VIV response of a long flexible riser fitted with strakes in uniform and linearly sheared currents

An experimental investigation was conducted on a flexible riser with and without various strake arrangements. The aim of the present work was to further improve the understanding of the response performance of the vortex-induced vibration (VIV) of a riser with helical strakes. Two current profiles, including uniform and linearly sheared flows, were simulated. The uniform current was simulated by towing the riser model in one direction using the towing carriage, and the linearly sheared current was simulated by fixing one end of the riser and using a driven cantilever to traverse a circular arc. Based on the modal superposition method, the displacement responses were obtained from the measured strain. Strakes with different heights and pitches were analysed, and response parameters such as the displacement response and fatigue damage were studied. The results of the bare model test show that the lock-in phenomenon displays multi-order characteristics, and the VIV displacement decreases with an increased order of the lock-in regime. The results of the straked model test indicate that the response characteristics of a bare riser can be quite distinct from those of a riser with helical strakes, and the response performance depends closely on the geometry of the strake configuration.     

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.     

海洋立管复模态动力特性分析

考虑阻尼的影响,研究海洋立管的动力特性。通过分析管内流体及管外海洋环境荷载的共同作用,建立海洋立管涡激振动偏微分方程,进而得到立管动力特性方程,用复模态分析法求解动力特性方程得到立管考虑阻尼的自振频率。算例计算表明:考虑阻尼的立管自振频率略小于不考虑阻尼的立管自振频率;立管的自振频率随着内流流速的增加而减小,但内流流速不大时,影响较小;管道长度对立管的自振频率影响较大。     

Nonplanar multi-modal vibrations of fluid-conveying risers under shear cross flows

Risers/pipes conveying fluid are a typical kind of slender structures commonly used in marine engineering. It is of great academic significance and application value for us to evaluate and understand the vibration characteristics and nonlinear responses of these risers under the combined action of internal and external fluid flows. In this paper, the nonplanar vibrations and multi-modal responses of pinned-pinned risers in shear cross flow are numerically studied. With this objective in mind, the van der Pol wake oscillators are used to simulate the dynamical behavior of the vortex shedding in the wake. Two nonlinear equations of motion of the riser are proposed to govern the lateral responses of the riser structure. The nonplanar nonlinear equations for the riser and wake are then discretized by employing Galerkin's method and solved by using a fourth-order Runge–Kutta integration algorithm. Theoretical results show that the coupled frequencies for cross-flow (CF) and in-line (IL) motions and the corresponding coupled damping ratio could be influenced by the external and/or internal fluid velocities. Based on extensive calculations, the dynamical behavior of the riser with various internal and external flow velocities are presented in the form of bifurcation diagrams, time traces, phase portraits, oscillation trajectories and response spectrum curves. It is shown that some interesting dynamical phenomena, such as ‘lock-in’ state, ‘figure-of-eight’ trajectory and quasi-periodic oscillation, could occur in such a fluid-structure interaction system. Our results also demonstrate that the shear parameter can significantly affect the dynamic responses of the riser. When the shear parameter of the cross flow is large, multi-modal quasi-periodic responses of the riser can be excited, showing some new features undetected in the system of fluid-conveying risers in uniform cross flow.     

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。     

Effects of mass and damping ratios on VIV of a circular cylinder

In this study the basic characteristics of the dynamic response and vortex shedding from an elastically mounted circular cylinder in laminar flow is numerically investigated. The Reynolds number ranges from 80 to 160, a regime that is fully laminar. The governing equations of fluid flow are cast in terms of vorticity. The two-dimensional vorticity transport equation is solved using a vortex method. Effects of important parameters on the system response and vortex shedding are investigated; these include: mass ratio, damping ratio, Reynolds number and reduced velocity. The numerical results show that a decrease in either the mass ratio or damping ratio of the system can lead to an increase in both the oscillation amplitude and the reduced velocity range over which lock-in occurs. The results also suggest that the mass-damping parameter may characterize the system response adequately, although the effect of changing mass ratio appears to be a little more profound compared to damping ratio. Vorticity contour plots suggest that the vortex shedding occurs in the 2S mode, although a wake structure similar to the C(2S) mode appears at distances 15–20 diameters downstream in the lock-in region. The simulation results are in good agreement with previously published data.     

Experimental Investigation on Vortex-Induced Vibration of Deep-Sea Risers of Different Excitation Water Depths

The vortex-induced vibration test of the deep-sea riser was carried out with different excitation water depths in the wave-current combined water flume.By dimensionally changing the multi-stage water depth and hydrodynamic parameters such as outflow velocity at various water depths,the dynamic response parameters such as dominant frequency,dimensionless displacement and vibration trajectory evolution process of the riser under different excitation water depths were explored to reveal the sensitive characteristics of the dynamic response of vortexinduced vibration of the risers under different excitation water depths.The results show that different excitation water depths will change the additional mass of the riser and the fluid damping and other parameters,which will affect the spatial correlation and stability of the vortex shedding behind the riser.In the lock-in region,the distribution range of the characteristic frequency becomes narrow and centered on the lock-in frequency.The increase of the excitation water depth gradually advances the starting point of the lock-in region of the riser,and at the same time promotes the excitation of the higher-order vibration frequency of the riser structure.Within the dimensionless excitation water depth,the dominant frequency and dimensionless displacement are highly insensitive to the excitation water depth at high flow velocity.The change of the excitation water depth will interfere with the correlation of the non-linear coupling of the riser.The“8-shaped”gradually becomes irregular,and the vibration trajectories of the riser show“O-shape”,“X-shape”and“Crescent-shape”.     

Hydrodynamics of A Flexible Riser Undergoing the Vortex-Induced Vibration at High Reynolds Number

This study proposed a method to obtain hydrodynamic forces and coefficients for a flexible riser undergoing the vortex-induced vibration (VIV), based on the measured strains collected from the scale-model testing with the Reynolds numbers ranging from 1.34E5 to 2.35E5. The riser is approximated as a tensioned spatial beam, and an inverse method based on the FEM of spatial beam is adopted for the calculation of hydrodynamic forces in the cross flow (CF) and inline (IL) directions. The drag coefficients and vortex-induced force coefficients are obtained through the Fourier Series Theory. Finally, the hydrodynamic characteristics of a flexible riser model undergoing the VIV in a uniform flow are carefully investigated. The results indicate that the VIV amplifies the drag coefficient, and the drag coefficient does not change with time when the CF VIV is stable. Only when the VIVs in the CF and IL directions are all steady vibrations, the vortex-induced force coefficients keep as a constant with time, and under “lock-in” condition, whether the added-mass coefficient changes with time or not, the oscillation frequency of the VIV keeps unchanged. It further shows that the CF excitation coefficients at high frequency are much smaller than those at the dominant frequency, while, the IL excitation coefficients are in the same range. The axial distributions of the excitation and damping region at the dominant frequency and high frequency are approximately consistent in the CF direction, while, in the IL direction, there exists a great difference.     

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.     

Time domain prediction approach for cross-flow VIV induced fatigue damage of steel catenary riser near touchdown point

Previous steel catenary riser (SCR) models targeted for VIV prediction are truncated at touchdown point (TDP) where simple constrain and rotation stiffness are generally applied. In this study, a time domain approach accounting for the SCR–soil interaction is proposed to predict the cross-flow (CF) VIV induced fatigue damage of a SCR near TDP. The hydrodynamic force is simulated based on the forced vibration test data as a function of the non-dimensional amplitude and frequency, and an empirical damping model. When the non-dimensional frequency associated with the calculated frequency falls in the excitation region, the natural frequency closer to the frequency corresponding to the maximum excitation force is taken to be the dominant frequency, and applied to obtain the excitation force. The SCR–soil interaction model takes into account the trench shape, and the mobilization and release of the soil suction. Fatigue damage is linearly accumulated by using the rain-flow counting methodology. To validate the proposed models, simulation for a riser model test is carried out, and the envelopes of RMS displacement, curvature, and fatigue damage are compared. Further works focus on the sensitivity of VIV induced fatigue damage near TDP to the seabed parameters, such as mudline shear strength, shear strength gradient and soil suction, and some conclusions are obtained.     

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。     

Cross-Flow VIV-Induced Fatigue Damage of Deepwater Steel Catenary Riser at Touch-Down Point简

A prediction model of the deepwater steel catenary riser VIV is proposed based on the forced oscillation test data, taking into account the riser-seafloor interaction for the cross-flow VIV-induced fatigue damage at touch-down point （TDP）. The model will give more reasonable simulation of SCR response near TDP than the previous pinned truncation model. In the present model, the hysteretic riser-soil interaction model is simplified as the linear spring and damper to simulate the seafloor, and the damping is obtained according to the dissipative power during one periodic riser-soil interaction. In order to validate the model, the comparison with the field measurement and the results predicted by Shear 7 program of a full-scale steel catenary riser is carried out. The main induced modes, mode frequencies and response amplitude are in a good agreement. Furthermore, the parametric studies are carried out to broaden the understanding of the fatigue damage sensitivity to the upper end in-plane offset and seabed characteristics. In addition, the fatigue stress comparison at TDP between the truncation riser model and the present full riser model shows that the existence of touch-down zones is very important for the fatigue damage assessment of steel catenary riser at TDP.     

Stream-wise and cross-flow vortex induced vibrations of single tapered circular cylinders: An experimental study

Tapered circular cylinders are employed in a variety of ocean engineering applications. While being geometrically simple, this configuration creates a complex flow pattern in the near wake of the structure. Most previous experimental studies on tapered circular cylinders were dealing with stationary cylinders to explore the wake flow field and vortex shedding patterns past the cylinder. Few studies paid attentions to the vortex induced vibration of the tapered cylinders. This paper reports some results from in-water towing-tank experiments on the vortex-excited vibrations of tapered circular cylinders in a uniform flow. Cylinders with different mean diameters (28 and 78 mm), mass ratios (6.1 and 2.27) and tapers (5–20), along with their equivalent uniform cylinders, have been examined. The single degree of freedom vibrating system has a low mass-damping parameter (m*ξ = 0.0084–0.0279). The Reynolds number, based on mean diameter of the cylinders, ranges from 1400 to 70,200. The reduced velocities vary from 1.5 to 22. Effects of variations in the taper and mass ratios on the lock-in range, the reduced response amplitude, the reduced velocity for the peak vibration response and other stream-wise and cross-flow VIV parameters are reported and discussed.     

Experimental investigation of the effects of the coverage of helical strakes on the vortex-induced vibration response of a flexible riser

The effects of different helical strake coverage on the vortex-induced vibration (VIV) of a model flexible riser were studied experimentally, with the aim of further improving the understanding of VIV responses. Uniform and linearly sheared currents were simulated to study response parameters such as non-dimensional displacement, fatigue damage, suppression efficiency, and the comprehensive evaluation is further studied. Test results of the bare model for a uniform current showed that the behavior of both the standing wave and traveling wave dominated VIV displacement. However, for a linearly sheared current, traveling wave behavior dominated VIV displacement in the high-velocity range. The results of the straked model tests indicated that the response was strongly dependent upon the amount of coverage of helical strakes. The flexible riser with 75% strake coverage gave the best comprehensive evaluation in a uniform current, and 50% strake coverage gave the best comprehensive evaluation in a linearly sheared current.     

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.     

Simulating fundamental and higher harmonic VIV of slender structures

Vortex-induced vibrations (VIV) of slender marine structures are complicated response processes, where a number of distinct frequency components might be simultaneously active. These are categorized as fundamental and higher harmonics respectively, where the latter can have a tremendous impact on the fatigue life. The present work proposes a method for time domain simulation of such multi-frequency response, by introducing a higher harmonic load term to a pre-existing semi-empirical hydrodynamic force model. Forced motion tests of a circular cylinder were simulated to experimentally and qualitatively validate the fluid-structure energy transfer. Next, the model was used to predict the response of a tension dominated riser in uniform current, for 22 velocities in the range 0.3 m/s to 2.4 m/s. The empirical input was chosen to give an average best fit with respect to the cross-flow strain measurements, which allowed dominating frequencies, fatigue damage, higher harmonics and response variability to be predicted with a high level of realism. Same set of empirical coefficients was subsequently used to predict VIV of three additional flexible pipe experiments in uniform flow, with significant differences in structural properties. The results were satisfactory for all cases, but could be improved by moderate changes to the empirical input.     

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.     

A practical approach to predicting cross-flow and in-line VIV response for deepwater risers

In this study, a practical model is proposed to predict cross-flow (CF) and in-line (IL) vortex-induced vibrations of a flexible riser in time domain. The hydrodynamic force as a function of non-dimensional amplitude and frequency is obtained from the forced vibration experimental data of a two-dimensional cylinder. An empirical nonlinear damping model is used to simulate the hydrodynamic damping outside the experiment's range. Coupling effect of CF and IL-VIV is taken into account by implanting a magnification model for the IL hydrodynamic force associated with CF amplitude, and by increasing the non-dimensional amplitude corresponding to the IL hydrodynamic coefficient in the second excitation region. The experimental models of flexible riser under the uniform and sheared current are simulated to validate the proposed model. The predicted displacement, curvatures, excited modes and fatigue damage show reasonable agreement with the measured data.     

Reynolds and Mass-Damping Effect on Prediction of the Peak Amplitude of A Freely Vibrating Cylinder

The Reynolds effect and mass-damping effect on the peak amplitude of a freely vibrating cylinder is studied by using forced oscillating data from Gopalkrishnan＇ s research in 1993, in which all experimental cases were carried out at a fixed Reynolds and the tested cylinder was recognized as a body that had no mass and damping. However, the Reynolds and roass-damping are the very important parameters for the peak amplitude of a freely vibrating cylinder. In the present study, a function F is introduced to connect the forced oscillation and free vibration. Firstly the peak amplitude AG^＊ can be obtained from the function F using forced oscillation data of Gopalkrishnan＇ s experimental at Re = 10^4, and then the Reynolds effect is taken into account in the function f（Re）, while the mass-damping effect is considered in the function K（ α ）, where a is the mass-damping ratio. So the peak amplitude of a freely vibrating cylinder can be predicted by the expression： A ^＊ = K（ α ）f（ Re ）AG^＊ . It is found that the peak transverse amplitudes predicted by the above equation agree very well with many recent experimental data under both high and low Reynolds conditions while roass-damping varies. Furthermore, it is seen that the Reynolds number does have a great effect on the peak amplitude of a freely vibrating cylinder. The present idea in this paper can be applied as an update in the empirical models that also use forced oscillation data to predict the vortex induced vibration （VIV） response of a long riser in the frequency domain.     

High aspect ratio (L/D) riser VIV prediction using wake oscillator model

A two-dimensional (2-D) vortex-induced vibration (VIV) prediction model for high aspect ratio (L/D) riser subjected to uniform and sheared flow is studied in this paper. The nonlinear structure equations are considered. The near wake dynamics describing the fluctuating nature of vortex shedding is modeled using classical van der Pol equation. A new approach was applied to calibrate the empirical parameters in the wake oscillator model. Compared the predicted results with the experimental data and computational fluid dynamic (CFD) results. Good agreements are observed. It can be concluded that the present model can be used as simple computational tool in predicting some aspects of VIV of long flexible structures.