An Experimental Study on Dynamics Features of Three Side-by-Side Flexible Risers Undergoing Vortex-Induced Vibrations in A Uniform Flow

A vortex-induced vibration(VIV) experiment on three side-by-side risers subjected to a uniform flow was carried out in a combined wave-current flume. The dynamic features of interference effect on three side-by-side risers were investigated by varying fluid velocity and inter-riser spacing. The distributions of dimensionless displacement,dominant frequency, and displacement trajectory of the model risers were measured using mode decomposition and wavelet transform techniques. The coupled interference of inter-riser fluid to adjacent risers at different spacings was disclosed by introducing the "interference ratio" concept. The results show that at spacings smaller than 6.0 D, the three model risers display appreciable deviations in their displacement responses in cross-flow or in-line direction,attributable to the strong proximity disturbance and wake interference between the risers. When the spacing is increased to 8.0 D, wake interference still makes great difference to the dynamic response of the risers in both directions. As reduced velocity increases, the three risers show higher agreement with an isolated riser in overall dominant vibration frequency in CF direction than that in IL direction at all spacings and the side risers, although symmetrically placed, do not vibrate symmetrically, as a result of the steady deflection of clearance flow within the riser group. Interference effect results in a remarkable unsteady mode competition within the risers; quantitation of the interference levels for the three risers at different spacings with interference ratio revealed that under low flow velocities and large spacing ratios, clearance flow constitutes a non-neglectable interferer for three side-by-side risers.     

Experimental Investigation on Vortex-Induced Vibration of Steel Catenary Riser

Steel catenary riser(SCR) is the transmission device between the seabed and the floating production facilities. As developments move into deeper water, the fatigue life of the riser can become critical to the whole production system, especially due to the vortex-induced vibration(VIV), which is the key factor to operational longevity. As a result, experimental investigation about VIV of the riser was performed in a large plane pool which is 60 m long, 36 m wide and 6.5 m deep. Experiments were developed to study the influence of current speed and seabed on VIV of SCR. The results show that amplitudes of strain and response frequencies increase with the current speed both in cross-flow(CF) and in-line(IL). When the current speed is high, multi-mode response is observed in the VIV motion. The amplitudes of strain in IL direction are not much smaller than those in CF direction. The seabed has influence on the response frequencies of riser and the positions of damage for riser.     

Experimental Investigation on Vortex-Induced Vibration of Steel Catenary Riser

Steel catenary riser (SCR) is the transmission device between the seabed and the floating production facilities. As developments move into deeper water, the fatigue life of the riser can become critical to the whole production system, especially due to the vortex-induced vibration (VIV), which is the key factor to operational longevity. As a result, experimental investigation about VIV of the riser was performed in a large plane pool which is 60 m long, 36 m wide and 6.5 m deep. Experiments were developed to study the influence of current speed and seabed on VIV of SCR. The results show that amplitudes of strain and response frequencies increase with the current speed both in cross-flow (CF) and in-line (IL). When the current speed is high, multi-mode response is observed in the VIV motion. The amplitudes of strain in IL direction are not much smaller than those in CF direction. The seabed has influence on the response frequencies of riser and the positions of damage for riser.     

海洋立管复模态动力特性分析

考虑阻尼的影响,研究海洋立管的动力特性。通过分析管内流体及管外海洋环境荷载的共同作用,建立海洋立管涡激振动偏微分方程,进而得到立管动力特性方程,用复模态分析法求解动力特性方程得到立管考虑阻尼的自振频率。算例计算表明:考虑阻尼的立管自振频率略小于不考虑阻尼的立管自振频率;立管的自振频率随着内流流速的增加而减小,但内流流速不大时,影响较小;管道长度对立管的自振频率影响较大。     

大长细比柔性杆件涡激振动实验

涡激振动(vortex-induced vibration,VIV)是导致深海细长柔性立管发生疲劳破坏的重要因素。采用实验观测手段研究了长细比为1 750的柔性立管多模态涡激振动特性。实验中,通过采用拖车拖拉立管模型在水池中匀速行进来模拟均匀流作用下的涡激振动响应。利用光纤光栅传感器测量立管模型在横流向(cross-flow,CF)和顺流向(in-line,IL)的应变,进而通过模态分解的方法,获得立管模型涡激振动的位移。在此基础上,研究了CF以及IL方向的响应频率、位移标准差的平均值和最大值等随流速的变化规律,并分析了立管模型上测点的运动轨迹及其影响因素。     

Tension and Drag Forces of Flexible Risers Undergoing Vortex-Induced Vibration

This paper presents the results of an experimental investigation on the variation in the tension and the distribution of drag force coefficients along flexible risers under vortex-induced vibration (VIV) in a uniform flow for Reynolds numbers (Re) up to 2.2×10⁵. The results show that the mean tension is proportional to the square of the incoming current speed, and the tension coefficient of a flexible riser undergoing VIV can be up to 12. The mean drag force is uniformly and symmetrically distributed along the axes of the risers undergoing VIV. The corresponding drag coefficient can vary between 1.6 and 2.4 but is not a constant value of 1.2, as it is for a fixed cylinder in the absence of VIV. These experimental results are used to develop a new empirical prediction model to estimate the drag force coefficient for flexible risers undergoing VIV for Reynolds number on the order of 10⁵, which accounts for the effects of the incoming current speed, the VIV dominant modal number and the frequency.     

Simplified Prediction Model for Vortex-Induced Vibrations of Top Tensioned Risers

According to the characteristics of deepwater top tensioned risers, a simplified model is presented to predict the multi-modal response of vortex-induced vibration （VIV） in non-uniform flow based on energy equilibrium theory and the exporimental data from VIV self-excited and forced oscillations of rigid cylinders. The response amplitude of each mode is determined by a balance between the energy fed into the riser over the lock-in regions and the energy dissipated by the fluid damping over the remainders. Compared with the previous prediction models, this method can take fully account of the intrinsic nature of VIV for low mass ratio structures on lock-in regions, added mass and nonlinear fluid damping effect, etc. Moreover, it is the first time to propose the accurate calculating procedure for VIV amplitude correction factor by solving energy equilibrium equation and a closed form solution is presented for the case of a riser of uniform mass and cross-section oscillating in a uniform flow. The predicted values show a reasonable agreement with VIV experiments of riser models in stepped and sheared currents.     

The effect of yaw angle on VIV suppression for an inclined flexible cylinder fitted with helical strakes

Experimental studies were carried out to investigate the response features of an inclined flexible bare cylinder as well as a straked cylinder in a towing tank, with the main purpose of further improving the understanding of the effect of yaw angle on vortex-induced vibration (VIV) suppression. Four yaw angles (a = 0°, 15°, 30°, 45°), which is defined as the angle between the cylinder axis and the plane orthogonal to the oncoming fluid flow, were tested. The cylinder model was towed along the tank to generate a uniform fluid flow. The towing velocity was in the range of 0.05–1.0 m/s with an interval of 0.05 m/s. The corresponding Reynolds number ranged from 800 to 16000. The strakes selected for the experiments had a pitch of 17.5D and a height of 0.25D, which is generally considered as the most effective configuration for VIV suppression of a flexible cylinder in water. The experimental results indicate that VIV suppression effectiveness of the inclined flexible straked cylinder is closely related to the yaw angle. The displacement amplitudes are significantly suppressed in both cross-flow (CF) and in-line (IL) directions at a = 0°. However, with increasing yaw angle, the suppression efficiencies of the CF and IL displacement amplitudes gradually decrease. In addition, the CF dominant frequencies of the straked cylinder obviously deviate from those of the bare cylinder at a = 0° and 15°. This deviation is substantially alleviated with increasing yaw angle. The IL dominant frequencies show less dependency on the yaw angle. Similar trends are also observed on the dominant modes of vibration and the mean drag coefficients.     

Hydrodynamics of A Flexible Riser Undergoing the Vortex-Induced Vibration at High Reynolds Number

This study proposed a method to obtain hydrodynamic forces and coefficients for a flexible riser undergoing the vortex-induced vibration (VIV), based on the measured strains collected from the scale-model testing with the Reynolds numbers ranging from 1.34E5 to 2.35E5. The riser is approximated as a tensioned spatial beam, and an inverse method based on the FEM of spatial beam is adopted for the calculation of hydrodynamic forces in the cross flow (CF) and inline (IL) directions. The drag coefficients and vortex-induced force coefficients are obtained through the Fourier Series Theory. Finally, the hydrodynamic characteristics of a flexible riser model undergoing the VIV in a uniform flow are carefully investigated. The results indicate that the VIV amplifies the drag coefficient, and the drag coefficient does not change with time when the CF VIV is stable. Only when the VIVs in the CF and IL directions are all steady vibrations, the vortex-induced force coefficients keep as a constant with time, and under “lock-in” condition, whether the added-mass coefficient changes with time or not, the oscillation frequency of the VIV keeps unchanged. It further shows that the CF excitation coefficients at high frequency are much smaller than those at the dominant frequency, while, the IL excitation coefficients are in the same range. The axial distributions of the excitation and damping region at the dominant frequency and high frequency are approximately consistent in the CF direction, while, in the IL direction, there exists a great difference.     

硬悬挂钻井隔水管涡激振动特性研究

针对深水钻井过程中遭遇强台风,基于安全性考虑要求钻井平台悬挂隔水管提前撤离的问题,采用软件SHEAR7针对HYSY981钻井平台硬悬挂隔水管系统避台风撤离作业过程中,受南海一年一遇海流作用时诱发涡激振动(VIV)的情况,研究航速与悬挂长度对VIV特性的影响。研究表明,浮力块覆盖率越高,隔水管系统张力越小;浮力块分布对隔水管系统VIV响应影响较大,25%交错布置方案VIV响应最弱。隔水管并非越短越好,要综合考虑洋流剖面、隔水管配置和平台航行的影响;在不同悬挂长度及航行条件下的VIV响应,在撤离作业前应尽量避免在高流速区布置浮力单根,撤离作业时应尽量采用顺流而避免平台逆流航向。     

Analysis and prediction of vortex-induced vibrations of variable-tension vertical risers in linearly sheared currents

Many studies have tackled the problem of vortex-induced vibrations (VIV) of a vertical riser with a constant tension and placed in uniform currents. In this study, attention is focused on the cross-flow VIV modelling, time-domain analysis and prediction of variable-tension vertical risers in linearly sheared currents. The partial-differential equation governing the riser transverse motion is based on a flexural tensioned-beam model with typical pinned-pinned supports. The hydrodynamic excitation model describing the modulation of lift force is based on a distributed van der Pol wake oscillator whose nonlinear equation is also partial-differential due to the implementation of a diffusion term. The variation of empirical wake coefficients with system parameters and the water depth-dependent Reynolds number is introduced. Based on the assumed Fourier mode shape functions obtained by accounting for the effect of non-uniform tension, the Galerkin technique is utilized to construct a low-dimensional multi-mode model governing the coupled fluid-riser interaction system due to VIV. Numerical simulations in the case of varying sheared flow profiles are carried out to systematically evaluate riser nonlinear dynamics and highlight the influence of fluid-structure parameters along with associated VIV aspects. In particular, the effects of shear and tensioned-beam (tension versus bending) parameters are underlined. Some comparisons with published experimental results and observations are qualitatively and quantitatively discussed. Overall parametric analysis and prediction results may be worthwhile for being a new benchmark against future experimental testing and/or numerical results predicted by an alternative model and methodology.     

Application of Helical Strakes for Suppressing the Flow-Induced Vibration of Two Side-by-Side Long Flexible Cylinders

Helical strakes have been widely applied for suppressing the vibration of flexible cylinders undergoing vortexshedding in offshore engineering. However, most research works have concerned on the application of helical strakes for the isolated flexible cylinder subjected to vortex-induced vibration(VIV). The effectiveness of helical strakes attached to side-by-side flexible cylinders in vibration reduction is still unclear. In this paper, the response characteristics of two side-by-side flexible cylinders with and without helical strakes were experimentally investigated in a towing tank. The configuration of the helical strakes used in the experiment had a pitch of 17.5D and a height of 0.25D(where D is the cylinder diameter), which is usually considered the most effective for VIV suppression of isolated marine risers and tendons. The center-to-center distance of the two cylinders was 3.0D. The uniform flow with a velocity ranging from 0.05 m/s to 1.0 m/s was generated by towing the cylinder models along the tank. Experimental results, including the displacement amplitude, the dominant frequency, the dominant mode,and the mean drag force coefficient, were summarized and discussed. For the case where only one cylinder in the two-cylinder system had helical strakes, the experimental results indicated that helical strakes can remarkably reduce the flow-induced vibration(FIV) of the staked cylinder. For the case of two straked cylinders in a side-by-side arrangement, it was found that the performance of helical strakes in suppressing the FIV is as good as that for the isolated cylinder.     

Effect of upward internal flow on dynamics of riser model subject to shear current

Numerical study about vortex-induced vibration(VIV) related to a flexible riser model in consideration of internal flow progressing inside has been performed.The main objective of this work is to investigate the coupled fluid-structure interaction(FSI) taking place between tensioned riser model,external shear current and upward-progressing internal flow(from ocean bottom to surface).A CAE technology behind the current research which combines structural software with the CFD technology has been proposed.According to the result from dynamic analysis,it has been found that the existence of upward-progressing internal flow does play an important role in determining the vibration mode(/dominant frequency),vibration intensity and the magnitude of instantaneous vibration amplitude,when the velocity ratio of internal flow against external current is relatively high.As a rule,the larger the velocity of internal flow is,the more it contributes to the dynamic vibration response of the flexible riser model.In addition,multi-modal vibration phenomenon has been widely observed,for asymmetric curvature along the riser span emerges in the case of external shear current being imposed.     

Response of Two Unequal-Diameter Flexible Cylinders in A Side-by-Side Arrangement: Characteristics of FIV

Till now, little information is available on the flow-induced vibration(FIV) of multiple flexible cylinders with unequal diameters. Some FIV characteristics of unequal-diameter cylinders can be predicted based on the knowledge of equal-diameter cylinders, while there are still other features remaining unrevealed. In this paper, the FIV characteristics of two flexible cylinders with unequal diameters arranged side-by-side are experimentally investigated. The diameter ratio of the small cylinder(Small Cyl.) to the large cylinder(Large Cyl.) is nearly 0.5.The aspect ratios and mass ratios of the two flexible cylinders are 350/181 and 1.90/1.47, respectively. The centre-tocentre spacing ratio in the cross-flow(CF) direction is kept constant as 6.0 and the two cylinders can oscillate freely in both the CF and in-line(IL) directions. The towing velocity varies from 0.05 m/s to 1.00 m/s. The dominant modes and frequencies, CF and IL displacement amplitudes and response trajectories are discussed. Compared with the case of two identical cylinders in our previous study, the FIV responses demonstrate some similarities and differences. The similarities are as follows. Both cylinders exhibit multi-mode vibration features and they interact with each other. Meanwhile, the IL FIV shows a more complex behaviour than that in the CF direction. The difference is that as the diameter of one cylinder is increased, the effect on the smaller cylinder becomes more significant. For Large Cyl., the FIV response is similar to its isolated counterpart, which indicates that Small Cyl. has a negligible effect on the FIV of the larger one. Whereas Large Cyl. perplexes the FIV of Small Cyl. during the vibration process. The spacing would change when both cylinders are oscillating. Proximity interference between the two cylinders and wake shielding effect of the Large Cyl. may occur. The dominant frequencies of Small Cyl. are reduced and the wake-induced flutter of Small Cyl. is observed from the response trajectories at different measuring points.     

Vortex-Induced Vibrations of A Long Flexible Cylinder in Linear and Exponential Shear Flows

A numerical study based on a wake oscillator model was conducted to determine the response performance of vortex-induced vibration(VIV) on a long flexible cylinder with pinned-pinned boundary conditions subjected to linear and exponential shear flows. The coupling equations of a structural vibration model and wake oscillator model were solved using a standard central finite difference method of the second order. The VIV response characteristics including the structural displacement, structural frequency, structural wavenumber, standing wave behavior,travelling wave behavior, structural velocity, lift force coefficient and transferred energy from the fluid to the structure with different flow profiles were compared. The numerical results show that the VIV displacement is a combination of standing waves and travelling waves. For linear shear flow, standing waves and travelling waves dominate the VIV response within the low-velocity and high-velocity zones, respectively. The negative values of the transferred energy only occur within the low-velocity zone. However, for exponential shear flow, travelling waves dominate the VIV response and the negative energy occurs along the entire length of the cylinder.     

悬跨海底电缆涡激振动特性及疲劳损伤分析

悬跨海底电缆作为细长柔性结构,在静力平衡状态下具有一定的垂度,在水流作用下的涡激振动特性与海底管线和海洋立管等结构也有很大的不同,其振动模态受垂跨比影响很大。通过物理模型试验开展了不同垂跨比下悬跨海缆的涡激振动和疲劳损伤特性研究。试验模型按照水弹性相似准则设计,试验中测量了不同流速下海缆模型产生涡激振动时的应变历时数据,采用模态分析法获得了模型涡激振动时的振动模态和振幅。分析了不同流速下海缆模型的振动模态、应变和疲劳损伤的变化和分布特征。试验结果表明：垂跨比显著影响了海缆的涡激振动模态和应变幅值大小。在本试验流速范围内,对一定长度的悬跨海缆模型,当垂跨比较大时,随着流速的增大,模型涡激振动的主响应振动依次出现反对称1阶和对称1阶模态;当垂跨比较小时,模型涡激振动的主响应模态依次出现反对称1阶和对称2阶模态。当涡激振动主响应模态为反对称1阶时,疲劳损伤最大值达到0. 1~0.7。     

Stress Wave Propagation Analysis on Vortex-Induced Vibration of Marine Risers

To analyze the stress wave propagation associated with the vortex-induced vibration (VIV) of a marine riser, this paper employed a multi-signal complex exponential method. This method is an extension of the classical Prony''s method which decomposes a complicated signal into a number of complex exponential components. Because the proposed method processes multiple signals simultaneously, it can estimate the "global" dominating frequencies (poles) shared by those signals. The complex amplitude (residues) corresponding to the estimated frequencies for those signals is also obtained in the process. As the signals were collected at different locations along the axial direction of a marine riser, the phenomena of the stress wave propagation could be analyzed through the obtained residues of those signals. The Norwegian Deepwater Program (NDP) high mode test data were utilized in the numerical studies, including data sets in both the in-line (IL) and cross-flow (CF) directions. It was found that the most dominant component in the IL direction has its stress wave propagation along the riser being dominated by a standing wave, while that in the CF direction dominated by a traveling wave.     

Laboratory Measurements of Vortex- and Wake-Induced Vibrations of A Tandem Arrangement of Two Flexible Risers

The dynamic response of two flexible model risers in tandem arrangement immersed in a stepped current was analyzed. The risers, with an external diameter of 20 mm and a total length of 6200 mm, had an aspect ratio of 310. They were hinged to the support structure at the center-to-center distances away 3?12 times the external diameter. The top 1200 mm was exposed to a uniform current at a speed which was up to 0.9 m/s (the Reynolds number was 18000) and the rest in still water. The dynamic responses, which were obtained through the Fiber Bragg Grating strain gauges mounted on the surface, were analyzed by studying the cross-flow amplitudes and modal weights. The cross-flow vibration were observed up to the third mode, and the modal transformation from the second mode to the third mode was clearly observed. The experiment confirmed that the typical vortex-induced vibration (VIV) had occurred on the up-stream riser. But for the down-stream riser, the main excitation mechanism was wake-induced vibration (WIV). The modal transformation of WIV was more complex than that of VIV, which might be helpful for other researchers to study the interference effect.     

Nonplanar multi-modal vibrations of fluid-conveying risers under shear cross flows

Risers/pipes conveying fluid are a typical kind of slender structures commonly used in marine engineering. It is of great academic significance and application value for us to evaluate and understand the vibration characteristics and nonlinear responses of these risers under the combined action of internal and external fluid flows. In this paper, the nonplanar vibrations and multi-modal responses of pinned-pinned risers in shear cross flow are numerically studied. With this objective in mind, the van der Pol wake oscillators are used to simulate the dynamical behavior of the vortex shedding in the wake. Two nonlinear equations of motion of the riser are proposed to govern the lateral responses of the riser structure. The nonplanar nonlinear equations for the riser and wake are then discretized by employing Galerkin's method and solved by using a fourth-order Runge–Kutta integration algorithm. Theoretical results show that the coupled frequencies for cross-flow (CF) and in-line (IL) motions and the corresponding coupled damping ratio could be influenced by the external and/or internal fluid velocities. Based on extensive calculations, the dynamical behavior of the riser with various internal and external flow velocities are presented in the form of bifurcation diagrams, time traces, phase portraits, oscillation trajectories and response spectrum curves. It is shown that some interesting dynamical phenomena, such as ‘lock-in’ state, ‘figure-of-eight’ trajectory and quasi-periodic oscillation, could occur in such a fluid-structure interaction system. Our results also demonstrate that the shear parameter can significantly affect the dynamic responses of the riser. When the shear parameter of the cross flow is large, multi-modal quasi-periodic responses of the riser can be excited, showing some new features undetected in the system of fluid-conveying risers in uniform cross flow.     

细长输流管内外流耦合振动特性研究

管内流动会影响输流管的振动响应,目前关于输流弹性管涡激振动方面的研究较少。基于计算流体力学(CFD)方法,开展内外流对细长输流弹性管振动特性影响的研究。首先在不考虑内流的情况下将弹性管涡激振动数值预报结果与模型试验数据进行对比,验证了数值方法的可靠性。再者考虑内外流耦合作用情况下,对不同内流流速下细长输流弹性管振动位移时—空分布、顺流向最大平均偏移、振动轨迹、内部横向涡的形成与分布等进行了对比分析。结果发现,与外流流速相比,内流流速的增加虽然难以改变弹性管的主振模态,但对沿管体的振动强度影响显著。顺流向最大偏移处管体运动轨迹发生明显的变形和跳跃。在剪切外流和均匀内流对弹性管的联合作用下,沿管跨方向模态间能量转换频繁,伴随着间歇性出现或消失的沿弹性管传播的行波组分,这主要归因于复杂的双重流固耦合系统(外流—管体,内流—管体)。在内流以附加质量力、离心力和科氏力形式的激励下,弹性管内二次流现象明显。在振动过程中,内部横向涡沿管壁生成、脱落并逐渐散布于整个横截面。