Multi-frequency vortex-induced vibrations of a long tensioned beam in linear and exponential shear flows

The multi-frequency vortex-induced vibrations of a cylindrical tensioned beam of aspect ratio 200, free to move in the in-line and cross-flow directions within first a linearly and then an exponentially sheared current are investigated by means of direct numerical simulation, at a Reynolds number equal to 330. The shape of the inflow profile impacts the spectral content of the mixed standing-traveling wave structural responses: narrowband vibrations are excited within the lock-in area, which is limited to a single region lying in the high flow velocity zone, for the linear shear case; in contrast, the lock-in condition occurs at several spanwise locations in the exponential shear case, resulting in broadband responses, containing a wide range of excited frequencies and spatial wavenumbers. The broadband in-line and cross-flow vibrations occurring for the exponential shear current have a phase difference that lies within a specific range along the entire span; this differs from the phase drift noted for narrowband responses in linear shear flow. Lower vibration amplitudes, time-averaged and fluctuating in-line force coefficients are observed for the exponential shear current. The cross-flow force coefficient has comparable magnitude for both inflow profiles along the span, except in zones where the broadband vibrations are under the lock-in condition but not the narrowband ones. As in the narrowband case, the fluid forces associated with the broadband responses are dominated by high frequencies related to high-wavenumber vibration components. Considerable variability of the effective added mass coefficients along the span is noted in both cases.     

Lock-in of the vortex-induced vibrations of a long tensioned beam in shear flow

The occurrence of lock-in, defined as the local synchronization between the vortex shedding frequency and the cross-flow structural vibration frequency, is investigated in the case of a tensioned beam of length to diameter ratio 200, free to move in both the in-line and cross-flow directions, and immersed in a linear shear current. Direct numerical simulation is employed at three Reynolds numbers, from 110 to 1100, so as to include the transition to turbulence in the wake. The Reynolds number influences the response amplitudes, but in all cases we observed similar fluid–structure interaction mechanisms, resulting in high-wavenumber vortex-induced vibrations consisting of a mixture of standing and traveling wave patterns.Lock-in occurs in the high oncoming velocity region, over at least 30% of the cylinder length. In the case of multi-frequency response, at any given spanwise location lock-in is principally established at one of the excited vibration frequencies, usually the locally predominant one. The spanwise patterns of the force and added mass coefficients exhibit different behaviors within the lock-in versus the non-lock-in region. The spanwise zones where the flow provides energy to excite the structural vibrations are located mainly within the lock-in region, while the flow damps the structural vibrations in the non-lock-in region.     

Active vortex-induced vibration control of a circular cylinder at low Reynolds numbers using an adaptive fuzzy sliding mode controller

An adaptive fuzzy sliding mode control (AFSMC) scheme is applied to actively suppress the two-dimensional vortex-induced vibrations (VIV) of an elastically mounted circular cylinder, free to move in in-line and cross-flow directions. Laminar flow regime at Re=90, low non-dimensional mass with equal natural frequencies in both directions, and zero structural damping coefficients, are considered. The natural oscillator frequency is matched with the vortex shedding frequency of a stationary cylinder at Re=100. The strongly coupled unsteady fluid/cylinder interactions are captured by implementing the moving mesh technology through integration of an in-house developed User Define Function (UDF) into the main code of the commercial CFD solver Fluent. The AFSMC approach comprises of a fuzzy system designed to mimic an ideal sliding-mode controller, and a robust controller intended to compensate for the difference between the fuzzy controller and the ideal one. The fuzzy system parameters as well as the uncertainty bound of the robust controller are adaptively tuned online. A collaborative simulation scheme is realized by coupling the control model implemented in Matlab/Simulink to the plant model constructed in Fluent, aiming at determination of the transverse control force required for complete suppression of the cylinder streamwise and cross-flow oscillations. The simulation results demonstrate the high performance and effectiveness of the adopted control algorithm in attenuating the 2D-VIV of the elastic cylinder over a certain flow velocity range. Also, the enhanced transient performance of the AFSM control strategy in comparison with a conventional PID control law is demonstrated. Furthermore, the effect of control action on the time evolution of vortex shedding from the cylinder is discussed. In particular, it is observed that the coalesced vortices in the far wake region of the uncontrolled cylinder, featuring the C(2S)-type vortex shedding characteristic mode, are ultimately forced to switch to the classical von Kármán vortex street of 2S-type mode, displaying wake vortices of moderately weaker strengths very similar to those of the stationary cylinder. Lastly, robustness of AFSMC is verified against relatively large structural uncertainties as well as with respect to a moderate deviation in the uniform inlet flow velocity.     

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.     

An experimental investigation of one- and two-degree of freedom VIV of cylinders

In the paper,an experiment investigation was conducted for one-and two-degree of freedom vortex-induced vibration(VIV) of a horizontally-oriented cylinder with diameter of 11 cm and length of 120 cm.In the experiment,the spring constants in the cross-flow and in-line flow directions were regulated to change the natural vibration frequency of the model system.It was found that,in the one-degree of freedom VIV experiment,a "double peak" phenomenon was observed in its amplitude within the range of the reduced velocities tested,moreover,a "2T" wake appeared in the vicinity of the second peak.In the two-degree of freedom VIV experiment,the trajectory of cylinder exhibited a reverse "C" shape,i.e.,a "new moon" shape.Through analysis of these data,it appears that,besides the non-dimensional in-line and cross-flow natural vibration frequency ratios,the absolute value of the natural vibration frequency of cylinder is also one of the important parameters affecting its VIV behavior.     

Cross-flow past a pair of nearly in-line cylinders with the upstream cylinder subjected to a transverse harmonic oscillation

An experimental investigation is presented for the cross-flow past a pair of staggered circular cylinders, with the upstream cylinder subject to forced harmonic oscillation transverse to the flow direction. Experiments were conducted in a water tunnel with Reynolds numbers, based on upstream velocity, U, and cylinder diameter, D, in the range 1440⩽Re⩽1680. The longitudinal separation between cylinder centres is L/D=2.0, with a transverse separation (for the mean position of the upstream cylinder) of T/D=0.17; the magnitude of the harmonic oscillation is 0.44D peak-to-peak and the nondimensional frequency range of the excitation is 0.05⩽f_eD/U⩽0.44. Flow visualization of the wake-formation region and hot-film measurements of the wake spectra are used to investigate the wake-formation process. An earlier study showed that stationary cylinders in this nearly in-line configuration straddle two very different flow regimes, the so-called shear-layer reattachment (SLR) and induced separation (IS) regimes. The present study, demonstrates that oscillation of the upstream cylinder causes considerable modification of the flow patterns around the cylinders. In particular, the wake experiences strong periodicities at the frequency of the oscillating cylinder; in addition to the usual fundamental lock-in, both sub- and superharmonic resonances are obtained. It is also observed that, although the flow exhibits regions of SLR and IS for excitation frequencies below the fundamental lock-in, for frequencies above the lock-in range the flow no longer resembles either of these flow regimes and vortices are formed in the gap between the cylinders.     

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.     

Shear flow induced vibrations of long slender cylinders with a wake oscillator model

A time domain model is presented to study the vibrations of long slender cylinders placed in shear flow. Long slender cylinders such as risers and tension legs are widely used in the field of ocean engineering. They are subjected to vortex-induced vibrations(VIV) when placed within a transverse incident flow. A three dimensional model coupled with wake oscillators is formulated to describe the response of the slender cylinder in cross-flow and in-line directions. The wake oscillators are distributed along the cylinder and the vortex-shedding frequency is derived from the local current velocity. A non-linear fiuid force model is accounted for the coupled effect between cross-flow and in-line vibrations. The comparisons with the published experimental data show that the dynamic features of VIV of long slender cylinder placed in shear flow can be obtained by the proposed model,such as the spanwise average displacement,vibration frequency,dominant mode and the combination of standing and traveling waves. The simulation in a uniform flow is also conducted and the result is compared with the case of nonuniform flow. It is concluded that the flow shear characteristic has significantly changed the cylinder vibration behavior.     

TWO-DIMENSIONAL VORTEX-INDUCED VIBRATION OF CABLE SUSPENSIONS

Resonant responses of suspended elastic cables driven by a steady current are investigated. Phenomenological fluid force models for alternate vortex-shedding are coupled with the nonlinear partial differential equations of cable motion. Decoupled cross-flow and in-line vortex-induced vibrations (VIV) are examined first using linearized and nonlinear cable models. The linearized cable model predicts well the basic characteristics of VIV and the nonlinear cable model captures the hysteresis often observed in experiments. Next, coupled cross-flow and in-line vibrations are evaluated by considering two principal coupling mechanisms: (i) cable structural nonlinearities, and (ii) coupled fluid lift and drag. Attention is focused on a “worst-case” resonant response where the natural frequencies for cable modes in the cross-flow and in-line directions are in the same 1:2 ratio as the excitation frequencies associated with lift and drag. The inclusion of cable structural nonlinearities alone leads to coupled responses that differ qualitatively (i.e., in number and stability of periodic motions) when compared to those of the decoupled model. The inclusion of coupled fluid lift and drag produces non-planar “figure eight” motions of the cable cross-section that exhibit similar characteristics to those previously measured on spring supported cylinders.     

A simplified method for time domain simulation of cross-flow vortex-induced vibrations

A new method for time domain simulation of cross-flow vortex-induced vibrations of slender circular cylindrical structures is developed. A model for the synchronization between the lift force and structure motion is derived from already established data for the cross-flow excitation coefficient. The proposed model is tested by numerical simulations, and the results are compared to experimental observations. When a sinusoidal cross-flow motion is given as input to the algorithm, the generated force time series are generally in good agreement with experimental measurements of cross-flow force in phase with cylinder velocity and acceleration. The model is also utilized in combination with time integration of the equation of motion to simulate the cross-flow vibration of a rigid cylinder. The resulting amplitude and frequency of motion as functions of reduced velocity are compared to published experimental results. In combination with the finite element method, the model is used to simulate cross-flow vibrations of a flexible cylinder in shear flow. Comparison with experiments shows that the model is capable of reproducing important quantities such as frequency, mode and amplitude, although some discrepancies are seen. This must be expected due to the complexity of the problem and the simple form of the present method.     

柔性圆柱涡激振动流体力系数识别及其特性

涡激振动是诱发海洋立管、浮式平台系泊缆和海底悬跨管道等柔性圆柱结构疲劳损伤的重要因素.目前,海洋工程中用于柔性圆柱涡激振动预报的流体力系数主要来源刚性圆柱横流向受迫振动的实验数据,存在一定缺陷和误差.本文综合考虑横流向与顺流向振动耦合作用,建立了柔性圆柱涡激振动流体力模型,运用有限元法和最小二乘法确定升力系数、脉动阻力系数和附加质量系数.为了准确识别柔性圆柱涡激振动流体力系数,设计并开展了拖曳水池模型实验,实验用柔性圆柱模型的质量比为1.82,长径比为195.5.通过与刚性圆柱流体力系数对比,深入分析了柔性圆柱流体力系数的特性.结果表明:柔性圆柱在一阶模态控制区,流体力系数随约化速度变化趋势与刚性圆柱大致相似;二阶模态控制区,升力系数和脉动阻力系数显著增大;附加质量系数在响应频率较低时与振动位移的相关性增强;当响应频率较低时,振动位移较大区域为能量耗散区,当响应频率较高时,振动位移较大区域为能量输入区.     

Flow-induced oscillation of two circular cylinders in tandem arrangement at low Re

Results are presented for flow-induced vibrations of a pair of equal-sized circular cylinders of low nondimensional mass (m^*=10) in a tandem arrangement. The cylinders are free to oscillate both in streamwise and transverse directions. The Reynolds number, based on the free-stream speed and the diameter of the cylinders, D is 100 and the centre-to-centre distance between the cylinders is 5.5D. The computations are carried out for reduced velocities in the range 2≤U^*≤15. The structural damping is set to zero for enabling maximum amplitudes of oscillation. A stabilized finite element method is utilized to carry out the computations in two dimensions. Even though the response of the upstream cylinder is found to be qualitatively similar to that of an isolated cylinder, the presence of a downstream cylinder is found to have significant effect on the behaviour of the upstream cylinder. The downstream cylinder undergoes very large amplitude of oscillations in both transverse and streamwise directions. The maximum amplitude of transverse response of the downstream cylinder is quite similar to that of a single cylinder at higher Re beyond the laminar regime. Lock-in and hysteresis are observed for both upstream and downstream cylinders. The downstream cylinder undergoes large amplitude oscillations even beyond the lock-in state. The phase between transverse oscillations and lift force suffers a 180 jump for both the cylinders almost in the middle of the synchronization regime. The phase between the transverse response of the two cylinders is also studied. Complex flow patterns are observed in the wake of the freely vibrating cylinders. Based on the phase difference and the flow patterns, the entire flow range is divided into five sub-regions.     

On shear flow single mode lock-in with both cross-flow and in-line lock-in mechanisms

A long flexible cylinder exposed to ocean currents is known to undergo vortex-induced vibration (VIV). In a spatially sheared flow the response of a riser to VIV can vary from single mode lock-in to multimodal. A new experimental facility was designed and built to investigate the above-mentioned areas. The facility consisted of a long flexible cylinder in either a uniform or a simplified vertically sheared flow. The instrumentation consisted of direct local fluid force measurement at two locations on the cylinder as well as accelerometers spaced along the cylinder axis. The simplified shear flow was a 2-slab flow, with each slab having uniform velocity. Test conditions included forcing the cylinder simultaneously at resonance in both regions to investigate modal competition issues and multimodal response patterns. Resonant VIV excitation of two different modes simultaneously, was conducted which revealed single mode lock-in of the higher frequency through an unexpected mechanism. The higher frequency mode's damping region underwent in-line excitation at four times the predicted shedding frequency that provided a power-in effect to support the dominant mode's cross-flow response.     

Characterization of long time fluctuations of forces exerted on an oscillating circular cylinder at KC=10

Flow dynamics, in-line and transverse forces exerted on an oscillating circular cylinder in a fluid initially at rest are studied by numerical resolution of the two-dimensional Navier-Stokes equations. The Keulegan-Carpenter number is held constant at KC=10 and Re is increased from 40 to 500. For the different flow regimes, links between flow spatio-temporal symmetries and force histories are established. Besides simulations of long duration show that in two ranges of Re, forces exhibit low frequency fluctuations compared to the cylinder oscillation frequency. Such observations have been only mentioned in the literature and are more deeply examined here. In both ranges, force fluctuations correspond to oscillations of the front and rear stagnation points on the cylinder surface. However, they occur in flow regimes whose basic patterns (V-shaped mode or diagonal mode) have different symmetry features, inducing two distinct behaviors. For 80≤Re≤100, fluctuations are related to a spectral broadening of the harmonics and to a permutation between three vortex patterns (V-shaped, transverse and oblique modes). In the second range 150≤Re≤280, amplitude fluctuations are correlated to the appearance of low frequency peaks interacting with harmonics of the cylinder frequency. Fluctuations are then a combination of a wavy fluctuation and an amplitude modulation. The carrier frequency corresponding to the wavy fluctuation depends on Re and is related to a fluid characteristic time; the modulation frequency is independent of Re and equal to 1/4 of the cylinder oscillation frequency.     

Three-dimensional computation for flow-induced vibrations of an upstream circular cylinder in two tandem circular cylinders

It is well known from a lot of experimental data that fluid forces acting on two tandem circular cylinders are quite different from those acting on a single circular cylinder. Therefore, we first present numerical results for fluid forces acting on two tandem circular cylinders, which are mounted at various spacings in a smooth flow, and second we present numerical results for flow-induced vibrations of the upstream circular cylinder in the tandem arrangement. The two circular cylinders are arranged at close spacing in a flow field. The upstream circular cylinder is elastically placed by damper-spring systems and moves in both the in-line and cross-flow directions. In such models, each circular cylinder is assumed as a rigid body. On the other hand, we do not introduce a turbulent model such as the Large Eddy Simulation (LES) or Reynolds Averaged Navier-Stokes (RANS) models into the numerical scheme to compute the fluid flow. Our numerical procedure to capture the flow-induced vibration phenomena of the upstream circular cylinder is treated as a fluid-structure interaction problem in which the ideas of weak coupling is taken into consideration.     

Vortex-shedding from single and tandem cylinders in the presence of applied sound

A single cylinder and two tandem cylinder configurations with longitudinal pitch ratios L/D=1.75 and 2.5 were rigidly mounted in an open circuit wind tunnel and a standing acoustic pressure wave was imposed so that the acoustic particle velocity was normal to both the cylinder axis and the mean flow velocity. The effect of sound on the vortex-shedding was investigated for various amplitudes by means of pressure taps on the cylinders and wake hot-wire probes. These tests show that applied sound can entrain and shift the natural vortex-shedding frequency to the frequency of excitation and produce nonlinearities in the wake. The lock-in envelope for the tandem cylinders is considerably larger than for the single cylinder. The lock-in range for the smaller tandem cylinder spacing was broader still than either the single cylinder, or the L/D=2.5 tandem cylinder case. The pressure and hot-wire measurements show for the single cylinder, and tandem cylinder configuration with pitch ratio L/D=2.5, that there was a phase jump near the coincidence of the vortex-shedding frequency and the excitation frequency, while there was no jump for the pitch ratio of 1.75. As well, the applied sound field was also noted to induce vortex-shedding in the gap for the L/D=2.5 case, while no vortex-shedding was noted for the smaller pitch ratio.     

System identification of the kinematics of an oscillating cylinder using wake velocities

A classical problem in vortex-induced vibration is to know the flow field past an oscillating cylinder. In this paper we use system theory to identify the oscillatory behaviour of a circular cylinder from flow variables in the wake. We use numerical simulations (CFD) of the flow past a cylinder oscillating in the cross-flow direction at different oscillation frequencies and amplitudes to construct a transfer function that relates the displacement of the cylinder and the resulting flow field. This transfer function can then be inverted to ‘predict’ the displacement of the cylinder given the flow field (as determined by simulations or measurements). We investigate this technique in the so-called lock-in region, where the vortex shedding frequency is synchronised with the oscillation frequency of the cylinder.     

Wake-induced vibrations of an elastically mounted cylinder located downstream of a stationary larger cylinder at low Reynolds numbers

Two-dimensional numerical simulations of flow past two unequal-sized circular cylinders in tandem arrangement are performed at low Reynolds numbers (Re). The upstream larger cylinder is stationary, while the downstream cylinder has both one (transverse-only) and two (transverse and in-line) degrees of freedom (1-dof and 2-dof, respectively). The Re, based on the free stream velocity U_∞ and the downstream cylinder diameter d, varies between 50 and 200 with a wide range of reduced velocities U_r. The diameter of the upstream cylinder is twice that of the downstream cylinder, and the center-to-center spacing is 5.5d. In general, for the 1-dof case, the calculations show that the wake-induced vibrations (WIV) of the downstream cylinder are greatly amplified when compared to the case of a single cylinder or two equal-sized cylinders. The transverse amplitudes build up to a significantly higher level within and beyond the lock-in region, and the U_r associated with the peak amplitude shifts toward a higher value. The dominant wake pattern is 2S mode for Re=50 and 100, while with the increase of Re to 150 and 200, the P+S mode can be clearly observed at some lower U_r. For the 2-dof vibrations, the transverse response characteristics are similar to those presented in the corresponding 1-dof case. The in-line responses are generally much smaller, except for several significant vibrations resulting from in-line resonance. The obvious in-line vibration may induce a C (chaotic) vortex shedding mode for higher Re (Re=200). With regard to the 2-dof motion trajectories, besides the typical figure-eight pattern, several odd patterns such as figure-double eight and single-looped trajectories are also obtained due to the wake interference effect.     

Vortex-induced vibration of two elastically coupled cylinders in side-by-side arrangement

Vortex-induced vibration (VIV) of two elastically coupled circular cylinders in side-by-side arrangement is investigated numerically. The Reynolds-averaged Navier–Stokes equations are solved by the finite element method for simulating the flow and the equation of motion is solved for calculating the vibration. The mass ratio (the ratio of the mass of the cylinder to the displaced fluid mass) is 2 and the Reynolds number is 5000 in the simulations. Simulations are carried out for one symmetric configuration (referred to be Case A) and one asymmetric configuration (referred to be Case B). In both Case A and Case B, the primary response frequencies of the two cylinders are found to be the same both inside and outside the lock-in regimes. Five response regimes are found in both cases and they are the first-mode lock-in regime, the second-mode lock-in regime, the sum-frequency lock-in regime and two transition regimes. When the vibration is transiting from the first- to the second-mode lock-in regimes, the vibration of each cylinder contains both first- and the second-mode natural frequencies, and the vibrations are usually irregular. In the transition regime between the second-mode lock-in and the sum-frequency lock-in regimes, the response frequencies of both cylinders increases with an increase in the reduced velocity until they are close to the sum of the two natural frequencies. In both cases, the lower boundary reduced velocity of the total lock-in regime (the sum of the five lock-in regimes) is about 3 and the upper boundary reduced velocity is about 11 times the first-to-second-mode natural frequency ratio.     

Free v/s forced vibrations of a cylinder at low Re

Free vibrations of a circular cylinder of low non-dimensional mass are investigated at low Reynolds numbers. Computations are carried out for 5% blockage. Lock-in is observed for a range of Re and is accompanied with hysteresis at both lower as well as higher Re ends of the synchronisation/lock-in region. It is well known that the lock-in regime for free vibrations depends on the non-dimensional mass of the oscillator. The results from the present computations are compared with the data for forced vibrations from Koopmann (Journal of Fluid Mechanics, 28, 501–512, 1967) on a Y _max/D vs. f* plot, where Y _max is the maximum oscillation amplitude and f* is the ratio of cylinder vibration frequency to the vortex shedding frequency for a stationary cylinder. Good agreement is observed for the critical amplitude needed for onset of synchronisation between the forced and free vibrations. The results from the free vibrations are compared to the predictions from the linear oscillator model by assuming that the forces on the cylinder are unaffected as a result of vibrations. It is found that, for low mass oscillators, the modification of vortex shedding frequency and lift coefficient due to cylinder oscillations leads to the enhancement of the lock-in regime.