A linear stability approach to vortex-induced vibrations and waves

The motion induced by vortex shedding on slender flexible structures subjected to cross-flow is considered here. This phenomenon of vortex-induced vibration (VIV) is analysed by considering the linear stability of a coupled system that includes the structure dynamics and the wake dynamics. The latter is modelled by a continuum of wake oscillators, distributed along the span of the structure. In the case of uniform flows over a straight tensioned cable, VIV are found to arise as an instability related to the merging of two waves. In the case of a cable of finite length, the selection of modes that experience lock-in with the wake is found using the same stability argument. In non-uniform flows, several unstable wave systems are identified, and competition between them is discussed. Comparison is then made with existing experimental and computational data of VIV of slender structures under uniform and non-uniform flows. Phenomena previously identified in these systems, such as mode switching when the flow velocity is varied, time sharing of the response between two frequencies, or the coexistence of several regions of VIV with different dynamics in the same structure, are discussed with the help of the proposed model.     

Dynamics of Branched Continuous-Discrete Systems Towed in Rough Water

A method is proposed for dynamic analysis of towed spatial branched structures. The method permits determining the kinematic and force characteristics of a structure towed either downwave or upwave. The slacking of certain elements of the structure and changed speed of its motion are taken into account. The dynamics of a specific system is analyzed in the cases of abruptly changing towing speed and towing in regularly rough water with different wave parameters __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 84–89, October 2005.     

On the spatio-temporal structure of cylinder wakes

The wake of a short aspect ratio cylinder placed in a uniform flow is experimentally investigated. After having characterized the temporal behavior of the Bénard–Von Kàrmàn vortex shedding by the use of a classical hot-wire anemometer, an ultrasound anemometry technique is applied to study the spatial critical behavior of the envelope of the transverse velocity of the wake. It is shown that this envelope which represents the spatial form of the global mode of the wake, follows universal scaling laws which are in agreement with a second order phase transition. In a second set of experiments, the behavior of the longitudinal velocity fluctuations is also investigated. It is discovered that there is a special point several diameters behind the cylinder, which plays a role of a wave maker. Finally, for very small aspect ratio cylinders, symmetric vortex shedding is reported and interpreted using a system of coupled oscillators. Received: 15 May 1997/Accepted: 20 January 1998     

Traversing field of view and AR-PIV for mid-field wake vortex investigation in a towing tank

Wake vortex flow experiments are performed in a water tank where a 1:48 scaled model of a large transport aircraft A340-300 is towed at the speed of 3 and 5 ms^-1 with values of the angle of attack !={2°, 4°, 8°}. Particle image velocimetry (PIV) measurements are performed in a plane perpendicular to the towing direction describing the streamwise component of the wake vorticity. The instantaneous field of view (I-FOV) is traversed vertically with an underwater moving-camera device tracking the vortex core during the downward motion. An adaptive resolution (AR) image-processing technique is introduced that enhances the PIV interrogation in terms of spatial resolution and accuracy. The main objectives of the investigation are to demonstrate the applicability of PIV diagnostics in wake vortex research with towing-tank facilities. The specific implementation of the traversing field-of-view (T-FOV) technique and the AR image processing are driven by the need to characterize the vortex wake global properties as well as the vortex decay phenomenon in the mid- and far-field. Relevant aerodynamic information is obtained in the mid-field where the time evolution of the vortex structure (core radius and tangential velocity) and of the overall vortex wake (vortex trajectory, descent velocity, circulation) are discussed.     

高速电梯系统时变动力学模型与分析

以往关于电梯系统的研究指出，引起电梯系统振动的主要原因在于外部激励－由曳引机，承重装置，拖动和控制系统等引起。这是基于经典的结构共振理论得出的结论，但不能解释某些电梯的振动行为。本文从时变结构力学的观点出发，计及电梯曳引钢丝绳的长度随时间变化，建立起电梯系统的变刚度动力学模型，采用解析方法给出了高速电梯弹性振动的位移和加速度响应表达式。从理论上证明作为时变系统的电梯，具有振荡运动的特征，存在由变刚度引起的自激振动。进一步研究表明，电梯提速意味着曳引钢丝绳的初始扰动增大，导致电梯振动的加速度也增大，对电梯的舒适性有负面影响。     

Exotic vortex wakes—point vortex solutions

Von Kármán was the first to present a quantitative model of the “vortex street” wake as a double row of point vortices, to determine which configurations propagate in the direction of the rows, and to consider the linear stability theory for such states. In the early literature one works with infinite rows of vortices. The vortex street is assumed to continue to infinity both upstream and downstream. Another analytical approach is to use periodic boundary conditions in the direction of the wake. This representation was used by Domm in his analysis of the instability of the Kármán vortex street. Birkhoff and Fisher in 1959 were the first to treat vortices in a periodic strip as a dynamical system in its own right. We have used the periodic system to address problems of vortex wake patterns, in particular vortex wakes that are more complicated than the traditional two-vortices-per-strip configurations. We use the term “exotic” for such wakes. We submit that this approach can yield a number of insights, including results of direct relevance to experiments, in the same sense that von Kármán's analysis has been helpful to the understanding of the regular vortex street wake, and we present the results obtained to date following this program.     

Three-dimensional evolution of vortices and early features of coherent structure in the turbulent wake behind a 2-D circular cylinder

3-D evolution of Kármán vortex filaments and vortex filaments in braid regions in the turbulent wake of a 2-D circular cylinder is investigated numerically based on inviscid vortex dynamics by analyzing the response of the initially 2-D spanwise vortex filaments to periodic spanwise disturbance of varying magnitude, wavelength and initial phase angles. Our results reveal a kind of 3-D vortex system in the wake which consists of large scale horseshoe-shaped vortices and small scale γ-shaped vortex filaments as well as vortex loops. The mechanism and the dynamic process about the generation of streamwise vortical structure and the 3-D coherent structure are reported. currently published in the Chinese Edition of Acta Mechanica Sinica, Vol.25, No.3, 1993 The project supported by National Natural Science Foundation of China and the National Basic Research Project “Nonlinear Science”     

Study on the mechanisms and quantitative law of mode I supersonic crack propagation

Continuum mechanics predicts that the propagation speed of non-equilibrium information in solids is limited by the longitudinal wave speed, so is crack propagation. However, solids are essentially discrete systems. In this paper, via theoretical analysis and numerical simulations, it is demonstrated in a straightforward way that non-equilibrium disturbance (e.g. force, displacement, energy, and so on) can propagate at a supersonic speed in discrete systems, although the magnitude of the disturbance attenuates very quickly. In dynamic fracture, a cascade of atomic-bond breaking events provides an amplification mechanism to counterbalance the attenuation of the disturbance. Therefore, supersonic crack propagation can be realized in a domino way. Another key factor for supersonic crack propagation is to ensure sufficient energy flowing into the crack tip. Since most energy can only be transferred at a speed limited by the longitudinal wave speed, the conditions for the occurrence of supersonic crack propagation are not easily met in most situations, unless there is high pre-stored energy along the crack path or continuous energy supply from the loading concomitantly moving with the crack tip. A quantitative relation between supersonic crack propagation speed and material properties and parameters is given, which implies that knowing all the classical macroscopic quantities is not enough in determining the supersonic crack propagation speed, and the microstructure does play a role. Moreover, it is interesting to note that fracture toughness affects the crack propagation speed in the subsonic regime, but not in the supersonic regime, because the deformation/stress is uniform in front of a supersonic crack where strength criterion dominates.     

Low Order Modelling of Freely Vibrating Flexible Cables

A highly efficient, low-order model for vortex-induced vibration of flexible cables at low Reynolds number has been developed. A coupled map lattice (CML) wake model, based on circle maps, is combined with a cable model (linear wave equation). With this model, both the self-excited response of the cable oscillation in the crossflow direction and the resulting wake structures are examined at Re = 100. This represents an improvement over earlier CML models capable of only modelling wakes behind externally forced cables. For comparison, spectral-element based numerical simulations, in addition to experiments on a freely vibrating cable flow, were conducted. The freely vibrating CML model predicted lace-like structures consistent with these numerical simulations and experimental results. Little difference was noted between the vortex shedding wake patterns determined for forced cables (from previous CML models) and freely vibrating cables. The freely vibrating CML matched experimental data for maximum cable amplitude reasonably well over a range of mass-damping parameter employed in offshore structural applications.     

Aeroelastic analysis of large horizontal wind turbine baldes

A nonlinear aeroelastic analysis method for large horizontal wind turbines is described. A vortex wake method and a nonlinear finite element method (FEM) are coupled in the approach. The vortex wake method is used to predict wind turbine aerodynamic loads of a wind turbine, and a three-dimensional (3D) shell model is built for the rotor. Average aerodynamic forces along the azimuth are applied to the structural model, and the nonlinear static aeroelastic behaviors are computed. The wind rotor modes are obtained at the static aeroelastic status by linearizing the coupled equations. The static aeroelastic performance and dynamic aeroelastic responses are calculated for the NH1500 wind turbine. The results show that structural geometrical nonlinearities significantly reduce displacements and vibration amplitudes of the wind turbine blades. Therefore, structural geometrical nonlinearities cannot be neglected both in the static aeroelastic analysis and dynamic aeroelastic analysis.     

Stability of motion of two rigid bodies connected by a cable in the atmosphere

The spatial motion of two rigid bodies connected by a weightless inextensible cable in the atmosphere is considered. They are assumed to be bodies of revolution with static and dynamic symmetry. The condition of static stability of the system angular motion with respect to the direction of the incident airflow velocity vector is written out and analyzed. The influence of gyroscopic terms and damping moments on the stability condition is studied. An example of analysis of motion in the atmosphere of two connected bodies that are cones with a spherical tip is given. It is shown that the stable motion in the atmosphere can always be ensured by an appropriate matched choice of the parameters of the entire system on the basis of the obtained stability conditions. A numerical example of estimating the cable tension forces arising as the system descends on a ballistic trajectory in the atmosphere is presented.     

基于相交不稳定性的尾流自消散机翼实验研究

飞机尾流是复杂的流动现象,相关控制的研究常采用简化模型,抓住主要矛盾进行尾流不稳定性的学术探索. 采用结构化矩形机翼模型,通过添加扰流片来模拟襟翼的一种作动方式,引入一对与主翼涡反向的小涡,以期诱发尾涡的瑞利-路德维希相交不稳定性. 改变模型在水槽中的拖曳速度以及机翼攻角,采用粒子图像速度场仪定量研究单主翼尾涡发展特性以及双涡相互作用特性. 研究表明,未添加扰流片时,尾涡环量在45 个翼展内相对于初始环量衰减了10%;而添加了扰流片的实验中,在较好的实验参数组合情况下,主翼尾涡环量较初始环量降低35%~45%. 结果表明添加适当扰流片产生的反向小涡能诱发与主翼尾涡的相交不稳定性,在尾流涡系中引入自消散机制,加速机翼尾涡的消散过程,达到提早消弱尾涡的目的.      

降落伞膜索非线性有限元模拟

用膜单元和索单元模拟降落伞织物绳索系统,基于完全拉格朗日格式的非线性有限元方法编程计算降落伞的结构动力学特性。采用增量与迭代混合方法改善非线性计算的收敛特性并结合HHT隐式时间推进方法减小整体迭代计算量。使用修正应力应变张量导数的方法模拟膜单元单向应力状态并针对膜单元和索单元分别进行了非线性有限元计算验证。最后针对C-9型降落伞建立三维有限元模型,根据设定流速对伞衣施加均匀压强载荷,将模拟展开的结果与使用相同模型、不同方法商业软件的文献进行对比,显示了隐式非线性有限元方法模拟降落伞膜索系统大变形动力学的能力。     

IMPROVEMENT OF EXPLICIT ALGORITHMS STABILITY WITH VISCO-ELASTIC ARTIFICIAL BOUNDARY ELEMENTS 1)

黏弹性人工边界单元是目前常用的处理半无限空间波动问题的数值模拟方法,可有效吸收计算区域内产生的外行波动.黏弹性人工边界单元具有与内部介质不同的质量密度、刚度和阻尼,受其影响,对整体模型进行显式时域逐步积分时,在边界区域易发生失稳现象,影响整体系统显式积分的计算效率. 针对该问题目前尚无行之有效的解决方法.本文针对二维黏弹性人工边界单元,建立可代表整体系统典型特征的侧边子系统和角点子系统,利用传递矩阵谱半径分析方法,基于传统中心差分格式,推导得到局部子系统稳定性条件的解析解.在此基础上通过研究解析解中各物理参数对稳定性条件的影响,给出通过增加人工边界单元的质量密度,以改善采用黏弹性人工边界单元时显式算法稳定性的方法.均匀和成层半空间波动问题算例分析表明,将内部单元质量密度设置为人工边界单元质量密度的上限,可以在保证黏弹性人工边界计算精度的前提下,有效改善整体系统显式时域逐步积分的数值稳定性,大幅提高计算效率.     

一种风力机气动计算的全自由涡尾迹模型

采用全自由方式建立风力机尾流场的涡尾迹模型,引入“虚拟周期”的概念,并发展一种自适应松弛因子方法,从而改善了自由尾迹迭代的稳定性,提高了迭代收敛速度。利用建立的自由涡尾迹模型,计算了风力机叶片的尾流场结构、气动性能及叶片载荷,并与实验结果进行了对比分析。结果表明,尖速比越大,自适应松弛因子方法对缩小模型计算时间越有效;全自由涡尾迹模型能准确给出风力机尾流场的结构,包括尾迹的扩张以及叶尖涡和叶根涡的产生、发展和耗散的过程,风轮扭矩与实验数据吻合;叶片载荷分布的计算结果在低风速下与实验值基本一致,但是在大风速下差别较大,说明需要一个准确的失速模型。     

探测器对超音速刚性盘-缝-带型降落伞系统的影响

研究了流体初始马赫数为 2.0 时, 探测器的存在与否对刚性盘-缝-带型降落伞系统气动减速性能以及流场流体结构特性的影响. 对于非定常可压缩流体的数值模拟, 流场采用了三层块结构自适应网格加密技术, 配合混合形式的TCD (tuned center difference)和WENO (weighted essentially non-oscillatory)计算格式以及基于拉伸涡亚格子模型的大涡模拟方法来处理超音速流中的激波以及大尺度湍流旋涡结构等. 结果表明: 无探测器时, 降落伞系统的流场结构稳定, 扰动较小; 有探测器存在时, 探测器后端的湍流尾迹和伞衣内部逆向运动溢出的流体与伞衣前端的弓形激波周期性的相互作用, 使得激波位置发生前移、激波倾角变小, 伞衣内部流场难以达到平衡稳定状态. 这加剧了降落伞系统的气动阻力振荡脉动变化, 降低了降落伞系统气动阻力系数, 同时也使得降落伞系统流场尾迹结构更加复杂.      

Stability of flow past a cylinder: Energy budget of eigenmodes

Global linear stability analysis of the flow past a circular cylinder at the onset of primary wake instability is carried out. The real and imaginary parts of the most unstable eigenmode, responsible for vortex shedding, are very similar but associated with a spatial shift in the vortex structures. This shift results in the convection of vortices that are observed in the unsteady flow, which is actually a consequence of global absolute instability. The kinetic energy density, associated with the most unstable eigenmode, is studied. At the onset of the instability the energy density of the disturbance field is found to be stronger in the far wake compared with the near wake. With increase in Re the region where the disturbance is strong moves upstream closer to the cylinder. However, the maximum value of the kinetic energy density of the disturbance lies outside the recirculation zone even for Re upto 100. A linearized mechanical energy equation for the time evolution of the kinetic energy density of the disturbance is utilized to examine the energy budget of the most unstable eigenmode at various Re. It is found that the most significant contribution to the growth rate of the disturbance arises from the transfer of the energy due to the strain rate of the base flow to the perturbation. The stabilizing effect of the viscous dissipation increases with increase in Re, but saturates for Re beyond ～70. Copyright © 2009 John Wiley & Sons, Ltd.     

圆柱尾流的绝对不稳定性

在水槽和低湍流度水洞中进行亚临界雷诺数圆柱尾流稳定性实验来流速度由零缓慢增长到一定值后保持不变,稳定足够长时间后,在流向某站位处给流场一个有限幅值的脉冲扰动,测量扰动前后相当长时间内下游尾流速度信号的变化情况当雷诺数处于高亚临界值时,未受扰动的尾流速度脉动很小,处于定常状态,但对近尾流进行脉冲扰动后,能够激发出不衰减的旋涡脱落发现扰动位置限制在圆柱后一定范围内才能有效,再往下游则扰动随时间衰减．说明圆柱近尾流中存在一个绝对不稳定区,在该区域内的扰动将在当地放大,经过复杂的演化,最后形成不衰减的旋涡脱落.     

考虑阻尼的无限长小垂度缆索弹性波的传播

缆索结构被广泛应用于电气、土木、海洋和航空工程等领域,随着缆索在工程中的应用长度越来越长,高阶振动越来越明显,研究时应该考虑扰动沿着缆索的传播.现有对缆索弹性波传播的研究中,通常不考虑阻尼项,然而阻尼对于波的传播有着重要影响.文章考虑阻尼的影响,发展了包含阻尼项的三维弹性缆索运动方程.通过求解上述含阻尼项的运动方程,分别考察了面内面外弹性波的频率关系、相速度和群速度等自由传播特性,进而通过计算无限长弹性缆索在初始余弦型脉冲作用下的位移响应,分析扰动沿着该缆索的传播规律,考察波的色散现象以及阻尼对于缆索弹性波传播的影响.结果表明,考虑阻尼后,面内波和面外波均为色散波,面内波在曲率的作用下,为高度色散波.此外,在阻尼的影响下,波的峰值在传播过程不断减小,且波的后缘端点响应总是高于前缘端点响应.     

Recurrence and Reconnection Effect in an Attached Two-Dimensional Internal Wave Field

The shadow pattern of the wake behind a horizontal cylinder uniformly towed in a linearly stratified fluid is analyzed. In the “imbedded turbulent vortex” and “narrow turbulent wake” regimes the structure of the attached internal waves with fairly large amplitudes in the neighborhood of the body satisfactorily agrees with calculations based on the linear theory. As the distance from the source increases, the pattern becomes more complex. The internal waves radiated by the body itself and by the isolated vortices in the wake interfere and nonlinearly interact with each other and with the other flow elements. At large ages τ=t/T_b > 5.8 — time is normalized with respect to the buoyancy period) recurrence (spatial structure restored) and restructuring (phase surfaces reconnected) of a group of longest internal waves (of the attached type) are observed. The recurrent waves penetrate through the wake. These effects are associated with a general restructuring of the stratification modulated by a particular wave scale.