Vortex modes and vortex-induced vibration of a long,flexible riser

Investigations of the velocity and vorticity fields in the wake of a flexible riser with a length to diameter ratio of 181 were conducted in a towing tank at moderate Reynolds numbers in the range of 9400–47,000. Wake velocity measurements were made with the riser freely vibrating in both in-line and cross-flow directions. The motion and wake field of the riser, undergoing free vibration, were simultaneously measured by accelerometers installed inside the riser and by using a digital particle image velocimetry (DPIV) system. The vortex-induced vibration (VIV) results show that the riser freely oscillated at multiple vibration frequencies and amplitudes at each Reynolds number. Mixed vortex modes, ‘2S’, ‘2P’ and ‘P+S’, were observed in the near wake of the riser at different instants of time. The occurrence of these vortex modes depended on the Reynolds number, dominant frequency and mean amplitude. At lower Reynolds number, the single stable mode ‘2S’ dominated the wake. With the increase of Reynolds number, the percentage of the ‘2S’ modes decreased while the percentage of ‘2P’ modes increased steadily except at Reynolds numbers of 14,100 and 47,000. The ‘P+S’ modes occurred mostly at a Reynolds number of 14,100 accompanied by more ‘2P’ modes and less ‘2S’ modes. At this Reynolds number, the frequency of the VIV was very close to the natural frequency of 0.72 Hz, which was obtained from a riser decay test in steady water and the average amplitude to diameter ratio reached 0.95, the highest found in these tests.     

Laboratory Measurements of Vortex- and Wake-Induced Vibrations of A Tandem Arrangement of Two Flexible Risers

The dynamic response of two flexible model risers in tandem arrangement immersed in a stepped current was analyzed. The risers, with an external diameter of 20 mm and a total length of 6200 mm, had an aspect ratio of 310. They were hinged to the support structure at the center-to-center distances away 3?12 times the external diameter. The top 1200 mm was exposed to a uniform current at a speed which was up to 0.9 m/s (the Reynolds number was 18000) and the rest in still water. The dynamic responses, which were obtained through the Fiber Bragg Grating strain gauges mounted on the surface, were analyzed by studying the cross-flow amplitudes and modal weights. The cross-flow vibration were observed up to the third mode, and the modal transformation from the second mode to the third mode was clearly observed. The experiment confirmed that the typical vortex-induced vibration (VIV) had occurred on the up-stream riser. But for the down-stream riser, the main excitation mechanism was wake-induced vibration (WIV). The modal transformation of WIV was more complex than that of VIV, which might be helpful for other researchers to study the interference effect.     

Experiments with a steel catenary riser model in a towing tank

A model test with a steel catenary riser (SCR) was conducted in a towing tank. The main purpose of the experiment was to gain further understanding of the global SCR dynamic behavior with vortex-induced vibration (VIV). To this end, a large model scale factor (250) was considered. The mass and stiffness of the riser model are very low, and the Reynolds number in the experiment ranged from 400 to 600. The experimental results demonstrated the influence of traveling waves on the cross-flow response of the riser model, which was verified by several analytical methods. This study provided important indications that the sources of the traveling waves (power-in regions) seem to change position along the riser length over time. Finally, the experimental design, data processing procedure, experimental set-up, and results are described in detail.     

Numerical Simulation of the Vortex-Induced Vibration of A Curved Flexible Riser in Shear Flow

A series of fully three-dimensional(3 D) numerical simulations of flow past a free-to-oscillate curved flexible riser in shear flow were conducted at Reynolds number of 185–1015. The numerical results obtained by the two-way fluid–structure interaction(FSI) simulations are in good agreement with the experimental results reported in the earlier study. It is further found that the frequency transition is out of phase not only in the inline(IL) and crossflow(CF) directions but also along the span direction. The mode competition leads to the non-zero nodes of the rootmean-square(RMS) amplitude and the relatively chaotic trajectories. The fluid–structure interaction is to some extent reflected by the transverse velocity of the ambient fluid, which reaches the maximum value when the riser reaches the equilibrium position. Moreover, the local maximum transverse velocities occur at the peak CF amplitudes, and the values are relatively large when the vibration is in the resonance regions. The 3 D vortex columns are shed nearly parallel to the axis of the curved flexible riser. As the local Reynolds number increases from 0 at the bottom of the riser to the maximum value at the top, the wake undergoes a transition from a two-dimensional structure to a 3 D one. More irregular small-scale vortices appeared at the wake region of the riser, undergoing large amplitude responses.     

基于神经网络优化算法的海洋动态缓波型立管设计

柔性立管连接海上平台和水下生产系统,缓波型构型可以减轻其受到的顶部张力和疲劳损伤,触地点处系链对于固定水下立管起着重要作用,然而加装系链的缓波型立管系统设计更为复杂。通过缓波型基本理论计算出合理的立管初始状态,之后使用立管分析软件OrcaFlex,在充分考虑环境因素、船体结构、立管材料和线型以及重力块、浮力块、系链等配置参数的情况下,建立缓波型立管系统有限元模型,通过静动态分析验证其满足设定的关于立管构型、张力、弯曲半径,系链张力和FPSO偏移量5个约束条件。结合神经网络优化算法和遗传算法制定出针对文中立管系统的优化算法并通过MATLAB编程将浮力块数量优化至最少,之后基于L-M算法构建神经网络模型,通过迭代训练提升精度,得到最终参数优化结果。通过对比优化前后静动态分析结果可知：优化后浮力块数量大幅减少,立管最大有效张力大幅减小,而悬挂段最低点深度有一定程度的增大,整体构型更趋向于合理的缓波型构型。     

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.     

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.     

An inverse problem methodology for multiple parameter estimation in bend stiffeners

The flexible riser top connection is a critical region for lifetime assessment due to large tension/curvature variations and modeling uncertainties. The bend stiffener polyurethane mechanical response not only presents a nonlinear loading rate and temperature dependency but is also subjected to weather ageing during operation, which may affect its mechanical behavior over time. The top tension, employed for riser local cross-section stress calculation, is usually obtained from global dynamic analyses performed under selected environmental conditions, if direct measurement is not available. As a consequence, both the bend stiffener effect on the curvature distribution and the top tension time series present inherent uncertainties for riser lifetime (re)assessment. In the present work, a proposed monitoring approach composed by gyrometers installed along flexible riser/bend stiffener top connection system length combined with an inverse problem methodology is numerically investigated to estimate the following parameters: (i) polyurethane hyperelastic response and (ii) effective top tension. The top connection system is modeled using a large deflection beam bending model and the parameters are estimated using a damped least-square minimization approach with the Levenberg–Marquardt algorithm. For the preliminary feasibility investigation, the gyrometer experimental data is numerically estimated through Monte Carlo simulations. A case study is carried out to investigate the influence that the number of sensors, sensors arrangement, loading conditions and top connection model have on the inverse parameters estimation. The results indicate that the proposed monitoring approach and inverse parameter estimation methodology may effectively reduce flexible riser lifetime calculation uncertainties.     

Numerical benchmark studies on drag and lift coefficients of a marine riser at high Reynolds numbers

Numerical benchmark studies on drag and lift coefficients of a marine riser have been organized by the 27th ITTC Ocean Engineering Committee. The purpose of the studies was to benchmark the capabilities of CFD methods through quantitative comparisons and validation studies against the model test results of a circular cylinder by MARIN. Studies were focused on the drag crisis phenomenon for the stationary smooth cylinder in the critical Reynolds number regime. Eight organizations have participated in the studies by using RANS, DES and LES methods. An overview of the model test results, test cases, submissions and comparison results are presented in this paper. Conclusions and recommendations are made for future studies.     

An Experimental Study on Dynamics Features of Three Side-by-Side Flexible Risers Undergoing Vortex-Induced Vibrations in A Uniform Flow

A vortex-induced vibration(VIV) experiment on three side-by-side risers subjected to a uniform flow was carried out in a combined wave-current flume. The dynamic features of interference effect on three side-by-side risers were investigated by varying fluid velocity and inter-riser spacing. The distributions of dimensionless displacement,dominant frequency, and displacement trajectory of the model risers were measured using mode decomposition and wavelet transform techniques. The coupled interference of inter-riser fluid to adjacent risers at different spacings was disclosed by introducing the "interference ratio" concept. The results show that at spacings smaller than 6.0 D, the three model risers display appreciable deviations in their displacement responses in cross-flow or in-line direction,attributable to the strong proximity disturbance and wake interference between the risers. When the spacing is increased to 8.0 D, wake interference still makes great difference to the dynamic response of the risers in both directions. As reduced velocity increases, the three risers show higher agreement with an isolated riser in overall dominant vibration frequency in CF direction than that in IL direction at all spacings and the side risers, although symmetrically placed, do not vibrate symmetrically, as a result of the steady deflection of clearance flow within the riser group. Interference effect results in a remarkable unsteady mode competition within the risers; quantitation of the interference levels for the three risers at different spacings with interference ratio revealed that under low flow velocities and large spacing ratios, clearance flow constitutes a non-neglectable interferer for three side-by-side risers.     

Laboratory tests of vortex-induced vibrations of a long flexible riser pipe subjected to uniform flow

Laboratory tests have been conducted on vortex-induced vibration (VIV) of a long flexible riser towed horizontally in a wave basin. The riser model has an external diameter of 16 mm and a total length of 28.0 m giving an aspect ratio of about 1750. Reynolds numbers ranged from about 3000 to 10,000. Fiber optic grating strain gages are adopted to measure the dynamic response in both cross-flow and in-line directions. The cross-flow vibrations were observed to vibrate at modes up to 6 and the in-line reached up to 12. The fundamental response frequencies can be predicted by a Strouhal number of about 0.18. Multi-mode responses and the asymmetry of the bare pipe response in uniform flow were observed and analyzed. The experimental results confirmed that the riser pipe vibrated multi-modally despite it being subject to a uniform current profile and all of the excited modes vibrated at the Strouhal frequency. The asymmetrical distribution of displacement mainly resulted from the modal composition. Higher harmonics of the VIV response such as the third, fourth and fifth harmonics frequencies were found to be steady over the entire duration of the test even if they varied along the length of the riser pipe.     

Experimental Investigation of Disturbing the Flow Field on the Vortex-Induced Vibration of Deepwater Riser Fitted with Gas Jetting Active Vibration Suppression Device

An experimental investigation on the disturbance effect of jet-type active vibration suppression device on vortexinduced vibration of deep-sea riser was carried out in the wave-flow combined flume. The vibration suppression device was designed in which the jet pipe was horizontally fixed to the front end of the riser. By varying three different excitation spacings and multi-stage outflow velocities, the influence law of the dominant frequency,dimensionless displacement and other dynamic response parameters was studied under different excitation spacings,and the mechanism and sensitive characteristics of the disturbance suppression were explored. The results indicate that the variation of excitation spacing makes gas curtain enter the strong disturbed flow region at different velocities and angles, and the coupling relationship between excitation spacing and reduced velocity is the key factor to enter the strong disturbed flow region to achieve the optimal disturbance suppression. In the strong disturbed flow region,the influence of gas curtain on the dominant frequency is obviously affected by the flow velocity, while the vibration displacement is stable at the same amplitude and is weakly affected by the flow velocity. Gas curtain can effectively disturb the formation of vortex shedding, destroy the strong nonlinear coupled vibration of the riser, and achieve better vibration suppression effect. In the weak disturbed flow region, the vortex length of the riser tail is prolonged,the strong nonlinear coupled vibration of the riser is gradually restored, and the vibration suppression effect of the device gradually decreases.     

Modeling of coastal effluent transport: an approach to linking far-field and near-field models

One of the challenges in effluent transport modeling in coastal tidal environments is the proper specification of initial dilution in connection with the far-field transport phenomena. An approach of external linkage of far-field and near-field effluent transport models is presented, and applied to simulating the effluent transport in the Port Angeles Harbor, Washington in the Strait of Juan de Fuea. A near-field plume model was used to calculate the effluent initial dilution and a three-dimensional (3-D) hydrodynamic model was developed to simulate the tidal circulation and far-field effluent transport in the Port Angeles Harbor. The hydrodynamic model was driven by tides and surface winds. Observed water surface elevation and velocity data were used to calibrate the model over a period covering the neap-spring tidal cycle. The model was also validated with observed surface drogue trajectory data. The model successfully reproduced the tidal dynamics in the study area and good agreements between model results and observed data were obtained. It is demonstrated that the linkage between the near-field and far-field models in effluent transport modeling can be achieved through iteratively adjusting the model grid sizes such that the dilution ratio and effluent concentration in the circulation model grid cell match the concentration calculated by the near-field plume model.     

Reliability-based design optimization of an FPSO riser support using moving least squares response surface meta-models

The paper deals with the reliability-based design optimization (RBDO) of a riser support installed on a floating production storage and offloading (FPSO) unit under operation, extreme, damaged, and one line failure cases and installation loading conditions. The optimization problem is formulated such that probabilistic thickness variables described with random characteristics are determined by minimizing the weight of the riser support structure subjected to stress constraints for the given target reliability. The initial design model is generated based on actual FPSO riser support specifications. The finite element analysis is conducted using NASTRAN, and the probabilistic optimal solutions are obtained via the moving least squares method in the context of RBDO using a response surface meta-model. For the meta-modeling of the inequality constraint functions of stresses, a constraint-feasible moving least squares method (CF-MLSM) is adopted in the present study. The CF-MLSM has been shown to ensure constraint feasibility regardless of the nonlinearity of the constraint function, the feasible bounds, and the random characteristics during the meta-model-based RBDO process. The solution results from the proposed RBDO strategy present improved design performances under various riser operating conditions.     

基于遗传算法的缓波型立管多目标集成优化

缓波型立管由于设计参数较多且优化目标之间相互影响,设计结果具有很大的不确定性。随着代理模型和智能优化算法的发展,针对缓波型立管的优化可以提出更好的解决方案。以提高力学性能和经济效益为优化目标,采用基于Kriging插值模型和NSGA-II算法的多目标优化策略,对考虑顶部浮体影响的深水缓波型立管进行动力响应分析,并开展线型—截面双目标优化集成设计和线型—浮筒三目标优化集成设计。将处于不同几何尺度的设计变量进行集成,旨在各目标存在相互竞争的情况下,与截面、浮筒设计形成有效互动以提高线型设计的总体性能。结果表明,Pareto最优解集可提供多个选择方案,以满足工程实际需要。将所选最优方案与初始设计进行对比,并以疲劳性能和成本估算作为优化的校核指标,取得了理想的优化效果。     

钢悬链线立管与海床相互作用小尺寸三维试验研究

围绕钢悬链线立管(SCR)与海床的相互作用,在水箱内开展三维试验研究,研究在不同模拟运动激励下SCR触地点的应力状态。针对当前模拟试验中,全尺寸试验耗资巨大,且试验环境难以控制,缩尺试验大多模拟立管二维运动等现状,提出一套简单易行的三维管土作用试验装置,通过横向、纵向、垂向三个方向轨道位置的合理布置,使得立管可在单向、二维耦合和三个方向同时运动,对模型立管的顶端、底端的边界条件进行处理,通过驱动器在顶端施加位移,模拟在周期运动作用下,立管触地区与土的相互作用,在三维空间内研究立管的力学特性。由此指导立管的整体设计与分析,对保证SCR在深水油气开采中的安全可靠性,具有非常重要的意义。     

不同布设间距和来流速度下方型人工鱼礁上升流效应的数值模拟

合理的人工鱼礁组合可以有效改善投放水域的流场效应,提高投放水域底层与上层水体之间的扰动。通过使用并行大涡模拟模式及被动示踪物模块,并通过调整人工鱼礁布设间距,研究了在不同背景流速条件(0.1、0.5、0.6和1.0 m/s)下,在不同的横向间距(1L、2L、3L)(L表示人工鱼礁的边长)或纵向间距(1L、2L、3L、4L、5L)情况下,方型人工鱼礁对上升流体积、营养盐的抬升和垂向涡黏系数的影响。研究结果表明,在同一布置条件下,单排布置下的三块人工鱼礁形成的上升流体积大小与来流速度成正相关,体积随来流流速增加而增大6.4%～80.5%;在同一流速条件下,上升流体积大小与纵向布置的间距成正比,与横向布置的间距成反比;在横向布置条件下,当来流速度为1.0 m/s、布设间距为1L时,上升流体积参数最佳。总体来说,上升流体积参数、示踪物浓度差和垂向涡黏性系数均显示横向布置优于纵向布置,相较于布设间距,来流速度是影响上升流体积最重要的因素。     

The effect of nonlinear multi-contact coupling with gap between risers and guide frames on global spar motion analysis

Nonlinear multi-contact coupling between vertical risers and guide frames inside the spar moon-pool is studied. The existing numerical model for hull/mooring/riser coupled dynamics analysis treats riser as an elastic rod truncated at the keel (truncated riser model), and the risers are free to slide in vertical direction with constant tension, while restricted in horizontal direction. The truncated riser model neglects the portion of the riser inside the moon-pool and tends to overestimate the spar pitch motion. In the newly developed model, the risers are extended through the moon-pool with realistic boundary conditions at multiple guide frames, and thus additional contact forces and moments on the spar hull are considered. The gap effects between the riser buoyancy-cans and riser guide frames are also modeled using three different types of gap springs. Their different dynamic characteristics are extensively studied. The new riser model also considers the Coulomb damping between buoyancy-cans and riser guide frames and also allows the impact-like contact force calculation on risers for ensuring fatigue analysis.     

Experimental Investigation of Vibration Response of A Free-Hanging Flexible Riser Induced by Internal Gas-Liquid Slug Flow

The vibration response of a free-hanging flexible riser induced by internal gas-liquid slug flow was studied experimentally in a small-diameter tube model based on Froude number criterion. The flow regime in a curved riser model and the response displacements of the riser were simultaneously recorded by high speed cameras. The gas superficial velocity ranges from 0.1 m/s to 0.6 m/s while the liquid superficial velocity from 0.06 m/s to 0.3 m/s. Severe slugging type 3, unstable oscillation flow and relatively stable slug flow were observed in the considered flow rates. Severe slugging type 3 characterized by premature gas penetration occurs at relatively low flow rates. Both the cycle time and slug length become shorter as the gas flow rate increases. The pressure at the riser base undergoes a longer period and larger amplitude of fluctuation as compared with the other two flow regimes. Additionally, severe slugging leads to the most vigorous in-plane vibration. However, the responses in the vertical and horizontal directions are not synchronized. The vertical vibration is dominated by the second mode while the horizontal vibration is dominated by the first mode. Similar to the vortex-induced vibration, three branches are identified as initial branch, build-up branch and descending branch for the response versus the mixture velocity of gas-liquid flow.     

A flexible-segment-model-based dynamics calculation method for free hanging marine risers in re-entry

In re-entry,the drilling riser hanging to the holding vessel takes on a free hanging state,waiting to be moved from the initial random position to the wellhead.For the re-entry,dynamics calculation is often done to predict the riser motion or evaluate the structural safety.A dynamics calculation method based on Flexible Segment Model(FSM) is proposed for free hanging marine risers.In FSM,a riser is discretized into a series of flexible segments.For each flexible segment,its deflection feature and external forces are analyzed independently.For the whole riser,the nonlinear governing equations are listed according to the moment equilibrium at nodes.For the solution of the nonlinear equations,a linearization iteration scheme is provided in the paper.Owing to its flexibility,each segment can match a long part of the riser body,which enables that good results can be obtained even with a small number of segments.Moreover,the linearization iteration scheme can avoid widely used Newton-Rapson iteration scheme in which the calculation stability is influenced by the initial points.The FSM-based dynamics calculation is timesaving and stable,so suitable for the shape prediction or real-time control of free hanging marine risers.