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.     

AN IMPROVEMENT OF THE TIME DELAYED QUASI-STEADY MODEL FOR THE OSCILLATIONS OF CIRCULAR CYLINDERS IN CROSS-FLOW

This paper is devoted to an improvement of the time-delayed quasi-steady model for the prediction of the movement-induced vibrations of tubes mounted in tandem or in an in-line bundle. The improvement lies in the physical interpretation and calculation of the time lag which is based on measured steady force coefficients. In order to calculate the time lag, a mean convection velocity between cylinders is estimated at each time step. A linear analysis of the present model gives a critical velocity which is in good agreement with an unsteady experiment found in the literature. Moreover, limit-cycle amplitudes are relatively well predicted and show that instability is triggered by the time lag, whereas amplitude is governed by nonlinear aerodynamic damping as for a Van der Pol oscillator.     

大湍流度高雷诺数时并列双圆柱的平均和脉动压力分布

本文通过风洞实验研究了来流湍流度,Iu=10％雷诺数分别为Re=1.95×10~9和Re=6.5×10~5时单个圆柱和不同间距比下并列双圆柱的平均和脉动压力分布。结果表明:在Re=1.95×10~5时单个圆柱的平均压力分布类似于低湍流度高超临界雷诺数时的压力分布;当雷诺数增大至6.5×10~5时,绕圆柱表面流动的分离点前移和背压绝对值提高,总的阻力系数随之增加。并列双圆柱的间距比变化对圆柱表面压力分布影响很大,在极小间距比(N/d=1.05)时,双圆柱间的缝隙流使附近柱面产生高达-5的压力系数峰值(Re=6.5×10~5),同时脉动压力也大为增加;在较小间距比时(1.5     

THE FLUID AND MECHANICAL COUPLING BETWEEN TWO CIRCULAR CYLINDERS IN TANDEM ARRANGEMENT

The effect of the fluid and mechanical coupling between two flexible circular cylinders on their vortex-induced oscillations is examined in a wind tunnel. The cylinders are in a tandem arrangement and a mechanical coupling allows vibrations in phase and out of phase. The separation between the cylinders ranges between 7 and 25 diameters. When the cylinders are coupled only by fluid, the upstream cylinder behaves as an isolated one, while the downstream cylinder response depends on the separation and presents a hysteresis and three discontinuities. The hysteresis and its discontinuities agree with those of the upstream cylinder and the third discontinuity coincides with the end of synchronization of the windward cylinder. The addition of the mechanical coupling complicates the dynamic response which is greatly influenced by the separation and the coupling mode involved. The results are interpreted according to those dealing with the fluid coupling only. The effect of small-scale grid turbulence is also examined.     

FLUID DAMPING OF AN ELASTIC CYLINDER IN A CROSS-FLOW

Damping characteristics of fluid–structure systems are difficult to measure or calculate. In the past, such data have been rather scarce. This study reports an attempt on the use of a numerical approach to derive damping ratios related to fluid–structure interactions. It is based on an autoregressive moving-average (ARMA) method, which is used to analyse the displacement time series obtained from a numerical simulation of an elastic cylinder in a uniform cross-flow. The damping ratios show a similar trend to those obtained in previous experiments. An alternative way to deduce damping ratios is to decompose the transverse force in the structural dynamics equation into a drag (or out-of-phase) and an inertia (or in-phase) component for analysis. The damping thus deduced is in fair agreement with that obtained from ARMA; however, at or near synchronization, where the natural frequency of the stationary cylinder is close to the vortex shedding frequency, there is a very substantial difference between the two results.     

FLOW OF A VISCOELASTIC FLUID BETWEEN TWO ROTATING CIRCULAR CYLINDERS SUBJECT TO SUCTION OR INJECTION

The steady flow of an Oldroyd-B fluid between two porous concentric circular cylinders is studied. The equation of motion and the constitutive equations form a system of non-linear ODEs that is solved numerically, and in a few cases the numerical results are compared with a known analytical solution. We consider the effect of the non-Newtonian nature of the fluid on the drag and on the boundary layer structure near the walls. Numerical computations show the effect of the non-Newtonian quantities on the velocity and on the shear stress as the dimensionless parameters are varied. © by 1997 John Wiley & Sons, Ltd.     

并列弹性双圆柱在均匀流场中的流体激励力的研究

实验研究了并列弹性双圆柱体在均匀流场中的水动力特性，其中包括柱表面稳态及脉动压力系数，稳态阻力及升力系数，脉动阻力和升力系数，结果表明：Ｖ＿ｒ＞Ｖ＿（ｒｃ）时，柱的振动对其流体激励力有明显影响。     

涡激诱导并列双圆柱碰撞数值模拟研究

圆柱类结构物的涡激振动是工程中较为常见的一种现象,如果圆柱结构物之间的距离较小, 就会产生涡激诱导碰撞现象,而涡激碰撞会比涡激振动对结构物疲劳破坏产生更严重的威胁.采用浸入边界法模拟流体中的动边界问题,避免了传统贴体网格方法在求解流体中存在固体间碰撞问题时出现数值求解不稳定问题,采用有限元方法对圆柱的运动和碰撞进行求解,通过数据回归方法建立了流体流动条件下的润滑模型,对不同间隙比下涡激诱导并列双圆柱振动及碰撞过程进行了数值模拟, 数值结果表明,如果两圆柱产生了碰撞将会有连续的碰撞发生, 碰撞时出现了多阶频率,振动主频率要比无碰撞时大, 两圆柱碰撞时的相对速度比自由来流速度小;当两圆柱相互接近时, 随着涡环分离角度的逐渐倾斜, 横向流体力先逐渐减小,当两圆柱间涡环开始相互影响发生挤压时, 横向流体力开始逐渐增大;当两圆柱开始反弹时, 两圆柱间形成了低压区, 改变了横向流体阻力的方向,使两圆柱又产生了接近运动,如此反复从而产生了碰撞后横向流体力和圆柱速度的振荡现象.      

并列双圆柱流致振动的不对称振动和对称性迟滞研究

对雷诺数Re = 100 间距比s/D = 2.5 和5.0 的并列双圆柱流致振动进行了数值模拟研究, 其中圆柱质量比m = 2.0, 折合流速U_r 在2.0~10.0 之间, 两圆柱仅能做横流向振动. 研究发现, 当间距比s/D = 2.5 时, 在折合流速4.4 < U_r< 4.8区间内, 两圆柱流致振动响应出现不对称振动现象, 在折合流速4.4 < U_r< 4.8 区间内, 两圆柱流致振动响应出现对称性迟滞现象; 而当间距比s/D = 2.5时, 圆柱流致振动响应与单圆柱涡激振动响应相似, 没有出现不对称振动和对称性迟滞现象. 在不对称振动区间内, 两圆柱的升、阻力参数也出现了不相等的情况. 此外, 当两圆柱不对称振动时, 圆柱间隙流稳定地偏斜向其中的一个圆柱; 相应地, 尾涡也出现了宽窄不等的模式. 窄尾流圆柱的振幅和升、阻力均较宽尾流圆柱的大. 通过对比不对称振动现象发生前后的尾涡模式, 对新现象的产生机制进行了阐述.      

MODELLING THE UNSTEADY AXIAL FORCES ON A FINITE-LENGTH CIRCULAR CYLINDER IN CROSS-FLOW

A semi-empirical model for unsteady axial forces is developed to predict the spectral features of the force generated by the flow over the end-caps on a finite-length, right circular cylinder in cross-flow. In general, the model consists of two parts: the spatial variation of r.m.s. wall pressure on the cylinder end-caps, and the correlation lengths and areas, which describe the spatial extent of the correlation of the unsteady wall pressures. Experiments were conducted in a low-noise wind tunnel as a function of cylinder diameter Reynolds number (19 200<Re<32 000) and the Strouhal number (0·05<St<3·33) to measure the statistics of the unsteady wall pressures on a model cylinder. These results are incorporated into the theoretical models, and prediction of the spectral characteristics of the axial force are made. The r.m.s. wall pressures on the end-caps are found to have the largest amplitude at circumferential locations (from the forward stagnation point) in the 90–120° range. The high levels at these locations are attributed to reattachment of the separated flow over the end-cap. The radial and circumferential correlation areas have a maximum value at St=0·21. Due to the 3-D flow over the end-caps, the radial correlation areas are found to depend on the circumferential measurement reference location, and the circumferential correlation lengths are found to depend on the radial measurement location. The unsteady axial force predictions using the model show a very broad spectral character.     

理想流体中定常自由涡环运动

本文研究理想均质不可压缩无界流体中的轴对称定常涡环运动。通过对柱坐标系下的定常Euler方程的高精度数值求解,给出了求涡核区有任意涡量分布情况下轴对称定常涡环解的方法,并就涡环的运动特性进行了讨论,其极限情况与已有的理论解完全一致。在此基础之上,还发展了一种柱坐标系下以傅氏级数为基函数作展开的高效谱方法,成功地解决了奇性(r=0)问题。     

平面剪切来流作用下串列布置三圆柱流致运动特性研究

基于四步半隐式特征线分裂算子有限元方法,对Re=100时,剪切来流作用下串列三圆柱体双自由度流致振动问题进行了数值计算. 首先,与现有文献结果进行对比验证该方法的正确性. 然后,着重分析剪切率、固有频率比和折减速度三个关键参数对串列三圆柱体结构流致动力响应及流场特性的影响. 数值计算结果表明:剪切率、固有频率比与折减速度对结构振幅和运动轨迹的影响较大. 随剪切率的增大,上游圆柱最大振幅的变化与单圆柱工况类似. 中下游圆柱最大振幅会增大且会出现双向共振现象,同时,发生共振响应区域会扩大. 随固有频率比的增大,上游圆柱顺流向锁定区间范围会减小,而中下游圆柱双向锁定区间会扩大. 另一方面,均匀来流作用下,结构运动轨迹以"8"字形和不规则形状为主. 随剪切率的增大,锁定区间内运动轨迹会由"8"字形转变为"雨滴"形. 在大剪切率与高固有频率比工况下,中游圆柱体结构运动轨迹会出现"双雨滴"形状. 最后,通过对流场特性的分析,揭示了剪切来流作用下串列三圆柱结构流致运动响应的内在机理.      

幂率流体圆管非定常流动的数值分析

本文讨论水平圆管中幂率流体的起动问题。用显式和隐式两种格式,我们得到了问题的数值解并从而得到流动建立时间的近似公式。     

ONSET OF ASYMMETRY: FLOW PAST CIRCULAR AND ELLIPTIC CYLINDERS

A computational study of the development of two- dimensional unsteady viscous incompressible flow around a circular cylinder and elliptic cylinders is undertaken at a Reynolds number of 10,000. A higher- order upwind scheme is used to solve the Navier–Stokes equations by the finite difference method in order to study the onset of computed asymmetry around bluff bodies. For the computed cases the ellipses develop asymmetry much earlier than the circular cylinder. The receptivity of the computed flows in the presence of discrete roughness and surface vibration is studied. Finally, the role of discrete roughness in triggering asymmetry for flow past a circular cylinder is studied and compared with flow visualization experiments at Re=10,000     

MODELING THE UNSTEADY LIFT AND DRAG ON A FINITE-LENGTH CIRCULAR CYLINDER IN CROSS-FLOW

Semi-empirical models for unsteady lift and drag are developed to predict the spectral features of the unsteady forces on a finite-length, right circular cylinder in cross-flow. In general, the models consist of two parts; the spatial variation of r.m.s wall pressure on the cylinder, and the correlation lengths which describe the spatial extent of the correlation of the unsteady wall pressures. Experiments were conducted in a low noise wind tunnel as a function of cylinder diameter Reynolds number (19 200<Re<32 000) and the Strouhal number (0·05< St<3·33), to measure the statistics of the unsteady wall pressures on a model cylinder. These results are incorporated into the theoretical models, and predictions of the spectral characteristics of the lift and drag are made. The r.m.s. wall pressures on the cylindrical surface are found to have the largest amplitude near the cylinder end-cap, and on the rearward portion of the cylinder body. The high levels in these locations are attributed to the separated flow region over the end-cap. The circumferential and axial length-scales decrease exponentially with Strouhal number. Both length-scales exhibit maxima near the Strouhal shedding frequency of St=0·21. The axial length-scales are found to depend on the measurement reference location due to the three-dimensional flow and separated flow region near the end-cap. The unsteady lift and drag predictions using the models developed in this work agree well with previously measured unsteady force data measured on inertial hydrophones exposed to flow. The broadband unsteady lift is found to be greater than the broadband unsteady drag by nominally 3dB.     

黏弹性流体在圆管内流动的谱方法模拟计算

采用修正Jeffreys模型来描述聚丙烯酰胺水溶液流变特性. 首先用具有二阶精度的差分法与拟谱法求解幂率模型, 分别与解析解进行比较, 结果表明拟谱法具有极高精度. 然后用拟谱法求解PAM水溶液在圆管中流动, 得到速度分布、应力分布,为三维模拟作准备.     

串列布置三圆柱涡激振动频谱特性研究

对串列三圆柱体双自由度涡激振动问题进行了数值计算, 并分析了雷诺数、固有频率比和约化速度对串列三圆柱体结构动力响应及频谱特性的影响. 研究发现: 雷诺数、频率比对上游圆柱的振幅和流体力系数的影响较小. 中游圆柱频率锁定区域随着雷诺数的增大而增大, 其动力响应受上游圆柱尾流的影响较大, 但频率比的影响较小. 同时, 流体力系数在约化速度较小时受雷诺数和频率比的影响较大. 另外, 下游圆柱的振幅和流体力系数受雷诺数及频率比的影响较大. 雷诺数、频率比和约化速度对圆柱流体力系数能量谱密度(PSD)曲线中主峰幅值、频谱成分及波动性的影响较大. 流体力系数PSD曲线波动性的增强, 导致圆柱运动轨迹会从"8"字形转变成不规则形状. 当频率比为2.0时, 上游圆柱尾流出现P$+$S模式, 导致其发生非对称运动, 且升、阻力系数PSD曲线主峰重合. 最后, 激励荷载平均功率值随约化速度的变化趋势与对应的结构动力响应的变化类似. 在同一约化速度区间内, 结构振动响应的强弱与位移的平均功率值成正比. 对不同约化速度区间内的升力系数功率谱密度分析时, 振动频率比($f_{s}/f_{n, y})$对结构振动响应的影响更大.      

水平圆管中受压扭作用管桩屈曲后的解析解

首先建立了考虑自重、受水平圆管约束的管柱在压担组合作用下的屈曲方程：此方程为四阶强非线性常微分方程，难以直接精确求解；通过管柱的正弦屈由分析，找到了方程中的小参数；利用小参数摄动法求解了强非线性屈曲方程，得到了管柱螺旋屈曲后的实际屈曲构形解析解，由此可进一步得到管柱发生螺旋屈曲的临界载荷；所得解析结果与数值计算结果及本文结果退化后与文献中的相关结果比较都有良好的一致性．     

水平圆管中受压扭作用管桩屈曲后的解析解

首先建立了考虑自重、受水平圆管约束的管柱在压担组合作用下的屈曲方程：此方程为四阶强非线性常微分方程,难以直接精确求解;通过管柱的正弦屈由分析,找到了方程中的小参数;利用小参数摄动法求解了强非线性屈曲方程,得到了管柱螺旋屈曲后的实际屈曲构形解析解,由此可进一步得到管柱发生螺旋屈曲的临界载荷;所得解析结果与数值计算结果及本文结果退化后与文献中的相关结果比较都有良好的一致性．