Flutter Margin Research Articles

Flutter margin research based on system stability analysis methods

Flutter margin research based on system stability analysis methods

Identification of flutter boundary of a bridge deck section using CFD and flutter margin analysis

Aeroelastic flutter identification of a two-dimensional bridge deck section using time domain techniques is studied. Aeroelastic simulations are performed using the aeroelastic solver available in open source OpenFOAM 5.0, wherein aerodynamic loads are computed using Unsteady Reynolds Average Naiver–Stokes (URANS) solver. The bridge deck section, modelled as a rigid body, exhibits pitch and heave degrees of freedom. Time domain system identification techniques, which include VAR and ERA (Vector auto-regressive and Eigensystem realization algorithm), are used to extract frequency and damping parameters from the aeroelastic response for various wind speeds.Two approaches are used for identification of the flutter boundary. The first consists of tracking the behaviour of damping and identifying the speed at which damping vanishes. The second approach is based on the flutter margin for discrete-time system (FMDS), which exhibits a linear behaviour with dynamic pressure in the vicinity of flutter.Results presented indicate that the ERA yielded slightly better estimates of damping compared to VAR. Furthermore, the FMDS parameter provided a reasonable estimate of the flutter boundary using only two data points, suggesting that this is an efficient strategy (as compared to tracking the damping) for flutter identification when the cost per aeroelastic response data point is high.

Data-Driven Bifurcation Analysis of Experimental Aeroelastic Systems Using Preflutter Measurements

Identification of flutter margins in modern aeroelastic systems is a challenging task due to increased nonlinearities in novel designs, which can result in instabilities occurring below the linear flutter speed. These instabilities pose a significant risk as they may involve multiple stable solutions, such as large-amplitude self-sustained oscillations. The lack of efficient nonlinear bifurcation analysis methods for experimental systems exacerbates the challenges associated with postflutter analysis. This paper presents a data-driven method for predicting flutter instabilities and bifurcation diagrams of an experimental nonlinear 2-degree-of-freedom (2-DOF) airfoil. The approach uses measurement data from the preflutter regime to forecast the postflutter dynamics, eliminating the need for computationally expensive models. This study is the first application of the recently introduced data-driven bifurcation forecasting method to experimental aeroelastic systems. The results show that the proposed method is accurate, with predictions matching the measured behavior of the system. The presented study provides valuable insights into the nonlinear stability and dynamics of experimental airfoils and demonstrates the potential for applicability of this approach in the analysis of experimental systems. The findings have significant implications for online monitoring and evaluation of the nonlinear dynamics of aeroelastic systems in the aerospace industry, where safety is of crucial importance.

Aeroelastic System Identification for Flutter Prediction via Multi-Output Autoregressive Modeling

The paper presents a study of aeroelastic system identification and flutter prediction in a wind tunnel test. Multi-output autoregressive moving-average and multi-output autoregressive models are fitted to acceleration and strain data and their correlation functions, respectively, to generate models that account for the dependencies between the different measured data. The modal frequencies and damping values are extracted from these models and used to assess the flutter margin at different airspeeds and predict the flutter onset speed. The method is applied in a flutter prediction wind tunnel study of a full-scale, half-span aeroelastic demonstrator aircraft using multiple acceleration data and strain data from fiber-optic strain sensors. Both models provide a smooth variation of the modal parameters (frequencies and damping values), from which it is easy to identify the critical aeroelastic modes that coalesce in flutter. Based on the different data sets, all models accurately predict flutter onset at approximately the same airspeed. An advantage of the proposed system identification approaches is that they concurrently account for the data from multiple sensors, avoiding the need to average the modal dynamics estimated from different sensors. The proposed method can be used to support safe flutter tests, as accurate system identification leads to accurate flutter prediction based on structural data recorded at safe airspeeds, remote from flutter.

Flutter Qualification of a Composite Light Trainer Aircraft (Csir-Nal Hansa - 3 (Vt-Hoa))

This paper presents the aeroelastic analysis and flight flutter tests aimed at ascertaining the freedom from flutter instability in the design flight envelope of a composite light trainer aircraft. The critical flutter, divergence and control reversal velocities of the complete aircraft were computed using MSC/NASTRAN and the typical section method. The results thus obtained from the analyses have been correlated with the ground vibration and flight flutter test results. The dispersion in the damping and frequency results obtained from computations and the flight flutter tests were within acceptable limits showing a good correlation. The flutter margins and the total damping of the aircraft satisfy the JAR-VLA/ FAR 23 requirements, thus enabling the aircraft to be type certified for the required flight safety standards.

Incremental Nonlinear Control for Aeroelastic Wing Load Alleviation and Flutter Suppression

This paper proposes an incremental nonlinear control method for an aeroelastic system’s gust load alleviation and active flutter suppression. These two control objectives can be achieved without modifying the control architecture or the control parameters. The proposed method has guaranteed stability in the Lyapunov sense and also has robustness against external disturbances and model mismatches. The effectiveness of this control method is validated by wind tunnel tests of an active aeroelastic parametric wing apparatus, which is a typical wing section containing heave, pitch, flap, and spoiler degrees of freedom. Wind tunnel experiment results show that the proposed nonlinear incremental control can reduce the maximum gust loads by up to 46.7% and the root mean square of gust loads by up to 72.9%, while expanding the flutter margin by up to 15.9%.

Probabilistic prediction of coalescence flutter using measurements: Application to the flutter margin method

Zimmerman and Weissenburger’s flutter margin method is widely used to estimate the aeroelastic coalescence flutter speed. In contrast to aeroelastic decay rates, the flutter margin exhibits monotonic decay with respect to airspeed rendering it effective in extrapolating the flutter speed using flight test data conducted at pre-flutter airspeeds. This paper reports the generalization of the Bayesian formulation of the flutter margin method by Khalil et al. developed to tackle measurement and modeling uncertainties. This paper improves the predictive performance of the previous algorithm by incorporating the joint prior of aeroelastic modal frequencies and decay rates among airspeeds in order to better estimate the joint posterior of modal parameters using observational data. The modal parameter prior is constructed using the classical two-degree-of-freedom pitch–plunge aeroelastic model whose system matrices (e.g. structural stiffness and damping matrices) vary randomly. Such joint modal parameter prior enforces statistical dependence among posteriors of modal parameters and the associated flutter margins across airspeeds. Numerical studies demonstrate a considerable reduction of uncertainties on the predicted flutter speed obtained from the generalized Bayesian flutter margin method. This improved algorithm can cut cost by reducing the number of flight tests and better assess the uncertainty against aeroelastic flutter.

Active flutter control of the wind turbines using double-pitched blades

Classical flutter of a wind turbine blade is a concerned issue to hinder the wind utilization to a large extent. Recent predictions showed a decreasing flutter margin (the ratio of flutter speed to rated rotor speed) with the increase in wind turbine size. To address this issue, a new blade configuration called the double-pitched blade is proposed and analytically investigated for its potential to enhance the flutter suppressing capability of modern large-size wind turbine blades. This new blade comprise an inner part and a tip part, where the tip part can rotate (or pitch) independently with respect to the inner part through a tip actuator commanded by a feedback control law. The aerodynamic loads of blade tip due to the actively controlled rotation of the tip part provide a torque on the inner part, which provides damping for the torsional mode of the wind turbine blade. The effectiveness of this new double-pitched blade for suppressing flutter is verified through a simulation study conducted on a 907-DOF aero-servo-elastic wind turbine model. Parametric studies are performed on two main design parameters, i.e. the length of the tip part and the associated chordwise location of tip shaft with respected to the blade cross section, and flutter control performance are obtained by numerical optimization process. Simulation results show the optimal length of tip part is around 3.3%of blade length, and the associated chordwise location of tip shaft is around 45%of chord length, the flutter amplitude of the conventional blade can be mitigated to around 4%using this double-pitched blade.

A comparative assessment of flutter prediction techniques

ABSTRACTTo establish flutter onset boundaries on the flight envelope, it is required to determine the flutter onset dynamic pressure. Proper selection of a flight flutter prediction technique is vital to flutter onset speed prediction. Several methods are available in literature, starting with those based on velocity damping, envelope functions, flutter margin, discrete-time Autoregressive Moving Average (ARMA) modelling, flutterometer and the Houbolt–Rainey algorithm. Each approach has its capabilities and limitations. To choose a robust and efficient flutter prediction technique from among the velocity damping, envelope function, Houbolt–Rainey, flutter margin and auto-regressive techniques, an example problem is chosen for their evaluation. Hence, in this paper, a three-degree-of-freedom model representing the aerodynamics, stiffness and inertia of a typical wing section is used(1). The aerodynamic, stiffness and inertia properties in the example problem are kept the same when each of the above techniques is used to predict the flutter speed of this aeroelastic system. This three-degree-of-freedom model is used to generate data at speeds before initiation of flutter, during flutter and after occurrence of flutter. Using these data, the above-mentioned flutter prediction methods are evaluated and the results are presented.

Investigation of flutter for large, highly flexible wind turbine blades

Improvements to the Sandia blade aeroelastic stability tool have been implemented to predict flutter for large, highly flexible wind turbine blade designs. The aerodynamic lift and moment caused by harmonic edge-wise motion are now included, but did not change the flutter solution, even for highly flexible blades. Flutter analysis of future, large blade designs is presented based on scaling trends. The analysis shows that flutter speed decreases at a rate similar to maximum rotor speed for increasing blade sizes: . This indicates the flutter margin is not directly affected by blade length. Rather, it was innovative design technology choices that predicted flutter in previous studies. A 100 m blade, flexible enough to be rail transported, was analyzed and it exhibited soft flutter below rated rotor speed. This indicated that excessive fatigue damage may occur due to limit cycle oscillations for blades that incorporate highly flexible designs.

Flutter Onset Prediction Based on Parametric Model Estimation

This paper presents a thorough evaluation of three flutter prediction techniques based on the well-understood autoregressive moving-average (ARMA) parametric model. Other than the original stability parameter that is derived from the identified autoregressive coefficients, the flutter margin and the Houbolt–Rainey (H-R) method are also presented and adjusted to provide alternative flutter predictions. From the application aspects, the empirical flutter margin, which is insensitive to the damping estimation, is first proposed. Feasibility of the empirical flutter indictor is demonstrated in this study. Taking advantage of the inherent recursive nature, the recursive least-squares algorithm with forgetting factor is suggested to perform the linear extrapolation iteratively at different flow conditions to facilitate an accurate flutter prediction. To verify the performance of the inspected methods, a linear pitch–plunge aeroelastic system and a dedicated wind-tunnel flutter test of an elastic wing are adopted to carry out the analyses for flutter statistics. While the extensive simulations are easy to implement on the aeroelastic idealization, the challenge of generating an adequate sample size based on the limited experimental data arises. To this end, the concept of surrogate data is first introduced to the flutter statistical analysis. Surrogate datasets generated via the iterative amplitude adjusted Fourier transform algorithm manage to describe the statistical behavior of the evaluated stability parameters. Both numerical and experimental results further substantiate the validity of the ARMA parametric model for aeroelastic modeling and provide alternative flutter prediction parameters with their own scope of application.

Data-Driven Forecasting of Postflutter Responses of Geometrically Nonlinear Wings

Ensuring adequate flutter margins is a critical step in aircraft design. However, in the presence of nonlinear effects, subcritical limit-cycle oscillations can arise even before flutter occurs. When nonlinear effects are anticipated, postflutter analyses have to be integrated into aircraft design in addition to flutter computations for preventing this undesirable subcritical behavior. Therefore, there is a need for computationally fast postflutter analysis methods suitable for design applications. This paper investigates a data-driven method to forecast the bifurcation behavior of a geometrically nonlinear wing, demonstrating its suitability to analyze realistic nonlinear aeroelastic systems. The method efficiently forecasts postflutter responses using only a few system transient computations in the preflutter regime. First, the accuracy of forecasted bifurcation diagrams is verified against time-marching results. Next, wing design parameters are varied to investigate their impact on postflutter responses and show the method suitability to parametric studies.

Design Methodology for Aeroelastic Tailoring of Additively Manufactured Lattice Structures Using Low-Order Methods

Additively manufactured wings can be aeroelastically tailored, which offers the potential for increased air vehicle efficiency via lighter structures. This paper develops a methodology to design aeroelastically tailored wings using additively manufactured lattice structures. Adaptive meshing techniques are used to design the topology of the lattice to align with the load direction, and the lattice is optimized to minimize the structural weight and to improve the flutter margin. To alleviate the computational effort of aeroelastically tailoring a structure, a low-order model for the dynamics of the lattice structure is developed. This structural low-order model is coupled to a previously developed physics-based transonic flutter model to compute the aeroelastic behavior of wings with internal lattice structures. The structural low-order model is validated by comparing against the full-order structural dynamics model. Finally, the design methodology is applied to the design of an internal structure of an aircraft wing to increase that wing’s flutter speed.

Development and Testing of Hypersonic Flutter Test Capability

To investigate the hypersonic flutter behavior of wings and all-movable control surfaces, a hypersonic wind tunnel flutter test capability has been developed by the China Academy of Aerospace Aerodynamics. This Paper outlines the design of the hypersonic flutter test rig; demonstrates the utility of the rig and the flutter test technique for hypersonic flutter research; and assesses the repeatability of the hypersonic flutter test, the application of subcritical flutter boundary identification methods, the effect of the rate of increase of dynamic pressure on flutter, and the aerodynamic heating effect. Descriptions of the data acquisition system and the experimental procedure are presented. Four models with the same design were tested for flutter at Mach numbers of 4.95 and 5.95. A wavelet time–frequency domain analysis method was employed to evaluate the trend of structural frequency coupling. The results showed good repeatability of the test. Both the flutter margin method and the damping ratio extrapolation method had high prediction accuracy in flutter boundary prediction. The rate of increase of dynamic pressure did not have any significant effect on the flutter boundary. However, a high rate of increase of dynamic pressure resulted in unsuccessful flutter prediction for the damping ratio extrapolation method. The leading edge and the windward side of the model were the parts subject to severe aerodynamic heating, but their temperatures were lower than the stagnation temperature of the airflow.

Multiple-Input Multiple-Output Experimental Aeroelastic Control Using a Receptance-Based Method

This paper presents the first experimental study of multiple-input multiple-output (MIMO) active vibration suppression by pole placement using the receptance method. The research is based on a purpose-built modular flexible wing equipped with leading- and trailing-edge control surfaces and two displacement sensors for measuring its position. The MIMO controller has the advantage of being designed entirely on frequency response functions, which are measured between the control surface position (control inputs) and the structural displacements (outputs), and include the actuator dynamics. There is no requirement to evaluate or to know the structural , , and matrices or the aerodynamic loads; and the formulation eliminates the need for a state observer. The controller is first implemented numerically and then experimentally on the aeroelastic system. Both frequencies and damping are assigned (together or independently) for the first two vibration modes. The research includes a procedure for assessing the control effort required and demonstrates an effective means of increasing the flutter margin while the effort is minimized.

Improving the Flutter Margin of an Unstable Fan Blade

The aim of this paper is to introduce design modifications that can be made to improve the flutter stability of a fan blade. A rig fan blade, which suffered flutter in the part-speed range and for which good quality measured data in terms of steady flow and flutter boundary is available, is used for this purpose. The work is carried out numerically using the aeroelasticity code AU3D. Two different approaches are explored: aerodynamic modifications and aero-acoustic modifications. In the first approach, the blade is stabilized by altering the radial distribution of the stagger angle based on the steady flow on the blade. The re-staggering patterns used in this work are therefore particular to the fan blade under investigation. Moreover, the modifications made to the blade are very simple and crude, and more sophisticated methods and/or an optimization approach could be used to achieve the above objectives with a more viable final design. This paper, however, clearly demonstrates how modifying the steady blade aerodynamics can prevent flutter. In the second approach, flutter is removed by drawing bleed air from the casing above the tip of the blade. Only a small amount of bleed (0.2% of the total inlet flow) is extracted such that the effect on the operating point of the fan is small. The purpose of the bleed is merely to attenuate the pressure wave that propagates from the trailing edge to the leading edge of the blade. The results show that extracting bleed over the tip of the fan blade can improve the flutter margin of the fan significantly.

Sensitivity of Aeroservoelastic Stability Characteristics Using Parametric Flutter Margins

The recently developed parametric flutter margin method is expanded to perform efficient sensitivity studies in which linear and nonlinear flutter characteristics are calculated for changes in selected parameters. Two approaches are suggested: one for structural, aerodynamic, or control parameters that can be formulated as single-input/single-output feedback loops and one for parameters that require multiple-input/multiple-output realization. The single-input/single-output analysis is based on frequency response functions, with the formulation aiming to track the important flutter mechanisms, and is arranged such that the sensitivity to different parameters, over large-variation ranges, may be based on the same set of response functions. The multiple-input/multiple-output analysis is similarly effective but is based on eigensolutions that indicate the parametric changes needed to obtain flutter. Three numerical examples using a generic transport aircraft model, in which sensitivity with respect to stiffness and mass variations were studied, are presented. The single-input/single-output and multiple-input/multiple-output approaches are also applied for calculating damping and frequency variations with velocity that may be used as traditional plots in aeroelastic design and certification tasks. The results demonstrate excellent agreement with those obtained by separate solutions of the MSC/NASTRAN code and nonlinear time marching simulations.

Safe Flutter Tests Using Parametric Flutter Margins

The recently developed numerical parametric flutter margin method is applied to perform safe flutter tests in which the flutter-onset conditions of a nominal configuration are positively identified, while the system is stabilized by an added concentrated mass. A known excitation force is applied to the added mass, and the collocated normal acceleration response is measured. Fourier transforms of the two signals are used for calculating flutter margins that change sign at flutter-onset conditions of the nominal system. The stability of the modified model at these conditions facilitates safe, flutter-free, testing conditions with a robustly measured response. The method is applied in wind-tunnel flutter tests of a clamped wing with a tip store, to which a stabilizing mass is added at a forward location. The added mass is connected through a thin cord and a pulley to a weight outside the tunnel. The excitation is performed by cutting the cord, and the mass acceleration is extrapolated from other accelerometers on the wing. The process is repeated at several airspeeds to compute frequency response functions and pinpoint the flutter-onset velocity of the nominal system. The resulting flutter boundaries are within a few percent of those measured by direct-flutter tests.

On the Importance of Engine-Representative Models for Fan Flutter Predictions

Discrepancies between rig tests and numerical predictions of the flutter boundary for fan blades are usually attributed to the deficiency of computational fluid dynamics (CFD) models for resolving flow at off-design conditions. However, as will be demonstrated in this paper, there are a number of other factors, which can influence the flutter stability of fan blades and lead to differences between measurements and numerical predictions. This research was initiated as a result of inconsistencies between the flutter predictions of two rig fan blades. The numerical results agreed well with rig test data in terms of flutter speed and nodal diameter (ND) for both fans. However, they predicted a significantly higher flutter margin for one of the fans, while measured flutter margins were similar for both blades. A new set of flutter computations including the whole low-pressure system was therefore performed. The new set of computations considered the effects of the acoustic liner and mistuning for both blades. The results of this work indicate that the previous discrepancies between CFD and tests were caused by, first, differences in the effectiveness of the acoustic liner in attenuating the pressure wave created by the blade vibration and second, differences in the level of unintentional mistuning of the two fan blades. In the second part of this research, the effects of blade mis-staggering and inlet temperature on aerodynamic damping were investigated. The data presented in this paper clearly show that manufacturing and environmental uncertainties can play an important role in the flutter stability of a fan blade. They demonstrate that aeroelastic similarity is not necessarily achieved if only aerodynamic properties and the traditional aeroelastic parameters, reduced frequency and mass ratio, are maintained. This emphasizes the importance of engine-representative models, in addition to accurate and validated CFD codes, for the reliable prediction of the flutter boundary.

Frequency, Damping, and Flutter Prediction from Aircraft Flight Data Using Autoregressive Model

Demonstration of flutter stability over the design envelope and identification of a safe flight envelope is a prerequisite for operational clearance of any new aircraft design. Generally, in all the flight flutter-testing programs, frequency and modal damping ratios are estimated at each flight-test point, and the trend of variation of frequency and damping is established. Frequencies and damping value estimations have to be as accurate as possible to define the aircraft flutter margin at each test point. In this study, stability parameters are estimated directly from the flight flutter-test time response data using an autoregressive (AR) model, which in turn is used to estimate the frequency and damping. In this paper, the focus is on determining an optimized AR model to ensure the accuracy of the model so that the estimation of stability parameters as well as frequency and damping parameters will be more accurate. Toward that, model order estimation techniques such as Akaike’s information criteria and final prediction error were used to predict the model order efficiently. Studies have been presented for different data lengths to prove the capability of this method to produce an accurate spectral estimate even with short data records. This will enable a quick evaluation of spectral estimate and flutter stability parameter using the same AR model, facilitating a quick flight envelope expansion.