Aerodynamic characteristics of an inclined and yawed circular cylinder with artificial rivulet

Stay cables of cable-stayed bridges often experience vibrations with large amplitudes induced by wind or jointly by both wind and rain. To understand the aerodynamic characteristics of the stay cables and excitation mechanics of rain–wind-induced vibration (RWIV), an inclined and yawed circular cylinder with and without an artificial upper rivulet is studied through a series of wind tunnel tests. The impacts of upper rivulet and axial flow on the aerodynamics of the cylinder are investigated. It is found that for an inclined and yawed cylinder without rivulet there exists a non-zero lift force at large wind angle. Furthermore, the wind pressures and aerodynamic forces acting on both the cylinder and the upper rivulet are obtained, which can be used to develop more rational theoretical models for RWIV of stay cables. Results show that the upper rivulet can both enhance and depress Karman vortex shedding depending on the position of the rivulet. As a result, dramatic variations of the aerodynamic forces acting on the cylinder and the rivulet will occur, which may eventually result in RWIV. Also axial flow may have a noticeable influence on the aerodynamic characteristics of the inclined and yawed cylinder. And the presence of the rivulet can enhance such influence from the axial flow.     

斜拉桥合理成桥状态确定的序列二次规划法

本文首先介绍斜拉桥合理成桥状态的概念和现有的斜拉桥索力优化方法。然后基于序列二次规划(SQP)算法，提出了一种用于确定斜拉桥成桥合理状态的实用方法，序列二次规划法。该方法通过建立斜拉桥索力优化的非线性规划模型，以斜拉桥主梁和索塔的弯曲应变能为目标函数，以各斜拉索的索力为设计变量，结构的应力和索力为约束条件，并计人大跨度斜拉桥各种几何非线性因素的影响，采用强次可行序列二次规划法进行优化求解，确定斜拉桥成桥合理状态的索力。运用该方法和空间非线性有限元分析程序分析了某斜拉桥的合理成桥状态，计算结果表明该方法简单、有效。     

Numerical simulation of rivulet evolution on a horizontal cable subject to an external aerodynamic field

On wet and windy days, the inclined cables of cable-stayed bridges may experience a large amplitude oscillation known as rain-wind-induced vibration (RWIV). It has previously been shown by in situ and wind-tunnel studies that the formation of rain-water accumulations or ‘rivulets’ at approximately the separation points of the external aerodynamic flow field and the resulting effect that these rivulets have on this field may be one of the primary mechanisms for RWIV. A numerical method has been developed to undertake simulations of certain aspects of RWIV, in particular, rivulet formation and evolution. Specifically a two-dimensional model for the evolution of a thin film of water on the outer surface of a horizontal circular cylinder subject to the pressure and shear forces that result from the external flow field is presented. Numerical simulations of the resulting evolution equation using a bespoke pseudo-spectral solver capture the formation of two-dimensional rivulets, the geometry, location and growth rate of which are all in good agreement with previous studies. Examinations of how the distribution and magnitude of aerodynamic loading and the Reynolds number influence the rivulet temporal evolution are undertaken, the results of which indicate that while all three affect the temporal evolution, the distribution of the loading has the greatest effect.     

Numerical investigation of the coupled interaction between an unsteady aerodynamic flow field and a water film coating on a circular cylinder

Rain–wind induced vibration is an aeroelastic phenomenon that occurs on the inclined cables of cable-stayed bridges and arises due to the interaction between the unsteady wind loading and the formation of water rivulets on the cable surface. A new numerical method has been developed at the University of Strathclyde to simulate the influence of the external flow field on the rivulet dynamics and vice versa. The approach is to couple a Discrete Vortex Method solver to determine the external flow field and unsteady aerodynamic loading, and a pseudo-spectral solver based on lubrication theory to model the evolution and growth of the water rivulets on the cable surface under external loading. Results of this coupled model are presented, to provide detailed information on the development of water rivulets and their interaction with the aerodynamic field. In particular, the effect of the initial water film thickness and the angle of attack in plane on the resulting rivulets are investigated. The results are consistent with previous full scale and experimental observations with rivulets forming on the upper surface of the cable only in configurations where rain–wind induced vibration has been observed. Additionally, the thickness of the lower rivulet is found to be self-limiting in all configurations. The results demonstrate that the model can be used to enhance the understanding of the underlying physical mechanisms of rain–wind-induced vibration.     

Theoretical and experimental studies on the aerodynamic instability of a two-dimensional circular cylinder with a moving attachment

Rain–wind induced vibration of cables in cable-stayed bridges is a worldwide problem of great concern. The effect of the motion of water rivulets on the instability of stay cables has been recognized as one of the mechanisms of this complex phenomenon. In order to investigate how the motion of rivulets affects the unstable vibration of cables without considering the effects of axial flow and axial vortex, a real three-dimensional cable was modeled as a two-dimensional circular cylinder, around which an attachment representing the rivulet can move. This could also be regarded as a new kind of two-dimensional 2-dof dynamic system. This paper studies the aerodynamic instability of the system theoretically and experimentally. Equations governing the motions of the cylinder and the attachment are first established. The Lyapunov stability criterion is applied to the equations of motion to derive the criterion for the unstable balance angle of the attachment. Moreover, a new two-dimensional 2-dof cable model system with a movable attachment is designed and tested in a wind tunnel. Parametric studies are carried out to investigate the effects of major factors such as wind speed, frequency and damping of the dynamic system on the unstable balance angle of the rivulet attachment. Theoretical and experimental results match well. These results may be valuable in elucidating the mechanism of rain–wind induced vibration of stay cables.     

Numerical simulation of flows around two circular cylinders by mesh‐free least square‐based finite difference methods

In this paper, the mesh‐free least square‐based finite difference (MLSFD) method is applied to numerically study the flow field around two circular cylinders arranged in side‐by‐side and tandem configurations. For each configuration, various geometrical arrangements are considered, in order to reveal the different flow regimes characterized by the gap between the two cylinders. In this work, the flow simulations are carried out in the low Reynolds number range, that is, Re=100 and 200. Instantaneous vorticity contours and streamlines around the two cylinders are used as the visualization aids. Some flow parameters such as Strouhal number, drag and lift coefficients calculated from the solution are provided and quantitatively compared with those provided by other researchers. Copyright © 2006 John Wiley & Sons, Ltd.     

CFRP索斜拉桥的索-浅拱模型及面内自由振动分析

本文针对斜拉桥的受力特点,基于索和浅拱的经典动力学运动方程,结合拉索与浅拱之间的耦合边界条件,并且考虑两者的几何非线性,建立了斜拉桥的多索-浅拱面内自由振动模型。将浅拱分段处理,结合索、浅拱连接处的动态平衡条件,应用分离变量法,建立多索-浅拱模型的面内自由振动理论。以双索浅拱模型为例,求解其特征值问题。同时,建立了相应的有限元模型,有限元计算结果与本文理论分析吻合良好。最后针对CFRP索斜拉桥的关键参数,基于本文的索-浅拱理论,对面内自由振动进一步研究。研究表明：浅拱的矢高在一定范围内变化,仅对某一阶频率产生影响,而其他各阶频率几乎没影响;CFRP拉索能显著改善索-浅拱组合结构的基本动力学特性。     

Numerical simulation and analysis of the effects of water-film morphological changes on the aerodynamic lift of stay cables

The cables in cable-stayed bridges can vibrate at large amplitudes during rain and windy conditions, a phenomenon known as rain-wind induced vibration (RWIV). Previous studies have demonstrated that the formation and oscillation of rivulets on stay cable surfaces play an important role in RWIV.This paper presents a new numerical method for simulating the evolution of rivulets on stay cable surfaces based on a combination of the gas–liquid two-phase theory and the volume of fluid method (VOF method), which allows for the straightforward determination of the cables’ aerodynamic lift when RWIV occurs. To verify the accuracy of this method and analyze the effects of wind velocity on the water film and the aerodynamic lift around the cable, three cases with different loadings were investigated using the computational fluid dynamics (CFD) software CFX. To verify the method’s accuracy, the aerodynamic lifts calculated from these cases were applied to the cable to obtain its vibrational response. In accordance with the experimental results, the numerical results demonstrated that an upper rivulet with a periodic oscillation was formed at a specific wind speed, causing the aerodynamic lift to change with a similar periodicity. The aerodynamic lift’s frequency was approximately the cable’s natural frequency, and induced large vibrations in the cable. No obvious upper rivulets were formed at sufficiently low wind speeds. The frequency of an aerodynamic lift that was significantly larger than the cable’s natural frequency induced small vibrations in the cable. When the wind speed was sufficiently high, despite the eventual formation of a continuous upper rivulet, the frequencies of the upper rivulet’s oscillation and the aerodynamic lift remained distinct from the natural frequency, and the cable continued to exhibit small-amplitude vibrations. These observations confirmed the conclusion that periodic variations in the water film morphology could lead to periodic changes in the aerodynamic lift that would induce RWIV.     

Two circular cylinders in cross-flow: A review

Pairs of circular cylinders immersed in a steady cross-flow are encountered in many engineering applications. The cylinders may be arranged in tandem, side-by-side, or staggered configurations. Wake and proximity interference effects, which are determined primarily by the longitudinal and transverse spacing between the cylinders, and also by the Reynolds number, have a strong influence on the flow patterns, aerodynamic forces, vortex shedding, and other parameters. This paper reviews the current understanding of the flow around two “infinite” circular cylinders of equal diameter immersed in a steady cross-flow, with a focus on the near-wake flow patterns, Reynolds number effects, intermediate wake structure and behaviour, and the general trends in the measurements of the aerodynamic force coefficients and Strouhal numbers. A primary focus is on the key experimental and numerical studies that have appeared since the last major review of this subject more than 20 years ago.     

斜拉桥索力张拉过程的最优控制

以影响结构为基础，通过拉索张拉过程的结构分析，建立了张拉过程的最优控制数学模型，并采用综合参数法进行求解。该方法不但适合斜拉桥索力张拉过程，而且能够应用于悬索桥、拱桥的施工控制中，对同类问题有重要的参考价值。     

谐波激励下斜拉桥面内非线性振动试验研究

斜拉桥拉索的振动问题一直是桥梁工程领域的研究热点。为揭示拉索大幅振动的力学机理，课题组建立了斜拉桥的全桥精细化模型，本文测试和研究了单频激励下的斜拉桥可能的非线性振动行为。首先，通过自由振动试验测试了模型的模态参数，并与两类有限元模型（OECS模型和MECS模型）进行对比，结果吻合良好。其次，试验研究了在单个竖向简谐激励下斜拉桥模型的非线性响应。研究发现：当激励频率与斜拉桥某阶全局模态频率接近时，主梁产生主共振，并引起多根长索产生大幅的参强振动；当激励频率与某根斜拉索面内一阶频率之比为1：2或者2：1时，可以观测到索中产生超谐波和亚谐波共振现象。     

Self-sustained oscillations between two tandem cylinders at Reynolds number 1,000

This study focuses on the self-sustained oscillatory flow characteristics between two tandem circular cylinders of equal diameter placed in a uniform inflow. The Reynolds number (Re _D ), based on the cylinder diameter, was around 1,000 and all experiments were performed in a recirculating water channel. The streamwise distance between two tandem cylinders ranged within 1.5 ≤ X _c/D ≤ 7.0. Here X _c denotes the center-to-center distance between two tandem cylinders. For all experiments studied herein, quantitative velocity measurements were performed using hot-film anemometer and the LDV system. The laser sheet technique was employed for qualitative flow visualization. The wavelet transform was applied to elucidate the temporal variation and phase difference between two spectral components of the velocity signals detected in the flow field. The remarkable finding was that when two tandem circular cylinders were spaced at a distance within 4.5 ≤ X _c/D ≤ 5.5, two symmetrical unstable shear layers with a certain wavelength were observed to impinge onto the downstream cylinder. The responding frequency (f _u ), measured between these two cylinders, was much higher than the natural shedding frequency behind a single isolated cylinder at the same Re _D . This responding frequency decreased as the distance X _c/D increased. Not until X _c/D ≥ 6.0, did it recover to the natural shedding frequency behind a single isolated cylinder. Between two tandem cylinders, the Strouhal numbers (St _c = f _u X _c/U_c) maintained a nearly constant value of 3, indicating the self-sustained oscillating flow characteristics with a wavelength X _c/3. Here U _c is the convection speed of the unstable shear layers between two tandem cylinders. At Re _D = 1,000, the self-sustained oscillating characteristics between two tandem circular cylinders were proven to exhibit a sustained flow pattern, not just a sporadic phenomenon.     

Rain-wind-induced vibrations of a simple oscillator

In this paper a relatively simple mechanical oscillator which may be used to study rain-wind-induced vibrations of stay cables of cable-stayed bridges is considered. In recent publications, mention is made of vibrations of (inclined) stay cables which are excited by a wind field containing rain drops. The rain drops that hit the cables generate a rivulet on the surface of the cable. The presence of flowing water on the cable changes the cross section of the cable experienced by the wind field. A symmetric flow pattern around the cable with circular cross section may become asymmetric due to the presence of the rivulet and may consequently induce a lift force as a mechanism for vibration. During the motion of the cable the position of rivulet(s) may vary as the motion of the cable induces an additional varying aerodynamic force perpendicular to the direction of the wind field. It seems not too easy to model this phenomenon, several author state that there is no model available yet.The idea to model this problem is to consider a horizontal cylinder supported by springs in such a way that only one degree of freedom, i.e. vertical vibration is possible. We consider a ridge on the surface of the cylinder parallel to the axis of the cylinder. Additionally, let the cylinder with ridge be able to oscillate, with small amplitude, around the axis such that the oscillations are excited by an external force.It may be clear that the small amplitude oscillations of the cylinder and hence of the ridge induce a varying lift and drag force. In this approach it is assumed that the motion of the ridge models the dynamics of the rivulet(s) on the cable. By using a quasi-steady approach to model the aerodynamic forces, one arrives at a non-linear second-order equation displaying three different kinds of excitation mechanisms: self-excitation, parametric excitation and ordinary forcing. The first results of the analysis of the equation of motion show that even in a linear approximation for certain values of the parameters involved, stable periodic motions are possible. In the relevant cases where in linear approximation unstable periodic motions are found, results of an analysis of the non-linear equation are presented.     

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.     

两不等直径圆柱高雷诺数时均风力场的数值模拟

圆柱间气动干扰研究具有重要的理论和现实意义.尽管国内外开展了圆柱组合风效应的风洞试验研究,但主要针对等直径圆柱,并且雷诺数多为10~5以下.考虑到工程结构风场的高雷诺数特征,采用数值模拟方法,模拟两不等直径圆柱在串列、并列及交错排列下的高雷诺数(Re=4.5×10~5)时均绕流场.通过改变组合的间距和风向,分析探讨两柱阻力、升力及总风力的变化规律.     

THE FLOW INTERACTION BETWEEN A STATIONARY CYLINDER AND A DOWNSTREAM FLEXIBLE CYLINDER

This paper deals with an experimental investigation of the dynamic response of a long flexible circular cylinder in the wake of a stationary geometrically similar cylinder. The system has a low damping ratio. The tandem and staggered arrangements have been considered. The separations investigated are typical of transmission line bundles and range from 7 to 25 diameters and Reynolds number ranges from 5 000 to 27 000. For the tandem cylinders, the results indicate that (a) the dynamic response of the downstream cylinder is no longer hysteretic, (b) the synchronization onset is at higher reduced velocities and (c) the synchronization region is wider than that of an isolated cylinder; this region is twice as large for a separation of 10 diameters and decreases with increasing spacing. Despite the absence of the hysteresis loop and its associated discontinuities, two vortex patterns are present around the resonance velocity. A small decrease of the maximum amplitude of oscillation with increasing spacing has also been observed, as well as a reduction of the velocity for which this maximum occurs. For separations of 7 and 8·5 diameters, the leeward cylinder exhibits a combination of vortex-induced and wake-galloping oscillations. For the staggered arrangement, the increase of the stagger angle β reduces the synchronization onset velocity and the synchronization region and beyond β=20°, the downstream cylinder behaves as an isolated one.     

斜拉桥索力优化的强次可行序列二次规划法

提出了一种斜拉桥索力优化的实用方法-强次可行序列二次规划法. 该方法通过建立斜拉 桥索力优化的非线性规划模型，以主梁和索塔的弯曲应变能为目标函数，斜拉索的索力为设 计变量，结构应力和索力为约束条件，计入大跨度斜拉桥各种几何非线性因素的影响，采用 强次可行序列二次规划算法进行优化求解，确定斜拉桥成桥合理状态的索力. 运用该方法对 某斜拉桥进行索力优化，结果表明该方法简单、有效.     

圆角化对方柱气动性能影响的流场机理

方形截面柱体的圆角化处理是常用的流动控制方法,但其流场作用机理尚未被澄清.采用大涡模拟方法,在雷诺数为2.2$\times$10$^{4}$时,考虑风攻角的影响,对均匀流作用下的标准方柱和圆角方柱的气动性能和流场特性进行了研究,定量分析了圆角化气动措施和风攻角变化对分离泡特性的影响规律,从流场角度澄清了圆角化气动措施对方柱气动性能的影响机理.研究表明:与标准方柱相比,圆角方柱的表面风压、气动力和涡脱强度呈整体下降的趋势,但圆角方柱的斯特劳哈尔数更高;圆角方柱的"分离泡流态'发生在更小的风攻角范围内,分离泡的出现会进一步造成方柱的尾流变窄,涡脱强度减弱;随着风攻角的增大,分离泡的长度会逐渐减小直至消失,分离泡的中心会逐渐向方柱前角(迎风向)和方柱壁面移动;与标准方柱相比,圆角方柱的气流发生初次分离的位置向下游移动,分离后的剪切层更贴近方柱,因而更易发生再附现象;方柱尾流宽度的减小和涡脱强度的减弱是导致圆角方柱气动力减小和斯特劳哈尔数增大的主要原因.      

斜拉桥合理成桥状态确定的一阶分析法

本文建立了斜拉桥索力优化的非线性规划模型，其中以斜拉桥主梁和索塔的弯曲应变能为目标函数，以各斜拉索的索力为设计变量，结构的应力及索力为约束条件，采用一阶分析法进行求解，用以确定成桥合理状态的索力。在计算中，考虑大跨度斜拉桥各种几何非线性因素的影响，并列出了优化模型的具体表达式及优化过程中的关键求解策略。应用该法和空间非线性有限元分析程序分析了某千米级斜拉桥方案的合理成桥状态，计算结果表明：该方法简单、有效。     

Third-Order Upwind Finite Element Simulation of Flow Around Two Square Cylinders

The aerodynamic behavior of the flow around two square cylinders is presented on the basis of the numerical simulation of the incompressible Navier-Stokes equations using a third-order upwind finite element scheme. It is well known that flow patterns around the two square cylinders are more complicated than flow patterns around one square cylinder because of interference between the Karman vortices behind the two square cylinders. In this paper, two kinds of cylinder arrangements are chosen as computational models. One type is that of two square cylinders arranged vertically to the direction of a uniform flow, and the other is arranged horizontally to the direction of a uniform flow.