Investigation of passive oscillations of flexible splitter plates attached to a circular cylinder

This paper presents a numerical study to address wake control of a circular cylinder subjected to two-dimensional laminar flow regime using single and multiple flexible splitter plates attached to the cylinder. Three different cases are presented in the study, covering cylinders with one, two and three horizontally attached splitter plates while the locations of the plates around the cylinders are varied. The length of the splitter plates was equal to the cylinder diameter and Reynolds number was 100. Due to the flexibility of the plates, the problem was modeled as a Fluid–Structure Interaction (FSI) problem and the commercial finite element software, Comsol Multiphysics, was utilized to solve this problem using Arbitrary Lagrangian–Eulerian (ALE) method. Vortex shedding frequency and fluid forces acting on the cylinder are investigated, along with a comprehensive parametric study to identify the optimum arrangement of the plates for maximum drag reduction and maximum vortex shedding frequency reduction. The numerical results associated to the flexible splitter plates are also compared with the corresponding rigid splitter plate cases investigated in a previous study. Moreover, the tip amplitude of the plates and the maximum strains were measured in order to find an optimum position for placing a piezoelectric polymer to harvest energy from the flow.     

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height circular cylinder

The influence of a wake-mounted splitter plate on the flow around a surface-mounted circular cylinder of finite height was investigated experimentally using a low-speed wind tunnel. The experiments were conducted at a Reynolds number of Re=7.4×10⁴ for cylinder aspect ratios of AR=9, 7, 5 and 3. The thickness of the boundary layer on the ground plane relative to the cylinder diameter was δ/D=1.5. The splitter plates were mounted on the wake centreline with negligible gap between the base of the cylinder and the leading edge of the plate. The lengths of the splitter plates, relative to the cylinder diameter, ranged from L/D=1 to 7, and the plate height was always equal to the cylinder height. Measurements of the mean drag force coefficient were obtained with a force balance, and measurements of the vortex shedding frequency were obtained with a single-component hot-wire probe situated in the wake of the cylinder–plate combination. Compared to the well-studied case involving an infinite circular cylinder, the splitter plate was found to be a less effective drag-reduction device for finite circular cylinders. Significant reduction in the mean drag coefficient was realized only for the finite circular cylinder of AR=9 with intermediate-length splitter plates of L/D=1–3. The mean drag coefficients of the other cylinders were almost unchanged. In terms of its effect on vortex shedding, a splitter plate of sufficient length was able to suppress Kármán vortex shedding for all of the finite circular cylinders tested. For AR=9, vortex shedding suppression occurred for L/D≥5, which is similar to the case of the infinite circular cylinder. For the smaller-aspect-ratio cylinders, however, the splitter plate was more effective than what occurs for the infinite circular cylinder: for AR=3, vortex shedding suppression occurred for all of the splitter plates tested (L/D≥1); for AR=5 and 7, vortex shedding suppression occurred for L/D≥1.5.     

Suppression of wake-induced vibration of tandem cylinders with free-to-rotate control plates

Experiments have been carried out on a pair of circular cylinders to investigate the effectiveness of pivoting parallel plates as wake-induced vibration suppressors. Measurements of amplitude of vibration and average drag are presented for a circular cylinder, free to respond in the cross-flow direction, with mass ratio 2 and a damping level of 0.7% of critical damping. Reduced velocities were up to nearly 30, with associated Reynolds numbers up to 2.3×10⁴ and the results presented are for a centre-to-centre separation of cylinders of 4 diameters. It is shown how vortex-induced vibration and wake-induced vibration of the downstream cylinder of a tandem pair can be practically eliminated by using free to rotate parallel plates. The device achieves vibration suppression with a substantial drag reduction when compared to a pair of fixed tandem cylinders at the same Reynolds number. Results for a single splitter plate and helical strakes are also presented for comparison and were found not to be effective in suppressing wake-induced vibration.     

隔离板对流向振荡圆柱尾流旋涡脱落的抑制

用隔离板对直径为D, 沿流向振荡的圆柱后涡脱落进行抑制. 隔离板放于圆柱尾流中心线上,控制参数包括隔离板长度L/D以及隔离板前缘到柱体振荡中心的距离G/D. 实验的雷诺数范围Re=V_∞D/v=1.01×10⁴～1.69×10⁴,柱体折减振频范围f_eD/V_∞=0～0.03, 柱体振幅固定为A/D=0.2. 风洞烟线显示和热线测量结果表明:当 G/D位于一个有效区域内时,可有效抑制振荡柱体尾流的旋涡脱落. 该有效区的大小随着隔离板板长的增大而增大, 随着Re数和圆柱振荡频率的增大而减小.     

The effect of a splitter plate on the flow around a finite prism

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height square prism was investigated experimentally in a low-speed wind tunnel. Measurements of the mean drag force and vortex shedding frequency were made at Re=7.4×10⁴ for square prisms of aspect ratios AR=9, 7, 5 and 3. Measurements of the mean wake velocity field were made with a seven-hole pressure probe at Re=3.7×10⁴ for square prisms of AR=9 and 5. The relative thickness of the boundary layer on the ground plane was δ/D=1.5–1.6 (where D is the side length of the prism). The splitter plates were mounted vertically from the ground plane on the wake centreline, with a negligible gap between the leading edge of the plate and rear of the prism. The splitter plate heights were always the same as the heights of prisms, while the splitter plate lengths ranged from L/D=1 to 7. Compared to previously published results for an “infinite” square prism, a splitter plate is less effective at drag reduction, but more effective at vortex shedding suppression, when used with a finite-height square prism. Significant reduction in drag was realized only for short prisms (of AR≤5) when long splitter plates (of L/D≥5) were used. In contrast, a splitter plate of length L/D=3 was sufficient to suppress vortex shedding for all aspect ratios tested. Compared to previous results for finite-height circular cylinders, finite-height square prisms typically need longer splitter plates for vortex shedding suppression. The effect of the splitter plate on the mean wake was to narrow the wake width close to the ground plane, stretch and weaken the streamwise vortex structures, and increase the lateral entrainment of ambient fluid towards the wake centreline. The splitter plate has little effect on the mean downwash. Long splitter plates resulted in the formation of additional streamwise vortex structures in the upper part of the wake.     

Modal analysis of cantilever plate flutter

This study illustrates the mechanism of modal coupling in cantilever plate flutter using the full Theodorsen airfoil theory within the linear framework. An accurate, pseudo-spectral method is employed to calculate the fluid loading and the eigenvalue problem is solved numerically following the Galerkin procedure. For plates with a structure-to-fluid mass ratio around unity, the first two in vacuo modes are dominant and the Kutta condition at the trailing edge plays a central role in the flutter mechanism. The fluid loading induced by the first mode excites significant second and higher order modes. The fluid loading on the second mode is coupled strongly with the structural vibration velocity of the first mode, which is identified as the main mechanism of energy transfer from flow to plate. It is demonstrated that the response of the second mode is suppressed and the plate is stabilized when a concentrated mass is added near the middle of the plate length. Theoretical prediction is supported by experimental data although the latter is affected by many practical factors that are difficult to model precisely.     

圆柱体双自由度涡激振动轨迹的模型试验

对水平放置的直径 5cm,长120cm的圆柱体开展了双自由度涡激振动模型试验研究. 试验中发现,圆柱体在顺流向上的振动频率表现为"多频"的现象,即不光有2倍横向振动的频率,在某些振动固有频率和约化速度的条件下,还出现了单倍横向振动的频率,从而使圆柱体的轨迹呈现出"卵"形以及"雨滴"形等明显异于传统"8"字形与"新月"形的运动轨迹. 此外,通过研究初步得到了各种其他形式的振动轨迹向"8"字形变化的趋势,并认为不同的横向、顺流向振动固有频率以及流速是导致圆柱体涡激振动轨迹产生多种形式的主要原因.      

不同控制角下附加圆柱对圆柱涡激振动影响

在弹性支撑的圆柱周围布置直径更小圆柱会影响剪切层发展以及旋涡脱落,进而改变其涡激振动状态.通过不同的布置形式和附加小圆柱个数可以实现对圆柱涡激振动的促进或抑制.激励更大幅值的振动可以更好地将水流动能转化为可利用的机械能或电能,抑制其振动则可以实现对海洋平台等结构物的保护.采用基于迭代的嵌入式浸入边界法对前侧对称布置两个小圆柱的圆柱涡激振动进行数值模拟研究,系统仅做横向振动,其中基于主圆柱直径的雷诺数为100,质量比为2.0,折合流速为3~11.小圆柱与主圆柱的直径比为0.125,间隙比为0.125.结果表明,在研究的控制角范围内(30°~90°),附加小圆柱可以很大程度上改变圆柱涡激振动的状态.当控制角较小(30°)时,附加小圆柱对主圆柱的振动起抑制作用;当控制角为45°~60°时,圆柱的振动分为涡振和弛振两个阶段,在弛振阶段,圆柱振幅随折合流速增加而持续增加;当控制角较大(75°~90°)时,附加小圆柱的促进作用随着控制角增加而减小.进一步地,结合一个周期内不同时刻旋涡脱落以及圆周压强分布,解释了附加小圆柱对主圆柱涡激振动的作用机制.应用能量系数对圆柱系统的进一步分析发现,弛振阶段由流体传递到主圆柱的能量系数随折合流速的增加逐渐下降,旋涡结构的改变是产生这种变化的直接原因.      

低雷诺数下串列三圆柱涡激振动中的弛振现象及其影响因素

对间距比为1.2和雷诺数为100的串列三圆柱涡激振动进行数值模拟, 发现在某个折合流速之后, 三圆柱的响应均呈现为随着折合流速增大而增大的弛振现象, 平衡位置偏移、低频振动以及旋涡脱落与圆柱运动之间的时机三个因素共同决定了弛振现象的出现. 进一步的研究发现, 串列三圆柱的弛振现象仅出现在质量比不大于2.0和雷诺数不大于100的工况下. 当质量比较大时, 串列三圆柱的平衡位置固定不变, 且圆柱的振动不规律, 使得旋涡脱落与圆柱运动的时机处于变化之中. 当雷诺数较高时, 最上游圆柱的平衡位置在折合流速较大时回到初始位置, 不再参与对圆柱振动的调节, 使得圆柱的振动响应不再规律, 旋涡脱落与圆柱运动的时机也一直处于变化之中.      

Interference effect of an upstream larger cylinder on the lock-in vibration of a flexibly mounted circular cylinder

Experiments have been carried out to investigate the flow-induced vibration response of a flexibly mounted circular cylinder located in the vicinity of a larger cylinder and subjected to cross-flow. The interfering larger cylinder was placed upstream and had a diameter twice that of the vibrating cylinder. Complex interaction was observed between the flow over the two cylinders. The vibration responses of the flexible cylinder were classified into different regimes according to the relative positions of the two cylinders. In the-side-by-side arrangement and the tandem or near-tandem arrangement, flow-induced vibrations of the flexible cylinder were greatly suppressed. In the staggered arrangement which covered a large portion of the relative cylinder positions being investigated, vibrations of the smaller cylinder were greatly amplified. The vibration response curves were also largely modified with a broadening of the lock-in resonance range. A shift of the peak reduced velocity for maximum vibration response was also found. Flow visualizations and wake velocity measurements suggested that the modifications of the vibration responses were related to the presence or absence of constant or intermittent flow through the gap region between the two cylinders. The proposed mechanisms of flow interactions and the resulting vibration response characteristics could explain previous observations on flow-induced vibrations of two equal-sized circular cylinders reported in the literature.     

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.     

The effect of end conditions on the vortex-induced vibration of cylinders

In the present investigation we study the effect of end conditions on the vortex-induced vibration of an elastically mounted rigid cylinder. This work was triggered by some initial controlled vibration experiments which showed that spanwise end conditions can have a large effect on measured fluid forces on a cylinder, and this suggested that some of the disparity amongst previous free vibration studies may possibly be attributed to differences in end conditions. In the principal experiments here, we are concerned with a vertical cylinder piercing the clean free surface of a water channel, and attached to a carriage system mounted atop the channel. The upper end of the submerged cylinder is thus the free surface, while the lower end is manipulated to yield three different conditions, namely: an attached endplate; an unattached endplate fixed to the channel floor (with a variable gap between cylinder and plate); and a condition of no endplate at all. Interestingly, we find that the free vibration response for the attached and unattached endplate cases were nearly identical. One expectation was that the case without an endplate would lead to a flow around the end of the body, modifying the vortex dynamics, and thereby reducing the correlation of the induced fluid forces on the body. Surprisingly, over the entire response plot, the vibration amplitude is markedly higher in the absence of an endplate, with the exception of the peak amplitude, which remains nearly unchanged. Unexpectedly, the vibrations become much more steady at flow velocities in the vicinity of the peak response, if the endplate is removed. In a further set of experiments, we undertake controlled vibration, where we vary the gap between cylinder and endplate. We discover a large discontinuous jump in the magnitude of fluid excitation, when the gap exceeds 15% of a diameter. For larger gaps, the fluid excitation becomes independent of the gap size, effectively equivalent to having no plate at all. This study is consistent with some of the disparity between the character of vibration response plots in previous studies, if one takes into account the particular end conditions chosen in those studies.     

近壁面柱体涡激振动的迟滞效应

柱体涡激振动是典型的流固耦合问题,其响应规律标识码在升速流动和远离壁面条件下获得的. 而自然环境流动通常不断经历升速和降速过程,近壁面柱体的涡激振动可呈现与远离标识码体不同的响应特征. 本研究结合大型波流水槽,设计了具有微结构阻尼的柱体涡激振动装置. 基于量纲分析,开展系列水槽标识码验,通过同步测量柱体涡激振动位移时程和绕流流场变化,研究了升降流速作用下柱体涡激振动触发和停振的临界速度(即上临标识码临界速度)变化规律,探究了近壁面柱体涡激振动迟滞效应. 采用自下向上激光扫射的 PIV 流场测量系统,对比分析了固定柱体标识码振动柱体的绕流特征. 实验观测表明,近壁面柱体涡激振动触发的临界速度呈现随壁面间距比减小而逐渐减小的变化趋势;但标识码速条件下的涡激振动停振所对应的下临界速度却明显小于升速时的涡激振动触发所对应的上临界速度. 采用上临界与下临界约标识码差值可定量表征涡激振动迟滞程度,研究发现该值随着柱体间距比减小呈线性增大趋势. 涡激振动迟滞现象通常伴随振幅阶跃标识码阶跃值则随着间距比减小而非线性减小.      

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.     

Effects of a splitter plate on the near wake of a circular cylinder in 2 and 3-dimensional flow configurations

 Results of flow visualization, hot wire, and base pressure measurements were conducted for an investigation of the near wake of a circular cylinder at subcritical Reynolds numbers between 2700 to 46000. A base mounted splitter plate allowed for the modification of the formation region characteristics without disrupting the normal Kármán shedding. The results provide an explanation for the non-linearity in the relationship between shedding frequency and splitter plate length and extend the previous investigations of Roshko (1954), Gerrard (1966) and Apelt et al. (1973). In addition to the nominal 2-D configurations, a sinuous trailing edge splitter plate, cylinder taper, and shear flow were incorporated to study the effects of mild 3-dimensionality. A strong spanwise coherence was found to exist in the formation region. A superposition principle was discovered which showed that certain 3-D geometry and flow configurations could be combined to produce a nominal 2-D wake. Received: 26 June 1996 / Accepted: 7 January 1997     

Flow structure around two finite circular cylinders located in an atmospheric boundary layer: side-by-side arrangement

The flow structure around the free-end region of two adjacent finite circular cylinders embedded in an atmospheric boundary layer (ABL) was investigated experimentally. The experiments were carried out in a closed-return-type subsonic wind tunnel, in which two finite cylinders with an aspect ratio of 6 were mounted vertically on a flat plate in a side-by-side arrangement. The Reynolds number based on the cylinder diameter was about Re=2×10⁴. Systems with gap ratios (i.e., center-to-center distance/cylinder diameter) in the range 1.0–2.0 were investigated. A hot-wire anemometer was employed to measure the wake velocity, and the mean pressure distribution on the cylinder surface was also measured. The flow past two finite cylinders was found to have a complicated three-dimensional wake structure in the region near the free ends. As the gap ratio increases, regular vortex-shedding becomes dominant, but the length of the vortex formation region decreases. The pressure distribution and flow structure around two cylinders were found to differ substantially from the behavior of a two-dimensional circular cylinder due to mutual interference. The three-dimensional flow structure seems to originate from the strong entrainment of irrotational fluids caused by the downwash counter-rotating vortices separated from the finite cylinder (FC) free ends.     

Vibrations of a cylinder in a uniform flow in the presence of a no-slip side-wall

A circular cylinder placed in a uniform flow, and that spans the entire length between two side walls, may experience either parallel or oblique vortex shedding depending on the end conditions. It was shown by Mittal and Sidharth (2014) that the spatio-temporal periodicity of the oblique vortex shedding results in constant-in-time force experienced by the cylinder. On the contrary, parallel vortex shedding leads to fluid force that fluctuates with time. The free vibrations of a circular cylinder, in the presence of a wall, are investigated. For comparison, computations with end walls, where a slip condition on velocity is specified, are also carried out. The Reynolds number, based on the diameter of the cylinder and free-stream speed of the flow, is Re=100. The initial condition for the free vibrations is the fully developed unsteady flow past a stationary cylinder with oblique shedding. It is found that as the amplitude of vibration of the cylinder builds up, the vortices shed from the cylinder align with its axis leading to parallel shedding. The response of the cylinder is associated with two branches: initial and lower. On the lower branch, the response of the cylinder is virtually identical from two- and three-dimensional computations. The flow as well as the response is different on the initial branch and outside the synchronization regime. Forced vibrations confirm the phenomena.     

Suppression of Low-frequency Variations in Vortex Shedding by a Splitter Plate Behind a Bluff Body

Measurements of instantaneous pressure fluctuations on a trapezoidal cross-section cylinder indicate that the low-frequency variations embedded in the vortex-shedding process can be successfully suppressed by insertion of a splitter plate whose length is twice the maximum width of the trapezoidal cylinder. The experiments were performed at Reynolds numbers in a range of 5 × 10³ to 4·5 × 10⁴. Spanwise correlation of the pressure fluctuations measured on the cylinder further indicates that the suppression of low-frequency variations improves the degree of two-dimensionality of vortex shedding. These findings are attributed to the presence of the splitter plate having an effect on stabilizing the vortex formation length which is comparable to the length of the splitter plate, thus eliminating the low-frequency variations embedded in the base pressure.