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.     

Experimental and numerical study of the shielding effect of two tandem rough cylinders in flow-induce oscillation

The shielding effect of the downstream cylinder in flow induced oscillation (FIO) of two cylinders arranged in tandem is studied experimentally and numerically at Reynolds number 30,000 to 120,000. Both cylinders are in one degree-of-freedom, transverse-oscillations, and have turbulence stimulation in the form of selective surface roughness to expand FIO beyond vortex-induced vibration (VIV) into galloping. Shielding of the downstream cylinder has a negative effect on harnessing hydrokinetic energy. To study its effect and mechanics, selective cases are studied both numerically and experimentally and discussed to demonstrate the shielding effect on the downstream cylinder and understand its cause. The main conclusions are: (1) The shielding effect for the downstream cylinder shows a strong relation to the damping ratio. As the damping ratio increases, the shielding effect is mitigated. Additionally, the oscillation of the rear cylinder becomes stable and shows stable frequency. (2) In the VIV region, as the stiffness and natural frequency increase, the shielding effect decreases substantially. (3) In the VIV region, the vorticity of the vortices shedding from both the upper and the lower sides of the downstream cylinder does not accumulate enough due to the attraction by the vortices shed from the upstream cylinder, thus resulting in partial suppression of the oscillation on the downstream cylinder. (4) In the galloping region, the shielding effect for the downstream cylinder depends on whether the vorticity near the downstream cylinder is strengthened by the vortices generated by the shear layers of the upstream cylinder or weakened.     

Effect of surface roughness and initial gap on the vortex-induced vibrations of a freely vibrating cylinder in the vicinity of a plane wall

We studied the effects of the surface roughness and initial gap on the responses of vortex-induced vibration (VIV) of a circular cylinder near a stationary plane wall, employing numerical methods. The VIV response amplitudes, lock-in regions, hydrodynamic forces, VIV trajectories and flow fields for three different surface roughnesses and two different initial gaps were systematically compared. The results reveal that the reduced velocity range can be divided into three regions based on the VIV amplitude as pre-lock-in, lock-in, and post-lock-in regions. The width of the lock-in region is not sensitive to the variation of the roughness. The mean drag coefficient has a decreasing tendency with the increased roughness. For a small initial gap, the clockwise wall boundary layer vortices has coalesced with the clockwise vortices shed from the upper side of the cylinder, which further suppresses the shedding of the counter-clock wise vortices from the lower side of the cylinder. The vortex shedding flow pattern displays a weak 2S mode. However, for a large initial gap, there is no coalescing action operating in the wake region and hence most of the vortex shedding flow patterns show an asymmetric 2S mode.     

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.     

质量比和阻尼比对高阻尼涡激振动的影响

涡激振动水生能源是一种可在低流速条件下利用水中涡激振动现象从周围流场中提取水流动能的新兴可再生清洁能源技术,其能量转换装置在进行能量传递和转换过程中会对涡激振动系统引入较高的阻尼,使其不同于以往研究较多的低阻尼涡激振动系统。文章建立了一个单自由度涡激振动模型,模型采用受迫振动实验得到的流体力数据,通过迭代求解涡激振动能量转换装置的动力响应,进而计算系统转换功率。通过对质量比m*和阻尼比ζ等重要参数对涡激振动响应及能量转换效率影响的细致研究,揭示出:频率锁定的发生及较大能量转换效率的无量纲流速范围主要受质量比控制;最大能量转换效率主要受质量—阻尼参数m*ζ控制,并且存在一个最优值;出现最大能量转换效率的无量纲流速与m*ζ有关,在m*ζ0.2的范围内出现最大能量转换效率的无量纲流速随质量比和阻尼比的变化而变化,而在0.2m*ζ0.7的范围内与阻尼比无关,主要取决于质量比。     

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。     

Fatigue damage induced by vortex-induced vibrations in oscillatory flow

Vortex-induced vibration (VIV) of a flexible cylinder in oscillatory flow was experimentally investigated in an ocean basin. An intermittent VIV was confirmed to have occurred during the tests. The fatigue damage caused by VIV was calculated based on rainflow counting and a standard S–N curve. There are 3 main observations for fatigue damage from VIV in oscillatory flow: 1) the damage varied significantly with the KC number, which is a unique feature for VIV in oscillatory flow. 2) Fatigue damage at small KC number cases was found to be larger compared to those at large KC numbers owing to the fact that number of vortex shedding cycles per half of the motion cycle is low, and damping within half of the motion cycle will hence become low. The fact that vortices from the previous cycle still are active during the next may also contribute to the large response at small KC numbers. 3) ‘Amplitude modulation’ and ‘mode transition’, two specific features for VIV in oscillatory flow, were found to have a strong influence on fatigue. Fatigue damage has also been calculated by an empirical VIV prediction model assuming that all cases have steady flow at an equivalent velocity. Finally, a simplified method for calculating fatigue damage from VIV in oscillatory flow based on steady flow conditions is proposed. A modification factor diagram is presented, but the scope of the present study is too limited to provide a good basis for a general model for this factor. A general model for how to apply results from constant current analysis to predict fatigue in oscillatory flow will therefore need further research.     

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。     

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.     

Intelligent VIV control of 2DOF sprung cylinder in laminar shear-thinning and shear-thickening cross-flow based on self-tuning fuzzy PID algorithm

A self-tuning fuzzy PID (ST-FPID) control scheme is implemented within a joint interactive (Matlab/Simulink/Fluent) co-simulation framework for effective two degrees of freedom (2DOF) vortex-induced vibration (VIV) control of an elastically-mounted circular cylinder in laminar cross-flow of incompressible non-Newtonian power-law fluids based on the control action of a single transverse force actuator. The model-free controller, which systematically tunes the control parameters online in real time based on given rules, is well-known to be highly advantageous over the previously employed conventional PID controllers. It is particularly capable of handling the intricate non-linear dynamic effects inherent in the complex fluid rheology of non-Newtonian flow past the cylinder in presence of unmodeled system dynamics, high parametric uncertainties, diverse operational conditions, and time-varying external disturbances and control signals. Extensive numerical simulations reveal that the complex shear-thinning and shear-thickening behaviors of fluid viscosity can substantially influence the cylinder dynamic response, applied hydrodynamic forces, and flow structure. In particular, effectiveness and high performance of the adopted ST-FPID control strategy in substantial suppression of the high amplitude coupled 2DOF VIV of the elastically-mounted cylinder at selected critical reduced velocities in the lock-in region are established for a wide range of power-law index parameters (e.g., up to 83% reduction in RMS value of cylinder cross-flow displacement and up to 35% reduction in RMS value of cylinder in-line displacement for n=1and U* = 5 at Re = 100). Also, the vigorous action of the error-driven ST-FPID controller in forcing the high strength vortex shedding patterns of the uncontrolled cylinder out of the lock-in condition into the classical von Kármán vortex street of 2S-type mode of moderately weaker strengths is verified.     

稳定流作用下海底悬跨管线涡激振动研究

讨论了目前用于海底悬跨管线涡激振动预报的主要数值模型,针对海底管线悬跨段涡激振动问题编制了有限元分析程序,程序采用梁单元模拟管跨结构,动力响应计算方法采用VIVANA模型,模型控制方程采用Newton-Raphson迭代算法求解。采用Larsen,Koushan等人(2002)和Larsen,Baarholm等人(2004)给出的两组不同的用于确定升力曲线的参数曲线进行计算,将计算结果与Tsahalis(1984,1987)的模型实验结果进行了比较。结果表明本文的涡激振动模型能够预报间隙比e/D=∞时海底悬跨管线的涡激振动响应;采用Larsen,Koushan等人(2002)参数曲线得到的计算结果与间隙比e/D=∞时的实验结果符合较好,Larsen,Koushan等人(2002)参数曲线较Larsen,Baarholm等人(2004)参数曲线更适合于海底悬跨管线的涡激振动预报。     

基于一种固体区域迭代算法的圆柱涡激振动数值计算

利用Fluent平台的用户自定义程序（UDF）以及动网格模型,实现了圆柱运动方程的一种迭代求解算法,分别对层流、湍流状态下,弹性支承圆柱体在一定约化速度下的涡激响应进行了数值模拟,探讨了不同阻尼比对涡激响应的影响。结果表明：采用该迭代求解算法对弹性支承圆柱涡激振动的预测结果较为合理;随着阻尼比的逐渐增加,初始支振幅、升阻力系数时程曲线将由多频率拍振,最终变为单一频率主导的振动,且涡激振幅逐渐减小;除了质量-阻尼比联合参数m*ζ外,阻尼比ζ本身也应作为一个重要的涡激影响参数单独进行考量。     

动波壁对圆柱体涡激振动的抑制作用研究

文章基于有限体积法,通过控制壁面的波动方式,考察了动波浪壁面对低雷诺数下两自由度弹性支撑圆柱体涡激振动的抑制作用。结果表明:由圆柱两侧向下游行进的壁面波能抑制漩涡的脱落;适当的壁面波动频率能大幅降低圆柱的横向振动;当雷诺数Re=500时,随着约化速度的增大,动波壁圆柱的横向位移值相对标准圆柱体始终维持在较低值区间内(0～0.05D),动波壁圆柱流向位移值相对标准圆柱体的减小幅度逐渐增加。     

海底多段悬跨管道涡激振动特性分析

深海海底多跨管道相比于单跨,其涡激振动行为却更为复杂。文章考虑了两端跨肩和中间支撑处的管—土作用边界条件,提出了多跨管道涡激振动预报模型,标定了模型参数,并重点分析了跨肩边界条件、中间支撑条件和悬跨长度对管道涡激振动特性的影响。结果表明:较大的两端边界处扭转弹簧弹性系数、较大的中间支撑处扭转和拉伸弹簧弹性系数和较短的悬跨长度,会限制管道结构高阶模态的激发,同时还发现了振动能量会在相邻管跨之间传递的现象。     

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.     

Experimental investigation on the dynamic responses of a free-hanging water intake riser under vessel motion

A large-scale model test of a free-hanging water intake riser (WIR) is performed in an ocean basin to investigate the riser responses under vessel motion. Top end of the WIR is forced to oscillate at given vessel motion trajectories. Fiber Brag Grating (FBG) strain sensors are used to measure the WIR dynamic responses. Experimental results firstly confirms that the free-hanging WIR would experience out-of-plane vortex-induced vibrations (VIVs) under pure vessel motion even for the case with a KC number as low as 5. Meanwhile, comparison between numerical results and experimental measurements suggests a significant drag amplification by out-of-plane vessel motion-induced VIV. What’s more, further study on WIR response frequencies and cross section trajectories reveals a strong correlation between vessel motion-induced VIV and local KC number distribution, owing to the small KC number effect. The presented work provides useful references for gaining a better understanding on VIV induced by vessel motion, and for the development of future prediction models.     

Two degree of freedom flow-induced vibration of cylindrical structures in marine environments: frequency ratio effects

The flow-induced vibration of a cylindrical structure is a very common problem in marine environments such as undersea pipelines, offshore risers, and cables. In this study, the vortex-induced vibration (VIV) of an elastically mounted cylinder at a low Reynolds number is simulated by a transient coupled fluid–structure interaction numerical model. Considering VIV with low damping ratio, the response, hydrodynamic forces, and vortex shedding modes of the cylinder is systematically analyzed and summed up the universal rule under different frequency ratios. On the basis of the analysis, we find that the frequency ratio α is a very important parameter. It decides the locked-in, beat, and phase-switch phenomena of the cylinder, meanwhile, it also influence the vortex mode of the cylinder. The trajectory of the two degrees of freedom (2 DOF) case at different natural frequency ratios is discussed, with most trajectories having a “figure of 8” shape and a few having a “crescent” shape. A fast Fourier transformation technique is used to obtain the frequency characteristics of the vibration of the cylindrical structure. Using the 2 DOF cylinder model in place of the 1 DOF model presents several advantages in simulating the nonlinear characteristics of cylindrical structures, including the capacity to model the crosswise vibration generated by in-line vibration.     

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.     

Estimation of the response of a deeply immersed cylinder to the shock wave generated by an underwater explosion

The work presented in this paper is focused on the development of a simplified method to study the structural response of a deeply immersed cylinder subjected to the primary shock wave generated by an underwater explosion. The proposed analytical model is based on the string-on-foundation method initially developed by Hoo Fatt and Wierzbicki, who converted the two dimensional boundary value problem of a cylindrical shell to an equivalent one-dimensional problem of a plastic string on a plastic foundation. This method has already been extended by the authors to study the shock wave response of an unstiffened cylinder immersed in shallow water. The present work focuses on deep-immersed cylinders subjected to both high hydrostatic pressure and explosion shock wave. The elastic deformation energy of the cylinder under hydrostatic pressure is first calculated and used to determine the initial conditions of the dynamic problem. Cylinder deflection and plastic deformation energy are then calculated for various immersion depths. When confronted to numerical results, the proposed model appears to underestimate the increase of deflection and absorbed energy with the immersion depth. A thorough analysis of the results post-processed from Ls-Dyna/USA finite element simulations highlights a new mechanism which is due to the action of hydrostatic pressure that continues to push inward the immersed cylinder. In order to improve the analytical model, a correction factor on the hydrostatic pressure is introduced but it is finally concluded that a new mechanism dedicated to the late action of the hydrostatic pressure still needs to be developed.     

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.