Parametric aeroelastic modeling based on component modal synthesis and stability analysis for horizontally folding wing with hinge joints

To investigate the aeroelastic stability of a folding wing effectively, a parametric aeroelastic analysis approach is proposed. First, the fixed interface component modal synthesis is used to derive the structural dynamic equation for a folding wing, in which the elastic connection is considered. The unsteady aerodynamic model is established by the doublet lattice method (DLM), and the aeroelastic model is achieved from integration of the DLM with the component modal analysis. The generalized aerodynamic influence coefficient matrix is established by modes kept and constraint modes of each component. The aeroelastic stability of a folding wing is investigated based on the Gram matrix in control theory. The effectiveness of the proposed method is verified via comparison with traditional flutter eigenvalue analysis for both extended and folded configurations. The proposed method identifies coupled modes and improves computational efficiency when compared to classical aeroelastic stability analysis methods, such as the p–k method.     

Aeroelastic stability analysis considering a continuous flight envelope

This paper presents a new methodology to analyze aeroelastic stability in a continuous range of flight envelope with varying parameter of velocity and altitude. The focus of the paper is to demonstrate that linear matrix inequalities can be used to evaluate the aeroelastic stability in a region of flight envelope instead of a single point, like classical methods. The proposed methodology can also be used to study if a system remains stable during an arbitrary motion from one point to another in the flight envelope, i.e., when the problem becomes time-variant. The main idea is to represent the system as a polytopic differential inclusion system using rational function approximation to write the model in time domain. The theory is outlined and simulations are carried out on the benchmark AGARD 445.6 wing to demonstrate the method. The classical pk-method is used for comparing results and validating the approach. It is shown that this method is efficient to identify stability regions in the flight envelope.     

Stability of a two-dimensional airfoil with time-delayed feedback control

This paper presents a systematic study on aeroelastic stability of a two-dimensional airfoil with a single or multiple time delays in the feedback control loops. Firstly, the delay-independent stability region of the aeroelastic system with a single time delay is determined on the basis of the generalized Sturm criterion for polynomials. Then, the stability switches with variations in time delay are analyzed when the system parameters fall out of the delay-independent stability region. Flutter boundaries of the controlled aeroelastic system as time delay varies are predicted in a continuous way by the predictor-corrector technique. Finally, two methods, the polynomial eigenvalue method and the infinitesimal generator method, are introduced to investigate the stability of the controlled aeroelastic system with multiple time delays. Numerical simulations are made to demonstrate the effectiveness of all the above approaches.     

Aircraft T-tail flutter predictions using computational fluid dynamics

The paper presents the application of computational aeroelasticity (CA) methods to the analysis of a T-tail stability in transonic regime. For this flow condition unsteady aerodynamics show a significant dependency from the aircraft equilibrium flight configuration, which rules both the position of shock waves in the flow field and the load distribution on the horizontal tail plane. Both these elements have an influence on the aerodynamic forces, and so on the aeroelastic stability of the system. The numerical procedure proposed allows to investigate flutter stability for a free-flying aircraft, iterating until convergence the following sequence of sub-problems: search for the trimmed condition for the deformable aircraft; linearize the system about the stated equilibrium point; predict the aeroelastic stability boundaries using the inferred linear model. An innovative approach based on sliding meshes allows to represent the changes of the computational fluid domain due to the motion of control surfaces used to trim the aircraft. To highlight the importance of keeping the linear model always aligned to the trim condition, and at the same time the capabilities of the computational fluid dynamics approach, the method is applied to a real aircraft with a T-tail configuration: the P180.     

Nonlinear aeroelastic stability analysis of wind turbine blade with bending–bending–twist coupling

In this study, the nonlinear aeroelastic stability of wind turbine blade with bending–bending–twist coupling has been investigated for composite thin-walled structure with pretwist angle. The aerodynamic model used here is the differential dynamic stall nonlinear ONERA model. The nonlinear aeroelastic equations are reduced to ordinary equations by Galerkin method, with the aerodynamic force decomposition by strip theory. The nonlinear resulting equations are solved by a time-marching approach, and are linearized by small perturbation about the equilibrium point. The nonlinear aeroelastic stability characteristics are investigated through eigenvalue analysis, nonlinear time domain response, and linearized time domain response.     

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.     

Convergence predictions for aeroelastic calculations of tuned and mistuned bladed disks

Mistuning changes the dynamics of bladed disks significantly. Frequency domain methods for predicting the dynamics of mistuned bladed disks are typically based on iterative aeroelastic calculations. Converged aerodynamic stiffness matrices are required for accurate aeroelastic results of eigenvalue and forced response problems. The tremendous computation time needed for each aerodynamic iteration would greatly benefit from a fast method of predicting the number of iterations needed for converged results. A new hybrid technique is proposed to predict the convergence history based on several critical ratios and by approximating as linear the relation between the aerodynamic force and the complex frequencies (eigenvalues) of the system. The new technique is hybrid in that it uses a combined theoretical and stochastic/computational approach. The dynamics of an industrial bladed disk is investigated, and the predicted convergence histories are shown to match the actual results very well. Monte Carlo simulations using the new hybrid technique show that the aerodynamic ratio and the aerodynamic gradient ratio are the two most important factors affecting the convergence history.     

Methods of fluid–structure coupling in frequency and time domains using linearized aerodynamics for turbomachinery

Two methods of fluid–structure coupling for turbomachinery are presented, the first one in the frequency domain and the second in both frequency and time domains. In both methods, the structure and the fluid are assumed to have circumferential cyclic symmetric properties and the unsteady aerodynamic forces are assumed to be linear in terms of the structural displacements. The motion equation of the reference sector in the travelling wave coordinates is projected on the complex eigenmodes for each phase number. The generalized unsteady aerodynamic forces are computed by solving the Euler equations and by assuming the structural motion to be harmonic with a constant phase angle between two adjacent sectors. In the frequency domain, the complex, nonlinear eigenvalue problem for the aeroelastic stability analysis is solved iteratively either by the double scanning method or by using Karpel's minimum state smoothing of the aerodynamic coefficient matrix. In the time domain, Karpel's smoothing method is used to obtain an approximation of the generalized unsteady aerodynamic forces by means of auxiliary state variables. These coupling methods are tested on a compressor blade row and the good agreement obtained between their results and those of the direct coupling method shows that the proposed numerical methods, already used in aircraft applications, are adapted to turbomachinery.     

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 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.     

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.     

Aeroelastic stability analysis of a flexible over-expanded rocket nozzle using numerical coupling by the method of transpiration

The aim of this paper is to present and compare two different approaches for aeroelastic stability analysis of a flexible over-expanded rocket nozzle. The first approach is based on the aeroelastic stability models developed in a previous work, while the second uses the numerical fluid–structure coupling via the transpiration method. The aeroelastic frequencies of the nozzle obtained by various stability models are compared with those extracted from the numerical coupling by the method of transpiration. Both set of results show an overall good agreement.     

Laplace transform-boundary element coupling method for viscous fluid-structure impact analysis

Based on linearized 2-D Navier-Stokes equation, a Laplace transform-boundary element coupling method for viscous fluid-structure impact analysis is proposed. Under assumption of incompressibility for the fluid, the corresponding equivalent boundary integral equation in terms of the potential function and stream function is first established by Lamb's transform in the Laplace transform domain. It enables us to solve impact water problems in frequency domain by the boundary element method, in which the effect of viscous flow on the dynamic response can be taken into account. Then a complete solution of the problem under consideration in time domain is obtained by means of Durbin's formulas for the numerical inversion of the Laplace transform. Finally, a practical example is given to confirm the validity of the present method. Project supported by the National Defence Foundation of Science & Technology of China (No. J14. 8. 1. JW0515).     

Effect of thrust on the aeroelastic instability of a composite swept wing with two engines in subsonic compressible flow

This paper aims to investigate aeroelastic stability boundary of subsonic wings under the effect of thrust of two engines. The wing structure is modeled as a tapered composite box-beam. Moreover, an indicial function based model is used to calculate the unsteady lift and moment distribution along the wing span in subsonic compressible flow. The two jet engines mounted on the wing are modeled as concentrated masses and the effect of thrust of each engine is applied as a follower force. Using Hamilton's principle along with Galerkin's method, the governing equations of motion are derived, then the obtained equations are solved in frequency domain using the K-method and the aeroelastic instability conditions are determined. The flutter analysis results of four example wings are compared with the experimental and analytical results in the literature and good agreements are achieved which validate the present model. Furthermore, based on several case studies on a reference wing, some attempts are performed to analyze the effect of thrust on the stability margin of the wing and some conclusions are outlined.     

考虑结构失稳特征的复合材料机翼气动弹性优化设计

从工程数学求解和有限元分析角度对复合材料结构的稳定性分析方法进行研究,基于这两个方面分别建立了同时考虑壁板稳定性约束和气动弹性约 束的气动弹性优化技术,并以大展弦比复合材料机翼为对象,进行气动弹性综合优化设计。研究表明,机翼气动弹性优化中若不考虑稳定性约束条件,虽然可以获得较小结构重量,但往往不满足稳定性要求;相比从有限元角度考虑结构失稳特征的气动弹性综合优化设计方法,通过工程数学方法对机翼结构进行分区失稳分析优化可以更加精准地控制变量,在满足各项性能指标,特别是稳定性约束的同时,进一步减轻了结构重量,提高了结构失稳因子。     

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...     

Limit cycle oscillations of rectangular cantilever wings containing cubic nonlinearity in an incompressible flow

Limit cycle oscillations (LCO) as well as nonlinear aeroelastic analysis of rectangular cantilever wings with a cubic nonlinearity are investigated. Aeroelastic equations of a rectangular cantilever wing with two degrees of freedom in an incompressible potential flow are presented in the time domain. The harmonic balance method is modified to calculate the LCO frequency and amplitude for rectangular wings. In order to verify the derived formulation, flutter boundaries are obtained via a linear analysis of the derived system of equations for five different cases and compared with experimental data. Satisfactory results are gained through this comparison. The problem of finding the LCO frequency and amplitude is solved via applying the two methods discussed for two different cases with hardening cubic nonlinearities. The results from first-, third- and fifth-order harmonic balance methods are compared with the results of an exact numerical solution. A close agreement is obtained between these harmonic balance methods and the exact numerical solution of the governing aeroelastic equations. Finally, the nonlinear aeroelastic analysis of a rectangular cantilever wing with a softening nonlinearity is studied.     

Non-Fourier heat conduction in an exponentially graded slab

The present article investigates one-dimensional non-Fourier heat conduction in a functionally graded material by using the differential transformation method. The studied geometry is a finite functionally graded slab, which is initially at a uniform temperature and suddenly experiences a temperature rise at one side, while the other side is kept insulated. A general non-Fourier heat transfer equation related to the functionally graded slab is derived. The problem is solved in the Laplace domain analytically, and the final results in the time domain are obtained by using numerical inversion of the Laplace transform. The obtained results are compared with the exact solution to verify the accuracy of the proposed method, which shows excellent agreement.     

AEROELASTIC OPTIMIZATION DESIGN OF COMPOSITE WING WITH CONSIDERATION OF STRUCTURAL INSTABILITY

从工程数学求解和有限元分析角度对复合材料结构的稳定性分析方法进行研究,基于这两个方面分别建立了同时考虑壁板稳定性约束和气动弹性约 束的气动弹性优化技术,并以大展弦比复合材料机翼为对象,进行气动弹性综合优化设计。研究表明,机翼气动弹性优化中若不考虑稳定性约束条件,虽然可以获得较小结构重量,但往往不满足稳定性要求;相比从有限元角度考虑结构失稳特征的气动弹性综合优化设计方法,通过工程数学方法对机翼结构进行分区失稳分析优化可以更加精准地控制变量,在满足各项性能指标,特别是稳定性约束的同时,进一步减轻了结构重量,提高了结构失稳因子。     

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.