Unsteady aerodynamic reduced-order modeling of an aeroelastic wing using arbitrary mode shapes

Computational fluid dynamics (CFD) based unsteady aerodynamic reduced-order model (ROM) can offer significant improvements to the efficiency of transonic aeroelastic analysis. To construct a ROM based on mode shapes, one run of CFD solver is needed to compute aerodynamic responses corresponding to mode excitations. When mode shapes change with structure, another run of the CFD solver is required to construct the new ROM. The typically large computational cost associated with repeated runs of the CFD solver impedes the application of existing unsteady aerodynamic reduced-order modeling methods to transonic aeroelastic design optimization and aeroelastic uncertainty analysis. This paper demonstrates a method that can replace the CFD solver used in the process of existing unsteady aerodynamic reduced-order modeling. It can produce aerodynamic responses corresponding to mode excitations for arbitrary mode shapes within a few seconds. Computational cost can be reduced by two orders of magnitude using the mode excitations and the corresponding aerodynamic responses computed by the method to construct the ROMs used for flutter analyses in aeroelastic design optimization or aeroelastic uncertainty analysis in transonic regime compared with the existing unsteady aerodynamic reduced-order modeling methods. Results show that the method can accurately produce the aerodynamic responses corresponding to the mode excitations and predict the flutter characteristics of AGARD 445.6 wings root-attached in three different ways.     

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.     

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.      

Aeroelastic analysis of helicopter rotor blade in hover using an efficient reduced-order aerodynamic model

This paper presents a coupled flap–lag–torsion aeroelastic stability analysis and response of a hingeless helicopter blade in the hovering flight condition. The boundary element method based on the wake eigenvalues is used for the prediction of unsteady airloads of the rotor blade. The aeroelastic equations of motion of the rotor blade are derived by Galerkin's method. To obtain the aeroelastic stability and response, the governing nonlinear equations of motion are linearized about the nonlinear steady equilibrium positions using small perturbation theory. The equilibrium deflections are calculated through the iterative Newton–Raphson method. Numerical results comprising steady equilibrium state deflections, aeroelastic eigenvalues and time history response about these states for a two-bladed rotor are presented, and some of them are compared with those obtained from a two-dimensional quasi-steady strip aerodynamic theory. Also, the effect of the number of aerodynamic eigenmodes is investigated. The results show that the three-dimensional aerodynamic formulation has considerable impact on the determination of both the equilibrium condition and lead-lag instability.     

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 dynamics of an aeroelastic airfoil with free-play in transonic flow

Nonlinear dynamic behaviors of an aeroelastic airfoil with free-play in transonic air flow are studied. The aeroelastic response is obtained by using time-marching approach with computational fluid dynamics (CFD) and reduced order model (ROM) techniques. Several standardized tests of transonic flutter are presented to validate numerical approaches. It is found that in time-marching approach with CFD technique, the time-step size has a significant effect on the calculated aeroelastic response, especially for cases considering both structural and aerodynamic nonlinearities. The nonlinear dynamic behavior for the present model in transonic air flow is greatly different from that in subsonic regime where only simple harmonic oscillations are observed. Major features of the responses in transonic air flow at different flow speeds can be summarized as follows. The aeroelastic responses with the amplitude near the free-play are dominated by single degree of freedom flutter mechanism, and snap-though phenomenon can be observed when the air speed is low. The bifurcation diagram can be captured by using ROM technique, and it is observed that the route to chaos for the present model is via period-doubling, which is essentially caused by the free-play nonlinearity. When the flow speed approaches the linear flutter speed, the aeroelastic system vibrates with large amplitude, which is dominated by the aerodynamic nonlinearity. Effects of boundary layer and airfoil profile on the nonlinear responses of the aeroelastic system are also discussed.     

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.      

Aeroelastic analysis of cantilever plates using Peters’ aerodynamic model,and the influence of choosing beam or plate theories as the structural model

In this paper, the aeroelastic analyses of a rectangular cantilever plate of varying aspect ratio is presented. The classical plate theory has been selected as the structural model. The main point that distinguishes this study from previously reported research is employing Peters’ theory to model aerodynamic effect which is not straightforward. The Peters’ aerodynamic model was originally developed to provide lift and moment, which is only applicable to the structural model based on the beam theories. In this study, using the basic concept of the Peters’ aerodynamic model in addition to utilizing the Fourier series, the pressure distribution is derived, which makes Peters’ model applicable to structural models based on plate theory. This combination provides a much simpler state–space aeroelastic model for plates in comparison to the prevalent panel methods, which could lead to a significant reduction in computational time. In addition, the aeroelastic response of the plate with respect to changes in the structural model from the beam theory to the plate theory is evaluated. By using data from an experiment carried out at Duke University, the theoretical results are evaluated. Furthermore, the differences in structural models obtained from the plate and beam theories can be divided into two distinct parts, which are responsible for differences in bending and torsional behaviors of the structure, separately. This approach enables us to measure the effects of differences of each behavior separately, which could provide with a new insight into the problem. It has been determined that the flutter speeds obtained from the beam and plate aeroelastic models are little affected by the difference in bending behavior, but rather is mainly caused by the difference in torsional frequencies.     

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.     

An efficient implementation of aeroelastic tailoring based on efficient computational fluid dynamics-based reduced order model

Current and future trends in the aerospace industry leverage on the potential benefits provided by lightweight materials that can be tailored to realize desired mechanical characteristics when loaded. For aircraft design, the deployment of aeroelastic tailoring is hindered by the need to re-compute, for any possible modification of the structure, the dependence of the aerodynamic field on the underlying structural properties. To make progress in this direction, the work presents a rapid computational fluid dynamics based aeroelastic tool which is built around a reduced order model for the aerodynamics that is updated for any modification of the structure by using the structural dynamics reanalysis method. The aeroelastic tailoring tool is demonstrated in transonic flow for the AGARD 445.6 wing, suitably modified with composite materials. It was found that the proposed method provides accurate engineering predictions for the aeroelastic response and stability when the structure is modified from the baseline model.     

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.      

Coupled framework for limit-cycle oscillations modeling based on leading-edge vortex shedding

Current trends in the aircraft industry involve higher aspect-ratio wings made of lighter materials. These trends seek to reduce fuel emissions and increase flight efficiency by reducing drag to lift ratio and overall weight, respectively, of the aircraft. This results in reduced structural stiffness and coupling between the aeroelastic modes and flight dynamics. The flutter phenomenon is of particular interest for aeroelastic studies, and modeling post-flutter limit-cycle oscillations (LCO) is a challenging problem.Several studies have been developed to allow fast simulations of the highly non-linear aerodynamic situations, with leading-edge vortex modulation been a proved solution for modeling some forms of LCOs in airfoils. This article proposes a framework based on the 3D expansion of this method using strip theory and coupling with modal structural model for simulations of aerodynamic based non-linear phenomenon. A cantilevered flat plate is used for testing and validating the framework against wind-tunnel experiments and the industry standard approach. The results show that the proposed model is able to capture the main behavior of the LCO observed in the experiments and is directly comparable with the current approaches used at the industry. The framework allows for scalability and is also fast enough to provide time-based results in under two days for a desktop simulation, reducing the need of expensive cluster computations. Finally, since it is completely physics-based it allows for the engineer to get insights on the aerodynamic flow at a fraction of the cost of more detailed CFD models.     

Aeroelastic analysis of swept pre-twisted wings

In this paper, aeroelastic modeling of aircraft wings with variations in sweep angle, taper ratio, and variable pre-twist angle along the span is considered. The wing structure is modeled as a classical beam with torsion and bending flexibility. The governing equations are derived based on Hamilton’s principle. Moreover, Peters’ finite state aerodynamic model which is modified to take into account the effects of the wing finite-span, the wing sweep angle, and the wing pre-twist angle, is used to simulate the aerodynamic loads on the wing. The coupled partially differential equations are discretized to a set of ordinary differential equations using Galerkin’s approach. By solving these equations the aeroelastic instability conditions are derived. The results are compared with some experimental and analytical results of previous published papers and good agreement is attained. Effects of the wing sweep angle, taper ratio, bending to torsional rigidity, and pre-twist angle on the flutter boundary in several cases are studied. Results show that these geometrical and physical parameters have considerable effects on the wing flutter boundary.     

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。     

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.     

自适应摄动法在失谐叶盘受迫振动分析中的应用

针对自适应摄动法在失谐叶盘受迫振动分析中,选择接近激振力频率的相应模态数目难于控制的问题,基于质量-弹簧模型,提出一种自动选择模态的方法。该方法可根据激振力频率与基系统固有频率集的关系,自动选择最接近激振力频率的相应模态个数。计算结果显示,对失谐叶盘系统,特别是在弱耦合情况下,该方法比人为选择模态更为可靠,可以使用较少机时,获得较高的求解精度。     

基于流形切空间插值的折叠翼参数化气动弹性建模

变体飞行器的气动弹性力学建模是当前先进飞行器设计的研究热点和难点.然而传统的气动弹性动力学建模方法对于具有结构参变特性的变体飞行器气动弹性力学研究存在建模效率低、计算复杂等问题.本研究提出了一种基于流形切空间插值的可折叠式变体机翼参数化气动弹性建模方法.首先,该方法建立若干个典型折叠角下的折叠翼结构有限元模型,通过流形...     

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.