Aerodynamic control of bridge cables through shape modification: A preliminary study

This paper examines the viability of modifying bridge cable shape and surface for the purpose of controlling wind-induced vibrations. To this end, an extensive wind-tunnel test campaign was carried out on various cable shapes about the critical Reynolds number region. Cable shapes were chosen to passively modify the flow in a particular manner. Tested shapes included those which have some form of waviness, faceting and shrouding. Section models were tested using a static inclined rig, allowing them to be installed at yawed cable-wind angles for both smooth and turbulent flow conditions. The aerodynamic damping of the tested cylinders is evaluated by applying both 1- and 2-dof quasi-steady aerodynamic instability models. This allows for the prediction of regions of aerodynamic instability, as a function of flow angle and Reynolds number. Whilst the plain, wavy and faceted cylinders are predicted to suffer from either dry inclined galloping, “drag crisis” or Den Hartog galloping, the shrouded cylinder is found to be stable for all angles of attack, albeit with an increase in drag at typical design wind velocities. Finally, turbulent flow is found to introduce an increased amount of aerodynamic damping mainly by providing a more constant lift force over tested Reynolds numbers.     

Power harvesting from transverse galloping of square cylinder

The concept of exploiting galloping of square cylinders to harvest energy is investigated. The energy is harvested by attaching a piezoelectric transducer to the transverse degree of freedom. A representative model that accounts for the coupled cylinder displacement and harvested voltage is used to determine the levels of the harvested power. The focus is on the effect of the Reynolds number on the aerodynamic force, the onset of galloping, and the level of the harvested power. The quasi steady approximation is used to model the aerodynamic loads. A linear analysis is performed to determine the effects of the electrical load resistance and the Reynolds number on the onset of galloping, which is due to a Hopf bifurcation. We derive the normal form of the dynamic system near the onset of galloping to characterize the type of the instability and to determine the effects of the system parameters on its outputs near the bifurcation. The results show that the electrical load resistance and the Reynolds number play an important role in determining the level of the harvested power and the onset of galloping. The results also show that the maximum levels of harvested power are accompanied with minimum transverse displacements for both low- and high-Reynolds number configurations.     

Wake transition of two-dimensional cylinders and axisymmetric bluff bodies

This article presents a short review of the three-dimensional transition of wakes from two-dimensional bodies, such as cylinders of various cross-sectional shape, and axisymmetric tori or rings. The nature and sequence of instabilities are compared and contrasted, especially with reference to the base case of the circular cylinder wake. The latter has been the subject of intense interest and scrutiny for well over a century, and has implicitly assumed the role of providing the generic transition scenario for turbulent wake flow. For elongated cylinders with streamlined leading edges, the analogues of the instability modes for a circular cylinder become unstable in the reverse order, which may have implications for the route to wake turbulence for such bodies. As well, the analogue of mode B has a significantly increased relative spanwise wavelength and appears to have a different near-wake structure. At the other extreme, for a normal flat plate, the wake first becomes unstable to a nonperiodic mode that appears distinct from either of the dominant circular cylinder wake modes. For tori, which have a local geometry approaching a two-dimensional circular cylinder for high aspect ratios (ARs), the sequence of transitions with increasing Reynolds number is a strong function of AR. For intermediate ARs, the first occurring wake instability mode is a subharmonic mode. Possible underlying physical mechanisms leading to some of these instabilities are also examined. In particular, support is provided for the role of idealized physical instability mechanisms in controlling wavelength selection and amplification for the dominant wake instability modes. The results presented in this article focus on relevant research undertaken by the Monash group but draws in results from many other international groups.     

Numerical predictions for unsteady viscous flow past an array of cylinders

The unsteady two-dimensional flow around an array of circular cylinders submerged in a uniform onset flow is analysed. The fluid is taken to be viscous and incompressible. The array of cylinders consists of two horizontal rows extending to infinity in the upstream and downstream directions. The centre-to-centre distance between adjacent cylinders is fixed at three diameters, and the rows are staggered. Advantage is taken of spatially periodic boundary conditions in the flow direction. This reduces the computational domain to a rectangular region surrounding a single circular cylinder. Two cases, for Reynolds numbers of 1000 and 10,000, are presented.     

Secondary instabilities of the in-phase synchronized wakes past two circular cylinders in side-by-side arrangement

In the present study we investigate the secondary instability of the in-phase synchronized vortex shedding from two side-by-side circular cylinders at low Reynolds numbers. Two distinct Floquet modes become unstable for different values of the Reynolds number and of the non-dimensional gap spacing, leading to the onset of the well-known flip-flop instability of the two cylinder wakes. In both cases the two-dimensional Floquet analysis reveals that at very low Reynolds numbers, a pair of complex-conjugate multipliers crosses the unit circle, showing the same frequency as the biased gap-flow flip-over. In the past literature this behaviour has been often ascribed to a bistability of the flow. On the contrary, the present DNS and stability results provide evidence that at low Reynolds numbers, the flip-flopping behaviour originates from a Neimark–Sacker bifurcation of the in-phase shedding cycle.     

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.      

Flow investigation of circular cylinder having different cavities in shallow water

The control of the unsteady flow structure formed behind a cylinder placed horizontally in shallow water was analyzed experimentally using bare cylinder and cylinders with cavities having square and rectangular geometries, respectively. Reynolds number, Froude number and water height had been chosen as 5000, 0.27 and 90 mm, respectively and also these parameters were kept constant for all experiments. To consider the influence of height (h), the cylinder level was located at various heights from h: 0 mm to 60 mm. Furthermore, cavity angle (a) had been selected from 0°, 80°, 85°, 90° and 95° to consider influence of cavity angle on flow. With the help of Particle Image Velocimetry (PIV), average velocity vectors were measured in two dimensions at many points simultaneously in a planar flow area. The results uncovered that large negative counter was observed at h: 37.5 mm in bare cylinder as well as cylinders having square and rectangular cavities at h: 45 mm. Also, no negative counter was observed for cylinders having rectangular cavity at h: 0 mm and a: 90° and 95° due to the bottom effect. Due to surface effects, a foci point was formed in all cylinders where close to the surface and close to the base. Two foci points and a saddle point were seen as they moved away from the surface for all cylinders. Also, the smallest vortex region was observed for cylinders having rectangular cavity at h: 37.5 mm and a: 90° and 95° in whole cylinders. Also, the highest drag coefficient (C_d) value was obtained for cylinder having square cavity at h: 52.5 mm and a: 80° while the highest drag coefficient value was obtained for cylinder having rectangular cavity at h: 37.5 mm and a: 95°.     

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.     

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.     

Numerical Simulation of Aerodynamic Characteristics of Two Rectangular Cylinders in Side-by-side Arrangement

We present numerical results of flows around two rectangular cylinders in side-by-side arrangement by three-dimensional computations. The two rectangular cylinders are arranged with various distances between the cylinders. The three-dimensional flow structures around two rectangular cylinders denote significant features depending on the distance between the cylinders. In our computations, the Reynolds number Re is set as 10,000, and both the aspect ratio of section of two rectangular cylinders and the distance between the cylinders are considered as parameters to calculate the flow around two rectangular cylinders. The obtained numerical results are also compared with experimental data.     

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.     

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.      

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.     

Numerical simulation of three-dimensional instability of flow past a short cylinder

The plane-parallel flow past an infinitely long circular cylinder becomes three-dimensional starting with Reynolds numbers Re ≈ 190. The corresponding instability mode is called mode A. When Re ≈ 260, vortex structures with a smaller cross scale are formed in the wake as a result of a secondary three-dimensional instability (mode B). The transition to three-dimensionality for a short cylinder bounded by planes is considered. The length of the cylinder is chosen to eliminate the unstable perturbations of mode A. Two instability modes similar to modes A and B modified under the effect of the bounding lateral planes are found. The problems of three-dimensional flow are numerically solved using the Navier-Stokes equations.     

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.     

Electromagnetic control of seawater flow around circular cylinders

We investigate numerically the electromagnetic control of seawater flows over an infinitely long circular cylinder. Stripes of electrodes and magnets, wrapped around the cylinder surface, produce a tangential body force (Lorentz force) that stabilizes the flow. This mechanism delays flow separation, reduces drag and lift, and finally suppresses the von Kármán vortex street. Results from two-dimensional simulations of the Navier–Stokes equations in a range 10<Re<300 and Lorentz force calculations are presented. Emphasis is placed on the disclosure of physical phenomena as well as a quantitative detection of the flow field and forces. It is shown that the drag strongly depends on the geometry of the electromagnetic actuator and on its location at the cylinder surface. The effect of flow control increases with larger Reynolds numbers, since the boundary layer thickness and the penetration depth of the Lorentz force are closely connected.     

SOME EXPERIMENTS ON FLOW-INDUCED VIBRATION OF A CIRCULAR CYLINDER WITH SURFACE ROUGHNESS

Aeroelastic instability of a circular cylinder with surface roughness was experimentally studied by free-oscillation tests in a wind tunnel. Flows at high Reynolds numbers could be simulated at relatively low wind velocities, by introducing surface roughness, so as to reduce the value of the critical Reynolds number. The response amplitudes of a roughened cylinder oscillating in the transverse (cross-flow) direction in the flow were measured. The measured range of reduced velocity is about 1·5–8, which includes the critical velocity. The value of a reduced mass-damping parameter (the Scruton number) is constant at about 6. For the aeroelastic instability in the transverse direction, it was found that the oscillation of the roughened cylinder induced by a vortex-excitation is damped down in a small velocity range covering the critical Reynolds number. At Reynolds numbers higher than the critical value, a roughened cylinder vibrates with a large amplitude again, associated with a lock-in phenomenon due to the coincidence of the wake-frequency and the natural frequency of the oscillating 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.