Flutter Prediction Research Articles

A flutter prediction method with low cost and low risk from test data

The most common approach to flight flutter testing is to track estimated modal damping ratios of an aircraft over a number of fight conditions. However, the risk is inevitable when this method is utilized since the aircraft must fly near the flutter boundary. In this paper, a method with low cost and low risk for flutter boundary prediction is proposed. Based on structural modal parameters from the ground vibration test (GVT) and the structural response at the sub-critical speed, the generalized aerodynamic force coefficient vector can be solved. The generalized displacement vector is designed as the input and the generalized aerodynamic force coefficient vector as the output. System identification is used to construct the reduced-order aerodynamic model. The aeroelastic model based on experimental results can be constructed by coupling the structural motion equation and the aerodynamic equation in state space. Analyzing the characteristics of the fluid–structure coupling system changing with the dynamic pressure, the flutter onset behaviors can be solved by the eigenvalue method. Wind tunnel tests confirm that this method only needs one wind-on test at the sub-critical speed to predict the flutter onset with a certain precision even the reference dynamic pressure is far from the flutter critical point.

A comparative study of coupled and decoupled fan flutter prediction methods under variation of mass ratio and blade stiffness

Flutter is a long standing issue for fan blades of civil aero-engines and becomes of further concern for modern light-weight designs with increasing fan diameters to reach ultra-high bypass ratios. Accurate flutter prediction is therefore of prime consideration in the design process in order to avoid catastrophic blade failure in operation or expensive redesign iterations if spotted in ground or flight tests. The traditional energy method, which is based on the assumption of negligible aeroelastic coupling, has been used to great extend to predict flutter of turbomachinery components including aero-engine fan blades, and is today by far the most widely applied technique. The underlying assumption of fluid–structure decoupling, however, has to be questioned for large fan blades that are characterized by low mass ratios and low stiffness. Implications of the violation of the system decoupling assumption on the prediction capabilities of the energy method are important to understand for the fan designer in order to allow an informed decision on the flutter prediction tool to use. In this work a comprehensive comparative study is presented in which the energy method is contrasted to the predictions of a strongly coupled fluid–structure interaction method for varying values of mass ratio and blade stiffness of a transonic three-dimensional fan rotor. The strength of aeroelastic coupling is evaluated in terms of the aeroelastic frequency shift and its impact on the prediction accuracy of the energy method is investigated. The results show the capability of the energy method to accurately predict flutter for a wide range of mass ratio and stiffness configurations, but its prediction accuracy is reduced for combined low mass ratio and low stiffness blades. Mechanisms governing the aeroelastic frequency shift are explained to allow a better understanding of the effect and a method for its prediction based on results of a decoupled analysis is shown.

Modeling of self-excited forces during multimode flutter: an experimental study

The prediction of multimode flutter relies, to a larger extent than bimodal flutter, on accurate modeling of the self-excited forces since it is challenging to perform experimental validation by using aeroelastic tests for a multimode case. This paper sheds some light on the accuracy of predicted self-excited forces by comparing numerical predictions of self-excited forces with measured forces from wind tunnel tests considering the flutter vibration mode. The critical velocity and the corresponding flutter vibration mode of the Hardanger Bridge are first determined using the classical multimode approach. Then, a section model of the bridge is forced to undergo a motion corresponding to the flutter vibration mode at selected points along the bridge, during which the forces that act upon it are measured. The measured self-excited forces are compared with numerical predictions to assess the uncertainty involved in the modeling. The self-excited lift and pitching moment are captured in an excellent manner by the aerodynamic derivatives. The self-excited drag force is, on the other hand, not well represented since second-order effects dominate. However, the self-excited drag force is very small for the cross-section considered, making its influence on the critical velocity marginal. The self-excited drag force can, however, be of higher importance for other cross-sections.

Novel Nonstationarity Assessment Method for Hypersonic Flutter Flight Tests

Hypersonic aircraft have been rapidly developed in recent years both theoretically and experimentally. Aerothermoelastic simulation is very challenging due to its inherent complexity, but physical tests are a workable approach. Flutter tests with variable speed are a popular alternative to hypersonic tests which provide nonstationary structural response data. This paper proposes a nonstationarity assessment method based on energy distribution in the time-frequency domain. The proposed method reveals the nonstationarity level corresponding to the appropriate modal identification algorithm or flutter boundary prediction (FBP) method. Several classic flutter criteria are utilized to build a hypersonic aircraft FBP framework. Numerical simulation and experimental applications demonstrate the effectiveness and feasibility of the proposed method, which facilitates accurate flutter predictions for the subcritical turbulence response during hypersonic flutter flight.

A novel approach for flutter prediction of pitch–plunge airfoils using an efficient one-shot method

In this work, the one-shot method previously developed for the solution of limit cycle oscillation problems is extended to predict flutter boundaries of aeroelastic systems. In essence, the one-shot method determines the aeroelastic response of wings and airfoils in a tightly-coupled fashion where both aerodynamic and structural dynamic problems are solved simultaneously using harmonic balance. This approach is superior to the frequency-based techniques previously reported in the literature such that it eliminates the need to sweep over a range of frequencies to determine flutter conditions. For each Mach number of interest, the values of flutter frequency and flutter velocity are determined as part of a single aeroelastic run. A method for identifying appropriate initial conditions is also presented. It is shown that the flutter onset point for given flow conditions can be accurately identified by prescribing a very small pitch amplitude treating flutter prediction as a response problem instead of the classical stability problem. Using this technique, three two-degree-of-freedom aeroelastic models, including a flat plate, the NACA 64A010 airfoil and the supercritical NLR 7301 airfoil, are studied under different flow conditions ranging from low-speed, inviscid flow to transonic, viscous, turbulent flow. The results are verified against reference results from the literature. In addition, two other established flutter methods are implemented in this work for verification purposes, and the efficiency and robustness of the one-shot method are investigated.

Multioutput Autoregressive Aeroelastic System Identification and Flutter Prediction

The paper presents a methodology for reduced-order modeling of aeroelastic systems identification and flutter prediction. The aeroelastic system is modeled as a multioutput autoregressive process, and the model parameters are identified based on aeroelastic responses simulated in a computational fluid dynamics (CFD) code. The aeroelastic system is identified at a few subcritical (preflutter) dynamic pressure values. Flutter onset is determined from a stability parameter that is computed for the two dominant aeroelastic modes. The methodology is demonstrated on three test cases: a linear two-dimensional airfoil, transonic two-dimensional wing with reference to a wind-tunnel test, and a generic transport aircraft model. The paper compares the multioutput autoregressive to the single-output autoregressive model and shows that the former is more straightforward to implement, is robust, and requires shorter identification data. Overall, the methodology is simple to implement because it only requires an aeroelastic simulation capability and basic processing. It is computationally efficient and is therefore suitable for CFD-based flutter prediction. Other than predicting the flutter onset dynamic pressure, the method can be used to determine whether the aeroelastic system is stable at a specific dynamic pressure value without resorting to a lengthy CFD aeroelastic simulation.

Aeroelastic Investigation of a Transonic Compressor Rotor with Multi-Row Effects

According to the modern turbomachinery design trend, blades are getting more and more flexible and loaded, and therefore prone to vibration issues due to forced response and flutter phenomena. For this reason, the flutter stability assessment has become a key aspect to avoid high cycle fatigue (HCF) blade failures. The aim of this paper is to numerically evaluate the influence of unsteady aerodynamic effects, due to upstream and downstream rows, on flutter predictions using an uncoupled method. Both CFD aeroelastic and modal analyses have been carried out for a one and half compressor stage in transonic conditions. Flutter results are reported for the classic single-row approach and then for the multi-row model which includes rotor/stator unsteady interactions: a good agreement with measured data is shown for both cases and also a no negligible impact of adjacent rows can be observed.

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.

Assessment of flutter prediction and trends in the design of large-scale wind turbine rotor blades

With the progression of novel design, material and manufacturing technologies, the wind energy industry has successfully produced larger and larger wind turbine rotor blades while driving down the levelized cost of energy (LCOE). Though the benefits of larger turbine blades are appealing, larger blades are prone to instabilities due to their long and slender nature, and one of the concerning aero-elastic instabilities of these blades is classical flutter. In this work we assess classical flutter prediction tools for predicting flutter speeds in the design of large blades. Flutter predictions are benchmarked against predictions of previous studies. Then, we turn to the main focus of the study, which is design to mitigate flutter. Trends in flutter speeds and flutter mode shapes are examined for a series of 100-meter blade designs. Then, a sensitivity study is performed to assess the impacts of blade design choices (e.g. materials choice and material placement) on flutter speed in a redesign study of a lightweight 100-meter blade with small flutter margin. A new design is developed to demonstrate the ability to increase the flutter speed while reducing blade mass through structural design.

Comparison of Comprehensive Analyses Predicting Whirl Flutter Stability of the Wing and Rotor Aeroelastic Test System

Whirl flutter stability is a critical limitation for tiltrotor aircraft. This paper investigates whirl flutter predictions for the Wing and Rotor Aeroelastic Test System (WRATS) using comprehensive analysis, focusing on the comparison of the whirl flutter stability predictions between Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics (CAMRAD) II and the Rotorcraft Comprehensive Analysis System (RCAS). The analytical models were created using a modular approach to systematically validate the modeling process of the WRATS tiltrotor. Comparison of nonrotating frequencies for blade, flexbeam, flexbeam and cuff, and blade with flexbeam and cuff shows excellent agreement between CAMRAD II and RCAS. The assembled model is then used to predict the whirl flutter stability boundary for various configurations with varying levels of fidelity. Results show near exact agreement between the two analyses for a rigid rotor and linear aerodynamics, and good to fair agreement when an elastic rotor is used. Predicted wing beam mode frequencies and damping values are also compared against the wind tunnel test data, and the frequencies are shown to be reasonably well-predicted. However, damping values, and thus stability boundaries, are not accurately predicted.

Identification of Volterra kernels for improved predictions of nonlinear aeroelastic vibration responses and flutter

Aeroelastic structural systems are intrinsically nonlinear and accurate predictions of dynamic responses of nonlinear aeroelastic systems have become of paramount importance since these directly affect the accuracy and reliability of subsequent stability analyses. Such nonlinear systems can be generally represented with Volterra series whose kernels have been found to be effective in their dynamic characterizations. This paper examines how first- and second-order Volterra kernels of nonlinear aeroelastic systems can be accurately identified and then incorporated into the theoretical models of aeroelastic analyses such as predictions of dynamic response and onset of aeroelastic flutter. A novel identification method based on correlation analysis to extract frequency components has been developed which can be applied to general nonlinear aeroelastic systems to obtain accurately the required Volterra transfer functions. The method is very accurate and extremely robust against measurement noise contaminations in both input and output signals, due to the correlation scheme which effectively filters uncorrelated signal components. Detailed aeroelastic behavior of a representative pitch-plunge airfoil dynamic model with nonlinear pitch stiffness has been examined. Its Volterra transfer functions are then identified which are found to be close to their exact analytical counterparts, though interaction between kernels becomes apparent as input level increases. Once inverse Fourier transformed, these identified Volterra kernels are then included in the modeling of the dynamics of aeroelastic systems for vibration response and flutter. Extensive numerical simulation results have demonstrated that the proposed method is very accurate and resilient to measurement errors when applied to the identification of second-order Volterra kernels, and the improvement in predictions of vibration response and flutter become significant when the contributions of these second-order Volterra kernels are included in the overall aeroelastic system dynamics. The identification and subsequent inclusion of second-order Volterra kernels into system dynamics model offer improved design capabilities of nonlinear aeroelastic structural systems.

Prediction of Flutter Boundary Using Flutter Margin for The Discrete-Time System

Flutter testing in a wind tunnel is generally conducted at subcritical speeds to avoid damages. Hence, The flutter speed has to be predicted from the behavior some of its stability criteria estimated against the dynamic pressure or flight speed. Therefore, it is quite important for a reliable flutter prediction method to estimates flutter boundary. This paper summarizes the flutter testing of a wing cantilever model in a wind tunnel. The model has two degree of freedom; they are bending and torsion modes. The flutter test was conducted in a subsonic wind tunnel. The dynamic data responses was measured by two accelerometers that were mounted on leading edge and center of wing tip. The measurement was repeated while the wind speed increased. The dynamic responses were used to determine the parameter flutter margin for the discrete-time system. The flutter boundary of the model was estimated using extrapolation of the parameter flutter margin against the dynamic pressure. The parameter flutter margin for the discrete-time system has a better performance for flutter prediction than the modal parameters. A model with two degree freedom and experiencing classical flutter, the parameter flutter margin for the discrete-time system gives a satisfying result in prediction of flutter boundary on subsonic wind tunnel test.

Dynamic Stiffness Transfer Function of an Electromechanical Actuator Using System Identification

In the aeroelastic analysis of flight vehicles with electromechanical actuators (EMAs), an accurate prediction of flutter requires dynamic stiffness characteristics of the EMA. The dynamic stiffness transfer function of the EMA with brushless direct current (BLDC) motor can be obtained by conducting complicated mathematical calculations of control algorithms and mechanical/electrical nonlinearities using linearization techniques. Thus, system identification approaches using experimental data, as an alternative, have considerable advantages. However, the test setup for system identification is expensive and complex, and experimental procedures for data collection are time-consuming tasks. To obtain the dynamic stiffness transfer function, this paper proposes a linear system identification method that uses information obtained from a reliable dynamic stiffness model with a control algorithm and nonlinearities. The results of this study show that the system identification procedure is compact, and the transfer function is able to describe the dynamic stiffness characteristics of the EMA. In addition, to verify the validity of the system identification method, the simulation results of the dynamic stiffness transfer function and the dynamic stiffness model were compared with the experimental data for various external loads.

CFD prediction of flutter of turbine blades and comparison with an experimental test case

Last stage blades are a key element of steam turbines and in many ways determine the turbine configuration alongside with the overall turbine performance. The total efficiency of the low pressure turbine section can be increased by extending the last stage blades. The design process of such long blades involves a flutter analysis using CFD tools which have to be validated by measurements in test facilities under various operating conditions. Experimental data obtained from a subsonic wind tunnel with an oscillating turbine blade cascade, which is available at the Department of Power System Engineering at the University of West Bohemia, was compared with simulations in ANSYS CFX currently used in the Doosan Škoda Power. The paper provides a brief summary of experimental rig description, CFD tool setup and the results for the case of a travelling wave mode with the pure torsion motion of amplitude of 0.5°, Ma = 0.2, reduced frequency of 0.38 and angle of attack +5°.

Multiobjective optimization of an aircraft wing design with respect to structural and aeroelastic characteristics using neural network metamodel

The multidisciplinary design optimization (MDO) is an important concept that focuses on bringing together disciplines involved with machine design. It is possible to use MDO in any stage of an aircraft design, that is in the conceptual, preliminary, or detailed design, as long as the numerical models are fitted to each of these stages. This work describes the development of a multidisciplinary design optimization applied to flexible aircraft wings, with respect to structural and aeroelastic characteristics. As tools for the aircraft designer, the numerical models must be fairly accurate and fast. Therefore, metamodels for the critical flutter speed prediction of aircraft wings were considered, thereby reducing significantly the computational cost of the optimization. For this purpose, artificial neural networks (NN) metamodeling is evaluated, based on their inherent properties in dealing with complex mappings. The NN metamodel is prepared using an aeroelastic code based on finite-element model coupled with linear potential aerodynamics. Results of the metamodel performance are presented, from where one can note that the NN is well suited for flutter prediction. Multiobjective optimization (MOO) using the genetic algorithm (GA) based on non-dominance approach is considered. The objectives were the maximization of critical flutter speed and minimization of structural mass. One case study is presented to evaluate the performance of the MOO, revealing that overall optimization process actually achieves the search for the Pareto frontier.

Physics-Based Low-Order Model for Transonic Flutter Prediction

This paper presents a physical low-order model for two-dimensional unsteady transonic airfoil flow, based on small unsteady disturbances about a known steady flow solution. This is in contrast to traditional small-disturbance theory, which assumes small disturbances about the freestream. The states of the low-order model are the flowfield’s lowest moments of vorticity and volume-source density perturbations, and their evolution equation coefficients are calibrated using off-line unsteady computational fluid dynamics simulations through dynamic mode decomposition. The resulting low-order unsteady flow model is coupled to a typical-section structural model, thus enabling prediction of transonic flutter onset for wings with moderate to high aspect ratios. The method is fast enough to permit incorporation of transonic flutter constraints in conceptual aircraft design calculations. The accuracy of this low-order model is demonstrated for forced pitching and heaving simulations of an airfoil in compressible flow. Finally, the model is used to describe the influence of compressibility on the flutter boundary, and its accuracy is demonstrated for the Isogai Case A classical flutter test case.

Analyses for the Second Aeroelastic Prediction Workshop Using the EZNSS Code

The paper presents analyses that were performed with the EZNSS flow solver for the second Aeroelastic Prediction Workshop. The reference test cases for the Aeroelastic Prediction Workshop are based on two wind-tunnel experiments of the Benchmark Supercritical Wing, including a flutter test and forced excitation tests. Three cases are addressed at different transonic flow conditions: two cases at lower Mach numbers of 0.7 and 0.74 and 3 and 0 deg angles of attack, respectively; and one more physically complex case at Mach 0.85 and a 5 deg angle of attack. The cases are analyzed with the EZNSS code, using several computational setups and turbulence models. The simulations are able to predict relatively accurately the flutter response and the response to prescribed motion at the lower Mach number. The higher-Mach-number case, which involves a strong shock, separated flow behind the shock, and some flow unsteadiness, is more challenging. In the static analysis, different turbulence models yield different upper-surface shock positions, and none of the models are able to capture accurately the pressure recovery behind the shock. However, the unsteady aerodynamic response to prescribed pitch motion is simulated with good correlation to the wind-tunnel data. The paper also presents flutter predictions based on unsteady aerodynamic reduced-order modeling, thus validating and assessing the efficiency of the reduced-order modeling and the flutter prediction methodology.

Flutter Analysis of Propfan–Open Rotors

This work aims at showing the importance of flutter predictions in the preliminary design of propfan–open rotors. Both single rotating propellers and contrarotating open rotors are investigated. The related structural subsystems are modeled through finite element analyses; the aerodynamic subsystems exploit a finite volume, full potential formulation suitable for unsteady transonic flows. An ad hoc technique is developed for simulating the flowfield around a contrarotating open rotor configuration. The effectiveness of the proposed aeroelastic analysis is successfully assessed for single propellers through comparisons with reference numerical and experimental data available in the literature, as well as against Euler flow-based solutions. The results for contrarotating open rotors cannot be validated because of the lack of corresponding open-literature data.

Transonic Panel Flutter Predictions Using a Linearized Stability Formulation

A methodology is presented for prediction of dynamic instabilities arising from fluid–structure coupling. The inviscid compressible Euler equations are linearized about a steady-state solution and converted to the frequency domain for evaluation of the unsteady generalized aerodynamic forces used in the flutter solution procedure. The coupled fluid–structure interaction problem is formulated as a linearized stability eigenvalue problem. Using Schur complement factorization, an assumption of harmonic frequency response, and projection onto the structural modal basis, the stability equations are rewritten in a form well known as the flutter solution method. The scheme is used to study the flutter instability boundary of simply supported semi-infinite and square panels in the transonic and low supersonic region for mass ratio 0.1. The critical instability at subsonic Mach numbers is divergence (zero frequency), whereas oscillatory unstable modes are found for all Mach numbers greater than 1.0. At low supersonic Mach numbers ( for semi-infinite panel and for square panel), multiple high-frequency flutter modes become critical in a very narrow range of dynamic pressures. For higher Mach numbers, the classic supersonic flutter mode is recovered for both panels.