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.     

A Novel Wake Oscillator Model for Vortex-Induced Vibrations Prediction of A Cylinder Considering the Influence of Reynolds Number

It is well known that the Reynolds number has a significant effect on the vortex-induced vibrations (VIV) of cylinders. In this paper, a novel in-line (IL) and cross-flow (CF) coupling VIV prediction model for circular cylinders has been proposed, in which the influence of the Reynolds number was comprehensively considered. The Strouhal number linked with the vortex shedding frequency was calculated through a function of the Reynolds number. The coefficient of the mean drag force was fitted as a new piecewise function of the Reynolds number, and its amplification resulted from the CF VIV was also taken into account. The oscillating drag and lift forces were modelled with classical van der Pol wake oscillators and their empirical parameters were determined based on the lock-in boundaries and the peak-amplitude formulas. A new peak-amplitude formula for the IL VIV was developed under the resonance condition with respect to the mass-damping ratio and the Reynolds number. When compared with the results from the experiments and some other prediction models, the present model could give good estimations on the vibration amplitudes and frequencies of the VIV both for elastically-mounted rigid and long flexible cylinders. The present model considering the influence of the Reynolds number could generally provide better results than that neglecting the effect of the Reynolds number.     

Application of Helical Strakes for Suppressing the Flow-Induced Vibration of Two Side-by-Side Long Flexible Cylinders

Helical strakes have been widely applied for suppressing the vibration of flexible cylinders undergoing vortexshedding in offshore engineering. However, most research works have concerned on the application of helical strakes for the isolated flexible cylinder subjected to vortex-induced vibration(VIV). The effectiveness of helical strakes attached to side-by-side flexible cylinders in vibration reduction is still unclear. In this paper, the response characteristics of two side-by-side flexible cylinders with and without helical strakes were experimentally investigated in a towing tank. The configuration of the helical strakes used in the experiment had a pitch of 17.5D and a height of 0.25D(where D is the cylinder diameter), which is usually considered the most effective for VIV suppression of isolated marine risers and tendons. The center-to-center distance of the two cylinders was 3.0D. The uniform flow with a velocity ranging from 0.05 m/s to 1.0 m/s was generated by towing the cylinder models along the tank. Experimental results, including the displacement amplitude, the dominant frequency, the dominant mode,and the mean drag force coefficient, were summarized and discussed. For the case where only one cylinder in the two-cylinder system had helical strakes, the experimental results indicated that helical strakes can remarkably reduce the flow-induced vibration(FIV) of the staked cylinder. For the case of two straked cylinders in a side-by-side arrangement, it was found that the performance of helical strakes in suppressing the FIV is as good as that for the isolated cylinder.     

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

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

Analytical solution of mean top tension of long flexible riser in modeling vortex-induced vibrations

The vortex-induced vibration (VIV) of flexible long riser with combined in-line and cross-flow motion has been studied using a wake oscillator in this paper. The analytical solution of mean top tension of long flexible riser is evaluated and compared with experimental results, and good agreement is observed to verify its validity. Then the nonlinear coupled dynamics of the in-line and cross-flow VIV of a long tension-dominated riser were analyzed through wake oscillator model with the consideration of variation of the mean top tension. The in-line and cross-flow resonant frequencies, lift and drag coefficients, dominant mode numbers, amplitudes and instantaneous deflections are reported and compared with experimental results, and excellent agreements are observed. The comparison of mode numbers between the calculation with and without consideration of variation of mean top tension shows that the proposed analytical solution of the mean top tension can produce a better prediction of multi-mode VIV.     

On splitter plate coverage for suppression of vortex-induced vibrations of flexible cylinders

Experimental results show how vortex-induced vibration (VIV) amplitudes of flexible cylinders can be reduced up to a 90% by covering less than half of the length of the cylinder with splitter plates elastically mounted to the surface of the cylinder.The VIV amplitude reduction takes place along with drag coefficient reductions of up to a 50% for the reduced velocities investigated.     

Benchmark computations for flows around a stationary cylinder with high Reynolds numbers by RANS-overset grid approach

The aim of this paper is to evaluate the accuracy, stability and efficiency of the overset grid approach coupled with the RANS (Reynolds Averaged Navier-Stokes) model via the benchmark computations of flows around a stationary smooth circular cylinder. Two dimensional numerical results are presented within a wide range of Reynolds numbers (6.31 × 10⁴ ∼ 7.57 × 10⁵) including the critical flow regime. All the simulations are carried out using the RANS solver pimpleFoam provided by OpenFOAM, an open source CFD (Computational Fluid Dynamics) toolkit. Firstly, a grid convergence study is performed. The results of the time-averaged drag and lift force coefficients, root-mean square value of lift force coefficient and Strouhal number (St number) are then compared with the experimental data. The velocity, vorticity fields and pressure distribution are also given. One main conclusion is that the numerical solutions in regard to a fixed cylinderare not deteriorated due to the implementation of the overset grid. Furthermore, it can be an appealing approach to facilitate simulations of Vortex Induced Vibrations (VIV), which involves grid deformation. The present study is a good start to implement the overset grid to solve VIV problems in the future.     

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.     

In-line force on a cylinder translating in oscillatory flow

Experiments were conducted with smooth and sand-roughened cylinders moving with constant velocity in a sinusoidally oscillating flow to determine the drag and inertia coefficients and to examine the effect of wake biasing on the modified Morison equation. The various flow parameters such as the relative cylinder velocity. Reynolds number, and the Keulegan-Carpenter number were varied systematically and the in-line force measured simultaneously. The principal results, equally valid for both smooth and rough cylinders, are as follows: the drag coefficient decreases with increasing relative current for a given Reynolds number and Keulegan-Carpenter number; the effect of wake biasing on the drag and inertia coefficients is most pronounced in the drag-inertia dominated regime; and the two-term Morison equation with force coefficients obtained under no-current conditions is not applicable to the prediction of wave and current induced loads on circular cylinders.     

Hydrodynamics of the Semi-Immersed Cylinder by Forced Oscillation Model Testing

In this paper, the hydrodynamic coefficients of a horizontal semi-immersed cylinder in steady current and oscillatory flow combining with constant current are obtained via forced oscillation experiments in a towing tank. Three non-dimensional parameters (Re, KC and Fr) are introduced to investigate their effects on the hydrodynamic coefficients. The experimental results show that overtopping is evident and dominates when the Reynolds number exceeds 5×10⁵ in the experiment. Under steady current condition, overtopping increases the drag coefficient significantly at high Reynolds numbers. Under oscillatory flow with constant current condition, the added mass coefficient can even reach a maximum value about 3.5 due to overtopping while the influence of overtopping on the drag coefficient is minor.     

Dynamic Response Analysis of Risers Subjected to Combined Wave and Current Loading

A dynamic response analysis in the frequency domain is presented for risers subjected to combined wave and current loading. Considering the effects of current, a modified wave spectrum is adopted to compute the linearized drag force. An additional drag force convolution term is added to the linearized drag force spectrum, therefore the error is reduced which arises from the truncation of higher order terms in the drag force auto-correlation function. An expression of linearized drag force spectrum is given taking the relative velocity into account. It is found that the additional term is a fold convolution integral. In this paper dynamic responses of risers are investigated, while the influence of floater motion on risers is considered. The results demonstrate that the accuracy of the present method reaches the degree required in time domain analysis.     

硬悬挂钻井隔水管涡激振动特性研究

针对深水钻井过程中遭遇强台风,基于安全性考虑要求钻井平台悬挂隔水管提前撤离的问题,采用软件SHEAR7针对HYSY981钻井平台硬悬挂隔水管系统避台风撤离作业过程中,受南海一年一遇海流作用时诱发涡激振动(VIV)的情况,研究航速与悬挂长度对VIV特性的影响。研究表明,浮力块覆盖率越高,隔水管系统张力越小;浮力块分布对隔水管系统VIV响应影响较大,25%交错布置方案VIV响应最弱。隔水管并非越短越好,要综合考虑洋流剖面、隔水管配置和平台航行的影响;在不同悬挂长度及航行条件下的VIV响应,在撤离作业前应尽量避免在高流速区布置浮力单根,撤离作业时应尽量采用顺流而避免平台逆流航向。     

The effect of yaw angle on VIV suppression for an inclined flexible cylinder fitted with helical strakes

Experimental studies were carried out to investigate the response features of an inclined flexible bare cylinder as well as a straked cylinder in a towing tank, with the main purpose of further improving the understanding of the effect of yaw angle on vortex-induced vibration (VIV) suppression. Four yaw angles (a = 0°, 15°, 30°, 45°), which is defined as the angle between the cylinder axis and the plane orthogonal to the oncoming fluid flow, were tested. The cylinder model was towed along the tank to generate a uniform fluid flow. The towing velocity was in the range of 0.05–1.0 m/s with an interval of 0.05 m/s. The corresponding Reynolds number ranged from 800 to 16000. The strakes selected for the experiments had a pitch of 17.5D and a height of 0.25D, which is generally considered as the most effective configuration for VIV suppression of a flexible cylinder in water. The experimental results indicate that VIV suppression effectiveness of the inclined flexible straked cylinder is closely related to the yaw angle. The displacement amplitudes are significantly suppressed in both cross-flow (CF) and in-line (IL) directions at a = 0°. However, with increasing yaw angle, the suppression efficiencies of the CF and IL displacement amplitudes gradually decrease. In addition, the CF dominant frequencies of the straked cylinder obviously deviate from those of the bare cylinder at a = 0° and 15°. This deviation is substantially alleviated with increasing yaw angle. The IL dominant frequencies show less dependency on the yaw angle. Similar trends are also observed on the dominant modes of vibration and the mean drag coefficients.     

A Prediction Method of Internal Solitary Wave Loads on the Semi- Submersible Platform

An investigation into the prediction method for internal solitary waves (ISWs) loads on the columns and caissons of the semi-submersible platform found on three kinds of internal solitary wave theories and the modified Morison Equation is described. The characteristics of loads exerted on the semi-submersible platform model caused by the ISWs have been observed experimentally, and the inertial and drag coefficients in Morison Equation are determined by analyzing the forces of experiments. From the results, it is of interest to find that Reynolds number, KC number and layer thickness ratio have a considerable influence on the coefficients. The direction of incoming waves, however, is almost devoid of effects on the coefficients. The drag coefficient of columns varies as an exponential function of Reynolds number, and inertia coefficient of columns is a power function related to KC number. Meanwhile, the drag coefficient of caissons is approximately constant in terms of regression analysis of experimental data. The results from different experimental conditions reveal that the inertia coefficient of caissons appears to be exponential correlated with upper layer depths.

     

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

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

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

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

Calibration of estuarine current crosses

Tethered current crosses are simple, reliable tools in making measurements of estuarine currents in the absence of surface waves. The standard error of the estimate of current speed is less than 5 cm s^?1 for the particular crosses and weights used in a calibration experiment. The useful velocity range of these current crosses was 8–147 cm s^?1, corresponding to a measured angle, α, from 2° to 30°. Regression of the independently measured current speed on $\text{(tan α)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ yielded coefficients of determination greater than 0·94, indicating that the drag coefficient is not a function of current speed. However, the calculated drag coefficients varied widely from 0·66 to 2·55, depending on the particular combination of cross and weight, varying drastically from the commonly assumed drag coefficient value of 1·12. Thus, in using current crosses, it is imperative to calibrate each cross against a current meter reading to determine an appropriate value for the drag coefficient for a particular current cross and weight.     

立管对深水半潜式生产平台定位性能影响研究

基于三维频域势流理论,计算船体的水动力参数;采用动态耦合方法分析了深海半潜式生产平台各系统之间的相互作用特征,研究了立管系统对锚泊系统定位能力的影响。计算结果表明,立管系统在一定程度上增加了整个系统的刚度,其所受的附加质量和阻尼可降低平台的低频响应,从而降低平台的偏移和系泊缆的张力;海流将增大立管上的拖曳力,使平台偏移更远,锚索上的张力更大;立管系统对锚泊系统定位性能的最终影响需综合考虑多种因素的叠加。对目标平台而言,由于服役海域的流速较大,对立管的拖曳作用较为明显。因此,为确保平台的安全性,当服役海域流速较大时,带有多立管的平台,其锚泊系统的设计应考虑立管的影响。     

张力腿平台绕流数值模拟分析

在一定来流条件下,张力腿平台(tension leg platform,简称TLP)的立柱后缘出现周期性的交替旋涡脱落,致使立柱受到垂直于来流方向的升力和平行于来流方向的阻力作用,导致TLP产生大幅度往复运动,显著增加平台结构和系泊系统的负载。目前,关于单柱、多柱结构绕流问题的研究较多,但对于TLP绕流特性的研究较少,机理尚存不明确的地方。为研究TLP的绕流力变化情况和流场特征,开展了数值模拟分析。利用计算流体动力学数值模拟软件,基于雷诺平均(RANS)法和分离涡模拟(DES)法对TLP绕流场进行仿真分析,揭示了TLP的绕流特性。结果表明,在3种来流角度和多个折合速度V_r下,TLP绕流的流体力系数存在明显差异,升力系数时域曲线呈现脉动性。TLP的上、下游立柱间存在明显的相互作用,影响了旋涡的形成与发展。TLP的旋涡脱落大多集中在平台固有频率附近,且在V_r=7,来流角度为0°时,升力系数频谱峰值最大,旋涡脱落集中。     

Drag force on a circular cylinder in unseparated laminar high Reynolds number nonlinear random oscillatory flow

The stochastic properties of the drag force maxima on a circular cylinder subjected to nonlinear random waves are investigated. Unseparated laminar high Reynolds number flow is considered. A simplified approach based on second order Stokes waves is presented, including the sum-frequency effect only. It is demonstrated how a drag force formula valid for regular linear waves can be used to find the cumulative distribution function of individual drag force maxima for nonlinear irregular waves. Here the [Wang, 1968] drag force coefficient is used.