Wing Oscillations Research Articles

The effect of sweep angle on the limit cycle oscillations of aircraft wings

This study focuses on the limit cycle oscillations (LCOs) of cantilever swept-back wings containing a cubic nonlinearity in an incompressible flow. The governing aeroelastic equations of two degrees-of-freedom swept wings are derived through applying the strip theory and unsteady aerodynamics. In order to apply strip theory, mode shapes of the cantilever beam are used. The harmonic balance method is used to calculate the frequencies of LCOs. Linear flutter analysis is conducted for several values of sweep angles to obtain the flutter boundaries.

Dynamic Unstructured Grids Method with Applications to Unsteady Flows Involving Moving Boundaries

Spring analogy method for dynamic unstructured grids is studied. The stiffness of the springs in the vertex spring method is analyzed. Improvements considering squashing spring effect and boundary effect are developed to the standard method. Applications of the improved spring analogy method to dynamic grids generation show that the new method greatly improves the deforming ability and the quality of the grids. This improved unstructured dynamic mesh method, coupled with ALE Euler solver, is then applied to simulate unsteady transonic flow about harmonious oscillation of rigid wing and bend-torsion oscillation of high-aspect ratio sweepback wing of High-Altitude-Long-Endurance Unmanned Aerial Vehicles; computational results are in good agreement with those of other literatures and experiments

Energy harvesting from self-sustained aeroelastic limit cycle oscillations of rectangular wings

Three different aspect-ratio rectangular wings are designed and experimentally tested to produce self-sustained aeroelastic oscillations for energy harvesting via implementing a piezoelectric generator. Sensitivity measurements are conducted first to determine the critical conditions producing such oscillations with a dominant frequency of 1 Hz. Furthermore, the energy harvesting performance is maximized as the piezoelectric generator is implemented in parallel with oncoming flow streamline. Approximately 55 mW electricity is produced from a wing with a surface area of 0.025 m2. Unlike conventional wind turbine technology, the present work opens up another possible way to harvest energy via nonlinear aeroelastic oscillations.

Simulation of Aeroelastic Limit-Cycle Oscillations of Aircraft Wings with Stores

Aircraft wings carrying stores are susceptible to nonlinear aeroelastic limit-cycle oscillations, which can lead to reduced flight and mission performance. Limit-cycle-oscillation dynamics and control simulation studies, although of great importance, are often based on simplified typical-section airfoil models. In this work, the more accurate beam–rod representation is used to capture the spanwise varying displacement of a wing with store. The spanwise variation of wing geometry and structural properties, as well as the presence of multiple stores on rigid or flexible mounts, is efficiently modeled by the primitive-modes approach. Aeroelastic limit-cycle oscillation due to structural nonlinearity is demonstrated via time-marching simulations, as well as the computationally more efficient harmonic-balance method. Some novel forms of limit-cycle-oscillation behavior are observed as the model parameters are varied, and these are explained in terms of the flutter/divergence properties of the base linear aeroelastic system.

Leading-Edge Flow Structure of a Dynamically Pitching NACA 0012 Airfoil

The leading-edge flow structure of the NACA 0012 airfoil is experimentally investigated under dynamic-stall conditions (; , 22.4 deg; ) using planar particle image velocimetry. The airfoil was dynamically pitched about the one-fourth chord at a reduced frequency, . As expected, on the upstroke, the flow remains attached in the leading-edge region above the static stall angle, whereas during downstroke, the flow remains separated below the static stall angle. A phase-averaging procedure involving triple velocity decomposition in combination with the Hilbert transform enables the entire dynamic-stall process to be visualized in phase space, with the added benefit of the complete phase space composed of numerous wing oscillations. The formation and complex evolution of the leading-edge vortex are observed. This vortex is seen to grow, interact with the surrounding vorticity, detach from the surface, and convect downstream. A statistical analysis coupled with instantaneous realizations results in the modification of the classical dynamic-stall conceptual model, specifically related to the dynamics of the leading-edge vortex.

Frequency lock-in phenomenon for self-sustained roll oscillations of rectangular wings undergoing a forced periodic pitching motion

The free-to-roll behaviour of rigid and membrane rectangular wings with an aspect ratio of two was studied in wind tunnel experiments conducted at a chord Reynolds number of Rec = 46 000. Self-excited roll oscillations resulting from the fluid-structure interaction were studied in forced sinusoidal pitching motion in order to simulate gust encounters of small air vehicles. For the dynamic pitching cases, the frequency and phase of the self-excited roll oscillations can become synchronized (or locked-in) with the fundamental pitching frequency and its subharmonics. This is believed to be the first documented example of synchronization for this type of fluid-structure interaction. Depending on the amplitude and frequency of excitation (pitching motion), there are regions of decreased roll oscillations, which may be important for the gust response of small vehicles.

Parametric oscillations of wings excited during nonuniform fluid flow

The mechanism of excitation of rotary parametric oscillations during nonuniform fluid flow in a partially filled wing with a pivotal bearing and elastic connections is examined. It is experimentally revealed that at a certain flow velocity, intensive wing oscillations are excited with an eigenfrequency approximately twice as high as rotary oscillations alone. When the air cushion is removed and the wing is filled completely by the liquid, these oscillations stop. It is shown that significant modulation of the mass moment of inertia with a period equal to the half-period of self-oscillations appear due to significant displacements of the air cushion and liquid displacement towards the peripheral segments of an incompletely filled wing during rotary oscillations. Therefore, the parametric intensification of rotary oscillations of a wing in nonuniform liquid flow at a frequency approximately twice as high as the eigenfrequency can take place. The intensive rotary oscillations of an incompletely filled wing, which are excited by a nonuniform liquid flow, can be efficiently used for driving the different mechanisms in machine manufacturing, power engineering and the shipbuilding industry

Resonance of flexible flapping wings at low Reynolds number

Using three-dimensional computer simulations, we examine hovering aerodynamics of flexible planar wings oscillating at resonance. We model flexible wings as tilted elastic plates whose sinusoidal plunging motion is imposed at the plate root. Our simulations reveal that large-amplitude resonance oscillations of elastic wings drastically enhance aerodynamic lift and efficiency of low-Reynolds-number plunging. Driven by a simple sinusoidal stroke, flexible wings at resonance generate a hovering force comparable to that of small insects that employ a very efficient but much more complicated stroke kinematics. Our results indicate the feasibility of using flexible wings driven by a simple harmonic stroke for designing efficient microscale flying machines.

Remote radio control of insect flight

We demonstrated the remote control of insects in free flight via an implantable radio-equipped miniature neural stimulating system. The pronotum mounted system consisted of neural stimulators, muscular stimulators, a radio transceiver-equipped microcontroller and a microbattery. Flight initiation, cessation and elevation control were accomplished through neural stimulus of the brain which elicited, suppressed or modulated wing oscillation. Turns were triggered through the direct muscular stimulus of either of the basalar muscles. We characterized the response times, success rates, and free-flight trajectories elicited by our neural control systems in remotely controlled beetles. We believe this type of technology will open the door to in-flight perturbation and recording of insect flight responses.

Mechanical phase shifters for coherent acoustic radiation in the stridulating wings of crickets: the plectrum mechanism

Male crickets produce stridulatory songs using engaged tegmina (forewings): a plectrum on the left sweeps along a tooth row on the right. During stridulation, the plectrum moves across the teeth and vibrations are amplified by the surrounding cells and veins, resonating at the frequency of tooth impacts. The advance of the plectrum on the file is controlled by an escapement mechanism so that passing each single tooth generates one wave of a highly tonal signal. Both tegmina must oscillate in phase to avoid destructive interference. But as each plectrum-tooth contact begins, the right and left tegmina react in opposite oscillatory directions. A mechanical phase shifter is part of the left tegmen and compensates to achieve wing oscillation synchrony. We use a new technique to simulate plectrum-on-file interactions: in combination with laser vibrometry, this technique assessed plectrum mechanics in the cricket Gryllus bimaculatus. Using an excised teneral file, shaped like a partial gear and moved by a motor, and a microscan Doppler laser vibrometer, plectrum and left-tegmen mechanics were explored. The results show that plectrum and harp oscillate with a phase difference of ca. 156 deg., a shift rather than a complete phase inversion (180 deg.). This phase shift occurs at the site of a large wing vein (possibly A3). Plectrum and harp vibrate with similar fundamental frequency, therefore, plectrum torsion resonant frequency is important for maintaining vibration coherence. The mechanical aspects involved in this partial phase inversion are discussed with respect to the escapement mechanism. The plectrum mechanics and its implications in katydid stridulation are also considered.

Flow Reattachment and Vortex Re-formation on Oscillating Low-Aspect-Ratio Wings

Effects of small-amplitude wing oscillations on flow reattachment and vortex re-formation in the poststall region were studied experimentally. Low-aspect-ratio delta and cropped delta wings with sweep angles in the range of A = 20-50 deg were tested. Effects of forcing frequency, amplitude, wing sweep angle, and mode of the wing oscillations were investigated. It was shown that wing oscillations at an appropriate frequency promotes the reattachment of the otherwise separated flow at poststall incidences. Moreover, with increasing frequency, leading-edge vortices develop with axial flow in the cores, followed by their breakdown. For an optimum range of Strouhal numbers, Sr = 1-2, vortex breakdown is delayed to a maximum distance from the apex. This range of Strouhal numbers compares well with the dominant frequencies of the shear layer instabilities. For sweep angles larger than 20 deg, the reattachment process is generic for all nonslender wings and there is an optimum range of Strouhal numbers.

The sound field generated by tethered stingless bees (Melipona scutellaris): inferences on its potential as a recruitment mechanism inside the hive

In stingless bees, recruitment of hive bees to food sources involves thoracic vibrations by foragers during trophallaxis. The temporal pattern of these vibrations correlates with the sugar concentration of the collected food. One possible pathway for transferring such information to nestmates is through airborne sound. In the present study, we investigated the transformation of thoracic vibrations into air particle velocity, sound pressure, and jet airflows in the stingless bee Melipona scutellaris. Whereas particle velocity and sound pressure were found all around and above vibrating individuals, there was no evidence for a jet airflow as with honey bees. The largest particle velocities were measured 5 mm above the wings (16.0+/-4.8 mm s(-1)). Around a vibrating individual, we found maximum particle velocities of 8.6+/-3.0 mm s(-1) (horizontal particle velocity) in front of the bee's head and of 6.0+/-2.1 mm s(-1) (vertical particle velocity) behind its wings. Wing oscillations, which are mainly responsible for air particle movements in honey bees, significantly contributed to vertically oriented particle oscillations only close to the abdomen in M. scutellaris (distances < or =5 mm). Almost 80% of the hive bees attending trophallactic food transfers stayed within a range of 5 mm from the vibrating foragers. It remains to be shown, however, whether air particle velocity alone is strong enough to be detected by Johnston's organ of the bee antenna. Taking the physiological properties of the honey bee's Johnston's organ as the reference, M. scutellaris hive bees are able to detect the forager vibrations through particle movements at distances of up to 2 cm.

A nonlinear analysis of stability and gust response of aeroelastic systems

In this paper, the mechanism of limit-cycle excitation is investigated for an aeroelastic system with structural nonlinearities. The analysis is performed on a simplified aeroelastic model retaining only two structural modes (first bending and first torsional modes) and with a simplified description of both unsteady loads due to wing oscillation and external gust excitation. Two cases are considered, without and with gust excitation. In the first case, normal form analysis is employed to give an approximation of the basin of attraction of stable limit cycles in the space of initial conditions. In the second case, a critical gust intensity for a given gust gradient leading again to undamped oscillations is identified.

低速デルタ翼フラッタ現象における大変形振動流れ場の解析

The problem of low subsonic delta wing flutter was studied experimentally and numerically. Two kinds of oscillation: low- and high-amplitude oscillation modes were observed in experiment. Moreover, the transition velocity between the two modes significantly depends on angle of attack. When angle of attack is high, the transition from low- to high-amplitude mode is made more suddenly. The flutter velocity obtained in the present experiment shows good agreement with other experimental data as well as results of the present computation. In addition, the flow field around an oscillating delta wing with large deformation is made clear, where vortex motion is coupled with wing motion. It is found that aerodynamic force produced by the vortex near the wing leading edge is closely related with the large amplitude wing oscillation.

Limit cycle oscillations of rectangular cantilever wings containing cubic nonlinearity in an incompressible flow

Limit cycle oscillations (LCO) as well as nonlinear aeroelastic analysis of rectangular cantilever wings with a cubic nonlinearity are investigated. Aeroelastic equations of a rectangular cantilever wing with two degrees of freedom in an incompressible potential flow are presented in the time domain. The harmonic balance method is modified to calculate the LCO frequency and amplitude for rectangular wings. In order to verify the derived formulation, flutter boundaries are obtained via a linear analysis of the derived system of equations for five different cases and compared with experimental data. Satisfactory results are gained through this comparison. The problem of finding the LCO frequency and amplitude is solved via applying the two methods discussed for two different cases with hardening cubic nonlinearities . The results from first-, third- and fifth-order harmonic balance methods are compared with the results of an exact numerical solution. A close agreement is obtained between these harmonic balance methods and the exact numerical solution of the governing aeroelastic equations. Finally, the nonlinear aeroelastic analysis of a rectangular cantilever wing with a softening nonlinearity is studied.

Identification of new lift generation mechanism in flapping flight

In this paper the combined effect of two mechanisms for lift enhancement at low Reynolds numbers are considered, wing oscillations and wing flexibility. The force, deformation and flow fields of rigid and flexible low aspect ratio (AR=3) and high aspect ratio (AR=6) wings oscillating at a fixed post-stall angle of attack of 15° and amplitude of 15% of chord are measured. The force measurements show that flexibility can increase the time-averaged lift coefficient significantly. For low aspect ratio wings the maximum lift coefficient across all Strouhal numbers was Cl=1.38 for the rigid wing as opposed to Cl=2.77 for the flexible wing. Very similar trends were observed for the high aspect ratio wings. This increase is associated with significant deformation of the wing. The root is sinusoidally plunged with small amplitude but this motion is amplified along the span resulting in a larger tip motion but with a phase lag. The amount it is amplified strongly depends on Strouhal number. A Strouhal number of Src=1.5 was selected for detailed flow field measurements due to it being central to the high-lift region of the flexible wings, producing approximately double the lift of the rigid wing. For this Strouhal number the rigid wings exhibit a Leading Edge Vortex (LEV) ring. This is where the clockwise upper-surface LEV pairs with the counter-clockwise lower-surface LEV to form a vortex ring that self-advects upstream and away from the wing's upper surface. Conversely the deformation of the flexible wings inhibits the formation of the LEV ring. Instead a strong upper-surface LEV forms during the downward motion and convects close to the airfoil upper surface thus explaining the significantly higher lift. These measurements demonstrate the significant gains that can be achieved through the combination of unsteady aerodynamics with flexible structures.

Investigation of the near-field tip vortex behind an oscillating wing

The near-field tip-vortex flow structure behind an oscillating NACA 0015 wing was investigated at . For attached-flow and light-stall oscillations, a small hysteretic property existed between the pitch-up and pitch-down motion, and many of the vortex flow features were found to be qualitatively similar to those of a static wing. For deep-stall oscillations, the wing oscillations imposed a strong discrepancy in contour shapes and magnitudes between the pitch-up and pitch-down phases of the oscillation cycle. The vortex was less organized during pitch-down (as a result of leading-edge-vortex-induced massive flow separation) than during pitch-up. The tangential velocity, circulation and lift-induced drag increased progressively with the airfoil incidence, and had higher magnitudes during pitch-up than during pitch-down, while varying slightly with the downstream distance. The vortex size, however, was larger during pitch-down than during pitch-up. The axial flow was always wake-like during the deep-stall oscillation cycle. The normalized circulation within the inner region of the tip vortex also exhibited a self-similar structure, similar to that of a static wing, and was insensitive to the reduced frequency.

Tip Vortex Behind a Wing Undergoing Deep-Stall Oscillation

The flow structure of a tip vortex in the near field of a NACA 0015 wing with an effective aspect ratio of 5.04 undergoing a deep-stall oscillation with a(t) = 18 deg + 6 deg sin ωt at Re = 1.86 × 10 5 was investigated. The wing oscillation imposed a strong discrepancy in contour shapes and magnitudes between the pitch-up and pitch-down phases of the oscillation cycle. The vortex was more organized and nearly axisymmetric for x/c > 0.5 during pitch-up than during pitch-down. The peak tangential velocity and vorticity and the strength and size of the vortex increased with a(t), except in the vicinity of α max , and had higher values during pitch-up than during pitch-down. The axial flow was always wake like and the velocity deficit decreased with α(t), while exhibiting a sharp increase and decrease on the upstroke and downstroke in the vicinity of α max , respectively. The tangential velocity decreased slightly with the downstream distance. The vortex size increased rather significantly with x/c during pitch-down while remaining virtually unchanged during pitch-up. The inner region of the vortex exhibited a self-similar structure, similar to that of a stationary wing. The induced drag increased with a(t) and had a local maximum at 20 deg during pitch-up.

The mechanics of sound production inPanacanthus pallicornis(Orthoptera: Tettigoniidae: Conocephalinae): the stridulatory motor patterns

To examine whether sound production in katydids relies on an escapement mechanism similar to that of crickets we investigated the functional anatomy and mechanical properties of the stridulatory apparatus in the katydid Panacanthus pallicornis. Males of this species produce sustained pulses with a sharp low frequency peak of approximately approximately 5 kHz and a broad band spectrum between 15 and 25 kHz. Simultaneous recordings of movement and sound indicate that the entire stridulatory file is used for sound production and there is nearly a 1:1 correspondence between the number of cycles in a song and the number of teeth on the file. There is an overall tendency for both the spacing of teeth to increase along the file and the velocity of wing closure to increase as the scraper traverses the file. There is considerable variation, however, in the evenness of tooth spacing and in the instantaneous velocity of wing closure during sound production. The production of sustained pulses appears to depend on resonance in the right tegmen, with the left tegmen acting primarily as a damping element. This resonance is not strongly coupled to the scraper and, unlike crickets, the timing of file-scraper interactions, and therefore the phasing of energy input to wing oscillations, is variable. Similarly, the quality of the sound spectrum varies over the course of a single stridulatory wing-stroke. Based on measurements of tooth spacing on the stridulatory file and cycle-by-cycle frequency of sound output, we predicted the velocity of wing movement that would provide consistent phasing of file-scraper interactions with respect to sound-radiating wing oscillations and compared this with measurements of wing velocity. Acceleration of wing velocity during stridulation results in a closer match to the velocity required for optimal phasing during a portion of the call, and this corresponds with higher amplitudes of radiated sound and the excitation of higher order modes of vibration (evident as distinct harmonic peaks in spectrograms). Our results suggest that in katydid stridulation, the movement of the scraper along the file is not regulated by an escapement mechanism as it is in crickets. Instead, katydids that produce pure-tone songs sweep their wings over a range of velocities, within which some portion matches file tooth spacing to give optimal phasing of energy input to excite a resonance in the right tegmen.

AWIATOR's Study of a Wing Load Control: Design and Flight-Test Results

Loads at the wing root sections of an aircraft are mainly induced by the vertical accelerations encountered in manoeuvre or in turbulence, but a non-negligible part comes from the wing bending deflections. In an attempt to reduce such loads and hence reduce structural weight, a load alleviation function has been studied by Airbus flight-control research-engineers. This study was conducted under the auspices of AWIATOR, a European research program aimed at developing and testing challenging flying technologies.The load alleviation function developed in this study is divided into 3 parts, each with a dedicated objective. First, a passive control reduces the loads induced by pilot inputs or by turbulence, by deflecting ailerons and spoilers proportionally to the vertical acceleration of the aircraft. Secondly, an active control deals with wing oscillations induced by the bending structural modes. This part has been designed with modern H methods, to take into account and optimise various specifications: load reduction, robustness to payload, but also roll-on and roll-off criteria to avoid any interaction possibly modifying handling qualities. The third part concerns the activation logics of the first two parts. This last part is not discussed hereafter.