Transonic Flutter Research Articles

Effects of Structural Damage and External Stores on Transonic Flutter Stability

In this study, the structural damage and external store effects on the transonic flutter stability of a fighter type aircraft are investigated. As the damage area, the control surface-supporting structure has been selected because it is expected to affect the flutter stability sensitively. The transonic small disturbance (TSD) method is used for the analysis of unsteady aerodynamics because it is much faster than other computational fluid dynamics (CFD) schemes and is reliable for considering the control surface motions. The flutter analysis results are also compared with the results using a linear flutter analysis program to demonstrate the reliability of the analysis. This research shows that the flutter stability in the transonic regime can be further reduced after external stores are installed. This study also shows that although there is no significant decrease of flutter stability due to structural damage in subsonic regime, the flutter stability can be seriously deteriorated in the transonic regime at a certain level of damage. The effects of structural damage on the flutter stability should be carefully examined during the development of aircraft especially transonic regime.

The complexity and mechanism of transonic aeroelastic problems

In high-speed flight, transonic aeroelasticity commonly exists, leading to various problems such as transonic flutter, buffeting and buzz. To solve these problems, a good understanding of the underlying physical mechanisms is critical. Unfortunately, the nonlinearity and unsteadiness of airflows complicate this process and consequently impede the development of aircraft design. Here using the numerical simulation and modeling of complex transonic flows, we developed a unified analytical method for aeroelastic stability and response problems. We then explored the mechanisms of three complex aeroelastic phenomena and unveiled their relationships. (1) Transonic buzz is in essence a single degree of freedom (SDOF) flutter caused by the coupling between the most unstable fluid mode and structural mode. SDOF flutter of this kind is possible only when the fluid exhibits sufficiently low damping; that is, the freestream flow is near the buffet boundary or in the low supersonic zone. Besides, the unstable frequency boundaries are determined by zero and pole of the open loop system. (2) The frequency lock-in phenomenon in the transonic buffeting flow is caused by the SDOF flutter in the unstably separated flow rather than resonance. In this process, the response undergoes a transition from the forced vibration to the self-excited flutter, which results in a deviation of the lock-in region from the resonance point. By contrast, the traditional uncoupled method misestimates the risk range and underestimates the amplitude of a vibration. (3) When the pitching degree of freedom is released, transonic buffet will be induced at a lower angle of attack, indicative of the drawbacks of predicting buffet onset by a rigid model. Actually, the elastic characteristic plays a key role in predicting buffet onset in aircraft design. Collectively, the large-amplitude structural vibration in the transonic flow is closely related to aeroelastic instability. The dynamic linear model can correctly predict the boundary of some complex dynamic phenomena. The complexity of transonic aeroelasticity mainly arises from the stability reduction of airflows. Different from classical aeroelastic problems, the new fluid mode is derived from the reduction of fluid stability. The coupling between such a fluid mode and structural mode often leads to complex phenomena in transonic flows.

Flutter Boundary Prediction of a Two Dimensional Airfoil in Transonic Flight Regime with the Preset Angles of Attack

Angle of attack has impact on transonic flow filed and aerodynamic force, but most of current researches on flutter use zero angle hypothesis, which has no consideration about angle of attack. Therefore, we use unsteady Reynold Averaged Navier-Stokes (RANS) equation and structural dynamic equation to establish the time domain aeroelastic analysis method. The solution in time domain is the fourth-order implicit Adams linear multi-step method which is based on prediction-correction method. The numerical simulations were used to analyze the transonic flutter boundary of Isogai Case A Model which was based on zero angle condition and nonzero angle respectively. The simulation results show that the reduced flutter speed decreases as the preset angle of attack decreases between 0.73 and 0.76, which shows a 12.5% decrease of the flutter speed at the farthest. Nonzero angle makes the transonic dip weaker and wider than fully turbulent flow. Changing in angle of attack of 6°, the flutter speed in the deepest position of transonic dip has increased by 124% compared to the flutter speed of 0°. Therefore, when flutter characters of airfoil is analyzed, the effects of the initial angle of attack must be taken into account in order to analyze flutter boundary correctly. In other words, increasing the angle of attack offers a way to control the system in terms of delaying flutter.

Rapid Transonic Flutter Analysis for Aircraft Conceptual Design Applications

This study presents a new approach for the rapid transonic flutter analysis of large-aspect-ratio wings via a combination of time-linearized two-dimensional unsteady indicial functions and a database of steady two-dimensional Reynolds-averaged Navier–Stokes simulations. The approach is limited to large-aspect-ratio wings that can be discretized into multiple, streamwise, independent strips; and the well-documented “strip theory” with sweep corrections is applicable. This formulation allows the extension of Leishman’s indicial functions (“Validation of Approximate Indicial Aerodynamic Functions for Two-Dimensional Subsonic Flow,” Journal of Aircraft, Vol. 25, No. 10, 1988, pp. 914–922) to three-dimensional wings but also restricts the present method to attached flows. However, when supported with two-dimensional steady Reynolds-averaged Navier–Stokes simulations, the present method predicts flutter speeds that are within 10% of that predicted by two-dimensional time-accurate Reynolds-averaged Navier–Stokes simulations. Application of the proposed method for a large-aspect-ratio wing is validated by comparing the predicted flutter boundary against wind-tunnel experiments. More importantly, the current method predicts the transonic dip phenomena observed in the experiments but not predicted by NASTRAN analysis. This is achieved at several orders-of-magnitude lower computation time than high-fidelity time-accurate computational fluid dynamics simulations. The level of accuracy obtained at such an extremely low computation time makes the present approach very suitable for applications in conceptual design studies of large-aspect-ratio transonic vehicles.

Aeroelastic Optimization with an Economical Transonic Flutter Constraint Using Navier–Stokes Aerodynamics

Structural optimization with a flutter constraint for a vehicle designed to fly in the transonic regime is a particularly difficult task. In this speed range, the flutter boundary is very sensitive to aerodynamic nonlinearities, typically requiring high-fidelity Navier–Stokes simulations. However, the repeated application of unsteady computational fluid dynamics to guide an aeroelastic optimization process is very computationally expensive. This expense has motivated the development of methods that incorporate aspects of the aerodynamic nonlinearity, classical tools of flutter analysis, and more recent methods of optimization. Although it is possible to use doublet-lattice method aerodynamics, this paper focuses on the use of an unsteady high-fidelity aerodynamic reduced-order model combined with successive transformations that allows for an economical way of using high-fidelity aerodynamics in the optimization process. This approach is applied to the common research model wing structural design. The high-fidelity aerodynamics produces a heavier wing than that optimized with doublet-lattice aerodynamics. It is found that the optimized lower wing skin thickness distribution using high-fidelity aerodynamics differs significantly from that using doublet-lattice aerodynamics.

Investigation of viscosity influence on transonic flutter

Abstract The paper is devoted to computational study of transonic flutter when the viscosity can influence significantly on dynamic aeroelasticity characteristics of aircraft. The work has been done in the direction of development of methodology and software, which are used in ARGON (TsAGI) system for multidisciplinary analysis and optimization in airplane design. Considerable attention is paid to the validation of the proposed software. Experimental results of the NASA Common Research Model in the European Transonic Wind Tunnel (ETW) are used for comparison with computations. The results of flutter analysis are presented for the passenger middle range airplane with the high aspect ratio wing and the engine under the wing. Comparisons of aeroelasticity characteristics in transonic flow are carried out for cases of a set of Mach and Reynolds numbers. The computational results presented in the paper show the essential influence of transonic features on flutter characteristics.

Математическая модель оценки влияния аэродинамической компенсации поверхностей управления на уровень их колебаний при возникновении трансзвукового флаттера

Математическая модель оценки влияния аэродинамической компенсации поверхностей управления на уровень их колебаний при возникновении трансзвукового флаттера

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.

Passive control of transonic flutter with a nonlinear energy sink

Among different control approaches, the nonlinear energy sink has been proposed as an effective strategy for passive flutter control toward expanding the flight envelope of aircraft. We validate and introduce the capability for coupling the NES within OpenFOAM to simulate and evaluate its usability in controlling transonic flutter. Particular attention is paid to the extent to which variations in the parameters of the sink impact regions of complete and partial suppression. The results show that in the region of complete suppression the nonlinear energy sink may cause the wing to assume a new equilibrium position, in terms of mean value of the oscillations. In the region of partial suppression, the response is dependent on the initial conditions that may lead to multiple pitch and plunge frequencies or potentially a chaotic response.

Shock–boundary layer interaction and energetics in transonic flutter

We study the influence of shock and boundary layer interactions in transonic flutter of an aeroelastic system using a Reynolds-averaged Navier–Stokes (RANS) solver together with the Spalart–Allmaras turbulence model. We show that the transonic flutter boundary computed using a viscous flow solver can be divided into three distinct regimes: a low transonic Mach number range wherein viscosity mimics increasing airfoil thickness thereby mildly influencing the flutter boundary; an intermediate region of drastic change in the flutter boundary due to shock-induced separation; and a high transonic Mach number zone of no viscous effects when the shock moves close to the trailing edge. Inviscid transonic flutter simulations are a very good approximation of the aeroelastic system in predicting flutter in the first and third regions: that is when the shock is not strong enough to cause separation, and in regions where the shock-induced separated region is confined to a small region near the trailing edge of the airfoil. However, in the second interval of intermediate transonic Mach numbers, the power distribution on the airfoil surface is significantly influenced by shock-induced flow separation on the upper and lower surfaces leading to oscillations about a new equilibrium position. Though power contribution by viscous forces are three orders of magnitude less than the power due to pressure forces, these viscous effects manipulate the flow by influencing the strength and location of the shock such that the power contribution by pressure forces change significantly. Multiple flutter points that were part of the inviscid solution in this regime are now eliminated by viscous effects. Shock motion on the airfoil, shock reversal due to separation, and separation and reattachment of flow on the airfoil upper surface, also lead to multiple aerodynamic forcing frequencies. These flow features make the flutter boundary quantitatively sensitive to the turbulence model and numerical method adopted, but qualitatively they capture the essence of the physical phenomena.

Design of Thermally Stressed Panels Subject to Transonic Flutter Constraints

The objective of this study is to design a two-dimensional panel subject to transonic flutter constraints in the presence of an extreme thermal environment. The unsteady aerodynamic model is based on a high-order stabilized finite element formulation of the Euler equations. The linearized dynamic instability problem is converted into the flutter-stability problem, and an iterative procedure is used to identify the flutter velocity at a given design point. The design variables include the lengthwise thickness and density distributions, with the objective function as the minimization of structural mass. The first set of designs are obtained for an unstressed panel with flutter constraints at Mach 1.1 and Mach 2.0, and it is found that the optimal thickness distribution closely mimics the amplitude of the constraining flutter mode. The thermally stressed panel is designed for aeroelastic stability about the nonlinear static equilibrium. It is found that the optimum mass of the thermally stressed panels is lower than the optimum mass of the unstressed panels due to the additional stiffening from the transverse deformations.

Design of an Active Disturbance Rejection Control for Transonic Flutter Suppression

Conventional controls, such as an optimal control with a notch filter, are able to remove the flutter instability under subsonic flows but may need higher adaptability to make the controllers stable under transonic flows with oscillating shocks, especially for the wing model with parameter uncertainties. In this paper, an error-based control law designed via the active disturbance rejection control algorithm is proposed for the transonic flutter suppression of a wing model with parameter uncertainties and measurement noises taken into account. With the proposed control law, the observed output signal and its time derivative, the unmodeled dynamics, and the measurement noises are consistently estimated. The observed output signal and its time derivative are used to design a feedback control law for adjusting the output errors, whereas the observed unmodeled dynamics and the measurement noises are used to guarantee the adaptability and anti-interference of the proposed controller. To demonstrate the control performances, the wing of benchmark active control technology is studied for the transonic flutter suppression. The numerical results show that the present control law can effectively suppress the transonic flutter at a wide range of Mach numbers and has noticeable adaptability to the variation in stiffness parameters.

Coupled fluid structure analysis for wing 445.6 flutter using a fast dynamic mesh technology

ABSTRACTThe flow around wing 445.6 was modelled using Navier–Stokes equations and S-A model. The wing vibration and flow mesh deformation were computed using a fast dynamic mesh technology proposed by our own group. Wing 445.6 flutter was analysed through a strong coupling between the wing vibration and flow. The reduced flutter velocity was predicted and results are in good agreement with the experimental data. It is found that the subsonic flutter is mainly induced by the flow separation and the transonic and supersonic flutter are mainly caused by the oscillating shock wave and its induced flow separation. The positive aerodynamic work increases due to the oscillating shock wave when the subsonic flow becomes transonic reducing the flutter velocity. While the positive aerodynamic work induced by the oscillating shock wave decreases when the transonic flow becomes supersonic increasing the flutter velocity. That is why the transonic dip exists.

Nonlinear dynamics of an aeroelastic airfoil with free-play in transonic flow

Nonlinear dynamic behaviors of an aeroelastic airfoil with free-play in transonic air flow are studied. The aeroelastic response is obtained by using time-marching approach with computational fluid dynamics (CFD) and reduced order model (ROM) techniques. Several standardized tests of transonic flutter are presented to validate numerical approaches. It is found that in time-marching approach with CFD technique, the time-step size has a significant effect on the calculated aeroelastic response, especially for cases considering both structural and aerodynamic nonlinearities. The nonlinear dynamic behavior for the present model in transonic air flow is greatly different from that in subsonic regime where only simple harmonic oscillations are observed. Major features of the responses in transonic air flow at different flow speeds can be summarized as follows. The aeroelastic responses with the amplitude near the free-play are dominated by single degree of freedom flutter mechanism, and snap-though phenomenon can be observed when the air speed is low. The bifurcation diagram can be captured by using ROM technique, and it is observed that the route to chaos for the present model is via period-doubling, which is essentially caused by the free-play nonlinearity. When the flow speed approaches the linear flutter speed, the aeroelastic system vibrates with large amplitude, which is dominated by the aerodynamic nonlinearity. Effects of boundary layer and airfoil profile on the nonlinear responses of the aeroelastic system are also discussed.

Computational fluid dynamics-based transonic flutter suppression with control delay

This work investigates the effects of control input time delay on closed-loop transonic computational aeroelastic analysis. Control input time delays are becoming critical as the demand for high frequency control actions is increasing. The flow in transonic conditions exhibits strong nonlinearities which require accurate physical modeling techniques, in turn resulting in large dimensional systems that are computationally costly to solve. A unified framework is demonstrated for the robust and efficient generation of reduced order models. Once generated, the reduced order model is employed for the flutter boundary search, and excellent agreement with the large order coupled model is demonstrated. The aero-servo-elastic reduced order model is then exploited to design a feedback control law, which is implemented in the fully coupled computational fluid/structural dynamics solver. As expected, the controller effectiveness is found to degrade for increasing time delay, up to a critical value where the controller fails to suppress flutter. It is shown that a controller for a time-delay system may be designed using the same aero-servo-elastic reduced order model, incurring in no extra costs or complications. The new controller is found to achieve excellent flutter suppression characteristics. The aero-servo-elastic reduced order model may also be used to identify, for a given feedback controller, the critical value of control input time delay at which the closed-loop aero-servo-elastic system loses its stability. The test cases are for a two-dimensional pitch-plunge aerofoil section and the AGARD 445.6 wing modified with a trailing-edge control surface.

Transonic flutter analysis using a fully coupled density based solver for inviscid flow

This paper focuses on the coupling between the high fidelity aerodynamic model for the flow field and the modal analysis of a typical wing section to carry out flutter analysis. This coupled aeroelastic model is implemented in one of the most widely used open source CFD codes called OpenFOAM. The model is designed to calculate the structural displacement in the time domain based on the free vibration modes of the structure by constructing the numerical model directly from the modal analysis. Essentially a second order ordinary differential equation is solved for each mode as a function of the generalised coordinates. A density based solver using central difference scheme of Kurganov and Tadmor is used to model the flow field. Two main cases of transonic flow over NACA 64A010 are modelled for a forced pitching oscillation airfoil and a self-sustained aerofoil respectively. The self-sustained two degrees of freedom case is modelled for three different possibilities covering damped, neutral and divergent oscillations. Predicted results show very good agreement with the numerical and experimental data available in the literature.

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.

Nonlinear Aeroelastic Analysis of Control Surface with Freeplay Using Computational-Fluid-Dynamics-Based Reduced-Order Models

A computational-fluid-dynamics-based aeroelastic analysis method is proposed to simulate control-surface limit-cycle oscillation (LCO) induced by freeplay gap. The present method is based on the previously proposed aeroelastic reduced-order model (ROM), in which an unsteady aerodynamic state-space model is generated from aerodynamic responses to step excitation of individual mode using the eigensystem realization algorithm, and connected to a structural dynamic state-space model within the MATLAB/SIMULINK environment. The aeroelastic ROM is extended to treat structural nonlinearity due to the control-surface freeplay by generating an additional feedback line of generalized residual forces in the SIMULINK model. To reduce the problem size and the computation time, a fictitious-mass modal approach is used, which can afford the possible local change of stiffness. The present method is first validated for its capability to simulate aeroelastic responses of a regional-jet horizontal-tail (HT) model without freeplay, and shows good prediction of flutter characteristics measured in the transonic flutter wind-tunnel testing. The present method is then applied to the HT model with the elevator freeplay gaps. Although there are some differences between the computed and measured limit-cycle-oscillation ranges, the present method well predicts the nonlinear limit-cycle-oscillation behavior in its amplitude and frequency measured in the test, and shows promise toward accurate prediction of control-surface LCO due to its freeplay gap.

Influence of boundary layer transition on the flutter behavior of a supercritical airfoil

This paper presents a flutter analysis for the supercritical CAST 10-2 airfoil in a flow with free boundary layer transition based on CFD computations with the \(\gamma \)-\(\hbox {Re}_{\theta }\) transition model. The results are compared to fully turbulent results obtained with the SST \(k\)-\(\omega \) turbulence model. Unsteady RANS computations at \(\hbox {Re}_{\rm{c}} = 2 \times 10^{6}\) are used to determine the aerodynamic derivatives. These derivatives are required to identify the flutter boundary for a 2 degree-of-freedom model by a k method. The transonic flutter boundary decreases for a flow with free boundary layer transition compared to a fully turbulent flow in the vicinity of the transonic dip. However, the flutter boundary at subsonic Mach numbers is raised for a transitional flow. In addition, the transitional frequency response is discussed: an aerodynamic resonance in connection with an instability of the transition region is observed and the possibility of a 1 degree-of-freedom flutter for transitional flows is shown.

Hybrid Finite-Volume Reduced-Order Model Method for Nonlinear Aeroelastic Modeling

A fully coupled partitioned fluid–structure interaction technology is developed for transonic aeroelastic structures undergoing nonlinear displacements. The Euler equations, written in an arbitrary Lagrangian–Eulerian coordinate frame, describe the fluid domain, whereas the structure is represented by a quadratic modal reduced-order model. A Runge–Kutta dual time-stepping method is employed for the fluid solver, where three upwind schemes are considered, viz., Advection Upwind Splitting Method plus-up, Harten-Lax-van Leer with Contact, and Roe schemes. The Harten-Lax-van Leer with Contact implementation is found to offer a superior balance between efficiency and robustness. The developed fluid–structure interaction technology is applied to modeling transonic flutter, and the quadratic reduced-order model is demonstrated to offer dramatic improvements in accuracy over the more conventional linear method.