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.     

Experimental study and numerical simulation on vortex-induced vibration of flexible riser

In order to study the effect of internal flow on vortex-induced vibration of flexible riser, the experiment on the vortex-induced vibration of flexible riser transporting fluid in the current was conducted in the physical oceanography laboratory of Ocean University of China. Considering the internal flowing fluid and external marine environment, the dynamic response of the flexible riser was measured. The corresponding numerical simulation was performed using the wake oscillatory model considering the extensibility of the riser system. Both the experiment and the numerical simulation indicated that with the increase of internal flow speed, the response amplitude increases, while the response frequency decreases.     

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.     

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.     

Three-dimensional flow around a square cylinder near a wall

In this study, two- and three-dimensional numerical simulations were performed to investigate the effect of the flow structure in the wake of a square cylinder placed near a plane wall by applying a fully implicit finite-difference method to the Navier-Stokes equations. The gap ratio between the cylinder and the wall, G/D, was varied from 0.2 to 4 for the Reynolds numbers of 175, 185 and 250. The role of the 3D structure on the lift and drag coefficients and Strouhal number was investigated. The results were compared with those of the 2D numerical simulations. The deviations of the 3D flow structure of the cylinder-wall pair from that of a single cylinder were also reported. At Re=250, B type secondary vortices were determined in the wake region. At Re=175 and 185, transition from A type vortex to fully periodic B type vortices was observed when the cylinder was brought closer to the wall.     

Laboratory, numerical, and theoretical modeling of the flow in a far wake in a stratified fluid

The far-wake flow past a sphere towed in a fluid with high Reynolds and Froude numbers and with a pycnocline-form salt-density stratification is studied in a laboratory experiment based on particle image velocimetry and in numerical and theoretical modeling. In the configuration under consideration, the axis of sphere towing is located under a pycnocline. Flow parameters, the profiles of density and average velocity, and the initial field of velocity fluctuation in numerical modeling are specified from the data of the laboratory experiment. The fields of fluid velocity at different times and the time dependences of integral parameters of wake flow, such as the average velocity at the axis and the transverse width of the flow, are obtained. The results of numerical modeling are in good qualitative and quantitative agreement with the data of the laboratory experiment. The results of the laboratory experiment and numerical modeling are compared to the predictions of a quasi-linear and quasi-two-dimensional theoretical model. The time evolution of both the average velocity at the axis and the transverse width of the wake is obtained with the model and is in good agreement with the experimental data. The results of numerical modeling also show that, under the effect of velocity fluctuation in the wake, internal waves whose spatial period is equal to the characteristic period of the wake’s vortex structure are excited efficiently in the pycnocline.     

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.     

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.     

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.     

低雷诺数下圆柱强迫振动特性光滑粒子流体动力学模拟

基于光滑粒子流体动力学(SPH)方法,开发了能够准确描述水流作用下圆柱强迫振动特性的数学模型。通过引入适合于无网格粒子法的开边界算法,来模拟出入流边界条件,建立了具有造流功能的SPH数值水槽。圆柱及计算域的上下边界均采用修正的动力边界条件进行模拟。借助于粒子位移矫正和压力修正算法,避免了圆柱周围流体粒子压力大幅震荡以及结构下游区域出现空腔等非物理性现象。使用典型的圆柱绕流数据,验证了所建SPH模型的计算性能,研究了固定圆柱在低雷诺数情况下的尾涡脱落模式和升阻力变化规律。明确了低雷诺数下强迫振动圆柱在频率锁定以及非锁定区间内的升力变化规律,量化了升力与外界激励频率之间的关系。     

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.     

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.     

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.     

Effect of upward internal flow on dynamics of riser model subject to shear current

Numerical study about vortex-induced vibration(VIV) related to a flexible riser model in consideration of internal flow progressing inside has been performed.The main objective of this work is to investigate the coupled fluid-structure interaction(FSI) taking place between tensioned riser model,external shear current and upward-progressing internal flow(from ocean bottom to surface).A CAE technology behind the current research which combines structural software with the CFD technology has been proposed.According to the result from dynamic analysis,it has been found that the existence of upward-progressing internal flow does play an important role in determining the vibration mode(/dominant frequency),vibration intensity and the magnitude of instantaneous vibration amplitude,when the velocity ratio of internal flow against external current is relatively high.As a rule,the larger the velocity of internal flow is,the more it contributes to the dynamic vibration response of the flexible riser model.In addition,multi-modal vibration phenomenon has been widely observed,for asymmetric curvature along the riser span emerges in the case of external shear current being imposed.     

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.     

不同雷诺数下倾斜圆柱绕流三维数值模拟研究

基于计算流体力学(CFD)开源代码OpenFOAM开展了不同雷诺数(Re=100、1500和3900)和倾斜角度(-60°≤α≤60°)工况下倾斜圆柱绕流流场的三维数值模拟,研究倾斜圆柱绕流的三维瞬时及时均尾流流场、流线拓扑、升阻力系数与旋涡脱落频率随雷诺数及倾斜角度变化的规律,探讨在顺流向及逆流向情况下独立性原则对倾斜圆柱绕流的适用性。研究结果表明:随着圆柱倾角的增大,倾斜圆柱尾流产生较为明显的轴向流,尾流旋涡脱落受到明显抑制,细碎旋涡逐渐消失,尾流宽度随之减小;随着雷诺数的增大,圆柱尾流涡管发生明显的变形,展向掺混使得大量细碎旋涡产生,呈现出明显的三维特性。在不同雷诺数下,阻力系数均值、升力系数均方根及无量纲涡脱频率在一定倾角范围内符合独立性原则。     

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).     

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.     

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.     

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.