Towards a model of hydrodynamic damping for a circular cylinder with helical strakes at low KC

This paper investigates the hydrodynamic damping of a circular cylinder with helical strakes at Keulegan-Carpenter (KC) number from 0.07 to 3 in the presence of steady currents. Experiments were performed with a straked cylinder oscillating in either in-line or cross currents over Reynolds number (based on the oscillating velocity amplitude) varying from 1260 to 54,000. With in-line current being present, the measured drag coefficients of the straked cylinder are found to depend on the ratio between the oscillating velocity amplitude and the steady current velocity. This phenomenon is further confirmed by computational fluid dynamics using large-eddy simulations. The drag coefficients obtained from the numerical simulations agree well with the experimentally determined values. Similar phenomenon is observed for the cases with cross background current. Based on the experimental data, empirical formulae are proposed to evaluate drag coefficients. These results are of importance in estimating the resonant motion and the fatigue life of risers, e.g. water intake risers, in the flow regime of low KC. Finally, recommendations are provided for fatigue analysis of risers with helical strakes from the perspective of engineering practice.     

Fatigue damage induced by vortex-induced vibrations in oscillatory flow

Vortex-induced vibration (VIV) of a flexible cylinder in oscillatory flow was experimentally investigated in an ocean basin. An intermittent VIV was confirmed to have occurred during the tests. The fatigue damage caused by VIV was calculated based on rainflow counting and a standard S–N curve. There are 3 main observations for fatigue damage from VIV in oscillatory flow: 1) the damage varied significantly with the KC number, which is a unique feature for VIV in oscillatory flow. 2) Fatigue damage at small KC number cases was found to be larger compared to those at large KC numbers owing to the fact that number of vortex shedding cycles per half of the motion cycle is low, and damping within half of the motion cycle will hence become low. The fact that vortices from the previous cycle still are active during the next may also contribute to the large response at small KC numbers. 3) ‘Amplitude modulation’ and ‘mode transition’, two specific features for VIV in oscillatory flow, were found to have a strong influence on fatigue. Fatigue damage has also been calculated by an empirical VIV prediction model assuming that all cases have steady flow at an equivalent velocity. Finally, a simplified method for calculating fatigue damage from VIV in oscillatory flow based on steady flow conditions is proposed. A modification factor diagram is presented, but the scope of the present study is too limited to provide a good basis for a general model for this factor. A general model for how to apply results from constant current analysis to predict fatigue in oscillatory flow will therefore need further research.     

Fatigue analysis of water intake risers: Hydrodynamic damping effect and a hybrid frequency-time domain method

The fatigue performance is key to the design of water intake risers (WIRs), which is a novel concept used to convey cooling water for liquefaction of natural gas at sea. To estimate the fatigue life, it is crucial to accurately predict the response amplitude of the WIRs, which is dominated by hydrodynamic damping. In operational conditions, the motion amplitudes of WIRs are usually smaller than their diameter, and thus leading to a flow regime of KC < 5. It is found in this flow regime; the hydrodynamic damping largely depends on the motion magnitude of the risers. To consider this coupling effect, a hybrid frequency-time domain fatigue analysis method is proposed, where a nonlinear stress transfer function is adopted. The hybrid method accounts for the coupling effect between the hydrodynamic damping and the structural motion. Significantly reducing the computational cost, this method provides results as accurate as that from a time domain analysis based on the relative velocity model with a constant drag coefficient. Furthermore, recommendations for further simplification of the fatigue analysis recognizing the coupling effect are given.     

Unsteady numerical simulation of flow around 2-D circular cylinder for high Reynolds numbers

In this paper, 2-D computational analyses were conducted for unsteady high Reynolds number flows around a smooth circular cylinder in the supercritical and upper-transition flow regimes, i.e. 8.21×10⁴<Re<1.54×10⁶. The calculations were performed by means of solving the 2-D Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations with a k-? turbulence model. The calculated results, produced flow structure drag and lift coefficients, as well as Strouhal numbers. The findings were in good agreement with previous published data, which also supplied us with a good understanding of the flow across cylinders of different high Reynolds numbers. Meanwhile, an effective measure was presented to control the lift force on a cylinder, which points the way to decrease the vortex induced vibration of marine structure in future.     

Vortex-induced vibrations of piggyback pipelines near the horizontal plane wall in the upper transition regime

Slender subsea structures like pipelines, jumpers and umbilicals when exposed to currents may experience vortex-induced vibrations (VIV), which can shorten their fatigue life and increase the risk of structural failure. In the present study, flow around different configurations of a piggyback pipeline close to a flat seabed has been investigated using the two-dimensional (2D) Unsteady Reynolds-Averaged Navier Stokes (URANS) equations with the k − ω Shear Stress Transport (SST) turbulence model. The Reynolds number (based on the free stream velocity and large cylinder diameter) is equal 3.6 × 10⁶ corresponding to upper-transition regime. The drag forces acting on the cylinders and base pressure coefficient value are well predicted by the present simulations, while the other hydrodynamic quantities (root-mean-square lift coefficient, Strouhal number) are predicted reasonably well as compared to published experimental data. The piggyback pipeline in the present study is modeled as two circular cylinders with a diameter ratio d/D = 0.2 (D denoting diameter of the large cylinder, d is diameter of the small cylinder). These two cylinders are clamped together at a distance G/D = 0.2. The two rigidly coupled cylinders are elastically supported and free to vibrate in two degrees of freedom. The effects on the vibration amplitudes and hydrodynamic forces are analyzed. The flow structures around the cylinders are investigated to explain the variations in observed structural responses. Depending on the angular position (α) of the small cylinder, the lock-in regime is narrower (α = 0°) or significantly wider (α = 180°) when compared to that of a single cylinder.     

Numerical investigation of mooring line damping and the drag coefficients of studless chain links

The chain/wire rope/chain combination is a commonchoice for mooring offshore floating platforms. However, data ofthe drag coefficients of chain links are rather limited, resulting inuncertainties with the calculations of the drag force, and hence thedamping of the mooring system. In this paper, the importance of theselection of the drag coefficient is first investigated. Thecomputational fluid dynamics （CFD） method is then used todetermine the drag coefficients of a studless chain under steadyflows. Numerical model validation is first completed by simulatinga smooth circular cylinder under steady flows. In particular, theperformance of different turbulence models is assessed through thecomparisons between the calculations and the experimental results.The large eddy simulation （LES） model is finally selected for thesimulation of steady flows past a chain. The effects of the Reynoldsnumber on the drag coefficient of a stud-less chain is also studied.The results show that the calculated drag coefficients of a stud-lesschain are fairly consistent with the available experimental data.     

Effect of mass ratio on hydrodynamic response of a flexible cylinder

The effect of the mass ratio on the flow-induced vibration (FIV) of a flexible circular cylinder is experimentally investigated in a towing tank. A Tygon tube with outer and inner diameters of 7.9 mm and 4.8 mm, respectively, was employed for the study. The tube was connected to a carriage and towed from rest to a steady speed up to 1.6 m/s before slowing down to rest again over a distance of 1.6 m in still water. Reynolds number based on the cylinder’s outer diameter was 800–13,000, and the reduced velocity (velocity normalized by the cylinder’s natural frequency and outer diameter) spanned from 2 to 25. When connected, the cylinder was elongated from 420 mm to 460 mm under an axial pre-tension of 11 N. Based on the cylinder’s elongated length, the aspect ratio (ratio of the cylinder’s length to outer diameter) was calculated as 58. Three mass ratios (ratio of the cylinder’s structural mass to displaced fluid mass, m*) of 0.7, 1.0, and 3.4 were determined by filling the cylinder’s interior with air, water, and alloy powder (nickel-chromium-boron matrix alloy), respectively. An optical method was adopted for response measurements. Multi-frequency vibrations were observed in both in-line (IL) and cross-flow (CF) responses; at high Reynolds number, vibration modes up to the 3^rd one were identified in the CF response. The mode transition was found to occur at a lower reduced velocity for the highest tested mass ratio. The vibration amplitude and frequency were quantified and expressed with respect to the reduced velocity. A significant reduced vibration amplitude was found in the IL response with increasing mass ratios, and only initial and upper branches existed in the IL and CF response amplitudes. The normalized response frequencies were revealed to linearly increase with respect to the reduced velocity, and slopes for linear relations were found to be identical for the three cases tested.     

Numerical simulation of flow around a smooth circular cylinder at very high Reynolds numbers

High Reynolds number flows (Re = 1 × 10⁶, 2 × 10⁶ and 3.6 × 10⁶, based on the free stream velocity and cylinder diameter) covering the supercritical to upper-transition flow regimes around a two-dimensional (2D) smooth circular cylinder, have been investigated numerically using 2D Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations with a standard high Reynolds number k ? ? turbulence model. The objective of the present study is to evaluate whether the model is applicable for engineering design within these flow regimes. The results are compared with published experimental data and numerical results. Although the k ? ? model is known to yield less accurate predictions of flows with strong anisotropic turbulence, satisfactory results for engineering design purposes are obtained for high Reynolds number flows around a smooth circular cylinder in the supercritical and upper-transition flow regimes, i.e. Re > 10⁶. This is based on the comparison with published experimental data and numerical results.     

An experimental investigation by towing tank on VIV of a long flexible cylinder for deepwater riser application

In this study, the dynamic response of a vertical flexible cylinder vibrating at low mode numbers with combined x?y motion was investigated in a towing tank. The uniform flow was simulated by towing the flexible cylinder along the tank in still water; therefore, the turbulence intensity of the free flow was negligible in obtaining more reliable results. A lower branch of dominant frequencies with micro vibration amplitude was found in both cross-flow and in-line directions. This justifiable discrepancy was likely caused by an initial lock-in. The maximum attainable amplitude, modal analysis and x?y trajectory in cross-flow and in-line directions are reported here and compared with previous literature, along with some good agreements and different observations that were obtained from the study. Drag and lift coefficients are also evaluated by making use of a generalized integral transform technique approach, yielding an alternative method to study fluid force acting upon a flexible cylinder.     

Experimental investigation on hydrodynamics of floating cylinder in oscillatory and steady flows by forced oscillation test

In this paper the hydrodynamic characteristics of a floating cylinder are investigated via forced oscillation experiments in towing tank. The effects of Keulegan–Carpenter number, Reynolds number, reduced velocity and overtopping on hydrodynamics of the floating cylinder in oscillatory and steady flow are studied. The results show a considerably difference of the hydrodynamic characters between the floating and the fully immerged cylinders due to the influences of free surface. The growth of the reduced velocity, a proven notable effect on hydrodynamics, will lead to the increase of added mass coefficient and the decrease of drag coefficient. Meanwhile the overtopping, a particular phenomenon for the floating cylinder, render the added mass coefficients reach up to 3.6 while for the drag coefficient small influences were made.     

基于LES方法圆柱绕流三维数值模拟(英文)

采用计算流体软件CFX5中large.eddy simulation(LES)模型计算了均匀流场中三维圆柱绕流的水动力特性.使用有限体积法对三维N-S方程进行求解.数值模拟着重研究了高雷诺数时展向各截面的压力、阻力、升力及涡管特性.数值计算结果表明:展向各截面柱体受力关于中截面对称且小于二维情况,柱体周围流场呈现明显的三维特性.     

Numerical analysis of vortex-induced motion of two-dimensional circular cylinder by lattice Boltzmann method

Vortex-induced motion of two-dimensional circular cylinder was numerically analyzed by using the lattice Boltzmann method. Unlike conventional methods, in which the computational grids are fit to the solid body, the present method adopts rectangular grids and the movement of the solid body was treated by the boundary condition for the simplicity of computation. The hydrodynamic force acting on the cylinder was estimated by integrating the momentum of the fluid over the cylinder surface. The quantitative validation of the simulation results was confirmed for the fixed cylinder at Re = 500. When the cylinder is allowed to move only in the spanwise direction, the resonance between the vortex-shedding frequency and the natural frequency of damping force by spring was confirmed. When the natural frequency is larger than the vortex-shedding frequency, secondary mode appears which may be resulted from the nonlinear effect. Finally, the motion in the streamwise direction is considered as well as the spanwise direction and the characteristic of the cylinder motion in the horizontal direction was demonstrated in relation to the damping force by the mooring. Although the target of the present study is limited to two-dimensional and low Re, the applicability of the lattice Boltzmann method to vortex-induced motion was confirmed.     

Intelligent VIV control of 2DOF sprung cylinder in laminar shear-thinning and shear-thickening cross-flow based on self-tuning fuzzy PID algorithm

A self-tuning fuzzy PID (ST-FPID) control scheme is implemented within a joint interactive (Matlab/Simulink/Fluent) co-simulation framework for effective two degrees of freedom (2DOF) vortex-induced vibration (VIV) control of an elastically-mounted circular cylinder in laminar cross-flow of incompressible non-Newtonian power-law fluids based on the control action of a single transverse force actuator. The model-free controller, which systematically tunes the control parameters online in real time based on given rules, is well-known to be highly advantageous over the previously employed conventional PID controllers. It is particularly capable of handling the intricate non-linear dynamic effects inherent in the complex fluid rheology of non-Newtonian flow past the cylinder in presence of unmodeled system dynamics, high parametric uncertainties, diverse operational conditions, and time-varying external disturbances and control signals. Extensive numerical simulations reveal that the complex shear-thinning and shear-thickening behaviors of fluid viscosity can substantially influence the cylinder dynamic response, applied hydrodynamic forces, and flow structure. In particular, effectiveness and high performance of the adopted ST-FPID control strategy in substantial suppression of the high amplitude coupled 2DOF VIV of the elastically-mounted cylinder at selected critical reduced velocities in the lock-in region are established for a wide range of power-law index parameters (e.g., up to 83% reduction in RMS value of cylinder cross-flow displacement and up to 35% reduction in RMS value of cylinder in-line displacement for n=1and U* = 5 at Re = 100). Also, the vigorous action of the error-driven ST-FPID controller in forcing the high strength vortex shedding patterns of the uncontrolled cylinder out of the lock-in condition into the classical von Kármán vortex street of 2S-type mode of moderately weaker strengths is verified.     

Experimental investigations on hydrodynamic interactions between the cylinder and nets of a typical offshore aquacultural structure in steady current

A series of physical experiments were performed in steady current to investigate the hydrodynamic interactions between the cylinder and nets which constitute a main part of offshore aquacultural platforms. The hydrodynamic characteristics of only the cylinder, only nets and combined cylinder-net structures are measured and analyzed systematically under different current velocities, inflow angles and solidity ratios of nets. Based on experimental data, fitted formulas for hydrodynamic coefficients of a single resin net are proposed and compared to previously published empirical formulas. It is observed that the existence of the cylinder brings an increment up to 9.2% to drag coefficient of net panels whose solidity ratios are higher than 0.347, whereas this effect is negligible for nets with lower solidity ratios and perpendicular to the inflow. For nets inclined with 45°, the increment of the drag coefficient of net panels due to the existence of the cylinder is more significant (up to 22.9%) than that for perpendicularly placed nets. Furthermore, the existence of nets also leads to a noticeable increase in the drag coefficient of the cylinder, up to 40.18% for a relatively large net solidity ratio of 0.458, representative of biofouling condition. The increment increases with the rise of the solidity ratio of nets and it is larger for nets placed perpendicularly to the inflow than inclined. Effects of the cylinder and nets on lift coefficients of each other are a bit complicated, leading to an increase or reduction of lift coefficients depending on the inflow velocity, inflow angle and net solidity ratios. Finally, it is worth noting that the hydrodynamic interaction between the cylinder and nets deserves to be considered in current practice of hybrid methods by combining potential flow theory, Morison and screen models for aquacultural structures, especially for biofouling conditions.     

The effects of free surface and end cell on flow around a finite circular cylinder with low aspect ratio

Vortex-induced motion is an oscillatory phenomenon which occurs to a floating body with low aspect ratio. The basic phenomenological study about the effects of free surface and end cell on flow around a finite fixed circular cylinder was investigated in this study using particle image velocimetry and hydrodynamic force measurement. It was found from the former experiment that the wake of the cylinder is influenced by the both end cell and free surface. Blowup and back flow are generated from the end cell, and their effects are suspended by free surface. The result of hydrodynamic force measurement showed the effect of Reynolds number, Froude number, and the aspect ratio of the floating body on the hydrodynamic force. Fluctuating components of hydrodynamic coefficients decrease for increasing Reynolds number, Froude number, and the aspect ratio. On the other hand, the mean drag coefficient increases as Froude number increases and decreases as the aspect ratio increases. The interpretation to these results was discussed in comparison with flow structures observed in the experiment. In addition, it was found that the effect of Reynolds number on the mean drag coefficient changes at different aspect ratios. A possible interpretation to this phenomenon was proposed.     

Experimental investigation on the dynamic responses of a free-hanging water intake riser under vessel motion

A large-scale model test of a free-hanging water intake riser (WIR) is performed in an ocean basin to investigate the riser responses under vessel motion. Top end of the WIR is forced to oscillate at given vessel motion trajectories. Fiber Brag Grating (FBG) strain sensors are used to measure the WIR dynamic responses. Experimental results firstly confirms that the free-hanging WIR would experience out-of-plane vortex-induced vibrations (VIVs) under pure vessel motion even for the case with a KC number as low as 5. Meanwhile, comparison between numerical results and experimental measurements suggests a significant drag amplification by out-of-plane vessel motion-induced VIV. What’s more, further study on WIR response frequencies and cross section trajectories reveals a strong correlation between vessel motion-induced VIV and local KC number distribution, owing to the small KC number effect. The presented work provides useful references for gaining a better understanding on VIV induced by vessel motion, and for the development of future prediction models.     

基于高雷诺数的并联双圆柱绕流研究

文章采用基于边界瞬时涡量守候的拉格朗日方法(IVCBC),结合并列双圆柱的特点,建立了双圆柱绕流数值计算模型。对高雷诺数下Re=6×10~4,间隙率为T/D=1.1~7的并联圆柱双圆柱二维绕流特性进行了研究。提出了双圆柱间隙中点的速度区别宽窄尾流的新方法。分别讨论了流体力系数随间距增加的特点,脉动流体力的特点,尾流特征以及斯托哈尔数特征。研究发现:区别宽窄尾流的新方法是可靠的;在双圆柱尾流附近有五种尾流模型存在;同时发现了在宽窄尾流的频率,存在一个中间频率。     

亚临界区雷诺数下电磁力控制圆柱绕流场特性研究

采用脱体涡模拟方法对弱电解质中电磁力作用下圆柱绕流场及其升阻力特性进行了数值模拟与分析。研究结果表明,在亚临界区雷诺数下电磁力可以提高圆柱体边界层内的流体动能,延缓圆柱体近壁面流动分离,减弱绕流场中流向和展向大尺度涡的强度,减小圆柱体阻力及其升力脉动幅值;当电磁力作用参数大于某个临界值后,流动分离角消失,在圆柱体尾部产生射流现象,电磁力产生净推力作用,出现负阻力现象,而且升力脉动幅值显著减小且接近于零。     

Circulation on the Armorican shelf (Bay of Biscay) in autumn

Three drifters drogued at 65 m were launched on a transect on the Armorican shelf of the Bay of Biscay for 4 years. The experiments were conducted in autumn. They revealed a north-westward, poleward current over the 100 m isobath and a very weak eastward current over depths comprised between 120 and 150 m. A model was used to assess the role of residual tidal currents and wind-induced circulation. The results show that the former are quite weak and the latter do not explain the average velocity of over 10 cm s^− 1. It is thought that this current is mainly driven by the density gradient induced by the breakdown of stratification. Hydrological data and satellite images from the period are discussed, in the light of this hypothesis.     

弹性支撑低质量比圆柱涡激振动数值模拟

近年来,随着深海石油工业的发展,立管的涡激振动现象越来越受学者们关注.使用RANS方程求解器,并结合SST κ-ω湍流模型,对横向和流向自然频率比为1的低质量比弹性支撑圆柱体的两自由度运动进行了数值模拟,计算雷诺数范围为5 300至32 000.采用四阶Runge-Kutta方法求解柱体的振动方程.并结合近期物理实验结果对升力系数、阻力系数、位移和尾涡模式进行了详细比较和讨论.较好地再现了试验观察到的锁定、迟滞、差拍等现象.