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.     

Experimental study on reflection coefficient of curved perforated plate

A set of experiments is carried out in a towing tank to study the effects of the curvature of perforated plates on the wave reflection coefficient (C _r ). The curvature of a perforated plate can be changed by rotating a reference perforated plate aboutits origin according to the parabolic equation y=?x ². A plunger-type wave maker is used to generate regular waves. The reflection coefficients are calculated using Goda and Suzuki’s (1976) method. The results are compared with those of vertical or sloped passive wave absorbers. The comparison shows that a perforated plate with a curved profile is highly efficient in terms of reducing the wave reflection coefficient. A correlation is established to estimate the reflection coefficient of curved perforated plates as a function of both flow and geometry characteristics.     

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.     

Vortex-induced vibration (VIV) dynamics of a tensioned flexible cylinder subjected to uniform cross-flow

This paper presents the experimental results of a study on the effects of axial applied tension on the vibration amplitude, the suppression of vibration, hydrodynamic force coefficients and in-line (IL) and cross-flow (CF) frequency responses during vortex-induced vibration of a horizontally mounted flexible cylinder with a low mass ratio (cylinder’s mass/mass of displaced water), low bending-stiffness, and high aspect ratio (length/diameter 200) in the subcritical Reynolds number regime (Re = 1000–16000). The effect of tension is studied by applying four different tensions. It was revealed that higher applied tensions, which reduce the vibration amplitude, could significantly raise the hydrodynamic lift force coefficient. In addition, higher applied tensions generate narrower lock-in bandwidths. After the highest vibration amplitude and during the region of lower vibration amplitudes, within the first lock-in region (in the first mode of vibration), power spectral densities show broad bandwidth, while within other regions and higher modes they appear narrow-banded. The ratio of the dominant IL to CF frequency is approximately equal to 2.0, except for the lower reduced velocities, where the ratio values reach 3.83 for the highest tension accompanied by widening of the region in which this ratio is over 2.0. This ratio is 2.76 for the lowest applied tension with a narrower region.     

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.     

柔性立管涡激振动响应轨迹特性研究

为了深入研究细长柔性立管的涡激振动响应特性,进行了柔性立管的拖曳水池试验。由拖车拖动立管产生相对来流,根据应变测试得到的应变数据,基于模态叠加法得到位移响应。试验分析前,通过数值方法先针对刚性立管的涡激振动响应轨迹特性进行了分析。紧接着,通过试验方法对柔性立管的单模态以及多模态涡激振动响应轨迹特性进行了深入的分析和讨论。通过分析发现:柔性立管在低速下具有与刚性立管类似的轨迹响应特性,均呈现经典的8字形状;柔性立管在高速下,其轨迹开始变得混乱,这主要是由位移的多模态响应特性所产生。     

Three-dimensional vortex-induced vibrations of a circular cylinder predicted using a wake oscillator model

This paper reports a numerical study based on a wake oscillator model, to determine the three-dimensional vortex-induced vibration (VIV) responses on a flexible cylinder with pinned-pinned boundary conditions subjected to a uniform flow. Four different aspect ratios have been selected for the study. The coupling equations of the structural oscillator models and wake oscillator models in both the cross-flow (CF) and in-line (IL) directions have been solved using a standard central difference method of the second order. The structural displacement, structural frequency, response wave pattern, response trajectory, and lift force coefficient, for four aspect ratios, have been compared. The numerical results establish that, for a small aspect ratio, the CF displacements have absolute standing wave behaviors without travelling wave behaviors, and the IL displacements have dominant standing wave behaviors with slight travelling wave behaviors. Further, the VIV trajectory is repeatable and displays figure-eight shapes. However, for a large aspect ratio, the CF displacements display identical characteristics with the IL displacements for a small aspect ratio, and the IL displacements for a large aspect ratio are simultaneously dominated by standing and travelling wave behaviors. Moreover, the VIV trajectory is apparently aperiodic and shows chaotic shapes.     

不同质量比对刚性圆柱体涡激振动振幅的影响

涡激振动发电装置是一种能够捕获浅海区域低流速海流能的新型能源装置,为了在不同海况下均能高效地对能量进行转换,需要对振动参数进行探讨,因此本文对质量比在振动响应和能量方面进行了分析。结合尾流振子模型和结构振动模型,得到双自由度涡激振动耦合模型,将Stappenbelt实验设置输入该模型,模型计算结果与其实验结果吻合,验证了模型的正确性。通过对中低质量比、超低质量比和高质量比三种条件下的柱体涡激振动响应进行分析,结果表明：中低质量比条件下,振幅和频率锁定区间宽度随质量比增加而减小;超低质量比条件下,顺流向无量纲振幅接近1,无法忽略,双向最大振幅发生约化速度Ur=6附近;高质量比条件下,最大振幅所对应的约化速度随着质量比的增加而增加,顺流向第二次波峰消失,横向出现两次波峰。     

VIV response of a flexible cylinder with varied coverage by buoyancy elements and helical strakes

Many significant engineering challenges have emerged as the petroleum industry has moved their field development and production activities into increasingly deeper water depths. The design of deepwater marine risers presents the combined challenges to minimize top tensioning requirements, mitigate any flow-induced vibrations, and if possible to increase the expected fatigue life of these slender structural members. As part of the design process to achieve these goals external buoyancy modules and strakes have been employed. To gain insight into the complex multi-mode response behavior a recent experimental study was performed and the analysis of selected data sets is presented. In the experiments a horizontal cylinder with a length to diameter ratio of 263 was fitted with a variety of strake and buoyancy element configurations. The models were towed at uniform speeds ranging from 0.4 to 2.0 m/s and fiber optic strain gages were used to measure both in-line and cross-flow strain response. The resulting time series information was processed utilizing the method of time domain decomposition formulated for strain data input and the introduction of modal assurance criterion to resolve the modal strain information that included frequency, mode shape, and critical damping ratio information. The pre-tensioned cylinder without appendages was used as a base case and the results were basically consistent with expectations. In the case of 0.8 m/s low-tension test, multiple closely spaced non-overlapping peaks were observed in both in-line and cross-flow directions and were identified as being of the same mode with mode shapes distorted away from purely sinusoidal behavior. The test data for the 100% coverage by helical stakes demonstrated the effectiveness of that suppression device over the range of current velocities investigated. The most interesting case was that of a staggered combination of helical strakes and buoyancy element whose total for each type of coverage was equal. This effective asymmetric VIV suppression approach is presented and discussed in detail.     

Effect of internal flow on vortex-induced vibration dynamics of a flexible mining riser in external shear current

Vortex-induced vibration (VIV) of flexible risers with both internal and external flows has received much attention recently. Hence, VIV dynamics of a fluid-conveying flexible riser subjected to external shear current is investigated. The effect of internal flow velocity and fluid density on VIV response is mainly examined and analyzed. A time domain model is introduced and elaborated. Then the finite element method is adopted to discretize the governing equations. Firstly, the model is validated based on the comparison between the numerical and experimental results. Then the influence of the internal flow velocity and fluid density on VIV dynamics is studied. The results show that multi-frequency response occurs when the flexible riser with various internal flow velocities and densities is subjected to external shear current. Under same shear current velocity, the IL mean deflection is enlarged with the increase of the internal flow velocity and fluid density. In addition, the internal flow velocity and fluid density have an evident effect on the vibrating frequency and the root mean square (RMS) displacement in both in-line (IL) and cross-flow (CF) directions. Moreover, mode and frequency transitions can be observed under different internal flow velocities and fluid densities.     

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.     

表面粗糙度对立管涡激振动响应影响的试验研究

应用模型试验的方法,研究了表面粗糙度对立管涡激振动响应特性的影响规律,对不同粗糙度条件下立管所受拖曳力、升力、端部张力、漩涡泄放频率、结构振动响应频率、位移响应等参数的变化规律进行了对比分析。结果表明：与立管横向振动相比,立管流向振动更早出现锁定现象,因此当折合速度较低时,立管流向振动的涡激振动响应要大于横向振动。立管张力均存在两个峰值频率,其中一个峰值频率为主导频率,与拖曳力主导频率吻合,由流向涡激振动所产生;另一个峰值频率为主导频率的一半,与升力主导频率吻合,由横向涡激振动所产生。因此可以看出：横向涡激振动与流向涡激振动通过张力作用而相互影响。与光滑立管相比,表面粗糙度降低了立管的涡激振动位移响应,减小了涡激振动的锁定区域,但提高了漩涡泄放频率。对于不同粗糙度下的粗糙立管,随着粗糙度的增加,立管的锁定区域开始点逐渐提前,锁定结束点逐渐推迟,锁定区域逐渐变宽。     

Fatigue damage from time domain simulation of combined in-line and cross-flow vortex-induced vibrations

A semi-empirical method for time domain simulation of vortex-induced vibrations (VIV) is used to calculate the in-line and cross-flow fatigue damage of a tensioned riser in uniform and sheared flow. Simulations are run for flow velocities ranging from 0.3 m/s to 2.4 m/s, and a detailed comparison with experimental observations is performed. Results are reported in terms of dominating frequency, mode of vibration and mean of r.m.s. of displacement, as well as fatigue damage distribution along the length of the structure and maximum fatigue damage rates for each case. Fatigue damage is calculated by rainflow counting of the strain time series together with an idealized S–N curve with slope m = 3. The results show that the model reproduces the measured fatigue damage with a satisfactory level of realism, using a consistent set of parameters. This indicates that the model is usable for calculation of riser VIV fatigue damage in various current conditions, assuming the Reynolds number is in the subcritical range.     

Hydrodynamic damping of a circular cylinder at low KC: Experiments and an associated model

This paper investigates the hydrodynamic damping of a smooth circular cylinder undergoing forced oscillations at Keulegan-Carpenter (KC) numbers smaller than 5 and Reynolds (Re) numbers from 10³–10⁵ with and without background steady currents. A series of experiments are conducted with a circular cylinder oscillating in still water, in-line currents and cross currents. The measured drag coefficients of the smooth cylinder in the still water condition match with the well-published results and the theoretical solution of Stokes and Wang at very small KC numbers. The hydrodynamic damping increases with the in-line steady current whereas it remains almost constant at small transverse velocities and increases notably when the latter becomes large. To predict the hydrodynamic damping in in-line steady currents, the performance of the Morison equation based on relative velocity and independent velocity is explored, respectively. The latter model, by separating the drag into two independent parts, leads to a better fit of the drag force than the former, which is not surprising. However, the former is still a preferable option for engineering design due to its simplicity. The experimental data suggest that the existing design guidelines such as ISO-19902 or DNVGL-RP-C205 should be used with caution for KC < 5.     

Characteristics of VIV in multi-degree-of-freedom tensioned beams using a numerical method

The object of this study is to analyze the characteristics of vortex-induced vibration of a slender marine structure with the numerical method. Applying a dynamic analysis method for a slender marine structure based on the 3D finite difference method, we carried out case studies for a tensioned beam model at a constant flow speed. The hydrodynamic forces, in the direction of inline and cross-flow, created by vortex shedding are simultaneously considered based on Morison equation. The frequency of force in the inline direction corresponding to the unstable zone is evaluated. An eigenvalue analysis for different flow speeds of a tensioned beam considering the effect of the tension increase due to the inline and cross-flow drag forces is performed. We found that a revision of the eigenvalue should be considered if the tension along a riser or beam is significantly affected by an environmental or functional load. From a trajectory on the XY plane it was shown that the riser did not move in an exact 8 shape for all flow conditions due to the phase angle difference between inline and cross-flow displacement. It is believed that the phase angles between inline and cross-flow displacements in high modes are different among the nodes.     

Numerical prediction of the modal response of flexible cylinders in cross-flow with a current dependent form of damping

A quadratic eigenvalue problem (QEP) was posed in order to study the dynamics of flexible cylinders in cross-flow, simulating slender offshore structures such as risers, catenaries or tendons. The Euler–Bernoulli equation was used to model the structure assuming a fluid loading model, and yielding a quadratic eigenvalue problem that included a form of damping dependent not only on the structural damping itself, but also on the free stream velocity and the fluid force coefficients. We solved the QEP using the finite element method. We also derived a simplified analytical solution in this work for comparison with the QEP, however this solution does not consider changes in tension along the length of the cylinder as the QEP does. In our study, the QEP solutions were first validated against the simplified analytical solution, and also against a well-known experimental dataset obtained in 2003, in which a flexible circular cylinder model was used to model the dynamics of a riser undergoing multi-mode vortex-induced vibrations.     

关于二维平面圆柱涡激振动的数值模拟

利用有限元软件Adina建立平面二维圆柱绕流的数值模型,模拟低雷诺数条件下流体与圆柱间的涡激振动。随着流速加大,圆柱振动经历非锁定一锁定一脱离锁定的过程,由于锁定形态下圆柱振动与尾涡脱落引起的流体力形成共振,使圆柱的振幅增大。仅考虑圆柱顺流向振动时,横流向振幅略有增加;同时考虑圆柱在平面内的旋转和顺流向振动时,横流向振幅显著增加、锁定区间加宽,且质量比越低变化就越明显。     

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.     

Study on the maneuverability of a large vessel installed with a mariner type Super VecTwin rudder

The suitability of the Mariner type Super VecTwin rudder (hereinafter, the MSV rudder) for a large vessel is assessed in this article. Several experiments in a maneuvering pond were carried out and their results analyzed and summarized. Free-running tests such as turning, zigzag, and stopping tests were carried out with a 4-m free-running model of a very large crude carrier (VLCC) ship with the MSV rudder and the Mariner rudder. The results were compared to validate the maneuverability of a VLCC-sized a ship installed with the MSV rudder. A mathematical model of an MSV rudder is proposed for maneuvering simulation of a large vessel. To develop a maneuvering simulation for the model ship that was used in the free-running tests, hydrodynamic coefficients were estimated based on Kijima's regression formula. The coefficients of interaction between the hull and rudder (t_R, a_H, x_H) were obtained from a self-propulsion test in a towing tank. The complicated flow around the rudders is simplified to model the flow speed around the rudders. This simplified flow speed is utilized to compare the time histories of the free-running tests with the simulations. The mathematical model of the MSV rudder was further improved using the results of this comparison.     

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.