Suppression of vortex-induced vibration of a circular cylinder using suction-based flow control

In the present study, a flow control method is employed to mitigate vortex-induced vibration (VIV) of a circular cylinder by using a suction flow method. The VIV of a circular cylinder was first reproduced in a wind tunnel by using a spring–mass system. The time evolution of the cylinder oscillation and the time histograms of the surface pressures of 119 taps in four sections of the circular cylinder model were measured during the wind tunnel experiments. Four steady suction flow rates were used to investigate the effectiveness of the suction control method to suppress VIV of the circular cylinder. The vibration responses, the mean and fluctuating pressure coefficients, and the resultant aerodynamic force coefficients of the circular cylinder under the suction flow control are analyzed. The measurement results indicate clearly that the steady suction flow control method exhibits excellent control effectiveness and can distinctly suppress the VIV by dramatically reducing the amplitudes of cylinder vibrations, fluctuating pressure coefficients and lift coefficients of the circular cylinder model. By comparing the test cases with different suction flow rates, it is found that there exists an optimal suction flow rate for the maximum VIV control. The cases with higher suction flow rates do not necessarily behave better than those with lower suction flow rates. With the experimental setting used in the present study, the suction flow control method is found to behave better for VIV suppression when the ratio of the suction flow velocity to the oncoming flow velocity is less than one.     

近壁面柱体涡激振动的迟滞效应

柱体涡激振动是典型的流固耦合问题,其响应规律标识码在升速流动和远离壁面条件下获得的. 而自然环境流动通常不断经历升速和降速过程,近壁面柱体的涡激振动可呈现与远离标识码体不同的响应特征. 本研究结合大型波流水槽,设计了具有微结构阻尼的柱体涡激振动装置. 基于量纲分析,开展系列水槽标识码验,通过同步测量柱体涡激振动位移时程和绕流流场变化,研究了升降流速作用下柱体涡激振动触发和停振的临界速度(即上临标识码临界速度)变化规律,探究了近壁面柱体涡激振动迟滞效应. 采用自下向上激光扫射的 PIV 流场测量系统,对比分析了固定柱体标识码振动柱体的绕流特征. 实验观测表明,近壁面柱体涡激振动触发的临界速度呈现随壁面间距比减小而逐渐减小的变化趋势;但标识码速条件下的涡激振动停振所对应的下临界速度却明显小于升速时的涡激振动触发所对应的上临界速度. 采用上临界与下临界约标识码差值可定量表征涡激振动迟滞程度,研究发现该值随着柱体间距比减小呈线性增大趋势. 涡激振动迟滞现象通常伴随振幅阶跃标识码阶跃值则随着间距比减小而非线性减小.      

An experimental investigation on vortex induced vibration of a flexible inclined cable under a shear flow

In the present study, an experimental investigation was performed to characterize the vortex induced vibration (VIV) of a flexible cable in an oncoming shear flow. The VIV tests were conducted in a wind tunnel with a flexible cable model. It was found that, under different oncoming velocity profiles, the cable model behaved in single-mode and multi-mode VIVs. The displacement amplitudes of the single mode VIVs were found to be larger than those of multi-mode VIVs, and the cross-flow (CF) response was larger than that of in-line (IL) direction for either the single mode or multi-mode VIVs. For a single mode vibration, the largest CF response occurs in the 1st mode VIV, and the motion trajectory of the 1st mode VIV was found to be an inclined figure of eight shape, while other single mode VIVs behaved in ellipse or straight line trajectories. For multi-mode VIVs, no stable vibration trajectories were found to exist since the vibration frequency bands covered two or more vibration modes. The vortex-shedding frequencies in the wake behind the inclined cable were also characterized in the present study. The shedding frequencies of the wake vortices were found to coincide well with the vibration modes: for a single mode VIV, they were close to the dominant vibration mode; for a multi-mode VIV, they could also cover the appearing vibration modes.     

Vortex- and wake-induced vibrations of a tandem arrangement of two flexible circular cylinders with far wake interference

The dynamic response of two flexible cylinders in tandem arrangement partially immersed in a uniform flow is analysed. The centre-to-centre separations, larger than 4 and up to 8 diameters, were chosen to fall in the regime in which two separate wakes exist behind each one of the models. For the cases presented here, it has been confirmed that the main excitation mechanism is wake-induced vibration (WIV). The rear cylinder shows large amplitudes of response, at reduced velocities over the expected ones at lock-in when a cylinder is undergoing VIV being isolated. This type of response has been also observed by other researchers in experiments with flexibly mounted cylinders in the wake of stationary ones, we also provide data here, for cases with the front cylinder being stationary.     

Numerical simulation of two-degree-of-freedom vortex-induced vibration of a circular cylinder close to a plane boundary

Two-degree-of-freedom vortex-induced vibrations (VIV) of a circular cylinder close to a plane boundary are investigated numerically. The Reynolds-Averaged Navier-Stokes (RANS) equations are solved using the Arbitrary Lagrangian Eulerian (ALE) scheme with a k-ω turbulence model closure. The numerical model is validated against experimental data of VIV of a cylinder in uniform flow and VIV of a cylinder close to a plane boundary at low mass ratios. The numerical results of the vibration mode, vibration amplitude and frequency agree well with the experimental data. VIV of a circular cylinder close to a plane boundary is simulated with a mass ratio of 2.6 and gap ratios of e/D=0.002 and 0.3 (gap ratio is defined as the ratio of gap between the cylinder and the bed (e) to cylinder diameter (D)). Simulations are carried out for reduced velocities ranging from 1 to 15 and Reynolds numbers ranging from 1000 to 15 000. It is found that vortex-induced vibrations occur even if the initial gap ratio is as small as e/D=0.002, although reported research indicated that vortex shedding behind a fixed circular cylinder is suppressed at small gap ratios (e/D<0.3 or 0.2). It was also found that vibration amplitudes are dependant on the bouncing back coefficient when the cylinder hits the plane boundary. Three vortex shedding modes are identified according to the numerical results: (i) single-vortex mode where the vortices are only shed from the top of the cylinder; (ii) vortex-shedding-after-bounce-back mode; (iii) vortex-shedding-before-bounce-back mode. It was found that the vortex shedding mode depends on the reduced velocity.     

倾斜圆柱结构涡激振动研究进展

圆柱结构涡激振动现象在生活中十分常见,如海洋工程中的管道、土木工程中的高耸建筑、桥梁斜拉索,核工程中的热交换器等频繁受到涡激振动影响,诱发结构的疲劳损伤,甚至破坏失效.现阶段,人们对垂直来流作用下圆柱结构涡激振动机理已有较为全面的认识.然而,当圆柱倾斜置于流场中,结构后缘的尾流形态与垂直放置差异显著,结构与流体的耦合作用机理更为复杂.为简化倾斜圆柱涡激振动问题,提出了不相关原则,来流速度被分解为垂直圆柱结构轴向和平行圆柱结构轴向的两个速度分量,仅考虑垂直结构轴向速度分量的影响,忽略平行结构轴向速度分量的影响.近年来,针对倾斜圆柱涡激振动及不相关原则的适用性,出现了大量实验和数值模拟研究成果.为了深化对倾斜圆柱结构涡激振动相关机理的认知,本文全面阐述了倾斜圆柱结构涡激振动响应规律、尾迹流场模式和流体力特性等方面的研究进展,分析了不相关原则的适用范围,探讨了倾斜圆柱结构涡激振动抑制措施,并对今后该领域的研究进行了力所能及的展望.     

Wake-boundary layer interaction subject to convex and concave curvatures and adverse pressure gradient

Measurements of mean velocity and turbulent quantities have been carried out when the wake of a symmetrical airfoil interacts with the boundary layer on the (i) walls of a straight duct/diffuser and (ii) convex and concave walls of a curved duct/diffuser. The effects of adverse pressure gradient and of curvatures on the interaction are studied separately and in combination. Six cases are considered, viz. with (i) neither pressure gradient nor curvature, (ii) adverse pressure gradient and no curvature, (iii) and (iv) convex curvature with zero and adverse pressure gradients, respectively, (v) and (vi) concave curvature with zero and adverse pressure gradients, respectively. For the flows with curvature, the curvature parameter δ/R is 0.023, and for the flows with adverse pressure gradient, the Clauser pressure gradient parameter β is 0.62. The individual influences of adverse pressure gradient and convex and concave curvatures on the boundary layer are similar to those observed by earlier investigations. It is further observed that the combined effect of concave/convex curvature and the adverse pressure gradient causes higher turbulence intensities than the sum of the individual effects. The effect of curvature is to make the wake asymmetric, and in combination with adverse pressure gradient the asymmetry increases. It is observed that the adverse pressure gradient causes faster wake–boundary-layer interaction. Comparing measurements in a straight duct, a curved duct, a curved diffuser and a straight diffuser, it is seen that the convex curvature reduces the boundary layer thickness. The asymmetry in wake development compensates for this effect and the wake–boundary-layer interaction on a convex surface is almost the same as that on a straight surface. In the case of interaction with the boundary layer on a concave surface, the curvature increases the boundary layer thickness and causes enhanced turbulence intensities. However, the asymmetry in wake is such that the extent of wake is lower towards the boundary layer side. As a result, the wake–boundary-layer interaction on concave surface is almost the same as on a straight surface. The interaction is faster in the presence of adverse pressure gradient. Received: 16 June 2000 / Accepted: 17 May 2001     

A harmonic balance technique for the reduced-order computation of vortex-induced vibration

We present a harmonic balance (HB) method to model frequency lock-in effect during vortex-induced vibration (VIV) of elastically mounted circular cylinder and a flexible riser section in a freestream uniform flow. The fluid flow and structure are coupled by a fixed-point iteration process through a frequency updating algorithm. By minimizing the structural residual in the standard least-square norm, the convergence of HB-based fixed-point algorithm is achieved for a range of reduced velocity. To begin with, the HB solver is first assessed for a periodic unsteady flow around a stationary circular cylinder. A freely vibrating circular cylinder is then adopted for the reduced-order computation of VIV at low Reynolds numbers of Re=100 and 180 with one- and two-degrees-of-freedom. The coupled VIV dynamics and the frequency lock-in phenomenon are accurately captured. The results show that the HB solver is able to predict the amplitude of vibration, frequency and forces comparable to its time domain counterpart, while providing a significant reduction with regard to overall computational cost. The proposed new scheme is then demonstrated for a fully-coupled three dimensional (3D) analysis of a linear-elastic riser section undergoing vortex-induced vibration in the lock-in range. The results reveal the 3D effects through isosurfaces of streamwise vorticity blobs distributed over the span of flexible riser section. In comparison to time domain results, the 3D flow-structure interactions are accurately predicted while providing a similar speed up rate that of 2D simulations. This further corroborates that the HB solver can be extended to 3D flow-structure dynamics without compromising efficiency and accuracy.     

Numerical investigation on vortex-induced vibration of an elastically mounted circular cylinder at low Reynolds number using the fictitious domain method

A direct numerical simulation of two-dimensional (2D) flow past an elastically mounted circular cylinder at low Reynolds number using the fictitious domain method had been undertaken. The cylinder motion was modelled by a two degree-of-freedom mass–spring–damper system. The computing code was verified against a benchmark problem in which flow past a stationary circular cylinder is simulated. Then, analyses of vortex-induced vibration (VIV) responses, drag and lift forces and the phase and vortex structures were carried out. Results show that the cylinder's non-dimensional cross-flow response amplitude reaches its summit of 0.572 in the ‘lock-in’ regime. The ‘2S’, instead of the ‘2P’, vortex shedding mode is dominated in the ‘lower’ branch for this 2D low-Re VIV. A secondary oscillation is observed in the lift force when ‘lock-in’ occurs. It is shown that this secondary component changes the phase, offset the energy input by the primary component and thus reduces the cylinder responses. Effects of the Skop–Griffin parameter on cylinder responses were also investigated.     

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.     

URANS vs. experiments of flow induced motions of multiple circular cylinders with passive turbulence control

Two-dimensional Unsteady Reynolds-Average Navier–Stokes equations with the Spalart–Allmaras turbulence model are used to simulate the flow induced motions of multiple circular cylinders with passive turbulence control (PTC) in steady uniform flow. Four configurations with 1, 2, 3, and 4 cylinders in tandem are simulated and studied at a series of Reynolds numbers in the range of 30 000<Re<120 000. Simulation results are verified by experimental data measured in the Marine Renewable Energy Laboratory. Good agreement was observed between the values of vorticity, amplitude ratio, and frequency ratio predicted by numerical simulations and experimental measurements. The amplitude and frequency response show the initial and upper branches in vortex induced vibration (VIV), transition from VIV to galloping, and galloping branch for all PTC-cylinders. The maximum amplitude of 2.9 diameters for the first cylinder is achieved at Re=104 356 in the numerical results. Compared with the first cylinder, the VIV initial branch starts at higher Re for the downstream cylinders due to the presence of the upstream cylinder(s). 2P and 2P+2S vortex patterns are observed at Re=62 049 and Re=90 254 for the single PTC-cylinder. Furthermore, the shed vortices of the downstream cylinders are strongly disrupted and modified by the vortices shed from the upstream one in the cases of multiple PTC-cylinders.     

Internal resonance of pipes conveying fluid in the supercritical regime

This paper treats nonlinear vibration of pipes conveying fluid in the supercritical regime. If the flow speed is larger than the critical value, the straight equilibrium configuration becomes unstable and bifurcates into two possible curved equilibrium configurations. The paper focuses on the nonlinear vibration around each bifurcated equilibrium. The disturbance equation is derived from the governing equation, a nonlinear integro-partial-differential equation, via a coordinate transform. The Galerkin method is applied to truncate the disturbance equation into a two-degree-of-freedom gyroscopic systems with weak nonlinear perturbations. The internal resonance may occur under the certain condition of the supercritical flow speed for the suitable ratio of mass per unit length of pipe and that of fluid. The method of multiple scales is applied to obtain the relationship between the amplitudes in the two resonant modes. The time histories predicted by the analytical method are compared with the numerical ones and the comparisons validate the analytical results when the nonlinear terms are small.     

Three-dimensional numerical simulation of vortex-induced vibration of an elastically mounted rigid circular cylinder in steady current

Vortex-induced vibration (VIV) of an elastically mounted rigid circular cylinder in steady current is investigated by solving the three-dimensional Navier–Stokes equations. The cylinder is allowed to vibrate only in the cross-flow direction. The aim of this study is to investigate the variation of the vortex shedding flow in the axial direction of the cylinder and to study the transition of the flow from two-dimensional (2D) to three-dimensional (3D) for VIV of a cylinder. Simulations are carried out for a constant mass ratio of 2, the Reynolds numbers ranging from 150 to 1000 and the reduced velocities ranging from 2 to 12. The three-dimensionality of the flow is found to be the strongest in the upper branch of the VIV response and weakest in the initial branch. The 2S and 2P vortex shedding modes are found to coexist along the cylinder span in the upper branch, leading to strong variations of the lift coefficient in the axial direction of the cylinder. The difference between the flow transition from 2D to 3D in the VIV lock-in regime and that in the wake of a stationary cylinder is identified. The transition mode B found in the wake of a stationary cylinder is also found in the wake of a vibrating cylinder. The critical Reynolds number for flow transition from 2D to 3D of a cylinder undergoing cross-flow VIV at a reduced velocity of 6 is found to be greater than that for a stationary cylinder. For a constant reduced velocity of 6, the wake flow changes from 2D to 3D as the Reynolds number is increased from 250 to 300. Some 2D numerical simulations are performed and it is found that the 2D Navier–Stokes (NS) equations are not able to predict the VIV in the turbulent flow regime, while the 2D Reynolds-averaged Navier–Stokes (RANS) equations improve the results.     

Vortex-induced vibration and mode transition of a curved flexible free-hanging cylinder in exponential shear flows

This paper presents an experimental study of vortex-induced-vibration (VIV) of a curved flexible free-hanging cylinder in exponential shear flows. The emphasis is on previously unexplained phenomena in our early research and in some cases offers insights on the mode transition of nonlinear vibration behavior of long flexible cylinders. The experimental results illustrate that the cylinder undergoes multi-frequency response and the dominant frequency varies spatially. The IL and CF response and transition are out-of-sync. In the second (2nd) mode response, the spanwise response exhibits a mixed pattern with standing wave and traveling wave. The contribution of traveling wave becomes greater as the reduced velocity increases. Only two distinct branches of response, namely the initial and lower branches, are observed in each mode. The lower branches of the first (1st) and 2nd modes present the same normalized frequency. A phase jump around 180°occurs at the transition between initial branches and lower branches, accompanying with a switch between 2S $\leftrightarrow$ 2P or P+S vortex shedding modes.     

Theoretical and experimental investigations of the flow of a viscous fluid near the line of intersection of a cylindrical surface and a flat surface

Flow along a corner was investigated at large Reynolds numbers in, for example, [1–3]. The present author [4] considered flow in the neighborhood of a corner formed by the intersection of a plane and a concave cylindrical surface, the main attention being devoted to the formation of the three-dimensional boundary layer on the plane near the corner. It was shown that the curvature of one of the intersecting surfaces changes the flow pattern qualitatively. In the present paper, we report an investigation of the formation of the flow on a concave cylindrical surface near such a corner and consider how the flow is rearranged in the neighborhood of a corner in, for example, a channel of rectangular cross section that has an initial straight section and then a bend with a discontinuity of the curvature of the line of intersection of the concave and flat sides of the channel. The results are given of some experimental investigations of flow near the line of intersection of a flat wall and a curved (concave and convex) wall at a bend in a rectangular channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 64–68, January–February, 1983.I thank G. M. Bam-Zelikovich for constant interest in the work and A. I. Ruban for a number of extremely helpful comments.     

两端铰接的细长柔性圆柱体涡激振动响应特性数值研究

目前细长柔性圆柱体涡激振动响应的研究方法主要包括实验方法、计算流体动力学方法以及半经验模型方法. 鉴于实验方法研究成本较高、计算流体动力学方法计算时间较长,本文基于尾流振子模型对线性剪切来流下两端铰接的细长柔性圆柱体涡激振动响应特性进行了半经验模型方法研究. 先建立了柔性圆柱体结构振子以及尾流振子之间的耦合模型,紧接着基于二阶精度中心差分格式对耦合模型先离散后迭代进行求解. 对不同剪切参数下柔性圆柱体涡激振动响应的振动波长、振动频率、振动位移以及响应频率随时间的变化特性等参数进行了分析. 分析结果表明:圆柱体的涡激振动响应由驻波和行波混合组成. 当无量纲弯曲刚度较小时,在圆柱体两端附近,驻波占主导;而在圆柱体中间段附近,行波占主导. 当无量纲弯曲刚度较大时,在圆柱体整个长度区间上均为驻波占主导. 随着剪切参数的增大,振动位移以及振动波长均逐渐减小,而振动频率和频率带宽均逐渐增大.      

正弦振荡来流下柔性立管涡激振动发展过程

在风浪流的作用下,海洋浮式结构物将带动悬链线立管在水中作周期性往复运动,从而在立管运动方向上产生相对振荡来流,这种振荡来流将激励立管悬垂段发生“间歇性” 的涡激振动. 在海洋工程水池中对一个4m 长的立管微段进行模型试验研究,以探索相对振荡来流作用下立管涡激振动产生的机理及其发展的物理过程. 试验通过振荡装置带动模型作正弦运动来模拟不同最大约化速度U_Rmax、不同KC（Keulegan-Carpenternumber）的相对振荡来流,利用光纤应变片测量立管涡激振动响应. 结合模态分析方法处理试验数据得到位移响应时历,继而提出相对振荡来流下柔性立管涡激振动发展的3 个阶段:建立阶段、锁定阶段以及衰减阶段. 并进一步总结了最大约化速度U_Rmax,KC 对涡激振动发展过程的影响规律. 最终获得不同最大约化速度U_Rmax下,涡激振动各发展阶段随KC 所占时间分布比例图.      

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.     

Application of wake oscillators to two-dimensional vortex-induced vibrations of circular cylinders in oscillatory flows

A nonlinear time-domain simulation model for predicting two-dimensional vortex-induced vibration (VIV) of a flexibly mounted circular cylinder in planar and oscillatory flow is presented. This model is based on the utilization of van der Pol wake oscillators, being unconventional since wake oscillators have typically been applied to steady flow VIV predictions. The time-varying relative flow–cylinder velocities and accelerations are accounted for in deriving the coupled hydrodynamic lift, drag and inertia forces leading to the cylinder cross-flow and in-line oscillations. The system fluid–structure interaction equations explicitly contain the time-dependent and hybrid trigonometric terms. Depending on the Keulegan–Carpenter number (KC) incorporating the flow maximum velocity and excitation frequency, the model calibration is performed, entailing a set of empirical coefficients and expressions as a function of KC and mass ratio. Parametric investigations in cases of varying KC, reduced flow velocity, cylinder-to-flow frequency ratio and mass ratio are carried out, capturing some qualitative features of oscillatory flow VIV and exploring the effects of system parameters on response prediction characteristics. The model dependence of hydrodynamic coefficients on the Reynolds number is studied. Discrepancies and limitations versus advantages of the present model with different feasible solution scenarios are illuminated to inform the implementation of wake oscillators as a computationally efficient prediction model for VIV in oscillatory flows.