Airfoil Flutter Research Articles

Active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning

This paper presents a novel framework for the active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning (DRL). The research, conducted in a wide range of Mach numbers and flutter velocities, involves an elastically mounted airfoil with two degrees of freedom of pitching and plunging oscillations, subjected to transonic flow conditions at varying Mach numbers. Synthetic jets with zero-mass flux are strategically placed on the airfoil's upper and lower surfaces. This fluid–structure interaction (FSI) problem is treated as the learning environment and is addressed by using the arbitrary Lagrangian–Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with a structural solver on dynamic meshes. DRL strategies with proximal policy optimization agents are introduced and trained, based on the velocities probed around the airfoil and the dynamic responses of the structure. The results demonstrate that the pitching and plunging motions of the airfoil in the limited cycle oscillation (LCO) can be effectively alleviated across an extended range of Mach numbers and critical flutter velocities beyond the initial training conditions for control onset. Furthermore, the aerodynamic performance of the airfoil is also enhanced, with an increase in lift coefficient and a reduction in drag coefficient. Even in previously unseen environments with higher flutter velocities, the present strategy is achievable satisfactory control results, including an extended flutter boundary and a reduction in the transonic dip phenomenon. This work underscores the potential of DRL in addressing complex flow control challenges and highlights its potential to expedite the application of DRL in transonic flutter control for aeronautical applications.

Random flutter analysis of a novel binary airfoil with fractional order viscoelastic constitutive relationship

The fractional order model emerges naturally when the integer order model fails to meet practical requirements and finds extensive applications in engineering practice. However, there is still limited research on the random flutter of fractional order viscoelastic binary airfoils. This study aims to explore the random flutter of such airfoils under the influence of Gaussian white noise excitation by utilizing the pth moment Lyapunov exponent. Firstly, a two-degree-of-freedom fractional order stochastic dynamic equation is established for the viscoelastic binary airfoil through the introduction of fractional order damping. The singular perturbation method is then employed to derive the pth moment Lyapunov exponent of the system. An approximate analytical solution of the pth moment Lyapunov exponent is obtained through Fourier series expansion, which exhibits good agreement with numerical results obtained from Monte Carlo simulations. Subsequently, a comprehensive analysis is conducted to examine the impacts of fractional order, airflow velocity, noise intensity, and key structural parameters on the stochastic flutter of the fractional order viscoelastic binary airfoil. The findings indicate that compared with the typical binary airfoil model, the flutter speed of the fractional-order viscoelastic binary airfoil is significantly increased, the stability of the system is highly sensitive to the natural frequency of the system, and the fractional-order factor has a positive effect on the stochastic stability of the binary airfoil before the critical value. The above research results can guide the design optimization of the fractional-order viscoelastic airfoil.

Research of biomimetic corrugation on the blade flutter suppression in large-scale wind turbine systems

Aiming at the blade flutter of large horizontal-axis wind turbines, a method by utilizing biomimetic corrugation to suppress blade flutter is first proposed. By extracting the dragonfly wing corrugation, the biomimetic corrugation airfoil is constructed, finding that mapping corrugation to the airfoil pressure side has better aerodynamic performance. The influence of corrugation type, amplitude λ, and intensity on airfoil flutter is analyzed using orthogonal experiment, which determines that the λ has the greatest influence on airfoil flutter. Based on the fluctuation range of the moment coefficient ΔC m, the optimal airfoil flutter suppression effect is obtained when the type is III, λ= 0.6, and intensity is denser (n = 13). The effective corrugation layout area in the chord direction is determined to be the leading edge, and the ΔC m of corrugation airfoil is reduced by 7.405%, compared to the original airfoil. The application of this corrugation to NREL 15 MW wind turbine 3D blades is studied, and the influence of corrugation layout length in the blade span direction on the suppressive effect is analyzed by fluid-structure interaction. It is found that when the layout length is 0.85 R, the safety margin S f reaches a maximum value of 0.3431 Hz, which is increased 2.940%. The results show that the biomimetic corrugated structure proposed in this paper can not only improve the aerodynamic performance by changing the local flow field on the surface of the blade, but also increase the structural stiffness of the blade itself, and achieve the effect of flutter suppression.

Sinusoidally Pitching Foils in Transonic Flow: Insights into Flutter from Time Accurate Simulations

The impact of shock formation and vortex dynamics on airfoil flutter in the transonic regime is investigated through a series of two-dimensional time-accurate simulations of a sinusoidally pitching airfoil at a Reynolds number of 10,000. To gain insight into transonic flutter in the fully nonlinear regime, an energy-based approach that employs prescribed kinematics is utilized. Flutter stability boundaries are identified as a function of the Mach number and the reduced velocity, the latter of which is a surrogate for structural stiffness or flight speed. The results show a subcritical instability near Mach numbers of M∞=0.7 for a range of oscillation frequencies. Additionally, three shock-induced mechanisms are identified that influence the transfer of energy from the flow to the airfoil. The primary mechanism is flow separation triggered by the generation of a lambda shock. The influence of the lambda-shock dynamics on airfoil flow separation is determined for different Mach numbers, providing insight into the well-known “transonic dip” observed in flutter boundaries.

Numerical Investigation of Double Transonic Dip Behaviors in Supercritical Airfoil Flutter

This numerical study examines the behavior of the double transonic dip with a supercritical airfoil. A two-dimensional model of a wing section with two degrees of freedom was used for the investigation. The flowfield was modeled by solving the unsteady Reynolds-averaged compressible Navier–Stokes equations using the Spalart–Allmaras turbulence model, and the equations of motion were solved to determine the structural dynamics. The present model successfully captured the behavior of the double transonic dip on the flutter boundary of the supercritical airfoil, which contrasts with the well-known behavior of the single transonic dip exhibited by conventional symmetric airfoils. Although the mechanism of the first dip at a lower Mach number corresponded to that of the well-known conventional transonic dip, the second dip at a higher Mach number was uniquely observed for the supercritical airfoil. The analysis established that, for the supercritical airfoil, the motion of the shock wave over the upper surface was significantly affected by the behavior of the boundary layer around the highly cambered aft region of the lower surface during flutter. The behavior of the boundary layer involving the separation and reattachment over the lower surface caused the unusual shock wave motion over the upper surface under the Mach number condition at the bottom of the second dip. This motion exerted negative damping forces on the motion of the airfoil, thereby becoming the primary contributor to generating the second dip experienced by the supercritical airfoil.

Flutter suppression of an airfoil using a nonlinear energy sink combined with a piezoelectric energy harvester

We propose an absorber combined with a nonlinear energy sink and piezoelectric energy harvester (NES-PEH) for suppressing the flutter of a two-degree-of-freedom (2-DOF) airfoil. The NES-PEH is a cascade device comprising of a magnetic nonlinear energy sink (NES) and a tuned piezoelectric beam for broadening the vibration absorption frequency band. It is installed inside a 2-DOF airfoil, supported by four spring cantilever beams and a spring steel wire, for suppressing the flutter response and harvesting mechanical energy. A flutter model of the airfoil connected to the NES-PEH is established using unsteady aerodynamic theory. The influence of the dimensionless parameters of the NES-PEH on the flutter response and output voltage is explored. Furthermore, experiments are designed and tested for verifying the effectiveness of airfoil flutter suppression by the NES-PEH. The results indicate a significant influence of the installation position of the NES-PEH on the flutter response. The NES-PEH installed behind an elastic axis can increase the flutter speed by 20.4%, whereas that installed in front of the elastic axis can effectively suppress the pitch amplitude of the limit cycle oscillation (LCO) by 24.2%. Moreover, at d = −35 mm, the NES-PEH exhibits the best performance compared with the nonlinear energy sink and its fixed counterpart, suppresses flutter and the LCO, and outputs 10 μW power. Overall, this study presents a novel method for suppressing flutter and harvesting energy simultaneously.

Arbitrary Lagrangian-Eulerian-type conserved discrete unified gas kinetic scheme for the simulations of transonic continuum and rarefied gas flows with moving boundaries

In this paper, an arbitrary Lagrangian-Eulerian (ALE) framework is incorporated into the conserved discrete unified gas-kinetic scheme (CDUGKS) to solve the transonic continuum and rarefied gas flows with moving boundary. This is a continuation of our earlier work [Y. Wang et al., Phys. Rev. E, 100(6), 063310 (2019)]. Compared to the original low-speed ALE-DUGKS, in which only the governing equation of the distribution function is solved, the mesh motion velocity is introduced in the proposed ALE-CDUGKS for updating both the distribution function and the conservative flow variables. For a flow in the continuum regime, the potential energy double-distribution-functions framework and the circle equilibrium distribution function model are incorporated for inviscid and viscous flows. In the rarefied flow regime, the technique of unstructured velocity-space mesh is introduced to decrease the total number of discrete particle-velocity points and reduce the computational load. In addition, a loosely-coupled algorithm for simulating the fluid-structure interaction problem (airfoil flutter) is also presented. As a result, under this unified framework based on the distribution function, the numerical simulations have relatively high computational efficiency for flows in both continuum and rarefied regimes. A series of flows around a stationary or moving airfoil in the continuum regime is simulated, and a plunging airfoil in rarefied gas flow is also studied. The consistent and good results obtained from the above test cases demonstrate the capability of the proposed ALE-CDUGKS for solving the compressible moving boundary problems with the rarefied gas effect.

Simple adaptive V-stack piezoelectric based airfoil flutter suppression system

The suppression of aeroelastic vibrations due to flutter using a trailing edge flap is analyzed to increase the speed operability range of wings. The aeroelastic model of a 3DOF airfoil in incompressible flow is presented and an augmented state-space representation is used for the time domain analysis. A finite element model of a V-stack piezoelectric actuator, used to move the trailing edge flap, is introduced to model the actuator dynamics. The use of the simple adaptive controller is investigated to realize an adaptive flutter suppression system. A parallel feedforward compensator is tuned to make the plant almost strictly passive and a metaheuristic algorithm is used to determine the invariant parameters. Numerical simulations are carried out to verify the performance of the simple adaptive flutter suppression system in presence of speed variations and disturbances. Numerical results proved that the SAC flutter suppression system improves the closed loop system flutter boundary with respect to a gain scheduled PID controller.

Flutter instability and active aeroelastic control with time delay for a two-dimensional airfoil

This paper studies the stability of a two-dimensional controlled airfoil system with time delay. First of all, a hybrid approach based on the frequency sweep test and the eigenvalue problem approximation using the Taylor series expansion of the delayed term is proposed to predict the critical time delay as well as the angular frequency of flutter instability. The efficiency of the proposed approach is illustrated by numerical examples for the prediction of self-sustaining vibrations of a phenomenological airfoil model with two degrees of freedom. One point of interest is to bring an understanding of the physical phenomena of the dynamic behavior involved in the appearance of flutter for the controlled airfoil system with time delay. Numerical results indicate that although one active controller is effective in suppressing airfoil flutter in a controlled system without time delay, control failure may happen depending on the time delay in control design. Secondly not only the effectiveness but also some drawbacks of two proposed controllers, namely the linear quadratic regulator state-feedback controller and the pole placement approach, are discussed through numerical simulations.

Influence of Bistable Plunge Stiffness on Nonlinear Airfoil Flutter

Abstract Aeroelastic systems have nonlinearities that provide a wide variety of complex dynamic behaviors. Nonlinear effects can be avoided in practical applications, as in instability suppression or desired, for instance, in the energy harvesting design. In the technical literature, there are surveys on nonlinear aeroelastic systems and the different manners they manifest. More recently, the bistable spring effect has been studied as an acceptable nonlinear behavior applied to mechanical vibration problems. The application of the bistable spring effect to aeroelastic problems is still not explored thoroughly. This paper contributes to analyzing the nonlinear dynamics of a typical airfoil section mounted on bistable spring support at plunging motion. The equations of motion are based on the typical aeroelastic section model with three degrees-of-freedom. Moreover, a hardening nonlinearity in pitch is also considered. A preliminary analysis of the bistable spring geometry's influence in its restoring force and the elastic potential energy is performed. The response of the system is investigated for a set of geometrical configurations. It is possible to identify post-flutter motion regions, the so-called intrawell and interwell. Results reveal that the transition between intrawell to interwell regions occurs smoothly, depending on the initial conditions. The bistable effect on the aeroelastic system can be advantageous in energy extraction problems due to the jump in oscillation amplitudes. Furthermore, the hardening effect in pitching motion reduces the limit cycle oscillation (LCO) amplitudes and also delays the occurrence of the snap-through.

Beating phenomenon in frequency lock-in 2DOF stall flutter

A particular behaviour is observed in the pitch-heave stall flutter of a NACA0012 airfoil at transitional chord-based Reynolds numbers during lock-in. When the air speeds is such that the airfoil oscillates at the pitch structural natural frequency, and the structural natural frequencies of the two motions are close and their ratio ω̄ (= fh∕fθ) is smaller than 1, the system exhibits a beating phenomenon in both pitching and heaving motions. The modulated amplitude of the two motions presents a phase shift allowing a feedback energy transfer alternatively from pitch to heave and from heave to pitch. Through this energy exchange, the limit cycle oscillation (LCO) is maintained with two frequencies. This phenomenon fades when the ratio ω̄ become greater than one.

Controlling the Chaotic Motions of an Airfoil with a Nonlinear Stiffness Using Closed-Loop Harmonic Parametric Excitation

The purpose of this research is to conduct a preliminary investigation into the possibility of suppressing the flutter and post-flutter (chaotic) responses of a two-dimensional self-excited airfoil with a cubic nonlinear stiffness (in torsion) and linear viscous damping via closed-loop harmonic parametric excitation. It was found that the initial configuration of the proposed control scheme caused the torsional/pitch dynamics to act as a nonlinear energy sink; as a result, it was identified that the mechanisms of vibration suppression are the resonance capture cascade and the short duration or isolated resonance capture. It is the isolated resonance capture that is responsible for the second-order-like damping and full vibration suppression of the aeroelastic system. The unforced and closed-loop system was subjected to random excitation to simulate aerodynamic turbulence. It was found that the random excitation suppresses the phase-coherent chaotic response, and the closed-loop system is susceptible to random excitation.

Aeroelastic Flutter Prediction Using Multifidelity Modeling of the Generalized Aerodynamic Influence Coefficients

This work proposes a multifidelity modeling approach for predicting aeroelastic flutter of airfoils and wings. Using aerodynamic models based on the doublet-lattice method and time-accurate Euler equations, cokriging-based surrogates of the generalized aerodynamic influence coefficients are generated as functions of Mach number and reduced frequency. The surrogate-based matrix terms are then used in the method to determine flow conditions at flutter onset. To demonstrate the multifidelity process, a widely used pitching and plunging airfoil case is considered. Verification of the approach is done by comparing with results from a mode-based time-domain aeroelastic solver, as well as data from the literature. The approach draws inspiration from Timme et al., but focuses more on widely used industry tools (namely, the method, panel-based aerodynamics, and time-domain computational fluid dynamics). The benefit of using multiple aerodynamic fidelities, rather than high-fidelity kriging models, is also quantified by examining a flutter speed error metric as the number of high-fidelity samples is varied.

Bifurcation analysis in the system with the existence of two stable limit cycles and a stable steady state

Van der Pol–Duffing oscillator, which can be used a model for many dynamical system, has been widely concerned. However, most of the systems by scholars are either stable steady states or limit cycles. Here, the self-sustained oscillator with the coexistence of steady state and limit cycles, which is famous for describing the flutter of airfoils with large span ratio in low-speed wind tunnels, is treated in this paper. Using the energy balance method, the deterministic bifurcation of the tristable system with time-delay feedback is investigated. The presence of time-delay feedback expands the bifurcation range of the parameters, making the bifurcation phenomenon more abundant. In addition, according to the stationary probability density function obtained by the stochastic averaging method, stochastic bifurcation of the system with time-delay feedback and noise is explored theoretically. The numerical results confirm the correctness of the theoretical analysis. Transition between the unimodal structure, the bimodal structure and the trimodal structure is found. Many rich bifurcations are available by adjusting the time-delay and noise intensity, which may be conductive to achieve the desired phenomenon in the real-world application.

Flow analysis of the deep dynamic stall of wind turbine airfoil with single-row and double-row passive vortex generators

This paper aims to understand the influence of vortex generators (VGs) on deep dynamic stall of the NREL S809 airfoil. The fully-resolved URANS method is used to predict aerodynamic responses of the airfoil with both single-row and double-row VGs. On one hand, single-row and double-row VGs are found to attenuate the force fluctuation and postpone the extension of flow separation when the airfoil pitches up. The onset of deep dynamic stall is therefore significantly delayed with the maximum lift coefficient increased beyond 40%. This indicates that VGs are effective in controlling deep dynamic-stall behavior. On the other hand, single-row and double-row VGs are found to make a great difference in aerodynamic responses when the airfoil pitches down. Single-row VGs undermine the torsional aeroelastic stability and have the potential risk of making the airfoil flutter. Double-row VGs can accelerate the flow reattachment effectively, and quickly restore the decreased aerodynamic force near the maximum angle of attack. These findings also imply that deep dynamic stall with VGs becomes highly complicated, because VGs can be fully submerged in separation vortices. In general, double-row VGs perform better than single-row VGs to control deep dynamic stall. This study is believed to assess the VG performance in controlling highly unsteady aerodynamic loads on wind turbines.

에어포일의 플러터 현상을 이용한 에너지 수확 장치의 타당성

플러터는 비행기 날개와 같은 구조물에서 풍하중에 의해 유도되는 공력 불안정 현상이다. 플러터 현상은 다리와 같은 거대한 구조물을 파괴할 만한 큰 진동을 유발할 수 있지만 플러터 현상을 이용하면 충분한 양의 전기 에너지를 얻는 것도 가능할 것이다. 본 연구에서는 낮은 풍속에서 풍향과 관계없이 플러터 현상을 발생시키는 에어포일 형상의 에너지 수확 장치를 제안하고 가능성을 확인한다. 제작된 에너지 수확 장치에서 플러터 발생을 확인하기 위해 에어포일의 받음각이 임계각보다 작게 제한하여 풍동실험을 진행하였다. 플러터 속도는 풍동 실험으로부터 장치의 감쇠 계수를 추출하여 계산한다. 그리고 에너지 수확 장치의 일률은 플러터 속도와 에어포일의 변위를 기반으로 예측한다.

Stochastic flutter of multi-stable non-linear airfoil in turbulent flow

Stochastic flutter of multi-stable non-linear airfoil in turbulent flow

Flutter Fault-Tolerant Control with Observer Considering Actuator Faults and Time Delay

To suppress airfoil flutter, a lot of control methods have been proposed, such as classical control methods and optimal control methods. However, these methods did not consider the influence of actuator faults. We designed a new finite-time H∞ adaptive fault-tolerant flutter controller by radial basis function neural network technology and adaptive fault-tolerant control methods, taking into account actuator faults, actuator saturation, modeling uncertainties and external disturbances. The theoretical section of this paper is about airfoil flutter dynamic modeling and the design of adaptive fault-tolerant controller. Lyapunov function and linear matrix inequality are employed to prove the stability of the proposed control method of this paper. The numeral simulation section further proves the effectiveness and robustness of the proposed control algorithm of this paper.

A Gain Scheduling Control of Incompressible Airfoil Flutter Tuned by the Population Decline Swarm Optimizer—$$P_{D}SO$$

The phenomenon of flutter is a self-excited aeroelastic vibration which can occur on flexible aerodynamic structures moving within a fluid domain, whereby the structure absorbs energy from the fluid; this phenomenon is related to variations in configuration with respect to the relative wind that the structure undergoes as a consequence of its oscillations. Based on the aeroelastic model of a three-degree-of-freedom airfoil, an adaptive controller for flutter suppression is designed and investigated in this work. A population decline swarm optimization $$P_{D}SO$$ is used to find the optimal parameters of the controller to set a gain scheduling approach to make the control adaptive in velocity. The integral of time absolute error is minimized to attribute a greater weight to the divergence error that can manifest far after the disturbing instant. Numerical results are reported to show how the gain scheduling control allows to obtain damped oscillation beyond the critical speed without destructive picks.

Active dynamic vibration absorber for flutter suppression

A novel flutter suppression technique is proposed using an active dynamic vibration absorber (ADVA). The ADVA is introduced by adding an active element to a classical mass-spring-damper system. This active element drives the mass by a controlling force using feedback signal from the response of the aeroelastic system. An aeroelastic mathematical model of a 2 degrees of freedom (DOFs) airfoil equipped with the proposed ADVA is established based on unsteady aerodynamics theory. The proposed ADVA is experimentally realized by a cantilever beam with a bonded Macro-fiber Composite (MFC) and a lumped mass. MFC nonlinearities are compensated by applying Prandtl-Ishlinskii approach to design a proportional integral (PI)-based hysteresis compensator controller. A test rig is designed, fabricated and the parameters of the physical airfoil model and the connected ADVA are identified. The feasibility of the ADVA for flutter suppression is assessed via a wind tunnel testing. The experimental results show that applying the closed-loop ADVA increases the airfoil flutter speed by 42.9%. Whereas the open-loop ADVA results in 26.6% improvement in the flutter speed. Moreover, if the airfoil experiences a high amplitude limit cycle oscillation (LCO), the ADVA efficiently suppresses up to 93.3% of its amplitude when turned to the closed-loop control.