Phenomenology of Kármán vortex streets in oscillatory flow

Vortex wakes of circular cylinders at low Reynolds numbers have been investigated. Sound waves are superimposed on the flow in mean flow direction. In this configuration the Kármán vortices are shed at the sound frequency or at subharmonics of the sound frequency. The Karman vortex street is treated as a nonlinear self-excited flow oscillator with forced oscillations. Using a flow visualization technique a variety of wake structures has been identified as a function of sound frequency and sound amplitude, but independent of the Reynolds number. The superimposed sound influences the distribution of circulation and accordingly the shedding mechanism. Primary vortex and secondary vortex are shed simultaneously from one side of the cylinder. The alternate vortex shedding is arranged spatially and temporally. Structures along the vortex axes are revealed.Parts of this paper have been presented at IUTAM Congress 1984, Lyngby, Denmark, and at ICNM Conference 1985, Shanghai, P. R. China     

Flow regimes and frequency selection of a cylinder oscillating in an upstream cylinder wake

This paper describes flow around a pair of cylinders in tandem arrangement with a downstream cylinder being fixed or forced to oscillate transversely. A sinusoidal parietal velocity is applied to simulate cylinder oscillation. Time-dependent Navier-Stokes equations are solved using finite element method. It is shown that there exist two distinct flow regimes: ‘vortex suppression regime’ and ‘vortex formation regime’. Averaged vortex lengths between the two cylinders, pressure variations at back and front stagnant points as well as circumferential pressure profiles of the downstream cylinder are found completely different in the two regimes and, thus, can be used to identify the flow regimes. It is shown that frequency selection in the wake of the oscillating cylinder is a result of non-linear interaction among vortex wakes upstream and downstream of the second cylinder and its forced oscillation. Increasing cylinder spacing results in a stronger oscillatory incident flow upstream of the second cylinder and, thus, a smaller synchronization zone.     

涡激诱导并列双圆柱碰撞数值模拟研究

圆柱类结构物的涡激振动是工程中较为常见的一种现象,如果圆柱结构物之间的距离较小, 就会产生涡激诱导碰撞现象,而涡激碰撞会比涡激振动对结构物疲劳破坏产生更严重的威胁.采用浸入边界法模拟流体中的动边界问题,避免了传统贴体网格方法在求解流体中存在固体间碰撞问题时出现数值求解不稳定问题,采用有限元方法对圆柱的运动和碰撞进行求解,通过数据回归方法建立了流体流动条件下的润滑模型,对不同间隙比下涡激诱导并列双圆柱振动及碰撞过程进行了数值模拟, 数值结果表明,如果两圆柱产生了碰撞将会有连续的碰撞发生, 碰撞时出现了多阶频率,振动主频率要比无碰撞时大, 两圆柱碰撞时的相对速度比自由来流速度小;当两圆柱相互接近时, 随着涡环分离角度的逐渐倾斜, 横向流体力先逐渐减小,当两圆柱间涡环开始相互影响发生挤压时, 横向流体力开始逐渐增大;当两圆柱开始反弹时, 两圆柱间形成了低压区, 改变了横向流体阻力的方向,使两圆柱又产生了接近运动,如此反复从而产生了碰撞后横向流体力和圆柱速度的振荡现象.      

双圆柱斜置排列时下游圆柱压力分布和振荡频率的实验研究

当两个圆柱斜置排列并靠得较近时,绕流下游圆柱的流动明显地不同于单一圆柱.本文研究了下游圆柱压力分布受到的影响,并着重于用FFT来分析圆柱表面某些特征点上的压力频谱,研究频谱与圆柱之间的相对距离和位置的关系.当圆柱间距较远时,压力振荡的频率与单圆柱卡门涡节的频率相接近,随着横向间距的接近,频率逐渐降低,然而当两圆柱十分接近时,外侧压力振荡的频率继续降低,但圆柱内侧压力振荡的频率却突然提高,出现了一个圆柱体两侧作用有不同频率压力的情况.     

A numerical study on the flow patterns of two oscillating cylinders

Flow around two oscillating cylinders in a side-by-side arrangement at Reynolds number (Re)=185 is simulated using the immersed boundary method. The purpose of this study is to investigate the combined effects of the gap between the two cylinders and their oscillation in the flow. The cylinders oscillate transversely to a uniform cross-flow with a prescribed sinusoidal function in the opposite direction, with the oscillation amplitude equal to 20% of the cylinder diameter. The gap between the two cylinders and the oscillating frequency are chosen as major variables for the parametric study to investigate their influence on the flow pattern. The ratio of mean gap distance between the two oscillating cylinders to the cylinder diameter is chosen to be 0.6, 1.0, 1.4, and 1.8, and the ratio of oscillating frequencies to the natural vortex shedding frequency of a fixed cylinder is 0.8, 1.0, and 1.2. Wake patterns and the drag and lift coefficients are described and compared with those from a single oscillating cylinder and two stationary cylinders. The wake patterns of two oscillating cylinders can be explained by flow mechanisms of two stationary cylinders, a single oscillating cylinder, and their combinations, and are in agreement with classifications of flow over two stationary cylinders presented in previous studies. In the case of two oscillating cylinders, the modulation phenomenon appears from a lower excitation frequency than in a single oscillating cylinder. Generally, oscillating cylinders have higher drag and root-mean-square (r.m.s.) values of drag coefficients than stationary cylinders.     

Circular cylinder wakes and vortex-induced vibrations

This paper presents a selective review of recent research on vortex-induced vibrations of isolated circular cylinders and the flow and vibration of circular cylinders in a tandem arrangement; a common thread being that the topics raised are of particular interest to the author. The influence of Reynolds number on the response of isolated cylinders is presented and recent developments using forced vibration are discussed. The response of a cylinder free to respond in the in-line and transverse directions is contrasted with that of a cylinder responding in only one direction. The interference between two circular cylinders is discussed and prominence given to the case of cylinders in a tandem arrangement. The origin of the time–mean lift force on the downstream cylinder is considered together with the cause of the large amplitude transverse vibration experienced by the cylinder above vortex resonance. This wake-induced vibration is shown to be a form of vortex-induced vibration.     

Formation of vortex street and vortex pair from a circular cylinder oscillating in water

The flow around a circular cylinder undergoing sinusoidal oscillating movement in still water is investigated by phase-locked PIV measurements. The pattern and development of large-scale vortex structures in the flow are studied from the velocity vectors and vorticity contours obtained at eight successive phases of an oscillating cycle. Experiments are performed at three Keulegan–Carpenter numbers; KC=12, 6.28 and 4.25. Results at KC=12 reveal the mechanism of vortex formation and the development of the shed vortices into a vortex street at a lateral direction to the line of cylinder movement. The role of a biased flow stream and the length of the cylinder stroke in the formation of the vortex street are discussed. At the lower KC numbers, a symmetric pair of vortices is found attached to the leeward face of the cylinder. The vortex pair exhibits an increasing degree of asymmetry when KC increases from 4.25 to 6.28. An explanation in terms of the length of the cylinder strokes and the degree of flow asymmetry is offered for the transition of flow regimes from a vortex pair to a vortex street. The present results are compared with the observations made in previous experimental and numerical studies in the literature.     

侧柱与串列双柱绕流之间的干扰

本文给出了关于串列双柱与创柱间流动干扰的实验研究结果。当三个圆柱排成等边三角形并靠得很近时，由于三圆柱间强烈的缝隙流动，大大地改变了绕流其中的串列双圆柱的流态。特别，当三圆柱中心距等于二倍圆柱直径时，在串列双柱的前、后柱之间形成了强烈的偏斜的缝隙流，出现了独特的压力分布以及要比单柱高出三倍以上的旋涡脱落频率。     

Stability of viscoelastic flow around periodic arrays of cylinders

Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (We_c), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above We_c which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above We_c a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplifieds spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.     

Numerical study of flow-induced vibrations of cylinders under the action of nonlinear energy sinks (NESs)

An isolated two-dimensional circular cylinder with two linear degrees of freedom, parallel and perpendicular to the free-stream direction, and owning a nonlinear energy sink (NES) is investigated by fluid–structure interaction (FSI) simulations to assess vortex-induced vibrations (VIV) at moderate Reynolds numbers. Subsequently, the wake-induced vibration (WIV) of a pair of identical cylinders under the action of two NES in a tandem arrangement and in a proximity–wake interference regime is explored using the same approach. The NES parameters (mass, nonlinear stiffness and damping) are investigated to determine their effects on the dynamic response of a single degree of freedom (in transverse flow direction) coupled system by a reduced-order model based on an experimentally validated van der Pol oscillator. The CFD model coupled with FSI method is also validated against VIV experimental data for an isolated cylinder in a uniform flow. The study is aimed to investigate the effect of the passive suppression NES device on VIV and WIV. The amplitude response, trajectories of cylinder motion and temporal evolutions of vortex shedding are obtained by conducting a series of numerical simulations. It is found that placing a tuned NES in the cylinders can provide good suppression effect; however, the effectiveness is function of the reduced velocity.     

串列双圆柱绕流问题的数值模拟

本文运用有限体积方法,对绕串列放置的双圆柱的二维不可压缩流动进行了数值计算。为研究两圆柱不同间距对圆柱相互作用和尾流特征的影响,选取间距比Ｌ／Ｄ（Ｌ为两圆柱中心间的距离,Ｄ为圆柱直径）在１．５～５．０之间每隔０．５共八个有代表性的间距进行了计算模拟。计算均在Ｒｅ＝２００条件下进行。计算结果表明：对该绕流问题,流动特征在很大程度上取决于间距的大小。且间距存在一临界值,间距比从小于临界值变化到大于临界     

Critical Reynolds number and galloping instabilities: experiments on circular cylinders

The current paper considers large galloping-like vibrations of circular cylinders, generically inclined and yawed to the flow. The case of a round section prone to galloping is seemingly a paradox since rotational symmetry (or close to it) and classical galloping are apparently contradictory. Still there seems to be a range of wind speeds far from those for typical Kármán vortex shedding resonance where such a phenomenon does occur. Experimental results from both static and dynamic large-scale rigid cable models, presented here, show that this range coincides with the critical Reynolds number regime, where notable symmetry-breaking characteristics such as nonzero mean lift emerge. It is shown that a fundamental difference between the inclined and non-inclined cylinder aerodynamics may exist accommodating different pressure distributions and different resulting dynamic behaviours. Unsteady pressure measurements showing avalanche-like “jumps” and vortex dislocations building between cell structures in the cylinder spanwise direction are conjectured to be a key element in the unstable behaviour experienced.     

Vortex-induced vibrations of a diamond cross-section: Sensitivity to corner sharpness

This paper studies the fluid–structure interaction of an elastically mounted square cross-section cylinder immersed in a free stream. The cross-section is mounted such that its sides are at 45° to the free stream direction, in a “diamond” configuration, and its motion is constrained to the transverse direction relative to the flow direction. Apart from the cross-section, this setup is the same as the majority of single-degree-of-freedom vortex-induced vibration studies of cylinders. Two-dimensional direct numerical simulations of this system have been performed. The Reynolds number based on the point-to-point distance of the cross-section has been fixed at Re=200). Simulations at this Reynolds number allow a direct comparison with previous results from circular cylinders, and therefore focus directly on the impact of the geometry.The sensitivity of the flow, and therefore the motion of the cylinder, to geometrical effects is considered. This is done by rounding the two side corners (those pointing across the flow) at a given radius. For well-rounded corners, the flow behaviour resembles that of a circular cylinder undergoing vortex-induced vibration. However, below a critical radius, the dynamics are considerably altered. Highly disordered and irregular wakes and body motions are observed, as well as a synchronized, periodic P+S wake mode (Williamson and Roshko, 1988), which consists of a pair of vortices on one side, and a single vortex on the other side, shed per oscillation cycle, which results in a non-zero mean lift force. A period-doubled version of this P+S wake is also presented. The spatial structure, and the spatio-temporal symmetries of each of these modes is reported. The results show that even though the spatio-temporal symmetry of the flow is unaffected by the geometry when the body is rigidly mounted (the flow always saturating to a Kármán vortex street) geometric features such as sharp corners can induce a number of spontaneous symmetry breaking bifurcations when the body is elastically mounted. Which of these various modes is observed is shown to be a function of both the corner radius and the spring stiffness, expressed through the reduced velocity.     

Coherent and turbulent processes in the bistable regime around a tandem of cylinders including reattached flow dynamics by means of high-speed PIV

The turbulent flow around two cylinders in tandem at the sub-critical Reynolds number range of order of 10⁵ and pitch to diameter ratio of 3.7 is investigated by using time-resolved Particle Image Velocimetry (TRPIV) of 1 kHz and 8 kHz. The bi-stable flow regimes including a flow pattern I with a strong vortex shedding past the upstream and the downstream cylinder, as well as a flow pattern II corresponding to a weak alternating vortex shedding with reattachment past the upstream cylinder are investigated. The structure of this “reattachment regime” has been analyzed in association with the vortex dynamics past the downstream cylinder, by means of POD and phase-average decomposition. These elements allowed interconnection among all the measured PIV planes and hence analysis of the reattachment structure and the flow dynamics past both cylinders. The results highlight fundamental differences of the flow structure and dynamics around each cylinder and provide the ‘gap’ flow nature between the cylinders. Thanks to a high-speed camera of 8 kHz, the shear-layer vortices tracking has been possible downstream of the separation point and the quantification of their shedding frequency at the present high Reynolds number range has been achieved. This issue is important regarding fluid instabilities involved in the fluid–structure interaction of cylinder arrays in nuclear reactor systems, as well as acoustic noise generated from the tandem cylinders of a landing gear in aeronautics.     

Investigation of turbulent flow past a yawed wavy cylinder

A large eddy simulation (LES) study was conducted to investigate the three-dimensional characteristics of the turbulent flow past wavy cylinders with yaw angles from 0° to 60° at a subcritical Reynolds number of 3900. The relationships between force coefficients and vortex shedding frequency with yaw angles for both wavy cylinders and circular cylinders were investigated. Experimental measurements were also performed for the validation of the present LES results. Comparing with corresponding yawed circular cylinders at similar Reynolds number, significant differences in wake vortex patterns between wavy cylinder and circular cylinder were observed at small yaw angles. The difference in wake pattern becomes insignificant at large yaw angles. The mean drag coefficient and the Strouhal number obey the independence principle for circular cylinders at yaw angle less than 45°, while the independence principle was found to be unsuitable for yawed wavy cylinders. In general, the mean drag coefficients and the fluctuating lift coefficients of a yawed wavy cylinder are less than those of a corresponding yawed circular cylinder at the same flow condition. However, with the increase of the yaw angle, the advantageous effect of wavy cylinder on force and vibration control becomes insignificant.     

Resonance in flow past oscillating cylinder under subcritical conditions

Flow around an oscillating cylinder in a subcritical region are numerically studied with a lattice Boltzmann method(LBM). The effects of the Reynolds number,oscillation amplitude and frequency on the vortex wake modes and hydrodynamics forces on the cylinder surface are systematically investigated. Special attention is paid to the phenomenon of resonance induced by the cylinder oscillation. The results demonstrate that vortex shedding can be excited extensively under subcritical conditions, and the response region of vibration frequency broadens with increasing Reynolds number and oscillation amplitude. Two distinct types of vortex shedding regimes are observed. The first type of vortex shedding regime(VSR I) is excited at low frequencies close to the intrinsic frequency of flow, and the second type of vortex shedding regime(VSR II)occurs at high frequencies with the Reynolds number close to the critical value. In the VSR I, a pair of alternately rotating vortices are shed in the wake per oscillation cycle,and lock-in/synchronization occurs, while in the VSR II, two alternately rotating vortices are shed for several oscillation cycles, and the vortex shedding frequency is close to that of a stationary cylinder under the critical condition. The excitation mechanisms of the two types of vortex shedding modes are analyzed separately.     

分块法研究圆柱绕流升阻力

使用新的分块耦合方法，分别对单圆柱和串列双圆柱绕流进行了数值模拟．对于单圆柱绕流，低Re下计算所得到的定常涡尺寸与实验非常接近．对于串列双圆柱绕流，研究分析了改变双圆柱中心间距对上下游圆柱的升阻力系数和脉动频率所产生的影响，计算结果与实验非常吻合，为进一步研究涡致振动提供了依据．     

Passive control of wake flow by two small control cylinders at Reynolds number 80

Passive control of the wake behind a circular cylinder in uniform flow is studied by numerical simulation at Re_D=80. Two small control cylinders are placed symmetrically along the separating shear layers at various stream locations. In the present study, the detailed flow mechanisms that lead to a significant reduction in the fluctuating lift but maintain the shedding vortex street are clearly revealed. When the stream locations lie within 0.8≤X_C/D≤3.0, the alternate shedding vortex street remains behind the control cylinders. In this case, the symmetric standing eddies immediately behind the main cylinder and the downstream delay of the shedding vortex street are the two primary mechanisms that lead to a 70–80% reduction of the fluctuating lift on the main cylinder. Furthermore, the total drag of all the cylinders still has a maximum 5% reduction. This benefit is primarily attributed to the significant reduction of the pressure drag on the main cylinder. Within X_C/D>3.0, the symmetry of the standing eddy breaks down and the staggered vortex street is similar to that behind a single cylinder at the same Reynolds number. In the latter case, the mean pressure drag and the fluctuating lift coefficients on the main cylinder will recover to the values of a single cylinder.     

基于浸入边界-格子Boltzmann通量求解法的椭圆柱流动特性分析

基于浸入边界-格子Boltzmann通量求解法,开展了雷诺数Re=100不同几何参数下单椭圆柱及串列双椭圆柱绕流流场与受力特性对比研究。结果表明,随长短轴比值的增加,单椭圆柱绕流阻力系数先减小后缓慢上升,最大升力系数则随长短轴比值的增大而减小;尾迹流动状态从周期性脱落涡到稳定对称涡。间距是影响串列圆柱及椭圆柱流场流动状态的主要因素,间距较小时,串列圆柱绕流呈周期性脱落涡状态,而椭圆柱则为稳定流动;随着间距增加,上下游圆柱及椭圆柱尾迹均出现卡门涡街现象,且串列椭圆柱临界间距大于串列圆柱。串列椭圆柱阻力的变化规律与圆柱的基本相同,上游平均阻力大于下游阻力;上游椭圆柱阻力随着间距的变大先减小,下游随间距的变大而增加,当间距达到临界间距时上下游阻力跃升,随后出现小幅度波动再逐渐增加,并趋近于相同长短轴比值下单柱体绕流的阻力。     

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.