Flutter Boundary Prediction Research Articles

Local Piston Theory with Viscous Correction and Its Application

This paper introduces a local piston theory with viscous correction for the prediction of hypersonic unsteady aerodynamic loads at high attitudes and large Mach numbers. A semi-empirical relation accounting for the viscous interaction effects to determine the effective shape is proposed. The method is validated by applying to thin airfoils at various Mach numbers, angles of attack, and operating altitudes. Sample two- and three-dimensional aerodynamic forces calculations are conducted demonstrating this method. Furthermore, flutter boundary predictions for a two-dimensional airfoil and pitching-in-damping derivative evaluations for a three-dimensional waverider configuration are performed with this unsteady aerodynamic model. Compared with the Euler-based local piston theory, this model performs much better at high altitudes for a wide range of Mach numbers, angles of attack, and shapes. Results suggest the feasibility of using the effective shape of hypersonic vehicles to efficiently and accurately obtain the unsteady aerodynamic characteristics in hypersonic flow environment.

Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver

An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver (Euler/BL) in a “semi-inverse” manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the computational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics (HIRENASD) Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are significant for these cases and the further data analysis confirms the validity and practicability of the coupled method.

Transonic flutter analysis of an AGARD 445.6 wing in the frequency domain using the Euler method

ABSTRACTA method based on the Euler equations is proposed for solving transonic flutter problems. The transonic nonlinear flow field with local shock wave/boundary layer interaction is obtained by the Euler/boundary layer equations, and the aerodynamic forces are converted from the time domain to the frequency domain using system identification techniques. The structural dynamic equations in generalized coordinates are adopted for solving structure problems. The method is validated by a flutter boundary prediction of the AGARD 445.6 wing model. The simulation results show that the method presented in this paper is accurate for the prediction of transonic flutter boundary through comparison with experimental data and other simulation results. Furthermore, the present frequency domain method is also much more efficient than the time domain method.

Influence of Intake on Fan Blade Flutter

The main aim of this paper is to study the influence of upstream reflections on flutter of a fan blade. To achieve this goal, flutter analysis of a complete fan assembly with an intake duct and the downstream outlet guide vanes (OGVs) (whole low pressure (LP) domain) is undertaken using a validated computational fluid dynamics (CFD) model. The computed results show good correlation with measured data. Due to space constraints, only upstream (intake) reflections are analyzed in this paper. It will be shown that the correct prediction of flutter boundary for a fan blade requires modeling of the intake and different intakes would produce different flutter boundaries for the same fan blade. However, the “blade only” and intake damping are independent and the total damping can be obtained from the sum of the two contributions. In order to gain further insight into the physics of the problem, the pressure waves created by blade vibration are split into an upstream and a downstream traveling wave in the intake. The splitting of the pressure wave allows one to establish a relationship between the phase and amplitude of the reflected waves and flutter stability of the blade. By using this approach, a simple reflection model can be used to model the intake effects.

Methods and advances in the study of aeroelasticity with uncertainties

Uncertainties denote the operators which describe data error, numerical error and model error in the mathematical methods. The study of aeroelasticity with uncertainty embedded in the subsystems, such as the uncertainty in the modeling of structures and aerodynamics, has been a hot topic in the last decades. In this paper, advances of the analysis and design in aeroelasticity with uncertainty are summarized in detail. According to the non-probabilistic or probabilistic uncertainty, the developments of theories, methods and experiments with application to both robust and probabilistic aeroelasticity analysis are presented, respectively. In addition, the advances in aeroelastic design considering either probabilistic or non-probabilistic uncertainties are introduced along with aeroelastic analysis. This review focuses on the robust aeroelasticity study based on the structured singular value method, namely the μ method. It covers the numerical calculation algorithm of the structured singular value, uncertainty model construction, robust aeroelastic stability analysis algorithms, uncertainty level verification, and robust flutter boundary prediction in the flight test, etc. The key results and conclusions are explored. Finally, several promising problems on aeroelasticity with uncertainty are proposed for future investigation.

Flutter Prediction for Flight/Wind-Tunnel Flutter Test Under Atmospheric Turbulence Excitation

In this paper, a flutter-boundary prediction technique for an aeroelastic/aeroservoelastic structure is introduced. This approach uses time-series flight/wind-tunnel flutter test data to compute an accurate estimate of the flutter speed. The flutter-boundary prediction tool discussed in this paper can be categorized into three steps.1)Signal preprocessing techniques are introduced to estimate the frequency-response function if the external excitation signal is measurable or compute the autopower spectrum when only responses from sensors can be measured due to a strong turbulence perturbation during flight flutter test.2)A frequency-domain system-identification methodology combined with a stabilization diagram is implemented to extract the elastic modes of a flexible structure. Accuracy of modes estimated in the second step directly affects the robustness of flutter prediction.3)The flutter-prediction analysis can therefore be performed with the implementation of an appropriate flutter-prediction tool such as the Zimmerman–Weissenburger flutter margin and/or damping trends extrapolation methods.Application of the proposed flutter-boundary prediction method to the Aeroelastic Test Wing I and SuperSonic SemiSpan Transport model demonstrates that it is an efficient tool for flutter-boundary prediction of aeroelastic/aeroservoelastic structures.

Flutter-Boundary Prediction of a Morphing Wing in the Process of Adaptation

DOI: 10.2514/1.J051202 This paper presents a numerical simulation analysis of flutter-boundary prediction of a two-dimensional morphing wing, which starts to flutter in the process of structural adaptation, although the flight speed is kept constant.Thestructuraladaptationisexpressedrepresentativelybyacontinuouschangeinthenaturalfrequencyof the heaving or the pitching motion of the wing, which induces the closeness and coalescence of the two frequencies of the aeroelastic modes. The dynamic characteristics of the wing are evaluated by applying a digital estimation techniquetoasequenceofdigitalizednonstationaryresponsesofthewingexcitedbystationaryairturbulencein flow during the ongoing adaptation. The critical boundary of the wing is predicted by the flutter margin for digitalized systems based on Jury’s stability criterion, which is mathematically equivalent to Routh-Hurwitz’s criterion. Numericalresultsshowthatthispredictionapproachbasedonthe fluttermarginfordiscrete-timesystems,whichthe authorsproposedoriginallyforordinarynonmorphingwings,isalsoveryeffectiveinpredictingthe flutterboundary of the morphing wing in the process of adaptation.

Linearized Euler Solver for Rapid Frequency-Domain Aeroelastic Analysis

An unsteady Euler Solver based on stationary Cartesian grid using transpiration boundary conditions is enhanced with the linearized Euler method for rapid computation of the frequency-domain Generalized Aerodynamic Forces(GAFs). The linearized Euler method reduces the time-domain simulation to a steady flow solution, thus speeds up the traditional process of extracting GAFs from the time-domain CFD solutions by roughly an order. The new linearized Euler solver is first validated by the 2-D airfoil and 3-D wing rigid body pitching test cases, as well as a flutter boundary prediction of the AGARD 445.6 weakened wing model. Then, aeroelastic analysis of the Twin-Engine Transport Flutter Model(TETFM) is performed using this new solver. Good correlation between the flutter boundary obtained by this linearized Euler method and the TDT wind tunnel data is demonstrated.

An Overview of Flutter Prediction in Tests Based on Stability Criteria in Discrete-Time Domain

This paper presents an overview on flutter boundary prediction in tests which is principally based on a system stability measure, named Jury's stability criterion, defined in the discrete-time domain, accompanied with the use of autoregressive moving-average (AR-MA) representation of a sampled sequence of wing responses excited by continuous air turbulences. Stability parameters applicable to two-, three- and multi-mode systems, that is, the flutter margin for discrete-time systems derived from Jury's criterion are also described. Actual applications of these measures to flutter tests performed in subsonic, transonic and supersonic wind tunnels, not only stationary flutter tests but also a nonstationary one in which the dynamic pressure increased in a fixed rate, are presented. An extension of the concept of nonstationary process approach to an analysis of flutter prediction of a morphing wing for which the instability takes place during the process of structural morphing will also be mentioned. Another extension of analytical approach to a multi-mode aeroelastic system is presented, too. Comparisons between the prediction based on the digital techniques mentioned above and the traditional damping method are given. A future possible application of the system stability approach to flight test will be finally discussed.

Flutter boundary prediction of an adaptive morphing wing for unmanned aerial vehicle

We have developed a novel morphing wing design for UAV that makes use of shape memory alloys as actuators. The advantages of the novel design have already been addressed in earlier publications by Meguid and his collaborators. Because of the flexibility of the wing, it is highly desirable to investigate flutter instability. This study addresses flutter instability for our novel morphing wing at low speed considering different morphing wing configurations. Structural dynamics of the wing is obtained using lumped mass method and unsteady aerodynamic based on strip model is used to evaluate the aerodynamic forces and moments. Flutter boundary was predicted using p-k method. The results indicate that the newly designed flexible concept of the morphing wing increases the critical flutter velocity.

Flutter prediction in turbomachinery with energy method

The study described in this article is the application of energy method for the prediction of flutter boundary and the effects of some parameters on aeroelastic stability in turbomachinery. The unsteady flow with multi-layer moving grid technique for blade oscillation was undergone for aerodynamic work with the blade passage being discretized using a background fixed H-grid and a body-fitted O-grid moving with the blade. Also, with the assumption of equivalent viscous damping, aerodynamic modal damping ratio was defined based on energy method. The numerical method, with mode shapes and nodal diameter numbers considered, was applied for a transonic compressor rotor stage for which measured flutter boundary on characteristic map was available. It was found that the calculated flutter boundary in the first bending blade mode agreed well with the measured one. Furthermore, it was concluded that the mode shapes and inter-blade phase angle were key parameters on aeroelasticity in turbomachinery and that the flutter instability was mainly induced by the co-action of shock wave and separated flow.

Improved Flutter Boundary Prediction for an Isolated Two-Degree-of-Freedom Airfoil

A novel method of computing the flutter boundary for an isolated airfoil based on a high-fidelity CFD model reveals unusual behavior at certain Mach numbers for a NACA 0012 section. Inviscid and viscous predictions of the flutter boundary for the two airfoils are compared with results from a previous experimental study. Over a narrow range of Mach numbers, unusual aeroelastic response behavior occurs, and inviscid and viscous predictions dier significantly. Also in this range, solutions show increased sensitivity to grid topology as well as flow Mach number. This is found to be a consequence of flow shedding which occurs over a narrow range of Mach numbers. The nature of this shedding is captured only by using a greatly refined viscous grid, and unusual numerical results occur when using coarser viscous and inviscid meshes.

Higher-Order Time Integration Schemes for Aeroelastic Applications on Unstructured Meshes

Efficient techniques for computational aeroelasticity on unstructured meshes are investigated. These include the formulation of a fourth-order implicit Runge-Kutta time-integration scheme, a third-order backward-difference time-integration scheme, and a second-order backward-difference time-integration scheme for the coupled system of flow and structural equations. Strong coupling between the flow solution and structural equations is maintained by fully converging the fully coupled system at each time step or stage. The time-integration schemes are constructed such that discrete conservation is maintained in the flow solution in the presence of dynamically deforming meshes, by verifying the discrete geometric conservation law. Efficient multigrid solution techniques are devised for solving both the governing flow equations and the mesh motion equations, using the same agglomerated coarse levels for both problems. The flutter boundary prediction of the AGARD 445.6 wing is used to demonstrate the accuracy and efficiency of these techniques as well as the sensitivity of flutter boundary prediction to time-step size and temporal errors.

Aeroelastic analysis through linear and non-linear methods: a summary of flutter prediction in the PUMA DARP

AbstractThis paper presents a comparison of linear and non-linear methods for the analysis of aeroelastic behaviour and flutter boundary prediction. The methods in question include NASTRAN and ZAERO, based on linear aerodynamics, and the non-linear coupled CFD-CSD methods RANSMB and PMB, developed at the Universities of Bristol and Glasgow respectively. The test cases used for this comparison are the MDO and AGARD 445.6 weakened wing. In general, it was found that the non-linear methods demonstrate excellent agreement with respect to pressure distributions, deflections, dynamic behaviour, and flutter boundary locations for both cases. This is in contrast to previous studies involving similar methods, where notable differences across the MDO span were found, and is taken to imply good performance of the CFD-CSD interpolation schemes employed here. While the linear methods produce similar flutter boundaries to the coupled codes for the aerodynamically simple AGARD 445.6 wing, results for the transonic ‘rooftop’ MDO wing design did not agree as well.

Wavelet Denoising of Flight Flutter Testing Data for Improvement of Parameter Identification

The accuracy of modal parameter estimation plays a crucial role in flutter boundary prediction. A new wavelet denoising method is introduced for flight flutter testing data, which can improve the estimation of frequency domain identification algorithms. In this method, the testing data is first preprocessed with a gradient inverse weighted filter to initially lower the noise. The redundant wavelet transform is then used to decompose the signal into several levels. A “clean” input is recovered from the noisy data by level dependent thresholding approach, and the noise of output is reduced by a modified spatially selective noise filtration technique. The advantage of the wavelet denoising is illustrated by means of simulated and real data.

Accelerating CFD-Based Aeroelastic Analysis Using Distributed Processing

Distributed processing is applied to CFD-based aeroelastic analysis to accelerate the completion of flutter boundary predictions. The process for identifying an aeroelastic stability boundary is divided into several independent simulations that are distributed to multiple computers. The solutions are completed in parallel. This parallelism is used to accelerate the prediction of the instability boundary. This process is also applied to the generation of training data for the system identification of the unsteady aerodynamic response to motion and force on a modal structural model. The equipment used in this study is common, off-the-shelf computing hardware. This method is application ready with no required alterations to the CFD solver. Results address the extent to which this methodology is applicable to aerospace applications. Nomenclature f a = generalized aerodynamic force vector N = number of data points in training set Np = number of data points in a parallel training set na = number of previous aerodynamic forces nb = number of previous structural displacements np = number of Central Processing Units nr = number of roots or mode shapes q = free stream dynamic pressure q = generalized displacement vector ρ = free stream density

Effect of relative amplitude on bridge deck flutter

Self-excited wind forces on a bridge deck can be non-linear even when the vibration amplitude of the body is small. This phenomenon is evaluated in this paper. Experiments detecting the nonlinearity are performed first, with the concept of “relative amplitude”, i.e. the amplitude of the externally triggered free vibration relative to the envelope of the ambient response of an elastically supported rigid sectional model. Two types of sectional model, a twin-deck bluff model (model A) and a partially streamlined box girder model (model B) are tested with two extreme cases of relative amplitude. Based on the flutter derivatives of model B, a flutter boundary prediction is subsequently carried out on a cable-supported bridge to manifest the changes of critical flutter wind velocity due to different relative amplitudes. The effect of relative amplitude on flutter derivatives and on the flutter boundary reveals, from the structural point of view, a complex relationship between the self-excited forces and the “structural vibration noise” due to turbulence that is inherent in the interaction of the ambient wind with the structure. Although the aeroelastic forces are linear when the body motion due to an external trigger is not affected significantly by this turbulence, they are postulated to be nonlinear when this “vibration noise” cannot be neglected.

On Accuracy of Prediction of Flutter Boundaries on Unstructured Grids

The accuracies of unstructured grid methods for flutter analysis were investigated. Time accurate flow simulations with moving boundary were carried out on three types of unstructured grids. The results are compared with a recent report obtained by a structured, parallel flow solver. Semi-structured triangular grids and isotropic fine grids show similar results and agree well with the data. Poor grid resolution can result in wrong responses of the wing motion near the flutter boundary even when the same grid distribution is used on the wing. Typical wing responses for the lower- and higher-frequency modes are elaborated.

Implicit method for the time marching analysis of flutter

AbstractThis paper evaluates a time marching simulation method for flutter which is based on a solution of the Euler equations and a linear modal structural model. Jameson’s pseudo time method is used for the time stepping, allowing sequencing errors to be avoided without incurring additional computational cost. Transfinite interpolation of displacements is used for grid regeneration and a constant volume transformation for inter-grid interpolation. The flow pseudo steady state is calculated using an unfactored implicit method which features a Krylov subspace solution of an approximately linearised system. The spatial discretisation is made using Osher’s approximate Riemann solver with MUSCL interpolation. The method is evaluated against available results for the AGARD 445.6 wing. This wing, which is made of laminated mahogany, was tested at NASA Langley in the 1960s and has been the standard test case for simulation methods ever since. The structural model in the current work was built in NASTRAN using homogeneous plate elements. The comparisons show good agreement for the prediction of flutter boundaries. The solution method allows larger time steps to be taken than other methods.

Calculation of Wing Flutter by a Coupled Fluid-Structure Method

An integrated computational fluid dynamics (CFD) and computational structural dynamics (CSD) method is developed for the simulation and prediction of flutter. The CFD solver is based on an unsteady, parallel, multiblock, multigrid finite volume algorithm for the Euler/Navier-Stokes equations. The CSD solver is based on the time integration of modal dynamic equations extracted from full finite element analysis. A general multiblock deformation grid method is used to generate dynamically moving grids for the unsteady flow solver. The solutions of the flowfield and the structural dynamics are coupled strongly in time by a fully implicit method. The coupled CFD-CSD method simulates the aeroelastic system directly on the time domain to determine the stability of the aeroelastic system. The unsteady solver with the moving grid algorithm is also used to calculate the harmonic and/or indicial responses of an aeroelastic system, in an uncoupled manner, without solving the structural equations. Flutter boundary is then determined by solving the flutter equation on the frequency domain with the indicial responses as input. Computations are performed for a two-dimensional wing aeroelastic model and the three-dimensional AGARD 445.6 wing. Flutter boundary predictions by both the coupled CFD-CSD method and the indicial method are presented and compared with experimental data for the AGARD 445.6 wing.