Vortex-induced vibration of flexible cylinders in time-varying flows

Abstract

This thesis investigates two aspects of Vortex-Induced Vibrations (VIV) on long flexible cylinders. The work is split into a minor and major part. The minor part addresses the effect of Reynolds number on flexible cylinder VIV. The major contribution addresses the prediction of VIV under unsteady current excitation or time-varying flows. The study on the effect of Reynolds number makes extensive use of a recent set of experiments performed by MARINTEK on behalf of SHELL Exploration and Production Co. Three 38[gamma] long cylinders of different diameters were towed through the ocean basin over a wide range of Reynolds numbers in both uniform and sheared flows. The experimental data showed that the response amplitudes and dimensionless response frequency are strongly influenced by the Reynolds number. Both of these Reynolds effects should be of interest to riser designers that traditionally rely on experimental data obtained at much lower Reynolds numbers. In this thesis, I propose a dimensionless parameter, [gamma], that governs whether lock-in under unsteady flow conditions is possible and show that it is useful for determining a priori whether the response under unsteady conditions will be similar to the response under steady flows. The unsteady flow parameter, [gamma], describes the change in flow speed per cycle of cylinder vibration and is defined as: ... The experimental data necessary to support this work is taken from a set of experiments performed at the State Key Laboratory of Ocean Engineering at Shanghai Jiao Tong University (SJTU), where a 4[gamma] long flexible cylinder was towed through an ocean basin under carefully selected amounts of acceleration/deceleration. Analysis of the experimental data showed that the response can typically be divided into three regimes based on the [gamma] value: For very quickly accelerating flows ([gamma] > 0.1) the cylinder cannot react quickly enough and at most a couple of cycles of small amplitude vibration will be observed. For moderately accelerating flows (0.02 < [gamma] < 0.1), the cylinder will typically start vibrating and can build up a significant response. However, most of the time, the flow will have exited the required synchronization region before the cylinder manages to reach the large amplitudes observed in steady flows. For very slowly accelerating flows ([gamma] < 0.02), the flow is changing considerably slower than the cylinder's reaction time and thus, the cylinder has more than enough time to build up its response. Under these conditions, the observed response is qualitatively similar to the response of flexible cylinders in steady flows. The [gamma] dependence that was identified in the SJTU data is not limited to that specific situation but instead, is a general property of low mass ratio cylinders vibrating in unsteady flows. This is shown by demonstrating how the unsteady flow parameter, [gamma], can be used to analyze unsteady response data from the aforementioned SHELL tests where the riser models were considerably longer than the SJTU model. This thesis shows how a single ramp test -- where the towing speed is continuously varied in a control manner -- may be used to obtain the same information as 10 constant speed tests covering the range of speeds. This can and will significantly reduce the number of runs necessary to completely characterize the VIV response of flexible cylinders and will translate into large cost savings in the future. The thesis closes by describing the differences observed in the VIV response at high mode numbers depending on whether the time-varying flow was accelerating or decelerating. In both situations a 'hysteresis' effect is noted, where the cylinder is found to 'lag behind' preferring to vibrate in the previously excited mode as a result of cylinder lock-in. In accelerating flows, this means that the cylinder will typically be responding one mode lower than it would have in a steady flow. In decelerating flows, the same 'lag' or 'hysteresis' will cause the cylinder to respond one (or more) mode number(s) higher than it would have in a steady flow.