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.     

An efficient method for nonlinear aeroelasticy of slender wings

This paper aims the nonlinear aeroelastic analysis of slender wings using a nonlinear structural model coupled with the linear unsteady aerodynamic model. High aspect ratio and flexibility are the specific characteristic of this type of wings. Wing flexibility, coupled with long wingspan can lead to large deflections during normal flight operation of an aircraft; therefore, a wing in vertical/forward-afterward/torsional motion using a third-order form of nonlinear general flexible Euler–Bernoulli beam equations is used for structural modeling. Unsteady linear aerodynamic strip theory based on the Wagner function is used for determination of aerodynamic loading on the wing. Combining these two types of formulation yields nonlinear integro-differentials aeroelastic equations. Using the Galerkin’s method and a mode summation technique, the governing equations will be solved by introducing a numerical method without the need to adding any aerodynamic state space variables and the corresponding equations related to these variables of the problem. The obtained equations are solved to predict the aeroelastic response of the problem. The obtained results for a test case are compared with those of some other works and show a good agreement between results.     

Nonlinear Analysis of Store-Induced Limit Cycle Oscillations

Flight tests of modern high-performance fighter aircraft reveal the presence of limit cycle oscillation (LCO) responses for aircraft with certain external store configurations. Conventional linear aeroelastic analysis predicts flutter for conditions well beyond the operational envelope, yet these store-induced LCO responses occur at flight conditions within the flight envelope. Several nonlinear sources may be present, including aerodynamic effects such as flow separation and shock-boundary layer interaction and structural effects such as stiffening, damping, and system kinematics. No complete theory has been forwarded to accurately explain the mechanisms responsible. This research examines a two degree-of-freedom aeroelastic system which possesses kinematic nonlinearities and a strong nonlinearity in pitch stiffness. Nonlinear analysis techniques are used to gain insight into the characteristics of the behavior of the system. Numerical simulation is used to verify and validate the analysis. It is found that when system damping is low, the system clearly exhibits nonlinear interaction between aeroelastic modes. It is also shown that although certain applied forcing conditions may appear negligible, these same forces produce large amplitude LCOs under specific realizable circumstances.     

An Investigation of Internal Resonance in Aeroelastic Systems

Although the study of internal resonance in mechanical systems has been given significant consideration, minimal attention has been given to internal resonance for systems which consider the presence of aerodynamic forces. Herein, the investigators examine the possible existence of internal resonances, and the related nonlinear pathologies that such responses may have, for an aeroelastic system which possesses nonlinear aerodynamic loads. Evidence of internal resonance is presented for specific classes of aeroelastic systems, and such adverse response indicates nonlinearities may lead to aeroelastic instabilities that are not predicted by traditional (linear) approaches.     

Effects of actuator nonlinearity on aeroelastic characteristics of a control fin

The influences of actuator nonlinearities on actuator dynamics and the aeroelastic characteristics of a control fin were investigated by using iterative V-g methods in subsonic flows; in addition, the doublet-hybrid method (DHM) was used to calculate unsteady aerodynamic forces. The changes of actuator dynamics induced by nonlinearities, such as backlash or freeplay, and the variations of flutter boundaries due to the changes of actuator dynamics were observed. Results show that the aeroelastic characteristics can be significantly dependent on actuator dynamics. Thus, the actuator nonlinearities may play an important role in the nonlinear aeroelastic characteristics of an aeroelastic system. The present results also indicate that it is necessary to seriously consider the influence of actuator dynamics on the flutter characteristics at the design stage of actuators to prevent aeroelastic instabilities of aircraft or missiles.     

平流层飞艇空气动力估算

本文采用有限基本解方法与工程估算方法相结合的气动力工程计算方法,用以计算平流层飞艇的气动力。将飞艇所受的气动力分成飞艇艇身和尾翼所受气动力两部分,每一部分的气动力按照无粘性流产生的线性气动力和粘性引起的非线性气动力分别进行计算。根据势流理论对飞艇艇身线性气动力进行分析计算,由于飞艇艇体是旋成体,故根据Allen的横流阻力理论对其所受的非线性气动力进行计算;尾翼的线性气动力采用有限基本解方法进行计算,非线性气动力用Polhamus-Lamar吸力比拟方法估算。该方法中考虑了由于尾翼安装在体上后,处于艇体产生的上洗流场中,尾翼气动力的变化和尾翼对艇身气动力的干扰作用。通过算例的计算与实验结果比较得出该方法可以快速、准确的计算飞艇所受的气动力。     

跨音速极限环型颤振的高效数值分析方法

事先建立一个低阶的非线性、非定常气动力模型是开展非线性流场中气动弹性问题研究的一个捷径. 基于CFD方法, 通过计算结构在流场中自激振动的响应来获得系统的训练数据. 采用带输出反馈的循环RBF神经网络, 建立时域非线性气动力降阶模型.耦合结构运动方程和非线性气动力降阶模型, 采用杂交的线性多步方法计算结构在不同速度(动压)下的响应历程, 从而获得模型极限环随速度(动压)变化的特性. 两个典型的跨音速极限环型颤振算例表明, 基于气动力降阶模型方法的计算结果与直接CFD仿真结果吻合很好, 与后者相比其将计算效率提高了1~2个数量级.      

Effects of multiple structural nonlinearities on limit cycle oscillation of missile control fin

Aeroelastic analyses are performed for a 2-D typical section model with multiple nonlinearities. The differences between a system with multiple nonlinearities in its pitch and plunge spring and a system with a single nonlinearity in its pitch are thoroughly investigated. The unsteady supersonic aerodynamic forces are calculated by the doublet point method (DPM). The iterative V-g method is used for a multiple-nonlinear aeroelastic analysis in the frequency domain and the freeplay nonlinearity is linearized using a describing function method. In the time domain, the DPM unsteady aerodynamic forces, which are based on a function of the reduced frequency, are approximated by the minimum state approximation method. Consequently, multiple structural nonlinearities in the 2-D typical wing section model are influenced by the pitch to plunge frequency ratio. This result is important in that it demonstrates that the flutter speed is closely connected with the frequency ratio, considering that both pitch and plunge nonlinearities result in a higher flutter speed boundary than a conventional aeroelastic system with only one pitch nonlinearity. Furthermore, the gap size of the freeplay affects the amplitude of the limit cycle oscillation (LCO) to gap size ratio.     

平流层飞艇气动参数辨识

进入21世纪以来,随着科技的飞速发展,世界上掀起了研究和开发平流层平台的热潮。飞艇作为平流层平台可以实现无线通信、空间观测、大气测量以及军事侦查等目的。本文首先将飞艇所受的气动力分成由于来流速度产生的定常气动力和飞艇转动引起的非定常气动力两部分,通过理论分析建立了飞艇的气动力模型,从而得到需要辨识的气动参数。其次建立了以浮心为原点的六自由度非线性动力学模型和一种基于混合遗传算法的气动力系数辨识方法——混合遗传算法（遗传算法＋单纯型法）与极大似然法相结合的方法,并利用该方法对飞艇的气动参数进行辨识。通过仿真结果验证了该方法实用性和有效性。最后通过对气动参数的准确值与辨识值的分析比较,得出各个参数对飞艇运动性能的影响情况。     

飞行器非线性气动伺服弹性力学

现代飞行器日益呈现结构轻质化、控制系统宽通带和高权限的发展趋势. 因此, 非定常气动力、柔性结构和主动控制系统三者间的耦合力学成为重要的研究领域. 自20世纪80年代起, 航空界开始关注受控飞行器的气动弹性稳定性以及主动控制问题, 但对气动/结构的非线性效应、控制回路时滞对受控飞行器动力学行为的影响规律研究尚不充分. 研究这些影响规律不仅涉及非线性、高维数、多变参数和时滞效应等难题, 而且必须面对空气动力、飞行器结构、驱动机构、控制系统之间的强耦合问题. 其中的前沿难题是: 发展非线性气动伺服弹性动力学建模理论, 揭示上述因素诱发受控气动弹性振动的动力学机理, 开展气动伺服弹性控制风洞实验. 本文针对非线性气动伺服弹性力学所涉及的非线性非定常气动力建模、非线性结构动力学、气动伺服弹性控制律设计、气动伺服弹性实验, 总结相关研究现状和最新进展, 特别是近年来作者学术团队的研究成果, 并对进一步研究给出若干建议.      

Bifurcation analysis of an aeroelastic system with concentrated nonlinearities

Analytical and numerical analyses of the nonlinear response of a three-degree-of-freedom nonlinear aeroelastic system are performed. Particularly, the effects of concentrated structural nonlinearities on the different motions are determined. The concentrated nonlinearities are introduced in the pitch, plunge, and flap springs by adding cubic stiffness in each of them. Quasi-steady approximation and the Duhamel formulation are used to model the aerodynamic loads. Using the quasi-steady approach, we derive the normal form of the Hopf bifurcation associated with the system??s instability. Using the nonlinear form, three configurations including supercritical and subcritical aeroelastic systems are defined and analyzed numerically. The characteristics of these different configurations in terms of stability and motions are evaluated. The usefulness of the two aerodynamic formulations in the prediction of the different motions beyond the bifurcation is discussed.     

CHARACTERIZATION OF THE BEHAVIOUR OF A SIMPLE AEROSERVOELASTIC SYSTEM WITH CONTROL NONLINEARITIES

The characterization of the behaviour of nonlinear aeroelastic systems has become a very important research topic in the Aerospace Industry. However, most work carried to-date has concentrated upon systems containing structural or aerodynamic nonlinearities. The purpose of this paper is to study the stability of a simple aeroservoelastic system with nonlinearities in the control system and power control unit. The work considers both structural and control law nonlinearities and assesses the stability of the system response using bifurcation diagrams. It is shown that simple feedback systems designed to increase the stability of the linearized system also stabilize the nonlinear system, although their effects can be less pronounced. Additionally, a nonlinear control law designed to limit the control surface pitch response was found to increase the flutter speed considerably by forcing the system to undergo limit cycle oscillations instead of fluttering. Finally, friction was found to affect the damping of the system but not its stability, as long as the amplitude of the frictional force is low enough not to cause stoppages in the motion.     

Methods of fluid–structure coupling in frequency and time domains using linearized aerodynamics for turbomachinery

Two methods of fluid–structure coupling for turbomachinery are presented, the first one in the frequency domain and the second in both frequency and time domains. In both methods, the structure and the fluid are assumed to have circumferential cyclic symmetric properties and the unsteady aerodynamic forces are assumed to be linear in terms of the structural displacements. The motion equation of the reference sector in the travelling wave coordinates is projected on the complex eigenmodes for each phase number. The generalized unsteady aerodynamic forces are computed by solving the Euler equations and by assuming the structural motion to be harmonic with a constant phase angle between two adjacent sectors. In the frequency domain, the complex, nonlinear eigenvalue problem for the aeroelastic stability analysis is solved iteratively either by the double scanning method or by using Karpel's minimum state smoothing of the aerodynamic coefficient matrix. In the time domain, Karpel's smoothing method is used to obtain an approximation of the generalized unsteady aerodynamic forces by means of auxiliary state variables. These coupling methods are tested on a compressor blade row and the good agreement obtained between their results and those of the direct coupling method shows that the proposed numerical methods, already used in aircraft applications, are adapted to turbomachinery.     

Studies of Store-Induced Limit-Cycle Oscillations Using a Model with Full System Nonlinearities

The authors investigate limit-cycle oscillations of a wing/store configuration. Unlike typical aeroelastic studies that are based upon a linearized form of the governing equations, herein full system nonlinearities are retained, and include transonic flow effects, coupled responses from the structure, and store-related kinematics and dynamics. Unsteady aerodynamic loads are modeled with the equations from transonic small disturbance theory. The structural dynamics for the cantilevered wing are modeled by the nonlinear equations of motion for a beam. The effects of general store-placement are modeled by the nonlinear equations of motion related to the position-induced nonlinear kinematics. Chordwise deformations of the wing surface, as well as pylon and store flexibility, are assumed negligible. Nonlinear responses are studied by examining bifurcation and related response characteristics using direct simulation. Particular attention is given to cases for which large-time, time-dependent behavior is dependent on initial conditions, as observed for some configurations in flight test. Comparisons of results in which selective nonlinearities are excluded indicate that the accurate prediction of nonlinear responses such as limit cycle oscillations (LCOs) may depend upon consideration of all nonlinearities related to the full system.     

A theoretical and experimental investigation of the effects of a steady angle of attack on the nonlinear flutter of a delta wing plate model

Limit cycle oscillations (LCO) of wings on certain modern high performance aircraft have been observed in flight and in wind tunnel experiments. Whether the physical mechanism that gives rise to this behavior is a fluid or structural nonlinearity or both is still uncertain. It has been shown that an aeroelastic theoretical model with only a structural nonlinearity can predict accurately the limit cycle behavior at low subsonic flow for a plate-like wing at zero angle of attack. Changes in the limit cycle and flutter behavior as the angle of attack is varied have also been observed in flight. It has been suggested that this sensitivity to angle of attack is due to a fluid nonlinearity. In this investigation, we study the flutter and limit cycle behavior of a wing in low subsonic flow at small steady angles of attack. Experimental results are compared to those predicted using an aeroelastic theoretical model with only a structural nonlinearity. Results from both experiment and theory show a change in flutter speed as the steady angle of attack is varied. Also the LCO magnitude increased at a given velocity as the angle of attack was increased for both the experiment and theory. While not proving that the observed sensitivity to angle of attack of LCO in aircraft is due to a structural nonlinearity, the results do show that a change in the aeroelastic behavior at angles of attack can be caused by a structural nonlinearity as well as a fluid nonlinearity. In this paper, only structural nonlinearities are considered, but an extension to include aerodynamic nonlinearities would be very worthwhile.     

考虑几何非线性的复合材料机翼气动弹性分析

本文研究结构几何非线性与气动力非平面效应对大展弦比复合材料机翼的气动弹性行为的影响．将非线性有限元法与曲面涡格法结合,计算机翼静气动弹性变形;通过曲面偶极子格网法结合静气动弹性平衡位置处的结构切线刚度,建立气动弹性方程并求解得到机翼颤振速度．针对板模型机翼,分析了迎角对机翼几何非线性气动弹性特性的影响．结果表明：本文复合材料板模型机翼的颤振形式不受水平弯曲模态影响,属于经典弯扭颤振;在几何非线性的影响下,机翼扭转频率随结构变形增大而明显减小,颤振速度随迎角增大而减小．     

Transonic limit cycle oscillation behavior of an aeroelastic airfoil with free-play

The limit cycle oscillation (LCO) behaviors of an aeroelastic airfoil with free-play for different Mach numbers are studied. Euler equations are adopted to obtain the unsteady aerodynamic forces. Aerodynamic and structural describing functions are employed to deal with aerodynamic and structural nonlinearities, respectively. Then the flutter speed and flutter frequency are obtained by V-g method. The LCO solutions for the aeroelastic airfoil obtained by using dynamically linear aerodynamics agree well with those obtained directly by using nonlinear aerodynamics. Subsequently, the dynamically linear aerodynamics is assumed, and results show that the LCOs behave variously in different Mach number ranges. A subcritical bifurcation, consisting of both stable and unstable branches, is firstly observed in subsonic and high subsonic regime. Then in a narrow Mach number range, the unstable LCOs with small amplitudes turn to be stable ones dominated by the single degree of freedom flutter. Meanwhile, these LCOs can persist down to very low flutter speeds. When the Mach number is increased further, the stable branch turns back to be unstable. To address the reason of the stability variation for different Mach numbers at small amplitude LCOs, we find that the Mach number freeze phenomenon provides a physics-based explanation and the phase reversal of the aerodynamic forces will trigger the single degree of freedom flutter in the narrow Mach number range between the low and high Mach numbers of the chimney region. The high Mach number can be predicted by the freeze Mach number, and the low one can be estimated by the Mach number at which the aerodynamic center of the airfoil lies near its elastic axis. Influence of angle of attack and viscous effects on the LCO behavior is also discussed.     

平流层飞艇动力学与控制研究进展

本文简要介绍了飞艇的发展沿革和研究现状. 通过同传统的航空器、航天器、潜艇和低空飞艇进行比较, 阐述了平流层飞艇的飞行原理. 从基本运动模型和复杂受力情况的角度, 系统地讨论了飞艇动力学研究进展, 包括空气动力学研究、静力分析、热力学分析、柔性体动力学及流固耦合研究. 然后综述了飞艇控制方法研究进展, 包括小扰动线性化控制、输入输出反馈线性化控制、基于Lyapunov 非线性稳定性的控制及其他控制方法. 最后展望了在平流层飞艇动力学与控制领域需要从6 个方面加强研究.      

Aircraft T-tail flutter predictions using computational fluid dynamics

The paper presents the application of computational aeroelasticity (CA) methods to the analysis of a T-tail stability in transonic regime. For this flow condition unsteady aerodynamics show a significant dependency from the aircraft equilibrium flight configuration, which rules both the position of shock waves in the flow field and the load distribution on the horizontal tail plane. Both these elements have an influence on the aerodynamic forces, and so on the aeroelastic stability of the system. The numerical procedure proposed allows to investigate flutter stability for a free-flying aircraft, iterating until convergence the following sequence of sub-problems: search for the trimmed condition for the deformable aircraft; linearize the system about the stated equilibrium point; predict the aeroelastic stability boundaries using the inferred linear model. An innovative approach based on sliding meshes allows to represent the changes of the computational fluid domain due to the motion of control surfaces used to trim the aircraft. To highlight the importance of keeping the linear model always aligned to the trim condition, and at the same time the capabilities of the computational fluid dynamics approach, the method is applied to a real aircraft with a T-tail configuration: the P180.     

基于POD和代理模型的静气动弹性分析方法

静气动弹性问题考虑弹性结构与定常气动力间的相互耦合作用,对飞行器的性能和安全具有显著的影响.在现代飞行器设计阶段,计算流体力学(CFD)/计算结构力学(CSD)直接耦合方法是精确考察静气动弹性影响的重要手段.然而,基于CFD技术的气动力仿真手段在耦合过程中计算量大且耗时长,难以满足设计阶段的需求.因此,为了兼顾计算精度与效率,文章采用本征正交分解(POD)和Kriging代理模型相结合的模型降阶方法,替代CFD求解过程并耦合有限元分析(FEA)方法,建立了高效、准确的静气动弹性分析框架.相较于传统的以模态法为主的静气动弹性分析方法,该方法能够解决更为复杂的静气动弹性问题以及提供静气动弹性变形过程中的气动分布载荷.针对典型三维跨声速HIRENASD机翼模型开展的马赫数、迎角变化的算例验证表明:由建立的静气动弹性分析方法与CFD/CSD直接耦合方法计算得到机翼翼梢处的静变形量间的相对误差在5%以内;同时该方法预测静平衡位置处的气动分布载荷的误差在5%以内,静气动弹性分析的计算效率至少提升了6倍.