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.     

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.     

Slow drift damping force acting on a horizontal cylinder

The hydrodynamic forces acting on a circular cylinder and a rectangular cylinder undergoing slow drift oscillation in regular waves were investigated experimentally and numerically. Forced oscillation tests with low frequency and large amplitude in regular waves and forced two-harmonic oscillation with combined low and high frequencies were carried out in the experimental study. In the numerical study a finite-difference method was used to simulate viscous flow around a two-dimensional oscillating cylinder. The results of experiments showed that a horizontal rectangular cylinder oscillating slowly in waves has much higher damping coefficients than one oscillating in two-harmonic mode, while the numerical study indicated that such differences in the damping coefficient arise partly from the different effects of one-direction harmonic flow and rotating flow on the vortex shedding caused by the slow drift oscillation.     

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。     

上游静止柱体对圆柱体结构尾激振动的影响

文章运用半隐式特征线分裂算子有限元算法对串列布置的静止上游柱体和下游圆柱的尾激振动问题进行了数值模拟研究。数值结果表明:上游柱体结构的形状、尺寸比(d/D)和折减速度(Ur)三个参数对下游圆柱体结构的动力响应、运动轨迹与涡脱落模态有着显著的影响,且与单圆柱工况相比存在明显区别;随着尺寸比的增大,上/下游柱体结构之间的互扰作用会由流致效应逐渐转变为尾流效应,使得频率特性发生变化,并会导致下游圆柱体结构的振动响应增强;当d/D=0.5和1.0时,下游圆柱体结构的运动轨迹主要为“8”字形;当d/D=1.5时,除了“8”字形外,运动轨迹还会呈现双弯刀形、“双8”字形和不规则形状。通过对流体力系数与位移时程曲线及位移PSD曲线特性进行分析,揭示了其相互作用的内在机理。另外,下游圆柱体结构的尾流场特性也会随参数的变化而变化,其涡脱落模态主要为2S、P+S和2P三种。     

水下圆柱冲刷的时间演变（英文）

Temporal evolutions of scour at submerged circular cylinders were investigated. Flow visualization was carried out around the cylinders over plane, under developed and equilibrium scour holes. Video analysis technique was used to formulate the equations for determining the diameter of the horseshoe vortex around the submerged cylinders, which is also verified from the vector diagrams drawn using the velocity measurements. The scour process similar to live bed scour was noticed around the downstream cylinder. The diameter of the horseshoe vortex is found to depend on the diameter of respective cylinder, submergence ratio,spacing between the cylinders and skew angle. This formulation along with the dislodgement and transportation of a single sediment particle is further incorporated in the proposed model for determining the time variation of scour around the submerged cylinders. It is evident from the results that the upstream cylinder shelters the downstream cylinder and thereby reduces the scour at the downstream cylinder. Proposed model is further extended to incorporate the effect of non-uniformity of the sediment particles on the time variation of scour depth. The results indicate significant reduction of scour depth of around 6% and 35% for upstream and downstream cylinders respectively due to the formation of the armor layer. The model is also compared with the local scour component of field data around cylindrical bridge piers to establish the differences in the scour process around a partially submerged cylinder and fully submerged tandem and skewed cylinders.     

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.     

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.     

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.     

Investigation on the vortex structure of propeller wake influenced by loading on the blade

The vortex structure of the wake behind a marine propeller was investigated in terms of loading variation by using particle image velocimetry. One hundred and fifty instantaneous velocity fields were ensemble averaged to study the spatial evolution of the wake and the behavior of the tip vortices in the region ranging from the trailing edge to one propeller diameter downstream. The trailing vorticity was found to be related to the radial velocity jump, and the viscous wake was affected by the boundary layers developed on the blade surfaces. A vortex identification method using the swirling strength was employed to extract the location of the tip vortex. The loading on the blade made a clear difference to the contraction angles. Slipstream contraction occurred in the very near wake region, and unstable oscillation occurred because of reduced interaction between the tip vortex and the wake sheet behind the maximum contraction point for each loading condition. The maximum tangential velocity around the tip vortex center revealed the average radius of its core, which was used for calculating the vortex strength. Additionally, variation of the average radius of tip vortices with the change of blade loading was related to vortex tube stretching in the wake region. The nearly constant vortex strength continued up to one diameter downstream for light loading and design loading conditions.     

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.     

串列双圆柱流致振动数值模拟

基于开源程序OpenFOAM和动网格技术,利用切应力平衡法建立水流作用下的海上风电基础局部冲刷数学模型。通过模拟结果与实验数据的对比发现,所建立的冲刷数学模型能够合理反映圆柱型单桩基础周围的水流结构,冲刷深度与实验结果吻合较好。     

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。     

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.     

细长海洋结构物涡激振动研究综述

随着世界范围内深海石油开采的需要,近年来关于海洋结构物涡激振动的研究越来越受到重视.虽然此问题在数值模拟和实验方面都已取得了一定的进展,但是还有许多问题尚待解决.同时,新型海洋结构物的引入给涡激振动的预报方法和抑振手段提出了新的挑战.因此,细长海洋结构物的涡激振动仍将是未来几年里备受关注的研究课题.本文在介绍有关涡激振动基本概念和理论背景的基础上,总结了近年来关于以深水立管为代表的海洋结构物涡激振动的研究与进展,包括对现有涡激振动分析工具的分类与评估;对柱体及海洋结构物涡激振动的实验研究;对深水立管与涡激振动相关的疲劳评估准则的研究;海洋结构物的横向、流向及轴向涡激振动的耦合作用研究;关于海洋结构物涡激振动的抑振措施和设备的理论及实验研究.本文着重介绍了计算流体力学方法在海洋结构物涡激振动研究中的应用和进展.最后,对海洋结构物涡激振动相关的研究热点的现状进行了总结并对今后工作提出了展望.     

A numerical study on piezoelectric energy harvesting by combining transverse galloping and parametric instability phenomena

This paper aims to numerically investigate the effects of parametric instability on piezoelectric energy harvesting from the transverse galloping of a square prism. A two degrees-of-freedom reduced-order model for this problem is proposed and numerically integrated. A usual quasi-steady galloping model is applied, where the transverse force coefficient is adopted as a cubic polynomial function with respect to the angle of attack. Time-histories of nondimensional prism displacement, electric voltage and power dissipated at both the dashpot and the electrical resistance are obtained as functions of the reduced velocity. Both, oscillation amplitude and electric voltage, increased with the reduced velocity for all parametric excitation conditions tested. For low values of reduced velocity, 2:1 parametric excitation enhances the electric voltage. On the other hand, for higher reduced velocities, a 1:1 parametric excitation (i.e., the same as the natural frequency) enhances both oscillation amplitude and electric voltage. It has been also found that, depending on the parametric excitation frequency, the harvested electrical power can be amplified in 70% when compared to the case under no parametric excitation.     

Collapse of composite-repaired cylinders with internal metal loss subjected to external hydrostatic pressure

The present study investigates the collapse performance of composite-repaired cylinders with internal metal loss subjected to external pressure. Three groups of intact, thinned, and repaired cylinders were designed, analytically verified, fabricated, geometrically measured, externally tested, and numerically modeled. Each group had three nominally identical cylinders to ensure the repeatability of experiments. The cylinders had the same end closure, effective length, total length, external radius, and intact thickness for an equivalent comparison. The thinned cylinder was considered as the intact cylinder with internal metal loss, whereas the repaired cylinder was considered as the thinned cylinder with composite reinforcement. The results indicated that the external loading capacity of cylinders with internal metal loss could be fully restored and even enhanced by composite reinforcement. Composite-repaired cylinders are much less sensitive to initial geometrical imperfections than intact cylinders.     

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。     

Fluid forces acting on three and four long side-by-side flexible cylinders undergoing flow-induced vibration(FIV)

Multiple side-by-side cylinders are widely employed in many engineering applications. Consequently, flow-induced vibrations (FIV), which have a significant influence on structural reliability, have drawn considerable concern from many investigators. Due to the complicated wake interactions behind the cylinders, the hydrodynamic characteristics of multiple side-by-side cylinders subject to FIV are obviously different from those of a single cylinder. Hydrodynamic force coefficients play an important role in evaluating structural reliability and predicting fatigue damage. However, few relevant investigations have been performed on hydrodynamic force coefficients of multiple side-by-side flexible cylinders, which require further research. In this paper, the hydrodynamic force coefficients of three and four side-by-side flexible cylinders with a spacing ratio of 6.0 are obtained by an inverse analysis method based on the oscillation displacements. In the resonance regions, the hydrodynamic force coefficients of multiple cylinders exhibit variation trends similar to those of a single cylinder, especially at higher reduced velocities. In the mode switch regions, relatively large deviations exist between the coefficients of multiple cylinders and single cylinder. The inner cylinder in the three-cylinder system shows prominently distinctive behaviour compared with the outer two cylinders. For the four-cylinder system in a side-by-side arrangement, the outer two cylinders show relatively slight differences between each other compared with the inner two cylinders.     

Vortex-induced vibrations of piggyback pipelines near the horizontal plane wall in the upper transition regime

Slender subsea structures like pipelines, jumpers and umbilicals when exposed to currents may experience vortex-induced vibrations (VIV), which can shorten their fatigue life and increase the risk of structural failure. In the present study, flow around different configurations of a piggyback pipeline close to a flat seabed has been investigated using the two-dimensional (2D) Unsteady Reynolds-Averaged Navier Stokes (URANS) equations with the k − ω Shear Stress Transport (SST) turbulence model. The Reynolds number (based on the free stream velocity and large cylinder diameter) is equal 3.6 × 10⁶ corresponding to upper-transition regime. The drag forces acting on the cylinders and base pressure coefficient value are well predicted by the present simulations, while the other hydrodynamic quantities (root-mean-square lift coefficient, Strouhal number) are predicted reasonably well as compared to published experimental data. The piggyback pipeline in the present study is modeled as two circular cylinders with a diameter ratio d/D = 0.2 (D denoting diameter of the large cylinder, d is diameter of the small cylinder). These two cylinders are clamped together at a distance G/D = 0.2. The two rigidly coupled cylinders are elastically supported and free to vibrate in two degrees of freedom. The effects on the vibration amplitudes and hydrodynamic forces are analyzed. The flow structures around the cylinders are investigated to explain the variations in observed structural responses. Depending on the angular position (α) of the small cylinder, the lock-in regime is narrower (α = 0°) or significantly wider (α = 180°) when compared to that of a single cylinder.