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.     

Effects of tension on vortex-induced vibration (VIV) responses of a long tensioned cylinder in uniform flows

The effects of tension on vortex-induced vibra-tion (VIV) responses for a tension-dominated long cylinder with an aspect ratio of 550 in uniform flows are experimen-tally investigated in this paper. The results show that elevated tension suppresses fluctuations of maximum displacement with respect to flow velocity and makes chaotic VIV more likely to appear. With respect to periodic VIV, if elevated tension is applied, the dominant vibration frequency in the in-line (IL) direction will switch from a fundamental vibra-tion frequency to twice the value of the fundamental vibration frequency, which results in a ratio of the dominant vibration frequency in the IL direction to that in the cross-flow direc-tion of 2.0. The suppression of the elevated tension in the fluctuation of the maximum displacement causes the axial tension to become an active control parameter for the VIV maximum displacement of a tension-dominated long riser or tether of an engineering structure in deep oceans. However, the axial tension must be optimized before being used since the high dominant vibration frequency due to the elevated tension may unfavorably affect the fatigue life of the riser or tether.     

剪切流场中含内流立管横向涡激振动特性

立管是海洋工程中输送油气或其他矿产资源的必备结构, 外部洋流引起的立管涡激振动影响着立管的疲劳寿命, 危害深海资源开发. 本文基于欧拉?伯努利梁方程, 结合半经验时域水动力模型, 建立剪切流与内流耦合作用下海洋立管涡激振动预报模型, 运用有限元方法和Newmark-β逐步积分法求解方程, 首先将数值模拟结果与实验数据进行对比, 验证模型正确性. 然后, 运用此模型, 对剪切流作用下含内流的顶张立管在不同内流速度和密度下的横向涡激振动响应特性进行研究, 主要分析了立管的横向振动模态、振动频率以及均方根位移等涡激振动参数随内流速度和密度等参数的变化规律. 结果表明, 在剪切流场中, 含内流海洋立管在横向上表现出多模态多频率的涡激振动;立管横向振动的最大均方根位移随内流速度和密度的增大而增大, 特别是当内流速度较大时, 横向最大均方根位移增大明显;立管横向振动的主导频率随内流速度和密度的增大而减小, 并且内流密度的增大同样会引起模态转换和频率转换.      

海洋热塑性增强管(RTP)涡激振动数值计算

基于Van der Pol尾流振子模型和多体系统传递矩阵法(transfer matrix method for multibody systems, MSTMM), 建立了可以快速预测海洋热塑性增强管(reinforced thermoplastic pipe, RTP)振动特性和涡激振动响应的动力学模型. 仿真结果与ANSYS软件仿真结果以及文献实验数据对比, 验证了本文模型的准确性. 研究了考虑RTP立管刚性接头, 不同顶张力, 不同来流分布等情况对RTP立管涡激振动响应的影响. 计算结果表明: 流速越大, 立管涡激振动激发出的模态越高; 立管涡激振动主要受低阶模态控制; 立管的刚性接头对立管的湿模态影响较小, 但是对较高阶模态为主所激发出的涡激振动振幅分布影响较大; 剪切流对沿立管轴向的涡激振动振幅分布影响较大, 低流速能量小所引起的涡激振动幅值较小, 但是当剪切流流速达到能激发出较高阶模态时, 相比同等流速的均匀流所引起的涡激振动振幅要大.      

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.     

剪切流下发生涡激振动的柔性立管阻力特性研究

利用缩尺模型试验的方法研究了线性剪切流下涡激振动发生时柔性立管的阻力特性.文中基于光纤光栅应变传感器测得的模型应变信息,采用梁复杂弯曲理论计算了立管的平均阻力,继而分析了阻力系数沿管长方向和雷诺数的分布特性以及涡激振动对阻力系数的放大效应,并提出了用于估算柔性立管发生涡激振动时阻力系数的经验公式.结果表明:涡激振动对阻力系数有放大效应,使得立管局部阻力系数高达3.2;平均阻力系数在1.0×104到1.2×105的雷诺数区间内的值为1.3~2.0,并随雷诺数的增大而减小.本文提出的经验公式可准确估算高雷诺数下涡激振动发生时柔性立管的阻力系数,此经验公式考虑了流速、涡激振动主导模态以及主导频率对阻力系数的影响.      

Monitoring VIV fatigue damage on marine risers

Long flexible cylinders (e.g., risers, tendons and mooring lines) exposed to the marine environment encounter ocean currents leading to vortex-induced vibration (VIV). These oscillations, often driven at high frequencies over extended periods of time, may result in structural failure of the member due to fatigue damage accumulation. Recent developments in instrumentation and installation of data acquisition systems on board marine risers have made accurate measurement of riser responses possible. This paper aims at using the data from these data acquisition devices (typically strain gages and accelerometers) in order to understand the evolution of the riser VIV, with the final aim of estimating the fatigue damage. For this purpose we employ systematic techniques to reconstruct riser VIV response using the data from the available sensors. The reconstructed riser response allows estimation of the dynamic axial stresses due to bending and consequently the estimates of the fatigue damage along the entire riser. The above methods can take into account the fatigue damage arising from complicated riser motions involving the presence of traveling waves even with the use of very few sensors. An alternate approach using a Van der Pol wake oscillator model is also explored to obtain fatigue life estimates caused by riser VIV.     

Fluid-solid coupling and dynamic response of vortex-induced vibration of slender ocean cylinders

对近几十年来国内外在涡激振动的基础研究包括机理认识和动响应分析等方面的进展进行了论述,尤其针对海洋油气平台中的立管、隔水管等细长柔性结构的涡激振动.描述了涡激振动这种典型的非线性流固耦合现象所具有的特征,包括自激、自限制、展向相关、尾迹水动力与结构动力的流固耦合等及其主要影响参数.介绍了目前常用的结构响应预测方法和相关实验.通过讨论当前理论研究和实际工程中的热点问题,诸如多模态宽带振动、浮体运动与水下立管的耦合、响应抑制措施、双向振动、高雷诺数下的大尺度物理实验等,对今后该领域的研究方向进行了力所能及的展望.     

海洋柔性结构涡激振动的流固耦合机理和响应

对近几十年来国内外在涡激振动的基础研究包括机理认识和动响应分析等方面的进展进行了论述,尤其针对海洋油气平台中的立管、隔水管等细长柔性结构的涡激振动.描述了涡激振动这种典型的非线性流固耦合现象所具有的特征,包括自激、自限制、展向相关、尾迹水动力与结构动力的流固耦合等及其主要影响参数.介绍了目前常用的结构响应预测方法和相关实验.通过讨论当前理论研究和实际工程中的热点问题,诸如多模态宽带振动、浮体运动与水下立管的耦合、响应抑制措施、双向振动、高雷诺数下的大尺度物理实验等,对今后该领域的研究方向进行了力所能及的展望.     

深海采矿系统中悬臂式立管涡激振动分析

不同于传统的海洋立管, 深海采矿系统中的垂直提升管道可以被视为一个底部无约束的柔性悬臂式立管, 工作过程中同样面临涡激振动和柔性变形问题. 本文采用一种无网格离散涡方法和有限元耦合的准三维时域求解数值模型, 系统性地研究了不同流速下悬臂式立管的涡激振动问题. 结果表明: 悬臂式立管的横向振动模态阶数随折合速度增加而增大, 在一定折合速度范围内主导振动模态保持不变; 当主导模态转变时, 对应的横向振幅会发生突降, 但是当新的高阶模态被激发后, 立管振幅随来流速度增加而再次逐渐增大; 在相同的振动模态下, 立管底部位移均方根值随折合速度线性增加, 主导振动频率在模态转变时会出现跳跃现象; 特别地, 本文讨论了三阶主导模态下悬臂式立管的振动响应, 无约束的立管底部呈现出较大的振动能量, 且振幅的驻波特征随折合速度增加而逐渐增强; 本文比较了两端铰支立管与悬臂式立管的涡激振动响应特征, 两者在振幅和主导振动频率两方面均表现出了相同的变化趋势.      

Experimental study on dynamic response of smooth and straked risers in tandem arrangement coupling interference effect

An experiment was conducted in a combined wave–current water flume on two tandem risers subjected to uniform flow. The riser model has an effective length of 2.0 m. The aspect ratio is 111.11. The upstream riser is smooth and the downstream riser fitted with three-strand helical strakes with pitch 17.5D and height 0.25D. By varying the external flow velocities and spacing ratios, through comparisons with the dynamic response of isolated smooth and isolated straked riser, the paper observe how interference effect impacts the dynamic characteristics and dynamic response of two risers in tandem arrangement, reveal how the suppression efficiency of the three-strand helical strakes responds to spacing ratio and external flow velocity, and explore the wake excitation effect of inter-riser fluids on the downstream riser and their dynamic feedback to the upstream riser. The results show that the dominant frequency of the upstream smooth riser is sensitivity to the change of the spacing ratio is low, and the displacement response is offset or enhanced in different degree due to the difference of the interference efficiency. The downstream straked riser dominates frequency and displacement higher than the isolated straked riser. The wake vortex of the upstream smooth riser acts on the downstream riser, occupying a dominant position in the vibration of the downstream riser. It degrades the vibration suppression efficiency of the three-strand helical strakes: the suppression efficiency is the highest at spacing ratio of 8, being a merely 70.57%. With the increase of the spacing ratio, the CF displacement of the riser gradually decreases, and the IL displacement gradually increases. The interference efficiency partition and suppression efficiency at different spacing ratios reflects the dynamic feedback of the upstream smooth riser is much smaller than the interference effect of the downstream suppression riser.     

多用途输液立管涡激振动实验研究与疲劳分析

为研究输运不同流体的海洋立管在海流作用下的振动规律,在大型波浪流水槽中进行涡激振动模型实验。实验分别将四种不同质量比的立管模型竖直固定于支架上,立管外部承受不同速度的流体作用,上端施加顶张力。立管模型上均匀布置六个测点,根据每个测点布置的两个应变计,分别测得来流向和横向两个方向振动响应。通过小波变换对实验数据进行去噪处理,利用振型分解法求解立管各点涡激振动位移。考察输运不同流体对立管自振频率以及涡激振动响应的影响,并利用雨流计数法对模型进行疲劳分析。实验结果表明,随质量比增加立管涡激振动频率降低;低质量比的立管更容易产生大位移。     

Numerical study on the suppression of the vortex-induced vibration of an elastically mounted cylinder by a traveling wave wall

In the present paper, the commercial CFD code “Fluent” was employed to perform 2-D simulations of an entire process that included the flow around a fixed circular cylinder, the oscillating cylinder (vortex-induced vibration, VIV) and the oscillating cylinder subjected to shape control by a traveling wave wall (TWW) method. The study mainly focused on using the TWW control method to suppress the VIV of an elastically supported circular cylinder with two degrees of freedom at a low Reynolds number of 200. The cross flow (CF) and the inline flow (IL) displacements, the centroid motion trajectories and the lift and drag forces of the cylinder that changed with the frequency ratios were analyzed in detail. The results indicate that a series of small-scale vortices will be formed in the troughs of the traveling wave located on the rear part of the circular cylinder; these vortices can effectively control the flow separation from the cylinder surface, eliminate the oscillating wake and suppress the VIV of the cylinder. A TWW starting at the initial time or at some time halfway through the time interval can significantly suppress the CF and IL vibrations of the cylinder and can remarkably decrease the fluctuations of the lift coefficients and the average values of the drag coefficients; however, it will simultaneously dramatically increase the fluctuations of the drag coefficients.     

Experimental investigation of material effects on free vibration of a splitter plate

Fluid-structure interaction resulting from free vibration is a complex phenomenon, not fully understood today. In the present study the flow separation from the trailing edge of a splitter plate in a convergent channel involves Vortex-Induced Vibration (VIV) modifying the fundamental instability related to vortex shedding. Under certain conditions, the VIV produces cellular vortex shedding at the trailing edge. In this paper, we attempt experimentally to further investigate the important parameters affecting VIV phenomenon. We present results on measurements on the effect of plate material. Experimental techniques include Laser Telemetry (LT), which is a laser displacement sensor used to measure the vibrational response of the plate and Particle Image Velocimetry (PIV), which is used to measure the corresponding effect on the vortex shedding. Combining data from these techniques the variation in the response of the plate due to material effects can be addressed together with the imprint of the excited vibration mode on the flow. Measurements were performed with five different plate materials over a range of Reynolds numbers. The results show that the vibrational response of the combined fluid-structure system is modified by the VIV instability. A characteristic vibrational behaviour with a stepwise increase of the frequency of the dominant vibration mode is formed as the vortex shedding frequency (f _s) synchronizes to the plate vibration frequency (f _o). The synchronization takes place over a range of Re numbers. After certain Re number threshold is exceeded the frequency jumps to a new synchronization region. The dimensionless vibration frequency (St _o) of the plate, being a Strouhal number characterized by f _o forms a saw tooth profile centered to reduced velocity value inside the range of highest amplitude response. This behavior is explained by the natural frequencies of the combined fluid-structure system. The results further show that the vibration frequency and amplitude are modified due to material properties. As the mass ratio (M*) is increased the vibration frequency increases and the dimensionless amplitude (A/d) decreases. The number of synchronization regions decreases and the ranges extend wider in terms of Re number with increasing M*.     

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.     

基于流固耦合的锚索涡激振动抑制方法研究

悬浮隧道锚索的涡激振动会加剧锚索的疲劳破坏,进而影响悬浮隧道的使用寿命和安全.文章在海洋立管涡激振动抑制研究的基础上,考虑悬浮隧道锚索倾斜角度和来流方向的影响,采用流固耦合的数值方法,对整流罩方法和三控制杆方法的抑制效果进行了分析.结果表明,在顺来流方向,两种方法均具有良好的抑振效果;锚索有倾斜的情况下,三控制杆方法的效果会有所提升;但在来流方向改变时,整流罩方法具有较强的适应性.     

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.     

Numerical scheme for riser motion calculation during 3-D VIV simulation

This paper presents a numerical scheme for riser motion calculation and its application to riser VIV simulations. The discretisation of the governing differential equation is studied first. The top tensioned risers are simplified as tensioned beams. A centered space and forward time finite difference scheme is derived from the governing equations of motion. Then an implicit method is adopted for better numerical stability. The method meets von Neumann criteria and is shown to be unconditionally stable. The discretized linear algebraic equations are solved using a LU decomposition method. This approach is then applied to a series of benchmark cases with known solutions. The comparisons show good agreement. Finally the method is applied to practical riser VIV simulations. The studied cases cover a wide range of riser VIV problems, i.e. different riser outer diameter, length, tensioning conditions, and current profiles. Reasonable agreement is obtained between the numerical simulations and experimental data on riser motions and cross-flow VIV a/D. These validations and comparisons confirm that the present numerical scheme for riser motion calculation is valid and effective for long riser VIV simulation.     

A robust high-resolution method for the time–frequency analysis of vortex-induced-vibration signals

The dynamic interaction between ocean current and marine riser is complex in nature, and the riser׳s vortex-induced vibration (VIV) due to the current often strongly exhibits a non-stationary phenomenon. For investigating the time-varying dominant frequencies of the VIV motion, a joint time–frequency analysis is necessary. Traditional methods for time–frequency analysis include the Short Time Fourier Transform (STFT) and Wavelet Transform (WT) methods, though both methods have significant drawbacks. Specifically, the STFT method suffers frequency resolution and leakage problems, while the WT method is highly sensitive to its basic wavelet selection. This paper newly introduces a robust high-resolution method, named the STPT-SS method, which is the Short Time Prony Transform (STPT) using a State-Space (SS) model. In particular, the STPT algorithm contributes to the high-resolution feature of the proposed method, and the SS model to the robustness. Using test VIV data that include a synthesized signal and measurements from laboratory and field experiments, the STPT-SS method is found to significantly outperform the STFT and WT methods in the time–frequency analysis.     

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.