Limit cycle oscillation behavior of transonic control surface buzz considering free-play nonlinearity

The limit cycle oscillation (LCO) behaviors of control surface buzz in transonic flow are studied. Euler equations are employed to obtain the unsteady aerodynamic forces for Type B and Type C buzz analyses, and an all-movable control surface model, a wing/control surface model and a three-dimensional wing with a full-span control surface are adopted in the study. Aerodynamic and structural describing functions are used to deal with aerodynamic and structural nonlinearities, respectively. Then the buzz speed and buzz frequency are obtained by V-g method. The LCO behavior of the transonic control surface buzz system with linear structure exhibits subcritical or supercritical bifurcation at different Mach numbers. For nonlinear structural model with a free-play nonlinearity in the control surface deflection stiffness, the double LCO phenomenon is observed in certain range of flutter speed. The free-play nonlinearity changes the stability of LCOs at small amplitudes and turns the unstable LCO into a stable one. The LCO behavior is dominated by the aerodynamic nonlinearity for the case with large control surface oscillation amplitude but by the structural nonlinearity for the case with small amplitude. Good agreements between LCO behaviors obtained by the present method and available experimental data show that our study may help to explain the experimental observation in wind tunnel tests and to understand the physical mechanism of transonic control surface buzz.     

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.     

Numerical investigation of the effects of structural geometric and material nonlinearities on limit-cycle oscillation of a cropped delta wing

This article presents numerical simulations of the limit-cycle oscillation (LCO) of a cropped delta wing in order to investigate the effects of structural geometric and material nonlinearities on aeroelastic behavior. In the computational model, the structural part included both the geometric nonlinearity that arises from large deflections, and the material nonlinearity that originates from plasticity. The Euler equations were employed in the fluid part to describe the transonic aerodynamics. Moreover, the load transfer was conducted using a 3-D interpolating procedure, and the interfaces between the structural and aerodynamic domains were constructed in the form of an exact match. The flutter and LCO behaviors of the cropped delta wing were simulated using the coupling model, and the results were compared with existing experimental measurements. For lower dynamic pressures, the geometric nonlinearity provided the proper mechanism for the development of the LCO, and the numerical results correlated with the experimental values. For higher dynamic pressures, the material nonlinearity led to a rapid rise in the LCO amplitude, and the simulated varying trend was consistent with the experimental observation. This study demonstrated that the LCO of the cropped delta wing was not only closely related to geometric nonlinearity, but was also remarkably affected by material nonlinearity.     

Coupled fluid structure analysis for wing 445.6 flutter using a fast dynamic mesh technology

The flow around wing 445.6 was modelled using Navier–Stokes equations and S-A model. The wing vibration and flow mesh deformation were computed using a fast dynamic mesh technology proposed by our own group. Wing 445.6 flutter was analysed through a strong coupling between the wing vibration and flow. The reduced flutter velocity was predicted and results are in good agreement with the experimental data. It is found that the subsonic flutter is mainly induced by the flow separation and the transonic and supersonic flutter are mainly caused by the oscillating shock wave and its induced flow separation. The positive aerodynamic work increases due to the oscillating shock wave when the subsonic flow becomes transonic reducing the flutter velocity. While the positive aerodynamic work induced by the oscillating shock wave decreases when the transonic flow becomes supersonic increasing the flutter velocity. That is why the transonic dip exists.     

LIMIT-CYCLE OSCILLATIONS IN HIGH-ASPECT-RATIO WINGS

The paper presents results obtained for limit-cycle oscillations (LCOs) in high-aspect-ratio wings caused by structural and aerodynamic nonlinearities. The analysis is based on geometrically exact structural analysis and finite-state unsteady aerodynamics with stall. The results indicate that stall limits the amplitude of post-flutter unstable oscillations. At speeds below the linear flutter speed, LCOs can be observed if the stable steady state is disturbed by a finite-amplitude disturbance. A critical disturbance magnitude is required at a given speed and a critical speed is required at a given disturbance magnitude to initiate LCOs. The LCO initiation mechanism can be attributed to the change in structural characteristics of the wing with deformation. It is also observed that the LCO gets increasingly complex with increasing speed. Period doubling is observed at low speeds and as the speed increases the oscillations lose periodicity and become chaotic.     

两种湍流模型时域颤振计算方法研究

采用时域计算分析方法进行了机翼跨音速颤振特性研究。在结构运动网格的基础上,采用格点格式有限体积方法进行空间离散和双时间全隐式方法进行时间推进求解雷诺平均N-S方程。针对流动粘性分别应用了SST湍流模型和SSG雷诺应力模型,通过对跨音速标模算例AGARD445.6机翼的计算结果与实验值的对比分析,其中应用SST湍流模型得到的颤振速度与实验值最为接近,特别是在跨音速段平均相对误差在3%以内;并且计算结果整体上反映了跨音速颤振"凹坑"物理特性,验证了方法的有效性。     

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.      

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.     

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.      

Computational aeroelastic investigation of a transonic limit-cycle-oscillation experiment at a transport aircraft wing model

Aeroelastic measurements of a three-dimensional wing model, the so-called Aerostabil wing, were conducted in the Transonic Windtunnel Göttingen. This clean, backward-swept wing allowed the experimental investigation of limit cycle oscillations in a certain transonic parameter range. In this paper, a detailed insight into the observed physical phenomena, especially the measured limit cycle oscillations, is presented by means of CFD–CSM coupled simulations. These simulations on the basis of a detailed structural finite element model reveal the specific properties of the Aerostabil wing and furthermore allow investigating the unstable behavior of this windtunnel model for transonic flow settings. The aerodynamic characteristics include a two-shock system and large flow separation areas, further increasing the complexity of the aeroelastic problem. A structural single degree-of-freedom system is used for the prediction of the experimental stability range and the limit cycle oscillation investigations. Due to the good agreement of simulation and experiment the limit cycle oscillations can be explained by means of nonlinear aerodynamic effects.     

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.     

Subcritical, nontypical and period-doubling bifurcations of a delta wing in a low speed wind tunnel

Limit Cycle Oscillations (LCOs) involving Delta wings are an important area of research in modern aeroelasticity. Such phenomena can be the result of geometric or aerodynamic nonlinearity. In this paper, a flexible half-span Delta wing is tested in a low speed wind tunnel in order to investigate its dynamic response. The wing is designed to be more flexible than the models used in previous research on the subject in order to expand the airspeed range in which LCOs occur. The experiments reveal that this wing features a very rich bifurcation behavior. Three types of bifurcation are observed for the first time for such an aeroelastic system: subcritical bifurcations, period-doubling/period-halving and nontypical bifurcations. They give rise to a great variety of LCOs, even at very low angles of attack. The LCOs resulting from the nontypical bifurcation display Hopf-type behavior, i.e. having fundamental frequencies equal to one of the linear modal frequencies. All of the other LCOs have fundamental frequencies that are unrelated to the underlying linear system modes.     

Validation of CFD‐CSD coupling interface methodology using commercial codes

Coupling interface between computational fluid dynamics (CFD) and computational structural dynamics (CSD) is required to provide exchange of information for the simulation of fluid–structure interaction (FSI) phenomena. Accuracy and consistency of information exchanged through coupling interface between the independent CFD and CSD solvers plays a central role in the simulation and prediction of FSI phenomenon, like flutter. In this paper validation of an implemented coupling interface methodology is presented for subsonic, transonic and near supersonic mach regime. The test case chosen for this purpose is the flutter of AGARD445.6 standard I‐wing weakened model configuration for subsonic to near transonic flow regime. Gambit^® and Fluent^® are used for CFD grid generation and solution of fluid dynamic equations, respectively. CSD modeling and simulation are provided by numerical time integration of modal dynamic equations derived through the finite element modeling in ANSYS^® environment. Copyright © 2009 John Wiley & Sons, Ltd.     

Aeroelastic prediction of the limit cycle oscillations of a cropped delta wing

The flutter and limit cycle oscillation (LCO) behavior of a cropped delta wing are investigated using a newly developed computational aeroelastic solver. This computational model includes a well-validated Euler finite difference solver coupled to a high-fidelity finite element structural solver. The nonlinear structural model includes geometric nonlinearities which are modelled using a co-rotational formulation. The LCOs of the cropped delta wing are computed and the results are compared to previous computations and to experiment. Over the range of dynamic pressures for which experimental results are reported, the LCO magnitudes computed using the current model are comparable to those from a previous computation which used a lower-order von Karman structural model. However, for larger dynamic pressures, the current computational model and the model which used the von Karman theory start to differ significantly, with the current model predicting larger deflections for a given dynamic pressure. This results in a LCO curve which is in better qualitative agreement with experiment. Flow features which were present in the previous computational model such as a leading edge vortex and a shock wave are enhanced in the current model due to the prediction of larger deflections and rotations at the higher dynamic pressures.     

主动控制翼板抑制悬索桥颤振的研究

主动控制翼板是一种新型桥梁气动措施。本文基于非定常气动力理论，推演了安装主动控制翼板后作用在整个桥梁主梁单位长度上气动力表达式，从增加系统扭转阻尼的角度，研究了翼板主动扭转振动参数的选取。在此基础上，对某大跨悬索桥方案进行了二自由度颤振分析，结果表明：合理选取翼板的主动扭转振动参数，主动控制翼板能够有效地提高该桥的颤振稳定性。     

A simulation-based study on longitudinal gust response of flexible flapping wings

Winged animals such as insects are capable of flying and surviving in an unsteady and unpredictable aerial environment. They generate and control aerodynamic forces by flapping their flexible wings. While the dynamic shape changes of their flapping wings are known to enhance the efficiency of their flight, they can also affect the stability of a flapping wing flyer under unpredictable disturbances by responding to the sudden changes of aerodynamic forces on the wing. In order to test the hypothesis, the gust response of flexible flapping wings is investigated numerically with a specific focus on the passive maintenance of aerodynamic forces by the wing flexibility. The computational model is based on a dynamic flight simulator that can incorporate the realistic morphology, the kinematics, the structural dynamics, the aerodynamics and the fluid–structure interactions of a hovering hawkmoth. The longitudinal gusts are imposed against the tethered model of a hovering hawkmoth with flexible flapping wings. It is found that the aerodynamic forces on the flapping wings are affected by the gust, because of the increase or decrease in relative wingtip velocity or kinematic angle of attack. The passive shape change of flexible wings can, however, reduce the changes in the magnitude and direction of aerodynamic forces by the gusts from various directions, except for the downward gust. Such adaptive response of the flexible structure to stabilise the attitude can be classified into the mechanical feedback, which works passively with minimal delay, and is of great importance to the design of bio-inspired flapping wings for micro-air vehicles.     

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。     

Parametric studies on relationships between flutter derivatives of slender bridge （Ⅱ）

Based on curve fitting of coefficients of three component forces of the Messina Straits Bridge, and the previously proposed semi-analytical expressions of flutter derivatives of flexible structure, the change of flutter derivatives of slender bridge cross-section with respect to its aerodynamic center, rotational speed and angle variation is studied using a parametric method. The calculated results are compared with the measured ones, and expressions of flutter derivatives of the Messina Straits Bridge are derived. The intrinsic relationships existing in flutter derivatives are validated again. It is shown that the influence of the rotational speed on flutter derivatives is not negligible. Therefore, it provides an additional semi-analytical approach for analyzing flutter derivatives of the bridge with streamlined cross-section to get its aerodynamic information.     

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.     

Cyber-physical flexible wing for aeroelastic investigations of stall and classical flutter

The fluid–structure interactions of a finite aspect ratio, cantilevered, flexible wing were investigated using a cyber-physical system to virtually augment the torsional dynamics of the wing. Cyber-physical systems (CPS), which have recently been pursued by a small number of research groups, have proven to be a very useful mechanism to interrogate the fluid–structure interaction parameter space. The premise of a CPS is to use dynamic feedback control to make a system behave according to desired equations of motion. Systems are composed of embedded hardware and software coupled with real-time computing to give the user the flexibility to quickly explore a range of structural parameters. With the advancement of modern control theory, robotics and embedded systems, CPSs integrate both simulation and physical properties into a smart structure which can be used to push the boundaries of research investigations.The CPS in this work allows for the investigation of dynamic aeroelastic instabilities of a three-dimensional, flexible, rectangular planform wing. Two dynamic instability regimes are observed: first, stall flutter, in which the torsional or pitch mode is excited through the dynamic stall process, and second, coupled (or classical) flutter, in which the pitch mode couples with the bending mode. By varying the torsional stiffness and therefore the frequency of torsional versus bending oscillations of the wing, both of these regimes can be attained at the same aerodynamic conditions using the CPS.