非均匀流中立管涡激振动模型预测分析

文中分析了非均匀流中,张紧式海洋立管的涡激振动,采用新的加速度耦合尾流振子模型作为预测细长海洋工程柔性结构的计算工具,将预测结果中的横向位移包络线及最大幅值与实验观测值、shear7软件计算值进行了对比,可以发现模型的计算结果与实验观测结果吻合得很好.     

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.     

多跨海底管道横流向涡激振动预报模型

基于欧拉-伯努力梁理论确定了多跨管道结构振动方程,采用非线性Van der pol方程描述旋涡脱落的尾流动力特性,利用弹簧模拟两端和中间的复杂边界约束,构建了多跨海底管道横流向涡激振动预报模型。基于模态正交性展开流-固耦合作用方程,对各阶主坐标响应进行数值求解。对比了本模型预报结果与试验结果、软件分析以及DNV规范推荐值,吻合情况比较理想。本模型可为深海多跨管道涡激振动的研究、防范和治理提供有效的分析方法。     

Study on Pure IL VIV of A Free Spanning Pipeline Under General Boundary Conditions

Pipeline spans may occur due to natural seabed irregularities or local scour of bed sediment. The pure in-line (IL) vortex-induced vibrations (VIV) analysis of the free spans is an important subject for design of pipeline in uneven seabed. The main objective of this paper is to analyze the characteristics of pure IL VIV of a free spanning pipeline under general boundary conditions. An IL wake oscillator model which can describe the coupling of pipeline structure and fluctuating drag is introduced and employed. The coupled partial differential equations of structure and wake are transformed into a set of ordinary differential equations using two-mode Galerkin method. Some case studies are presented and thoroughly discussed in order to investigate the effects of internal fluid, axial force and boundary conditions on the pure IL VIV.     

Vortex-Induced Vibrations of A Long Flexible Cylinder in Linear and Exponential Shear Flows

A numerical study based on a wake oscillator model was conducted to determine the response performance of vortex-induced vibration(VIV) on a long flexible cylinder with pinned-pinned boundary conditions subjected to linear and exponential shear flows. The coupling equations of a structural vibration model and wake oscillator model were solved using a standard central finite difference method of the second order. The VIV response characteristics including the structural displacement, structural frequency, structural wavenumber, standing wave behavior,travelling wave behavior, structural velocity, lift force coefficient and transferred energy from the fluid to the structure with different flow profiles were compared. The numerical results show that the VIV displacement is a combination of standing waves and travelling waves. For linear shear flow, standing waves and travelling waves dominate the VIV response within the low-velocity and high-velocity zones, respectively. The negative values of the transferred energy only occur within the low-velocity zone. However, for exponential shear flow, travelling waves dominate the VIV response and the negative energy occurs along the entire length of the cylinder.     

Analysis and prediction of vortex-induced vibrations of variable-tension vertical risers in linearly sheared currents

Many studies have tackled the problem of vortex-induced vibrations (VIV) of a vertical riser with a constant tension and placed in uniform currents. In this study, attention is focused on the cross-flow VIV modelling, time-domain analysis and prediction of variable-tension vertical risers in linearly sheared currents. The partial-differential equation governing the riser transverse motion is based on a flexural tensioned-beam model with typical pinned-pinned supports. The hydrodynamic excitation model describing the modulation of lift force is based on a distributed van der Pol wake oscillator whose nonlinear equation is also partial-differential due to the implementation of a diffusion term. The variation of empirical wake coefficients with system parameters and the water depth-dependent Reynolds number is introduced. Based on the assumed Fourier mode shape functions obtained by accounting for the effect of non-uniform tension, the Galerkin technique is utilized to construct a low-dimensional multi-mode model governing the coupled fluid-riser interaction system due to VIV. Numerical simulations in the case of varying sheared flow profiles are carried out to systematically evaluate riser nonlinear dynamics and highlight the influence of fluid-structure parameters along with associated VIV aspects. In particular, the effects of shear and tensioned-beam (tension versus bending) parameters are underlined. Some comparisons with published experimental results and observations are qualitatively and quantitatively discussed. Overall parametric analysis and prediction results may be worthwhile for being a new benchmark against future experimental testing and/or numerical results predicted by an alternative model and methodology.     

Numerical Prediction of Vortex-Induced Vibrations on Top Tensioned Riser in Consideration of Internal Flow

In consideration of the effect of the internal flowing fluid and the external marine environmental condition on the vortex-induced vibration (VIV) of top tensioned riser (TTR), the differential equation is derived based on work-energy principles and the riser near wake dynamics is modeled by Facchinetti''s wake oscillator model.Then Galerkin''s finite element approximation is implemented to derive the nonlinear matrix equation of the coupled equations and the corresponding numerical programs are compiled which solve the coupled equations directly in the timedomain. The comparison of the predicted results with the recent experimental results and the prediction of SHEAR7is performed. The results show the validity of the proposed method on the prediction of VIV of deep water risers.The effect of internal flow on the dynamic characteristics and dynamic response of the riser is analyzed and severalvaluable conclusions are drawn.     

Vortex-Induced Vibrations of A Free-Spanning Pipe Based on A Nonlinear Hysteretic Soil Model at the Shoulders

The pipe-soil interactions at shoulders can significantly affect the vortex-induced vibrations (VIV) of free-spanning pipes in the subsea. In this paper, the seabed soil reacting force on the pipe is directly calculated with a nonlinear hysteretic soil model. For the VIV in the middle span, a classic van der Pol wake oscillator is adopted. Based on the Euler-Bernoulli beam theory, the vibration equations of the pipe are obtained which are different in the middle span and at the two end shoulders. The static configuration of the pipe is firstly calculated and then the VIV is simulated.The present model is validated with the comparisons of VIV experiment, pipe-soil interaction experiment and the simulation results of VIV of free-spanning pipes in which the seabed soil is modelled with spring-dashpots. With the present model, the influence of seabed soil on the VIV of a free-spanning pipe is analyzed. The parametric studies show that when the seabed soil has a larger suction area, the pipe vibrates with smaller bending stresses and is safer.While with the increase of the shear strength of the seabed soil, the bending stresses increase and the pipe faces more danger.     

Tension and Drag Forces of Flexible Risers Undergoing Vortex-Induced Vibration

This paper presents the results of an experimental investigation on the variation in the tension and the distribution of drag force coefficients along flexible risers under vortex-induced vibration (VIV) in a uniform flow for Reynolds numbers (Re) up to 2.2×10⁵. The results show that the mean tension is proportional to the square of the incoming current speed, and the tension coefficient of a flexible riser undergoing VIV can be up to 12. The mean drag force is uniformly and symmetrically distributed along the axes of the risers undergoing VIV. The corresponding drag coefficient can vary between 1.6 and 2.4 but is not a constant value of 1.2, as it is for a fixed cylinder in the absence of VIV. These experimental results are used to develop a new empirical prediction model to estimate the drag force coefficient for flexible risers undergoing VIV for Reynolds number on the order of 10⁵, which accounts for the effects of the incoming current speed, the VIV dominant modal number and the frequency.     

Numerical Prediction of Vortex Induced Vibrations on Top Tensioned Riser in Consideration of Internal Flow

In consideration of the effect of the internal flowing fluid and the external marine environmental condition on the vortex-induced vibration （VIV） of top tensioned riser （Till）, the differential equation is derived based on work-energy principles and the riser near wake dynamics is modeled by Facchinetti＇ s wake oscillator model. Then Galerkin＇ s finite element approximation is implemented to derive the nonlinear matrix equation of the coupled equations and file corresponding numerical programs are compiled which solve the coupled equations directly in the time domain. The comparison of the predicted results with the recent experimental results and the prediction of SHEAR7 is performed. The results show the validity of the proposed method on the prediction of VIV of deep water risers. The effect of internal flow on the dynamic characteristics and dynmnic response of the riser is analyzed and several valuable conelusions are drawn.     

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.     

Numerical simulation of a short flexible pipe subject to forced motion and vortex-induced vibration

A series of numerical simulations about a small scale(aspect ratio:63.2) flexible pipe undergoing forced harmonious oscillation and vortex-induced vibration(VIV) have been taken into account.The wake hydrodynamics and pipe deformation were accomplished by ANSYS MFX solution strategy designed for fluid-structure interaction(FSI) problem with well-performed LES model.The configuration of structured mesh,multi-domain design,different mesh stiffness admeasured by User Fortran ensured that the numerical task was competent to deal with large deformation related to this case.The introduction of instantaneous amplitude definition and modeless component decomposition method(Chen and Kim,2008) was helpful to reveal much more information from modal analysis.Most results from numerical simulation are generally consistent with those from model test(Choi and Hong,2000) via the comparison between them.As supplementary to model test,visualization of the vortex wake was also provided.It has been proved that the forced oscillation doesn't only excite a complicated dumbbell-like wake pattern around the outer thimble,but also results in inner flow inside the PVC pipe.The velocity of the inner flow increases with the frequency of forced oscillation.     

圆柱涡激振动研究进展与展望

圆柱涡激振动广泛存在于机械工程、海洋工程等诸多领域,研究者们取得了许多研究成果,而系统综述圆柱涡激振动的论文距今已近10 a,因此,有必要对近10 a的研究进展进行系统分析。文中系统地总结了近10 a圆柱涡激振动研究成果,阐述了圆柱涡激振动的尾流模态和其对应的响应分支之间的因果关系,分析了影响圆柱涡激振动的关键因素(如质量比、阻尼比和雷诺数)对涡激振动响应的影响,介绍了圆柱涡激振动最大响应振幅的曲线拟合公式及其局限性,最后对圆柱涡激振动的研究方向提出建议。     

Experiments with flexible shrouds to reduce the vortex-induced vibration of a cylinder with low mass and damping

Experiments employing a low-mass-damping cylinder have been conducted to determine the vortex-induced vibration (VIV) response of four suppressors of the flexible-shroud family. The VIV suppressors were inspired in the concept of the Ventilated Trousers (VT), a flexible shroud composed of a flexible net fitted with three-dimensional bobbins. Reynolds number varied between 5 × 10³ and 25 × 10³, while reduced velocity varied from 2 to 26. The VIV dynamic response showed that the VT suppressed the peak amplitude of vibration down to 40% of that of a bare cylinder. Other flexible shrouds also achieved suppression, but not as efficiently. Drag was reduced during the VIV synchronization range, but remained above the value for a bare static cylinder thereafter. Spectral analysis of displacement and lift revealed that, depending on the geometry and distribution of the bobbins, the flexible shroud can develop an unstable behavior, capturing energy from the wake and sustaining vibrations for higher reduced velocities. PIV measurements of the wake revealed that the entrainment flow through the mesh is necessary to extend the vortex-formation length of the wake; this mechanism only occurs for the VT mesh.     

Dynamic interaction between two parallel submarine pipelines considered vortex-induced vibration and local scour

Abstract

The mechanism of local scour under two vibrating pipelines is investigated numerically in this research. A sediment scour model is adopted to estimate the motion of sediment. The general moving objects model, which is dynamically coupled with fluid flow, is set up to simulate the vortex-induced vibration (VIV) of the pipeline. The sediment scour model and pipeline vibration model are verified with the previous experimental results and show good agreement. Then, the coupling effects between the pipeline vibration and the local scour are investigated numerically. The effects of G/D (the ratio of the distance between the two pipelines to the diameter of the pipelines) on the local scour and the VIV of the pipeline are examined. The results indicate that the maximum scour depth under the vibrating pipelines is much larger than the scour depth under the fixed pipelines. Due to the shadowing effect of the upstream pipeline, the maximum scour depth under the upstream pipeline is deeper than that under the downstream pipeline. The pipeline vibration magnitude is closely related to the strength of the vortex that sheds behind the pipeline. The effect of G/D on the shape and strength of the vortices that shed behind the pipelines is significant.     

结构与尾流非线性耦合涡激振动预测模型

预测圆柱涡激振动的尾流振子模型中,通常采用线性的耦合模型,例如位移或者速度、加速度耦合来表征结构对尾流的作用。三种线性模型在预测圆柱锁频阶段的动力特性时存在差异,而且适用范围也受质量比的限制。提出了考虑结构与尾流动力非线性耦合的模型,该模型基于加速度耦合并结合速度耦合进行修正,适用范围不受质量比的影响;与实验结果的对比表明该模型可以更合理地给出锁频区域以及结构位移响应和尾流升力。最后,利用新模型讨论了质量比对锁频阶段结构振动幅值、尾流升力及频率比的影响;结果表明,随着质量比的增大,结构锁频区域变窄,结构振幅和尾流升力幅值减小。     

Experimental investigation of the forces and motion responses of two interfering VIV circular cylinders at various tandem and staggered positions

Experimental results are presented in the paper of two elastically supported rigid circular cylinders subjected to steady flows in a flume. The two cylinders were initially placed at various tandem and staggered positions with one in the wake of the other when subject to the steady flows. The in-line centre-to-centre distance varied from 2 to 5 diameters whilst the cross-flow distance from 0 to 2 diameters. The nominal Reynolds numbers were in the sub-critical regime and ranged from 1.12 × 10⁴ to 5.52 × 10⁴, and the nominal reduced velocities from 1.78 to 8.77. The damping ratio of the test set-up is low at 0.003 which gives a combined mass-damping parameter of 0.0046. Both the cylinders were free to respond in both the in-line and the cross-flow directions. The cylinder motion was measured simultaneously with the hydrodynamic loading in the two directions. It was found that the motion trajectories of the downstream cylinder show qualitative difference depending upon whether it is in tandem with the upstream cylinder or in the wake with a transverse offset. The VIV response of the downstream cylinder is dependent upon the reduced velocity of the upstream cylinder and its own reduced velocity based upon the actual mean wake velocity. The drag amplification of the downstream cylinder in the wake appears to be fundamentally different from that of a single VIV cylinder in isolation. Furthermore, unlike the two fixed cylinders in cross flow, the downstream cylinder undergoing VIV no longer experiences a marked non-zero mean lift. The upstream cylinder is largely unaffected by the downstream cylinder when the initial spacing is greater than 3 diameters. On the other hand, the motion response of and the fluid loading on the downstream cylinder are strongly influenced by the upstream cylinder in the spacing range tested.     

VIV and galloping of single circular cylinder with surface roughness at 3.0×10≤Re≤1.2×10

Passive Turbulence Control (PTC) in the form of selectively distributed surface roughness is used to alter Flow Induced Motion (FIM) of a circular cylinder in a steady flow. The objective is to enhance FIM's synchronization range and amplitude, thus maximizing conversion of hydrokinetic energy into mechanical energy by oscillator in vortex-induced vibration and/or galloping. Through additional viscous damping, mechanical energy is converted to electrical harnessing clean and renewable energy from ocean/river currents. High Reynolds numbers (Re) are required to reach the high-lift TrSL3 (Transition-Shear-Layer-3) flow regime. PTC trips flow separation and energizes the boundary layer, thus inducing higher vorticity and consequently lift. Roughness location, surface coverage, and size are studied using systematic model tests with broad-field laser visualization at 3.0×10⁴<Re<1.2×10⁵ in the low-turbulence free-surface water-channel of the Marine Renewable Energy Laboratory of the University of Michigan. Test results show that 16° roughness coverage is effective in the range (10°-80°) inducing reduced vortex-induced vibration (VIV), enhanced VIV, or galloping. Range of synchronization may increase or decrease, galloping amplitude of oscillation reaches three diameters; wake structures change dramatically reaching up to ten vortices per cycle. Conversion of hydrokinetic energy to mechanical is enhanced strongly with proper PTC.     

均匀来流下尾翼型抑振装置效果试验研究

基于控制尾流,阻止立管尾流漩涡脱落转换路径的涡激振动抑制机理,设计三角形尾翼、片状尾翼及交错尾翼等三种抑振装置。三种抑振装置分别安装于立管模型表面,立管模型采用外径为18 mm的透明有机玻璃管。通过在均匀流场中进行安装有该抑振装置的立管模型涡激振动试验,研究三种抑振装置对立管涡激振动的抑制效率,并通过与配重裸管的涡激振动数据对比,分析抑振装置对立管动力响应的影响规律。研究结果表明,三种抑振装置均取得了明显的抑振效果,与配重裸管相比,安装片状尾翼及交错尾翼的立管模型抑制效率可达90%以上,安装三角形尾翼后立管模型振动频率略有减小,而安装片状尾翼及交错尾翼的立管模型没有明显的主导频率。     

Variation of Added Mass and Its Application to the Calculation of Amplitude Response for A Circular Cylinder

In the present study,analyzed are the variation of added mass for a circular cylinder in the lock-in(synchronization) range of vortex-induced vibration(VIV) and the relationship between added mass and natural frequency.A theoretical minimum value of the added mass coefficient for a circular cylinder at lock-in is given.Developed are semi-empirical formulas for the added mass of a circular cylinder at lock-in as a function of flow speed and mass ratio.A comparison between experiments and numerical simulations shows that the semi-empirical formulas describing the variation of the added mass for a circular cylinder at lock-in are better than the ideal added mass.In addition,computation models such as the wake oscillator model using the present formulas can predict the amplitude response of a circular cylinder at lock-in more accurately than those using the ideal added mass.