风力机叶片非线性挥舞分析

将风力机叶片简化为绕轮毂旋转的变截面Euler-Bernoulli悬臂梁,基于Greenberg公式给出非线性气动力,建立叶片挥舞振动非线性控制方程.由于变截面梁的弯曲刚度和线密度是沿梁轴线变化的函数,无法给出模态函数解析式,论文提出使用假设模态法计算的模态函数,作为基函数对控制方程进行Galerkin截断,通过将挥舞振动分解为静态位移和动态扰动合成,对其进行动态响应分析,同时讨论了叶轮转速、风速和旋转位置对振动特性的影响.研究表明:(1)叶轮转速对叶片挥舞特性影响显著,风速和叶片转角对振动特性影响很小.(2)静态位移随风速增加而增大,大体上成线性关系,气动阻尼随风速增加而减小.(3)风速较低时,非线性挥舞振动表现为衰减振动,随着风速增加,振动由衰减振动演化为周期运动,再由周期运动演化为拟周期运动.     

Analysis of Coupled Vibration Characteristics of Wind Turbine Blade Based on Green's Functions

This paper presents the analysis of dynamic characteristics of horizontal axis wind turbine blade, where the mode coupling among axial extension, flap vibration(out-of-plane bending), lead/lag vibration(in-plane bending) and torsion is emphasized. By using the Bernoulli-Euler beam to describe the slender blade which is mounted on rigid hub and subjected to unsteady aerodynamic force, the governing equation and characteristic equation of the coupled vibration of the blade are obtained. Due to the combined influences of mode coupling, centrifugal effect, and the non-uniform distribution of mass and stiffness, the explicit solution of characteristic equation is impossible to obtain. An equivalent transformation based on Green's functions is taken for the characteristic equation, and then a system of integrodifferential equations is derived. The numerical difference methods are adopted to solve the integrodifferential equations to get natural frequencies and mode shapes. The influences of mode coupling, centrifugal effect, and rotational speed on natural frequencies and mode shapes are analyzed. Results show that:(1) the influence of bending-torsion coupling on natural frequency is tiny;(2) rotation has dramatic influence on bending frequency but little influence on torsion frequency;(3) the influence of bending-bending coupling on dynamic characteristics is notable at high rotational speed;(4) the effect of rotational speed on bending mode is tiny.     

Coupled flapwise-chordwise-axial-torsional dynamic responses of rotating pre-twisted and inclined cantilever beams subject to the base excitation

A rotating pre-twisted and inclined cantilever beam model(RPICBM) with the flapwise-chordwise-axial-torsional coupling is established with the Hamilton principle and the finite element(FE) method. The effectiveness of the model is verified via comparisons with the literatures and the FE models in ANSYS. The effects of the setting and pre-twisted angles on the dynamic responses of the RPICBM are analyzed. The results show that:(i) the increase in the setting or pre-twisted angle results in the increases in the first-order flapwise and torsional frequencies while the decrease in the first-order chordwise frequency under rotating conditions;(ii) a positive/negative setting angle leads to a positive/negative constant component, while a positive/negative pre-twisted angle leads to a negative/positive constant component;(iii) when the rotation speed is non-zero, the pre-twisted angle or non-zero setting angle will result in the coupled flapwise-chordwiseaxial-torsional vibration of the RPICBM under axial base excitation.     

旋转SMA纤维混杂复合材料薄壁梁的自由振动

研究具有SMA主动纤维的旋转复合材料单闭室薄壁截面梁的耦合自由振动问题.基于Hamilton原理并结合SMA纤维复合材料薄壁梁的二维截面内力(矩)与位移(转角)关系方程,导出旋转单闭室截面薄壁复合材料梁的1D耦合自由振动分析模型.该模型还考虑薄壁梁调矩角和预锥角的作用.采用Galerkin法求解振动模型,获得梁耦合振动...     

大于切出风速的大型风力机运行控制策略研究

运用非定常叶素动量(BEM)理论计算气动载荷,叠加重力载荷和惯性载荷,建立并数值求解全机动力学模型。基于快速非支配排序遗传算法(NSGA),在切出风速以上,优化得到变速变桨和定速变桨两种控制规律曲线,实现大型风力机在25m/s~40m/s风速之间正常运行的目的。比较两种控制策略的输出功率、风轮推力和转矩,得出变速变桨控制策略更适合于25m/s~40m/s之间风力机运行控制的结论。计算稳态工况时8种叶根载荷的极限值,由各载荷的变化趋势可知,Fy在25m/s之后增大9%,其他载荷均安全。     

Aerothermoelastic behavior of supersonic rotating thin-walled beams made of functionally graded materials

In this study, a thin-walled beam made of functionally graded material (FGM) which is used as rotating blades in turbomachinery under aerothermoelastic loading is investigated. The governing equations, which are based on first-order shear deformation theory, include the effects of the presetting angle, the secondary warping, temperature gradient through the wall thickness of the beam and also the rotational speed. Moreover, quasi-steady aerodynamic pressure loadings are determined using first-order piston theory, and steady beam surface temperature is obtained from gas dynamics theory. Then, the blade partial differential equations are transformed into a set of ordinary differential equations using the extended Galerkin method. Finally, having solved the resulting structural–fluid–thermal eigenvalue system of equations, the effects of Mach number and geometric parameters on natural frequencies are presented. The results demonstrate that the natural frequencies decrease under aerothermoelastic loading at high Mach numbers.     

旋转圆板振动的热力控制

本文研究发现,热力对旋转圆盘动力特性有明显影响.可将此特征应用于旋转圆盘振动的热力自适应控制.仿真和试验均表明,这种控制方法对一些结构振动控制将是一种有效的方法.     

Influence of pitching angle of incidence on the dynamic stall behavior of a symmetric airfoil

This study presents the influence of pitch angle of an airfoil on its near-field vortex structure as well as the aerodynamic loads during a dynamic stall process. Dynamic stall behavior in a sinusoidally pitching airfoil is usually analyzed at low to medium reduced frequencies and with the maximum angle of attack of the airfoil not exceeding 25°. In this work, we study dynamic stall of a symmetric airfoil at medium to high reduced frequencies even as the maximum angle of attack goes from 25° to 45°. The evolution and growth of the laminar separation bubble, also known as a dynamic stall vortex, at the leading edge and the trailing edge are studied as the pitch cycle goes from the minimum to the maximum angle of attack. The effect of reduced frequencies on the vortex structure as well as the aerodynamic load coefficients is investigated. The reduced frequency is shown to be a bifurcation parameter triggering period doubling behavior. However, the bifurcation pattern is dependent on the variation of the pitch angle of incidence of the airfoil.     

Bifurcation and dynamic behavior analysis of a rotating cantilever plate in subsonic airflow

Turbo-machineries, as key components, have wide applications in civil, aerospace, and mechanical engineering. By calculating natural frequencies and dynamical deformations, we have explained the rationality of the series form for the aerodynamic force of the blade under the subsonic flow in our earlier studies. In this paper, the subsonic aerodynamic force obtained numerically is applied to the low pressure compressor blade with a low constant rotating speed. The blade is established as a pre-twist and presetting cantilever plate with a rectangular section under combined excitations, including the centrifugal force and the aerodynamic force. In view of the first-order shear deformation theory and von-Kármán nonlinear geometric relationship, the nonlinear partial differential dynamical equations for the warping cantilever blade are derived by Hamilton's principle. The second-order ordinary differential equations are acquired by the Galerkin approach. With consideration of 1:3 internal resonance and 1/2 sub-harmonic resonance, the averaged equation is derived by the asymptotic perturbation methodology. Bifurcation diagrams, phase portraits, waveforms, and power spectrums are numerically obtained to analyze the effects of the first harmonic of the aerodynamic force on nonlinear dynamical responses of the structure.     

风速不确定性对风力机气动力影响量化研究

风力机气动力学一直是国内外研究的热点课题之一.目前相关研究大都是基于确定性工况条件, 但因风力机常年工作在自然来流复杂环境,风速随机波动致使风电系统呈现不确定性, 对电网稳定性带来巨大挑战,因此进行不确定风速条件下风力机气动力学研究具有重要意义.为揭示不确定性对风力机流场影响机理并明确其对气动力的影响程度,本文提出一种风力机不确定空气动力学分析方法,基于修正叶素动量理论和非嵌入式概率配置点法,建立水平轴风力机不确定性空气动力学响应模型; 以NREL Phase VI S809风力机叶轮为研究对象, 基于该模型提取风力机输出随机响应信息,量化不确定风速对风力机风轮功率、推力、叶片挥舞弯矩和摆振弯矩的影响程度;通过分析流动诱导因子不确定性在叶片展长方向上的分布规律,揭示不确定因素在风力机本体上的传播机制,为风电系统设计及应用提供理论依据和重要参考. 结果表明,风速波动对风力机功率和气动力影响显著,高斯风速标准差由0.05倍增大至0.15倍均值,功率和推力最大波动幅度分别由13.44%和8.00%增大至35.11%和22.02%,叶片挥舞弯矩和摆振弯矩最大波动幅度分别由7.20%和12.84%增大至19.90%和33.49%.来流风速不确定性导致叶片根部位置气流明显波动,可以考虑在该部分采取流动控制措施降低叶片对风速不确定性的敏感程度.      

基于流固耦合的跨声速压气机叶片静气动弹性分析

采用时域推进的双向流固耦合方法对一级跨声速压气机叶片流场和固体域进行数值模拟,研究跨声速转子叶片静气动弹性变形及其对气动性能的影响,对比分析了100%转速下转子叶片的气动特性和固有频率的变化.结果表明:转子叶片在气动力和离心惯性力共同作用下的弹性变形以扭转变形为主,气动力对叶尖前缘变形量的影响可达总变形量的20%.转子叶片变形后通道流通能力增强,气动特性曲线向大流量方向偏移.     

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads is studied in the paper. Through deriving accurate expressions of inertial force and initial hoop tension, a rotating conical shell model is presented based upon the Love's thin shell theory. Considering the periodic axial loads, equations of motion of the system with periodic stiffness coefficients are obtained utilizing the generalized differential quadrature (GDQ) method. Hill's method is introduced for parametric instability analysis. Primary instability regions for various natural modes are computed. Effects of rotational speed, constant axial load, cone angle and other geometrical parameters on the location and width of various instability regions are examined.     

飞机大迎角俯仰运动下的横侧向气动特性及被动控制

在南航3m低速风洞内,利用一套两自由度动态试验机构,通过测力实验研究了某飞机模型静态和俯仰动态过程中大迎角下的横侧向气动特性,分析比较了在模型头部加上扰动片后,对横侧向气动特性产生的影响.研究结果表明,模型在静态大迎角下会产生较大的侧向力和偏航力矩,而模型的快速上仰过程则进一步加剧了模型头部流动的非对称性,在大迎角下产生较大的偏航力矩迟滞环;当在模型头部加扰动片后,不论是静态过程还是动态过程,都使得模型的侧向力和偏航力矩减小,从而改善了俯仰运动过程中大迎角下的横侧向气动特性.     

考虑刚体运动与弹性运动耦合影响的旋转叶片振动有限元分析

本文研究了旋转叶片的纵向振动和双向横振动,考虑了刚体运动和弹性振动的耦合关系,利用有限元法推导出离散系统动力学方程,从而引出陀螺特征值问题。本文就某一特例了计算了在不同转速时叶片振动的自然频率,讨论了转速对振动频率的影响。     

弹性地基上转动FGM梁自由振动的DTM分析

基于Euler-Bernoulli梁理论,利用广义Hamilton原理推导得到弹性地基上转动功能梯度材料(FGM)梁横向自由振动的运动控制微分方程并进行无量纲化,采用微分变换法(DTM)对无量纲控制微分方程及其边界条件进行变换,计算了弹性地基上转动FGM梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种边界条件下横向自由振动的无量纲固有频率,再将控制微分方程退化到无转动和地基时的FGM梁,计算其不同梯度指数时第一阶无量纲固有频率值,并和已有文献的FEM和Lagrange乘子法计算结果进行比较,数值完全吻合。计算结果表明,三种边界条件下FGM梁的无量纲固有频率随无量纲转速和无量纲弹性地基模量的增大而增大;在一定无量纲转速和无量纲弹性地基模量下,FGM梁的无量纲固有频率随着FGM梯度指数的增大而减小;但在夹紧-简支和夹紧-自由边界条件下,一阶无量纲固有频率几乎不变。     

随机风作用下高速列车非定常气动载荷的计算方法

基于Cooper理论和谐波叠加法计算随车移动点的脉动风速,分析不同风向角下脉动风速的功率谱密度特性.在横风下高速列车非定常气动载荷计算方法的基础上,建立了侧风下高速列车非定常气动载荷的计算方法,并用此方法分析了侧向随机风作用下非定常气动载荷的统计特性,给出了各气动载荷的峰值因子.研究表明,当风向角接近90°时,无量纲功率谱会往高频移动,风向角对脉动风速的影响较小;在各个风向角下,气动载荷的标准差与平均值的比值仅依赖于侧偏角,侧力与侧滚力矩的峰值因子相同,摇头力矩与点头力矩的峰值因子相同.     

气固耦合振动叶栅非定常流动分析研究

引入结构动力学方程建立了二维N-S/结构振动耦合方程组,采用双时间法建立了气固耦合方程组的非定常数值求解体系,研究了叶栅间的二维非定常粘性流动及叶栅振动特性。对两种叶型分别计算了不同折合振动频率下的流场,振动叶栅位移随时间变化的曲线表明,采用气固耦合得到的叶栅振动频率与非耦合自振频率相比均有所下降;振动位移-时间曲线在不同振动折合频率下有显著差别。在气固耦合情况下叶栅振动规律及其稳定性与非耦合情形差异较大,因此研究叶栅振动稳定性应当考虑气动/结构的耦合。     

Dynamic study of a wind turbine blade with horizontal axis

The study of the dynamic behavior of a wind turbine with horizontal axis can be undertaken by various methods of analysis. The effects of the change of the aerodynamic flow (in the steady and unsteady cases), the variation of parameters of the cinematic movement (angle of attack, pitch angle and yaw angle) and the definition of subsystems characteristics that makes the wind turbine (blade, nacelle and pylon) allow one to characterize the structural dynamic behavior of the wind turbine. It is therefore necessary to develop these items. Once this is done, the structural dynamic behavior of the system can be improved. The term `improve' means the increase of the life duration by mastering the fatigue effects and the reduction of cost without sacrificing the aerodynamic output. The present study aims to examine the behavior of the blade, which is the main part of the wind turbine in that it that transmits forces to all other parts of the structure. The model is based on the theory of three-dimensional beams, under the assumption of variable sections of the type NACA 4415 airfoil, and takes into account membrane, transversal shear, flexion and free torsion effects. With regards to the aerodynamic loads (the lift, the drag and the pitching moment), a validation has been undertaken by considering experimental data and numerical results obtained by a CFD code (Fluent). The forces are obtained by means of a parametric CAD method interpolation of the aerodynamic poles by Bézier patch under geometrical constraints solved by a Simplex type algorithm. The emphasis is put on dynamic aspects by a complete processing of the dynamic equilibrium equation, applied to the wind turbine blade with horizontal axis.     

车辆各轮相干桥面不平顺激励的车桥耦合振动

根据车辆左右轮的互功率谱密度和相干函数,推导了左右轮桥面不平顺特性中对应相位角的相干关系,提出了采用相位角相干生成车辆各轮相干桥面不平顺激励的方法,并通过数值算例验证了该生成方法的可靠性.工程应用结果表明,车辆各轮相干桥面不平顺激励增大了桥梁、车辆竖向和车辆俯仰角的振动响应,但降低了车辆侧倾角的振动响应;不同相干函数模型对桥梁振动响应影响较小,但对车辆振动响应影响较大;同一相干函数模型,桥梁振动响应随着相干强度的增大而增大,但车辆振动响应随着相干强度的增大而减小;研究桥面不平顺随机激励对车桥耦合系统振动响应的影响有必要考虑车辆各轮的相干关系.     

Multi-parameter aerodynamic modeling for aeroelastic coupling in turbomachinery

A multi-parameter method based on multivariate spline function approximation and minimum state smoothing for modeling the generalized aerodynamic forces is proposed in order to reduce the cost of the aerodynamic computations in the solution of the coupled fluid–structure problem in turbomachinery. This method allows simultaneous variations of several parameters and provides the solutions of the coupled systems at arbitrary values of the parameters using the generalized aerodynamic forces computed at the few values of the parameters. This multi-parameter aerodynamic modeling method is applied to a large-chord blade, for which the two chosen parameters are the rotation speed and the inter-blade phase angle.