Effect of tip flow on vortex induced vibration of circular cylinders

Abstract

As one of the complicated subject of flow-induced vibration (FIV), the physical background of Vortex-Induced Vibration (VIV) and its mathematical model can not be represented by a single theory. The solutions contain highly non-linear terms increasing the computational burden. Investigations on this area have not yet matured although it takes place in almost all fields of ocean engineering. VIV has destructive effects on deep-sea oil production and offshore industry equipment since the phenomenon is observed around the bluff bodies such as marine cables, moorings, risers and pipes. As the number of offshore structures around the world increased, the oil companies have identified new targets and started moving away from shallow waters to deep-waters. This is considered to increase the interest in VIV in the future. Moreover, recent researches have revealed that it is possible to benefit from this phenomenon. A recently invented device, VIVACE, succeeded to convert the energy in water currents into electric energy by fitting a power generator into conventional VIV models. Some other studies propose piezoelectric materials to derive energy from VIV mechanisms. Recent studies have also revealed that VIV may also be used for developing some gauges such as water measuring device. Taking these new developments into the account, the number of VIV researches are increasing rapidly in parallel with reachable higher computational technologies. Moreover, the reliability of numerical studies are improving thanks to the better approximations of flow and turbulence models. The nature of VIV phenomenon is highly non-linear. Mathematical models simplify the problem in many ways by leading to partly or entirely incompatible results between different studies, even if these studies are using the same non-dimensional parameters. At this point, three-dimensionality of the flow plays an important role in many of these studies. Depending on the mathematical model in numerical studies, or the lab setup in experimental ones; the oscillating body might be exposed to more 3D effects while in some others the flow might even be 2D in the entire wake. 3D effects are mostly dependent on the aspect ratio of the circular cylinder and end conditions (such as usage of end-plates or not). The flow partly escapes through the free-ends of the bluff body and creates a trailing vortex at the tips spoiling the shedding process, contributing to the oscillations of that body. The aspect ratio is inversely proportional to the three-dimensionality of the flow and its dominance on the VIV response. If the aspect ratio is sufficiently large, the escaping flow from the tips can even be neglected. Effect of tip flow on the VIV response are generally observed through the oscillation amplitude, the frequency response, and the phase difference between the oscillation of the cylinder and the vortex shedding. Due to the reasons explained above, the effect of tip flow should be taken into consideration in calculations. A 2D VIV approach typically neglects the finiteness of the aspect ratio and assumes that Karman vortex street covers the entire wake while it can be observed only around the mid-section of a three-dimensional VIV. Studies adopting a 3D model indicate that the vorticity type along a VIV cylinder changes from the mid-section to the tips of the cylinder due to cellular sheddings, cross-flow and tip-flow. Despite a boost in recent studies, numerical approaches to solve the VIV problem are still in progress since current methods are incapable of reflecting the experimental conditions sufficiently, requiring unaffordable computational power due to the complexity of spatial alteration of vortices in the wake. Therefore, researchers generally prefer relatively simpler 2D methods. Although these methods have the advantage of decreasing the computational cost; some characteristics of VIV phenomenon, observable in only 3D studies, such as cross-flows, cellular sheddings and tip flow (and tip vortices) can not be represented with a 2D flow assumption. An adoptable enhancement would be worth to pursue to implement into a 2D model, representing partial three-dimensional flow, so that these effects can be partly compensated to obtain more realistic results. A chapter of this thesis is devoted to this purpose by proposing a scaling factor to represent three-dimensional characteristics of the flow around circular cylinder in a 2D numerical model. The finite volume method is used to calculate force term at each time step acting on the oscillating cylinder. The lift force is scaled by a newly proposed term named as the "three-dimensionality factor". By using this factor in the equation of motion to reflect three-dimensionality, a reduction in oscillation amplitude is examined. This factor alters the lift force, the phase difference, and therefore the oscillation frequency. It also changes the synchronization range especially at the lower branch region. Eventually, the numerical method has been compared with some experimental data. The enhancement in the 2D numerical method is demonstrated and discussed. A suitable scaling factor is proposed for the chosen experimental cases. The experimental part of this thesis focuses on the effect of tip flow by changing systematically the aspect ratios and the distance from the edges of the cylinders to walls of the circulation channel. The experiments are carried out at İstanbul Technical University (İTÜ) Ata Nutku Ship Model Testing Laboratory (ANSMT Lab) located in the Faculty of Naval Architecture and Ocean Engineering. Mass ratios of 1.93, 2.24, and 2.52 are considered and the resulting Reynolds number range is 1.6×104 – 8×104 corresponding to the sub-critical TrSL2 and TrSL3 (transition in shear layer) flow regimes. The nondimensional velocities (U^*) range from 3 to 13. Six different circular cylinders are used with different aspect ratios varying from 11.225 to 17.7875. The cylinder with the longest length extends to the walls of the circulation channel (as much as possible) and the length of each cylinder is shortened systematically while the diameter is kept constant at 0.08m. As the length of the cylinder is reduced, three-dimensionality of the flow increases and the flow escaping from the tips gets higher. This is accompanied by vortex disturbances which causes a loss on the lift force due to the decreasing Karman vortex street in the wake of the cylinder. Eventually, VIV response of the cylinder differentiates into a narrower synchronization range, lower oscillation amplitude and larger differences in phase angles. In the last section of the thesis, effect of aspect ratio and tip flow on VIV is investigated through hydrokinetic energy harnessing from the phenomenon. Three-dimensional effects, reducing the effective length of the cylinder, are discussed in terms of energy generation. Converted power and maximum system efficiencies are calculated from experiments conducted in the recirculation channel of the ANSMT Laboratory. It was found that the end-zones of the cylinder, which do not induce lift due to tip flow, are more dominant in lower aspect ratio cylinders. More power can be captured from TrSL3 flows due to higher shear-flow momentum while higher efficiency in power conversion is achieved in TrSL2.