaneous relative velocit y between the cylinder and the flow, which results in coupled equation s of motion. The usefulness and limitations of each of the models are assessed by comparison with the experimental observations. In general, the simple models used here are able to predict the cylinder response in a satisfactory fashion, even though the interaction between the re sponse of the cylinder and the flow is very complicated.