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.     

Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos

Different types of structural and aerodynamic nonlinearities commonly encountered in aeronautical engineering are discussed. The equations of motion of a two-dimensional airfoil oscillating in pitch and plunge are derived for a structural nonlinearity using subsonic aerodynamics theory. Three classical nonlinearities, namely, cubic, freeplay and hysteresis are investigated in some detail. The governing equations are reduced to a set of ordinary differential equations suitable for numerical simulations and analytical investigation of the system stability. The onset of Hopf-bifurcation, and amplitudes and frequencies of limit cycle oscillations are investigated, with examples given for a cubic hardening spring. For various geometries of the freeplay, bifurcations and chaos are discussed via the phase plane, Poincaré maps, and Lyapunov spectrum. The route to chaos is investigated from bifurcation diagrams, and for the freeplay nonlinearity it is shown that frequency doubling is the most commonly observed route. Examples of aerodynamic nonlinearities arising from transonic flow and dynamic stall are discussed, and special attention is paid to numerical simulation results for dynamic stall using a time-synthesized method for the unsteady aerodynamics. The assumption of uniform flow is usually not met in practice since perturbations in velocities are encountered in flight. Longitudinal atmospheric turbulence is introduced to show its effect on both the flutter boundary and the onset of Hopf-bifurcation for a cubic restoring force.     

Active Control Law Design for Flutter/LCO Suppression Based on Reduced Order Model Method

 Active stability augmentation system is an attractive and promising technology to suppress flutter and limit cycle oscillation (LCO). In order to design a good active control law, the control plant model with low order and high accuracy must be pro-vided, which is one of the most important key points. The traditional model is based on low fidelity aerodynamics model such as panel method, which is unsuitable for transonic flight regime. The physics-based high fidelity tools, reduced order model (ROM) and CFD/CSD coupled aeroservoelastic solver are used to design the active control law. The Volterra/ROM is applied to constructing the low order state space model for the nonlinear unsteady aerodynamics and static output feedback method is used to active control law design. The detail of the new method is demonstrated by the Goland+ wing/store system. The simu-lation results show that the effectiveness of the designed active augmentation system, which can suppress the flutter and LCO successfully.     

基于CFD/CSD紧耦合的旋翼翼型气弹分析

采用CFD/CSD（计算流体力学/计算结构力学）紧耦合的方法,以Fluent软件作为主控平台,通过UDF（用户自定义函数）及I/O（输入/输出）文件读写的方式实现结构响应和气动载荷的数据交换,耦合求解了旋翼桨叶剖面的气动力和振动响应.在此基础上研究旋翼桨叶剖面在变距、沉降（挥舞）和周期交变来流条件下的气动特性和振动响应特性.结果表明:桨叶剖面在轻失速情况下,气动载荷周期性比较好,表现出光滑的迟滞环曲线,结构沉降响应也表现出光滑的周期性现象,扭转响应出现局部轻微振荡.深失速情况下,气动载荷及结构响应都表现出强烈的非线性振荡,高频成分较为明显.      

大振幅下薄翼和流线型箱梁的气动迟滞研究

回顾了机翼和箱梁的气动迟滞效应研究现状,介绍了大振幅下获取薄翼和流线型箱梁自激气动力的风洞试验。研究结果表明：薄翼在超过失速角的振幅条件下,升力并没有出现明显的失速现象,但气动力的高阶谐波分量显著增加;大振幅条件下,流线型箱梁的气动力高阶谐波分量也比较显著,并以第2和第3阶谐波分量为主。此外,在大振幅条件下,流线型箱梁的气动力矩迟滞曲线可出现“8字环”,即气动力在一个振动周期内既做了正功也做了负功;其中,迟滞曲线“8字环”的气动正功部分随着振幅和折算风速的增大而增加。该现象可导致桥梁也出现类似于失速机翼的极限环震荡。最后,基于不同振幅下流线型箱梁的力矩迟滞曲线,简要讨论了大跨度桥梁在颤振后状态可能出现的振动形式和气动稳定性。     

基于CFD/CSD的非线性气动弹性分析方法

提出了一种基于计算流体力学/计算结构动力学(CFD/CSD)的非线性气动弹性分析方法,并应用于切尖三角翼的非线性颤振和极限环振荡(LCO)研究。该方法将非线性有限元(FEM)和CFD计算相结合,并辅以高精度的界面插值,能够分析结构和气动非线性共存的气动弹性问题。结构部分以四边形平板壳元为基础,采用更新的拉格朗日(UL)方法分析结构大变形引起的几何非线性问题。气动部分以Navier-Stokes(N-S)方程作为控制方程,采用CFD方法计算跨声速气动力。机翼的非线性颤振计算表明了方法的有效性。最后应用该方法研究了切尖三角翼的LCO现象,其计算精度明显优于已有结果。     

翼型前缘变形对动态失速效应影响的数值计算

翼型或机翼的动态失速效应所引起的低头力矩和正气动阻尼限制了飞行器气动性能的提高,甚至可能诱导发生不稳定运动。应用于小尺寸机翼的前缘动态变形（DDLE）技术,通过实时改变前缘形状,能够改善翼型前缘区域的速度梯度,进而抑制动态失速效应。采用转捩剪切应力输运（SST）黏性模型结合分区混合动态网格技术,研究了这种前缘变形对机翼俯仰运动所引起的非定常流动的影响,得到通过小幅度前缘变形抑制和延迟动态失速的方法,从而提高翼型的气动性能。翼型NAC A0012的数值模拟结果与动态失速风洞试验结果比较表明：所使用的数值计算方法能够较为准确地模拟翼型在动态失速过程中升力系数与俯仰力矩系数的变化情况,可用于研究前缘变形对翼型俯仰运动所引起的非定常流动的影响。前缘动态变形翼型俯仰运动过程的非定常流场的数值模拟表明：在大迎角下不同幅度的前缘下垂运动能够抑制流动分离的发生,从而抑制动态失速,但在大迎角下小幅度高频率的前缘下垂变形能更高效地抑制动态失速;前缘变形幅度以及变形沿中弧线的分布对升力系数和俯仰力矩系数的影响并不明显。     

一种基于CFD的叶轮机非定常气动力组合建模方法

为了获得一个准确高效的非定常空气动力学模型并将其应用于叶轮机叶片颤振特性分析中去,论文发展了一种基于CFD方法的叶轮机非定常气动力组合建模方法,可以快速计算叶轮机叶片在等相角差振动时的气动阻尼系数。运用小扰动流场的叠加原理,通过不同通道数模型的非定常流场求解(通常需要两次或三次),针对流场的周期性边界条件,组合分析得到一系列更多通道数情况下的非定常气动力低阶模型。基于这种降阶模型计算的气动阻尼系数与直接的CFD方法计算结果吻合很好,计算效率提高10倍以上。     

Nonlinear Aeroelastic Response of High-aspect-ratio Flexible Wings

The aeroelastic analysis of high-altitude, long-endurance (HALE) aircraft that features high-aspect-ratio flexible wings needs take into account structural geometrical nonlinearities and dynamic stall. For a generic nonlinear aeroelastic system, besides the stability boundary, the characteristics of the limit-cycle oscillation (LCO) should also be accurately predicted. In order to conduct nonlinear aeroelastic analysis of high-aspect-ratio flexible wings, a first-order, state-space model is developed by combining a geometrically exact, nonlinear anisotropic beam model with nonlinear ONERA (Edlin) dynamic stall model. The present investigations focus on the initiation and sustaining mechanism of the LCO and the effects of flight speed and drag on aeroelastic behaviors. Numerical results indicate that structural geometrical nonlinearities could lead to the LCO without stall occurring. As flight speed increases, dynamic stall becomes dominant and the LCO increasingly complicated. Drag could be negligible for LCO type, but should be considered to exactly predict the onset speed of flutter or LCO of high-aspect-ratio flexible wings.     

基于神经网络模型的动态非线性气动力辨识方法

 在标准径向基函数（RBF）神经网络模型的基础上发展了带输出反馈的RBF神经网络。将计算流体力学(CFD)方法计算的时域气动载荷作为输入信号,建立跨声速非定常非线性气动力模型,并进一步运用CFD方法验证模型的精度。算例表明带输出反馈的RBF神经网络较标准RBF神经网络精度更高,能更准确描述跨声速激波大幅振荡时的非线性和非定常特性,并可推广用于多自由度运动的动态非线性气动力建模。用多级信号训练,预测简谐信号输入下的气动力算例表明带输出反馈的RBF神经网络能够预测不同振幅、不同频率的信号激励下的非线性气动力。     

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.     

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。     

基于联合射流的翼型动态失速流动控制研究

动态失速控制对于提高翼型气动特性具有重要意义。采用联合射流方法对翼型俯仰动态失速控制进行数值模拟,完成两方面的研究:一是射流关闭时射流通道对动态失速特性的影响,二是射流开启时不同射流动量系数对动态失速控制的影响和分析。结果表明:射流关闭时,射流通道的存在对翼型上仰过程中附着流阶段的气动特性产生不利影响,使得升力系数明显下降,但是对翼型下俯过程中失速分离流阶段的气动特性影响不明显;射流开启后,动态失速特性得到极大改善,迟滞环面积显著减小,升力增加,阻力减小,且阻力和力矩的峰值显著减小,原基准翼型力矩曲线的负阻尼区域消失。     

基于CFD/CSD耦合的叶轮机叶片失速颤振计算

为了研究叶轮机叶片的失速颤振特性,发展了一种计算流体力学与计算结构力学(CFD/CSD)时域耦合方法。该方法通过每一物理时刻CFD和CSD的循环迭代实现了耦合计算。在CFD分析中,采用鲁棒性较好的空间离散格式AUSM+-UP,并基于延迟脱体涡模型(DDES)模拟了带分离流动。在结构分析中,通过模态法构建了旋转叶片动力学方程并运用杂交多步方法进行求解。以孤立转子Rotor37为例,计算了不同工况下流场总体与细节参数,与实验结果的对比验证了CFD算法的精度。对某转子叶片进行了颤振特性研究,计算所得的广义位移时间响应曲线表明该叶片在近失速工况下会发生失速颤振,其表现形式为一阶弯曲模态发散且各阶模态之间不耦合。分析表明,流场不稳定和非定常效应是引起失速颤振的关键因素,同时折合频率的降低也会导致原本气动弹性稳定的叶片发生失速颤振。     

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.      

Numerical studies of a non-linear aeroelastic system with plunging and pitching freeplays in supersonic/hypersonic regimes

The flutter and post flutter of a two-dimensional double-wedge lifting surface with combined freeplay and cubic stiffness nonlinearities in both plunging and pitching degrees-of-freedom operating in supersonic/hypersonic flight speed regimes have been analyzed. In addition to the structural nonlinearities, the third-order piston theory aerodynamics is used to evaluate the unsteady non-linear aerodynamic force and moment. Such model accounts for stiffness and damping contributions produced by the aerodynamic loads. Responses involving limit cycle oscillation and chaotic motion are observed over a large number of parameters that characterizes the aeroelastic system. Results of the present study show that the freeplay in the pitching degree-of-freedom and soft/hard cubic stiffness in the pitching and plunging degrees-of-freedom have significant effects on the LCOs exhibited by the aeroelastic system in the supersonic/hypersonic flight speed regimes. The simulations also show that the aeroelastic system behavior is greatly affected by physical structural parameters, such as the radius of gyration and the frequency ratio, especially in post-flutter regimes, when accounting for all system nonlinearities. It has been shown that at high Mach numbers the non-linear aerodynamic stiffness yields detrimental effects from the aeroelastic point of view, while the damping one do not.     

基函数宽度对RBF神经网络气动力模型精度的影响研究

将带输出反馈的RBF（recursive radial basis function, RRBF）神经网络用于构建非定常气动力模型,能够得到一种动态非线性气动力降阶模型（reduced order model, ROM）。隐含层神经元的基函数宽度是该气动力模型的一个重要参数。为了研究基函数宽度对RRBF神经网络的影响,首先通过数学分析和计算仿真研究了训练过程中宽度与神经网络结构之间的关系,而后用NACA0012翼型俯仰运动作为算例,研究模型在不同训练信号、延迟阶数和流动状态的情况进行测试。测试结果表明,基函数宽度对此类非定常气动力模型的稳定性及泛化能力都有较大影响;最优宽度的选择随训练及预测信号的变化有所不同;较多样本时,通常选择55~75的宽度能够保证非定常气动力模型具有较高的预测精度。通过对随机俯仰运动样本的预测结果,验证了宽度的最优选择范围。     

Control law design for transonic aeroservoelasticity

Existing computational transonic aeroservoelastic researches focus on directly coupling the structural dynamic equations, CFD solver and servo system in time domain, study the effect of the given feedback control laws on the responses of the aeroelastic system. These works have not involved the design of the flutter active control law. The non-linearity of transonic flow brings great difficulties to aeroservoelastic analysis and design. Recent research of the unsteady aerodynamic reduced order models (ROM) based on CFD provides a challenging approach for transonic aeroservoelastic analysis and design. Coupling the structural state equations with the aerodynamic state equations of the wing and the control surface based on the ROM, we construct a transonic aeroservoelastic model in state-space. Then the sub-optimal control method based on output feedback is used to design the flutter suppressing law. The study first demonstrates the open loop of the Benchmark Active Controls Technology (BACT) wing. The computational results of the CFD direct simulation method and the ROM analysis method are both agree well with the experimental data. Then both the closed loop time responses and the flutter results by ROM technique are compared with those of numerical aeroservoelastic simulation based on Euler codes to validate the correctness of the design method of the control law and aeroservoelastic analysis method. An increase of up to 20% of the speed index can be achieved by the control law designed by sub-optimal control method for this model.     

三角翼俯仰振荡中若干参数影响的实验研究

本文研究一个 6 0°三角翼以不同振荡频率 ,不同振幅从不同起始迎角进行俯仰振荡的纵向气动力特性 ,研究发现跨越具有不同时间尺度的流态的振荡会产生明显的气动力迟滞现象 ,这一迟滞现象随减缩频率的增大有一个极限值 ;在同一种流态下振荡 ,气动力迟滞现象不明显 ,这一结果对充分利用非定常气动力有指导意义。     

考虑进排气的飞翼静、动态气动特性数值模拟

采用计算流体力学（CFD）数值模拟技术,以二维模型为例,建立了基于小幅度非定常运动的动导数计算方法,构建了考虑喷流引射效应的进排气模型、考虑管道效应的通气模型以及常规的保形模型,分别对其静态以及动态气动特性进行了数值模拟计算,并辨识了其纵向俯仰力矩系数组合动导数。研究表明:非定常动导数辨识方法较为准确可靠,相比保形模型,进排气以及通气模型的静态失速攻角（AOAs）增大,升力系数、阻力系数及俯仰力矩系数也增大,但力矩系数斜率基本不变,说明静态稳定性差异不大。而相同攻角下,进排气影响下的俯仰力矩系数组合动导数绝对值最大,表明了进排气模型具有最大的动态阻尼,而通气模型次之,保形模型的动导数绝对值最小。