Hummingbird wing efficacy depends on aspect ratio and compares with helicopter rotors

Hummingbirds are the only birds that can sustain hovering. This unique flight behaviour comes, however, at high energetic cost. Based on helicopter and aeroplane design theory, we expect that hummingbird wing aspect ratio (AR), which ranges from about 3.0 to 4.5, determines aerodynamic efficacy. Previous quasi-steady experiments with a wing spinner set-up provide no support for this prediction. To test this more carefully, we compare the quasi-steady hover performance of 26 wings, from 12 hummingbird taxa. We spun the wings at angular velocities and angles of attack that are representative for every species and measured lift and torque more precisely. The power (aerodynamic torque × angular velocity) required to lift weight depends on aerodynamic efficacy, which is measured by the power factor. Our comparative analysis shows that AR has a modest influence on lift and drag forces, as reported earlier, but interspecific differences in power factor are large. During the downstroke, the power required to hover decreases for larger AR wings at the angles of attack at which hummingbirds flap their wings (p < 0.05). Quantitative flow visualization demonstrates that variation in hover power among hummingbird wings is driven by similar stable leading edge vortices that delay stall during the down- and upstroke. A side-by-side aerodynamic performance comparison of hummingbird wings and an advanced micro helicopter rotor shows that they are remarkably similar.     

On the quasi-steady aerodynamics of normal hovering flight part I: the induced power factor

An analytical treatment to quantify the losses captured in the induced power factor, k, is provided for flapping wings in normal hover, including the effects of non-uniform downwash, tip losses and finite flapping amplitude. The method is based on a novel combination of actuator disc and lifting line blade theories that also takes into account the effect of advance ratio. The model has been evaluated against experimental results from the literature and qualitative agreement obtained for the effect of advance ratio on the lift coefficient of revolving wings. Comparison with quantitative experimental data for the circulation as a function of span for a fruitfly wing shows that the model is able to correctly predict the circulation shape of variation, including both the magnitude of the peak circulation and the rate of decay in circulation towards zero. An evaluation of the contributions to induced power factor in normal hover for eight insects is provided. It is also shown how Reynolds number can be accounted for in the induced power factor, and good agreement is obtained between predicted span efficiency as a function of Reynolds number and numerical results from the literature. Lastly, it is shown that for a flapping wing in hover k owing to the non-uniform downwash effect can be reduced to 1.02 using an arcsech chord distribution. For morphologically realistic wing shapes based on beta distributions, it is shown that a value of 1.07 can be achieved for a radius of first moment of wing area at 40% of wing length.     

柔性扑翼气动性能的数值研究

国内外对扑翼飞行的气动特性进行了大量研究,这些研究大多基于简谐扑动的刚性翼,然而大量观察发现鸟或昆虫飞行时,翅膀存在明显的柔性变形,这种变形对其气动性能具有显著的影响。该文针对一简化的二维柔性扑翼模型,采用数值求解N-S方程并耦合扑翼柔性变形方程的计算方法,研究了扑翼柔性变形对其气动性能的影响。结果显示扑翼的柔性变形改变了扑翼周围的涡结构,从而影响扑翼的气动性能;适当的柔性变形能延迟前缘涡的脱落,从而有效地改善扑翼的推进效率,但同时减弱了扑翼在低雷诺数环境中产生高升力的尾迹捕捉机制。     

Effect of flapping kinematics on aerodynamic force of a flapping two-dimensional flat plate

Potential applications of flapping-wing micro-aerial vehicles (MAVs) have prompted enthusiasm among the engineers and researchers to understand the flow physics associated with flapping flight. An incompressible Navier–Stokes solver that is capable of handling flapping flight kind of moving boundary problem is developed. Arbitrary Lagrangian–Eulerian (ALE) method is used to handle the moving boundaries of the problem. The solver is validated with the results of problems like inline oscillation of a circular cylinder in still fluid and a flat plate rapidly accelerating at constant angle of attack. Numerical simulations of flapping flat plate mimicking the kinematics of those like insect wings are simulated, and the unsteady fluid dynamic phenomena that enhance the aerodynamic force are studied. The solution methodology provides the velocity field and pressure field details, which are used to derive the force coefficients and the vorticity field. Time history of force coefficients and vortical structures gives insight into the unsteady mechanism associated with the unsteady aerodynamic force production. The scope of the work is to develop a computational fluid dynamic (CFD) solver with the ALE method that is capable of handling moving boundary problems, and to understand the flow physics associated with the flapping-wing aerofoil kinematics and flow parameters on aerodynamic forces. Results show that delayed stall, wing–wake interaction and rotational effect are the important unsteady mechanisms that enhance the aerodynamic forces. Major contribution to the lift force is due to the presence of leading edge vortex in delayed stall mechanism.     

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

In the analysis of flexible flapping wings of insects, the aerodynamic outcome depends on the combined structural dynamics and unsteady fluid physics. Because the wing shape and hence the resulting effective angle of attack are a priori unknown, predicting aerodynamic performance is challenging. Here, we show that a coupled aerodynamics/structural dynamics model can be established for hovering, based on a linear beam equation with the Morison equation to account for both added mass and aerodynamic damping effects. Lift strongly depends on the instantaneous angle of attack, resulting from passive pitch associated with wing deformation. We show that both instantaneous wing deformation and lift can be predicted in a much simplified framework. Moreover, our analysis suggests that resulting wing kinematics can be explained by the interplay between acceleration-related and aerodynamic damping forces. Interestingly, while both forces combine to create a high angle of attack resulting in high lift around the midstroke, they offset each other for phase control at the end of the stroke.     

Aerodynamic properties of a wing performing unsteady rotational motions at low Reynolds number

Summary The aerodynamic forces and flow structures of a wing of relatively small aspect ratio in some unsteady rotational motions at low Reynolds number (Re=100) are studied by numerically solving the Navier-Stokes equations. These motions include a wing in constant-speed rotation after a fast start, wing accelerating and decelerating from one rotational speed to another, and wing rapidly pitching-up in constant speed rotation. When a wing performs a constant-speed rotation at small Reynolds number after started from rest at large angle of attack (=35°), a large lift coefficient can be maintained. The mechanism for the large lift coefficient is that for a rotating wing: the variation of the relative velocity along the wing-span causes a pressure gradient and hence a spanwise flow which can prevent the dynamic stall vortex from shedding. When a wing is rapidly accelerating or decelerating from one rotational speed to another, or rapidly pitching-up during constant speed rotation, even if the aspect ratio of the wing is small and the flow Reynolds number is low, a large aerodynamic force can be obtained. During these rapid unsteady motions, new layers of strong vorticity are formed near the wing surfaces in very short time, resulting in a large time rate of change of the fluid impulse which is responsible for the generation of the large aerodynamic force.     

Aerodynamic effects of flexibility in flapping wings

Recent work on the aerodynamics of flapping flight reveals fundamental differences in the mechanisms of aerodynamic force generation between fixed and flapping wings. When fixed wings translate at high angles of attack, they periodically generate and shed leading and trailing edge vortices as reflected in their fluctuating aerodynamic force traces and associated flow visualization. In contrast, wings flapping at high angles of attack generate stable leading edge vorticity, which persists throughout the duration of the stroke and enhances mean aerodynamic forces. Here, we show that aerodynamic forces can be controlled by altering the trailing edge flexibility of a flapping wing. We used a dynamically scaled mechanical model of flapping flight (Re ≈ 2000) to measure the aerodynamic forces on flapping wings of variable flexural stiffness (EI). For low to medium angles of attack, as flexibility of the wing increases, its ability to generate aerodynamic forces decreases monotonically but its lift-to-drag ratios remain approximately constant. The instantaneous force traces reveal no major differences in the underlying modes of force generation for flexible and rigid wings, but the magnitude of force, the angle of net force vector and centre of pressure all vary systematically with wing flexibility. Even a rudimentary framework of wing veins is sufficient to restore the ability of flexible wings to generate forces at near-rigid values. Thus, the magnitude of force generation can be controlled by modulating the trailing edge flexibility and thereby controlling the magnitude of the leading edge vorticity. To characterize this, we have generated a detailed database of aerodynamic forces as a function of several variables including material properties, kinematics, aerodynamic forces and centre of pressure, which can also be used to help validate computational models of aeroelastic flapping wings. These experiments will also be useful for wing design for small robotic insects and, to a limited extent, in understanding the aerodynamics of flapping insect wings.     

一种提高飞机着陆性能的新方法探索研究

提出了一种新型气动方法,主要原理是通过将机翼上表面的一部分翼面设计为活动翼面,当飞机进入降落阶段、迎角较大时,适当抬高该活动翼面,在该翼面抬起后,形成一个台阶,通过台阶中产生的稳定驻涡来控制机翼上表面的流动,与此同时,打开安装在机翼上的Gurney襟翼,从而达到同时提高机翼升力和失速迎角的目的,该方法比较适合提高小型飞机或无人机的着陆性能。通过将该方法在某小型飞机上运用,数值模拟的结果表明:机翼的最大允许使用升力系数提高了33%,最大的允许使用迎角提高了30%。为提高小型飞机的着落性能探索出一种具有发展潜力的方法。     

Deformable wing kinematics in the desert locust: how and why do camber,twist and topography vary through the stroke?

Here, we present a detailed analysis of the wing kinematics and wing deformations of desert locusts (Schistocerca gregaria, Forskål) flying tethered in a wind tunnel. We filmed them using four high-speed digital video cameras, and used photogrammetry to reconstruct the motion of more than 100 identified points. Whereas the hindwing motions were highly stereotyped, the forewing motions showed considerable variation, consistent with a role in flight control. Both wings were positively cambered on the downstroke. The hindwing was cambered through an ‘umbrella effect’ whereby the trailing edge tension compressed the radial veins during the downstroke. Hindwing camber was reversed on the upstroke as the wing fan corrugated, reducing the projected area by 30 per cent, and releasing the tension in the trailing edge. Both the wings were strongly twisted from the root to the tip. The linear decrease in incidence along the hindwing on the downstroke precisely counteracts the linear increase in the angle of attack that would otherwise occur in root flapping for an untwisted wing. The consequent near-constant angle of attack is reminiscent of the optimum for a propeller of constant aerofoil section, wherein a linear twist distribution allows each section to operate at the unique angle of attack maximizing the lift to drag ratio. This implies tuning of the structural, morphological and kinematic parameters of the hindwing for efficient aerodynamic force production.     

Stable hovering of a jellyfish-like flying machine

Ornithopters, or flapping-wing aircraft, offer an alternative to helicopters in achieving manoeuvrability at small scales, although stabilizing such aerial vehicles remains a key challenge. Here, we present a hovering machine that achieves self-righting flight using flapping wings alone, without relying on additional aerodynamic surfaces and without feedback control. We design, construct and test-fly a prototype that opens and closes four wings, resembling the motions of swimming jellyfish more so than any insect or bird. Measurements of lift show the benefits of wing flexing and the importance of selecting a wing size appropriate to the motor. Furthermore, we use high-speed video and motion tracking to show that the body orientation is stable during ascending, forward and hovering flight modes. Our experimental measurements are used to inform an aerodynamic model of stability that reveals the importance of centre-of-mass location and the coupling of body translation and rotation. These results show the promise of flapping-flight strategies beyond those that directly mimic the wing motions of flying animals.     

Loss of lift due to thickness for low-aspect-ratio wings in incompressible flow

The problem under consideration is a numerical study of the effects of thickness on lift for low-aspect-ratio wings in steady incompressible inviscid flow at moderate of attack. At these angles of attack the flow separates along the leading edge giving rise to a lift substantially higher than that computed by classical attached-flow potential theory. The problem is treated as a perturbation expansion in a small thickness parameter. The lifting elements of the flow are modeled using a nonlinear vortex-lattice method which replaces the leading and trailing-edge vortex sheets by segmented straight vortex filaments. The thickness elements of the flow are modeled with a mean-plane source distribution and a modification to the wing boundary conditions. Results are obtained for wings with biconvex and NACA 0012 sections which compare well with available experimental data. The important observation that the effect of thickness is to decrease the lift is made.     

基于微秒脉冲激励的飞翼模型等离子体流动控制试验研究

为了改善飞翼布局的大迎角气动特性,采用飞翼全模和半模分别在低速和跨声速风洞中开展了微秒脉冲介质阻挡放电等离子体流动控制的试验研究。通过流动显示和测力的试验方法研究了等离子体流动控制的主要作用机制和激励频率与激励电压等对飞翼模型失速特性的影响规律,验证了微秒脉冲介质阻挡放电等离子体流动控制技术从低速到亚声速的有效性,有效的试验最高马赫数Ma达到0.6、雷诺数Re达到3.05×10⁶。试验研究表明：微秒脉冲介质阻挡放电等离子体通过非定常微尺度压缩波扰动的形式作用于翼面流场,通过频率耦合机制减弱模型的前缘分离涡、抑制翼面的流动分离;无量纲频率F⁺是影响等离子体流动控制效果的重要参数;在低速风洞试验风速V=30 m/s时,无量纲频率F⁺=0.35～1.06的控制效果较好,可将模型的最大升力系数提高25%以上、失速迎角推迟4°;在跨声速风洞试验马赫数Ma=0.6时,无量纲频率F⁺=0.22和F⁺=0.44的控制效果较好,可将模型的最大升力系数分别提高4.72%、4.77%,失速迎角分别推...     

On the quasi-steady aerodynamics of normal hovering flight part II: model implementation and evaluation

This paper introduces a generic, transparent and compact model for the evaluation of the aerodynamic performance of insect-like flapping wings in hovering flight. The model is generic in that it can be applied to wings of arbitrary morphology and kinematics without the use of experimental data, is transparent in that the aerodynamic components of the model are linked directly to morphology and kinematics via physical relationships and is compact in the sense that it can be efficiently evaluated for use within a design optimization environment. An important aspect of the model is the method by which translational force coefficients for the aerodynamic model are obtained from first principles; however important insights are also provided for the morphological and kinematic treatments that improve the clarity and efficiency of the overall model. A thorough analysis of the leading-edge suction analogy model is provided and comparison of the aerodynamic model with results from application of the leading-edge suction analogy shows good agreement. The full model is evaluated against experimental data for revolving wings and good agreement is obtained for lift and drag up to 90° incidence. Comparison of the model output with data from computational fluid dynamics studies on a range of different insect species also shows good agreement with predicted weight support ratio and specific power. The validated model is used to evaluate the relative impact of different contributors to the induced power factor for the hoverfly and fruitfly. It is shown that the assumption of an ideal induced power factor (k = 1) for a normal hovering hoverfly leads to a 23% overestimation of the generated force owing to flapping.     

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

We report a comprehensive scaling law and novel lift generation mechanisms relevant to the aerodynamic functions of structural flexibility in insect flight. Using a Navier–Stokes equation solver, fully coupled to a structural dynamics solver, we consider the hovering motion of a wing of insect size, in which the dynamics of fluid–structure interaction leads to passive wing rotation. Lift generated on the flexible wing scales with the relative shape deformation parameter, whereas the optimal lift is obtained when the wing deformation synchronizes with the imposed translation, consistent with previously reported observations for fruit flies and honeybees. Systematic comparisons with rigid wings illustrate that the nonlinear response in wing motion results in a greater peak angle compared with a simple harmonic motion, yielding higher lift. Moreover, the compliant wing streamlines its shape via camber deformation to mitigate the nonlinear lift-degrading wing–wake interaction to further enhance lift. These bioinspired aeroelastic mechanisms can be used in the development of flapping wing micro-robots.     

扑动轨迹对扑翼气动特性影响的数值研究

国内外对扑翼飞行的气动性能进行了大量研究,这些研究大多针对特定运动轨迹下的扑翼,然而大量观察发现,昆虫在飞行时其翅膀会出现各种不同的运动形式,这些不同的翅膀运动方式必定对其气动性能产生重要影响。该文基于对昆虫的实验和数值模拟中常用的几种扑动轨迹模型分析,建立了三种具有相同准稳态气动力的扑翼扑动轨迹,并采用数值求解N-S 方程的方法,研究了前飞状态下不同扑动轨迹对扑翼气动特性产生的影响。结果显示扑动和转动均为简谐函数轨迹形式的扑翼具有较高的升举效率和推进效率。进一步通过对不同扑动轨迹扑翼流场分析得出,扑动轨迹不能改变扑翼产生的尾流性质,但可以影响涡的强度,从而使扑翼产生不同的气动性能。     

Ionic Polymer Metal Composite Flapping Actuator Mimicking Dragonflies

In this study, variational principle is used for dynamic modeling of an Ionic Polymer Metal Composite (IPMC) flapping wing. The IPMC is an Electro-active Polymer (EAP) which is emerging as a useful smart material for `artificial muscle' applications. Dynamic characteristics of IPMC flapping wings having the same size as the actual wings of three different dragonfly species Aeshna Multicolor, Anax Parthenope Julius and Sympetrum Frequens are analyzed using numerical simulations. An unsteady aerodynamic model is used to obtain the aerodynamic forces. A comparative study of the performances of three IPMC flapping wings is conducted. Among the three species, it is found that thrust force produced by the IPMC flapping wing of the same size as Anax Parthenope Julius wing is maximum. Lift force produced by the IPMC wing of the same size as Sympetrum Frequens wing is maximum and the wing is suitable for low speed flight. The numerical results in this paper show that dragonfly inspired IPMC flapping wings are a viable contender for insect scale flapping wing micro air vehicles.     

Computational investigation of cicada aerodynamics in forward flight

Free forward flight of cicadas is investigated through high-speed photogrammetry, three-dimensional surface reconstruction and computational fluid dynamics simulations. We report two new vortices generated by the cicada''s wide body. One is the thorax-generated vortex, which helps the downwash flow, indicating a new phenomenon of lift enhancement. Another is the cicada posterior body vortex, which entangles with the vortex ring composed of wing tip, trailing edge and wing root vortices. Some other vortex features include: independently developed left- and right-hand side leading edge vortex (LEV), dual-core LEV structure at the mid-wing region and near-wake two-vortex-ring structure. In the cicada forward flight, approximately 79% of the total lift is generated during the downstroke. Cicada wings experience drag in the downstroke, and generate thrust during the upstroke. Energetics study shows that the cicada in free forward flight consumes much more power in the downstroke than in the upstroke, to provide enough lift to support the weight and to overcome drag to move forward.     

扑翼飞行器气动力测量技术研究进展与展望

扑翼飞行器是一种仿照鸟类飞行的新概念小型无人飞行器,区别于传统固定翼和旋翼飞行器,它主要通过机翼扑动与空气相互作用来提供飞行动力,从而实现飞行器的姿态变动。扑翼飞行器气动特性测试的实质是揭示在非定常流场环境下,扑翼飞行器气动力的产生机制,以及相关扑翼飞行器设计参数对气动特性的影响。通过气动试验方法为扑翼飞行器飞行控制和结构优化等研制工作提供数据支持,将对新型扑翼飞行器理论研究以及飞控品质的提升起到巨大的推动作用。     

扑翼飞行器测力平台设计与振动特性仿真分析

扑翼飞行器是基于鸟类仿生学理论衍生出的新型无人飞行器,主要通过机翼周期性上下扑动来提供飞行器所需的升力和推力,在军用和民用飞行器领域均有广阔的应用前景。扑翼飞行器气动力测量作为样机气动性测试的重要手段,多维气动力的准确测量可为新型扑翼飞行器设计优化和飞控品质的提高提供试验数据支持。本文介绍了一种新型组合式多维小量程测力平台,可实现扑翼飞行器六维气动力和气动力矩的测量。考虑到扑翼飞行器机翼上下扑动过程动态测力需求,应用Ansys Workbench有限元分析软件对测力平台进行了模态分析和频响分析,获得在工作频率下的频率响应,仿真结果表明测力平台的振动特性满足设计要求。     

双矩形拱肋间的气动干扰效应研究

以某拱桥为例,通过数值模拟研究了串列双矩形拱肋的气动干扰效应,及其对两截面气动力系数的影响。在对计算模型进行验证的基础上,进一步研究了截面宽高比、间距比和来流风攻角对拱肋周围流场的影响,并结合压力云图和湍动能云图解释了气动力系数的变化规律,讨论了不同宽高比截面的漩涡脱落频率与结构自振频率之间的关系,分析了两拱肋升力时程的差异对整体扭矩可能产生的增大效应。结果表明：串列拱肋间的气动干扰效应显著。受上游截面尾流的影响,下游截面的阻力系数明显减小,其值与漩涡的形态、能量大小、移动轨迹等因素密切相关。上、下游截面的升力时程在幅值和相位上存在明显差异,导致拱肋整体的力矩增大,其效应随宽高比或间距比的增大而明显加强,随风攻角的增大而有所降低。漩涡脱落频率随宽高比的增大呈先增大后减小的趋势,而受间距比、风攻角的影响有限。对漩涡脱落频率与宽高比的变化进行多项式拟合,结合结构的模态频率可为拱肋的气动外形设计提供参考。