Analyzing the fluctuating pressures acting on a circular cylinder using stochastic decomposition

Fluctuating wind pressures acting on bluff bodies are influenced by approaching turbulence and signature (body-induced) turbulence. For a circular cylinder, the signature turbulence is closely related to the formation of Karman vortex shedding. In this paper, proper orthogonal decomposition (POD) and spectral proper transformation techniques (SPT) are applied to the pressure fluctuations acting on a circular cylinder. The physical relationships between the decomposed modes and vortex shedding are discussed to identify the dominant aerodynamic behavior (lift or drag) and to evaluate its contribution to overall behavior. The effect of Reynolds number (Re) is also addressed. It is found that the application of POD and SPT can separate the along-wind and across-wind effects on the cylinder model in both subcritical and supercritical regimes. In contrast to POD, the SPT mode is formulated in the frequency domain, and the dynamic coherent structures can be defined in terms of amplitude and phase angle, which allows detection of the advection features of vortex shedding. In addition, it is observed that the energy contribution of the shedding induced lift force increases with Re and gradually becomes a dominant aerodynamic force at Reynolds numbers in the supercritical regime.     

Numerical simulation of two-degree-of-freedom vortex-induced vibration of a circular cylinder close to a plane boundary

Two-degree-of-freedom vortex-induced vibrations (VIV) of a circular cylinder close to a plane boundary are investigated numerically. The Reynolds-Averaged Navier-Stokes (RANS) equations are solved using the Arbitrary Lagrangian Eulerian (ALE) scheme with a k-ω turbulence model closure. The numerical model is validated against experimental data of VIV of a cylinder in uniform flow and VIV of a cylinder close to a plane boundary at low mass ratios. The numerical results of the vibration mode, vibration amplitude and frequency agree well with the experimental data. VIV of a circular cylinder close to a plane boundary is simulated with a mass ratio of 2.6 and gap ratios of e/D=0.002 and 0.3 (gap ratio is defined as the ratio of gap between the cylinder and the bed (e) to cylinder diameter (D)). Simulations are carried out for reduced velocities ranging from 1 to 15 and Reynolds numbers ranging from 1000 to 15 000. It is found that vortex-induced vibrations occur even if the initial gap ratio is as small as e/D=0.002, although reported research indicated that vortex shedding behind a fixed circular cylinder is suppressed at small gap ratios (e/D<0.3 or 0.2). It was also found that vibration amplitudes are dependant on the bouncing back coefficient when the cylinder hits the plane boundary. Three vortex shedding modes are identified according to the numerical results: (i) single-vortex mode where the vortices are only shed from the top of the cylinder; (ii) vortex-shedding-after-bounce-back mode; (iii) vortex-shedding-before-bounce-back mode. It was found that the vortex shedding mode depends on the reduced velocity.     

CHARACTERISTICS OF LOW-FREQUENCY VARIATIONS EMBEDDED IN VORTEX-SHEDDING PROCESS

Experiments were made to study the flow characteristics in the near-wake region of a two-dimensional bluff body, namely a trapezoidal cylinder (prism) or a circular cylinder. The instantaneous velocity signals obtained at the inner edge of the separated shear layer and in the neighbourhood of the rear end of the vortex formation region show the presence of low-frequency variations at Reynolds numbers of 10⁴. The low-frequency variations noted in the velocity signals and the base pressure measured at the bluff body appear to be well correlated. These experimental observations suggest a physical picture that the variations of vortex formation length and base pressure are closely related in a real-time manner.     

Vortex shedding from a circular cylinder with a slit and concave rear surface

Vortex shedding from short circular cylinders with a slit was studied using a flow visualization and amplitude spectrum analysis of a thermoanemometry probe signal. It was found that a circular cylinder with a slit and concave rear surface produces stronger vortices than other bluff cylinders but that these vortices are very vulnerable to the end wall conditions. It was established that two small splitter plates (tails) fixed directly behind the cylinder at the end walls effectively isolate the vortices shed from the cylinder from the end wall boundary layer effects. For this arrangement a perfect regularity of vortex shedding and almost constant Strouhal number were achieved in the Reynolds number test range of about 250 to 43,000.On a leave from Technical University, 60965 Poznan, Piotrowo 3, Poland.     

外部激励Stuart-Landau模型的数值研究

将非线性常微分方程组周期解的求解看作一个边值问题 ,运用Newton迭代构造求解这组方程的数值方法。利用上述方法求得了激励Stuart Landau方程的周期解 ,研究了圆柱振动对圆柱后Karman涡街的抑制现象 ,和振动的频率锁定现象 ,证明了激励Stuart Landau方程描写钝体尾迹动力系统的有效性     

Experimental study on the wake behind tapered circular cylinders

The flow around tapered cylinders can act as basic models for numerous bluff body flows with a spanwise variation of either the body shape or the inflow conditions. The well-known vortex street is influenced by strong three-dimensional effects from the spanwise variation of the shedding frequency, namely oblique vortex shedding and vortex dislocations. Stereo-PIV was chosen to study these phenomena, since it allows analyzing planes with the full three-component, instantaneous velocity fields and local, time-dependent variations in the same setting. Hence, detailed aspects of the vortex dislocation phenomenon are presented. Single vortex dislocation events are presented through the local variation of the three measured velocity components u, v and w. Longer time-series reveal both period and location of these dislocation events, as well as quantity and sizes of the cells of constant shedding velocity in between them. The influence of the Reynolds number and the cylinder aspect ratio on the vortex cells could be shown. The analysis of the vortex shedding behavior shows good agreement with previously published results. At the same time, the applied PIV technique provides more spatial information than point-based measurements and offers insight into a Reynolds number range that is currently out of reach of Direct Numerical Simulations.     

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.     

钝体尾流控制机理及方法研究进展

首先从涡脱落生成理论出发对钝体尾流控制方法进行了分类,并简单介绍了国内尾流控制研究情况. 之后介绍了我们用窄条或小方柱取代小圆柱后,对Strykowsky和Sreenivasan 控制方法的改进及其在高雷诺数下对圆柱和方柱尾流涡脱落的有效抑制情况, 并探讨了控制件钝度对抑制效果的影响.第3部分用实验数据对各个涡脱落生成模型做了分析与检验, 指出控制件方法的机理与改变钝体分离位置、减小钝体背压吸力、改变流动的展向相关性、 防止钝体两侧剪切层相互作用等无关,而与钝体近尾流速度剖面的局部修正及其稳定性的改变有关. 最后简单介绍了控制件方法今后研究工作展望及其工程应用前景.     

Hydrodynamics of flow over a transversely oscillating circular cylinder beneath a free surface

In this paper, hydrodynamic force coefficients and wake vortex structures of uniform flow over a transversely oscillating circular cylinder beneath a free surface were numerically investigated by an adaptive Cartesian cut-cell/level-set method. At a fixed Reynolds number, 100, a series of simulations covering three Froude numbers, two submergence depths, and three oscillation amplitudes were performed over a wide range of oscillation frequency. Results show that, for a deeply submerged cylinder with sufficiently large oscillation amplitudes, both the lift amplitude jump and the lift phase sharp drop exist, not accompanied by significant changes of vortex shedding timing. The near-cylinder vortex structure changes when the lift amplitude jump occurs. For a cylinder oscillating beneath a free surface, larger oscillation amplitude or submergence depth causes higher time-averaged drag for frequency ratio (=oscillation frequency/natural vortex shedding frequency) greater than 1.25. All near-free-surface cases exhibit negative time-averaged lift the magnitude of which increases with decreasing submergence depth. In contrast to a deeply submerged cylinder, occurrences of beating in the temporal variation of lift are fewer for a cylinder oscillating beneath a free surface, especially for small submergence depth. For the highest Froude number investigated, the lift frequency is locked to the cylinder oscillation frequency for frequency ratios higher than one. The vortex shedding mode tends to be double-row for deep and single-row for shallow submergence. Proximity to the free surface would change or destroy the near-cylinder vortex structure characteristic of deep-submergence cases. The lift amplitude jump is smoother for smaller submergence depth. Similar to deep-submergence cases, the vortex shedding frequency is not necessarily the same as the primary-mode frequency of the lift coefficient. The frequency of the induced free surface wave is exactly the cylinder oscillation frequency. The trends of wave length variation with the Froude number and frequency ratio agree with those predicted by the linear theory of small-amplitude free surface waves.     

虚拟边界法研究正交双圆柱及串列双圆球绕流

把Goldstein等人提出的虚拟边界法推广到三维情况,研究了 Re=150时不同间距下正交双圆柱绕流,和Re=250时不同间距下串列双 圆球绕流流场. 对于正交双圆柱绕流,当间距比大于3,下游圆柱对上游圆柱尾流的影响只 限定在下游圆柱的尾流所扫过的范围之内;当间距比小于等于3,下游圆柱对上游圆柱尾流 的影响扩大,下游圆柱尾流扫过区上下出现两排三维流向二次涡结构. 对于串列圆球绕流, 研究发现,在小间距比(L/D≈ 1.5)的情况下,由于上下游圆球尾流区的相互抑 制消除了压力不稳定性,整个流场呈现稳 态轴对称特征;间距比为2.0时,周向压力梯度诱发出流体的周向输运,流场呈现稳态非对 称性,但流场中存在特定的对称面;间距比增大到2.5后,绕流场开始周期振荡,原有的对 称面依旧存在;在间距比3.5时下游圆球下表面的涡结构强度有所减弱,导致占优频率发生 交替;间距比增至7.0时,整个流场恢复稳态特征,两圆球尾部同时出现双线涡,这时流场 对称面的位置发生了变动.     

Bluff body wakes with free, fixed, and discontinuous separation at low Reynolds numbers and low aspect ratio

Some comparative experimental results are presented of bluff body wakes with free, fixed, and discontinuous separation. The particular examples considered are a circular cylinder, a plain blunt trailing edge aerofoil and a segemented blunt trailing edge aerofoil. The evolution of the near wake and vortex shedding modes are compared and discussed.     

Turbulence properties in the cylinder wake at high Reynolds numbers

The present contribution analyses the turbulence properties in unsteady flows around bluff body wakes and provides a database for improvement and validation of turbulence models, concerning the present class of nonequilibrium flows. The flow around a circular cylinder with a low aspect ratio and a high blockage coefficient is investigated. This confined environment is used in order to allow direct comparisons with realisable 3-D Navier–Stokes computations avoiding ‘infinite’ conditions. The flow is investigated in the beginning of the critical regime at Reynolds number 140 000. The analysis is carried out by means of 2-D PIV, of 3-C PIV and of high-frequency 2-D PIV. The experimental analysis contributes to confirm the validity of advanced statistical turbulence modelling for unsteady flows around bodies.     

Vortex shedding from a circular cylinder near a moving wall

Flow over a circular cylinder near a moving plane wall is simulated numerically. The influence of the moving wall on the vortex shedding from the cylinder is demonstrated and the corresponding mechanism is illustrated using instability theory. A critical gap ratio between the circular cylinder and the moving wall is defined, and a precise method for determining the critical gap ratio is proposed. The drag and lift forces and the pressure coefficient are presented as a function of the gap ratio. The scaling of the Strouhal number is discussed.     

Vortex shedding flow behind a slowly rotating circular cylinder

This paper investigates flow past a rotating circular cylinder at 3600?Re?5000 and α?2.5. The flow parameter α is the circumferential speed at the cylinder surface normalized by the free-stream velocity of the uniform cross-flow. With particle image velocimetry (PIV), vortex shedding from the cylinder is clearly observed at α<1.9. The vortex pattern is very similar to the vortex street behind a stationary circular cylinder; but with increasing cylinder rotation speed, the wake is observed to become increasing narrower and deflected sideways. Properties of large-scale vortices developed from the shear layers and shed into the wake are investigated with the vorticity field derived from the PIV data. The vortex formation length is found to decrease with increasing α. This leads to a slow increase in vortex shedding frequency with α. At α=0.65, vortex shedding is found to synchronize with cylinder rotation, with one vortex being shed every rotation cycle of the cylinder. Vortex dynamics are studied at this value of α with the phase-locked eduction technique. It is found that although the shear layers at two different sides of the cylinder possess unequal vorticity levels, alternating vortices subsequently shed from the cylinder to join the two trains of vortices in the vortex street pattern exhibit very little difference in vortex strength.     

Vortex shedding and three-dimensional behaviour of flow past a cylinder confined in a channel

A numerical investigation of the flow past a circular cylinder centred in a two-dimensional channel of varying width is presented. For low Reynolds numbers, the flow is steady. For higher Reynolds numbers, vortices begin to shed periodically from the cylinder. In general, the Strouhal frequency of the shedding vortices increases with blockage ratio. In addition, a two-dimensional instability of the periodic vortex shedding is found, both empirically and by means of a Floquet stability analysis. The instability leads to a beating behaviour in the lift and drag coefficients of the cylinder, which occurs at a Reynolds number higher than the critical Reynolds number for the three-dimensional mode A-type instability, but lower than a Reynolds number for any mode B-type instability.     

Effect of blockage on critical parameters for flow past a circular cylinder

The effect of location of the lateral boundaries, of the computational domain, on the critical parameters for the instability of the flow past a circular cylinder is investigated. Linear stability analysis of the governing equations for incompressible flows is carried out via a stabilized finite element method to predict the primary instability of the wake. The generalized eigenvalue problem resulting from the finite element discretization of the equations is solved using a subspace iteration method to get the most unstable eigenmode. Computations are carried out for a large range of blockage, 0.005?D/H ?0.125, where D is the diameter of the cylinder and H is the lateral width of the domain. A non‐monotonic variation of the critical Re with the blockage is observed. It is found that as the blockage increases, the critical Re for the onset of the instability first decreases and then increases. However, a monotonic increase in the non‐dimensional shedding frequency at the onset of instability, with increase in blockage, is observed. The increased blockage damps out the low‐frequency modes giving way to higher frequency modes. The blockage is found to play an important role in the scatter in the data for the non‐dimensional vortex shedding frequency at the onset of the instability, from various researchers in the past. Copyright © 2005 John Wiley & Sons, Ltd.     

In-cylinder tumble flows and performance of a motorcycle engine with circular and elliptic intake ports

The temporal and spatial evolution processes of the flows in the cylinder of a four-valve, four-stroke, single cylinder, reciprocating motorcycle engine installed with the elliptic and circular intake ports were experimentally studied by using the particle image velocimetry (PIV). The engine was modified to fit the requirements of PIV measurement. The velocity fields measured by the PIV were analyzed and quantitatively presented as the tumble ratio and turbulence intensity. In the symmetry plane, both the circular and elliptic intake ports could initiate a vortex around the central region during the intake stroke. During the compression stroke, the central vortex created in the cylinder of the engine with the circular intake port disappeared, while that in the engine cylinder with the elliptic intake port further developed into the tumble motion. In the offset plane, weak vortical structures were initiated by the bluff-body effect of the intake valves during the intake stroke. The vortical structures induced by the elliptic intake port were more coherent than those generated by the circular intake port; besides, this feature extends to the compression stroke. The cycle-averaged tumble ratio and the turbulence intensity of the engine with the elliptic intake port were dramatically larger than those of the engine with the circular intake port. The measured engine performance was improved a lot by installing the elliptic intake port. The correlation between the flow features and the enhancement of the engine performance were argued and discussed.     

Roughness and turbulence intensity effects on the induced flow oscillation of a single cylinder

The effects of the surface roughness and the turbulence intensity on the dynamic characteristics of the flow induced oscillations of an elastically supported single circular cylinder in a cross flow in the vortex shedding and fluid elastic regions were experimentally investigated. The results of these experiments indicate that, for the vortex shedding region, increasing the surface roughness results in a reduction of the amplitude of oscillation, while in the fluid elastic region, increasing the surface roughness tends to enhance the oscillations. A similar trend for the dynamic response of the cylinder in the vortex shedding region was also observed when the free stream turbulence intensity was varied, while in the fluid elastic region variations in the free stream turbulence intensity were observed to have no drastic effect on the dynamic response of the cylinder.     

Roughness and turbulence intensity effects on the induced flow oscillation of a single cylinder

The effects of the surface roughness and the turbulence intensity on the dynamic characteristics of the flow induced oscillations of an elastically supported single circular cylinder in a cross flow in the vortex shedding and fluid elastic regions were experimentally investigated. The results of these experiments indicate that, for the vortex shedding region, increasing the surface roughness results in a reduction of the amplitude of oscillation, while in the fluid elastic region, increasing the surface roughness tends to enhance the oscillations. A similar trend for the dynamic response of the cylinder in the vortex shedding region was also observed when the free stream turbulence intensity was varied, while in the fluid elastic region variations in the free stream turbulence intensity were observed to have no drastic effect on the dynamic response of the cylinder.     

Hydrodynamic forces on dual cylinders of different diameters in steady currents

Turbulent flow past two circular cylinders of different diameters is numerically investigated. The two-dimensional Reynolds-averaged Navier–Stokes equations are solved by using a finite element method with a k–ω turbulence closure. Following a relevant numerical model validation process, effects of cylinder gap-to-diameter ratio, the angular position of the smaller cylinder and the diameter ratio of cylinders on the vortex shedding and the forces on the cylinders are investigated using the numerical model. It is found that the relative position of the small cylinder has significant effects on the hydrodynamic force and vortex shedding characteristics of the cylinders.