Single Degree Of Freedom Flutter Research Articles

Investigation of Stall Flutter Based on Peters-ONERA Aerodynamic Model

The Peters model is used to simulate the linear aerodynamic force and ONERA stall model is used to simulate the nonlinear aerodynamic force. The state-space equation of the aeroelastic system is established by coupling the structural equation. In order to solve problems, Euler predictor corrector method is used in the time domain and eigenvalue analysis method is used in the frequency domain. The case of dynamic stall is simulated based on Peters-ONERA model and the results imply that the validity of the aerodynamic model. The effect of under relaxation iteration on the stability of static aeroelastic solution is studied. It is found that under relaxation iteration can improve the static aeroelastic solution stability. Then based on frequency and time domain methods, flutter critical characteristic and bifurcation phenomenon are studied. It is found that:(1) Under large angle of attack, the coupling between nonlinear aerodynamic modal and structure modal could induce the instability of the structure modal and single degree of freedom flutter. (2) Under different angles of attack, bifurcation characteristic of aeroelastic system is far different. (3) The sensitivity to the disturbance of the system is different in different ranges. When the disturbance increases, the aeroelastic system will change from stable state to limit cycle oscillation.

Reduction of transonic buffet onset for a wing with activated elasticity

Transonic buffet, a kind of aerodynamic instability at a certain combination of Mach number and angle of attack, limits the aircraft flight envelope and fatigue life. The traditional method on transonic buffet onset prediction has an obvious limitation for an elastic wing, which ignores the feedback of oscillatory structure to the fluid. In this paper, the reduction of transonic buffet onset is observed when the feedback is considered for a wing with an activated pitching degree of freedom; that is, buffet will be provoked at some special structural parameters in pre-buffet flow conditions. This phenomenon is not caused by the static deformation of the structure but the coupling effect between fluid and structure. Besides, the dynamical characteristic and instability mechanism are significantly different from the SDOF (single degree of freedom) flutter [18]. The SDOF flutter is caused by the instability of the structural mode, and the flutter frequency locks into the structural frequency, while the present instability is governed by the fluid mode and the coupling frequency follows the buffet frequency in post-buffet conditions.

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.

Transonic limit cycle oscillation behavior of an aeroelastic airfoil with free-play

The limit cycle oscillation (LCO) behaviors of an aeroelastic airfoil with free-play for different Mach numbers are studied. Euler equations are adopted to obtain the unsteady aerodynamic forces. Aerodynamic and structural describing functions are employed to deal with aerodynamic and structural nonlinearities, respectively. Then the flutter speed and flutter frequency are obtained by V-g method. The LCO solutions for the aeroelastic airfoil obtained by using dynamically linear aerodynamics agree well with those obtained directly by using nonlinear aerodynamics. Subsequently, the dynamically linear aerodynamics is assumed, and results show that the LCOs behave variously in different Mach number ranges. A subcritical bifurcation, consisting of both stable and unstable branches, is firstly observed in subsonic and high subsonic regime. Then in a narrow Mach number range, the unstable LCOs with small amplitudes turn to be stable ones dominated by the single degree of freedom flutter. Meanwhile, these LCOs can persist down to very low flutter speeds. When the Mach number is increased further, the stable branch turns back to be unstable. To address the reason of the stability variation for different Mach numbers at small amplitude LCOs, we find that the Mach number freeze phenomenon provides a physics-based explanation and the phase reversal of the aerodynamic forces will trigger the single degree of freedom flutter in the narrow Mach number range between the low and high Mach numbers of the chimney region. The high Mach number can be predicted by the freeze Mach number, and the low one can be estimated by the Mach number at which the aerodynamic center of the airfoil lies near its elastic axis. Influence of angle of attack and viscous effects on the LCO behavior is also discussed.

Panel flutter prediction in two dimensional flow with enhanced piston theory

Piston theory may be used in the high Mach number supersonic flow region and/or in very high frequency subsonic or supersonic flow. In this flow model, the pressure at a point on the fluid-solid interface only depends on the downwash at the same point. However the classical piston theory may not be sufficient for some phenomena in aeroelasticity and aeroacoustics (far field prediction). Dowell and Bliss have created an extension of piston theory that allows for higher order effects that take into account the effect the distribution of downwash on pressure at any point. For simple harmonic motion, expansions in reduced frequency, inverse reduced frequency and/or inverse (square of) Mach number have all been created; The effects of higher order terms in these several expansion in creating an enhanced piston theory was illustrated for plunge and pitch motion of an airfoil (discrete system) by Ganji and Dowell. In the present paper, flutter prediction for a flexible panel in two –dimensional flow is investigated using enhanced piston theory. The goal of the present paper is to demonstrate that an enhance version of piston theory can analyze single degree of freedom flutter of a panel as compared to the classical piston theory and quasi-steady aerodynamic models which can only treat coupled mode flutter.

A new viewpoint on the mechanism of transonic single-degree-of-freedom flutter

Transonic single-degree-of-freedom (SDOF) flutter can be easily understood by the energy transferred from fluid to structure, but it can not explain why transonic SDOF flutter frequently takes place in special flow states and at the structure's natural frequencies. In this work, we develop a reduced-order model (ROM) for the pitching or plunging NACA 0012 airfoil in transonic pre-buffet flow. The instability of the SDOF system is also caused by the coupling of modes—one structural mode and one fluid mode, different from the classic flutter in potential flow caused by the coupling between two or more structural modes. By eigenvalue analysis, two prerequisites must be satisfied for the occurrence of transonic SDOF flutter: (a) the transonic flow is near the critical unstable state, where the fluid mode damping is small; (b) the ratio of the structure's natural frequency to the fluid characteristic frequency must be within a certain range. For a smaller mass ratio, flutter can be divided into two patterns. One is dominated by the instability of structural mode, and the flutter frequency locks onto the structure's natural frequency. The other is dominated by the instability of the fluid mode, and the flutter frequency follows the fluid characteristic frequency instead of the structure's natural frequency.

Numerical study on the correlation of transonic single-degree-of-freedom flutter and buffet

Transonic single-degree-of-freedom (SDOF) flutter and transonic buffet are the typical and complex aeroelastic phenomena in the transonic flow. In this study, transonic aeroelastic issues of an elastic airfoil are investigated using Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations. The airfoil is free to vibrate in SDOF of pitching. It is found that, the coupling system may be unstable and SDOF self-excited pitching oscillations occur in pre-buffet flow condition, where the free-stream angle of attack (AOA) is lower than the buffet onset of a stationary airfoil. In the theory of classical aeroelasticity, this unstable phenomenon is defined as flutter. However, this transonic SDOF flutter is closely related to transonic buffet (unstable aerodynamic models) due to the following reasons. Firstly, the SDOF flutter occurs only when the free-stream AOA of the spring suspended airfoil is slightly lower than that of buffet onset, and the ratio of the structural characteristic frequency to the buffet frequency is within a limited range. Secondly, the response characteristics show a high correlation between the SDOF flutter and buffet. A similar “lock-in” phenomenon exists, when the coupling frequency follows the structural characteristic frequency. Finally, there is no sudden change of the response characteristics in the vicinity of buffet onset, that is, the curve of response amplitude with the free-stream AOA is nearly smooth. Therefore, transonic SDOF flutter is often interwoven with transonic buffet and shows some complex characteristics of response, which is different from the traditional flutter.

Aircraft vibration and flutter

paper outlines the theoretical and experimental procedure one has to adopt for flutter prevention during the various stages (project, design and prototype) of the development of modern aircraft. With the advent of high speed, the aerodynamic coefficients have to be calculated with due regards to the effects of compressibility, finite aspect ratio of the lifting surfaces, sweep back and other peculiar shapes of the wings. The use of thin, small aspect ratio with external masses, necessitates the computation of higher frequency modes of vibration. Single degree of freedom flutter and the effect of control surface non-linearities has also become very important. Thus, it is shown how the availability of high speed computing machines, improved experimental technique for model and full scale testing has not kept pace with the uncertainties associated with the transonic speeds, low aspect ratio and the high frequency modes. Cross-checking of theoretical and experimental results at every stage seem to be the only answer.

Single Degree of Freedom Flutter of Compressor Blades in Separated Flow

Semiempirical results by Half man, et al., are employed to demonstrate the existence of steady-state oscillations (limitcycles) of pitching airfoils in separated How (stall flutter). The flow around an oscillating two-dimensional airfoil was studied with a Mach-Zehnder interferometer. This investigation shows the prime effects of frequency k = (c*b)/v, initial angle of attack at, cascade effect, and Mach Number on the aerodynamic reactions in separated flow.

Single Degree of Freedom Flutter of an Aileron

Single Degree of Freedom Flutter of an Aileron

Theoretical Investigation of Several Types of Single Degree of Freedom Flutter

The possibility of an undamped oscillation of an airfoil (or aerodynamic body) with a single degree of freedom in potential flow was first noted by Glauert in 1929 but has received relatively little attention until recently. These undamped oscillations might have a direct bearing on problems of both dynamic stability and of airplanes. Because of the many configurations of airplane design now being considered and because of the wide operational ranges of speed and altitude, knowledge of these single degree phenomena becomes more significant. The present paper gives theoretically predicted effects of several primary parameters associated with single degree of freedom flutter. Specific problems dealt with are: (a) pitching oscillation of an unswept wing, oscillation of an aileron about its hinge axis, and bending oscillation of a swept wing in subsonic streams; (b) pitching of an unswept rectangular wing, pitching of a delta or triangular wing, and oscillations of an aileron about its hinge line, in supersonic streams. Results for one series of experiments which confirm the existence of single degree of freedom pitching flutter of an unswept wing at low speeds are included.