Flexible Airfoil Research Articles

Unsteady fluid–structure interactions of membrane airfoils at low Reynolds numbers

Membrane wings are used both in nature and small aircraft as lifting surfaces. Separated flows are common at low Reynolds numbers and are the main sources of unsteadiness. Yet, the unsteady aspects of the fluid-structure interactions of membrane airfoils are largely unknown. An experimental study of unsteady aerodynamics of two-dimensional membrane airfoils at low Reynolds numbers has been conducted. Measurements of membrane shape with a high-speed camera were complemented with the simultaneous measurements of unsteady velocity field with a high frame-rate particle image velocimetry system and flow visualization. Vibrations of the membrane and mode shapes were investigated as a function of angle of attack and free stream velocity. While the mean membrane shape is not very sensitive to angle of attack, the amplitude and mode of the vibrations of the membrane depend on the relative location and the magnitude of the unsteadiness of the separated shear layer. The results indicate strong coupling of unsteady flow with the membrane oscillations. There is evidence of coupling of membrane oscillations with the vortex shedding in the wake, in particular, for the post-stall incidences. Comparison of rigid (but cambered) and flexible membrane airfoils shows that the flexibility might delay the stall. Hence this is a potential passive flow control method using flexibility in nature and engineering applications.

A comparison of the flow around a flexible and a non‐flexible airfoil for flapping wing propulsion

AbstractThe flow around flapping airfoils is evaluated using the Stereoscopic Particle Image Velocimetry (PIV) technique. Resulting from the measurements is the distribution of the turbulent shear stress. This serves as an indicator for the position of transition from laminar to turbulent flow. The distributions were compared for both a flapping non–flexible airfoil and a flexible airfoil. It was determined that there are differences between the flow around the flexible and the non–flexible airfoils. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Active Suppression of Flutter in a Typical Airfoil Section Fitted with a Smart Flap

T HE concept of the typical section is a two-dimensional idealization that allows for the synthesis and design of aeroelastic dynamic and control systems. It is usually modeled as an airfoil suspended by a plunging and by a pitching spring representing the structural dynamics of a typical wing section. Conventional airfoil sections are fitted with ailerons and trailing edge flaps which are generally hinged to the main section. In this study, we employ a continuouslyflexibleflap. Themechanization and actuation of such a flap, a model of which is currently being built and tested at Queen Mary, University of London, is accomplished by employing structurally embedded, multilayered, shape memory alloy actuators and active composites that are programmed to flex the flap into the desired shape. The structure is thus considered to be smart because it uses the sensor information to make decisions about how to modify its shape or other properties to improve the performance of the overall system. In this paper we consider the problem of active flutter suppression by employing such smart flaps. Could one expect that by introducing such a flexible flap, flutter can be more easily eliminated than by a rigid flap?To answer this question and to analyze the effectiveness of such a “smart” flap it is first intended to employ the flap as a feedback controller with an active feedback control law that is designed to actively regulate the structural vibrational amplitudes of the airfoil and thus suppress the occurrence of the flutter-type instabilities. To be able to actually establish the complete dynamics of a flexible flap airfoil, including significant but minimal aerodynamic vortex, wake, and interaction effects, we establish the idealized, incompressible potential flow based on unsteady aerodynamic generalized force coefficients for such flexible flaps by reconsidering the original work of Theodorsen and Garrick [1], in relation to hinged flaps. It is assumed that the continuous deflection of such flaps may be affected by means of a distribution of control effectors. It is further assumed thatmodal set point commands can be translated into a set of individual set point commands to these distributed actuators which would in turn deform the flap as in the desired mode. Such an assumption is now known to be valid for structures actuated by shape memory alloy (SMA)wire bundle actuators, which tend to behave as force-control integrators in the open loop. The methodology of optimal control is employed to obtain the relevantmulti-input–multioutput optimal regulation control laws and the relevant command signals that are needed to drive the actuators. Although it is always possible to model a flexible flap by a hinged rigid flap and tab combination, which has been thoroughly and completely studied by Nissim [2], there is sometimes a need to focus on the essential differences between a flexible and a rigid articulated flap. As pointed out by Theodorsen and Garrick [1] themselves, the latter suffers from a singularity in the pressure distribution at the leading edge of the flap. Although this does not significantly affect the hinge moment acting on the flap (or tab), it is important to ensure that its absence does not cause any detrimental effects in a flexibly actuated flap. This study shows that, while a flexible flap mode may not be as effective as a rigid hinged flap, the ability to deploy several control modes more than compensates the shortcomings. In fact, the multimode feature is an important aspect that is absent in a rigid flap. In a sense, the flexible flap is a natural generalization of the flap–tab combination.

Laminar-Turbulent Transition of a Low Reynolds Number Rigid or Flexible Airfoil

4-10 5 . In order to gain better understanding of the fluid physics and associated aerodynamics characteristics, we have coupled (i) a NavierStokes solver, (ii) the e N method transition model, and (iii) a Reynolds-averaged two-equation closure to study the low Reynolds number flow characterized with laminar separation and transition. A new intermittency distribution function suitable for low Reynolds number transitional flow is proposed and tested. To support the MAV applications, we investigate both rigid and flexible airfoils, which has a portion of the upper surface mounted with a flexible membrane, using SD7003 as the configuration. Good agreement is obtained between the prediction and experimental measurements regarding the transition location as well as overall flow structures. In the current transitional flow regime, though the Reynolds number affects the size of the laminar separation bubble, it does not place consistent impact on lift or drag. The gust exerts a major influence on the transition position, resulting in the lift and drag coefficients hysterisis. It is also observed that thrust instead of drag can be generated under certain gust condition. At α=4 o , for a flexible wing, self-excited vibration affects the separation and transition positions; however, the time-averaged lift and drag coefficients are close to those of the rigid airfoil.

Flexible Flapping Airfoil Propulsion at Low Reynolds Numbers

Water tunnel experiments on a flexible airfoil plunging with constant amplitude have been carried out for Reynolds numbers of 0 to 27000. Peaks in thrust coefficient at intermediate values of airfoil stiffness were observed at both zero and non-zero Reynolds numbers, indicating that a degree of flexibility is beneficial at low Reynolds numbers. Time-averaged velocity fields and momentum flux data revealed a broader, higher-velocity jet in cases of optimum airfoil stiffness. Stronger vortices, separated by a larger lateral distance, characterised the corresponding instantaneous velocity fields. The flexibility causes the airfoil to pitch passively; the phase angle of the pitch was found to lead the plunge. Pitch amplitude and trailing-edge amplitude were found to be single-valued functions of pitch phase angle. The shape characteristics of the airfoil could therefore be described by the pitch phase angle only. Thrust coefficient was found to be a function of only two parameters: Strouhal number and pitch phase angle. For each Strouhal number, a peak in thrust coefficient was observed at a particular value of the pitch phase angle. The optimum pitch phase angle was found to tend to a limit of 105±5 degrees at very large Strouhal numbers. A significant thrust benefit was observed over very stiff airfoils when the optimum flexibility is utilized.

Jet switching phenomenon for a periodically plunging airfoil

An experimental investigation has been carried out on rigid and flexible airfoils oscillating in still fluid. It was found that the vortex pairs generated by the oscillating airfoil move at an angle to the chordwise direction. The deflection angle of the induced jet was observed to change periodically in time. The switching period was found to increase with increasing airfoil stiffness and to decrease with increasing heave frequency and increasing amplitude. Over the range of frequency, amplitude, and stiffness tested, the switching period was found to be two orders of magnitude greater than the heave period. The development of the vorticity field for upward and downward deflected jets, as well as the transition between the two modes, was captured with the particle image velocimetry measurements. The deflection of the jet, and thus the jet switching effect, was found to diminish with increasing free stream velocity (decreasing Strouhal number).

Design and Numerical Optimization of Thick Airfoils Including Blunt Trailing Edges

The numerical optimization of thick airfoils by means of genetic- and gradient-based numerical optimization in combination with a Navier–Stokes code is described and the results are discussed. The objectives of the study are to maximize both the section moment of inertia, and the airfoil lift-to-drag ratio at fully turbulent conditions and a chord Reynolds number of 1 10 6 . A robust and flexible airfoil surface definition that is based on polynomial functions and allows for blunt trailing edges is used to generate section shapes with a maximum-thickness-to-chord ratio between 35 and 42%. To mitigate the unsteady vortex shedding, a splitter plate is added to the blunt trailing edge of the resulting airfoils. This allows steady-state simulations with the Navier–Stokes code and reduces the calculation time. The study resulted in a Pareto front, which represents a range of aerodynamically and structurally improvedairfoils.Althoughtheoptimizerwasgiventheopportunitytocreateairfoilswithanominallysharptrailing edge, the improved airfoils all contain significant trailing-edge thickness.

Numerical Analysis of Heaving Flexible Airfoils in aViscous Flow

A numerical model for two-dimensional unsteady viscous fluid flow around flexible bodies is used to analyze the effectofchordwise flexibilityonheavingairfoils.Flexibleairfoilsprovedtobemoreefficientthantherigidones.Both the output power and the input power increase in the flexible cases. The gain in efficiency is realized as a result of the output power increasing more than the input power. The density of the airfoils was shown to be a key factor in determining efficiency and power. In the parameter range analyzed, heavier airfoils are shown to generate less output power and to require proportionately less input power. Thus, heavier airfoils are more efficient than lighter airfoils. In the numerical model the bodies are represented by a distributed body force in the Navier–Stokes equations. The main advantage of this method is that the computations can be effected on a Cartesian grid, without having to fit the grid to the body surface. This approach is particularly useful when applied to the case of multiple bodies moving relative to each other, as well as flexible bodies, in which case the surface of the object changes dynamically.

Effect of flexure on aerodynamic propulsive efficiency of flapping flexible airfoil

Abstract The aim of present study is to investigate the effect of chord-wise flexure amplitude on unsteady aerodynamic characteristics for a flapping airfoil with various combinations of Reynolds number and reduced frequency. Unsteady, viscous flows over a single flexible airfoil in plunge motion are computed using conformal hybrid meshes. The dynamic mesh technique is applied to illustrate the deformation modes of the flexible flapping airfoil. In order to investigate the influence of the flexure amplitude on the aerodynamic performance of the flapping airfoil, the present study considers eight different flexure amplitudes ( a 0 ) ranging from 0 to 0.7 in intervals of 0.1 under conditions of Re=10 4 , reduced frequency k =2, and dimensionless plunge amplitude h 0 =0.4. The computed unsteady flow fields clearly reveal the formation and evolution of a pair of leading edge vortices along the body of the flexible airfoil as it undergoes plunge motion. Thrust-indicative wake structures are generated when the flexure amplitude of the airfoil is less than 0.5 of the chord length. An enhancement in the propulsive efficiency is observed for a flapping airfoil with flexure amplitude of 0.3 of the chord length. This study also calculates the propulsive efficiency and thrust under various Reynolds numbers and reduced frequency conditions. The results indicate that the propulsive efficiency has a strong correlation with the reduced frequency. It is found that the flow conditions which yield the highest propulsive efficiency correspond to Strouhal number St of 0.255.

A numerical method for the analysis of flexible bodies in unsteady viscous flows

A two-dimensional numerical model for unsteady viscous flow around flexible bodies is developed. Bodies are represented by distributed body forces. The body force density is found at every time-step so as to adjust the velocity within the computational cells occupied by the body to a prescribed value. The method combines certain ideas from the immersed boundary method and the volume of fluid method. The main advantage of this method is that the computations can be effected on a Cartesian grid, without having to fit the grid to the body surface. This is particularly useful in the case of flexible bodies, in which case the surface of the object changes dynamically, and in the case of multiple bodies moving relatively to each other. The capabilities of the model are demonstrated through the study of the flow around a flapping flexible airfoil. The novelty of this method is that the surface of the airfoil is modelled as an active flexible skin that actually drives the flow. The accuracy and fidelity of the model are validated by reproducing well-established results for vortex shedding from a stationary as well as oscillating rigid cylinder. Copyright © 2006 John Wiley & Sons, Ltd.

2P2-C10 空間移動ロボットの研究開発(第4報) : 空間移動ロボットの初飛行

First flight of the 3-dimentional-transportation robot (3DTR) was successfully achieved on November 22, 2005. The 3DTR is consisting of flexible airfoil, twin micro turbo jet engine and a gravity center control unit. The 3DTR meets all the following requirement for safety ; touchable (without any propellers of rotors), low down rate as same as parachute (below 1m/sec), low stole speed less than 25km/h, multi way control system and so on. The most significant specification is a large payload up to 60kg. In this report, result of the first flight is reported.

Flexible Flapping Airfoil Propulsion at Zero Freestream Velocity

Thrust generation for an airfoil plunging at zero freestream velocity, the case relevant to hovering birds and insects, has been studied. The objective was to investigate the effect of airfoil stiffness. Particle image velocimetry and force measurements were taken for three airfoils of relative bending stiffnesses 1:8:512 in a water tank. The deformation of the flexible airfoils produces an angle of attack that varies periodically with a phase angle with respect to the plunging motion. Amplitude and phase of this combined plunging/pitching motion play a major role in the flowfield and thrust generation. Vortex pairs or alternating vortex streets were observed depending on the amplitude and phase lag of the trailing edge. The strength of the vortices, their lateral spacing, and the time-averaged velocity of the induced jet were found to depend on the airfoil flexibility, plunge frequency, and amplitude. Direct force measurements confirmed that at high plunge frequencies the thrust coefficient of the airfoil with intermediate stiffness was greatest, although the least stiff airfoil can generate larger thrust at low frequencies. It is suggested that there is an optimum airfoil stiffness for a given plunge frequency and amplitude. The thrust/input-power ratio was found to be greater for the flexible airfoils than for the rigid airfoil.

저 레이놀즈 수 유동장에서의 유연 익형에 대한 연구

In the study, aeroelastic behaviors and aerodynamic performances of flexible airfoil in low Reynolds number environment are evaluated. To facilitate the present study, flexible airfoil in modeled through attaching massless membrane in portion of the upper CLARK-Y airfoil surface, which is often proposed low Reynolds number airfoil. The behavior of membrane in governed by aerodynamic forces and membrane equilibrium equation. Nondimensional parameter deducted by nondimensionalizing the membrane equilibrium equation, which represents the interaction between fluid and membrane has a great influence on membrane aeroelastic behavior. Changing the starting point of the membrane is conducted on aerodynamic performances. As a result, the value of nondimensional parameter should almost linearly increase according to moving the starting point of the membrane surface toward the trailing edge.ﾖ⨀‍܀㘲ㄮ㌶㬏A灰汩敳⁰桹獩捳

Theoretical Solutions for Unsteady Flows Past Oscillating Flexible Airfoils Using Velocity Singularities

A new method of solution is presented for the analysis of unsteady e ows past oscillating airfoils. This method is based on the derivation of the singular contributions of the leading edge and ridges (points where the airfoil boundary conditions change ) in the solutions of the e uid velocity and pressure coefe cient. The method has been validated by comparison with the results obtained by Theodorsen and by Postel and Leppert for rigid airfoil and aileron oscillations in translation and rotation. An excellent agreement was found between the present solutions and these previous results. This method has then been used to obtain solutions for the e exural oscillations of the e exible airfoils, e tted or not with oscillating e exible ailerons, which are of interest for the aeroelastic studies. The aerodynamic stiffness, damping, and virtual (or added) mass contributions in the solutions of the unsteady pressure distribution, lift coefe cient, and moment coefe cient are specie cally determined. An analysis of the relative magnitude of the quasi-steady and vortex shedding contributions in the aerodynamic coefe cients is also presented. In all cases studied, this method led to very efe cient and simple analytical solutions in closed form.

A Two-dimensional Sail In Turbulent Flow

The two-dimensional, incompressible flow at Reynolds number based on chord length of 1.3. 106 around an inextensible, massless sail (flexible membrane airfoil) with varying excess length is examined solving the Reynolds-Averaged NavierStokes (RANS) equations on computational grids deforming according to the sail movement. The grid deformation is computed using the same numerical procedure solving the basic equations of displacements for an isotropic, linearly elastic continuum. Results are presented for fully turbulent conditions employing closure models of different degree of complexity in comparison with experimental and analytical results obtained from literature. The sail is modelled as a chain with frictionless hinges. Good agreement can be found for low angle of attack and small excess length. However, for higher angle of attack, approaching onset of separation and beyond, the predictive accuracy varies significantly with the representation of turbulence in conjunction with strong unsteady phenomena.

A numerical method for flexible airfoils in incompressible inviscid flow

The paper deals with the aerodynamic analysis of flexible airfoils, based on a quasi-lattice vortex method (QVLM). The analysis is formulated in matrix form and leads, as in other similar studies, to a linear algebraic system when the angle of attack is nonzero, and to an eigenvalue problem when the incidence angle is zero. The aerodynamic characteristic curvesCL-α,Cm-α are presented. Finally, the airfoil shapes for several values of the tension coefficient and angles of attack are drawn. The results obtained with the present method are in good agreement with those reported in previous studies and evidentiate the flexibility of the QVLM as applied to flexible airfoils.

Computation of aerodynamic coefficients for a flexible membrane airfoil in turbulent flow: A comparison with classical theory

In the present paper an aeroelastic model of flexible membrane wing aerodynamics which incorporates the Reynolds-averaged Navier–Stokes equations is presented. The Reynolds stresses are prescribed by the k–ω shear-stress transport eddy-viscosity model recently proposed by Menter. The computed coefficients are compared with classical inviscid membrane airfoil theory and with a portion of the available experimental data for membrane wings. The results indicate that classical potential-based membrane airfoil theory can provide a meaningful description of membrane wing aerodynamics only for a small range of incidence angles near ideal and then only for membrane airfoils with small excess length ratios. For larger excess lengths and incidence angles viscous effects dominate the aerodynamics. The agreement of the computed results with the experimental data is mixed. The current status of the available experimental data for membrane airfoils is also reviewed.

AEROELASTIC ANALYSIS OF A FLEXIBLE AIRFOIL WITH A FREEPLAY NON-LINEARITY

A two-dimensional flexible airfoil with a freeplay non-linearity in pitch has been analyzed in the subsonic flow range. Structurally, the airfoil is modelled as finite beam elements and two spring elements in pitch and plunge. A doublet lattice method is used for the two-dimensional unsteady aerodynamics to include the camber deflection effect. The fictitious mass modal approach is adopted in order to use the consistent modal co-ordinates for the structures with non-linearity. Non-linear aeroelastic analyses for both the frequency domain and time domain are performed for rigid and flexible airfoil models to investigate the flexibility effect. Results are shown for models of different pitch-to-plunge frequency ratio. Responses involving limit cycle oscillation and chaotic motion are observed and they are highly influenced by the pitch-to-plunge frequency ratio.

Aerodynamic properties of a two-dimensional inextensible flexible airfoil

Resultats d'etudes theoriques et experimentales des caracteristiques aerodynamiques d'un profil flexible, bidimensionnel et inextensible. Experiences incluant la mesure de la portance, de la trainee et des forces de tension de membrane agissant sur une membrane de mylar supportee par des barres elliptiques aux bords d'attaque et de sortie. Resultats experimentaux en accord avec les resultats theoriques obtenus a partir d'une formulation plus simple que celle existant dans la litterature

Acoustics of turbulent flows: a report on Euromech 142

The European Mechanics Colloquium, Euromech 142, ww held at the Ecole Centrale de Lyon from 23 to 26 September 1981 and WM attended by 70 participants, from 9 countries, active in the fields of (i) sound production by turbulent flows and (ii) the effects of flow and turbulence on the propagation of acoustic waves. For topic (i), attention was mostly paid to shear-layer and jet instabilities and to the flow-surface interaction of flexible boundaries, vibrating blades and rigid thick airfoils. Applications were concerned in particular with propeller noise and airframe self-noise of large aircraft. Impinging shear layers were also considered for single and multiple cavities in which self-sustained oscillations can occur. Another subject discussed at the meeting was the noise from inhomogeneities, with applications to flames. For topic (ii), theoretical formulations were presented for the far field of moving multipole sources in the presence of flow and for sound propagation in ducts of variable cross section, with flow, for frequencies around the cut-off. The effect of turbulence was investigated in terms of the space–time coherence of the transmitted pressure fields. Broadband active sound control in the presence of flow was also considered, with emphasis on the progress made possible by use of digital filters. Finally, new experimental techniques, such as acoustic intensity measurements, were presented and large anechoic wind tunnels and other acoustic facilities were described.