Sparse Modal Decomposition Method Addressing Underdetermined Vortex-Induced Vibration Reconstruction Problem for Marine Risers

When investigating the vortex-induced vibration(VIV)of marine risers,extrapolating the dynamic response on the entire length based on limited sensor measurements is a crucial step in both laboratory experiments and fatigue monitoring of real risers.The problem is conventionally solved using the modal decomposition method,based on the principle that the response can be approximated by a weighted sum of limited vibration modes.However,the method is not valid when the problem is underdetermined,i.e.,the number of unknown mode weights is more than the number of known measurements.This study proposed a sparse modal decomposition method based on the compressed sensing theory and the Compressive Sampling Matching Pursuit(Co Sa MP)algorithm,exploiting the sparsity of VIV in the modal space.In the validation study based on high-order VIV experiment data,the proposed method successfully reconstructed the response using only seven acceleration measurements when the conventional methods failed.A primary advantage of the proposed method is that it offers a completely data-driven approach for the underdetermined VIV reconstruction problem,which is more favorable than existing model-dependent solutions for many practical applications such as riser structural health monitoring.

Suppression of Vortex-Induced Vibration Caused by A Terebridae-Inspired Cylinder with Different Helical Angles

Biomimetic design has recently received widespread attention.Inspired by the Terebridae structure,this paper provides a structural form for suppressing vortex-induced vibration(VIV)response.Four different structural forms are shown,including the traditional smooth cylinder(P0),and the Terebridae-inspired cylinder with the helical angle of 30°(P_(30)),60°(P_(60)),and 90°(P_(90)).Computational fluid dynamics(CFD)method is adopted to solve the flow pass the Terebridae-inspired structures,and the vibration equation is solved using the Newmark-βmethod.The results show that for P_(30),P_(60) and P_(90),the VIV responses are effectively suppressed in the lock-in region,and P_(60) showed the best VIV suppression performance.The transverse amplitude and the downstream amplitude can be reduced by 82.67%and 91.43%respectively for P_(60) compared with that for P0,and the peak of the mean-drag coefficient is suppressed by 53.33%.The Q-criterion vortices of P_(30),P_(60),and P_(90) are destroyed,with irregular vortices shedding.It is also found that the boundary layer separation is located on the Terebridae-inspired ribs.The twisted ribs cause the separation point to constantly change along the spanwise direction,resulting in the development of the boundary layer separation being completely destroyed.The strength of the wake flow is significantly weakened for the Terebridae-inspired cylinder.

Unlocking multidirectional and broadband wind energy harvesting with triboelectric nanogenerator and vortex-induced vibration of sphere

A unique oscillating wind-driven triboelectric nanogenerator(OWTENG)based on the sphere's vortex-induced vibration(VIV)behavior is proposed in this study,which can harvest wind energy across a multitude of horizontal directions.With the Euler-Lagrange method,the coupled governing equations of the OWTENG are established and subsequently validated by experimental tests.The vibrational properties and output performance of the OWTENG for varying wind speeds are analyzed,demonstrating its effectiveness in capturing wind energy across a broad range of wind speeds(from 2.20 m/s to 8.84 m/s),and the OWTENG achieves its peak output power of 106.3μW at a wind speed of 5.72 m/s.Furthermore,the OWTENG maintains a steady output power across various wind directions within the speed range of 2.20 m/s to 7.63 m/s.Nevertheless,when the wind speed exceeds 7.63 m/s,the vibrational characteristics of the sphere shift based on the wind direction,leading to fluctuations in the OWTENG's output power.This research presents an innovative approach for designing vibrational triboelectric nanogenerators,offering valuable insights into harvesting wind energy from diverse directions and speeds.

Numerical simulation of a short flexible pipe subject to forced motion and vortex-induced vibration

A series of numerical sinmlations about a small scale （aspect ratio： 63.2） flexible pipe undergoing forced harmonious oscillation and vortex-induced vibration （VIV） have been taken into account. The wake hydrodynamics and pipe deformation were accomplished by ANSYS MFX solution strat- egy designed for fluid-structure interaction （FSI） problem with well-performed LES model. The configuration of structured mesh, multi-domain design, different mesh stiffness admeasured by User Fortran ensured that the numerical task was competent to deal with large deformation related to this case. The introduction of instantaneous amplitude definition and modeless component decom- position method （Chen and Kim, 2008） was helpful to reveal much more information from modal analysis. Most results from numerical simulation are generally consistent with those from model test （Choi and Hong, 2000） via the comparison between them. As supplementary to model test, visualization of the vortex wake was also provided. It has been proved that the forced oscillation doesn＇t only excite a complicated dumbbell-like wake pattern around the outer thimble, but also results in inner flow inside the PVC pipe. The velocity of the inner flow increases with the frequency of forced oscillation.

Nonlinear Coupled in-Line and Cross-Flow Vortex-Induced Vibration Analysis of Top Tensioned Riser

The fluctuating furces of the fluid exerted on the top terrsioned riser （＇FIR） in the in-line and cross-flow directions are both modeled by van del Pol wake oscillator model and the nonlinear coupled dynamics of the in-line and cross-flow vortex-induced vibrations （VIV） of the riser are analyzed in time domain in this papar. The numencal shnulation results of the riser＇s in-line and cross-flow displacements and curvatures are compared with experimental measurements and the comparison shows the validity of this method in modeling some main features of the riser＇s VIV. Finally, the effects of the riser＇s top tensions and internal flow velocities on the coupled vibrations of the riser are investigated.

Fatigue Life Assessment of Top Tensioned Risers Under Vortex-Induced Vibrations

The fatigue life of top tensioned risers under vortex-induced vibrations (VIVs) with consideration of the effect of internal flowing fluid on the riser is analyzed in the time domain.The long-term stress histories of the riser under VIVs are calculated and the mean stresses,the number of stress cycles and amplitudes are determined by the rainflow counting method.The Palmgren-Miner rule for cumulative damage theory with a specified S-N curve is used to estimate the fatigue life of the riser.The corresponding numerical programs numerical simulation of vortex-induced vibrations (NSVIV) which can be used to calculate the VIV response and fatigue life of the riser are compiled.Finally the influences of the riser's parameters such as flexural rigidity,top tension and internal flow velocity on the fatigue life of the riser are analyzed in detail and some conclusions are drawn.

Prediction Model for Vortex-Induced Vibration of Circular Cylinder with Data of Forced Vibration

A model based on the data from forced vibration experiments is developed for predicting the vortex-induced vibra- tions （VIV） of elastically mounted circular cylinders in flow. The assumptions for free and forced vibration tests are explored briefly. Energy equilibrium is taken into account to set up the relationship between the dynamic response of selfexcited oscillations and the force coemcients from forced vibration experiments. The gap between these two cases is bridged straightforwardly with careful treatment of key parameters. Given reduced mass m^# and material damping ratio of an elastically mounted circular cylinder in flow, the response characteristics such as amplitude, frequency, lock-in range, added mass coefficient, cross-flow fluid force and the corresponding phase angle can be predicted all at once. In- stances with different combination of reduced mass and material damping ratio are compared to investigate their effects on VIV. The hysteresis phenomenon can be interpreted reasonably. The predictions and the results from recent experiments carried out by Wifliamson＇ s group are in rather good agreement.

Experimental Investigation of Disturbing the Flow Field on the Vortex-Induced Vibration of Deepwater Riser Fitted with Gas Jetting Active Vibration Suppression Device

An experimental investigation on the disturbance effect of jet-type active vibration suppression device on vortexinduced vibration of deep-sea riser was carried out in the wave-flow combined flume.The vibration suppression device was designed in which the jet pipe was horizontally fixed to the front end of the riser.By varying three different excitation spacings and multi-stage outflow velocities,the influence law of the dominant frequency,dimensionless displacement and other dynamic response parameters was studied under different excitation spacings,and the mechanism and sensitive characteristics of the disturbance suppression were explored.The results indicate that the variation of excitation spacing makes gas curtain enter the strong disturbed flow region at different velocities and angles,and the coupling relationship between excitation spacing and reduced velocity is the key factor to enter the strong disturbed flow region to achieve the optimal disturbance suppression.In the strong disturbed flow region,the influence of gas curtain on the dominant frequency is obviously affected by the flow velocity,while the vibration displacement is stable at the same amplitude and is weakly affected by the flow velocity.Gas curtain can effectively disturb the formation of vortex shedding,destroy the strong nonlinear coupled vibration of the riser,and achieve better vibration suppression effect.In the weak disturbed flow region,the vortex length of the riser tail is prolonged,the strong nonlinear coupled vibration of the riser is gradually restored,and the vibration suppression effect of the device gradually decreases.

Investigation of a New Vortex-Induced Vibration Suppression Device in Laboratory Experiments

In order to mitigate vortex-induced vibration (VIV) of marine risers, especially to eliminate the phenomenon of frequency 'lock-in', a new suppression device of crescent-shaped flow spoiler was designed with seven different layout schemes. VIV model tests with six flow levels were conducted in a large wind-wave-current flume. In all cases, vibration responses in both in-line and cross-flow cases were measured. With the installation of suppression devices vibration frequency evolution of a riser was analyzed by Morlet wavelet transform. The principle of VIV suppression was interpreted through vibration characteristics. Fatigue life of the riser was calculated by the Palmgren-Miner rule. Compared with a bare riser, vibration of an outfitted riser with suppression devices disturbed the steady flow, the vibration amplitudes in the two flow directions were reduced, and the riser fatigue life was improved.

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 Deep-Sea Risers of Different Excitation Water Depths

The vortex-induced vibration test of the deep-sea riser was carried out with different excitation water depths in the wave-current combined water flume.By dimensionally changing the multi-stage water depth and hydrodynamic parameters such as outflow velocity at various water depths,the dynamic response parameters such as dominant frequency,dimensionless displacement and vibration trajectory evolution process of the riser under different excitation water depths were explored to reveal the sensitive characteristics of the dynamic response of vortexinduced vibration of the risers under different excitation water depths.The results show that different excitation water depths will change the additional mass of the riser and the fluid damping and other parameters,which will affect the spatial correlation and stability of the vortex shedding behind the riser.In the lock-in region,the distribution range of the characteristic frequency becomes narrow and centered on the lock-in frequency.The increase of the excitation water depth gradually advances the starting point of the lock-in region of the riser,and at the same time promotes the excitation of the higher-order vibration frequency of the riser structure.Within the dimensionless excitation water depth,the dominant frequency and dimensionless displacement are highly insensitive to the excitation water depth at high flow velocity.The change of the excitation water depth will interfere with the correlation of the non-linear coupling of the riser.The“8-shaped”gradually becomes irregular,and the vibration trajectories of the riser show“O-shape”,“X-shape”and“Crescent-shape”.

Random vortex induced vibration response of suspended flexible cable to fluctuating wind

A popular dynamical model for the vortex induced vibration(VIV)of a suspended flexible cable consists of two coupled equations.The first equation is a partial differential equation governing the cable vibration.The second equation is a wake oscillator that models the lift coefficient acting on the cable.The incoming wind acting on the cable is usually assumed as the uniform wind with a constant velocity,which makes the VIV model be a deterministic one.In the real world,however,the wind velocity is randomly fluctuant and makes the VIV of a suspended flexible cable be treated as a random vibration.In the present paper,the deterministic VIV model of a suspended flexible cable is modified to a random one by introducing the fluctuating wind.Using the normal mode approach,the random VIV system is transformed into an infinite-dimensional modal vibration system.Depending on whether a modal frequency is close to the aeolian frequency or not,the corresponding modal vibration is characterized as a resonant vibration or a non-resonant vibration.By applying the stochastic averaging method of quasi Hamiltonian systems,the response of modal vibrations in the case of resonance or non-resonance can be analytically predicted.Then,the random VIV response of the whole cable can be approximately calculated by superimposing the response of the most influential modal vibrations.Some numerical simulation results confirm the obtained analytical results.It is found that the intensity of the resonant modal vibration is much higher than that of the non-resonant modal vibration.Thus,the analytical results of the resonant modal vibration can be used as a rough estimation for the whole response of a cable.

深海立管VIV预测模型及影响因素研究

为有效预测多因素作用下深海立管涡激振动(VIV),首先,基于欧拉-伯努利梁弯曲理论和改进范德波尾流振子方程,考虑管内流动流体和立管横向(CF)和顺向(IL)耦合作用,建立海洋立管涡激振动预测模型,用埃尔米特插值函数离散立管微分方程,纽马克-β法在时域内迭代求解立管位移;然后,设计VIV试验,并将试验数据与模型计算结果进行对比验证;最后,研究海流流速、内外流流速和顶张力对深海立管涡激振动特性的影响。结果表明:海流流速越大,立管振动频率越高,振动幅值越大;立管固有频率随内流流速的增大可能降低到锁振频率范围,加速立管的疲劳破坏,顶张力对立管内流影响有明显抑制作用,立管双向耦合作用在涡激振动分析中不容忽视。

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.

VIV analysis of pipelines under complex span conditions

Spans occur when a pipeline is laid on a rough undulating seabed or when upheaval buckling occurs due to constrained thermal expansion. This not only results in static and dynamic loads on the flowline at span sections,but also generates vortex induced vibration (VIV),which can lead to fatigue issues. The phenomenon,if not predicted and controlled properly,will negatively affect pipeline integrity,leading to expensive remediation and intervention work. Span analysis can be complicated by:long span lengths,a large number of spans caused by a rough seabed,and multi-span interactions. In addition,the complexity can be more onerous and challenging when soil uncertainty,concrete degradation and unknown residual lay tension are considered in the analysis. This paper describes the latest developments and a'state-of-the-art' finite element analysis program that has been developed to simulate the span response of a flowline under complex boundary and loading conditions. Both VIV and direct wave loading are captured in the analysis and the results are sequentially used for the ultimate limit state (ULS) check and fatigue life calculation.

Analysis of VIV for Barrel-Shaped Mast with Covering Ice by HPD-S Method

The vortex-induced vibrations （VIV） of barrel-shaped mast are calculated by three numerical metods, i.e. New- mark- β, HPD-L （High Precision Direct integration scheme-Linear form）, and HPD-S （High Precision Direct integration scheme-Sinusoidal form）. According to the measured value, the accuracy curves are given to show the advantages of HPD-S method over others. Based on the comparison above, HPD-S method is used to calculate the influence of ice covering on the mast to VIV responses. It has been proved that the vortex-induced responses of barrel-shaped mast are changed along with ice thicknesses and types.

An application of system identification in the two-degree-freedom VIV experiments

Experiments on the two-degree-freedom vortex-induced vibration （VIV） of a flexibly-mounted, rigid, smooth cylinder were performed at MIT. The research reported here is an analysis of the cylinder＇s trajectories. System identification methods were used to derive a best Fourier representation for these motions and to parse these motions into symmetric and asymmetric behaviors. It was postulated that the asymmetric behavior was due to distortions caused by the free surface and bottom used at the test facility, and that the symmetric behavior is representative of deepwater VIV. Further application of systems identification methods was used to associate the symmetric behavior and test conditions to a traditional vortex street model. These models were analyzed for their ability to predict details of VIV trajectories.

均匀流下水下机械臂涡激振动试验研究

为了揭示均匀流下水下机械臂的涡激振动响应特性,利用运动水下机械臂与静水间的相对运动,搭建了水下机械臂均匀流场涡激振动测试试验台,采集了不同约化速度下水下机械臂不同位置处的振动位移响应.试验结果表明:随着约化速度的增加,振动主频与无量纲振幅均为增长的趋势,横流向无量纲振幅小于0.04D,顺流向出现显著的多频以及更高的幅值,表明水下机械臂在顺流向受到的阻力更加明显.位移标准差随测试高度的增加先增后减,横流向位移标准差空间分布相较于顺流向对称性明显,主导模态控制在1阶.横流向的涡激振动规律性较强,基本符合圆柱绕流时的斯托哈尔规律.顺流向无因次主导频率在0.3~0.8之间,略大于横流向,斯托哈尔数为横流向工况的1~1.7倍,未出现频率锁定现象,但流速及测试高度对水下机械臂的涡激振动存在一定影响.该研究可为构建准确的水动力学模型保证水下机械臂的精准定位与控制提供一定的理论依据.

安装肋条斜拉索的涡激振动和气动力特性研究

以安装肋条斜拉索为研究对象,通过风洞试验系统研究肋条的安装方式(通长安装和间断交错安装)、尺寸和数量对斜拉索涡激振动和气动力的影响,并分析涡激振动的抑制机理.结果表明:和标准斜拉索相比,安装肋条斜拉索能有效抑制涡激振动,且间断交错安装方式的抑振效果优于通长安装方式,肋条数量为8根的控制效果优于6根和12根;增加肋条宽度和厚度都会减小涡激振动振幅;肋条斜拉索的脉动升力系数显著小于标准斜拉索,且功率谱尖峰幅值降低或不存在显著尖峰,表明间断交错肋条可以降低卡门涡脱落强度甚至完全抑制;对于气动力,在试验雷诺数范围内,安装肋条后平均气动力系数无明显雷诺数效应;相比于标准斜拉索,肋条为通长安装时均会增加斜拉索的平均阻力系数,而采用间断交错安装时,不同肋条数量、尺寸和风攻角对斜拉索的增阻减阻情况不同.当采用8根尺寸为20 mm×15mm的肋条间断交错安装时,在所有风攻角下都有良好的抑振效果,最大涡振振幅减小率可达到96.79%,且平均阻力系数均稳定在1.13附近,平均升力系数均稳定在0附近.

带挑臂PK箱梁涡振性能及优化措施机理研究

为研究带挑臂PK箱梁的涡振性能及气动优化措施,通过节段模型风洞试验研究了PK箱梁在0°、±3°风攻角下的涡振性能,并测试了人行道高度、封闭挑臂底部、栏杆透风率改变、不同倾角抑流板等气动措施对PK箱梁气动稳定性的影响,研究表明:主梁在0°、+3°风攻角下出现强烈的竖向涡激共振,并出现多个竖向涡振区间,同时在高风速下主梁出现了明显的扭转涡振;抬高人行道高度能降低各攻角下主梁的竖弯涡振响应,同时高风速下的扭转涡振得到极大程度的改善;通过封闭栏杆来改变栏杆透风率的研究发现,竖向间隔封闭人行道外侧护栏能破坏涡激气动力在展向的相关性,将主梁涡振峰值响应降低至规范限值的55.8%;0.25 m宽抑流板能有效改善主梁气动稳定性,抑流板倾角变化在20°~75°之间时,其均能完全抑制主梁涡振响应;气流在迎风侧人行道护栏处发生分离,在上表面卷起形成规律的大尺度旋涡,从而造成主梁剧烈的涡激振动,抑流板明显破坏了挑臂附近旋涡的形成,无法向下游发展形成规律的大尺度旋涡,从而能有效抑制主梁涡振。