Vortex shedding and aerodynamic forces on a circular cylinder in linear shear flow at subcritical Reynolds number

Vortex shedding and aerodynamic forces on a circular cylinder in a linear shear flow with its axis normal to the plane of the velocity shear profile at subcritical Reynolds number are investigated experimentally. The shear parameter β, which is based on the velocity gradient, cylinder diameter and upstream mean velocity at the center plane of the cylinder, varies from 0 to 0.27. The Strouhal number has no significant variation with the shear parameter. The time-mean base pressure increases and the fluctuating component of the base pressure decreases significantly with increasing shear parameter. Vortex shedding is suppressed by the velocity shear. Dislocation of the stagnation point takes place and this influences the pressure distribution around the cylinder together with the velocity shear. A mean lift force arises in the shear flow due to asymmetry of the pressure distribution, and it acts from the high velocity side to the low velocity side. In addition, the lift coefficient increases and the drag coefficient decreases with increasing shear parameter.     

旋转圆柱绕流流场特性分析

对雷诺数Re = 20000 ~ 90000、相对转速ɑ = 0 ~ 0.72的旋转圆柱后方流场进行了实验测量, 分析了旋转圆柱后方不同剖面处的速度分布规律和湍流度分布规律. 采用LES方法对旋转圆柱绕流问题进行了数值模拟, 分析旋转圆柱周围流场特性和自由剪切层变化规律, 最后通过理论模型对流场变化进行分析, 得出如下结论: 当圆柱逆时针旋转时, 同一雷诺数下随着相对转速的增加, 旋转圆柱尾迹区域下方速度突变处的位置随着相对转速的增加而上移, 而上方速度突变处的位置不变, 雷诺数的增加使旋转圆柱尾迹区域下方速度突变处位置有小幅度的下移. 通过数值模拟发现, 圆柱旋转之后, 圆柱后方下侧涡的位置明显上移, 且幅度较大. 下方的自由剪切层有明显的上移, 上方的自由剪切层位置变化较小. 最后通过理论分析发现, 圆柱后侧下方涡位置的上移对圆柱升力影响十分显著, 在高雷诺数、低相对转速的条件下, 旋转圆柱后侧下方涡位置的改变对旋转圆柱的升力、尾流区自由剪切层的变化起到了重要的影响.      

Numerical simulation of shear effect on vortex shedding behind a square cylinder

This paper is concerned with the numerical simulation of the flow structure around a square cylinder in a uniform shear flow. The calculations were conducted by solving the unsteady 2D Navier–Stokes equations with a finite difference method. The effect of the shear parameter K of the approaching flow on the vortex-shedding Strouhal number and the force coefficients acting on the square cylinder is investigated in the range K=0·0–0·25 at various Reynolds numbers from 500 to 1500. The computational results are compared with some existing experimental data and previous studies. The effect of shear rate on the Strouhal number and the force acting on the cylinder has a tendency to reduce the oscillation. The Strouhal number, mean drag and amplitude of the fluctuating force tend to decrease as the shear rate increases, but show no significant change at low shear rate. Increasing the Reynolds number decreases the Strouhal number and increases the force acting on the cylinder. At high shear rate the shedding frequencies of the fluctuating drag and lift coefficients are identical. © 1997 John Wiley & Sons, Ltd.     

On the origin of wake-induced vibration in two tandem circular cylinders at low Reynolds number

We numerically investigate flow-induced vibrations of circular cylinders arranged in a tandem configuration at low Reynolds number. Results on the coupled force dynamics are presented for an isolated cylinder and a pair of rigid cylinders in a tandem configuration where the downstream cylinder is elastically mounted and free to vibrate transversely. Contrary to turbulent flows at high Reynolds number, low frequency component with respect to shedding frequency is absent in laminar flows. Appearance and disappearance of the vorticity regions due to reverse flow on the aft part of the vibrating cylinder is characterized by a higher harmonic in transverse load, which is nearly three times of the shedding frequency. We next analyze the significance of pressure and viscous forces in the composition of lift and their phase relations with respect to the structural velocity. For both the isolated and tandem vibrating cylinders, the pressure force supplies energy to the moving cylinder, whereas the viscous force dissipates the energy. Close to the excitation frequency ratio of one, the ratio of transverse viscous force to pressure force is found to be maximum. In addition, movement of stagnation point plays a major role on the force dynamics of both configurations. In the case of isolated cylinder, displacement of the stagnation point is nearly in-phase with the velocity. During vortex-body interaction, the phase difference between the transverse pressure force and velocity and the location of stagnation point determines the loads acting on the cylinder. When the transverse pressure force is in-phase with velocity, the stagnation point moves to higher suction region of the cylinder. In the case of the tandem cylinder arrangement, upstream vortex shifts the stagnation point on the downstream cylinder to the low suction region. Thus a larger lift force is observed for the downstream cylinder as compared to the vibrating isolated cylinder. Phase difference between the transverse load and the velocity of the downstream cylinder determines the extent of upstream wake interaction with the downstream cylinder. When the cylinder velocity is in-phase with the transverse pressure load component, interaction of wake vortex with the downstream cylinder is lower compared to other cases considered in this study. We extend our parametric study of tandem cylinders for the longitudinal center-to-center spacing ranging from 4 to 10 diameter.     

大雷诺数线性剪切流绕圆柱的分离流动

本文采用离散涡方法计算了大雷诺数下线性剪切流绕圆柱的分离流动,计算结果给出阻力系数、横向力系数、边界层分离点、斯特罗哈数及尾流中旋涡的分布图案,计算数据与已有的实验数据相吻合。     

大雷诺数线性剪切流绕圆柱的分离流动

本文采用离散涡方法计算了大雷诺数下线性剪切流绕圆柱的分离流动,计算结果给出阻力系数、横向力系数、边界层分离点、斯特罗哈数及尾流中旋涡的分布图案,计算数据与已有的实验数据相吻合。     

电磁极宽度对圆柱绕流场影响的数值分析

在雷诺数Re=200的情况,利用Maxwell方程直接数值计算表面包覆电极与磁极圆柱体产生的电磁力分布,将其加入到动量方程中,在各种电磁力作用参数和电磁极宽度的组合下,对表面覆盖电磁极圆柱体在弱电解质中的绕流场结构及其升阻力特性进行了数值模拟与分析.结果表明,当电磁极宽度较小时,圆柱体绕流场的分离点越容易接近后驻点,而电磁力对总阻力的影响并不明显,但对压差和摩擦阻力均有明显影响.当电磁极宽度较大时,圆柱体尾部区域越容易产生射流现象,而且总阻力随电磁力作用参数和电磁极宽度增大而减小.在电磁力尚不足以完全抑制周期性涡脱落的情况下,升力幅值随电磁力作用参数增大而减小,但随电磁极宽度则先减小后略有增加,升力脉动频率则均随电磁力作用参数和电磁极宽度增大而增加.研究表明,电磁力可以有效地改善圆柱体绕流场结构,达到减小圆柱体阻力并抑制其脉动升力之目的,因此是圆柱型结构的一种有效流动控制手段.     

Numerical simulation of laminar flow past a circular cylinder with slip conditions

The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of the domain spanwise periodic length on the flow around a circular cylinder

We assess the effect of the choice of spanwise periodic length on simulations of the flow around a fixed circular cylinder. The Reynolds number is set to 400 because, at this value, both lift coefficient and shedding frequency show significant drop due to three-dimensional flow structures. From the analysis of the three-dimensionalities of the wake and of the integral quantities such as Strouhal number, RMS of lift coefficient and energy contained in the three-dimensional portion of the flow we obtain an estimate of the minimum spanwise length to satisfactorily represent the flow. Furthermore, we observe a distinct wake behavior when the spanwise length is approximately the mode B instability wavelength.     

Influence of the orientation of a square cylinder on the wake properties

An experimental investigation of flow around a square cylinder placed at various angles with respect to the approach fluid velocity is reported. The focus of the study is toward examining the sensitivity of the wake properties to the cylinder orientation and Reynolds number. Angles of incidence in the range of 0-60° and Reynolds numbers of 1340, 4990, and 9980 have been considered. Velocity measurements have been carried out using an X-wire hotwire anemometer. The Strouhal number and the drag coefficient of the cylinder have been computed from the wake measurements. Utilizing the velocity traces at distinct probe locations in the near and the far wake, statistical properties such as the RMS velocities and the spectra have been obtained. Results obtained in the present work revealed that for a cylinder with zero inclination, flow separates from the corners on the face exposed to the incoming flow. For inclinations greater than zero, the points of separation on the cylinder move downstream and the wake size increases, but the separated shear layer rolls up over a shorter distance. These factors lead to a reduced drag coefficient and a higher Strouhal number. The center-line recovery of the time-averaged velocity and the decay rates of velocity fluctuations depend on the Reynolds number. A marginal effect of the cylinder orientation is also seen.     

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.     

Flow about yawed,stranded cables

The development of a steady lift force on a stranded cable, which is yawed with respect to a flow, is a unique characteristic of a cable when compared to a circular cylinder. Comparisons of lift and normal drag coefficients and wake characteristics were made between stranded cable models and the cylinder. These were based upon surface pressure and hot-wire measurements and flow visualization studies conducted in a low speed wind tunnel on rigid cables and cylinders. The models were yawed to four different yaw angles and tested within the Reynolds number range of 5,000 and 50,000. Pressure profiles for the yawed cables indicated that the lift force is directed towards the side where the primary strands are more nearly aligned with the flow. The pressure profiles also indicated that the lift force is generated by asymmetric separation. The small scale irregularities associated with wires within individual strands also appeared to have an effect on the cable's lift and drag characteristics. Results show that cables have significantly different shedding characteristics and near-wake shear layer structure when compared to the circular cylinder. For the flow regime tested, the Strouhal number showed no dependence on Reynolds number nor spanwise position along the cable.List of symbols C _dn normal drag coefficient - C _l lift coefficient - C _p pressure coefficient - D actual diameter, based on circumscribing circle for the cable - f _v shedding frequency - L/D length to actual diameter ratio - ppd peak-to-peak distance, unit span - Re Reynolds number based on actual diameter - S Strouhal number, - V free stream velocity - cable angle - azimuthal angle     

Reduction in drag and vortex shedding frequency through porous sheath around a circular cylinder

A numerical study on the laminar vortex shedding and wake flow due to a porous‐wrapped solid circular cylinder has been made in this paper. The cylinder is horizontally placed, and is subjected to a uniform cross flow. The aim is to control the vortex shedding and drag force through a thin porous wrapper around a solid cylinder. The flow field is investigated for a wide range of Reynolds number in the laminar regime. The flow in the porous zone is governed by the Darcy–Brinkman–Forchheimer extended model and the Navier–Stokes equations in the fluid region. A control volume approach is adopted for computation of the governing equations along with a second‐order upwind scheme, which is used to discretize the convective terms inside the fluid region. The inclusion of a thin porous wrapper produces a significant reduction in drag and damps the oscillation compared with a solid cylinder. Dependence of Strouhal number and drag coefficient on porous layer thickness at different Reynolds number is analyzed. The dependence of Strouhal number and drag on the permeability of the medium is also examined. Copyright © 2009 John Wiley & Sons, Ltd.     

Interference effect of two equal‐sized square cylinders in tandem arrangement: With planar shear flow

Numerical simulations have been performed for flow past two equal‐sized square cylinders in tandem arrangement subjected to incoming planar shear flow. Effect of L/d ratio and the shear parameter has been studied. The range of L/d ratio (ratio of center‐to‐center distance (L) to cylinder width (d)) is varied from 2 to 7 and the non‐dimensional shear parameter (K) is varied from 0.0 to 0.4 in steps of 0.1. For all the cases the Reynolds number (Re) based on centerline velocity and cylinder width is fixed at 100. The results are compared with that of isolated square cylinder with uniform flow. Strouhal number decreases with increasing shear parameter. There are more than one shedding frequency at high shear parameters and L/d ratios. The mean drag coefficient is decreased with shear parameter and lesser than that of the single cylinder. The root mean square (RMS) value of both lift and drag coefficients is higher for the downstream cylinder for all values of shear parameter. With increasing L/d ratio, for both lift and drag, the RMS value increases and then decreases for upstream cylinder, whereas it continuously increases for the downstream cylinder. The stagnation point is moved towards the top leading edge with increasing shear. The critical L/d ratio, which is defined as the distance between two cylinders, beyond which the vortex shedding from the upstream cylinder occurs, decreases with increasing shear parameter. Copyright © 2007 John Wiley & Sons, Ltd.     

Suppression of lift fluctuations on a circular cylinder by inducing the symmetric vortex shedding mode

The flow around a stationary circular cylinder modified by two synthetic jets positioned at the mean separation points is numerically studied. The Reynolds number based on the free-stream velocity and the circular cylinder diameter is Re=500. The focus is to present a novel way to suppress the lift fluctuations by changing the vortex shedding mode, and thus particular attention is paid to the interactions between the synthetic jets and wake shear layers and the resulting vortex dynamics. The overall influences of both momentum coefficient and excitation frequency are discussed. In some simulated cases, the vortex lock-on phenomenon is discovered, which causes the typical Kàrmàn type vortex shedding to be converted into the symmetric shedding modes, leading to the complete suppression of lift fluctuations. In other cases, the asymmetric shedding mode still dominates the wake evolution. Detailed vortical evolution for each typical wake pattern is analyzed to reveal the control mechanism. Additionally, the control effectiveness is evaluated, indicating that the present control strategy contributes an effective way to suppress the lift fluctuations and reduce the mean drag.     

棱柱绕流流动的数值模拟

利用数值方法对长宽比为1／3, 1和3的棱柱绕流在雷诺数为100的非稳态流动特性进行了分析和研究。采用有限体积法对棱柱绕流的二维流动N-S方程进行离散求解,分析和研究了非稳态的棱柱绕流流场,升力系数,阻力系数和涡动特性,数值模拟的结果与相关文献的数据比较吻合。通过上述研究能够为了解棱柱绕流的非稳态流动特性提供有力的帮助。而对棱柱三维流动的模拟分析和对雷诺数的变化对棱柱流动特性的影响进行研究,将为掌握棱柱绕流的工程特性打下基础。     

Interaction between the near wake and the cross-section variation of a circular cylinder in uniform flow

The flow around a circular cylinder with a cross-section variation is experimentally investigated. Particle Image Velocimetry (PIV) is used to scrutinize the interaction of the cylinder’s wall with its near wake. The Reynolds number based on the cylinder’s diameter and freestream velocity is 80 × 10³, corresponding to the upper subcritical flow regime. At a forcing Strouhal number of St _f = 0.02, the maximum vorticity level around the cylinder is reduced by more than 50% as compared to its uncontrolled value. The topology of the bulk flow confined between the primary vortical structure and the cylinder surface is modified resulting in substantial drag reduction.     

The unsteady drag on a spherical bubble at large Reynolds numbers

The flow past a spherical bubble undergoing a rectilinear motion in the unsteady flow of an unbounded liquid medium is investigated. The liquid velocity field at infinity is assumed to be uniform and the Reynolds number to be large. The Strouhal number is taken to be of order unity. The velocity distribution is sought by superposition of a perturbation field on the potential flow past the bubble so that the flow field is divided into four regions, i.e. the external flow field where the potential flow holds, the boundary layer, the rear stagnation point region and the wake. The flow in the rear stagnation point region and the wake is assumed to be essentially inertial. The unsteady drag experienced by the bubble is calculated from the mechanical energy balance of the liquid.     

The Unsteady Wake of a Circular Cylinder near a Free Surface

The behaviour of the wake Strouhal number for flow past a cylinder close to a free surface at both low and moderate Froude numbers is investigated numerically. For the low Froude number case (i.e., gravity-dominated), the results obtained are similar to those for flow past a cylinder close to an adjacent no-slip boundary. As the distance between the wall and the cylinder is reduced, the Strouhal number, as measured from the time varying lift, increases to a maximum at a gap ratio of 0.70. Further gap reduction leads to a rapid decrease in the Strouhal number, with shedding finally ceasing altogether at gap ratios below 0.16. The agreement between the results for a free surface and a no-slip boundary suggests that the mechanism behind the suppression of vortex shedding is common. For flow at a fixed gap ratio and a moderate Froude number, two distinctly different wake states are observed with the flow passing over the cylinder tending to switch from a state of attachment to the free surface, to one of separation from it, and then back again in a pseudo-periodic fashion. Even though there is a significant difference in Reynolds number, the predicted numerical two-dimensional behaviour is found to compare favourably with the experimental observations at higher Reynolds number.     

Transition phenomena in the wake of an inclined square cylinder

The division of flow regimes in a square cylinder wake at various angles of attack (α) is studied. This study provides evidence of the existence of modes A and B instabilities in the wake of an inclined square cylinder. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the Strouhal number versus Reynolds number curves. The spectra and time traces of wake streamwise velocity were observed to display three distinct patterns in different flow regimes. Streamwise vortices with different wavelengths at various Reynolds numbers were visualized. A PIV technique was employed to quantitatively measure the parameters of wake vortices. The wavelengths of the streamwise vortices in the modes A and B regimes were measured by using the auto-correlation method. From the present investigation, the square cylinder wake at various angles of attack undergoes a similar transition path to that of a circular cylinder, although various quantitative parameters measured which include the critical Reynolds numbers, spanwise wavelength of secondary vortices, and the circulation and vorticity of wake vortices all show an α dependence.