LQR control on multimode vortex-induced vibration of flexible riser undergoing shear flow

Under the actions of ocean currents and/or waves, deep-sea flexible risers are often subject to vortex-induced vibration (VIV). The VIV can lead to severe fatigue and structural safety issues caused by oscillatory periodic stress and large-amplitude displacement. As flexible risers have natural modes with lower frequency and higher density, a multimode VIV is likely to occur in risers under the action of ocean currents, which is considered as shear flow. To decrease the response level of the VIV of the riser actively, a multimode control approach that uses a bending moment at the top end of the riser via an LQR optimal controller is developed in this study. The dynamic equations of a flexible riser including the control bending moment in shear flow are established both in the time and state-space domains. The LQR controllers are then designed to optimize the objective function, which indicates the minimum cost of the riser's VIV response and control input energy based on the Riccati equation of the closed-loop system under the assumption that the lift coefficient distribution is constant. Finally, the VIV responses of both the original and closed-loop systems under different flow velocities are examined through numerical simulations. The results demonstrate that the designed active control approaches can effectively reduce the riser displacement/angle by approximately 71%–89% compared with that of the original system. Further, for multimode control, the presented mode-weighted control is more effective than the mode-averaged control; the decrease in displacement is approximately 1.13 times than that of the mode-averaged control. Owing to the increase in flow velocity as more and higher-order modes are excited, the VIV response of the original system decreases slightly while the frequency response gradually increases. For the closed-loop system, the response becomes smaller and more complicated, and the efficiency of the controller becomes lower at a certain flow velocity.     

柔性立管涡激振动响应轨迹特性研究

为了深入研究细长柔性立管的涡激振动响应特性,进行了柔性立管的拖曳水池试验。由拖车拖动立管产生相对来流,根据应变测试得到的应变数据,基于模态叠加法得到位移响应。试验分析前,通过数值方法先针对刚性立管的涡激振动响应轨迹特性进行了分析。紧接着,通过试验方法对柔性立管的单模态以及多模态涡激振动响应轨迹特性进行了深入的分析和讨论。通过分析发现:柔性立管在低速下具有与刚性立管类似的轨迹响应特性,均呈现经典的8字形状;柔性立管在高速下,其轨迹开始变得混乱,这主要是由位移的多模态响应特性所产生。     

参激振动对顺应式垂直通路立管涡激振动的影响

顺应式垂直通路立管(CVAR)是目前处于研究阶段的一种新型的立管类型,在海流作用下产生涡激振动,在平台垂荡运动作用下产生参数激励振动。为了研究参数激励的影响,本文引入尾流振子模型模拟漩涡脱落对立管的作用,同时考虑浮式平台升沉运动产生的参数激励,建立了CVAR参激-涡激联合振动方程,获取联合作用下的动力响应,并与纯涡激振动响应进行对比。结果表明,在相同的流速下CVAR中部涡激振动幅值最大,流速的增大会导致涡激振动的频率增大,发生高阶锁振,高阶锁振振动幅值比低阶锁振振动幅值小。考虑参数激励之后,较纯涡激振动而言,立管的振动幅值增大;当参激频率与涡激振动频率接近时,立管的振动幅值最大。     

振荡来流下柔性立管涡激振动响应特性试验研究

在顶部浮体的带动下,悬链线立管的动力响应会诱发其周围产生相对来流,而这种振荡来流将激励立管悬垂段产生“间歇性”的涡激振动。文章在海洋工程水池中对不同最大约化速度URmax、KC数组合下的振荡来流作用下的柔性立管开展模型试验研究,利用光纤应变片测量模型的涡激振动响应。结合模态分析与小波变换对试验数据进行分析,讨论并总结了最大约化速度URmax以及KC数对涡激振动位移幅值响应特性的影响规律。文中进一步分析发现振荡来流下的涡激振动响应还存在“迟滞”及“高阶谐频”现象。     

剪切来流下柔性立管涡激振动抑制装置试验研究

文章针对柔性立管螺旋列板抑制装置在剪切流场中的涡激振动响应特性进行了试验研究,试验过程中通过旋转臂架从而形成相对剪切来流。通过测试得到的应变数据,基于模态叠加法,可得到立管的位移响应等参数。试验中针对螺旋列板的螺距和鳍高的变化进行了分析,系统地研究了不同螺旋列板状态下立管的主导频率、主导模态、无量纲振幅比以及疲劳损伤等参数。研究结果表明：螺旋列板可以很好地抑制立管的涡激振动响应;与螺距相比,鳍高对立管涡激振动响应会带来更大的影响;剪切流场中立管螺距恒定为5.0D（D为立管外径）时,鳍高为0.15D时的立管具有最好的抑制效果。     

塔式立管涡激疲劳损伤敏感参数研究

针对西非海域的塔式立管,考虑沿水深变化的不同流速截面,分析塔式立管在不同参数下的涡激振动响应及疲劳损伤沿管分布,讨论立管顶部张力、管内流体密度、立管外径、立管壁厚和SHEAR7能量阈值等参数的变化对疲劳损伤的影响.结果显示,由于制造和安装误差等因素导致这些参数的改变,对结构的涡激振动疲劳损伤影响显著,应该在工程设计中引起注意.     

钢悬链线的涡激振动分析

文章介绍了立管在不同流剖面下的涡激振动实验,然后给出了简支钢悬链线的静态方程和基于能量平衡原理的涡激振动频域预报理论.之后提出把钢悬链的参数转化为顶部张紧钻井隔水管的参数的思想.通过预报顶部张紧钻井隔水管的涡激振动响应,得到钢悬链线的涡激振动响应.文中还研究了不同的顶部预张力和不同流剖面对钢悬链线的涡激振动响应影响.结果表明立管的固有频率和模态数的关系足线性的,并且立管的均方根位移和激励的模态数不仅与流速的大小和变化范围有关,还与顶部预张力有关.     

Numerical analysis of vortex-induced vibration on a flexible cantilever riser for deep-sea mining system

The flexible cantilever riser, as a special form of the marine riser, can be encountered in a deep-sea mining system, where the bottom of the long vertical lifting pipeline is connected with the intermediate warehouse. The main objective of this paper is to investigate the effects of the bottom weight caused by the intermediate warehouse and the flow speed on the dynamic responses of the cantilever pipeline. A quasi-3D coupling algorithm based on the discrete vortex method and finite element method is employed to calculate the unsteady hydrodynamic forces and vortex-induced vibrations of this pipeline in the time domain, respectively. We first simulate the VIV of a long flexible riser with two fixed ends in a stepped flow to validate the feasibility of the present method. Then, systematic simulations of cross-flow VIV of the cantilever riser are carried out under a wide range of bottom weights and different current speeds. The number of the vibration mode shows the decreasing tendency with the increase of the bottom weight. In a certain range of the weight, the number of the dominant mode remains unchanged, while the vibration amplitude declines with increasing weight. An amplitude jump phenomenon can be observed when the transition of the dominant mode in two contiguous mode clusters occurs. Moreover, the higher-order modes are excited with the increase of the current speed.     

计及海底井口影响的隔水管涡激振动响应特性试验

在靠近海底井口位置,隔水管周围流场受井口系统的影响发生变化,流固耦合下涡激振动可能诱发隔水管在横流向(CF方向)更为剧烈的振动。为了研究受管土装置影响的隔水管涡激振动响应特性,使用自主设计的管土装置模拟海底井口,采用8 m柔性立管,进行了均匀流下单管和受管土装置影响的涡激振动对比试验。试验通过FBG光纤应变片测得应变信息,使用模态叠加法、FFT变换处理分析试验数据,对比分析2组隔水管的主导频率、应变时历与幅值谱、无因次振幅以及激励力系数等参数沿管径的分布情况。结果发现管土装置影响下,隔水管主导频率减小;CF方向涡激振动增大,振幅沿径向呈非对称特征;涡激振动振幅更大,隔水管受流场的激励与阻尼更为剧烈。     

钢悬链式立管涡激振动疲劳损伤参数分析

针对钢悬链式立管的结构特性,采用了简化后的振动模型。先对立管进行了模态分析;再根据立管的模态特性结合环境水流参数,采用模态叠加法对立管进行了涡激振动疲劳损伤分析。分析过程中,通过改变流速大小、立管壁厚、立管外径、内部介质以及抑制立管涡激振动的螺旋列板长度等参数,对立管的涡激振动疲劳损伤进行了相应的参数分析。结果表明:立管疲劳损伤随水流速度的增大、立管外径的增大以及内部介质密度的降低呈现上升趋势,但是壁厚变化对立管疲劳损伤大小影响却不显著。     

两自由度不同截面形式柱体涡激振动的CFD数值模拟

文章采用计算流体力学（CFD）方法,结合SST k-棕湍流模型,对低质量比柱体进行两自由度涡激振动数值模拟,得到了柱体升力、曳力系数的时程曲线,并观察了柱体进入锁振状态的幅值变化,研究了不同截面形式柱体在外流速处于0.1-1.0 m/s范围内的振动响应。将圆柱体在不同流速下两向振动的CFD数值模拟与实验数据进行比较,得到了较为满意的结果。通过分析不同截面柱体在不同外流速下的振动幅值发现,带有抑振装置的柱体截面形式能够有效地减小涡激振动,其中,板状截面柱体抑振效果较好。     

Fatigue damage from time domain simulation of combined in-line and cross-flow vortex-induced vibrations

A semi-empirical method for time domain simulation of vortex-induced vibrations (VIV) is used to calculate the in-line and cross-flow fatigue damage of a tensioned riser in uniform and sheared flow. Simulations are run for flow velocities ranging from 0.3 m/s to 2.4 m/s, and a detailed comparison with experimental observations is performed. Results are reported in terms of dominating frequency, mode of vibration and mean of r.m.s. of displacement, as well as fatigue damage distribution along the length of the structure and maximum fatigue damage rates for each case. Fatigue damage is calculated by rainflow counting of the strain time series together with an idealized S–N curve with slope m = 3. The results show that the model reproduces the measured fatigue damage with a satisfactory level of realism, using a consistent set of parameters. This indicates that the model is usable for calculation of riser VIV fatigue damage in various current conditions, assuming the Reynolds number is in the subcritical range.     

Three-dimensional vortex-induced vibrations of a circular cylinder predicted using a wake oscillator model

This paper reports a numerical study based on a wake oscillator model, to determine the three-dimensional vortex-induced vibration (VIV) responses on a flexible cylinder with pinned-pinned boundary conditions subjected to a uniform flow. Four different aspect ratios have been selected for the study. The coupling equations of the structural oscillator models and wake oscillator models in both the cross-flow (CF) and in-line (IL) directions have been solved using a standard central difference method of the second order. The structural displacement, structural frequency, response wave pattern, response trajectory, and lift force coefficient, for four aspect ratios, have been compared. The numerical results establish that, for a small aspect ratio, the CF displacements have absolute standing wave behaviors without travelling wave behaviors, and the IL displacements have dominant standing wave behaviors with slight travelling wave behaviors. Further, the VIV trajectory is repeatable and displays figure-eight shapes. However, for a large aspect ratio, the CF displacements display identical characteristics with the IL displacements for a small aspect ratio, and the IL displacements for a large aspect ratio are simultaneously dominated by standing and travelling wave behaviors. Moreover, the VIV trajectory is apparently aperiodic and shows chaotic shapes.     

Fatigue damage analysis of the deepwater riser from VIV using pseudo-excitation method

The fatigue damage of a long deepwater riser undergoing in-line and cross-flow vortex-induced vibration (VIV) in deepwater is numerically studied using pseudo-excitation method (PEM) in present paper. For evaluating the fluid–structure interaction problem of vortex-induced vibration of deepwater riser at high Reynolds number, the strip theory is employed in this paper, and the discrete vortex method (DVM) is used to calculate the VIV of each strip to obtain the load spectrum as the pseudo-excitation, while the finite volume method (FVM) is employed to evaluate the structure dynamics of a deepwater riser. The VIV is considered as a stationary random process. The response of riser to vortex induced excitation is calculated using pseudo-excitation method. The DVM model and pseudo-excitation method are both validated by comparing their numerical results with experiments. The fatigue damage of one deepwater riser is evaluated based on the Palmgren–Miner Rule.     

Empirical model of the wake-induced lift force on a cylinder with low mass ratio

The vortex-induced vibrations (VIV) of two flexible circular cylinders in a tandem configuration were studied numerically for spacing ratios ranging from 6 to 18 and the reduced velocities ranging from 2.35 to 12.59. The VIV response amplitude, response frequency, fluid force, pressure distribution and vortex structure of the tandem cylinders with different spacing ratios under different reduced velocities were compared. The results indicate that there is a great difference between the lift forces on the downstream and upstream cylinders. The lift coefficient of the downstream cylinder undergoing the wake-induced vibrations (WIV) is larger than that of the upstream cylinder, and the dominant frequency curves of the lift coefficients of the upstream and downstream cylinders separate. It can be found that the length and intensity of the wake are quite different under different reduced velocities and spacing ratios, and the reattachment positions between the wake and the downstream cylinder are different, which leads to a great change in the flow around the downstream cylinder and have a great effect on the wake-induced lift force on the downstream cylinder. Considering these factors, an empirical model for the wake-induced lift force on a cylinder with low mass ratio was proposed and verified.     

平台运动影响下张力腿涡激振动特性研究

张力腿涡激振动易引起系泊系统的疲劳损伤,危害张力腿平台的安全性和可靠性。该文借鉴细长立管涡激振动的相关研究,同时考虑张力腿与立管在截面尺度、预张力大小以及边界条件存在的巨大差距,采用切片理论结合CFD数值模拟方法,对平台运动影响下张力腿涡激振动开展了研究。考虑定常张力与时变张力对涡激振动的影响,采用GAMBIT软件分区建立了多切片计算网格,将编制求解涡激振动的UDF程序嵌入Fluent软件中,采用动网格技术实现流场的更新并计算作用于张力腿上的瞬时升力和拖曳力。文中还比较了仅考虑流和考虑浪、流联合作用张力腿的时变张力影响,研究了两种典型波高共计六种工况,计算结果表明：随着流速的增加,各模态权重比例将发生跳转现象;尽管由于平台运动导致张力腿受力的随机性,但平台运动对张力腿涡激振动影响较小。     

Time domain approach for coupled cross-flow and in-line VIV induced fatigue damage of steel catenary riser at touchdown zone

Existing VIV prediction approaches for steel catenary riser (SCR) typically employ truncation model without considering the interaction between the SCR and soil, and only allow for cross-flow (CF) VIV. In this study, a time domain approach accounting for the SCR-soil interaction is proposed to predict the CF and in-line (IL) VIV induced fatigue damage of a SCR at touchdown zone (TDZ). The hydrodynamic force resulting from the vortex shedding is modeled using the forced oscillation test data of a rigid cylinder and an empirical damping model, which are defined as functions of the non-dimensional dominant frequency and amplitude of the SCR response. Due to the coupling effect, the IL VIV force is magnified based on the CF VIV amplitude. By combining a linear hysteretic interaction model with a trench shape model, some particular phenomena during the vertical SCR-soil interaction are captured and qualitatively discussed, while for the horizontal direction, the seabed is simplified as nonlinear spring model. Based on these models, parametric studies are conducted to broaden the understanding of the sensitivity of VIV induced fatigue damage to the seabed characteristic. The results indicate trench depth, vertical and lateral stiffness, and clay suction are significantly affect the VIV induced maximum fatigue damage at TDZ.     

深海立管涡激振动疲劳损伤影响因素分析

根据我国南海、墨西哥湾和西非海域的流速沿深度方向的分布规律,利用涡激振动预报程序计算了立管在不同参数下的动力响应.在此基础上计算了立管沿长度方向涡激振动引起的疲劳损伤.分别讨论了立管顶部预张力、管内流体密度、管外流速分布、立管外径、立管壁厚等参数的变化对疲劳损伤的影响.结果显示立管顶部预张力、管外流速分布、立管外径对疲劳损伤的影响非常明显,而管内流体密度和立管壁厚因其变化范围有限,对疲劳损伤的影响没有上述三个参数显著.     

Reduction of VIV using suppression devices—An empirical approach

Helical strakes are known to reduce and even eliminate the oscillation amplitude of vortex-induced vibrations (VIV). This reduction will increase the fatigue life. The optimum length and position of the helical strakes for a given riser will vary with the current profile.

The purpose of the present paper is to describe how data from VIV experiments with suppressing devices like fairings and strakes can be implemented into a theoretical VIV model. The computer program is based on an empirical model for calculation of VIV. Suppression devices can be accounted for by using user-defined data for hydrodynamic coefficients, i.e. lift and damping coefficients, for the selected segments.

The effect of strakes on fatigue damage due to cross flow VIV is illustrated for a vertical riser exposed to sheared and uniform current. Comparison of measured and calculated fatigue life is performed for a model riser equipped with helical strakes. A systematic study of length of a section with strakes for a set of current profiles is done and the results are also presented.     

低质量-阻尼因子圆柱体的涡激振动预报模型

本文考查了在均匀来流中作横向振荡的圆柱体与周围流体之间的能量转移,由此建立了基于受迫振荡实验数据的弹性支撑圆柱体在均匀流中的涡激振动响应预报模型.根据此模型,分析了低质量-阻尼因子圆柱体的涡激振动响应特性.就水中圆柱体涡激振动响应特性相关的几个关键性问题进行了深入的讨论,包括响应振幅的决定因素、附加质量对锁定范围及响应频率的影响.正确理解这些问题对于深水立管涡激振动响应的有效预报至关重要.