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.     

A general modal frequency-domain vortex lattice method for aeroelastic analyses

The generalized aerodynamic force (GAF) matrix is derived for the Unsteady Vortex Lattice Method (UVLM) without the assumption of out-of-plane dynamics. As a result, the approach naturally includes in-plane motion and forces unlike the doublet lattice method (DLM). The derived UVLM GAF is therefore applicable to industry-standard techniques for aeroelastic stability analyses, such as the p–k method. In this work, the fluid–structure interpolation is performed with radial basis functions for surface interpolation. The generalized aerodynamic forces computed with the UVLM are verified against the DLM from NASTRAN on a simple flat plate configuration. The ability of the UVLM to include steady loads is verified with a T-tail flutter case and the results confirm the importance of including steady loads for T-tail flutter analysis. The modal frequency domain VLM therefore provides the same level of efficiency and accuracy than the DLM, but without the restrictions and with the ability to handle complex geometries. It is therefore a viable replacement to the DLM.     

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.     

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.     

Aeroelastic stability of a cantilevered plate in yawed subsonic flow

The aeroelastic stability of cantilevered plates with their clamped edge oriented both parallel and normal to subsonic flow is a classical fluid–structure interaction problem. When the clamped edge is parallel to the flow the system loses stability in a coupled bending and torsion motion known as wing flutter. When the clamped edge is normal to the flow the instability is exclusively bending and is referred to as flapping flag flutter. This paper explores the stability of plates during the transition between these classic aeroelastic configurations. The aeroelastic model couples a classical beam structural model to a three-dimensional vortex lattice aerodynamic model. The aeroelastic stability is evaluated in the frequency domain and the flutter boundary is presented as the plate is rotated from the flapping flag to the wing configuration. The transition between the flag-like and wing-like instability is often abrupt and the yaw angle of the flow for the transition is dependent on the relative spacing of the first torsion and second bending natural frequencies. This paper also includes ground vibration and aeroelastic experiments carried out in the Duke University Wind Tunnel that confirm the theoretical predictions.     

Efficient unsteady aerodynamic loads prediction based on nonlinear system identification and proper orthogonal decomposition

In the present work, an efficient surrogate-based framework is developed for the prediction of motion-induced surface pressure fluctuations and integral force and moment coefficients. The model construction is realized by performing forced-motion computational fluid dynamics (CFD) simulations, while the result is processed via the proper orthogonal decomposition (POD) to obtain the predominant flow modes. Subsequently, a nonlinear system identification is carried out with respect to the applied excitation and the resulting POD coefficients. For the input/output model identification task, a recurrent local linear neuro-fuzzy approach is employed in order to capture the linear and nonlinear characteristics of the dynamic system. Once the reduced-order model (ROM) is trained, it can substitute the flow solver within unsteady aerodynamic or aeroelastic simulation frameworks for a given configuration at fixed freestream conditions. For demonstration purposes, the ROM approach is applied to the LANN wing in high subsonic and transonic flow. Due to the characteristic lambda-shock system, the unsteady aerodynamic surface pressure distribution is dominated by nonlinear effects. Numerical investigations show a good correlation between the results obtained by the ROM methodology in comparison to the full-order CFD solution. In addition, the surrogate approach yields a significant speed-up regarding unsteady aerodynamic calculations, which is beneficial for multidisciplinary computations.     

Numerical analysis on flutter of Busemann-type supersonic biplane airfoil

The Busemann-type supersonic biplane can effectively reduce the wave drag through shock interference effect between airfoils. However, considering the elastic property of the wing structure, the vibration of the wings can cause the shock oscillation between the biplane, which may result in relative aeroelastic problems of the wing. In this research, fluid–structure interaction characteristics of the Busemann-type supersonic biplane at its design condition have been studied. A theoretical two-dimensional structure model has been established to consider the main elastic characteristics of the wing structure. Coupled with unsteady Navier–Stokes equations, the fluid–structure dynamic system of the supersonic biplane is studied through the two-way computational fluid dynamics/computational structural dynamics (CFD/CSD) coupling method. The biplane system has been simulated at its design Mach number with different nondimensional velocities. Different initial disturbance has been applied to excite the system and the effects of the position of the mass center on the system’s aeroelastic stability is also discussed. The results reveal that the stability of the airfoil in supersonic biplane system is decreased compared with that of the airfoil isolated in supersonic flow and such stability reduction effect should be given due attention in practical design.     

CHAOTIC MOTIONS AND LIMIT CYCLE FLUTTER OF TWO-DIMENSIONAL WING IN SUPERSONIC FLOW

Based on the piston theory of supersonic flow and the energy method, the flutter motion equations of a two-dimensional wing with cubic stiffness in the pitching direction are established. The aeroelastic system contains both structural and aerodynamic nonlinearities. Hopf bifurcation theory is used to analyze the flutter speed of the system. The effects of system parameters on the flutter speed are studied. The 4th order Runge-Kutta method is used to calculate the stable limit cycle responses and chaotic motions of the aeroelastic system. Results show that the number and the stability of equilibrium points of the system vary with the increase of flow speed. Besides the simple limit cycle response of period 1, there are also period-doubling responses and chaotic motions in the flutter system. The route leading to chaos in the aeroelastic model used here is the period-doubling bifurcation. The chaotic motions in the system occur only when the flow speed is higher than the linear divergent speed and the initial condition is very small. Moreover, the flow speed regions in which the system behaves chaos axe very narrow.     

平尾翼型后加载对飞机配平的影响研究

利用MGAERO 软件对搭配不同尾翼模型的某典型布局客机翼身组合体流场进行了计算,研究了平尾翼型后加载对全机配平的影响. 分析表明,采用后加载设计的平尾翼型在配平时升力和阻力损失较小,配合其他手段可以提高全机升阻比,进而改善全机配平后的气动性能. 这一结论从流场计算的角度揭示了客机平尾翼型采用后加载设计这一发展趋势的重要原因.     

Porous panels with fixed ends lose stability by divergence

The aeroelastic stability of one-dimensional porous panels with a Darcy boundary condition on its surface is examined theoretically. Analytical and numerical analyses demonstrate that a porous panel in a uniform, single-sided, incompressible flow becomes aeroelastically unstable via divergence. This primary route of instability is identical to the well-known mechanism for non-porous panels. However, the divergence speed of a porous panel is always greater than the non-porous limit and increases with a dimensionless porosity parameter formed by the aeroelastic system. Various chordwise porosity distributions along the panel are also investigated, where the uniformly-porous panel is shown to be the most stable configuration. The generality and robustness of the primary divergence instability for porous panels is established analytically using a simple but general flutter analysis approach based on the Routh–Hurwitz stability criterion.     

鲁棒匹配点颤振预测的高效μ方法

基于含有参数不确定性的时域鲁棒颤振μ预测工具, 首先提出一种不确定多项式建模方法, 该方法通过线性分式变换(LFT)最终可以得到较低阶次不确定描述; 然后, 考虑到参数不确定问题中实μ(realμ)的计算复杂性, 又提出一种包含二分法的鲁棒颤振预测技术, 该方法是基于在一定飞行范围内飞行速度与气弹系统稳定性间的简单关系, 它能够避免鲁棒匹配点颤振预测中包含的高阶速度摄动块, 从而大大提高颤振预测的计算效率. 最后数值验证和对比表明了该方法的高效性.      

超音速气流中受热壁板的稳定性分析

采用Galerkin方法建立二维壁板的非线性气动弹性运动方程,用一阶活塞理论模拟壁板 受到的气动力. 基于李雅普诺夫间接法分析了平壁板的稳定性,得到了壁板失稳的边界 曲线;采用牛顿迭代法分析了壁板的屈曲变形,进而分析了后屈曲状态下壁板的稳定性; 在时域中分析了后屈曲状态下壁板的颤振边界. 分析结果表明,为了保证计算精度, 在二维壁板的静态失稳及过屈曲变形分析中,至少要取二阶谐波模态;在平壁板的超音速颤 振(动态失稳)边界分析中至少应取四阶模态. 还对壁板的温升,壁板长厚比、壁板密 度和气流马赫数作了无量纲变参分析,研究了这些参数的变化对壁板稳定性的影响规律. 研 究中发现,当气流速压较低时壁板一般会稳定在低阶谐波模态的屈曲变形位置,但是如果系 统出现多个渐近稳定的不动点,即使作用在壁板上的气流速压很低,壁板也有可能在较低速 压下发生二次失稳型颤振.     

A Monte Carlo Algorithm for Immiscible Two-Phase Flow in Porous Media

We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that tracks the motion of the fluid interfaces. The Monte Carlo algorithm is based on the configuration probability, where a configuration is defined by the positions of all fluid interfaces. We show that the configuration probability is proportional to the inverse of the flow rate. Using a two-dimensional network, advancing the interfaces using time integration, the computational time scales as the linear system size to the fourth power, whereas the Monte Carlo computational time scales as the linear size to the second power. We discuss the strengths and the weaknesses of the algorithm.     

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.     

Identification of Nonlinear Aeroelastic Systems Based on the Volterra Theory: Progress and Opportunities

The identification of nonlinear aeroelastic systems based on the Volterra theory of nonlinear systems is presented. Recent applications of the theory to problems in computational and experimental aeroelasticity are reviewed. Computational results include the development of computationally efficient reduced-order models (ROMs) using an Euler/Navier–Stokes flow solver and the analytical derivation of Volterra kernels for a nonlinear aeroelastic system. Experimental results include the identification of aerodynamic impulse responses, the application of higher-order spectra (HOS) to wind-tunnel flutter data, and the identification of nonlinear aeroelastic phenomena from flight flutter test data of the active aeroelastic wing (AAW) aircraft.     

Aeroelastic stability analysis of flexible overexpanded rocket nozzle

The aim of this paper is to present a new aeroelastic stability model taking into account the viscous effects for a supersonic nozzle flow in overexpanded regimes. This model is inspired by the Pekkari model which was developed initially for perfect fluid flow. The new model called the “Modified Pekkari Model” (MPM) considers a more realistic wall pressure profile for the case of a free shock separation inside the supersonic nozzle using the free interaction theory of Chapman. To reach this objective, a code for structure computation coupled with aerodynamic excitation effects is developed that allows the analysis of aeroelastic stability for the overexpanded nozzles. The main results are presented in a comparative manner using existing models (Pekkari model and its extended version) and the modified Pekkari model developed in this work.     

Multi-Body Analysis of a Tiltrotor Configuration

The paper describes the aeroelastic analysis of a tiltrotor configuration. The 1/5 scale wind tunnel semispan model of the V-22 tiltrotor aircraft is considered. The analysis is performed by means of a multi-body code, based on an original formulation. The differential equilibrium problem is stated in terms of first-order differential equations. The equilibrium equations of every rigid body are written together with the definitions of the momenta. The bodies are connected by kinematic constraints applied in the form of Lagrangian multipliers. Deformable components are mainly modelled by means of beam elements based on an original finite volume formulation. Multi-disciplinary problems can be solved by adding user-defined differential equations. In the presented analysis, the equations related to the control of the swash-plate of the model are considered. Advantages of a multi-body aeroelastic code over existing comprehensive rotorcraft codes include the exact modelling of the kinematics of the hub, the detailed modelling of the flexibility of critical hub components, and the possibility to simulate steady flight conditions as well as wind-up and maneuvers. The simulations described in the paper include (1) the analysis of the aeroelastic stability, with particular regard to the proprotor/pylon instability that is peculiar to tiltrotors, (2) the determination of the dynamic behavior of the system and of the loads due to typical maneuvers, with particular regard to the conversion from helicopter to airplane mode, and (3) the stress evaluation in critical components, such as the pitch links and the conversion downstop spring.     

Tightly coupled aeroelastic model implementation dedicated to fast aeroelastic tailoring optimisation of high aspect ratio composite wing

This paper presents the development of a code, called GEBTAero, dedicated to very flexible aircraft (VFA) aeroelasticity and especially the evaluation of aeroelastic tailoring effect on critical speeds. GEBTAero is an open source code consisting in a tightly coupling between a geometrically exact beam theory -and a finite state induced flow unsteady aerodynamic model, including an homogenisation tool. This model has been implemented in Fortran using GEBT code and optimised open source libraries with particular focus on computation speed. Besides a non linear transient dynamic simulation capacity, a particular focus is put on the fast critical speed computation strategy using a non-iterative modal approach about the geometrically non linear deformed shape of the wing with the computation of only a few aeroelastic modes. Computation speed and accuracy of this implementation is assessed using widely used aeroelastic test cases and compared successfully to other aeroelastic codes. Configurations using aeroelastic tailoring, which are the core target of this solver, are then evaluated numerically on a representative high aspect ratio anisotropic composite wing and a simple 2-ply composite laminates with both variable ply orientations. It illustrates the strong correlation between the structural bending/twisting coupling of an unbalanced composite laminates and its critical aeroelastic speed. It also shows the high sensitivity of ply orientation on the aeroelastic behaviour.     

Influence of friction and asymmetric freeplay on the limit cycle oscillation in aeroelastic system: An extended Hénon’s technique to temporal integration

Nonlinear effects such as friction and freeplay on the control surfaces can affect aeroelastic dynamics during flight. In particular, these nonlinearities can induce limit cycle oscillations (LCO), changing the system stability, and because of this it is essential to employ computational methods to predict this type of motion during the aircraft development cycle. In this context, the present article presents a matrix notation for describing the Hénon’s method used to reduce errors when considering piecewise linear nonlinearities in the numerical integration process. In addition, a new coordinate system is used to write the aeroelastic system of equations. The proposal defines a displacement vector with generalized and physical variables to simplify the computational implementation of the Hénon’s technique. Additionally, the article discusses the influence of asymmetric freeplay and friction on the LCO of an airfoil with control surface. The results show that the extended Hénon’s technique provides more accurate LCO predictions, that friction can change the frequency and amplitude of these motions, and the asymmetry of freeplay is important to determine the LCO behavior.