Experimental study of vortex-induced vibrations of a pipeline near an erodible sandy seabed

Based on similarity analyses, a series of experiments have been conducted with a newly established hydro-elastic facility to investigate the transverse vortex-induced vibrations (VIVs) of a submarine pipeline near an erodible sandy seabed under the influence of ocean currents. Typical characteristics of coupling processes between pipe vibration and soil scour in the currents have been summarized for Case I: pipe is laid above seabed and Case II: pipe is partially embedded in seabed on the basis of the experimental observations. Pipe vibration and the corresponding local scour are usually two coupled physical processes leading to an equilibrium state. The influence of initial gap-to-diameter ratio (e₀/D) on the interaction between pipe vibration and local scour has been studied. Experimental results show that the critical values of V_r for the initiation of VIVs of the pipe near an erodible sand bed get bigger with decreasing initial gap-to-diameter ratio within the examined range of e₀/D (−0.25<e₀/D<0.75). The comparison of the pipe vibrations near an erodible soil with those near a rigid boundary and under wall-free conditions indicates that the vibration amplitudes of the pipe near an erodible sand bed are close to the curve fit under wall-free conditions; nevertheless, for the same stability parameter, the maximum amplitudes for the VIV coupled with local scour increase with the increase of initial gap-to-diameter ratio.     

海流作用下子母管结构横向涡激振动

基于量纲分析,设计模型试验研究稳态海流作用下子母管结构的横向涡激振动。通过对结构横向振动位移、水动力载荷和流场速度的同步测量分析,研究子母管结构横向涡激振动幅值和频率随约减速度的变化规律以及母管的水动力特性。实验结果表明,子母管间距比和质量比对管道横向振动和水动力有较大影响。在管间距比为0.1～0.5范围内,子母管结构涡激振动存在明显的不对称性。随着子母管间距比的减小,结构横向最大振幅增大,涡激振动的约减速度范围变宽;随着质量比的增大,涡激振动的约减速度范围变窄。母管的平均阻力系数随子母管间距比的增大单调递减,而平均升力系数则呈现非单调变化的特征。     

Physical Modeling and Parametric Study on Two-Degree-of-Freedom VIV of A Cylinder near Rigid Wall

Unlike most previous studies on the transverse vortex-induced vibration(VIV) of a cylinder mainly under the wallfree condition (Williamson & Govardhan,2004),this paper experimentally investigates the vortex-induced vibration of a cylinder with two degrees of freedom near a rigid wall exposed to steady flow.The amplitude and frequency responses of the cylinder are discussed.The lee wake flow patterns of the cylinder undergoing VIV were visualized by employing the hydrogen bubble technique.The effects of the gap-to-diameter ratio (e0/D) and the mass ratio on the vibration amplitude and frequency are analyzed.Comparisons of VIV response of the cylinder are made between one degree (only transverse) and two degrees of freedom (streamwise and transverse) and those between the present study and previous ones.The experimental observation indicates that there are two types of streamwise vibration,i.e.the first streamwise vibration (FSV) with small amplitude and the second streamwise vibration (SSV) which coexists with transverse vibration.The vortex shedding pattem for the FSV is approximately symmetric and that for the SSV is alternate.The first streamwise vibration tends to disappear with the decrease of e0/D.For the case of large gap-to-diameter ratios (e.g.e0/D = 0.54～1.58),the maximum amplitudes of the second streamwise vibration and transverse one increase with the increasing gapto-diameter ratio.But for the case of small gap-to-diameter ratios (e.g.e0/D = 0.16,0.23),the vibration amplitude of the cylinder increases slowly at the initial stage (i.e.at small reduced velocity V,),and across the maximum amplitude it decreases quickly at the last stage (i.e.at large Vr).Within the range ofthe examined small mass ratio (m＜4),both streamwise and transverse vibration amplitude of the cylinder decrease with the increase of mass ratio for the fixed value of V,.The vibration range (in terms of Vr ) tends to widen with the decrease of the mass ratio.In the second streamwise vibration region,the vibration frequency of the cylinder with a small mass ratio (e.g.mx = 1.44) undergoes a jump at a certain Vr,.The maximum amplitudes of the transverse vibration for two-degree-of-freedom case is larger than that for one-degree-of-freedom case,but the transverse vibration frequency of the cylinder with two degrees of freedom is lower than that with one degree of freedom (transverse).     

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.     

Behavior of vortex-induced vibration of a circular cylinder near a deformable wall with two degrees of freedom in steady flow

The behavior of vortex-induced vibration of a two-degree-of-freedom cylinder near a deformable wall in steady flow is investigated experimentally.The typical phenomenon of the two-degree-of-freedom cylinder’s VIV is discussed.The influences of initial gap between the cylinder and the wall on the dynamic responses of the cylinder are analyzed.The comparison is made about dynamic responses of the cylinder with one and two degrees of freedom.Experimental results show that the vibration of the cylinder near a deformable wall with a small value of initial gap-to-diameter ratios can generally be divided into two phases.The initial gap-to-diameter ratios have a noticeable influence on the occurrence of transverse vibration.The transverse maximum amplitude of the cylinder with two degrees of freedom is larger than that of the cylinder with one degree of freedom under the condition with the same values of other parameters.However,the vibration frequency of the cylinder for the two degrees of freedom case is smaller than that for the one degree of freedom case at the same value of Vr number.     

Scour of the Seabed Under A Pipeline in Oscillating Flow

The scour of the seabed under a pipeline is studied experimentally in this paper. Tests are carried out in a U-shaped oscillatory water tunnel with a box imbedded in the bottom of the test section. By use of the standard sand, clay and plastic grain as the seabed material, the influence of the bed material on the scour is studied. The relationship between the critical initial gap-to-diameter ratio above which no scour occurs and the parameters of the oscillating flow is obtained. The self-burial phenomenon, which occurs for the pipeline not fixed to two sidewalls of the test section, is not observed for the fixed pipeline. The effect of the pipe on sand wave formation is discussed. The maximum equilibrium scour depths for different initial gap-to-diameter ratios, different Kc numbers and different bed sands are also given in this paper.     

Analysis of Safe Span Length and Fatigue Life of Submarine Pipelines

Owing to the complex environmental conditions, suspension could induce complicated forces on submarine pipelines and even cause vortex-induced vibration, resulting in fatigue damage of pipelines. Through aiming at the 28-inch submarine pipeline in the East China Sea, the pipeline was segmented according to the similarity, considering the factors of pipe assembly, typhoon, current, wave and seabed topography. The effects of span length on natural frequency in each section of submarine pipeline were analyzed by finite element model. The maximum safe span length allowed by each pipeline section was verified by fatigue cumulative damage theory, and the fatigue life of each pipeline section were predicted. The results showed that each order natural frequency of the pipeline decreased with the increase of span length. The calculated results of empirical formulas were much smaller than those of the FEM analysis. The increase of the gap between the suspended pipeline and the seabed was beneficial to enhance the fatigue life of the suspended pipeline.     

Numerical Simulation of Self-Excited and Forced Vibrating Circular Cylinders in Current

Numerical simulations of a low-mass-damping circular cylinder which can oscillate freely at transverse and streamwise directions are presented in this work. The Navier-Stokes equations are solved with finite volume method, and large eddy simulation of vortex is also performed in the calculation. In order to implement dynamic mesh, overlapping grids are generated to lessen the computation for mesh field itself. Self-excited vibrations are firstly calculated to obtain the average amplitudes and frequencies of the target circular cylinder in the current flow situation, and then forced oscillations are implemented with parameters obtained in vortex-induced vibrations previously. With slight amplitude modulation, time series of displacements in vortex-induced vibrations are essentially harmonic. Regarding the fluid force, which are larger in forced oscillations than those in corresponding self-excited cases because the fluid subtracts energy from the forced cylinders. The phase angles between forces and displacements are 0o and 180o for self-excited case and forced case respectively. In vortex-induced vibrations, the interactions between fluid and structure produce some weakly energetic vortices which induce the modulations of amplitude and frequency.     

Numerical Simulation of Self-Excited and Forced Vibration of Circular Cylinders in Current

Numerical simulations of a low-mass-damping circular cylinder which can oscillate freely at transverse and streamwise directions are presented in this work.The Navier-Stokes equations are solved with finite volume method,and large eddy simulation of vortex is also performed in the calculation.In order to implement dynamic mesh,overlapping grids are generated to lessen the computation for mesh field itself.Self-excited vibrations are firstly calculated to obtain the average amplitudes and frequencies of the target circular cylinder in the current flow situation,and then forced oscillations are implemented with parameters obtained in vortex-induced vibrations previously.With slight amplitude modulation,time series of displacements in vortex-induced vibrations are essentially harmonic.Regarding the fluid force,which are larger in forced oscillations than those in corresponding self-excited cases because the fluid subtracts energy from the forced cylinders.The phase angles between forces and displacements are 0° and 180° for self-excited case and forced case respectively.In vortex-induced vibrations,the interactions between fluid and structure produce some weakly energetic vortices which induce the modulations of amplitude and frequency.     

高阶边界元方法求解规则波在三维局部渗透海床上的传播

基于线性势流理论,利用高阶边界元法研究了规则波在三维局部渗透海床上的传播。根据Darcy渗透定律推导出渗透海床的控制方程,利用渗透海床顶部和海底处法向速度和压强连续条件得到渗透海床顶部满足的边界条件。根据绕射理论,利用满足自由水面条件的格林函数建立了求解渗透海床绕射势的边界积分方程,采用高阶边界元方法求解边界积分方程进而得到自由水面的绕射势和波浪在局部渗透海床上传播过程中幅值的变化情况。通过与已发表的波浪对圆柱形暗礁的时域全绕射结果对比,证明了本文建立的频域方法计算波幅的正确性和有效性。利用这一模型研究了三维矩形渗透海床区域上波浪的传播特性,并分析了入射波波长、海床渗透特性系数等参数对波浪传播的影响。     

考虑流固耦合时的海底管道悬跨段非线性动力分析

通过对管道的涡激振动试验,提出了考虑流固耦合的非线性涡激升力表达式,并用该式进行了海底管线悬跨段非线性动力响应时程分析。对考虑流固耦合与未考虑流固耦合情况下得到的管道动力响应时程进行对比,算例表明:当管外流场流速与管道顺流向振动速度值较接近时,不考虑流固耦合时的计算结果明显小于考虑流固耦合时的计算结果。分析认为,在管外流场流速与管道顺流向振动速度值较接近的情况下,管道的涡激振动计算宜采用非线性涡激力模型。     

Numerical simulation of a partially buried pipeline in a permeable seabed subject to combined oscillatory flow and steady current

Hydrodynamic forces exerting on a pipeline partially buried in a permeable seabed subjected to combined oscillatory flow and steady current are investigated numerically. Two-dimensional Reynolds-Averaged Navier-Stokes equations with a k−ω turbulent model closure are solved to simulate the flow around the pipeline. The Laplace equation is solved to calculate the pore pressure below the seabed with the simulated seabed hydrodynamic pressure as boundary conditions. The numerical model is validated against the experimental data of a fully exposed pipeline resting on a plane boundary under various flow conditions. Then the flow with different embedment depths, steady current ratios and KC numbers is simulated. The amplitude of seepage velocity is much smaller than the amplitude of free stream velocity as expected. The normalized Morison inertia, drag and lift coefficients based on the corresponding force coefficients of a fully exposed pipeline are investigated. The normalized Morison force coefficients reduce almost linearly with the increase of embedment depth and that the KC only has minor effect on the normalized Morison coefficients. It is also found that the permeable seabed condition causes a slight increase on the inline force and has a little effect on the lift force, compared with corresponding conditions in an impermeable bed.     

波浪作用下粉质土海床液化界面波压力的研究

波浪作用下粉质土海床的液化是影响海上平台、海底管线等海洋构筑物安全的灾害之一。在进行构筑物设计中应考虑海床液化的深度问题,而液化土体对下部海床的界面波压力是计算海床孔隙水压力增长以及液化深度的重要参量。本文基于波致粉土海床自上而下的渐进液化模式,利用双层流体波动理论,推导了考虑海床土体黏性的海床界面波压力表达式,并与不考虑黏性时的界面波压力进行了比较分析。结果表明,计算液化后土体界面波压力时,是否考虑液化土体的黏性对结果影响较大,进而可能影响粉质土海床液化深度的确定。     

Global buckling of pipelines in the vertical plane with a soft seabed

Offshore pipelines are usually buried to avoid damage from fishing activities and to provide thermal insulation. Provided that the buried pipelines are sufficiently confined in the lateral direction by the passive resistance of the trench walls, they may be subject to vertical buckling caused by a rise in temperature. Vertical buckling is usually called upheaval buckling because the heated pipeline is assumed to move upwards conventionally. However, the seabed may be very soft, especially where a pockmark or abyssal ooze appears. Consequently, under thermal compressive force, the pipeline may buckle downward and penetrate into the seabed because the downward soil resistance is small. In this study, we extended an analytical solution for vertical pipeline buckling on a rigid seabed to a soft seabed, and the effects of soil resistance on pipeline stability, buckling mode and amplitude are illustrated and analyzed.     

Nonlinear dynamics of a fluid-conveying pipe under the combined action of cross-flow and top-end excitations

We report a theoretical investigation of an elastic and slender fluid-conveying pipe with a top-end excitation subjected to uniform cross flows. Considering the mean drag force and the time varying vortex-induced lift force which is modeled using a nonlinear van der Pol oscillator, the nonlinear partial differential equations of the motion of coupled fluid-structure system are constructed and simplified to a reduced-order model through the Galerkin-type discretization. By virtue of quasi-static displacement conditions, the characteristics of vortex-induced vibration of the pipe are evaluated for the first two lock-in modes. The results show that the top-end excitation can increase the vibration amplitude of the pipe when the cross-flow speed is out of the lock-in regions. When the cross-flow speed is within the lock-in region, however, the top-end oscillation causes a transition between quasi-periodic and periodic in the responses of the pipe, significantly reducing or increasing the vibration amplitudes depending on the excitation acceleration and frequency. This finding has an important guidance in suppressing vortex-induced vibrations by balancing the internal fluid velocity and the top-end excitation.     

埕岛油田海底管线在位稳定性的计算分析

埕岛油田主要分布粉土和淤泥质软土2类典型的海床.通过建立海床与其上裸置管线相互作用的有限元计算模型,对埕岛油田2类典型海床上裸置管线的在位稳定性进行了数值计算分析,并与现行常用的DNV(挪威船级社)管道设计方法的计算结果进行了对比.分析表明,对于埕岛油田粉土海床上裸置管线的在位稳定性分析,数值计算结果与DNV简化分析方法的结果较为一致;对于埕岛油田淤泥质软土海床上裸置管线的在位稳定性分析,DNV简化分析得到的裸置管线的在位稳定性一般高于相应的数值计算结果.     

海底管道检测与三维点云重建算法

随着海底油气管道的铺设规模越来越大,为防止管道油气泄漏而导致人员伤亡和财产损失,海底管道的日常巡检尤为重要。提出一种基于多波束点云的海底管道检测与三维重建算法,利用高频多波束声纳对水下管道进行成像,对声纳图像采用经典边缘检测算法检测管道边缘,得到相应的点云数据,将点云数据拼接成一组完整的空间点云集合,对点云集合进行三维重建。通过水池试验结果证明,提出的算法流程能够有效地实现水下管道的检测与三维重建,具有较好的工程应用前景。     

多频参激—涡激联合作用下顶张力立管分岔分析

复杂海洋环境中,顶张力立管顶部平台受到不同分量叠加的波浪作用,导致其轴向张力与多个频率相关,系统产生多频参激与涡激的联合振动,其动力学行为变得更为复杂,尤其是分岔和混沌等非线性振动特性有待进一步分析。首先,基于欧拉—伯努利梁理论,引入范德波尔尾流振子,建立和推导受多频参激—涡激联合作用下立管的动力学模型及其运动微分方程;接着,利用伽辽金法得到离散后的常微分方程组,采用多尺度法得到系统共振响应的调谐方程;最后,通过数值算例探究系统在多源和多频载荷联合作用下的共振响应。结果表明：对于多频参数激励,其中一个参数激励幅值在立管振动中起主导作用,而另一个会引起分岔的位置、数量和性质发生改变;随质量—阻尼参数增大,系统共振响应幅值整体先增大后减小,各分岔点出现的位置整体先向泄涡频率较大处移动,随后向泄涡频率较小处移动;质量—阻尼参数的变化还可能诱使系统发生倍周期分岔和混沌现象,危害结构安全。此外,采用直接数值积分求解微分方程组,验证近似分析结果,两者吻合较好。     

Physical modeling and swirling strength analysis of vortex shedding from near-bed piggyback pipelines

The vortex shedding from near-bed piggyback pipelines in a steady flow has been investigated experimentally in a large water flume. A specially arranged PIV system with upward-illumination of pulsed laser arrays from the flume bottom was employed for the flow visualization and quantitative measurement of the lee-wake flow in a sub-critical regime around the piggyback pipelines in the proximity of a plane boundary. Based on dimensional analyses, a dimensionless maximum swirling strength (W_m) is used for analyzing the vortex shedding intensity and its frequency. Time-averaged swirling strength analyses indicate that the lee-wake patterns for the near-bed piggyback pipelines are dependent on the configuration factors, including the gap-to-diameter ratio (e/D), the spacing-to-diameter ratio (G/D), and the diameter ratio of two pipes (d/D), etc. The swirling strength in the lee-wake is obviously asymmetric for piggyback pipelines with bed proximity. For the fixed values of G/D and d/D, the maximum swirling strength decreases with the decrease of e/D. Moreover, for the examined G/D range (0 ≤ G/D ≤ 0.5), minimum values of W_m and corresponding VIV amplitude for the piggyback pipelines are evidently within the same range of spacing-to-diameter ratio G/D ≈ 0.05–0.20.     

Analysis of VIV for Barrel-Shaped Mast with Covering Ice by HPD-S Method

The vortex-induced vibrations (VIV) of barrel-shaped mast are calculated by three numerical methods, i.e. Newmark-b, HPD-L (High Precision Direct integration scheme-Linear form), and HPD-S (High Precision Direct integration scheme-Sinusoidal form). According to the measured value, the accuracy curves are given to show the advantages of HPD-S method over others. Based on the comparison above, HPD-S method is used to calculate the influence of ice covering on the mast to VIV responses. It has been proved that the vortex-induced responses of barrel-shaped mast are changed along with ice thicknesses and types.