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.     

Aerodynamics and mechanisms of elementary morphing models for flapping wing in forward flight of bat

Large active wing deformation is a significant way to generate high aerodynamic forces required in bat's flapping flight. Besides the twisting, elementary morphing models of a bat wing are proposed, including wing-bending in the spanwise direction, wing-cambering in the chordwise direction, and wing area-changing. A plate of aspect ratio 3 is used to model a bat wing, and a three-dimensional unsteady panel method is used to predict the aerodynamic forces. It is found that the cambering model has great positive influence on the lift, followed by the area-changing model and then the bending model. Further study indicates that the vortex control is a main mechanism to produce high aerodynamic forces. The mechanisms of aerodynamic force enhancement are asymmetry of the cambered wing and amplification effects of wing area-changing and wing bending. Lift and thrust are generated mainly during downstroke, and they are almost negligible during upstroke by the integrated morphing model-wing.     

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.     

The influence of the wake of a flapping wing on the production of aerodynamic forces

The effect of the wake of previous strokes on the aerodynamic forces of a flapping model insect wing is studied using the method of computational fluid dynamics. The wake effect is isolated by comparing the forces and flows of the starting stroke (when the wake has not developed) with those of a later stroke (when the wake has developed). The following has been shown. (1) The wake effect may increase or decrease the lift and drag at the beginning of a half-stroke (downstroke or upstroke), depending on the wing kinematics at stroke reversal. The reason for this is that at the beginning of the half-stroke, the wing ``impinges' on the spanwise vorticity generated by the wing during stroke reversal and the distribution of the vorticity is sensitive to the wing kinematics at stroke reversal. (2) The wake effect decreases the lift and increases the drag in the rest part of the half-stroke. This is because the wing moves in a downwash field induced by previous half-stroke's starting vortex, tip vortices and attached leading edge vortex (these vortices form a downwash producing vortex ring). (3) The wake effect decreases the mean lift by 6%–18% (depending on wing kinematics at stroke reversal) and slightly increases the mean drag. Therefore, it is detrimental to the aerodynamic performance of the flapping wing. The project supported by the National Natural Science Foundation of China (10232010) and the National Aeronautic Science Fund of China(03A51049) The English text was polished by Xing Zhang     

Numerical simulation of a flapping four-wing micro-aerial vehicle

A three-dimensional numerical simulation of a four-wing (two wings on each side, one on top of another) flapping micro-aerial vehicle (FMAV), known as the Delfly micro, is performed using an immersed boundary method Navier–Stokes finite volume solver at Reynolds numbers of 5500 (forward flight condition). The objective of the present investigation is to gain an insight to the aerodynamics of flapping wing biplane configuration, by making an analysis on a geometry that is simplified, yet captures the major aspects of the wing behavior. The fractional step method is used to solve the Navier–Stokes equations. Results show that in comparison to the Delfly II flapping kinematics (a similar FMAV configuration but smaller flapping stroke angles), the Delfly-Micro flapping kinematics provides more thrust while maintaining the same efficiency. The Delfly-Micro biplane configuration generates more lift than expected when the inclination angle increases, due to the formation of a uniform leading edge vortex. Estimates of the lift produced in the forward flight conditions confirm that in the current design, the MAV is able to sustain forward flight. The potential effect of wing flexibility on the aerodynamic performance in the biplane configuration context is investigated through prescribed flexibility in the simulations. Increasing the wing׳ spanwise flexibility increases thrust but increasing chordwise flexibility causes thrust to first increase and then decrease. Moreover, combining both spanwise and chordwise flexibility outperforms cases with only either spanwise or chordwise flexibility.     

Aerodynamic force and flow structures of two airfoils in flapping motions

Aerodynamic force and flow structures of two airfoils in a tandem configuration in flapping motions are studied, by solving the Navier-Stokes equations in moving overset grids. Three typical phase differences between the fore- and aftairfoil flapping cycles are considered. It is shown that: (1) in the case of no interaction (single airfoil), the time average of the vertical force coefficient over the downstroke is 2.74, which is about 3 times as large as the maximum steady-state lift coefficient of a dragonfly wing; the time average of the horizontal force coefficient is 1.97, which is also large. The reasons for the large force coefficients are the acceleration at the beginning of a stroke, the delayed stall and the “pitching-up” motion near the end of the stroke. (2) In the cases of two-airfoils, the time-variations of the force and moment coefficients on each airfoil are broadly similar to that of the single airfoil in that the vertical force is mainly produced in downstroke and the horizontal force in upstroke, but very large differences exist due to the interaction. (3) For in-phase stroking, the major differences caused by the interaction are that the vertical force on FA in downstroke is increased and the horizontal force on FA in upstroke decreased. As a result, the magnitude of the resultant force is almost unchanged but it inclines less forward. (4) For counter stroking, the major differences are that the vertical force on AA in downstroke and the horizontal force on FA in upstroke are decreased. As a result, the magnitude of the resultant force is decreased by about 20 percent but its direction is almost unchanged. (5) For 90°-phase-difference stroking, the major differences are that the vertical force on AA in downstroke and the horizontal force on FA in upstroke are decreased greatly and the horizontal force on AA in upstroke increased. As a result, the magnitude of the resultant force is decreased by about 28% and it inclines more forward. (6) Among the three cases of phase angles, inphase flapping produces the largest vertical force (also the largest resultant force); the 90°-phase-difference flapping results in the largest horizontal force, but the smallest resultant force.     

The aerodynamic forces and pressure distribution of a revolving pigeon wing

The aerodynamic forces acting on a revolving dried pigeon wing and a flat card replica were measured with a propeller rig, effectively simulating a wing in continual downstroke. Two methods were adopted: direct measurement of the reaction vertical force and torque via a forceplate, and a map of the pressures along and across the wing measured with differential pressure sensors. Wings were tested at Reynolds numbers up to 108,000, typical for slow-flying pigeons, and considerably above previous similar measurements applied to insect and hummingbird wing and wing models. The pigeon wing out-performed the flat card replica, reaching lift coefficients of 1.64 compared with 1.44. Both real and model wings achieved much higher maximum lift coefficients, and at much higher geometric angles of attack (43°), than would be expected from wings tested in a windtunnel simulating translating flight. It therefore appears that some high-lift mechanisms, possibly analogous to those of slow-flying insects, may be available for birds flapping with wings at high angles of attack. The net magnitude and orientation of aerodynamic forces acting on a revolving pigeon wing can be determined from the differential pressure maps with a moderate degree of precision. With increasing angle of attack, variability in the pressure signals suddenly increases at an angle of attack between 33° and 38°, close to the angle of highest vertical force coefficient or lift coefficient; stall appears to be delayed compared with measurements from wings in windtunnels.     

Unsteady aerodynamic forces and power requirements of a bumblebee in forward flight

Aerodynamic forces and power requirements in forward flight in a bumblebee (Bombus terrestris) were studied using the method of computational fluid dynamics. Actual wing kinematic data of free flight were used in the study (the speed ranges from 0 m/s to 4.5 m/s; advance ratio ranges from 0–0.66). The bumblebee employs the delayed stall mechanism and the fast pitching-up rotation mechanism to produce vertical force and thrust. The leading-edge vortex does not shed in the translatory phase of the half-strokes and is much more concentrated than that of the fruit fly in a previous study. At hovering and low-speed flight, the vertical force is produced by both the half-strokes and is contributed by wing lift; at medium and high speeds, the vertical force is mainly produced during the downstroke and is contributed by both wing lift and wing drag. At all speeds the thrust is mainly produced in the upstroke and is contributed by wing drag. The power requirement at low to medium speeds is not very different from that of hovering and is relatively large at the highest speed (advance ratio 0.66), i.e. the power curve is J-shaped. Except at the highest flight speed, storing energy elastically can save power up to 20%–30%. At the highest speed, because of the large increase of aerodynamic torque and the slight decrease of inertial torque (due to the smaller stroke amplitude and stroke frequency used), the power requirement is dominated by aerodynamic power and the effect of elastic storage of energy on power requirement is limited.The project supported by the National Natural Science Foundation of China (10232010) and the National Aeronautic Science fund of China (03A51049)The English text was polished by Xing Zhang.     

Aerodynamic mechanism of forces generated by twisting model-wing in bat flapping flight

The aerodynamic mechanism of the bat wing membrane Mong the lateral border of its body is studied. The twist-morphing that alters the angle of attack （AOA） along the span-wise direction is observed widely during bat flapping flight. An assumption is made that the linearly distributed AOA is along the span-wise direction. The plate with the aspect ratio of 3 is used to model a bat wing. A three-dimensional （3D） unsteady panel method is used to predict the aerodynamic forces generated by the flapping plate with leading edge separation. It is found that, relative to the rigid wing flapping, twisting motion can increase the averaged lift by as much as 25% and produce thrust instead of drag. Furthermore, the aerodynamic forces （lift/drag） generated by a twisting plate-wing are similar to those of a pitching rigid-wing, meaning that the twisting in bat flight has the same function as the supination/pronation motion in insect flight.     

Wing kinematics measurement and aerodynamics of free-flight maneuvers in drone-flies

The time courses of wing and body kinematics of two free-flying drone-flies, as they performed saccades, were measured using 3D high-speed video, and the morpho- logical parameters of the wings and body of the insects were also measured. The measured wing kinematics was used in a Navier-Stokes solver to compute the aerodynamic forces and moments acting on the insects. The main results are as following. （1） The turn is mainly a 90° change of heading. It is made in about 10 wingbeats （about 55 ms）. It is of interest to note that the number of wingbeats taken to make the turn is approximately the same as and the turning time is only a little different from that of fruitflies measured recently by the same approach, even if the weight of the droneflies is more than 100 times larger than that of the fruitflies. The long axis of body is about 40° from the horizontal during the maneuver. （2） Although the body rotation is mainly about a vertical axis, a relatively large moment around the yaw axis （axis perpendicular to the long axis of body）, called as yaw moment, is mainly needed for the turn, because moment of inertial of the body about the yaw axis is much larger than that about the long axis. （3） The yaw moment is mainly pro- duced by changes in wing angles of attack： in a right turn, for example, the dronefly lets its right wing to have a rather large angle of attack in the downstroke （generally larger than 50°） and a small one in the upstroke to start the turn, and lets its left wing to do so to stop the turn, unlike the fruitflies who generate the yaw moment mainly by changes in the stroke plane and stroke amplitude.     

柔性扑翼的气动特性研究

以往扑翼的气动力计算研究都很少考虑扑翼的柔性,而在鸟的扑翼动作中,在外加气动力和鸟自身的扑动力作用下,扑翼的柔性变形相当大。本文在原有匀速刚性模型的基础上,提出考虑了扑翼扑动速率变化和形状变化的扑翼分析模型,使之更接近鸟翼柔性扑动真实情况。通过计算分析气动特性发现,控制适当的话,柔性变形能大大改善扑翼的气动性能。本文通过模拟鸟扑翼的柔性运动,计算了时柔性扑翼气动力以及平均升力系数和平均推力系数随着扑动角、倾斜角等参数变化的情况,从而从气动的角度解释了为什么鸟在不同的飞行阶段扑翼规律各不相同,并为柔性扑翼飞行器的设计提供了理论依据。     

Measurement of Thrust and Lift Forces Associated With Drag of Compliant Flapping Wing for Micro Air Vehicles Using a New Test Stand Design

Compliant wing designs have the potential of improving flapping wing Micro-Air Vehicles (MAVs). Designing compliant wings requires a detailed understanding of the effect of compliance on the generation of thrust and lift forces. The low force and high-frequency measurements associated with these forces necessitated a new versatile test stand design that uses a 250 g load cell along with a rigid linear air bearing to minimize friction and the dynamic behavior of the test stand while isolating only the stationary thrust or lift force associated with drag generated by the wing. Moreover, this stand is relatively inexpensive and hence can be easily utilized by wing designers to optimize the wing compliance and shape. The frequency response of the wing is accurately resolved, along with wing compliance on the thrust and lift profiles. The effects of the thrust and lift force generated as a function of flapping frequency were also determined. A semi-empirical aerodynamic model of the thrust and lift generated by the flapping wing MAV on the new test stand was developed and used to evaluate the measurements. This model accounted for the drag force and the effects of the wing compliance. There was good correlation between the model predictions and experimental measurements. Also, the increase in average thrust due to increased wing compliance was experimentally quantified for the first time using the new test stand. Thus, our measurements for the first time reveal the detrimental influence of excessive compliance on drag forces during high frequency operation. In addition, we were also able to observe the useful effect of compliance on the generation of extra thrust at the beginning and end of upstrokes and downstrokes of the flapping motion.     

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.     

Forward flight of a model butterfly: Simulation by equations of motion coupled with the Navier-Stokes equations

The forward flight of a model butterfly was studied by simulation using the equations of motion coupled with the Navier-Stokes equations. The model butterfly moved under the action of aerodynamic and gravitational forces, where the aerodynamic forces were generated by flapping wings which moved with the body, allowing the body oscillations of the model butterfly to be simulated. The main results are as follows: (1) The aerodynamic force produced by the wings is approximately perpendicular to the long-axis of body and is much larger in the downstroke than in the upstroke. In the downstroke the body pitch angle is small and the large aerodynamic force points up and slightly backward, giving the weight-supporting vertical force and a small negative horizontal force, whilst in the upstroke, the body angle is large and the relatively small aerodynamic force points forward and slightly downward, giving a positive horizontal force which overcomes the body drag and the negative horizontal force generated in the downstroke. (2) Pitching oscillation of the butterfly body plays an equivalent role of the wing-rotation of many other insects. (3) The body-massspecific power of the model butterfly is 33.3 W/kg, not very different from that of many other insects, e.g., fruitflies and dragonflies.     

扑翼柔性及其对气动特性的影响

以往对扑翼气动特性的研究基本上都是基于简单的匀速刚性模型,但是通过大量观察不同飞鸟的扑翼动作发现,该模型与鸟翼的实际扑动还有很大差别。鸟翼不但上扑段和下扑段所需时间不同,而且在扑动过程中,鸟翼的形状无论沿弦向或展向都存在着相当大的柔性变形。本文在原有匀速刚性模型的基础上,加入了扑动速率变化和形状变化的影响,得出新的变速柔性扑翼分析模型,使之更接近鸟翼柔性扑动的真实情况。通过对比计算发现,柔性变形对扑翼的升力与推力都有着显著影响,如果控制得当,柔性变形能大大改善扑翼的气动性能。     

微型飞行器低雷诺数空气动力学

微型飞行器(MAVs)设计绝不是常规飞行器在尺度上的简单缩小,面临许多技术难题.其中微型飞行器低雷诺数空气动力学是其最为根本的技术瓶颈之一,也是当前受到广泛关注的热点之一.本文紧密结合微型飞行器技术,对这一领域中所面临的低雷诺数空气动力学问题和近两年来该方向国内一些新的进展进行了较为详细的介绍.按照MAVs飞行方式和结构特性进行分类,简单介绍微型飞行器研究中的低$Re$数空气动力学问题.首先介绍了二维和三维固定翼低雷诺数空气动力学问题:包括层流分离泡,翼型升力系数小攻角非线性效应,静态迟滞效应,以及低$Re$数小展弦比机翼气动特性.第2,介绍了拍动翼低雷诺数空气动力学方面的研究工作.包括前人提出的昆虫低$Re$数下获得高升力的多种非定常拍动翼飞行机制:Wagner效应、Weis-Fogh效应(clap-and-fling)、延迟失速效应(delayedstall)、Kramer效应(rotational forces)、尾迹捕获效应(wakecapture)、附加质量效应(addedmass)等.以及国内学者近几年在拍动翼方面取得的一些研究成果.第3,介绍了柔性翼低雷诺数气动问题.研究表明柔性翼对于固定翼微型飞行器提高抗阵风能力,拍动翼微型飞行器产生足够的升力和推力.最后简单介绍了可变形翼(morphingwing)微型飞行器方面的一些研究工作,指出微型飞行器技术可以通过采用可变形翼设计,突破众多的技术瓶颈.另一方面,可变形翼概念可以通过在低成本,低速的MAVs上进行飞行试验,获得非常好的验证平台.      

Structural Analysis of a Dragonfly Wing

Dragonfly wings are highly corrugated, which increases the stiffness and strength of the wing significantly, and results in a lightweight structure with good aerodynamic performance. How insect wings carry aerodynamic and inertial loads, and how the resonant frequency of the flapping wings is tuned for carrying these loads, is however not fully understood. To study this we made a three-dimensional scan of a dragonfly (Sympetrum vulgatum) fore- and hindwing with a micro-CT scanner. The scans contain the complete venation pattern including thickness variations throughout both wings. We subsequently approximated the forewing architecture with an efficient three-dimensional beam and shell model. We then determined the wing’s natural vibration modes and the wing deformation resulting from analytical estimates of 8 load cases containing aerodynamic and inertial loads (using the finite element solver Abaqus). Based on our computations we find that the inertial loads are 1.5 to 3 times higher than aerodynamic pressure loads. We further find that wing deformation is smaller during the downstroke than during the upstroke, due to structural asymmetry. The natural vibration mode analysis revealed that the structural natural frequency of a dragonfly wing in vacuum is 154 Hz, which is approximately 4.8 times higher than the natural flapping frequency of dragonflies in hovering flight (32.3 Hz). This insight in the structural properties of dragonfly wings could inspire the design of more effective wings for insect-sized flapping micro air vehicles: The passive shape of aeroelastically tailored wings inspired by dragonflies can in principle be designed more precisely compared to sail like wings —which can make the dragonfly-like wings more aerodynamically effective.     

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.     

Propulsion velocity of a flapping wing at low Reynolds number

This paper presents a computational fluid–structure interaction analysis for free movements with a flapping wing in a quiescent fluid. We demonstrated the moving velocity of a flapping wing according to the phase difference between the angle of attack and the positional angle in the case of a fruit fly with a Reynolds number of 136. If we considered the moving velocity of the flapping wing, the physics were different from that of hovering flight of previous studies, which did not consider the propulsive velocity and presented the advanced rotation of the angle of attack as the best mechanism for propulsion force, as compared to symmetric rotation and delayed rotation. We found that symmetric rotation produced a better propulsion velocity with less fluctuation in other direction than the advanced rotation. The hairpin vortex generated at the end of a stroke did not clearly contribute to the enhancement of propulsion; the wake capture is considered to be one of the main enhancements of the advanced rotation in a previous studies. We studied the effects of the angle of attack to determine why the fruit fly uses a large angle of attack during a constant angle of attack period. Larger angles of attack produced greater propulsion velocities. Further, larger angles of attack did not generate greater peak force during the rotation of the angle of attack at the reversal of stroke, but they produced less fluctuation at the reversal of the stroke and greater force during the constant angle of attack period.