Circular cylinder wakes and vortex-induced vibrations

This paper presents a selective review of recent research on vortex-induced vibrations of isolated circular cylinders and the flow and vibration of circular cylinders in a tandem arrangement; a common thread being that the topics raised are of particular interest to the author. The influence of Reynolds number on the response of isolated cylinders is presented and recent developments using forced vibration are discussed. The response of a cylinder free to respond in the in-line and transverse directions is contrasted with that of a cylinder responding in only one direction. The interference between two circular cylinders is discussed and prominence given to the case of cylinders in a tandem arrangement. The origin of the time–mean lift force on the downstream cylinder is considered together with the cause of the large amplitude transverse vibration experienced by the cylinder above vortex resonance. This wake-induced vibration is shown to be a form of vortex-induced vibration.     

Hydrodynamics of a flexible cylinder under modulated vortex-induced vibrations

Both amplitude modulation and frequency modulation of Vortex-induced Vibration (VIV) are observed in a recent model test of a flexible cylinder under oscillatory flow, but its hydrodynamics has not yet been broached in detail. This paper employs the Forgetting Factor Least Squares (FF-LS) method for identification of time-varying hydrodynamics of a flexible cylinder under modulated VIV. The FF-LS method’s applicability to accurately identify time-varying hydrodynamic coefficients is demonstrated through an elastically mounted rigid cylinder under flow with a given modulated motion. Furthermore, we propose a framework to predict instantaneous amplitude (envelope) and frequency using time-varying hydrodynamic coefficients to establish their analytical relationship. This prediction method is further extended to a highly tensioned flexible cylinder through Fourier series expansion in the spatial domain. By performing the identification procedure for all sampled data of a flexible cylinder undergoing oscillatory flow, we obtain the corresponding time-varying hydrodynamics in the cross-flow direction considering the amplitude and frequency modulation. The results show that, under modulated VIV, hydrodynamic coefficients of the flexible cylinder also show time-varying characteristics. We further investigate differences between identified hydrodynamic coefficients and those obtained from the database of a cylinder with modulated motion under flow. Prediction results using these identified time-varying coefficients reveal that the time-varying excitation coefficients mainly influence the amplitude modulation, and the time-varying added-mass coefficients contain the major information of frequency modulation. These results further suggest including the temporal derivative of the instantaneous amplitude as one determining parameter in building databases to improve the prediction of modulated VIV.     

Wake modes of a cylinder undergoing free streamwise vortex-induced vibrations

Simultaneous measurements of the response of a circular cylinder experiencing vortex-induced vibrations (VIVs) in the streamwise direction and the resulting wake field were performed for a range of reduced velocities using time-resolved Particle-Image Velocimetry in the Reynolds number range 450–3700. The dominant vortex shedding mode was identified using phase-averaged vorticity fields. The cylinder response amplitude was characterised by two response branches, separated by a low amplitude region at resonance, as has been previously reported in the literature. During the first response branch the wake exhibited not only the symmetric S-I mode, but also the alternate A-II mode at slightly higher reduced velocities. For both modes, the vortices were observed to be shed at the cylinder response frequency, but rearranged downstream into a more stable structure in which the velocity fluctuations were no longer synchronised to the cylinder motion. A special case of the A-II mode, referred to as the SA mode, was found to dominate in the second response branch and the low amplitude region, while the far wake and the cylinder motion were synchronised (lock-in). A change in the timing of the vortex shedding with respect to the cylinder motion was observed between the low amplitude region and the second response branch. This is likely to correspond to a change in the fluid forcing and levels of excitation, and may explain the variation in the cylinder amplitude observed in this region. Lock-in and the second response branch were found to coincide with a contraction of the wake and an increase in strength of the shed vortices. This work reveals the inherent differences between the extensively studied case of transverse-only VIV and the streamwise-only case, which is crucial if the wealth of information available on transverse VIV is to be extended to the more practical two degree-of-freedom case.     

Employing controlled vibrations to predict fluid forces on a cylinder undergoing vortex-induced vibration

In the present study, we measure the fluid forces on a vertical cylinder that is forced to vibrate transversely to a water channel flow, and compare directly to the forces encountered by freely vibrating cylinders, under conditions where we carefully match the amplitude, frequency, and Reynolds number (Re) of the two cases. A key point is that we use precisely the same cylinder and submerged flow configuration for both the free and controlled cases. Where the free vibration exhibits closely sinusoidal motion, the controlled sinusoidal motion yields forces in close agreement with the free vibration case. Although this result might be expected, previous comparisons have not been uniformly close, which highlights the importance of matching the experimental conditions precisely, and of accurately measuring the phase between the force and body motion. For a lightly damped system, which is perhaps the most significant case to analyze, one typically finds that the maximum response amplitude is quite unsteady. One might conventionally expect prediction of forces to be difficult in such cases. However, it is of practical significance that, even in this case, a quasi-steady approximation is effective. This is a significant point because it suggests that controlled vibration measurements for constant amplitude motion might remain applicable to free vibration systems undergoing even transient or intermittent motions.     

Two-degree-of-freedom vortex-induced vibrations of a circular cylinder at Re=3900

The vortex-induced vibrations of an elastically mounted circular cylinder are investigated on the basis of direct numerical simulations. The body is free to move in the in-line and cross-flow directions. The natural frequencies of the oscillator are the same in both directions. The Reynolds number, based on the free stream velocity and cylinder diameter, is set to 3900 and kept constant in all simulations. The behavior of the coupled flow-structure system is analyzed over a wide range of the reduced velocity (inverse of the natural frequency) encompassing the lock-in range, i.e. where body motion and flow unsteadiness are synchronized. The statistics of the structural responses and forces are in agreement with prior experimental results. Large-amplitude vibrations develop in both directions. The in-line and cross-flow oscillations are close to harmonic; they exhibit a frequency ratio of 2 and a variable phase difference across the lock-in range. Distinct trends are noted in the force-displacement phasing mechanisms in the two directions: a phase difference jump associated with a sign change of the effective added mass and a vibration frequency crossing the natural frequency is observed in the cross-flow direction, while no phase difference jump occurs in the in-line direction. Higher harmonic components arise in the force spectra; their contributions become predominant when the cylinder oscillates close to the natural frequency. The force higher harmonics are found to impact the transfer of energy between the flow and the moving body, in particular, by causing the emergence of new harmonics in the energy transfer spectrum.     

Experimental study of vortex-induced vibrations of a cylinder near a rigid plane boundary in steady flow

In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocimeter and hydrogen bubbles. A parametric study is carded out to investigate the influences of reduced velocity, gap-to-diameter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate： （1） the Strouhal number （St） is around 0.2 for the stationary cylinder near a plane boundary in the sub-criti- cal flow regime; （2） with increasing gap-to-diameter ratio （eo/D）, the amplitude ratio （A/D） gets larger but frequency ratio （f/fn） has a slight variation for the case of larger values of eo/D（eo/D 〉 0.66 in this study）; （3） there is a clear difference of amplitude and frequency responses of the cylin- derbetween the larger gap-to-diameter ratios （e0/D 〉 0.66） and the smaller ones （e0/D 〈 0.3）; （4） the vibration of the cylinder is easier to occur and the range of vibration in terms of Vr number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; （5） with decreasing mass ratio, the width of the lock-in ranges in terms of Vr and the frequency ratio （f/fn） become larger.     

Effects of a non-linear energy sink (NES) on vortex-induced vibrations of a circular cylinder

We investigate in detail the passive control of vortex-induced vibrations of a freely oscillating circular cylinder using a non-linear energy sink consisting of a secondary system having linear damping and an essential non-linear cubic stiffness. The loads on the cylinder are calculated using a direct numerical simulation of the incompressible flow over the cylinder using a parallel computational fluid dynamics code. A strongly coupled fluid structure control numerical model is used to determine the responses of the cylinder and the sink as well as the flow. We vary the sink parameters (mass and damping) and determine their effects on the response of the coupled system. We find multiple stable responses of the coupled system for different mass ratios and damping coefficient of the sink, depending on the initial conditions.     

Wake structures and vortex-induced vibrations of a long flexible cylinder—Part 1: Dynamic response

Results showing the dynamic response of a vertical long flexible cylinder vibrating at low mode numbers are presented in this paper. The model had an external diameter of 16 mm and a total length of 1.5 m giving an aspect ratio of about 94, with Reynolds numbers between 1200 and 12 000. Only the lower 40% of its length was exposed to the water current in the flume and applied top tensions varied from 15 to 110 N giving fundamental natural frequencies in the range from 3.0 to 7.1 Hz. Reduced velocities based on the fundamental natural frequency up to 16 were reached. The mass ratio was 1.8 and the combined mass–damping parameter about 0.05. Cross-flow and in-line amplitudes, x–y trajectories and phase synchronisation, dominant frequencies and modal amplitudes are reported. Cross-flow amplitudes up to 0.7 diameters and in-line amplitudes over 0.2 were observed with dominant frequencies given by a Strouhal number of 0.16.     

On the force distribution along the axis of a flexible circular cylinder undergoing multi-mode vortex-induced vibrations

One of the main problems in predicting the response of flexible structures subjected to vortex shedding is that a totally reliable model for the fluid loading does not exist. It is also very difficult to measure the distributed force exerted by the fluid along the length of a marine riser without disturbing the system in some way. The methodology described here uses experimental response data obtained in a test programme undertaken in the Delta Flume in Holland during May 2003, linked to a finite element method model (FEM) of the riser. The length-to-diameter ratio of the model used was around 470, the mass ratio (mass/displaced mass) was 3 and the Reynolds number varied between 2800 and 28 000. By using the response data as the input to the numerical model, the instantaneous distributed in-line and transverse forces acting on a flexible cylinder can be studied.     

Parametric vibrations of cylindrical shells subject to geometrically nonlinear deformation: multimode models

The nonlinear parametric vibrations of cylindrical shell are described by the Donnell–Mushtari–Vlasov equations. The motions are represented as a mode expansion. Discretization is performed using the Bubnov–Galerkin method. The describing-function method is used to study traveling waves and nonlinear normal modes in systems with and without dissipation     

On the validity of the independence principle applied to the vortex-induced vibrations of a flexible cylinder inclined at 60°

The vortex-induced vibrations (VIV) of a flexible cylinder inclined at 60° are investigated by means of direct numerical simulation, at a Reynolds number equal to 500, based on the cylinder diameter and inflow velocity. The cylinder has a circular cross-section and a length to diameter aspect ratio equal to 50; it is modeled as a tension-dominated structure which is free to oscillate in the in-line and cross-flow directions. The behavior of the coupled fluid–structure system is examined for two values of the tension. Particular attention is paid to the validity of the independence principle (IP) which states that the inclined and normal-incidence body cases are comparable if the inflow velocity normal component is used to scale the physical quantities.The flexible cylinder exhibits regular VIV for both values of the tension. In the high-tension configuration, where the in-line bending of the structure remains small, the IP is shown to be valid for the prediction of the cylinder responses and the fluid forces. In contrast, in the lower-tension configuration, the behavior of the fluid–structure system deviates from the IP. It is shown that this deviation is connected to the larger in-line bending of the structure which leads to considerably different profiles of the flow velocity locally perpendicular to the body in the inclined and normal cylinder cases. Since the system behavior appears to be mainly driven by this component of the flow, the profile modification induced by the larger in-line bending results in distinct responses: multi-frequency vibrations are observed in the inclined cylinder case whereas mono-frequency oscillations of larger amplitudes develop at normal incidence.     

On the study of vortex-induced vibration of a cylinder with helical strakes

While the effect of helical strakes on suppression of Vortex-Induced Vibrations (VIV) has been studied extensively, the mechanism of VIV mitigation using helical strakes is much less well documented in the literature. In the present study, a rigid circular cylinder of diameter d=80 mm attached with three-strand helical strakes of dimensions of 10d in pitch and 0.12d in height was tested in a wind tunnel. It was found that the helical strakes can reduce VIV by about 98%. Unlike the bare cylinder, which experiences lock-in over the reduced velocity in the range of 5-8.5, the straked cylinder does not show any lock-in region. In exploring the mechanism of VIV reduction by helical strakes, measurements in stationary bare and straked cylinder wakes using both a single X-probe at four different Reynolds numbers, i.e. Re=10 240, 20 430, 30 610 and 40 800, and two X-probes with variable separations in the spanwise direction at Re=20 430 were conducted. It was found that vortices shed from the straked cylinder are weakened significantly. The dominate frequency varies by about 30% over the range of x/d=10-40 in the streamwise direction while that differs by about 37.2% of the averaged peak frequency over a length of 3.125d in the spanwise direction. The latter is supported by the phase difference between the velocity signals measured at two locations separated in the spanwise direction. The correlation length of the vortex structures in the bare cylinder wake is much larger than that obtained in the straked cylinder wake. As a result, the straked cylinder wake agrees more closely with isotropy than the bare cylinder wake. Flow visualization on the plane perpendicular to the cylinder axis at Reynolds number of about 300 reveals small-scale vortices in the shear layers of the straked cylinder wake. However, these vortices do not roll up and interact with each other to form the well-organized Karman-type vortices. Flow visualization on the plane parallel to the cylinder axis shows vortex dislocation and swirling flow, which should be responsible for the variations of the peak frequency in the streamwise as well as spanwise directions.     

Two-degree-of-freedom vortex-induced vibrations using a force assisted apparatus

We report results from two-degree-of-freedom vortex-induced vibration tests on a flexibly mounted, rigid, smooth cylinder in cross-flow. The tests are performed for six in-line natural frequency to transverse natural frequency ratios. The Reynolds number based on diameter ranged from 11 000 to 60 000. To reduce structural damping in both directions, an apparatus utilizing two linear motors was used. Increasing the in-line to transverse frequency ratio caused a shift in the peak amplitude response to increasingly higher reduced velocities; and at a frequency ratio of 1.9, two distinct response peaks appear, in agreement with earlier experiments by Sarpkaya in 1995. Other comparisons are made with the low mass-damping, two-degree-of-freedom experiments by Jauvtis and Williamson in 2004. The frequency ratio affects the phase lag between transverse and in-line oscillations and hence the shape of the cylinder orbital.     

A linear stability approach to vortex-induced vibrations and waves

The motion induced by vortex shedding on slender flexible structures subjected to cross-flow is considered here. This phenomenon of vortex-induced vibration (VIV) is analysed by considering the linear stability of a coupled system that includes the structure dynamics and the wake dynamics. The latter is modelled by a continuum of wake oscillators, distributed along the span of the structure. In the case of uniform flows over a straight tensioned cable, VIV are found to arise as an instability related to the merging of two waves. In the case of a cable of finite length, the selection of modes that experience lock-in with the wake is found using the same stability argument. In non-uniform flows, several unstable wave systems are identified, and competition between them is discussed. Comparison is then made with existing experimental and computational data of VIV of slender structures under uniform and non-uniform flows. Phenomena previously identified in these systems, such as mode switching when the flow velocity is varied, time sharing of the response between two frequencies, or the coexistence of several regions of VIV with different dynamics in the same structure, are discussed with the help of the proposed model.     

Limit-cycle vibrations of a rolling cylinder

An explanation for a violent vibration of a high-speed textile yarn winder is proposed based on the hypothesis that variations in radial compliance around the circumference of the yarn cylinder make the smooth winding process unstable due to parametric excitation. The amplitude of the resulting limit cycle depends on the non-linearity in the radial compliance. An analytical procedure for predicting the limit-cycle amplitude is developed and applied to a specially constructed mechanical model of a yarn winder. The actual response of the mechanical model is accurately predicted when its measured dynamic properties are inserted in the analysis.     

Single-degree-of-freedom model of displacement in vortex-induced vibrations

In contrast to the approach of coupling a nonlinear oscillator that represents the lift force with the cylinder’s equation of motion to predict the amplitude of vortex-induced vibrations, we propose and show that the displacement can be directly predicted by a nonlinear oscillator without a need for a force model. The advantages of the latter approach include reducing the number of equations and, subsequently, the number of coefficients to be identified to predict displacements associated with vortex-induced vibrations. The implemented single-equation model is based on phenomenological representation of different components of the transverse force as required to initiate the vibrations and to limit their amplitude. Three different representations for specific flow and cylinder parameters yielding synchronization for Reynolds numbers between 104 and 114 are considered. The method of multiple scales is combined with data from direct numerical simulations to identify the parameters of the proposed models. The variations in these parameters with the Reynolds number, reduced velocity or force coefficient over the synchronization regime are determined. The predicted steady-state amplitudes are validated against those obtained from high-fidelity numerical simulations. The capability of the proposed models in assessing the performance of linear feedback control strategy in reducing the vibrations amplitude is validated with performance as determined from numerical simulations.

     

The application of controlled variable magnetic eddy current damping to the study of vortex-induced vibrations

A powerful variable magnetic eddy current damping system has been constructed and utilized in an experimental study of vortex-induced vibrations (VIV). This damping system allows us to impose precise values of nearly ideal viscous damping over a wide range of damping values of interest. This new damping system offers improvements over previously utilized damping methods. Unlike most studies of VIV, where the damping cannot be independently controlled, we are able to impose our system damping independent of the other system parameters. Also, because the system only requires that a thin conductive plate be attached to the oscillating system, the overall mass of the system does not increase dramatically and still allows the investigation of very low mass systems. Finally, the system can operate in a steady-state fashion, supplying a constant damping value for an extended period of time, or in a transient fashion, where the damping value is intentionally varied over time. With this damping system, we have systematically explored both steady and transient damping effects on VIV behavior and provide a brief overview of some sample results.     

Influence of slip on vortex-induced motion of a superhydrophobic cylinder

The partial slip boundary condition produced by a superhydrophobic surface in the Cassie state has been shown capable of reducing skin friction drag as well as influencing the flow around coated bodies including cylinders and spheres. In this paper, we investigated how the changes in vortex shedding and separation previously observed on superhydrophobic cylinders affects the rms lift force and the resulting oscillations induced on an elastically mounted cylinder. Two hydrophobic polytetrafluoroethylene cylinders were studied. The first was smooth and the second was roughened to make it superhydrophobic and to induce slip. The presence of slip was found to decrease rms lift and amplitude of the oscillating cylinder by up to 15% with no measurable impact on drag or the natural frequency of the elastically mounted system. We show that the observed reductions are a direct result of reduced fluid forcing on the superhydrophobic cylinder.