Title:

Vortexinduced vibration of cylindrical structures

Vortexinduced vibration (VIV) of cylindrical structures is a classical topic within fluidstructure interaction (FSI). In offshore engineering, it often causes the fatigue of slender structures, such as risers, mooring lines and pipelines. Detailed understanding of this FSI phenomenon and an efficient prediction of such selfexcited and selfsustained oscillations are required for the reliable estimation of the fatigue damage and the development of VIV suppression techniques. Over the past few decades, VIV has been extensively studied and the majority of the existing publications in the literature are experiments or semiempirical modelling. In contrast, FSI simulations by combining highfidelity computational fluid dynamics (CFD) and computational structural dynamics (CSD) solvers have received less attention. The main objective of this thesis is to investigate VIV of elastically mounted rigid cylinders and flexible cylinders using fully threedimensional (3D) FSI simulations. Apart from important VIV aspects, such as response amplitude, response frequency and fatigue damage etc., the present research is also focussed on the aspects which have not been fully addressed by previous studies such as correlation lengths and timedependent 3D flow structures. Twodegreeoffreedom (2DOF) VIV of an elastically mounted circular cylinder with varying inline (IL) to crossflow (CF) natural frequency ratios (f* = fnx/fny) is first studied using a 3D CFD approach. Numerical simulation is carried out for a constant mass ratio m* = 2 at a fixed Reynolds number Re = 500. The reduced velocity Vr ranges from 2 to 12. Three natural frequency ratios are considered, i.e., f* = 1, 1.5 and 2. The structural damping is set to zero to maximise the response of the cylinder. The main objective of the first study is to investigate the effect of f* on the 2DOF VIV responses and the 3D characteristics of the flow. It is discovered that there is a significant increase in the vibration amplitude and the peak amplitude shifts to a higher reduced velocity when f* increases from 1 to 2. A singlepeak crossflow response is observed for the identical inline and crossflow mass ratios when f* = 2. Dual resonance is found to exist over the range of f* studied. The preferable trajectories of the cylinder in the lockin range are counterclockwise figureeight orbits, whereas clockwise orbits primarily occur in the initial branch. The number of clockwise orbits decreases as f* increases from 1 to 2. Oblique figureeight trajectories appear at Vr = 6, 7 and 8 when f* = 1. The third harmonic component which is observed in the lift fluctuation increases with f*. The correlation decreases in the lockin range and reaches its minimum value around the transition region between the lockin and postlockin ranges. Three vortex shedding modes (2S, P + S and 2P) appear in the present simulation. A dominant P + S mode is associated with the oblique figureeight trajectories. Variation of vortex shedding flows along the cylinder is observed leading to the poor correlation of the sectional lift forces. Then, a numerical investigation of VIV of a vertical riser subject to uniform and linearly sheared currents is presented. The model vertical riser tested at the MARINTEK by ExxonMobil is considered. The predicted numerical results are in good agreement with the experimental data. It is found that the dominant mode numbers, the maximum root mean square amplitudes, the dominant frequencies and the fatigue damage indices increase with the flow velocity. Dual resonance is found to occur at most of the locations along the riser. At some locations along the riser, a third harmonic frequency component is observed in the CF response and a frequency component at the CF response frequency is found in the IL response apart from the frequency component at twice the CF response frequency. The majority of the vortex shedding shows a clear 2S pattern, whereas a 2P mode is observed near the position where the maximum vibration amplitude appears. The higher IL fatigue damage in the second study emphasises the importance of the IL fatigue damage analysis especially in the design of low flow velocity or low mode number applications. The third study is on VIV of two tandem flexible cylinders at different spacing ratios (Sx/D) at a fixed Reynolds number Re = 500 using a twoway FSI method. The main objective is to investigate the effect of spacing on the hydrodynamic interactions and the VIV responses of these cylinders. It is found that the responses of the two tandem flexible cylinders are similar to the classical VIV responses when Sx/D is small. Once Sx/D is large enough for the vortices to be completely detached from the upstream cylinder, the response of the upstream cylinder is similar to the typical VIV response whereas the downstream cylinder undergoes wakeinduced vibration (WIV). The characteristics of the response of the downstream cylinder in the present study are similar to those of the first two response regimes. The third response regime is not observed for the flexible downstream cylinder with both ends fixed. The two changes in the phase relation between the crossflow displacements of the two tandem flexible cylinders are discovered to be linked with the initialupper branch transition and the upperlower branch transition, respectively. The correlation lengths of the two tandem flexible cylinders decrease significantly in the transition range between the upper and lower branches. Three vortex shedding modes (2S, P + S and 2P) have been identified in the present study. It is found that the upperbranch 2P mode is associated with largeamplitude vibration of the upstream cylinder and the P + S mode is related to largeamplitude vibration of the downstream cylinder for Sx/D = 3.5 and 5. On the other hand, the lowerbranch 2P mode leads to smallamplitude vibration of the downstream cylinder in the postlockin range at Sx/D = 2.5. The relative phase shifts of the sectional lift coefficients on different spanwise cross sections can be attributed to the variation of the vortex shedding flow along the flexible cylinders and these phase shifts result in poor phasing between the forces and the displacements which is related to the decrease of the correlation lengths.
