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.     

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。     

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。     

Influence of wing flexibility on the aerodynamic performance of a tethered flapping bumblebee

The sophisticated structures of flapping insect wings make it challenging to study the role of wing flexibility in insect flight. In this study, a mass-spring system is used to model wing structural dynamics as a thin, flexible membrane supported by a network of veins. The vein mechanical properties can be estimated based on their diameters and the Young's modulus of cuticle. In order to analyze the effect of wing flexibility, the Young's modulus is varied to make a comparison between two different wing models that we refer to as flexible and highly flexible. The wing models are coupled with a pseudo-spectral code solving the incompressible Navier–Stokes equations, allowing us to investigate the influence of wing deformation on the aerodynamic efficiency of a tethered flapping bumblebee. Compared to the bumblebee model with rigid wings, the one with flexible wings flies more efficiently, characterized by a larger lift-to-power ratio.     

Aerodynamic and functional consequences of wing compliance

A growing body of evidence indicates that a majority of insects experience some degree of wing deformation during flight. With no musculature distal to the wing base, the instantaneous shape of an insect wing is dictated by the interaction of aerodynamic forces with the inertial and elastic forces that arise from periodic accelerations of the wing. Passive wing deformation is an unavoidable feature of flapping flight for many insects due to the inertial loads that accompany rapid stroke reversals—loads that well exceed the mean aerodynamic force. Although wing compliance has been implicated in a few lift-enhancing mechanisms (e.g., favorable camber), the direct aerodynamic consequences of wing deformation remain generally unresolved. In this paper, we present new experimental data on how wing compliance may affect the overall induced flow in the hawkmoth, Manduca sexta. Real moth wings were subjected to robotic actuation in their dominant plane of rotation at a natural wing beat frequency of 25 Hz. We used digital particle image velocimetry at exceptionally high temporal resolution (2,100 fps) to assess the influence of wing compliance on the mean advective flows, relying on a natural variation in wing stiffness to alter the amount of emergent deformation (freshly extracted wings are flexible and exhibit greater compliance than those that are desiccated). We find that flexible wings yield mean advective flows with substantially greater magnitudes and orientations more beneficial to lift than those of stiff wings. Our results confirm that wing compliance plays a critical role in the production of flight forces. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

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.     

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.     

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.     

仿生扑翼飞行机器人翅型的研制与实验研究

模仿昆虫和小鸟飞行的扑翼飞行机器人将举升、悬停和推进功能集于一个扑翼系统,与固定翼和旋翼完全不同,因此研究只能从生物仿生开始。生物飞行的极端复杂性使得进行完整和精确的扑翼飞行分析非常复杂,因此本文在仿生学进展基础上,通过一些合适的假设和简化,建立了仿生翅运动学和空气动力学模型,并以此为基础研制了多种翅型。研制了气动力测量实验平台,对各种翅型进行了实验研究。实验结果表明,研制的翅型都能产生一定的升力,其中柔性翅具有较好的运动性能和气动性能,并且拍动频率和拍动幅度对升力有较大影响。     

Experimental study on interaction of aerodynamics with flexible wings of flapping vehicles in hovering and cruise flight

Flapping wings are promising lift and thrust generators, especially for very low Reynolds numbers. To investigate aeroelastic effects of flexible wings (specifically, wing’s twisting stiffness) on hovering and cruising aerodynamic performance, a flapping-wing system and an experimental setup were designed and built. This system measures the unsteady aerodynamic and inertial forces, power usage, and angular speed of the flapping wing motion for different flapping frequencies and for various wings with different chordwise flexibility. Aerodynamic performance of the vehicle for both no wind (hovering) and cruise condition was investigated. Results show how elastic deformations caused by interaction of inertial and aerodynamic forces with the flexible structure may affect specific power consumption. This information was used here to find a more suitable structural design. The best selected design in our tests performs up to 30% better than others (i.e., less energy consumption for the same lift or thrust generation). This measured aerodynamic information could also be used as a benchmarking data for unsteady flow solvers.     

Effects of camber angle on aerodynamic performance of flapping-wing micro air vehicle

This study investigates the unsteady aerodynamic characteristics of the cambered wings of a flapping-wing micro air vehicle (FW-MAV) in hover. A three-dimensional fluid–structure interaction solver is developed for a realistic modeling of large-deforming wing structure and geometry. Cross-validation is conducted against the experimental results obtained also in the present study to establish more accurate analyses of cambered wings. An investigation is carried out on the unsteady vortex structures around the wings caused by the passive twisting motion. A parametric study is then conducted to evaluate the aerodynamic performance with respect to the camber angle at three different flapping frequencies including normal operating conditions. The camber angles producing the largest thrust and highest propulsive efficiency are estimated at each flapping frequency, and their effects on aerodynamic performance are analyzed in terms of the stroke phase. The timing and magnitude of the passive twisting motion, which are dependent on the camber angle at the operating frequency, greatly affects the unsteady vortex structure. Consequently, the camber angle designed at the operating frequency plays a key role in enhancing the aerodynamic performance of FW-MAVs.     

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.     

昆虫飞行的高升力机理

对近年来关于昆虫产生非定常高升力的研究进行了综述和归纳.这方面的工作对生物学研究和微型飞行器等微型机械的仿生设计有重要意义.研究表明:果蝇等昆虫翅膀的拍动运动可产生很大的非定常升力,其平均值是定常值的2~3倍,足够平衡昆虫的重量,并有较大的富余用于机动飞行;产生高升力有三个因素:一是拍动开始阶段翅的快速加速运动,二是拍动中的不失速机制,三是拍动结束阶段翅的快速上仰运动.人们从能耗的角度考察了这些非定常高升力机制的正确性和可行性.当作悬停飞行的果蝇用以上机制产生平衡其重量的升力时,其比功率(支持单位身体质量所需的功率)约为29W/kg, 生化/机械效率约为17%. 这些值与人们基于对昆虫肌肉力学特性的研究所预估的值接近.果蝇前飞时,其比功率随速度变化的曲线是一J形曲线,而不是象飞机或鸟的那样是一U形曲线;这与人们基于昆虫新陈代谢率的测量数据所推断的结果一致.对于蜻蜒等(功能上)有前、后两对翅膀的昆虫,有以下初步结果:翅的下拍主要产生升力,上挥主要产生推力;下拍时的平均升力系数可达2~3,十分大,上挥时的平均推力系数可达1~2, 也很大,它们主要由非定常效应产生;前、后翅的相互干扰并未起增大升力和推力的作用,反而有一定的不利作用.      

昆虫拍翼方式的非定常流动物理再探讨

基于提出的理论模化方法来探讨昆虫拍翼方式的非定常流动物理. 以悬停飞行为 例,通过对拍翼运动的分析,不仅解释了昆虫利用高频拍翼的方式为何能够克服低雷诺数带 来的气动局限性(St \gg 1/Re),而且还指出高升力产生和调节的3个流动 控制因素：(1) 由于拍翼的变速运动即时引起了流体动力响应,这种附加惯性效应 可产生瞬时的高升力; (2) 保持前缘涡不脱离翼面有助于减少升力的下降; (3) 增大后缘涡的强度并加速其脱离后缘能够有效地提高升力.     

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.     

昆虫飞行的空气动力学

昆虫是最早出现、数量最多和体积最小的飞行者. 它们能悬停、跃升、急停、快速加速和转弯, 飞行技巧十分高超. 由于尺寸小, 因而翅膀的相对速度很小, 从而进行上述飞行所需的升力系数很大. 但昆虫翅膀的雷诺数又很低. 它们是如何在低雷诺数下产生高升力的, 是流体力学和生物学工作者都十分关心的问题. 近年来这一领域有了许多研究进展. 该文对这些进展进行综述, 并对今后工作提一些建议. 因2005 年前的工作已在几篇综述文章有了详细介绍, 该文主要介绍2005 年以来的工作. 首先简述昆虫翅的拍动运动及昆虫绕流的基本方程和相似参数; 然后对2005 年之前的工作做一简要回顾. 之后介绍2005 年后的进展, 依次为: 运动学观测; 前缘涡; 翅膀柔性变形及皱褶的影响; 拍动翅的尾涡结构; 翼/身、左右翅气动干扰及地面效应; 微小昆虫; 蝴蝶与蜻蜓; 机动飞行. 最后为对今后工作的建议.      

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.     

A parametric investigation of the propulsion of 2D chordwise-flexible flapping wings at low Reynolds number using numerical simulations

This paper presents a numerical investigation of the effects of chordwise flexibility on flapping wings at low Reynolds number. The numerical simulations are performed with a partitioned fluid–structure interaction algorithm using artificial compressibility stabilization. The choice of the structural dimensionless parameters is based on scaling arguments and is compared against parameters used by other authors. The different regimes, namely inertia-driven and pressure-driven wing deformations, are presented along with their effects on the topology of the flow and on the performance of a heaving and pitching flapping wing in propulsion regime. It is found that pressure-driven deformations can significantly increase the thrust efficiency if a suitable amount of flexibility is used. Significant thrust increases are also observed in zero pitching amplitude cases. The effects of the second and third deformation modes on the performances of pressure-driven deformation cases are discussed. On the other hand, inertia-driven deformations generally deteriorate aerodynamic performances of flapping wings unless the behavior of the wing deformation is modified by the presence of sustainable superharmonics in a way that produces slight improvements. It is also shown that wing flexibility can act as an efficient passive pitching mechanism that allows fair thrust and better efficiency to be achieved when compared to a rigid pitching–heaving wing.     

Reduced coupled flapping wing-fluid computational model with unsteady vortex wake

Insect flight research is propelled by their unmatched flight capabilities. However, complex underlying aerodynamic phenomena make computational modeling of insect-type flapping flight a challenging task, limiting our ability in understanding insect flight and producing aerial vehicles exploiting same aerodynamic phenomena. To this end, novel mid-fidelity approach to modeling insect-type flapping vehicles is proposed. The approach is computationally efficient enough to be used within optimal design and optimal control loops, while not requiring experimental data for fitting model parameters, as opposed to widely used quasi-steady aerodynamic models. The proposed algorithm is based on Helmholtz–Hodge decomposition of fluid velocity into curl-free and divergence-free parts. Curl-free flow is used to accurately model added inertia effects (in almost exact manner), while expressing system dynamics by using wing variables only, after employing symplectic reduction of the coupled wing-fluid system at zero level of vorticity (thus reducing out fluid variables in the process). To this end, all terms in the coupled body-fluid system equations of motion are taken into account, including often neglected terms related to the changing nature of the added inertia matrix (opposed to the constant nature of rigid body mass and inertia matrix). On the other hand—in order to model flapping wing system vorticity effects—divergence-free part of the flow is modeled by a wake of point vortices shed from both leading (characteristic for insect flight) and trailing wing edges. The approach is evaluated for a numerical case involving fruit fly hovering, while quasi-steady aerodynamic model is used as benchmark tool with experimentally validated parameters for the selected test case. The results indicate that the proposed approach is capable of mid-fidelity accurate calculation of aerodynamic loads on the insect-type flapping wings.