Wing Oscillations Research Articles

Self-consistent numerical model of mosquito dynamics with specified kinematic parameters of wing movement

Mosquito flight dynamics was considered using an advanced mathematical model with experimentally determined and biologically relevant parameters. The model was developed using a self-consistent algorithm. It described mosquito’s body and wing oscillations using mechanics equations and aerodynamic flows, simultaneously. Six equations were used for the mechanics of the mosquito (relative to the center of mass), and Navier–Stokes equations simulated aerodynamics. Numerical methods employed deformable computational mesh with specific mesh construction near the wing boundaries. Using size, shape and weight characteristics of the Culex quinquefasciatus (male) mosquito the flight dynamics was computed and analyzed. It was determined that the mosquito lift force was proportional to the square of the wing frequency. Specifically, we found a critical frequency of approximately 820 Hz that corresponded to mosquito freezing when the lift force compensated gravity. This number was consistent to experimentally determined mosquito flight characteristics. Mechanism of mosquito’s lift force generation was discussed.

Нелинейный флаттер переходного процесса наследственно-деформируемых систем при сверхзвуковом режиме полета

In this paper, the problem of nonlinear flutter of a transient process of a hereditarily deformable wing of an aircraft moving at supersonic speed is considered. The aim of the work is to study the flutter problem for plate elements of aircraft in a gas flow under loads caused by atmospheric turbulence. Aerodynamic effects are specified according to the linearized piston theory. Nonlinear wing oscillations are described by a system of nonlinear integro-differential equations. They are solved numerically by the method proposed by F. Badalov, which is based on the Bubnov–Galerkin method, finite difference method, and power series. Free vibration is analyzed under conditions of ideal elasticity with account for a hereditarily deformable thin wing. The displacements of characteristic points of the wing under flutter conditions are comparatively assessed. It is established that aerodynamic nonlinearity has little impact on the critical speed, but with an increase in the Mach number, this impact increases. The mechanical effect of a significant dependence of the critical flutter speed on the relaxation kernel amplitude and Poisson's ratio is revealed.

RBF interpolation을 이용한 효율적인 혼합형 격자 변형 기법

In the present study, radial basis function(RBF) interpolation based hybrid methods are developed for Multi-block structured grid deformation. The algorithm is combined with transfinite interpolation(TFI) and spring analogy(SPR). Each method uses RBF, TFI and SPR respectively for deformation of interior mesh points while block interface is deformed by RBF equally. The main objective of the paper is to compare the performance of hybrid schemes. Characteristics of RBF interpolation for different radial basis functions are also investigated. Two wind tunnel test cases are selected to validate the algorithm:NACA0012 airfoil in pitching oscillation and NACA0015 wing oscillation. The algorithm is validated by comparing the numerical results from grid deformation methods and the result from rigidly rotating grid. Finally, RBF-TFI hybrid scheme with high order radial basis function is suggested for efficient unsteady simulation on Multi-block structured grid.

Nonlinear aeroelastic analysis of a HALE aircraft with flexible components

In this study, a full HALE (high altitude, long endurance) aircraft, nonlinear, aeroelastic analysis is being performed. Nonlinear, general, flexible, Euler–Bernoulli beam equations are being used to model the wings and the tails, and the linear, Euler–Bernoulli beam equation is used to model the fuselage. A unified formulation for modeling flexible components dynamics based on kinetic energy coupling is also being employed to model the behavior of fully flexible aircrafts. Aerodynamic forces and moments on the wings and horizontal tails are modeled based on the Wagner's function and the Jones approximation. The results of flutter properties and nonlinear time response of the limit cycle oscillations are validated. The time response, the flutter boundary, the post flutter limit cycle oscillations of wings and tails, and the vibration behavior of the fuselage are investigated, and the effect of the fuselage rigidity on the system behavior is examined. The results show that to accurately predict the aeroelastic behavior, a full aircraft analysis is necessary, especially when the amount of the bending and the torsional rigidity of the fuselage is close to the amounts of the wings and tails.

Multiagent Control of Airplane Wing Stability with “Feathers” under the Flexural Torsional Flutter

This paper proposes a novel method for the unbounded oscillation prevention of an aircraft wing under the flexural torsional flutter, an innovative multiagent attitude to control an aircraft wing with a surface consisting of managed rotating “feathers” (agents). Theoretical evaluation of the method demonstrates its high aptitude to avoid an aircraft wing’s flexural-torsional vibrations via expansion of the model’s ability to dampen the wing oscillations. It potentially allows increasing an aircraft’s speed without misgiving of the flutter. A new way to control an aircraft wing based on the Speed-Gradient methodology is suggested to increase the maximal possible flight speed without a flutter occurrence. Provided experiments demonstrate the theoretical advantage of the multiagent approach to the “feathers” rotation control.

Gust mitigation with an oscillating airfoil at low Reynolds number

The encounter between micro-aerial vehicles (MAVs) and gusts is often detrimental and mitigating the effects of the gust is important for operating MAVs under severe environmental conditions. This study investigates the impact of vertical gusts on stationary and oscillating NACA0012 (National Advisory Committee for Aeronautics) airfoils at low Reynolds numbers using high-order computational fluid dynamics methods, and identifies key dynamics that dominate gust mitigation. The interaction of the gusts with the stationary airfoil generates large unsteady forces, which exceed the peak static lift coefficient. A simple pitch-down maneuver and oscillating airfoil motion were tested as methods for mitigating the effects of the gusts. A rapid and significant pitch-down maneuver is observed to inadvertently cause a stall event by exceeding the negative stall angle. A stepwise change in the angle of attack (AoA), as the gust develops, is shown to be more effective at mitigating the gust effect. However, this gust mitigation strategy is still not effective if the gust continues to grow in magnitude. Low amplitude wing oscillations were then tested as a novel method for gust mitigation. Increasing the reduced frequency of the oscillating airfoil is shown to dominate the gust and results in a predictable oscillatory lift and drag/thrust behavior. Results also show that this effect is relatively insensitive to variations in the Strouhal number. These results suggest there may be gust mitigation strategies leveraging oscillating wing behaviors on MAVs.

Wing movements underlying sound production in calling, rivalry, and courtship songs of the cricket Gryllus bimaculatus (DeGeer)

We recorded the wing movements and sound signals during the production of calling, rivalry, and courtship song in the bispotted field cricket Gryllus bimaculatus. Recordings confirm that salient sound pulses during calling and rivalry song are generated during the closing movements of the wings. Wing movements for calling and rivalry song start from an elevated wing position and are performed with a very similar opening-closing movement, indicating that both types of songs may be generated by the same neuronal network. Wing movements for courtship song start from a low wing position; rapid closing movements generate high-frequency ticks and low-amplitude wing oscillations lead to low–amplitude pulses, generated during the opening and closing movements with a carrier frequency corresponding to the calling song. The two types of wing movements underlying courtship song indicate a different motor control as compared to calling song and may represent an early evolutionary phenotype.

Randomness in appendage coordination facilitates strenuous ground self-righting

Randomness is common in biological and artificial systems, resulting either from stochasticity of the environment or noise in organisms or devices themselves. In locomotor control, randomness is typically considered a nuisance. For example, during dynamic walking, randomness in stochastic terrain leads to metastable dynamics, which must be mitigated to stabilize the system around limit cycles. Here, we studied whether randomness in motion is beneficial for strenuous locomotor tasks. Our study used robotic simulation modeling of strenuous, leg-assisted, winged ground self-righting observed in cockroaches, in which unusually large randomness in wing and leg motions is present. We developed a simplified simulation robot capable of generating similar self-righting behavior and varied the randomness level in wing–leg coordination. During each wing opening attempt, the more randomness added to the time delay between wing opening and leg swinging, the more likely it was for the naive robot (which did not know what coordination is best) to self-right within a finite time. Wing–leg coordination, measured by the phase between wing and leg oscillations, had a crucial impact on self-righting outcome. Without randomness, periodic wing and leg oscillations often limited the system to visit a few bad phases, leading to failure to escape from the metastable state. With randomness, the system explored phases thoroughly and had a better chance of encountering good phases to self-right. Our study complements previous work by demonstrating that randomness helps destabilize locomotor systems from being trapped in undesired metastable states, a situation common in strenuous locomotion.

Vibrational control: A hidden stabilization mechanism in insect flight.

It is generally accepted among biology and engineering communities that insects are unstable at hover. However, existing approaches that rely on direct averaging do not fully capture the dynamical features and stability characteristics of insect flight. Here, we reveal a passive stabilization mechanism that insects exploit through their natural wing oscillations: vibrational stabilization. This stabilization technique cannot be captured using the averaging approach commonly used in literature. In contrast, it is elucidated using a special type of calculus: the chronological calculus. Our result is supported through experiments on a real hawkmoth subjected to pitch disturbance from hovering. This finding could be particularly useful to biologists because the vibrational stabilization mechanism may also be exploited by many other creatures. Moreover, our results may inspire more optimal designs for bioinspired flying robots by relaxing the feedback control requirements of flight.

Study of Fast Prediction Method for Transonic Flutter Boundary Using Radial Basis Function

A spectral volume method for hybrid unstructured mesh developed earlier is built in an aeroelastic code to determine transonic flutter boundary of AGARD 445.6 wing. It is shown that the computed transonic dip of flutter boundary reasonably agrees with the experimental data. In the present study, we focus on to develop a fast numerical method for evaluating the bottom of transonic dip. In order to reduce the number of computational cases to determine the flutter boundary, an interpolation method using the radial basis function is examined. The initial sampling points are sparsely distributed over the entire parameter plane to roughly determine the flutter boundary by interpolating damping ratio of wing oscillation. Then, based on the consideration of load distribution over the wing, some additional sampling points are introduced in the region where the transonic dip likely appears. It is demonstrated that the present approach allows us to evaluate the bottom of transonic dip with less computational efforts for the present problem. Discussions are included to examine the possible efforts of the arrangement of initial sampling points and interpolation method on the shape of flutter boundary near the dip.

Motion Study of the Ornithopter with Periodic Wing Oscillations

The motion of an ornithopter, a flying robot, consisting of a body and two symmetric twolink wings, is considered. The device moves in a vertical plane perpendicular to the longitudinal axis of the robot. All the links of the object form a chain through cylindrical joints with parallel axes. A mathematical model of the ornithopter is developed based on a bird’s flight analysis taking into account the aerodynamic interaction of all the links with the environment. Sequences of flight phases are considered, each of which differs in the direction of motion of the wing links. As a result of numerical simulation, diagrams of the robot’s modes of motion are constructed (ascent, hovering, and descent) and the effect of the amplitude and frequency of oscillation of the wing links, as well as their area, is determined (the same wing area was achieved by varying the length and width of the wings).

Energy harvesting properties of a flapping wing with an adaptive Gurney flap

Flapping wing structures have drawn increasing attention for harvesting energy from flowing fluids. This work proposes the application of an adaptive Gurney flap to the trailing end of a flapping wing foil, which actively adjusts the position of a single Gurney flap to be consistently employed on the foil pressure side. The transient two-dimensional numerical simulations are conducted to compare the energy harvesting efficiency of the proposed adaptive flapping wing structure with that of a conventional flapping wing structure and the one with fixed Gurney flaps. In addition, the effects of wing oscillation frequency, Gurney flap length, and the position of the flap relative to the trailing edge of the foil were also considered. The results demonstrate that the adaptive Gurney flap provides greater energy harvesting efficiency for the oscillating wing primarily by increasing the heave force through the synchronous switching of the flap from one side to the other within the period of motion. Compared with fixed Gurney flaps, the adaptive flap can accommodate greater flap lengths and operation over a wider oscillation frequency range. The results indicate that the optimum position of the Gurney flap is as near as possible to the trailing edge of the foil. The results also reveal two relatively high harvesting efficiency oscillation frequency regions. In the low frequency region, if the leading edge vortex detaches from the trailing edge just when the foil exchanges the heaving direction, the foil can gain much more energy due to the positive power extraction contributed by the pitching moment. In the high frequency region, a small steady attached vortex maintains a high lift force on the foil, and, thus, the enhanced heaving force harvests more power.

Plunging Oscillations of Airfoils and Wings: Progress, Opportunities, and Challenges

The vortex dynamics of thrust and lift generation for periodically plunging airfoils and finite wings at low Reynolds numbers is reviewed. Effects of vortex lock-in phenomenon, leading-edge vortex, vortex merging and pairing, vortex–wing interactions, leading-edge geometry, wake deflection, and chordwise and spanwise flexibility on lift and thrust are discussed. Mean lift force of the oscillating airfoil at post-stall angles of attack becomes maximum at optimal frequencies due to the vortex lock-in at the fundamental frequency, subharmonic, and first harmonic of the natural shedding frequency. Bifurcations of wakes of plunging airfoils, which depend on the mean angle of attack and the initial conditions and can produce large mean lift coefficients, are not observed for finite wings. One or two arch-type vortical structures may develop from the leading-edge vortices shed on low-aspect-ratio wings. Significant spanwise flows can develop on finite wings due to the dynamics of tip vortices or leading-edge vortices. Chordwise and spanwise flexibility of plunging airfoils and wings are known to enhance the mean thrust and lift; however, the physical mechanism of the optimal conditions is not well understood. Various flow control opportunities to exploit the flow physics as well as remaining challenges and unresolved issues are summarized.

Interaction of a trailing vortex with an oscillating wing

A technique of particle image velocimetry is employed to characterize the flow structure of a trailing vortex incident upon the tip region of an oscillating wing (plate). The amplitude and velocity of the wing are nearly two orders of magnitude smaller than the wing chord and free stream velocity, respectively. Depending upon the outboard displacement of the incident vortex relative to the wing tip, distinctive patterns of upwash, downwash, and shed vorticity are observed. These patterns are a strong function of the phase of the wing motion during its oscillation cycle. At a given phase, the wing oscillation induces upwash that is reinforced by the upwash of the incident vortex, giving a maximum net upwash. Conversely, when these two origins of upwash counteract, rather than reinforce, one another during the oscillation cycle, the net upwash attains minimum value. Analogous interpretations hold for regions of maximum and minimum net downwash located outboard of the regions of upwash. The magnitude and scale of the vorticity shed from the tip of the wing are directly correlated with the net upwash, which takes different forms related to the outboard displacement of the incident vortex. As the location of the incident vortex is displaced towards the wing tip, both the maximum upwash and the maximum vorticity of the tip vortex initially increase and then decrease. For the limiting case where the incident vortex impinges directly upon the tip of the wing, there is no tip vortex or induced region of upwash. Furthermore, at small values of vortex displacement from the wing tip, the position of the incident vortex varies significantly from its nominal position during the oscillation cycle. All of the foregoing features are interpreted in conjunction with the flow topology in the form of streamlines and critical points, superposed on patterns of vorticity. It is shown that despite the small amplitude of the wing motion, the flow topology is fundamentally different at maximum positive and negative values of the velocity of the wing tip, that is, they are not symmetric.

Aerodynamics of Harmonically Oscillating Aerofoil at Low Reynolds Number

Two-dimensional flows over harmonically oscillating symmetrical aerofoil at reduced frequency of 0.1 were investigated for a Reynolds number of 135,000, with focus on the unsteady aerodynamic forces, pressure and vortex dynamics at post-stall angles of attack. Numerical simulations using ANSYS® FLUENT CFD solver, validated by wind tunnel experiment, were performed to study the method of sliding mesh employed to control the wing oscillation. The transport of flow was solved using incompressible, unsteady Reynolds-Averaged Navier-Stokes equations. The 2-equation k-e realizable turbulence model was used as turbulence closure. At large angle of attack, complex flows structure developed on the upper surface of the aerofoil induced vortex shedding from the activity of separated flows and interaction of the leading edge vortex with the trailing edge one. This interaction at some stage promotes the generation of lift force and delays the static stall. In this investigation, it was found that the sliding mesh method combined with the k-e realizable turbulence model provides better aerodynamic loads predictions compared to the methods reported in literature.

Linear drag law for high-Reynolds-number flow past an oscillating body

Flying is a delicate balance of lift versus weight and thrust versus drag. But the flapping wings of animals do not seem to abide by the aerodynamic laws of airplane wings. A new study shows that fast wing oscillations -- like that used by flying insects -- lead to fundamental changes in the physics of drag or wind resistance. The steady motion of airplane wings leads to a resistance that increases as the square of speed. The new research shows that flapping wings instead have a drag that increases in direct proportion to their speed through air. This means that, to go twice as fast, an airplane must generate four times the thrust, while an insect only needs to produce twice the thrust.

Lift enhancement through flexibility of plunging wings at low Reynolds numbers

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.

Batoid locomotion: effects of speed on pectoral fin deformation in the little skate, Leucoraja erinacea.

Most batoids have a unique swimming mode in which thrust is generated by either oscillating or undulating expanded pectoral fins that form a disc. Only one previous study of the freshwater stingray has quantified three-dimensional motions of the wing, and no comparable data are available for marine batoid species that may differ considerably in their mode of locomotion. Here, we investigate three-dimensional kinematics of the pectoral wing of the little skate, Leucoraja erinacea, swimming steadily at two speeds [1 and 2bodylengths(BL)s-1]. We measured the motion of nine points in three dimensions during wing oscillation and determined that there are significant differences in movement amplitude among wing locations, as well as significant differences as speed increases in body angle, wing beat frequency and speed of the traveling wave on the wing. In addition, we analyzed differences in wing curvature with swimming speed. At 1 BL s-1, the pectoral wing is convex in shape during the downstroke along the medio-lateral fin midline, but at 2 BL s-1 the pectoral fin at this location cups into the flow, indicating active curvature control and fin stiffening. Wing kinematics of the little skate differed considerably from previous work on the freshwater stingray, which does not show active cupping of the whole fin on the downstroke.

Periodic and chaotic flapping of insectile wings

Insects use flight muscles attached at the base of the wings to produce impressive wing flapping frequencies. The maximum power output of these flight muscles is insufficient to maintain such wing oscillations unless there is good elastic storage of energy in the insect flight system. Here, we explore the intrinsic self-oscillatory behavior of an insectile wing model, consisting of two rigid wings connected at their base by an elastic torsional spring. We study the wings behavior as a function of the total energy and spring stiffness. Three types of behavior are identified: end-over-end rotation, chaotic motion, and periodic flapping. Interestingly, the region of periodic flapping decreases as energy increases but is favored as stiffness increases. These findings are consistent with the fact that insect wings and flight muscles are stiff. They further imply that, by adjusting their muscle stiffness to the desired energy level, insects can maintain periodic flapping mechanically for a range of operating conditions.

Kinematics and Inertial Effects in Locust Flapping Wings

In the present study, inertial forces and kinematics of wings of locusts, Schistocerca americana, were investigated experimentally. The developed experimental setup includes freshly extracted hindwings and forewings, a mechanical transmission producing pitching and flapping, a vacuum chamber, and a high-speed video system. Flapping angle amplitudes determined at the middle section are practically the same in air and in vacuum in both forewings and hindwings. Pitching amplitudes in the root and in the middle section of hindwing differ by up to 50 % due to torsional deformation or twist. In air, the average twist angles are 3° and 17° in forewings and hindwings, respectively. Amplitudes of twist angle are higher in vacuum, especially at relatively high flapping frequencies. Inertial forces are calculated based on a rigid-body model of a wing with prescribed displacements. The 5-segment mesh for hindwings and 2-segment mesh for forewings provide accurate determination of inertial forces. Amplitudes of the fifth harmonic in accelerations in air are substantially smaller than in vacuum and, therefore, inertial forces in air are about 30 % smaller than those in vacuum. Thus, aerodynamic loads suppressed high-frequency component in wing oscillations resulting in substantially smaller inertial forces in air.