Simultaneous CFD evaluation of VIV suppression using smaller control cylinders

Two-degree-of-freedom vortex-induced vibrations (VIV) of a circular cylinder with and without two smaller control cylinders are investigated numerically by computational fluid dynamics (CFD) models coupling with a fluid–structure interaction (FSI) computational method. The numerical model is validated against experimental data of VIV of an isolated cylinder in uniform current. The study is aimed to investigate the effect of smaller control cylinders on VIV suppression. The trajectories of cylinder motion, amplitude response, and temporal evolution of vortex shedding and streamlines are obtained by conducting a series of simulations. And the effect of Reynolds number, located angle and rotational rate of small control cylinders are discussed in detail. It is found that placing small cylinders at 45° to the downstream vector can achieve a good suppression effect, but the effect is different at different Re. Rotating control cylinders with a reasonable rotation velocity can further enhance the VIV suppression by injecting enough momentum into the boundary layer of the main cylinder. The best effect is found at U_c=10, which has a 64.56% reduction in the transverse vibration response.     

The effect of arrangement of two circular cylinders on the maximum efficiency of Vortex-Induced Vibration power using a Scale-Adaptive Simulation model

The complex behaviour of an unsteady flow around two circular cylinders in tandem is of interest for many civil engineering applications across a wide range of aerospace, mechanical and marine applications. The present paper analyses Vortex-Induced Vibration (VIV) for the flow around two circular cylinders. It has been shown that the amount of kinetic energy which can be captured by VIV is a function of the arrangement of the two cylinders. The upstream cylinder is fixed while the downstream is mounted elastically with one degree of freedom normal to the mean flow direction. The efficiency of the VIV power obtained from downstream cylinder is compared for different arrangement of the cylinders. For this purpose, the longitudinal and lateral distances between the cylinders were varied and the Reynolds number was kept constant. Scale-Adaptive Simulation (SAS) and Shear Stress Transport (SST) CFD models are utilized to analyse the validity of the SAS turbulence model. The results indicate that both turbulence models predict the flow characteristics around the cylinders with reasonable precision; however, the predictions from SAS were more accurate compared to the SST. Based on this comparison, SAS model was chosen as a tool to analyse the VIV response of the downstream cylinder. The location of the downstream cylinder has been altered in the wake of upstream one in order to obtain the optimum efficiency of the VIV power. The results reveal that the arrangement of the cylinders can significantly change the efficiency. It is also observed that cylinders offset from one another show a higher efficiency compared to cylinders with their centres aligned.     

Vortex- and wake-induced vibrations of a tandem arrangement of two flexible circular cylinders with far wake interference

The dynamic response of two flexible cylinders in tandem arrangement partially immersed in a uniform flow is analysed. The centre-to-centre separations, larger than 4 and up to 8 diameters, were chosen to fall in the regime in which two separate wakes exist behind each one of the models. For the cases presented here, it has been confirmed that the main excitation mechanism is wake-induced vibration (WIV). The rear cylinder shows large amplitudes of response, at reduced velocities over the expected ones at lock-in when a cylinder is undergoing VIV being isolated. This type of response has been also observed by other researchers in experiments with flexibly mounted cylinders in the wake of stationary ones, we also provide data here, for cases with the front cylinder being stationary.     

Efficient coupling of direct forcing immersed boundary-lattice Boltzmann method and finite element method to simulate fluid-structure interactions

Fluid-structure interactions (FSI) of rigid and flexible bodies are simulated in this article. For the fluid flow, multidirect forcing immersed boundary method (IBM) is adopted to capture the moving boundary, and lattice Boltzmann method (LBM) is used to evolve the flow field. Compared with our previous no-penetration IBM, less iterations are required in this work. In addition, larger velocity in lattice units can be used and the nonphysical force oscillations are suppressed due to the C³ 6-point kernel. Multi-relaxation-time collision operator and local grid refinement are also adopted in LBM to enhance the numerical stability and efficiency. To improve the efficiency of the FSI coupling algorithm, the mesh of the deformable structure can be coarser than the Lagrangian mesh using Newton-Cotes formulas to integrate the traction on the structure surface. A variety of benchmarks, including flow around a circular cylinder with Reynold number ranging from 20 to 200, forced oscillation of a circular cylinder, vortex-induced vibration (VIV) of an elastically mounted circular cylinder in two degrees of freedom, and VIV of an elastic cantilever beam attached to a circular cylinder, are carried out to evaluate the accuracy and stability of the present coupling algorithm. For the benchmark FSI problem considered in this article, a reduction of 54% of the calculation time is achieved using coarser structure mesh. As an application of the FSI coupling algorithm, the mechanism of an elastic beam in the wake of a circular cylinder is discussed.     

Three-dimensional numerical simulation of vortex-induced vibration of an elastically mounted rigid circular cylinder in steady current

Vortex-induced vibration (VIV) of an elastically mounted rigid circular cylinder in steady current is investigated by solving the three-dimensional Navier–Stokes equations. The cylinder is allowed to vibrate only in the cross-flow direction. The aim of this study is to investigate the variation of the vortex shedding flow in the axial direction of the cylinder and to study the transition of the flow from two-dimensional (2D) to three-dimensional (3D) for VIV of a cylinder. Simulations are carried out for a constant mass ratio of 2, the Reynolds numbers ranging from 150 to 1000 and the reduced velocities ranging from 2 to 12. The three-dimensionality of the flow is found to be the strongest in the upper branch of the VIV response and weakest in the initial branch. The 2S and 2P vortex shedding modes are found to coexist along the cylinder span in the upper branch, leading to strong variations of the lift coefficient in the axial direction of the cylinder. The difference between the flow transition from 2D to 3D in the VIV lock-in regime and that in the wake of a stationary cylinder is identified. The transition mode B found in the wake of a stationary cylinder is also found in the wake of a vibrating cylinder. The critical Reynolds number for flow transition from 2D to 3D of a cylinder undergoing cross-flow VIV at a reduced velocity of 6 is found to be greater than that for a stationary cylinder. For a constant reduced velocity of 6, the wake flow changes from 2D to 3D as the Reynolds number is increased from 250 to 300. Some 2D numerical simulations are performed and it is found that the 2D Navier–Stokes (NS) equations are not able to predict the VIV in the turbulent flow regime, while the 2D Reynolds-averaged Navier–Stokes (RANS) equations improve the results.     

Shear flow induced vibrations of long slender cylinders with a wake oscillator model

A time domain model is presented to study the vibrations of long slender cylinders placed in shear flow. Long slender cylinders such as risers and tension legs are widely used in the field of ocean engineering. They are subjected to vortex-induced vibrations(VIV) when placed within a transverse incident flow. A three dimensional model coupled with wake oscillators is formulated to describe the response of the slender cylinder in cross-flow and in-line directions. The wake oscillators are distributed along the cylinder and the vortex-shedding frequency is derived from the local current velocity. A non-linear fiuid force model is accounted for the coupled effect between cross-flow and in-line vibrations. The comparisons with the published experimental data show that the dynamic features of VIV of long slender cylinder placed in shear flow can be obtained by the proposed model,such as the spanwise average displacement,vibration frequency,dominant mode and the combination of standing and traveling waves. The simulation in a uniform flow is also conducted and the result is compared with the case of nonuniform flow. It is concluded that the flow shear characteristic has significantly changed the cylinder vibration behavior.     

URANS vs. experiments of flow induced motions of multiple circular cylinders with passive turbulence control

Two-dimensional Unsteady Reynolds-Average Navier–Stokes equations with the Spalart–Allmaras turbulence model are used to simulate the flow induced motions of multiple circular cylinders with passive turbulence control (PTC) in steady uniform flow. Four configurations with 1, 2, 3, and 4 cylinders in tandem are simulated and studied at a series of Reynolds numbers in the range of 30 000<Re<120 000. Simulation results are verified by experimental data measured in the Marine Renewable Energy Laboratory. Good agreement was observed between the values of vorticity, amplitude ratio, and frequency ratio predicted by numerical simulations and experimental measurements. The amplitude and frequency response show the initial and upper branches in vortex induced vibration (VIV), transition from VIV to galloping, and galloping branch for all PTC-cylinders. The maximum amplitude of 2.9 diameters for the first cylinder is achieved at Re=104 356 in the numerical results. Compared with the first cylinder, the VIV initial branch starts at higher Re for the downstream cylinders due to the presence of the upstream cylinder(s). 2P and 2P+2S vortex patterns are observed at Re=62 049 and Re=90 254 for the single PTC-cylinder. Furthermore, the shed vortices of the downstream cylinders are strongly disrupted and modified by the vortices shed from the upstream one in the cases of multiple PTC-cylinders.     

Flow-induced vibrations of two circular cylinders in tandem with shear flow at low Reynolds number

The flow-induced vibrations of two elastically mounted circular cylinders subjected to the planar shear flow in tandem arrangement are studied numerically at Re=160. A four-step semi-implicit Characteristic-based split (4-SICBS) finite element method is developed under the framework of the fractional step method to cope with the vortex-induced vibration (VIV) problem. For the computational code verification, two benchmark problems are examined in the laminar region: flow-induced vibration of an elastically mounted cylinder having two degrees of freedom and past two stationary ones in tandem arrangement. Regarding the two-cylinder VIVs in shear flow, the computation is conducted with the cylinder reduced mass M_r=2.5π and the structural damping ratio ξ=0.0. The effects of some key parameters, such as shear rate (k=0.0, 0.05, 0.1), reduced velocity (U_r=3.0–18.0) and spacing ratio (L_x/D=2.5, 3.5, 4.5, 8.0), are demonstrated. It is observed that the shear rate and reduced velocity play an important role in the VIVs of both cylinders at various center-to-center distances. Additionally, in comparison with the single cylinder case, a further study indicated that the gap flow has a significant impact on such a dynamic system, leading it to be more complex. The results show that, the performances of ‘dual-resonant’ are discovered in the shear flow. A valley is formed in transverse oscillation amplitude of DC for each spacing ratio when U_r is about 6.0. For the X–Y trajectories of the circular cylinders, figure-eight, figure-O and oval shape are obtained. Finally, the interactions between cylinders are revealed, together with the wake-induced vibration (WIV) mechanism underlying the oscillation characteristics of both cylinders exposed to shear flow. Besides, the “T+P” wake pattern is discovered herein.     

大柔性圆柱体两自由度涡激振动试验研究

基于模型试验研究了柔性圆柱体两自由度涡激振动问题, 研究了顺流向涡激振动和横向涡激振动的频率与振幅关系, 提出了考虑流固耦合的两自由度涡激振动非线性分析模型. 研究表明, 在不同的流速(雷诺数)范围, 柔性圆柱体顺流向涡激振动与横向涡激振动的频率比和幅值比是不同的; 在非锁定区, 圆柱体的顺流向振动频率与横向振动频率相同, 在锁定区, 圆柱体的顺流向振动频率是横向振动频率的两倍; 在非锁定区, 顺流向振幅与横向振幅比约为1, 而在锁定区, 顺流向振幅与横向振幅比约为1/3~2/3.      

Numerical study on the suppression of the vortex-induced vibration of an elastically mounted cylinder by a traveling wave wall

In the present paper, the commercial CFD code “Fluent” was employed to perform 2-D simulations of an entire process that included the flow around a fixed circular cylinder, the oscillating cylinder (vortex-induced vibration, VIV) and the oscillating cylinder subjected to shape control by a traveling wave wall (TWW) method. The study mainly focused on using the TWW control method to suppress the VIV of an elastically supported circular cylinder with two degrees of freedom at a low Reynolds number of 200. The cross flow (CF) and the inline flow (IL) displacements, the centroid motion trajectories and the lift and drag forces of the cylinder that changed with the frequency ratios were analyzed in detail. The results indicate that a series of small-scale vortices will be formed in the troughs of the traveling wave located on the rear part of the circular cylinder; these vortices can effectively control the flow separation from the cylinder surface, eliminate the oscillating wake and suppress the VIV of the cylinder. A TWW starting at the initial time or at some time halfway through the time interval can significantly suppress the CF and IL vibrations of the cylinder and can remarkably decrease the fluctuations of the lift coefficients and the average values of the drag coefficients; however, it will simultaneously dramatically increase the fluctuations of the drag coefficients.     

Computational simulation of the flow-induced vibration of a circular cylinder subjected to wake interference

In this work, we considered the flow around two circular cylinders of equal diameter placed in tandem with respect to the incident uniform flow. The upstream cylinder was fixed and the downstream cylinder was completely free to move in the cross-stream direction, with no spring or damper attached to it. The centre-to-centre distance between the cylinders was four diameters, and the Reynolds number was varied from 100 to 645. We performed two- and three-dimensional simulations of this flow using a Spectral/hp element method to discretise the flow equations, coupled to a simple Newmark integration routine that solves the equation of the dynamics of the cylinder. The differences of the behaviours observed in the two- and three-dimensional simulations are highlighted and the data is analysed under the light of previously published experimental results obtained for higher Reynolds numbers.     

Vortex and wake-induced vibrations of a tandem arrangement of two flexible circular cylinders with near wake interference

Results showing the dynamic response of a tandem arrangement of two vertical high aspect ratio (length over diameter) and low mass ratio (mass over mass of displaced fluid) flexible cylinders vibrating at low mode number are presented in this paper. Two circular cylinder models were aligned with the flow, so the downstream or trailing cylinder was immersed in the wake of the leading one. Centre-to-centre distances from 2 to 4 diameters were studied. The models were very similar in design, with external diameters of 16 mm and a total length of 1.5 m. Reynolds numbers up to 12 000 were achieved with reduced velocities, based on the fundamental natural frequency of the downstream cylinder in still water, up to 16. The trailing model had a mass ratio of 1.8 with a combined mass-damping parameter of 0.049, whilst the corresponding figures for the leading cylinder were 1.45 and 0.043, respectively. The dynamic response of the trailing model has been analysed by studying cross-flow and in-line amplitudes, dominant frequencies and modal amplitudes. The dynamic response of the leading one is analysed by means of its cross-flow amplitudes and dominant frequencies and it is also related to the motion of the trailing cylinder by studying the synchronisation between their instantaneous cross-flow motions. Planar digital particle image velocimetry (DPIV) was used to visualise the wake. Different response regimes have been identified based on the type of oscillations exhibited by the cylinders: vortex-induced (VIV), wake-induced (WIV) or combinations of both.     

倾斜圆柱结构涡激振动研究进展

圆柱结构涡激振动现象在生活中十分常见, 如海洋工程中的管道、土木工程中的高耸建筑、桥梁斜拉索, 核工程中的热交换器等频繁受到涡激振动影响, 诱发结构的疲劳损伤, 甚至破坏失效. 现阶段, 人们对垂直来流作用下圆柱结构涡激振动机理已有较为全面的认识. 然而, 当圆柱倾斜置于流场中, 结构后缘的尾流形态与垂直放置差异显著, 结构与流体的耦合作用机理更为复杂. 为简化倾斜圆柱涡激振动问题, 提出了不相关原则, 来流速度被分解为垂直圆柱结构轴向和平行圆柱结构轴向的两个速度分量, 仅考虑垂直结构轴向速度分量的影响, 忽略平行结构轴向速度分量的影响. 近年来, 针对倾斜圆柱涡激振动及不相关原则的适用性, 出现了大量实验和数值模拟研究成果. 为了深化对倾斜圆柱结构涡激振动相关机理的认知, 本文全面阐述了倾斜圆柱结构涡激振动响应规律、尾迹流场模式和流体力特性等方面的研究进展, 分析了不相关原则的适用范围, 探讨了倾斜圆柱结构涡激振动抑制措施, 并对今后该领域的研究进行了力所能及的展望.      

Experimental investigation of the flow-induced vibration of a curved cylinder in convex and concave configurations

Experiments have been conducted to investigate the two-degree-of-freedom vortex-induced vibration (VIV) response of a rigid section of a curved circular cylinder with low mass-damping ratio. Two curved configurations, a concave and a convex, were tested regarding the direction of the flow, in addition to a straight cylinder that served as reference. Amplitude and frequency responses are presented versus reduced velocity for a Reynolds number range between 750 and 15 000. Results for the curved cylinders with concave and convex configurations revealed significantly lower vibration amplitudes when compared to the typical VIV response of a straight cylinder. However, the concave cylinder showed relatively higher amplitudes than the convex cylinder which were sustained beyond the typical synchronisation region. We believe this distinct behaviour between the convex and the concave configurations is related to the wake interference taking place in the lower half of the curvature due to perturbations generated in the horizontal section when it is positioned upstream. Particle-image velocimetry (PIV) measurements of the separated flow along the cylinder highlight the effect of curvature on vortex formation and excitation revealing a complex fluid–structure interaction mechanism.     

Application of wake oscillators to two-dimensional vortex-induced vibrations of circular cylinders in oscillatory flows

A nonlinear time-domain simulation model for predicting two-dimensional vortex-induced vibration (VIV) of a flexibly mounted circular cylinder in planar and oscillatory flow is presented. This model is based on the utilization of van der Pol wake oscillators, being unconventional since wake oscillators have typically been applied to steady flow VIV predictions. The time-varying relative flow–cylinder velocities and accelerations are accounted for in deriving the coupled hydrodynamic lift, drag and inertia forces leading to the cylinder cross-flow and in-line oscillations. The system fluid–structure interaction equations explicitly contain the time-dependent and hybrid trigonometric terms. Depending on the Keulegan–Carpenter number (KC) incorporating the flow maximum velocity and excitation frequency, the model calibration is performed, entailing a set of empirical coefficients and expressions as a function of KC and mass ratio. Parametric investigations in cases of varying KC, reduced flow velocity, cylinder-to-flow frequency ratio and mass ratio are carried out, capturing some qualitative features of oscillatory flow VIV and exploring the effects of system parameters on response prediction characteristics. The model dependence of hydrodynamic coefficients on the Reynolds number is studied. Discrepancies and limitations versus advantages of the present model with different feasible solution scenarios are illuminated to inform the implementation of wake oscillators as a computationally efficient prediction model for VIV in oscillatory flows.     

Suppression of vortex-induced vibration of a circular cylinder using suction-based flow control

In the present study, a flow control method is employed to mitigate vortex-induced vibration (VIV) of a circular cylinder by using a suction flow method. The VIV of a circular cylinder was first reproduced in a wind tunnel by using a spring–mass system. The time evolution of the cylinder oscillation and the time histograms of the surface pressures of 119 taps in four sections of the circular cylinder model were measured during the wind tunnel experiments. Four steady suction flow rates were used to investigate the effectiveness of the suction control method to suppress VIV of the circular cylinder. The vibration responses, the mean and fluctuating pressure coefficients, and the resultant aerodynamic force coefficients of the circular cylinder under the suction flow control are analyzed. The measurement results indicate clearly that the steady suction flow control method exhibits excellent control effectiveness and can distinctly suppress the VIV by dramatically reducing the amplitudes of cylinder vibrations, fluctuating pressure coefficients and lift coefficients of the circular cylinder model. By comparing the test cases with different suction flow rates, it is found that there exists an optimal suction flow rate for the maximum VIV control. The cases with higher suction flow rates do not necessarily behave better than those with lower suction flow rates. With the experimental setting used in the present study, the suction flow control method is found to behave better for VIV suppression when the ratio of the suction flow velocity to the oncoming flow velocity is less than one.     

An experimental investigation of one- and two-degree of freedom VIV of cylinders

In the paper,an experiment investigation was conducted for one-and two-degree of freedom vortex-induced vibration(VIV) of a horizontally-oriented cylinder with diameter of 11 cm and length of 120 cm.In the experiment,the spring constants in the cross-flow and in-line flow directions were regulated to change the natural vibration frequency of the model system.It was found that,in the one-degree of freedom VIV experiment,a "double peak" phenomenon was observed in its amplitude within the range of the reduced velocities tested,moreover,a "2T" wake appeared in the vicinity of the second peak.In the two-degree of freedom VIV experiment,the trajectory of cylinder exhibited a reverse "C" shape,i.e.,a "new moon" shape.Through analysis of these data,it appears that,besides the non-dimensional in-line and cross-flow natural vibration frequency ratios,the absolute value of the natural vibration frequency of cylinder is also one of the important parameters affecting its VIV behavior.     

Vortex Induced Vibrations of a Pair of Cylinders at Reynolds Number 1000

Vortex induced vibrations of two equal-sized cylinders in tandem and staggered arrangement placed in uniform incompressible flow is studied. A stabilized finite element formulation is utilized to solve the governing equations. The Reynolds number for these 2D simulations is 1000. The cylinders are separated by 5.5 times the cylinder diameter in the streamwise direction. For the staggered arrangement, the cross-flow spacing between the two cylinders is 0.7 times the cylinder diameter. In this arrangement, the downstream cylinder lies in the wake of the upstream one and therefore experiences an unsteady inflow. The wake looses its temporal periodicity, beyond a few diameters downstream of the front cylinder. The upstream cylinder responds as an isolated single cylinder while the downstream one undergoes disorganized motion. Soft-lock-in is observed in almost all the cases.     

Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number

Two- and three-dimensional numerical simulations of the flow around two circular cylinders in tandem arrangements are performed. The upstream cylinder is fixed and the downstream cylinder is free to oscillate in the transverse direction, in response to the fluid loads. The Reynolds number is kept constant at 150 for the two-dimensional simulations and at 300 for the three-dimensional simulations, and the reduced velocity is varied by changing the structural stiffness. The in-line centre-to-centre distance is varied from 1.5 to 8.0 diameters, and the results are compared to that of a single isolated flexible cylinder with the same structural characteristics, m^?=2.0 and ζ=0.007. The calculations show that significant changes occur in the dynamic behaviour of the cylinders, when comparing the flow around the tandem arrangements to that around an isolated cylinder: for the tandem arrangements, the lock-in boundaries are wider, the maximum displacement amplitudes are greater and the amplitudes of vibration for high reduced velocities, outside the lock-in, are very significant. The main responsible for these changes appears to be the oscillatory flow in the gap between the cylinders.