Effect of traveling wave on the vortex-induced vibration of a long flexible pipe

It is expected that the vortex-induced vibration response of long flexible tubular structures exposed to a shear current will consist of multiple modes of standing and traveling waves simultaneously. The vibration characteristics of traveling wave caused by VIV and its effect on the vibration form for a flexible pipe model are presented in this paper. Two methods are proposed to reveal the characteristics of standing and traveling waves from the perspective of an instantaneous illustration and a time-averaged statistical analysis separately. The first is associated with the adoption of an illustration method depending upon an instantaneous local upper envelope to identify the dominance of the standing or traveling wave. It is found that the in-line and cross-flow wave types show synchronization in that the wave types are mostly changeless or occasionally transform from one type to the other nearly simultaneously. In both the in-line and cross-flow directions, it is evident that the vibration response is not dominated by the standing wave characteristics but can often be characterized by the alternate presence of a traveling wave and a hybrid standing-traveling wave. The second method is associated with the adoption of the significant strain peak concept proposed to estimate the occurrence of the peak strain response and fatigue damage risk. It is found that the strain peak value attributed to in-line static strain accounts for a large proportion of the final equivalent significant strain peak near the pipe end with high reduced velocities, especially when the flow velocity is high. With the occurrence of a hybrid pattern of standing-traveling wave for higher velocities, the distribution of the significant cross-flow strain peak becomes uniform and its corresponding wave shape is apt to be flat.     

Laboratory tests of vortex-induced vibrations of a long flexible riser pipe subjected to uniform flow

Laboratory tests have been conducted on vortex-induced vibration (VIV) of a long flexible riser towed horizontally in a wave basin. The riser model has an external diameter of 16 mm and a total length of 28.0 m giving an aspect ratio of about 1750. Reynolds numbers ranged from about 3000 to 10,000. Fiber optic grating strain gages are adopted to measure the dynamic response in both cross-flow and in-line directions. The cross-flow vibrations were observed to vibrate at modes up to 6 and the in-line reached up to 12. The fundamental response frequencies can be predicted by a Strouhal number of about 0.18. Multi-mode responses and the asymmetry of the bare pipe response in uniform flow were observed and analyzed. The experimental results confirmed that the riser pipe vibrated multi-modally despite it being subject to a uniform current profile and all of the excited modes vibrated at the Strouhal frequency. The asymmetrical distribution of displacement mainly resulted from the modal composition. Higher harmonics of the VIV response such as the third, fourth and fifth harmonics frequencies were found to be steady over the entire duration of the test even if they varied along the length of the riser pipe.     

A practical approach to predicting cross-flow and in-line VIV response for deepwater risers

In this study, a practical model is proposed to predict cross-flow (CF) and in-line (IL) vortex-induced vibrations of a flexible riser in time domain. The hydrodynamic force as a function of non-dimensional amplitude and frequency is obtained from the forced vibration experimental data of a two-dimensional cylinder. An empirical nonlinear damping model is used to simulate the hydrodynamic damping outside the experiment's range. Coupling effect of CF and IL-VIV is taken into account by implanting a magnification model for the IL hydrodynamic force associated with CF amplitude, and by increasing the non-dimensional amplitude corresponding to the IL hydrodynamic coefficient in the second excitation region. The experimental models of flexible riser under the uniform and sheared current are simulated to validate the proposed model. The predicted displacement, curvatures, excited modes and fatigue damage show reasonable agreement with the measured data.     

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。     

Analytical solution of mean top tension of long flexible riser in modeling vortex-induced vibrations

The vortex-induced vibration (VIV) of flexible long riser with combined in-line and cross-flow motion has been studied using a wake oscillator in this paper. The analytical solution of mean top tension of long flexible riser is evaluated and compared with experimental results, and good agreement is observed to verify its validity. Then the nonlinear coupled dynamics of the in-line and cross-flow VIV of a long tension-dominated riser were analyzed through wake oscillator model with the consideration of variation of the mean top tension. The in-line and cross-flow resonant frequencies, lift and drag coefficients, dominant mode numbers, amplitudes and instantaneous deflections are reported and compared with experimental results, and excellent agreements are observed. The comparison of mode numbers between the calculation with and without consideration of variation of mean top tension shows that the proposed analytical solution of the mean top tension can produce a better prediction of multi-mode VIV.     

Instantaneous multi-mode identification and analysis of vortex-induced vibration via a mode decomposition method

The dynamic characteristics of marine risers/pipes often present serried modes with various frequencies due to high levels of structural flexibility and slenderness, especially when the flow velocity is non-uniformly distributed along the span. Therefore, the vortex-induced vibration (hence VIV) for slender risers/pipes is usually characterized by multi-mode motions. In this paper, by means of a newly developed empirical mode decomposition (EMD) method which contributes to more efficient instantaneous multi-mode identification and analysis, new characteristics of a multi-mode “lock-in” vibration process of a large-scale flexible pipe subject to shear flow were discussed. Because the two-degree vibration along the span can be analyzed simultaneously, the effects of multi-mode VIV were investigated systematically. From the given illustrative examples, it was found that the vibration energy diffusion between the fluid and the structure, and among the participating modes, may be repeatable and reversible, or even irreversible, which causes VIV to be highly intricate. The coexistence of multiple modes, energy transfer, and mode switching/jump is observed when the reduced velocity is relatively high. The multi-dominant mode phenomenon is also found in both cross-flow (CF) and in-line (IL) VIVs. Energy transfers between the CF and IL directions occasionally occur, and CF VIV is apt to dominate the vibration process, because it is superior to IL VIV with the increment of the reduced velocity.     

基于能量竞争载荷模型的海洋立管双向涡激振动时域预报方法研究

海洋立管是深海油气开发中用于连接海底井口和水面浮体的唯一通道。立管在洋流作用下极易发生涡激振动（vortex-induced vibration,简称VIV）,发展快速经验性涡激振动时域预报方法对立管的安全设计具有重要意义。通过柔性立管模型试验,结合载荷重构方法和最小二乘法,识别建立了能量竞争载荷模型下的经验水动力载荷系数模型。应用识别建立的经验水动力载荷系数模型,发展形成了海洋立管顺流向及横流向双向涡激振动时域预报方法。将预报结果与试验结果对比,结果表明：基于能量竞争载荷模型的海洋立管双向涡激振动预报方法能够有效预报海洋立管涡激振动主导模态、主导频率、流向平均位移响应和涡激振动位移响应等力学行为特性。研究成果对发展更为有效的涡激振动预报手段具有有益参考。     

Nonlinear dynamics of a fluid-conveying pipe under the combined action of cross-flow and top-end excitations

We report a theoretical investigation of an elastic and slender fluid-conveying pipe with a top-end excitation subjected to uniform cross flows. Considering the mean drag force and the time varying vortex-induced lift force which is modeled using a nonlinear van der Pol oscillator, the nonlinear partial differential equations of the motion of coupled fluid-structure system are constructed and simplified to a reduced-order model through the Galerkin-type discretization. By virtue of quasi-static displacement conditions, the characteristics of vortex-induced vibration of the pipe are evaluated for the first two lock-in modes. The results show that the top-end excitation can increase the vibration amplitude of the pipe when the cross-flow speed is out of the lock-in regions. When the cross-flow speed is within the lock-in region, however, the top-end oscillation causes a transition between quasi-periodic and periodic in the responses of the pipe, significantly reducing or increasing the vibration amplitudes depending on the excitation acceleration and frequency. This finding has an important guidance in suppressing vortex-induced vibrations by balancing the internal fluid velocity and the top-end excitation.     

考虑内流的海洋立管动力特性和动力响应的实验研究

本文考虑管内流体和管外流体的共同作用,对海洋立管进行试验研究。试验在中国海洋大学物理海洋试验室进行,通过试验得到了立管的一些有价值的规律:随着外流流速逐渐增大,立管的一阶激振频率也逐渐增大,在一定的外流速下,会激起立管的二阶激振频率甚至于三阶激振频率,由于立管的刚度较大,内流对立管的影响并不明显。但是当外流达到一定流速,这种影响就会显现出来,内流的存在会降低海洋立管的振动频率。     

Experimental Study on Response Performance of VIV of A Flexible Riser with Helical Strakes

Laboratory tests were conducted on a flexible riser with and without helical strakes. The aim of the present work is to further understand the response performance of the vortex induced vibration (VIV) for a riser with helical strakes. The experiment was accomplished in the towing tank and the relative current was simulated by towing a flexible riser in one direction. Based on the modal analysis method, the displacement responses can be obtained by the measured strain. The strakes with different heights are analyzed here, and the response parameters like strain response and displacement response are studied. The experimental results show that the in-line (IL) response is as important as the cross-flow (CF) response, however, many industrial analysis methods usually ignore the IL response due to VIV. The results also indicate that the response characteristics of a bare riser can be quite distinct from that of a riser with helical strakes, and the response performance depends on the geometry on the helical strakes closely. The fatigue damage is further discussed and the results show that the fatigue damage in the CF direction is of the same order as that in the IL direction for the bare riser. However, for the riser with helical strakes, the fatigue damage in the CF direction is much smaller than that in the IL direction.     

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.     

On the response of a free span pipeline subjected to ocean currents

A mechanistic study is performed to examine the coupling between the in-line and the cross-flow motion of a cylindrical structure subjected to current forces. The structure represents a free span pipeline but concerns marine risers as well.A time domain model is formulated in which the in-line and cross-flow deflections are coupled through the axial tension which in turn is computed from the pipeline prolongation at any time. This formulation introduces time dependent tensions and non-linearity into the problem.Preliminary validation of the model simulations vs. physical test data are carried out for one specific case to ensure that the sag and the in-line deflection are correctly resolved by the model. Using this as the initial condition a series of calculations are carried out to examine cross-flow induced deflections induced by an in-line prescribed deflection and vice versa. Finally, an idealistic simulation of flow induced vibration is presented.The model simulations demonstrate that the coupling varies with the mode shape and with which component it is initially introduced into. However, it is evident that the coupling effects may be significant and not negligible.     

Vortex modes and vortex-induced vibration of a long,flexible riser

Investigations of the velocity and vorticity fields in the wake of a flexible riser with a length to diameter ratio of 181 were conducted in a towing tank at moderate Reynolds numbers in the range of 9400–47,000. Wake velocity measurements were made with the riser freely vibrating in both in-line and cross-flow directions. The motion and wake field of the riser, undergoing free vibration, were simultaneously measured by accelerometers installed inside the riser and by using a digital particle image velocimetry (DPIV) system. The vortex-induced vibration (VIV) results show that the riser freely oscillated at multiple vibration frequencies and amplitudes at each Reynolds number. Mixed vortex modes, ‘2S’, ‘2P’ and ‘P+S’, were observed in the near wake of the riser at different instants of time. The occurrence of these vortex modes depended on the Reynolds number, dominant frequency and mean amplitude. At lower Reynolds number, the single stable mode ‘2S’ dominated the wake. With the increase of Reynolds number, the percentage of the ‘2S’ modes decreased while the percentage of ‘2P’ modes increased steadily except at Reynolds numbers of 14,100 and 47,000. The ‘P+S’ modes occurred mostly at a Reynolds number of 14,100 accompanied by more ‘2P’ modes and less ‘2S’ modes. At this Reynolds number, the frequency of the VIV was very close to the natural frequency of 0.72 Hz, which was obtained from a riser decay test in steady water and the average amplitude to diameter ratio reached 0.95, the highest found in these tests.     

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.     

Experimental study and numerical simulation on vortex-induced vibration of flexible riser

In order to study the effect of internal flow on vortex-induced vibration of flexible riser, the experiment on the vortex-induced vibration of flexible riser transporting fluid in the current was conducted in the physical oceanography laboratory of Ocean University of China. Considering the internal flowing fluid and external marine environment, the dynamic response of the flexible riser was measured. The corresponding numerical simulation was performed using the wake oscillatory model considering the extensibility of the riser system. Both the experiment and the numerical simulation indicated that with the increase of internal flow speed, the response amplitude increases, while the response frequency decreases.     

水下输液管道动力特性研究

该文研究水下横向输液管道的动力特性 ,假定管道系统承受外界均匀流的作用 ,同时考虑管内流体流动的影响 ,建立了水下输液管道侧向振动的微分方程。采用 Hermite插值函数和Galerkin法离散得到其有限元标准形式。研究管内流动为恒定流时输液管道长度、内部流体流动速度对管道动力特性的影响及管内流动含有谐波挠动的情况下输液管道固有频率的变化。结果表明 ,在管内恒定流动的情况下 ,输液的自振频率随管道长度及管内流速的增加而降低 ,同时管内流动的谐波挠动对管道的自振频率也有影响。     

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.     

Flow-Induced Vibration of Four Cantilever Cylinders Arranged in A Square Configuration

Flow-induced vibration (FIV) of four separately mounted cantilever cylinders are experimentally investigated in a water flume. The four cylinders with top ends screwed vertically into a turntable platform are subjected to uniform flows with Reynolds number ranging from 3840 to 16520. A non-intrusive measurement with high-speed cameras is employed to simultaneously capture the time-varying in-line and cross-flow vibrations in the reduced velocity range of 3.0–12.9. Experimental results highlight the continuous adjustment of flow regime caused by the spatial-temporal alteration of cylinders. Consequently, the space-time varying flow interference contributes to the occurrence of multiple response frequencies. The transition from a dominant frequency to a broad-band response illustrates the enhancement of wake interference. The combination of wake flow interactions results in the irregular oscillation trajectories and the appearance of a response trough with the associated switching in vortex shedding mode. The dual-resonance phenomenon is observed in the four cylinders due to the complicated wake-structure interaction. The greatest mechanical energy possessed by the four cylinders in an in-line square arrangement is mainly resulted from the downstream cylinders, signifying the positive role of wake excitation in extracting hydrokinetic energy from ambient flow.

     

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.     

A Novel Wake Oscillator Model for Vortex-Induced Vibrations Prediction of A Cylinder Considering the Influence of Reynolds Number

It is well known that the Reynolds number has a significant effect on the vortex-induced vibrations (VIV) of cylinders. In this paper, a novel in-line (IL) and cross-flow (CF) coupling VIV prediction model for circular cylinders has been proposed, in which the influence of the Reynolds number was comprehensively considered. The Strouhal number linked with the vortex shedding frequency was calculated through a function of the Reynolds number. The coefficient of the mean drag force was fitted as a new piecewise function of the Reynolds number, and its amplification resulted from the CF VIV was also taken into account. The oscillating drag and lift forces were modelled with classical van der Pol wake oscillators and their empirical parameters were determined based on the lock-in boundaries and the peak-amplitude formulas. A new peak-amplitude formula for the IL VIV was developed under the resonance condition with respect to the mass-damping ratio and the Reynolds number. When compared with the results from the experiments and some other prediction models, the present model could give good estimations on the vibration amplitudes and frequencies of the VIV both for elastically-mounted rigid and long flexible cylinders. The present model considering the influence of the Reynolds number could generally provide better results than that neglecting the effect of the Reynolds number.