Experimental investigation of the effect of chordwise flexibility on the aerodynamics of flapping wings in hovering flight

Ornithopters or mechanical birds produce aerodynamic lift and thrust through the flapping motion of their wings. Here, we use an experimental apparatus to investigate the effects of a wing's twisting stiffness on the generated thrust force and the power required at different flapping frequencies. A flapping wing system and an experimental set-up were designed to measure the unsteady aerodynamic and inertial forces, power usage and angular speed of the flapping wing motion. A data acquisition system was set-up to record important data with the appropriate sampling frequency. The aerodynamic performance of the vehicle under hovering (i.e., no wind) conditions was investigated. The lift and thrust that were produced were measured for different flapping frequencies and for various wings with different chordwise flexibilities. The results show the manner in which the elastic deformation and inertial flapping forces affect the dynamical behavior of the wing. It is shown that the generalization of the actuator disk theory is, at most, only valid for rigid wings, and for flexible wings, the power P varies by a power of about 1.0  of the thrust T. This aerodynamic information can also be used as benchmark data for unsteady flow solvers.     

A simulation-based study on longitudinal gust response of flexible flapping wings

Winged animals such as insects are capable of flying and surviving in an unsteady and unpredictable aerial environment. They generate and control aerodynamic forces by flapping their flexible wings. While the dynamic shape changes of their flapping wings are known to enhance the efficiency of their flight, they can also affect the stability of a flapping wing flyer under unpredictable disturbances by responding to the sudden changes of aerodynamic forces on the wing. In order to test the hypothesis, the gust response of flexible flapping wings is investigated numerically with a specific focus on the passive maintenance of aerodynamic forces by the wing flexibility. The computational model is based on a dynamic flight simulator that can incorporate the realistic morphology, the kinematics, the structural dynamics, the aerodynamics and the fluid–structure interactions of a hovering hawkmoth. The longitudinal gusts are imposed against the tethered model of a hovering hawkmoth with flexible flapping wings. It is found that the aerodynamic forces on the flapping wings are affected by the gust, because of the increase or decrease in relative wingtip velocity or kinematic angle of attack. The passive shape change of flexible wings can, however, reduce the changes in the magnitude and direction of aerodynamic forces by the gusts from various directions, except for the downward gust. Such adaptive response of the flexible structure to stabilise the attitude can be classified into the mechanical feedback, which works passively with minimal delay, and is of great importance to the design of bio-inspired flapping wings for micro-air vehicles.     

Saturation-based actuation for flapping MAVs in hovering and forward flight

Stringent weight and size constraints on flapping-wing microair-vehicles dictate minimal actuation. Unfortunately, hovering and forward flight require different wing motions and, as such, independent actuators. Therefore, either a hovering or a forward-flight requirement should be included in the mission and design statements of a flapping-wing microair-vehicle. This work proposes a design for an actuation mechanism that would provide the required kinematics in each flight condition using only one actuator. The idea is to exploit the nonlinear dynamics of the flapping wing to induce the saturation phenomenon. One physical spring in the plunging direction is needed along with a feedback of the plunging angle into the control torque of the actuator in the back and forth flapping direction. By detuning the feedback gains away from the saturation requirement, we obtain the flapping kinematics required for hovering. In contrast, tuning the feedback gains to induce the saturation phenomenon transfers the motion into the plunging direction. Moreover, the actuating torque (in the back and forth flapping direction) would then provide a direct control over the amplitude of the plunging motion, while the amplitude of the actuated flapping motion saturates and does not change as the amplitude of the actuating torque increases.     

Effect of skin flexibility on aerodynamic performance of flexible skin flapping wings for micro air vehicles

Experimental Techniques - As part of the ongoing research on micro air vehicles, the present work focuses on the effect of membrane flexibility on the aerodynamic performance of flexible latex...     

Effects of aspect ratio on flapping wing aerodynamics in animal flight

Morphology as well as kinematics is a critical determinant of performance in flapping flight.To understand the effects of the structural traits on aerodynamics of bioflyers,three rectangular wings with aspect ratios（AR）of1,2,and 4 performing hovering-like sinusoidal kinematics at wingtip based Reynolds number of 5 300 are experimentally investigated.Flow structures on sectional cuts along the wing span are compared.Stronger K-H instability is found on the leading edge vortex of wings with higher aspect ratios.Vortex bursting only appears on the outer spanwise locations of high-aspect-ratio wings.The vortex bursting on high-aspect-ratio wings is perhaps one of the reasons why bio-flyers normally have low-aspect-ratio wings.Quantitative analysis exhibits larger dimensionless circulation of the leading edge vortex（LEV）over higher aspect ratio wings except when vortex bursting happens.The average dimensionless circulation of AR1 and AR2 along the span almost equals the dimensionless circulation at the 50%span.The flow structure and the circulation analysis show that the sinusoidal kinematics suppresses breakdown of the LEV compared with simplified flapping kinematics used in similar studies.The Reynolds number effect results on AR4 show that in the current Re range,the overall flow structure is not sensitive to Reynolds number.     

Experimental study of wings undergoing active root flapping and pitching

This paper presents the results of experiments carried out on mechanical wings undergoing active root flapping and pitching in the wind tunnel. The objective of the work is to investigate the effect of the pitch angle oscillations and wing profile on the aerodynamic forces generated by the wings. The experiments were repeated for a different reduced frequency, airspeed, flapping and pitching kinematics, geometric angle of attack and wing sections (one symmetric and two cambered airfoils). A specially designed mechanical flapper was used, modelled on large migrating birds. It is shown that, under pitch leading conditions, good thrust generation can be obtained at a wide range of Strouhal numbers if the pitch angle oscillation is adjusted accordingly. Consequently, high thrust was measured at both the lowest and highest tested Strouhal numbers. Furthermore, the work demonstrates that the aerodynamic forces can be sensitive to the Reynolds number, depending on the camber of the wings. Under pitch lagging conditions, where the effective angle of attack amplitude is highest, the symmetric wing was affected by the Reynolds number, generating less thrust at the lowest tested Reynolds value. In contrast, under pure flapping conditions, where the effective angle of attack amplitude was lower but still significant, it was the cambered wings that demonstrated Reynolds sensitivity.     

On the aerodynamic characteristics of hovering rigid and flexible hawkmoth-like wings

Insect wings are subjected to fluid, inertia and gravitational forces during flapping flight. Owing to their limited rigidity, they bent under the influence of these forces. Numerical study by Hamamoto et al. (Adv Robot 21(1–2):1–21, 2007) showed that a flexible wing is able to generate almost as much lift as a rigid wing during flapping. In this paper, we take a closer look at the relationship between wing flexibility (or stiffness) and aerodynamic force generation in flapping hovering flight. The experimental study was conducted in two stages. The first stage consisted of detailed force measurement and flow visualization of a rigid hawkmoth-like wing undergoing hovering hawkmoth flapping motion and simple harmonic flapping motion, with the aim of establishing a benchmark database for the second stage, which involved hawkmoth-like wing of different flexibility performing the same flapping motions. Hawkmoth motion was conducted at Re = 7,254 and reduced frequency of 0.26, while simple harmonic flapping motion at Re = 7,800 and 11,700, and reduced frequency of 0.25. Results show that aerodynamic force generation on the rigid wing is governed primarily by the combined effect of wing acceleration and leading edge vortex generated on the upper surface of the wing, while the remnants of the wake vortices generated from the previous stroke play only a minor role. Our results from the flexible wing study, while generally supportive of the finding by Hamamoto et al. (Adv Robot 21(1–2):1–21, 2007), also reveal the existence of a critical stiffness constant, below which lift coefficient deteriorates significantly. This finding suggests that although using flexible wing in micro air vehicle application may be beneficial in term of lightweight, too much flexibility can lead to deterioration in flapping performance in terms of aerodynamic force generation. The results further show that wings with stiffness constant above the critical value can deliver mean lift coefficient almost the same as a rigid wing when executing hawkmoth motion, but lower than the rigid wing when performing a simple harmonic motion. In all cases studied (7,800 ≤ Re ≤ 11,700), the Reynolds number does not alter the force generation significantly.     

Control of flight forces and moments by flapping wings of model bumblebee

The control of flight forces and moments by flapping wings of a model bumblebee is studied using the method of computational fluid dynamics.Hovering flight is taken as the reference flight:Wing kinematic parameters are varied with respect to their values at hovering flight.Moments about(and forces along)x,y,z axes that pass the center of mass are computed.Changing stroke amplitude(or wingbeat frequency)mainly produces a vertical force.Changing mean stroke angle mainly produces a pitch moment.Changing wing angle of attack,when down-and upstrokes have equal change,mainly produces a vertical force,while when down-and upstrokes have opposite changes,mainly produces a horizontal force and a pitch moment.Changing wing rotation timing,when dorsal and ventral rotations have the same timing,mainly produces a vertical force,while when dorsal and ventral rotations have opposite timings,mainly produces a pitch moment and a horizontal force.Changing rotation duration has very small effect on forces and moments.Anti-symmetrically changing stroke amplitude(or wingbeat frequency)of the contralateral wings mainly produces a roll moment.Anti-symmetrically changing angles of attack of the contralateral wings,when down-and upstrokes have equal change,mainly produces a roll moment,while when down-and upstrokes have opposite changes,mainly produces a yaw moment.Anti-symmetrically changing wing rotation timing of the contralateral wings,when dorsal and ventral rotations have the same timing,mainly produces a roll moment and a side force,while when dorsal and ventral rotations have opposite timings,mainly produces a yaw moment.Vertical force and moments about the three axes can be separately controlled by separate kinematic variables.A very fast rotation can be achieved with moderate changes in wing kinematics.     

Characterization of vortical structures and loads based on time-resolved PIV for asymmetric hovering flapping flight

Flight agility, resistance to gusts, capability to hover coupled with a low noise generation might have been some of the reasons why insects are among the oldest species observed in nature. Biologists and aerodynamicists focused on analyzing such flight performances for diverse purposes: understanding the essence of flapping wings aerodynamics and applying this wing concept to the development of micro-air vehicles (MAVs). In order to put into evidence the fundamentally non-linear unsteady mechanisms responsible for the amount of lift generated by a flapping wing (Dickinson et al. in Science 284:1954–1960, 1999), experimental and numerical studies were carried out on typical insect model wings and kinematics. On the other hand, in the recent context of MAVs development, it is of particular interest to study simplified non-biological flapping configurations which could lead to lift and/or efficiency enhancement. In this paper, we propose a parametrical study of a NACA0012 profile undergoing asymmetric hovering flapping motions at Reynolds 1000. On the contrary to normal hovering, which has been widely studied as being the most common configuration observed in the world of insects, asymmetric hovering is characterized by an inclined stroke plane. Besides the fact that the vertical force is hence a combination of both lift and drag (Wang in J Exp Biol 207:1137–1150, 2004), the specificity of such motions resides in the vortex dynamics which present distinct behaviours, whether the upstroke angle of attack leads to a partially attached or a strong separated flow, giving more or less importance to the wake capture phenomenon. A direct consequence of the previous remarks relies on the enhancement of aerodynamic efficiency with asymmetry. If several studies reported results based on the asymmetric flapping motion of dragonfly, only few works concentrated on parametrizing asymmetric motions (e.g. Wang in Phys Rev Lett 85:2216–2219, 2000). The present study relies on TR-PIV measurements which allow determination of the vorticity fields and provide a basis to evaluate the resulting unsteady forces through the momemtum equation approach.     

Aeroelastic study of flexible flapping wings by a coupled lattice Boltzmann-finite element approach with immersed boundary method

In this paper, the behavior of two-dimensional symmetric flapping wings moving in a viscous fluid is investigated. Harmonic motion is applied to idealize flying organisms with flexible wings and extensive testing is carried out to investigate the resultant flight behavior related to the ability to take-off or accelerate the flapping wing system away from a starting location. Special attention is paid to analyze the effect of the main mechanical parameters, as well as the effect of lateral wind on flight performances. Moreover, aiming to investigate the possible benefits of flying in flocks, a couple of synchronously flapping wings is considered in addition to the single arrangement. The numerical simulations are performed by solving the fluid–structure interaction problem through a strongly coupled partitioned approach. Fluid dynamics are modeled at the mesoscopic scale by the lattice Boltzmann method. The resulting macroscopic quantities are derived, as usual, based on the statistical molecular-level interpretation.Wings are modeled by geometrically nonlinear, elastic beam finite elements and structure dynamics is solved by the time discontinuous Galerkin method. Fluid–structure interface conditions are handled using the immersed boundary method. The resultant numerical approach combines simplicity and high computational efficiency. A Monte Carlo simulation strategy is employed to characterize the flight behavior subjected to lateral wind. Various scenarios are discussed.     

Force production and asymmetric deformation of a flexible flapping wing in forward flight

Insect wings usually are flexible and deform significantly under the combined inertial and aerodynamic load. To study the effect of wing flexibility on both lift and thrust production in forward flight, a two-dimensional numerical simulation is employed to compute the fluid–structure interaction of an elastic wing section translating in an inclined stroke plane while pitching around its leading ledge. The effects of the wing stiffness, mass ratio, stroke plane angle, and flight speed are considered. The results show that the passive pitching due to wing deformation can significantly increase thrust while either maintaining lift at the same level or increasing it simultaneously. Another important finding is that even though the wing structure and actuation kinematics are symmetric, chordwise deformation of the wing shows a larger magnitude during upstroke than during downstroke. The asymmetry is more pronounced when the wing has a low mass ratio so that the fluid-induced deformation is significant. Such an aerodynamic cause may serve as an additional mechanism for the asymmetric deformation pattern observed in real insects.     

Computational aerodynamics of low Reynolds number plunging,pitching and flexible wings for MAV applications

Micro air vehicles （MAV＇s） have the potential to revolutionize our sensing and information gathering capabilities in environmental monitoring and homeland security areas. Due to the MAV＇s＇ small size, flight regime, and modes of operation, significant scientific advancement will be needed to create this revolutionary capability. Aerodynamics, structural dynamics, and flight dynamics of natural flyers intersects with some of the richest problems in MAV＇s, inclu- ding massively unsteady three-dimensional separation, transition in boundary layers and shear layers, vortical flows and bluff body flows, unsteady flight environment, aeroelasticity, and nonlinear and adaptive control are just a few examples. A challenge is that the scaling of both fluid dynamics and structural dynamics between smaller natural flyer and practical flying hardware/lab experiment （larger dimension） is fundamentally difficult. In this paper, we offer an overview of the challenges and issues, along with sample results illustrating some of the efforts made from a computational modeling angle.     

Experimental investigation on aerodynamic performance of a flapping wing vehicle in forward flight

The aerodynamic performance of a flexible membrane flapping wing has been investigated here. For this purpose, a flapping-wing system and an experimental set-up were designed to measure the unsteady aerodynamic forces of the flapping wing motion. A one-component force balance was set up to record the temporal variations of aerodynamic forces. The flapping wing was studied in a large low-speed wind tunnel. The lift and thrust of this mechanism were measured for different flapping frequencies, angles of attack and for various wind tunnel velocities. Results indicate that the thrust increases with the flapping frequency. An increase in the wind tunnel speed and flow angle of attack leads to reduction in the thrust value and increases the lift component. The aerodynamic and performance parameters were nondimensionalized. Appropriate models were introduced which show its aerodynamic performance and may be used in the design process and also optimization of the flapping wing.     

Wake patterns of the wings and tail of hovering hummingbirds

The flow fields of slowly flying bats and faster-flying birds differ in that bats produce two vortex loops during each stroke, one per wing, and birds produce a single vortex loop per stroke. In addition, the circulation at stroke transition approaches zero in bats but remains strong in birds. It is unknown if these difference derive from fundamental differences in wing morphology or are a consequence of flight speed. Here, we present an analysis of the horizontal flow field underneath hovering Anna’s hummingbirds (Calypte anna) to describe the wake of a bird flying at zero forward velocity. We also consider how the hummingbird tail interacts with the wake generated by the wings. High-speed image recording and analysis from three orthogonal perspectives revealed that the wing tips reach peak velocities in the middle of each stroke and approach zero velocity at stroke transition. Hummingbirds use complex tail kinematic patterns ranging from in phase to antiphase cycling with respect to the wings, covering several phase shifted patterns. We employed particle image velocimetry to attain detailed horizontal flow measurements at three levels with respect to the tail: in the tail, at the tail tip, and just below the tail. The velocity patterns underneath the wings indicate that flow oscillates along the ventral–dorsal axis in response to the down- and up-strokes and that the sideways flows with respect to the bird are consistently from the lateral to medial. The region around the tail is dominated by axial flows in dorsal to ventral direction. We propose that these flows are generated by interaction between the wakes of the two wings at the end of the upstroke, and that the tail actively defects flows to generate moments that contribute to pitch stability. The flow fields images also revealed distinct vortex loops underneath each wing, which were generated during each stroke. From these data, we propose a model for the primary flow structures of hummingbirds that more strongly resembles the bat model. Thus, pairs of unconnected vortex loops may be shared features of different animals during hovering and slow forward flight.     

The effect of phase angle and wing spacing on tandem flapping wings

In a tandem wing configuration, the hindwing often operates in the wake of the forewing and, hence, its performance is affected by the vortices shed by the forewing. Changes in the phase angle between the flapping motions of the fore and the hind wings, as well as the spacing between them, can affect the resulting vortex/wing and vortex/vortex interactions. This study uses 2D numerical simulations to investigate how these changes affect the leading dege vortexes (LEV) generated by the hindwing and the resulting effect on the lift and thrust coefficients as well as the efficiencies. The tandem wing configuration was simulated using an incompressible Navier-Stokes solver at a chord-based Reynolds number of 5 000. A harmonic single frequency sinusoidal oscillation consisting of a combined pitch and plunge motion was used for the flapping wing kinematics at a Strouhal number of 0.3. Four different spacings ranging from 0.1 chords to 1 chord were tested at three different phase angles, 0°, 90° and 180°. It was found that changes in the spacing and phase angle affected the timing of the interaction between the vortex shed from the forewing and the hindwing. Such an interaction affects the LEV formation on the hindwing and results in changes in aerodynamic force production and efficiencies of the hindwing. It is also observed that changing the phase angle has a similar effect as changing the spacing. The results further show that at different spacings the peak force generation occurs at different phase angles, as do the peak efficiencies.     

Effects of mass and chordwise flexibility on 2D self-propelled flapping wings

A self-propelled flexible flapping wing 2D numerical model undergoing a combined pitching and heaving motion is presented. Since such freely moving foil experiences zero net thrust, a definition of efficiency for this kind of problem is proposed and discussed against other formulations found in the literature. It is also shown that the deviation motion of wings such as that found in natural flyers is likely a consequence of the fluid–structure dynamics of the wings. The passive deviation motion observed in numerical simulations is either a consequence of a feathering mechanism referred to as rigid feathering or of the inertial displacement caused by the wing deformation. The effects of flexibility on the performance of the wing are also presented. It is found that flexibility may significantly enhance the efficiency in pressure-driven deformation cases. The rigid feathering mechanism is found to have an effect similar to that of the feathering caused by wing flexibility on the performances of pressure-driven deformation cases.