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.     

Effect of internal flow on vortex-induced vibration dynamics of a flexible mining riser in external shear current

Vortex-induced vibration (VIV) of flexible risers with both internal and external flows has received much attention recently. Hence, VIV dynamics of a fluid-conveying flexible riser subjected to external shear current is investigated. The effect of internal flow velocity and fluid density on VIV response is mainly examined and analyzed. A time domain model is introduced and elaborated. Then the finite element method is adopted to discretize the governing equations. Firstly, the model is validated based on the comparison between the numerical and experimental results. Then the influence of the internal flow velocity and fluid density on VIV dynamics is studied. The results show that multi-frequency response occurs when the flexible riser with various internal flow velocities and densities is subjected to external shear current. Under same shear current velocity, the IL mean deflection is enlarged with the increase of the internal flow velocity and fluid density. In addition, the internal flow velocity and fluid density have an evident effect on the vibrating frequency and the root mean square (RMS) displacement in both in-line (IL) and cross-flow (CF) directions. Moreover, mode and frequency transitions can be observed under different internal flow velocities and fluid densities.     

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。     

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.     

非线性管土耦合条件下悬跨管道涡激振动响应时域预报

海底悬跨管道与海床耦合呈现高度非线性,使得发展一种时域预报方法成为需要.文章运用有限元法对输液张紧悬跨管道进行空间离散,并应用Facchinetti等改进的尾流振子模型和切片假定模拟每个有限单元上的涡激振动水动力,发展了一种悬跨管道-海床-流场多场耦合的非线性时域预报方法.在合理选取尾流振子模型附加水动力阻尼参数的基础上,时域预报了线性、理想塑性和张力截断弹簧模型下悬跨管道的涡激振动响应.研究结果表明,基于尾流振子的时域预报方法能够合理地描述非线性管土耦合边界下VIV响应;非线性边界条件下,锁定产生的最大响应幅值低于线性结果.     

Effect of mass ratio on hydrodynamic response of a flexible cylinder

The effect of the mass ratio on the flow-induced vibration (FIV) of a flexible circular cylinder is experimentally investigated in a towing tank. A Tygon tube with outer and inner diameters of 7.9 mm and 4.8 mm, respectively, was employed for the study. The tube was connected to a carriage and towed from rest to a steady speed up to 1.6 m/s before slowing down to rest again over a distance of 1.6 m in still water. Reynolds number based on the cylinder’s outer diameter was 800–13,000, and the reduced velocity (velocity normalized by the cylinder’s natural frequency and outer diameter) spanned from 2 to 25. When connected, the cylinder was elongated from 420 mm to 460 mm under an axial pre-tension of 11 N. Based on the cylinder’s elongated length, the aspect ratio (ratio of the cylinder’s length to outer diameter) was calculated as 58. Three mass ratios (ratio of the cylinder’s structural mass to displaced fluid mass, m*) of 0.7, 1.0, and 3.4 were determined by filling the cylinder’s interior with air, water, and alloy powder (nickel-chromium-boron matrix alloy), respectively. An optical method was adopted for response measurements. Multi-frequency vibrations were observed in both in-line (IL) and cross-flow (CF) responses; at high Reynolds number, vibration modes up to the 3^rd one were identified in the CF response. The mode transition was found to occur at a lower reduced velocity for the highest tested mass ratio. The vibration amplitude and frequency were quantified and expressed with respect to the reduced velocity. A significant reduced vibration amplitude was found in the IL response with increasing mass ratios, and only initial and upper branches existed in the IL and CF response amplitudes. The normalized response frequencies were revealed to linearly increase with respect to the reduced velocity, and slopes for linear relations were found to be identical for the three cases tested.     

考虑跨肩管土作用的悬跨管道涡激振动特性研究

海底悬跨管道涡激振动是一个复杂的流场-管道结构-跨肩土体耦合问题,其发生机理和振动特性十分复杂,特别是两端跨肩处管土作用对涡激振动的影响有待深入讨论。为此,文章引入了P-y曲线描绘跨肩处管土耦合作用,提出了基于管道位移和速度的新非线性土体弹簧模型,根据能量平衡原理计算土体阻尼,采用尾流振子模型模拟悬跨管段流固耦合作用,建立了考虑流—固—土多场耦合作用的海底悬跨管道涡激振动预报模型,并重点研究了考虑跨肩管土作用时,悬跨管道涡激振动的诸多特性。     

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。     

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。     

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.     

不同质量比对刚性圆柱体涡激振动振幅的影响

涡激振动发电装置是一种能够捕获浅海区域低流速海流能的新型能源装置,为了在不同海况下均能高效地对能量进行转换,需要对振动参数进行探讨,因此本文对质量比在振动响应和能量方面进行了分析。结合尾流振子模型和结构振动模型,得到双自由度涡激振动耦合模型,将Stappenbelt实验设置输入该模型,模型计算结果与其实验结果吻合,验证了模型的正确性。通过对中低质量比、超低质量比和高质量比三种条件下的柱体涡激振动响应进行分析,结果表明：中低质量比条件下,振幅和频率锁定区间宽度随质量比增加而减小;超低质量比条件下,顺流向无量纲振幅接近1,无法忽略,双向最大振幅发生约化速度Ur=6附近;高质量比条件下,最大振幅所对应的约化速度随着质量比的增加而增加,顺流向第二次波峰消失,横向出现两次波峰。     

螺旋侧板的高度对VIV影响的CFD分析

深水立管在来流作用下容易产生流向和横向的周期性位移振动(VIV),这种流固耦合作用会加剧立管结构疲劳,最终导致其功能失效。之前的研究发现螺旋侧板可以有效的抑制VIV的影响,其中侧板高度和螺距等几何参数决定其抑制效率。文章主要基于CFD对不同高度螺旋侧板的立管的尾流场进行数值模拟。结果表明:在研究范围内,螺旋侧板随高度增大抑制VIV效果越好,在H=0.25D(D为立管直径)时作用最佳,但拖曳力系数明显增大,同时来流方向和螺旋侧板的夹角也会影响其抑制效率。     

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.     

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。     

Convergence of different wake alignment methods in a panel code for steady-state flows

Wake alignment models are always included in the modern panel codes for marine propeller analysis. The wake alignment algorithms influence directly the rate of convergence and the accuracy of calculations. In the present work, firstly, four different numerical methods to implement the wake alignment algorithms for the steady calculation are described. They perform quite differently in terms of convergence history and convergence rate. The comparison with the other methods shows that the direct application of the unsteady method leads to a much slower convergence rate. Secondly, high-order numerical methods including second-order and fourth-order Runge–Kutta methods are introduced into the wake alignment, which results in high-order wake alignment algorithms. The analysis of the results shows that the high-order methods generate a different wake geometry from the low-order method. The thrust coefficient and torque coefficient have also been compared.     

Vortex-induced vibration (VIV) dynamics of a tensioned flexible cylinder subjected to uniform cross-flow

This paper presents the experimental results of a study on the effects of axial applied tension on the vibration amplitude, the suppression of vibration, hydrodynamic force coefficients and in-line (IL) and cross-flow (CF) frequency responses during vortex-induced vibration of a horizontally mounted flexible cylinder with a low mass ratio (cylinder’s mass/mass of displaced water), low bending-stiffness, and high aspect ratio (length/diameter 200) in the subcritical Reynolds number regime (Re = 1000–16000). The effect of tension is studied by applying four different tensions. It was revealed that higher applied tensions, which reduce the vibration amplitude, could significantly raise the hydrodynamic lift force coefficient. In addition, higher applied tensions generate narrower lock-in bandwidths. After the highest vibration amplitude and during the region of lower vibration amplitudes, within the first lock-in region (in the first mode of vibration), power spectral densities show broad bandwidth, while within other regions and higher modes they appear narrow-banded. The ratio of the dominant IL to CF frequency is approximately equal to 2.0, except for the lower reduced velocities, where the ratio values reach 3.83 for the highest tension accompanied by widening of the region in which this ratio is over 2.0. This ratio is 2.76 for the lowest applied tension with a narrower region.     

附属分离盘抑制圆柱涡激振动的数值模拟

基于动网格技术，编写UDF程序计算附属不同长度分离盘的圆柱双自由度涡激振动，并借助FLUENT软件模拟计算其周围流场。通过模拟计算不同长度附属分离盘的圆柱涡激振动，系统地对比分析其所受升阻力系数、振动响应、尾流涡形态、运动轨迹和频率特征等方面内容，并总结其一般规律。分析发现，添加合适长度的分离盘可以大大降低涡泄频率，有助于避开“锁定”区域，降低涡激振动的响应，同时还应该注意附属分离盘带来的多频和宽频振动特征。该数值模拟方法也为附属抑制装置的立管涡激振动数值模拟奠定了基础。降低，当约化速度Ur=5.5附近，分离盘长度越长，升阻力系数与振动响应越小。（2）添加附属分离盘后，裸圆柱所对应的双排尾流涡将变为单排尾流涡；随着分离盘长度增大，涡泄的位置往后推移，与此同时，分离盘的两侧逐渐出现一组次漩涡（分离盘上产生的漩涡）；分离盘长度L=0.5D时，因其未能完全阻隔上下两侧漩涡的相互作用，并将一侧漩涡切分为二，与另一侧漩涡在尾流形成2P形态的涡。（3）附属分离盘长度的增加使得圆柱振动范围不断缩小，但会造成多频的振动特征，而且还有效地改变来流向响应与横向响应的相位角。（4）添加附属分离盘后，一方面圆柱阻力的主频率明显降低，而且主频率所对应的功率谱密度也明显降低，说明分离盘能降低来流向的振动频率与振动强度，但会造成附属分离盘的圆柱阻力表现为多频、宽频的振动特征；另一方面添加附属分离盘的圆柱升力频率明显降低，但同样会造成多频和宽频的振动特征。总的来说，添加合适长度的分离盘可以大大降低涡泄频率，有助于避开“锁定”区域，降低涡激振动的响应，同时还应该注意附属分离盘带来的多频和宽频振动特征。本文的数值模拟方法也为附属抑制装置的立管涡激振动数值模拟奠定基础。     

Numerical investigation of concrete-filled double skin steel tubular (CFDST) structure subjected to underwater explosion loading

With the increasing applications in the offshore industry such as oil and gas jackets, submarine pipelines and wind turbine foundations, concrete-filled double skin steel tubular (CFDST) structures are encountering the ever-increasing risk of threats to underwater explosions (UNDEX). This study presents a systematical investigation on the structural behaviors and design recommendations of the CFDST structures subjected to UNDEX loadings through finite element analysis (FEA) approaches. Finite element models have been developed, where the non-linear material properties of the constitutive steel and concrete parts and the composite actions in-between have been considered. The FEA models are verified against the experimentally determined shock wave pressure history, the deformation shapes, and the residual strength. The full-range analyses were firstly carried out on the structural responses of CFDST structures, including the typical damage patterns and residual strength of the specimen after UNDEX. Then, the parametric studies show that the cross-section hollow ratio, charge weight, and explosion distance play great roles in determining the residual strengths. Thereafter, damage indexes considering the parameter of the hollow ratio and the scaled explosion distance has been formulated, and design recommendations have been suggested accordingly.     

The effects of free surface and end cell on flow around a finite circular cylinder with low aspect ratio

Vortex-induced motion is an oscillatory phenomenon which occurs to a floating body with low aspect ratio. The basic phenomenological study about the effects of free surface and end cell on flow around a finite fixed circular cylinder was investigated in this study using particle image velocimetry and hydrodynamic force measurement. It was found from the former experiment that the wake of the cylinder is influenced by the both end cell and free surface. Blowup and back flow are generated from the end cell, and their effects are suspended by free surface. The result of hydrodynamic force measurement showed the effect of Reynolds number, Froude number, and the aspect ratio of the floating body on the hydrodynamic force. Fluctuating components of hydrodynamic coefficients decrease for increasing Reynolds number, Froude number, and the aspect ratio. On the other hand, the mean drag coefficient increases as Froude number increases and decreases as the aspect ratio increases. The interpretation to these results was discussed in comparison with flow structures observed in the experiment. In addition, it was found that the effect of Reynolds number on the mean drag coefficient changes at different aspect ratios. A possible interpretation to this phenomenon was proposed.     

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.