Response of a cylinder in oscillatory flow

Abstract

The two-dimensional response of a flexibly mounted rigid cylinder in oscillatory flow is studied in this paper. Both measurements of cylinder response obtained in a U-tube and mathematical modelling of this problem are considered. Trajectories of the cylinder response are obtained experimentally for ranges of Keulegan-Carpenter numbers from 2 to 60 and the ratio of the natural frequency of the cylinder in water to the 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 particular combinations of these parameters. Regions of repeatable two-dimensional response are identified. These are separated by transition regions characterized by poor synchronization between the vortex shedding and the motion of the cylinder, with resulting three-dimensional response. The ability of the cylinder to respond both in-line and transverse to the flow has a significant influence on the resulting response. In order to analyse this fluid-structure interaction problem, three simple mathematical models are formulated which attempt to predict this two-dimensional response. The first two models use the relative velocity formulation of the Morison equation for the force in-line with the flow, but with different expressions for the transverse force. The equations of motion for these models are uncoupled. In contrast, the third model considers drag and lift force components in directions parallel and perpendicular to the direction of instantaneous relative velocity between the cylinder and the flow, which results in coupled equations 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 response of the cylinder and the flow is very complicated.