基于边界元方法的气动弹性降阶模型及仿真

传统气动弹性的时域计算耗费了大量时间,为了提高计算效率,本文发展了基于边界元方法的降阶模型技术。首先基于边界元方法建立非定常流场的求解模型,结合特征值分析技术建立了非定常气动力的低阶模型;然后,利用边界元方法建立了气动网格和结构网格之间的信息转换矩阵;最后将非定常气动力降阶模型和结构动力学方程联合,建立了气动弹性系统的低阶状态空间模型。将所发展的降阶模型方法应用于NACA0012翼型的非定常气动力求解中,结果表明降阶模型可以在保证原系统计算精度的同时提高了计算效率;将降阶模型技术应用到三维机翼的气动弹性响应计算中,在系统阶数仅为12阶的情况下可以得到与原系统一致的极限环响应,说明降阶模型技术在求解气动弹性问题中的巨大优势。     

大长细比导弹的气动弹性降阶模型

对于大长细比导弹,需要在设计阶段准确计算气动弹性/气动伺服弹性,但其复杂的气动力给计算带来困难,因此气动力降阶模型是突破大长细比导弹跨音速气动弹性分析与控制瓶颈的关键技术.虽然气动力模型降阶方法已在预测二维机翼结构的气动弹性方面取得重要进展,但几乎未见关于全机模型的气动力降阶模型研究报道.本文基于递归Wiener模型的气动力降阶方法,利用CFD计算的气动力作为模型辨识数据,用鲁棒子空间和Levenberg-Marquardt算法辨识降阶模型参数,建立了大长细比导弹气动力降阶模型.在此基础上与大长细比导弹有限元模型相结合,构造出气动弹性降阶模型,并在数值仿真中测试气动弹性降阶模型在不同马赫数下的适用性.数值仿真结果表明,该气动弹性降阶模型能够精确预测导弹模型在不同飞行条件下的非定常气动力和导弹模型的气动弹性频率响应特性.     

弹性飞行器气动伺服弹性稳定性分析与控制

轻质结构大长细比弹性飞行器开环闭环颤振及控制系统设计是气动伺服弹性稳定性校核与分析的核心问题。本文利用振动模态试验数据修正了弹性飞行器结构有限元模型;使用涡格法进行非定常气动力计算,并利用最小状态法获得了弹性飞行器刚弹耦合频时域状态空间方程。绘制系统状态矩阵特征值随动压变化绘制的根轨迹图对该弹性飞行器开环颤振进行了分析。最后使用线性二次型方法设计了弹性飞行器主动颤振抑制控制律和纵向姿态控制器。仿真结果表明,系统在短的上升时间内实现了对指令的跟随,超调量合理,无静态误差。本文所采用的方法能够满足工程设计需求。     

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.      

基于特征正交分解的非定常气动力建模技术

采用特征正交分解(proper orthogonal decomposition, POD)方法, 建立了基于状态空间的非定常气动力降阶模型, 并耦合结构方程, 建立了降阶的气动弹性系统, 开展了颤振分析的初步研究, 计算效率提高了2~3个数量级. 具体过程是:首先获取全阶系统的频域快照构成关联矩阵, 通过对关联矩阵进行奇异值分解提取流场模态(或流场基), 对低能量模态截断形成降阶子空间, 并将其映射到全阶系统, 从而形成基于状态空间的降阶非定常气动力模型. 对气动弹性标模AGARD445.6进行算例验证, 证明了降阶方法正确, 可以提供高效、高精度的气动弹性分析.      

基于气动力降阶模型的跨音速气动弹性稳定性分析

基于离散型输入输出差分模型,运用非定常CFD方法训练信号,然后运用最小二乘方法进行参数辨识,得到降阶的非定常气动力模型,再将该离散差分模型转换为连续时间域内的状态方程。耦合气动状态方程和结构状态方程,得到耦合系统的气动弹性状态方程。求解不同动压下状态矩阵的特征值,根据根轨迹图分析系统的稳定性特性。分析结果与直接耦合CFD/CSD方法结果相吻合,可以计算跨音速非线性气动弹性问题。其计算效率比直接耦合CFD/CSD方法提高1~2个数量级。针对Isogai wing在跨音速出现的S型颤振边界进行了较为细致的分析,阐述了该现象是由于系统诱发颤振的分支随着速度(来流动压)的提高而发生转移所导致的。     

弹性支撑圆柱绕流稳定性分析

基于CFD 技术,采用系统辨识方法,建立了亚临界雷诺数(Re < 47) 下绕圆柱流动的非定常气动力模型(reduced order model, ROM). 耦合结构运动方程和降阶气动力模型,建立了弹性支撑圆柱绕流的稳定性分析模型. 算例分析了亚临界雷诺数下,结构固有频率、质量比等参数以及支撑方式对弹性系统稳定性的影响. 对于单自由度横向支撑圆柱,当结构固有频率趋近流动最不稳定模态频率时,弹性系统会在一定频率范围内失稳,这种现象最低可在Re~20 时出现. 旋转自由度的释放能够进一步降低系统的稳定性,可将临界雷诺数进一步降低至18 左右. ROM 方法不仅具有很高的效率,而且清晰地指出了弹性系统失稳的根本原因:流动模态和结构模态耦合作用导致结构模态失稳所致. 因此,失稳状态下系统振荡频率锁定于结构固有频率. 基于ROM 技术预测的失稳边界与直接CFD/CSD 仿真结果吻合,证明了该方法的正确性和精度.      

基于非线性状态空间辨识的气动弹性模型降阶

高维、非线性气动弹性系统的模型降阶是当前气动弹性力学与控制领域的研究热点之一.然而国内外现有的非线性模型降阶方法仍存在辨识算法复杂、精度有待提高等问题.本研究提出了一种基于非线性状态空间辨识的跨音速气动弹性模型降阶方法. 首先,该方法基于非定常空气动力的单位脉冲响应数据,采用特征系统实现算法对非线性状态空间模型的线性动力学部分进行系统辨识. 其次,引入状态和控制输入的非线性函数, 采用优化算法对非线性函数的系数矩阵进行优化,进而得到考虑非线性效应的空气动力降阶模型.为了验证该降阶模型在预测跨音速气动弹性力学行为的精确性,本文以三维机翼为研究对象,分别从基于非线性降阶模型的气动力辨识、跨声速颤振边界计算和极限环振荡预测三方面进行了算例验证,并与现有的模型降阶方法进行了对比, 进一步说明本文所提出方法的有效性.研究结果表明, 该降阶模型对上述三类问题的计算精度与直接流-固耦合方法相吻合,可用于高效预测飞行器跨声速气动弹性力学行为.      

时变系统地面颤振模拟试验方法研究

地面颤振模拟试验是一种颤振验证的全新试验技术,可作为当前颤振验证试验手段的有效补充。飞行器在实际飞行过程中,结构的动力学特性及承受的载荷是不断变化的,对于受气动加热影响的高超声速飞行器,这一时变特性则更加显著。本研究提出了基于代理模型的时变参数非定常气动力模型建模方法,建立了基于PID控制器的时变系统地面颤振试验方法,并通过标准试验件进行测试验证。试验结果表明,本研究提出的非定常气动力建模方法能够准确获得具有时变特性的气动力模型,建立的地面颤振试验方法能够有效应对颤振系统的时变特性获得准确的结构颤振边界数据。     

基于非线性状态空间辨识的气动弹性模型降阶

高维、非线性气动弹性系统的模型降阶是当前气动弹性力学与控制领域的研究热点之一.然而国内外现有的非线性模型降阶方法仍存在辨识算法复杂、精度有待提高等问题.本研究提出了一种基于非线性状态空间辨识的跨音速气动弹性模型降阶方法.首先,该方法基于非定常空气动力的单位脉冲响应数据,采用特征系统实现算法对非线性状态空间模型的线性动力学部分进行系统辨识.其次,引入状态和控制输入的非线性函数,采用优化算法对非线性函数的系数矩阵进行优化,进而得到考虑非线性效应的空气动力降阶模型.为了验证该降阶模型在预测跨音速气动弹性力学行为的精确性,本文以三维机翼为研究对象,分别从基于非线性降阶模型的气动力辨识、跨声速颤振边界计算和极限环振荡预测三方面进行了算例验证,并与现有的模型降阶方法进行了对比,进一步说明本文所提出方法的有效性.研究结果表明,该降阶模型对上述三类问题的计算精度与直接流-固耦合方法相吻合,可用于高效预测飞行器跨声速气动弹性力学行为.     

基于CFD的气动力建模及其在气动弹性中的应用

CFD技术为带有气动力非线性的气动弹性分析提供了一种研究途径,但是基于CFD的气动弹性直接数值模拟方法的计算量很大,不便开展定性分析和参数设计.基于CFD的非定常气动力模型的降阶技术为缓解计算效率与计算精度之间的矛盾以及系统的复杂性与易分析、易设计性之间的矛盾提供了行之有效的技术途径.综述了近年来发展的两类基于CFD技术的非定常气动力降阶技术和一种非线性气动力的谐波平衡方法,以及这些方法在非线性气动弹性研究中的运用.对比了各种方法的优越性并作了进一步的展望.      

Unsteady aerodynamics modeling for flight dynamics application

In view of engineering application, it is practicable to decompose the aerodynamics into three components: the static aerodynamics, the aerodynamic increment due to steady rotations, and the aerodynamic increment due to unsteady separated and vortical flow. The first and the second components can be presented in conventional forms while the third is described using a one-order differential equation and a radial-basis-function (RBF) network. For an aircraft configuration, the mathematical models of 6component aerodynamic coefficients are set up from the wind tunnel test data of pitch, yaw, roll, and coupled yawroll large-amplitude oscillations. The flight dynamics of an aircraft is studied by the bifurcation analysis technique in the case of quasi-steady aerodynamics and unsteady aerodynamics, respectively. The results show that: (1) unsteady aerodynamics has no effect upon the existence of trim points, but affects their stability; (2) unsteady aerodynamics has great effects upon the existence, stability, and amplitudes of periodic solutions; and (3) unsteady aerodynamics changes the stable regions of trim points obviously. Furthermore, the dynamic responses of the aircraft to elevator deflections are inspected It is shown that the unsteady aerodynamics is beneficial to dynamic stability for the present aircraft. Finally, the effects of unsteady aerodynamics on the post-stall maneuverability are analyzed by numerical simulation.     

Research on the hysteresis properties of unsteady aerodynamics about the oscillating wings

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Cascade aerodynamic gust response including steady loading effects

To predict the unsteady convected gust aerodynamic response of a cascade comprised of arbitrary thick and cambered aerofoils in an incompressible, inviscid, flow field, a complete first-order model is formulated. The flow is analysed by considering a periodic flow channel. The velocity potential is separated into steady and unsteady harmonic components, each described by a Laplace equation. The strong dependence of the unsteady aerodynamics on the steady effects of aerofoil and cascade geometry and incidence angle is manifested in the coupling of the unsteady and steady flow fields through the unsteady boundary conditions. Analytical solutions in individual grid elements of a body-fitted computational grid are then determined, with the complete solution obtained by assembly of these local solutions. The validity and capabilities of this model and solution technique are then demonstrated by analysing the steady and unsteady aerodynamics of both theoretical and experimental cascade configurations.     

Equivalent damping of aeroelastic system of an airfoil with cubic stiffness

This paper presents a mathematical study on the subsonic aerodynamics acting on an airfoil with a cubic stiffness. One portion of aerodynamics is assumed as and replaced by an equivalent damping. Using the harmonic balance method, an equivalent system is deduced and studied by a numerical integration method. Numerical examples show the validity and feasibility of the proposed mathematical treatment of the aerodynamics. It reveals that the unsteady aerodynamics acting on the airfoil can not only affect the pitch stiffness but also result in additional damping.     

A study of gridless method with dynamic clouds of points for solving unsteady CFD problems in aerodynamics

When solving unsteady computational fluid dynamics problems in aerodynamics with a gridless method, a cloud of points is usually required to be regenerated due to its accommodation to moving boundaries. In order to handle this problem conveniently, a fast dynamic cloud method based on Delaunay graph mapping strategy is proposed in this paper. A dynamic cloud method makes use of algebraic mapping principles and therefore points can be accurately redistributed in the flow field without any iteration. In this way, the structure of the gridless clouds is not necessarily changed so that the clouds regeneration can be avoided successfully. The spatial derivatives of the mathematical modeling of the flow are directly determined by using weighted least‐squares method in each cloud of points, and then numerical fluxes can be obtained. A dual time‐stepping method is further implemented to advance the two‐dimensional Euler equations in arbitrary Lagarangian–Eulerian formulation in time. Finally, unsteady transonic flows over two different oscillating airfoils are simulated with the above method and results obtained are in good agreement with the experimental data. Copyright © 2009 John Wiley & Sons, Ltd.     

Aerodynamic characteristics of flapping motion in hover

The aim of the present work is to understand the aerodynamic phenomena and the vortex topology of an unsteady flapping motion by means of numerical and experimental methods. Instead of the use of real insect/bird wing geometries and kinematics which are highly complex and difficult to imitate by an exact modeling, a simplified model is used in order to understand the unsteady aerodynamics and vortex formation mechanisms during the different phases of the flapping motion. The flow is assumed to be laminar with a Reynolds number of 1,000. Direct numerical simulations, laser sheet visualizations and particle image velocimetry (PIV) measurements are performed for the phenomenological analysis of the flow. The vortex dynamics and their identification are put in evidence with PIV measurements by considering velocity magnitude, streamlines, second invariant of velocity gradient (Q-criteria), vorticity contours and Eurlerian accelerations.     

Use of characteristics method with cubic interpolation for unsteady-flow computation

The specified-time-interval (STI) scheme has been used commonly in applying the method of characteristics (MOC) to unsteady open-channel flow problems. However, with the use of STI scheme, the numerical error for the simulation results can always be induced due to the interpolation used to approximate the characteristics trajectory. Hence, in order to remedy the numerical errors caused by the interpolation, one needs to seek some kind of interpolation technique with higher-order accuracy. Instead of the linear interpolation technique, which has been used very commonly and can induce serious numerical diffusion, the Holly--Preissmann two-point, method, which is a cubic interpolation technique with fourth-order of accuracy, is proposed here to integrate with the method of characteristics for the computation of one-dimensional unsteady flow in open channel. The concept of reachback and reachout in space and time directions for the characteristics is also introduced to assure the model stability. The computed results from this new model are compared with those computed by using the Preissmann four-point scheme and the multimode method of characteristics with linear interpolation.     

Numerical Study of the Effect of Periodic Velocity Excitation on Aerodynamic Characteristics of an Oscillating Circular Cylinder

A finite element method based on ALE formulation has been adopted in order to examine the effect of periodic velocity excitation on the aerodynamic characteristics of an oscillating circular cylinder. Periodic excitation, which was placed on the cylinder surface, stimulated the separated shear layers around the cylinder, and numerical results showed that some excitation can reduce negative damping, which is caused by unsteady lift force, and thereby stabilize the aerodynamics of the cylinder. Furthermore, the change of lift phase caused by periodic excitation seems to be important in stabilizing the aerodynamics of the cylinder. The simulation also confirmed that periodic excitation can suppress the vortex-induced vibration of the cylinder.