Global aerodynamic instability of twin cylinders in cross flow

This paper comprises an in-depth physical discussion of the flow-induced vibration of two circular cylinders in view of the time-mean lift force on stationary cylinders and interaction mechanisms. The gap-spacing ratio T/D is varied from 0.1 to 5 and the attack angle α from 0° to 180° where T is the gap width between the cylinders and D is the diameter of a cylinder. Mechanisms of interaction between two cylinders are discussed based on time-mean lift, fluctuating lift, flow structures and flow-induced responses. The whole regime is classified into seven interaction regimes, i.e., no interaction regime; boundary layer and cylinder interaction regime; shear-layer/wake and cylinder interaction regime; shear-layer and shear-layer interaction regime; vortex and cylinder interaction regime; vortex and shear-layer interaction regime; and vortex and vortex interaction regime. Though a single non-interfering circular cylinder does not correspond to a galloping following quasi-steady galloping theory, two circular cylinders experience violent galloping vibration due to shear-layer/wake and cylinder interaction as well as boundary layer and cylinder interaction. A larger magnitude of fluctuating lift communicates to a larger amplitude vortex excitation.     

Dynamic surface pressure measurements on a square cylinder with pressure sensitive paint

The dynamic and static surface pressure on a square cylinder during vortex shedding was measured with pressure sensitive paints (PSPs) at three angles of incidence and a Reynolds number of 8.9×10⁴. Oscillations in the phosphorescence intensity of the PSP that occurred at the vortex shedding frequency were observed. From these phosphorescent oscillations, the time-dependent changes in pressure distribution were calculated. This work extends PSP’s useful range to dynamic systems where oscillating pressure changes are on the order of 230 Pa and occur at frequencies in the range of 95–125 Hz.     

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.      

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.      

Experimental and theoretical investigation of galloping of transversely inclined slender prisms

Galloping is characterized by large and periodical oscillations which may lead to collapse of slender structures. This study is the first attempt of a comprehensive experimental and theoretical investigation of galloping of transversely inclined prisms. A modified quasi-steady model is proposed with a constant term to estimate the galloping of a transversely inclined prism, which is later experimentally investigated by conducting a static Synchronous Multi-Pressure Sensing System (SMPSS) test and an aeroelastic test in a boundary layer wind tunnel. The galloping responses of the prisms were measured in the aeroelastic test, while the aerodynamic force coefficients were determined from the SMPSS test. These experimental results were subsequently utilized to validate the quasi-steady model. Based on the proposed model, the galloping responses of the prisms were predicted and compared with the experimental results. The experimentally measured and theoretically predicted galloping responses are discussed with respect to aerodynamic damping ratios, onset galloping wind speeds, distributed pressure coefficients, point pressure spectra and vortex shedding frequencies. Interesting findings are summarized.     

ON THE AEROELASTIC BEHAVIOUR OF RECTANGULAR CYLINDERS IN CROSS-FLOW

An experimental and numerical study of the aeroelastic behaviour of elongated rectangular and square cylinders is presented. The main results are for a rectangular section with an aspect ratio of 2. The experiments were performed with a flexible cylinder clamped at both ends. This configuration leads to unusual lock-in of the vortex shedding with different bending modes, although the final steady oscillations occur in the fundamental mode. The galloping regime is also investigated, and the effect of free-stream turbulence intensity. Critical velocities are detected which do not correspond to calculations using the quasi-steady theory. A simple modelling of galloping is proposed to better fit the experiments, but it is shown that some of the configurations, in turbulent flow, are probably interacting with the vortex shedding and make the modelling inefficient. Numerical simulations on a 2-D rectangular section are presented and the resulting wall pressure distributions are analysed using the proper orthogonal decomposition technique. Indicators are proposed in order to link the proper functions with their contribution to the aerodynamic force components, and then a classification of the proper shapes of the decomposition is done. It is shown by comparison between the static case and forced oscillations, in the galloping range, that secondary vortices inside the shear layer become symmetrical and their effect on the forces is cancelled.     

Three-dimensional evolution of vortices and early features of coherent structure in the turbulent wake behind a 2-D circular cylinder

3-D evolution of Kármán vortex filaments and vortex filaments in braid regions in the turbulent wake of a 2-D circular cylinder is investigated numerically based on inviscid vortex dynamics by analyzing the response of the initially 2-D spanwise vortex filaments to periodic spanwise disturbance of varying magnitude, wavelength and initial phase angles. Our results reveal a kind of 3-D vortex system in the wake which consists of large scale horseshoe-shaped vortices and small scale γ-shaped vortex filaments as well as vortex loops. The mechanism and the dynamic process about the generation of streamwise vortical structure and the 3-D coherent structure are reported. currently published in the Chinese Edition of Acta Mechanica Sinica, Vol.25, No.3, 1993 The project supported by National Natural Science Foundation of China and the National Basic Research Project “Nonlinear Science”     

A unified approach to aerodynamic damping and drag/lift instabilities,and its application to dry inclined cable galloping

Inclined cables of cable-stayed bridges often experience large amplitude vibrations. One of the potential excitation mechanisms is dry inclined cable galloping, which has been observed in wind tunnel tests but which has not previously been fully explained theoretically. In this paper, a general expression is derived for the quasi-steady aerodynamic damping (positive or negative) of a cylinder of arbitrary cross-section yawed/inclined to the flow, for small amplitude vibrations in any plane. The expression covers the special cases of conventional quasi-steady aerodynamic damping, Den Hartog galloping and the drag crisis, as well as dry inclined cable galloping. A nondimensional aerodynamic damping parameter governing this behaviour is proposed, which is a function of only the Reynolds number, the angle between the wind velocity and the cable axis, and the orientation of the vibration plane. Measured static force coefficients from wind tunnel tests have been used with the theoretical expression to predict values of this parameter. Two main areas of instability (i.e. negative aerodynamic damping) have been identified, both in the critical Reynolds number region, one of which was previously observed in separate wind tunnel tests on a dynamic cable model. The minimum values of structural damping required to prevent dry inclined cable galloping are defined, and other factors in the behaviour in practice are discussed.     

Thermal characteristics of the wake shear layers from a slightly heated circular cylinder

In this paper, we investigate the thermal characteristics of wake shear layers generated by a slightly heated circular cylinder. Measurements of the fluctuating temperature were made in the region x/d = 0.6 to x/d = 3 (where x is the downstream distance from the cylinder axis and d is the cylinder diameter) using a single cold-wire probe. The Reynolds number Re was varied in the range 2,600–8,600. For Re = 5,500, simultaneous measurements were made with a rake of 16 cold wires, aligned in the direction of the mean shear, at x/d = 2 and 3. The results indicate that the passive temperature can be an effective marker of various instabilities of the wake shear layers, including the Kelvin–Helmholtz (KH) instability. The temperature data have confirmed the approximate Re ^m dependence of the KH instability frequency (f _KH) with different values of m over different ranges of Re, as reported previously in the literature. However, it is found that this power-law dependence is not exact, and a third-order polynomial dependence appears to fit the data well over the full range of Re. Importantly, it is found that the wake shear-layer instabilities can be grouped into three categories: (1) one with frequencies much smaller than the Bénard–Kármán-vortex shedding frequency, (2) one associated with the vortex shedding and (3) one related to the KH instability. The low-frequency shear-layer instabilities from both sides of the cylinder are in-phase, in contrast to the anti-phase high-frequency KH instabilities. Finally, the observed streamwise decrease in the mean KH frequency provides strong support for the occurrence of vortex pairing in wake shear layers from a circular cylinder, thus implying that both the wake shear layer and a mixing layer develop in similar fashion.     

Control of vortex shedding behind circular cylinder for flows at low Reynolds numbers

It has been observed by researchers in the past that vortex shedding behind circular cylinders can be altered, and in some cases suppressed, over a limited range of Reynolds numbers by proper placement of a second, much smaller, ‘control’ cylinder in the near wake of the main cylinder. Results are presented for numerical computations of some such situations. A stabilized finite element method is employed to solve the incompressible Navier–Stokes equations in the primitive variables formulation. At low Reynolds numbers, for certain relative positions of the main and control cylinder, the vortex shedding from the main cylinder is completely suppressed. Excellent agreement is observed between the present computations and experimental findings of other researchers. In an effort to explain the mechanism of control of vortex shedding, the streamwise variation of the pressure coefficient close to the shear layer of the main cylinder is compared for various cases, with and without the control cylinder. In the cases where the vortex shedding is suppressed, it is observed that the control cylinder provides a local favorable pressure gradient in the wake region, thereby stabilizing the shear layer locally. Copyright © 2001 John Wiley & Sons, Ltd.     

Effects of an upstream inclined rod on the circular cylinder–flat plate junction flow

An inclined rod is installed upstream of a circular cylinder mounted on a flat plate to mitigate the horseshoe vortices in the junction flow. Smoke-wire visualization, hot-wire velocity measurement and surface pressure measurement are employed to study the effects of the inclined rod on the laminar and turbulent junction flows. The results show a properly placed inclined rod can significantly weaken the horseshoe vortices in front of the cylinder, depress the unsteady oscillation of the vortex system, change the separation position on the flat plate and narrow the wake of the cylinder. The inclined rod method provides a promising way to suppress the horseshoe vortices in the junction flow because of its effectiveness and its easiness to implement and adjust to fit different flow conditions.     

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.     

Formation, evolution, and decay of a vortex street in the wake of a streamlined body

The decay of a Kármán vortex street and the formation of a secondary vortex structure in the far wake of a streamlined cylinder are studied. The dynamics of spatially evolving vortex structures is examined in the free flow and in the following ways of external influence on this flow: rotation with a constant velocity and translational and rotational oscillations of the cylinder. The results are obtained by numerically solving the Navier-Stokes equations with two different methods. The corresponding boundary value problems are formulated in the domains extended up to 500 radii of the cylinder.     

A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement

This paper describes a numerical study of the two‐dimensional and three‐dimensional unsteady flow over two square cylinders arranged in an in‐line configuration for Reynolds numbers from 40 to 1000 and a gap spacing of 4D, where D is the cross‐sectional dimension of the cylinders. The effect of the cylinder spacing, in the range G = 0.3D to 12D, was also studied for selected Reynolds numbers, that is, Re = 130, 150 and 500. An incompressible finite volume code with a collocated grid arrangement was employed to carry out the flow simulations. Instantaneous and time‐averaged and spanwise‐averaged vorticity, pressure, and streamlines are computed and compared for different Reynolds numbers and gap spacings. The time averaged global quantities such as the Strouhal number, the mean and the RMS values of the drag force, the base suction pressure, the lift force and the pressure coefficient are also calculated and compared with the results of a single cylinder. Three major regimes are distinguished according to the normalized gap spacing between cylinders, that is, the single slender‐body regime (G < 0.5), the reattach regime (G < 4) and co‐shedding or binary vortex regime (G ≥4). Hysteresis with different vortex patterns is observed in a certain range of the gap spacings and also for the onset of the vortex shedding. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonlinear modeling of combined galloping and vortex-induced vibration of square sections under flow

In this paper, we propose a model for the transverse oscillation of a square-section cylinder under flow. The fluctuating transverse force due to vortex shedding is represented using a coupled nonlinear wake oscillator, while the unsteady force for galloping caused by the varying incidence angle effects is modelled using the quasi-steady approach. First, we analytically investigate the lift behavior and phase angle variation of the square cylinder under forced vibrations. Comparison with experimental data is used to determine the form of the coupling terms and its values. The present model shows advantages in predicting the phase angle, and it successfully captures the change in sign of the phase. Second, the proposed model is directly applied in predicting free oscillation cases without any tuning. The dynamical behaviors predicted by this model are compared with published experiments under different Scruton numbers, and reasonable agreement can be found. The results indicate that the model can not only be applied in simulating the “pure galloping” and “pure VIV,” but also is able to capture the interactions of VIV and galloping, including combined and separate VIV-galloping motions.

     

OBLIQUE VORTEX SHEDDING BEHIND TAPERED CYLINDERS

The vortex shedding in the wake behind linearly tapered circular cylinders has been considered for the two taper ratios 75:1 and 100:1. The Reynolds number based on the velocity of the incoming flow and the largest diameter was in the range from 130 to 180. The low Reynolds number assured that laminar flow prevailed in the entire flow field. The full unsteady three-dimensional Navier–Stokes equations were solved numerically with the view of exploring the rather complex vortex shedding phenomena caused by the variation of the natural shedding frequency along the span of the cylinder. The accurate computer simulations showed that this variation gave rise to discrete shedding cells, each with its own characteristic frequency and inclined with respect to the axis of the cylinder. Flow visualizations revealed that vortex dislocation and splitting took place in the numerically simulated flow fields. The computer simulations compared surprisingly well with the extensive laboratory experiments reported by Piccirillo & Van Atta in 1993 for a range of comparable conditions; this has enabled detailed analyses of other flow variables (notably pressure and vorticity) than those readily accessible in a physical experiment. However, distinct differences in the vortex dynamics are observed in some of the cases.     

Unsteady RANS and detached-eddy simulations of flow around a circular cylinder in ground effect

Unsteady Reynolds-averaged Navier–Stokes (URANS) simulations and detached-eddy simulations (DES) were performed of flow around a circular cylinder placed near and parallel to a moving ground, on which substantially no boundary layer developed to interfere with the cylinder. The results were compared with experiments previously reported by the authors to examine how accurately the URANS and DES can predict the cessation of von Kármán-type vortex shedding and the attendant critical drag reduction of the cylinder in ground effect. The DES, which were performed in a three-dimensional domain with spanwise periodicity imposed, correctly captured the cessation of the vortex shedding, whereas both two- and three-dimensional URANS also predicted it but at a much smaller gap-to-diameter ratio compared with the experiments. The wake structures of the cylinder predicted by the DES were in good agreement with the experiments in both large- and small-gap regimes, and also in the intermediate-gap regime, where the DES captured the intermittence of the vortex shedding in the near-wake region. Based on the results obtained, further discussions are also given to the reason why the von Kármán-type vortices in the URANS solutions incorrectly ‘survived’ until the cylinder came much closer to the ground.     

Fluid-dynamic forces and wake frequencies on a tilted rectangular cylinder near a solid wall

We investigate the impact of different boundary conditions on the flow field developing around a tilted rectangular cylinder with two different values of the aspect ratio (l/s=3 and 4). We are mainly interested in analyzing the changes in force coefficients and in the vortex shedding Strouhal number when the cylinder is placed at various distances from a bottom wall and different values of attack angle. The angle of attack ranges between −30° and +30° and the cylinder elevation above the bottom wall is varied between almost zero and 5 times the thickness of the cylinder. A large body of experimental results is related to the small elevation conditions at different attack angles, where the presence of the wall has a non-negligible effect on the behavior of the force coefficients and Strouhal number of the vortex shedding.     

A note on the numerical simulations of flow past a wavy square-section cylinder

The flow past a square-section cylinder with a geometric disturbance is investigated by numerical simulations. The extra terms, due to the introduction of mapping transformation simulating the effect of disturbance into the transformed Navier-Stokes equations, are correctly derived, and the incorrect ones in the previous literature are pointed out and analyzed. Furthermore, the relationship between the vorticity, especially on the cylinder surface, and the disturbance is derived and explained theoretically. The computations are performed at two Reynolds numbers of 100 and 180 and three amplitudes of waviness of 0.006, 0.025 and 0.167 with another aim to explore the effects of different Reynolds numbers and disturbance on the vortex dynamics in the wake and forces on the body. Numerical results have shown that, at the mild waviness of 0.025, the Kairmain vortex shedding is suppressed completely for Re = 100, while the forced vortex dislocation is appeared in the near wake at the Reynolds number of 180. The drag reduction is up to 21.6% at Re = 100 and 25.7% at Re = 180 for the high waviness of 0.167 compared with the non-wavy cylinder. The lift and the Strouhal number varied with different Reynolds numbers and the wave steepness are also obtained.     

Flow above the free end of a surface-mounted finite-height circular cylinder: A review

The wake of a surface-mounted finite-height circular cylinder and the associated vortex patterns are strongly dependent on the cylinder aspect ratio and the thickness of the boundary layer on the ground plane relative to the dimensions of the cylinder. Above a critical aspect ratio, the mean wake is characterized by streamwise tip vortex structures and Kármán vortex shedding from the sides of the cylinder. Below a critical aspect ratio, a unique mean wake structure is observed. Recent experimental studies in the literature that used phase-averaged techniques, as well as recent numerical simulations, have led to an improved physical understanding of the near-wake vortex flow patterns. However, the flow above the free end of the finite circular cylinder, and its relationship to the near wake, has not been systematically studied. The effects of aspect ratio and boundary layer thickness on the free-end flow field are also not completely understood, nor has the influence of Reynolds number on the free-end flow field been fully explored. Common features associated with the free end include separation from the leading edge, a mean recirculation zone containing a prominent cross-stream arch (or mushroom) vortex, and reattachment onto the free-surface. Other flow features that remain to be clarified include a separation bubble near the leading edge, one or two cross-stream vortices within this separation bubble, the origins of the streamwise tip or trailing vortices, and various critical points in the near-surface flow topology. This paper reviews the current understanding of the flow above the free end of a surface-mounted finite-height circular cylinder, with a focus on models of the flow field, surface oil flow visualization studies, pressure and heat flux distributions on the free-end surface, measurements of the local velocity field, and numerical simulations, found in the literature.