Airfoil Aeroelastic Flutter Analysis Based on Modified Leishman-Beddoes Model at Low Mach Number

Based on modified Leishman-Beddoes (L-B) state space model at low Mach number (lower than 0.3), the airfoil aeroelastic system is presented in this paper. The main modifications for L-B model include a new dynamic stall criterion and revisions of normal force and pitching moment coefficient. The bifurcation diagrams, the limit cycle oscillation (LCO) phase plane plots and the time domain response figures are applied to investigating the stall flutter bifurcation behavior of airfoil aeroelastic systems with symmetry or asymmetry. It is shown that the symmetric periodical oscillation happens after subcritical bifurcation caused by dynamic stall, and the asymmetric periodical oscillation, which is caused by the interaction of dynamic stall and static divergence, only happens in the airfoil aeroelastic system with asymmetry. Validations of the modified L-B model and the airfoil aeroelastic system are presented with the experimental airload data of NACA0012 and OA207 and experimental stall flutter data of NACA0012 respectively. Results demonstrate that the airfoil aeroelastic system presented in this paper is effective and accurate, which can be applied to the investigation of airfoil stall flutter at low Mach number.     

带有气动及结构非线性的二元机翼颤振分析

研究了翼型在低马赫数条件下的非定常气动特性,从翼型表面气流运动的角度对Leishman-Beddoes(L-B)模型进行了修正,并在此基础上建立了适合低马赫数颤振研究且带有气动及结构非线性的二元机翼气弹系统分析模型.对比低马赫数翼型气动载荷试验结果表明对L-B模型的修正是有效的,且机翼颤振试验结果亦验证了二元机翼气弹分析模型.研究结果表明:二元机翼气弹系统的失速颤振与初始变距角和来流速度密切相关,且耦合的三次非线性变距和浮沉刚度是造成系统呈现准周期运动的主要原因.      

带后缘小翼的旋翼振动载荷计算

建立了考虑弹性桨叶、刚性小翼的旋翼气动弹性分析模型和旋翼载荷计算方法.以广义质量和广义力的形式描述小翼惯性力和气动力对系统的影响,以非定常/动态失速模型计算剖面气动力,结合基于实验数据修正的组合气动模型计算带小翼部分的剖面气动力,集成大变形桨叶模型考虑弹性变形的非线性,以力积分法计算桨叶剖面振动载荷.通过计算分析与实验结果相比较,验证了建立的气动弹性模型和载荷计算方法.结果表明:建立的桨叶结构模型精度很高,气弹模型能够准确预测旋翼的振动载荷,挥舞弯矩平均误差控制在9.1%,使用修正的小翼气动模型能有效提高小翼运动时桨叶振动载荷的计算精度.      

Unsteady oscillation of a deformable airfoil section in incompressible flow

The unsteady aerodynamic loads (pressure increment and generalized forces) acting on a deformable thin airfoil section are determined for its arbitrary motion in the incompressible flow with transverse gusts. In this case, the exact Küssner solution in series is used for harmonic oscillation of an airfoil, in which the Theodorsen function is approximated by a sum of fractional functions with poles. In the time domain, these functions are replaced by the unknown functions that satisfy the one-type ordinary first order differential equations. The equations obtained are combined with the differential equations of the airfoil motion in the generalized coordinates and are used for analyzing the aeroelastic system stability and calculating its dynamic response to gust loads.     

Recent advance in nonlinear aeroelastic analysis and control of the aircraft

A review on the recent advance in nonlinear aeroelasticity of the aircraft is presented in this paper. The nonlinear aeroelastic problems are divided into three types based on different research objects, namely the two dimensional airfoil, the wing, and the full aircraft. Different non- linearities encountered in aeroelastic systems are discussed firstly, where the emphases is placed on new nonlinear model to describe tested nonlinear relationship. Research techniques, especially new theoretical methods and aeroelastic flutter control methods are investigated in detail. The route to chaos and the cause of chaotic motion of two-dimensional aeroelastic system are summarized. Var- ious structural modeling methods for the high-aspect-ratio wing with geometric nonlinearity are dis- cussed. Accordingly, aerodynamic modeling approaches have been developed for the aeroelastic modeling of nonlinear high-aspect-ratio wings. Nonlinear aeroelasticity about high-altitude long- endurance （HALE） and fight aircrafts are studied separately. Finally, conclusions and the chal- lenges of the development in nonlinear aeroelasticity are concluded. Nonlinear aeroelastic problems of morphing wing, energy harvesting, and flapping aircrafts are proposed as new directions in the future.     

间隙非线性气动弹性系统的辨识

间隙非线性气动弹性系统有非常丰富的动力学特征。由于工程实际中间隙不易准确测量甚至无法测量,通常需要通过辨识来建立其数学模型,其中间隙开关点位置是辨识问题中的难点。本文利用间隙开关点将间隙非线性系统区分为3个线性子系统,用Hammerstein模型表示其非线性部分,构造了开关点的迭代序列;并采用非迭代和迭代相结合的方法进行求解,从而成功获得包含间隙开关点在内的该系统所有模型参数;以间隙非线性的二元翼段为例,验证了该辨识方法的有效性。     

不同迎角的翼型气弹特性风洞实验研究

基于可在不同迎角下作沉浮、俯仰两自由度运动的翼段振动装置,在低速风洞中分别针对普通薄翼型NA-CA0012和风力机翼型NREL S809进行气动弹性测试,得到不同实验状态的气动弹性振动时域响应。分别观察到经典颤振和失速颤振现象,并证明了迎角改变对两种翼型颤振特性的影响。     

翼型尾缘低频大功率合成射流的动态载荷特性研究——A：实验方案设计

为了获得翼型在尾缘合成射流作用下的气动特性,针对NACA0015翼型,设计了适用于风洞研究的尾缘合成射流实验,设计内容包括实验模型的设计,低频大功率合成射流致动器的设计,以及测量方案的设计。该实验方案在伺服电机达到适当转速时,合成射流器能够达到较好的吹／吸气效果。通过调节地面气缸的行程和电机的工作频率,可以实现对喷口速度、频率等参数的调节,为研究合成射流动量系数和减缩频率对气动力和力矩的影响规律提供了便利。针对二元实验段,采用自行设计的二分量应变天平测量动态升力和力矩。该实验模型在二元风洞中顺利开展了相关实验研究。研究结果显示,当合成射流频率为3Hz时,升力系数的幅值约为0．16。因此,尾缘低频大功率合成射流可以使翼型获得较大的用于控制气动弹性的控制力。这种新型作动方式为未来飞行器气动弹性稳定性控制提供了一种新途径。     

CFD数学模型的线性化方法及其应用

计算流体力学(CFD)方法不仅仅起到数值模拟的作用,它本身是一个复杂的非线性系统。在流动稳定性分析、气动弹性分析、优化设计以及流动控制等领域,从系统的角度出发,对CFD数学模型线性化后,可以对模型的系统矩阵进行定量分析获得更多的系统特性。但是CFD数学模型往往非常复杂且阶数很高,因此其线性化系统矩阵的获得比较困难。鉴于此,采用人工编程和自动微分相结合,构造有限体积法并行CFD模型的线性化系统矩阵。其中自动微分只被用来得到每个界面通量的局部雅可比矩阵,而采用人工编程方法来实现并行环境下的稀疏雅可比矩阵的组装。线性化系统的并行求解采用了块雅可比预处理的广义最小残量法,每个并行进程内部则采用零填充不完全LU分解预处理。为了验证这种线性化方法,上述方法被用于:① NACA 0012翼型的非定常绕流线性系统构造与求解;② NACA 0012翼型稳态流动的伴随方程构造与求解;③ AGARD wing 445.6机翼颤振问题降阶建模。上述三个算例的结果与CFD模拟的吻合一致。     

不同振动形式下的翼型失速特性

通过求解雷诺平均Navier-Stokes方程,研究了翼型在强迫振动和自然结构振动下的大迎角流场特性,尤其是失速迎角附近的流场和气动特性.研究结果表明:在接近颤振临界速度情况下结构自然振动可以引起翼型大尺度的分离,导致失速分离涡提前出现;强迫性的沉浮运动和俯仰运动在一定幅度下也可以引起失速性质的大分离,而且沉浮和俯仰振动的频率和振幅都是影响翼型大尺度分离的重要因素.     

Correction method of airfoil thickness effect in hinge moment calculation of a folding wing

The influences of airfoil thickness on the aerodynamic loading distribution and the hinge moments of folding wing aircraft are presented in this work. The traditional panel method shows deficiencies in the calculation of folding wing’s hinge moments. Thus, a thickness correction strategy for the aerodynamic model with CFD results is proposed, and an aeroelastic flight simulation platform is constructed based on the secondary development of ADAMS. Based on the platform, the developed aerodynamic model is verified, then the flight-folding process of the folding wing aircraft is simulated, and the influences of airfoil thickness on the results are investigated. Results show that the developed aerodynamic model can effectively describe the thickness effect of the folding wing. Airfoil thickness, which cannot be considered by the panel method, has a great influence on the hinge moments during the folding process, and the thickness correction has great significance in the calculation of folding wing’s hinge moments.     

大展弦比复合材料机翼结构建模与气动弹性分析

建立了具有任意截面形状的大展弦比复合材料翼的结构模型。研究了机翼的两种铺设方式：即周向均匀刚度配置（CUS）和周向反对称刚度配置（CAS）。对于复合箱梁情形,目前的结构建模方法正确性通过ANSYS有限单元软件得到了验证。为了研究具有NACA0012翼型的大展弦比复合材料机翼的气动弹性问题,利用线性ONERA空气动力模型来描述小攻角情形下的非定常空气动力载荷。最后,利用U—g法预示了机翼在各种复合层铺设角度下的颤振速度。     

非线性机翼极限环颤振的研究

在定常空气动力的作用下,对含立方非线性刚度的二元机翼颤振系统的极限环颤振进行了研究.应用中心流形理论将原四维系统降为二维,采用后继函数法对分岔点类别进行了定性的分析,从而确定平衡点的性质,并应用范式理论对分岔点处中心流形约化方程进行化简,进而研究了系统参数对极限环颤振的稳定性以及幅值的影响.     

受宽带噪声激励的二元机翼随机振动系统的矩Lyapunov指数

通过计算受宽带噪声参激的二元机翼随机振动系统的矩Lyapunov指数,研究了系统的矩稳定和概率1稳定。首先在经典二元机翼颤振方程中加入随机激励,通过随机平均法、Girsanov定理和Feynmann-Kac公式得到关于矩Lyapunov指数的特征值问题。其次采用Fourier余弦级数对特征函数进行正交展开,得到系统矩Lyapunov指数的近似解析式。最后,通过Monte Carlo仿真验证了矩Lyapunov指数近似解析式的可信性,并讨论了系统参数、来流平均速度以及随机噪声谱密度对机翼稳定性的影响。     

具有不对称间隙的二元机翼自激振动的混沌分析

利用数值方法分析了无预荷载情况下具有不对称间隙的气动弹性非线性与结构非线性耦合的二元机翼颤振问题的动力学响应.通过研究速度比U*/U*L从零逐渐增大到1时系统的全局演化规律,发现在无预荷载的不对称分段线性系统中存在混沌运动形式,并对其进行具体分析,得到产生混沌的原因,为进一步控制和减小颤振提供理论帮助,对飞机的飞行结构设计及飞机结构的日常维护具有指导意义.     

操纵面对跨声速机翼气动弹性特性的影响

 运用基于非定常CFD的气动力辨识技术，得到跨声速非定常气动力降阶模型。耦合结构动力学方程，建立了基于状态空间的跨声速气动弹性分析模型。分析了典型三自由度二元机翼的颤振边界，分析结果与CFD/CSD直接耦合方法吻合。然后研究了操纵面结构参数（固有频率和重心位置）对跨声速气动弹性特性的影响。研究发现,一些传统的结构设计准则和颤振排除技术未必适用于跨声速状态;操纵面偏转模态常常成为诱发跨声速颤振的主要模态;经典的质量平衡技术可能会降低跨声速气动弹性系统的稳定性。     

Nonlinear dynamics of a two dimensional airfoil with freeplay in an inviscid compressible flow

A state space model for the aerodynamic loads calculated by means of a linearized CFD code which models the inviscid compressible flow is used to analyze the dynamic behavior of a two dimensional airfoil with a freeplay structural nonlinearity in pitch. The state space aeroelastic equations of motion are utilized to study the existence of Hopf bifurcation points and of limit cycle oscillations. Comparisons between the solutions of the coupled Euler-structural equations and the state space equations are provided.     

Static aeroelastic analysis including geometric nonlinearities based on reduced order model

This paper describes a method proposed for modeling large deflection of aircraft in non-linear aeroelastic analysis by developing reduced order model (ROM). The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geo-metric nonlinearities; meanwhile, the non-planar effects of aerodynamics and follower force effect have been considered. ROMs are computational inexpensive mathematical representations com-pared to traditional nonlinear finite element method (FEM) especially in aeroelastic solutions. The approach for structure modeling presented here is on the basis of combined modal/finite ele-ment (MFE) method that characterizes the stiffness nonlinearities and we apply that structure mod-eling method as ROM to aeroelastic analysis. Moreover, the non-planar aerodynamic force is computed by the non-planar vortex lattice method (VLM). Structure and aerodynamics can be cou-pled with the surface spline method. The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to anal-ysis based on the FEM and experimental result.     

基于非定常气动力辨识技术的气动弹性数值模拟

选择离散型输入输出差分模型,运用最小二乘方法进行非定常气动力建模,并将辨识得到的降阶模型用于气动弹性的数值模拟。1个马赫数下的颤振临界点的计算仅需调用一次非定常流场求解器。计算精度保持与非定常欧拉方程计算方法相当的同时计算效率提高了1~2个量级。计算了跨声速具有S型颤振边界的气动弹性标准算例－Isogaiwing和三维气动弹性标模算例AGARD445.6,辨识模型计算边界与非定常Euler方程计算结果吻合。证明非定常气动力辨识技术可以提供高效的高精度的气动弹性分析。     

Aerodynamic shape optimization for alleviating dynamic stall characteristics of helicopter rotor airfoil

In order to alleviate the dynamic stall effects in helicopter rotor, the sequential quadratic programming(SQP) method is employed to optimize the characteristics of airfoil under dynamic stall conditions based on the SC1095 airfoil. The geometry of airfoil is parameterized by the class-shape-transformation(CST) method, and the C-topology body-fitted mesh is then automatically generated around the airfoil by solving the Poisson equations. Based on the grid generation technology, the unsteady Reynolds-averaged Navier-Stokes(RANS) equations are chosen as the governing equations for predicting airfoil flow field and the highly-efficient implicit scheme of lower–upper symmetric Gauss–Seidel(LU-SGS) is adopted for temporal discretization. To capture the dynamic stall phenomenon of the rotor more accurately, the Spalart–Allmaras turbulence model is employed to close the RANS equations. The optimized airfoil with a larger leading edge radius and camber is obtained. The leading edge vortex and trailing edge separation of the optimized airfoil under unsteady conditions are obviously weakened, and the dynamic stall characteristics of optimized airfoil at different Mach numbers, reduced frequencies and angles of attack are also obviously improved compared with the baseline SC1095 airfoil. It is demonstrated that the optimized method is effective and the optimized airfoil is suitable as the helicopter rotor airfoil.