An analytic approach to theoretical modeling of highly unsteady viscous flow excited by wing flapping in small insects

Numerous studies on the aerodynamics of insect wing flapping were carried out on different approaches of flight investigations, model experiments, and numerical simulations, but the theoretical modeling remains to be explored. In the present paper, an analytic approach is presented to model the flow interactions of wing flapping in air for small insects with the surrounding flow fields being highly unsteady and highly viscous. The model of wing flapping is a 2-D flat plate, which makes plunging and pitching oscillations as well as quick rotations reversing its positions of leading and trailing edges, respectively, during stroke reversals. It contains three simplified aerodynamic assumptions: (i) unsteady potential flow; (ii) discrete vortices shed from both leading and trailing edges of the wing; (iii) Kutta conditions applied at both edges. Then the problem is reduced to the solution of the unsteady Laplace equation, by using distributed singularities, i.e., sources/sinks, and vortices in the field. To validate the present physical model and analytic method proposed via benchmark examples, two elemental motions in wing flapping and a case of whole flapping cycles are analyzed, and the predicted results agree well with available experimental and numerical data. This verifies that the present analytical approach may give qualitatively correct and quantitatively reasonable results. Furthermore, the total fluid-dynamic force in the present method can be decomposed into three parts: one due to the added inertial (or mass) effect, the other and the third due to the induction of vortices shed from the leading-and the trailing-edge and their images respectively, and this helps to reveal the flow control mechanisms in insect wing flapping. The project supported by the National Natural Science Foundation of China (10072066) and the Chinese Academy of Sciences (KJCX-SW-LO4, KJCX2-SW-L2)     

Effects of unsteady deformation of flapping wing on its aerodynamic forces

Effects of unsteady deformation of a flapping model insect wing on its aerodynamic force production are studied by solving the Navier-Stokes equations on a dynamically deforming grid.Aerodynamic forces on the flapping wing are not much affected by considerable twist,but affected by camber deformation.The effect of combined camber and twist deformation is similar to that of camber deformation.With a deformation of 6% camber and 20°twist(typical values observed for wings of many insects),lift is increased bv 10%～20%and lift-to-drag ratio by around 10%compared with the case of a rigid flat-plate wing.As a result.the deformation can increase the maximum lift coefficient of an insect.and reduce its power requirement for flight.For example,for a hovering bumblebee with dynamically deforming wings(6?mber and 20°twist),aerodynamic power required is reduced by about 16%compared with the case of rigid wings.     

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.     

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.     

VISCOELASTIC CONSTITUTIVE MODEL RELATED TO DEFORMATION OF INSECT WING UNDER LOADING IN FLAPPING MOTION

Flexible insect wings deform passively under the periodic loading during napping flight. The wing flexibility is considered as one of the specific mechanisms on improving insect flight performance. The constitutive relation of the insect wing material plays a key role on the wing deformation, but has not been clearly understood yet. A viscoelastic constitutive relation model was established based on the stress relaxation experiment of a dragonfly wing (in vitro). This model was examined by the finite element analysis of the dynamic deformation response for a model insect wing under the action of the periodical inertial force in flapping. It is revealed that the viscoelastic constitutive relation is rational to characterize the biomaterial property of insect wings in contrast to the elastic one. The amplitude and form of the passive viscoelastic deformation of the wing is evidently dependent on the viscous parameters in the constitutive relation.     

高速飞行器中空翼结构高温热振动特性试验研究

远程高速飞行器飞行速度快, 滞空时间长, 飞行过程中翼、舵等结构会出现长时间的剧烈振动, 由气动加热产生的高温还会使飞行器材料和结构的弹性性能发生变化, 从而引起翼、舵等结构振动特性的改变.因此获得高温与振动复合环境下的远程高速飞行器翼、舵等结构的振动特性参数对于高速飞行器的安全设计具有非常重要的意义.将高温热环境试验系统与振动试验系统相结合, 在对中空翼面结构进行振动激励的同时使用红外辐射加热方式对翼面结构生成可控的热环境, 并通过自行设计的耐高温引伸装置将中空翼结构的振动信号传递到非高温区进行数据采集与分析的方式, 实现了高达800℃~900℃的力热复合环境下的翼结构固有频率、模态等振动特性参数的试验测试, 其试验结果为远程高速飞行器中空翼结构在高温振动环境下的动特性分析和安全可靠性设计提供了重要依据.     

Wing/body kinematics measurement and force and moment analyses of the takeoff flight of fruitflies

In the paper, we present a detailed analysis of the takeoff mechanics of fruitflies which perform voluntary takeoff flights. Wing and body kinematics of the insects during takeoff were measured using high-speed video techniques.Based on the measured data, inertia force acting on the insect was computed and aerodynamic force and moment of the wings were calculated by the method of computational fluid dynamics. Subtracting the aerodynamic force and the weight from the inertia force gave the leg force. The following has been shown. In its voluntary takeoff, a fruitfly jumps during the first wingbeat and becomes airborne at the end of the first wingbeat. When it is in the air, the fly has a relatively large "initial" pitch-up rotational velocity(more than5 000°/s) resulting from the jumping, but in about 5 wingbeats, the pitch-up rotation is stopped and the fly goes into a quasi-hovering flight. The fly mainly uses the force of jumping legs to lift itself into the air(the force from the flapping wings during the jumping is only about 5%–10% of the leg force). The main role played by the flapping wings in the takeoff is to produce a pitch-down moment to nullify the large "initial" pitch-up rotational velocity(otherwise, the fly would have kept pitching-up and quickly fallen down).     

基于CFD的斜置翼翼型选型研究

斜置翼飞行器是一种通过改变扫掠角而能在亚声速、跨声速、超声速三个速度段都能获得最优效率的宽速域飞行器.根据斜置翼的设计需求,其基本翼型应该是超临界翼型,翼型选择应在考虑翼型最佳气动效率的同时兼顾翼型内部有效体积和操稳特性.基于以上选型标准,先从NASA超临界翼型族中选出5种超临界翼型,然后运用商业CFD软件Fluent对这5种超临界翼型的气动特性进行计算.最后通过对比分析这5种翼型的气动特性、几何参数和操稳特性,选择性能较优的NASA SC(2)-0714翼型作为斜置翼的基本翼型.     

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。     

N-S方程数值研究翼型对微型扑翼气动特性的影响

首先基于嵌套网格发展了一套适用于三维扑翼研究的非定常雷诺平均Navier-Stokes(RANS)方程数值模拟方法.为了解决微型扑翼在低马赫数下的收敛问题,使用了预处理方法,湍流模型为BL模型.在该方法的基础上,保持状态参数和扑翼表面形状一定的情况下,分别研究了一系列不同厚度、不同弯度的翼型对于微型扑翼气动特性的影响....     

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.     

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.     

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。     

复合材料翼面结构优化设计及分析

复合材料具有比强度高、比刚度大、抗疲劳等诸多优异性能,在航空航天结构中得到了广泛的应用.复合材料在新研制的飞机上的应用比重也越来越高,在大型民用飞机Boeing787上,复合材料结构重量占到了全机结构重量的50%.复合材料层合板具有无与伦比的设计潜力,成为复合材料中使用最多的一种结构形式.本文以某型号飞机机翼翼盒为研究...     

Analogy between a flapping wing and a wind turbine with a vertical axis of revolution

Based on an analysis of available experimental data, the hypothesis about an analogy between a flapping wing and a wind turbine of the Darrieus rotor type is justified. It is demonstrated that the torque on the shaft of the Darrieus rotor is generated by thrust forces acting on the blades in a pulsed flow. A conclusion is drawn that it is necessary to perform aerodynamic calculations of blades on the basis of the nonlinear theory of the wing in an unsteady flow with allowance for the airfoil thickness. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 152–155, March–April, 2009.     

低Re数下变弯度机翼的非定常气动特性实验研究

利用变弯度机翼模型及相关的风洞实验平台,开展了以弯度变化速率影响为重点的机翼非定常特性研究。实验结果显示,在低Re数(~105)下,机翼弯度非定常变化得到的升阻力系数曲线与准定常条件下的结果存在显著差异。具体表现为:准定常状态下,曲线表现出明显的可逆性;而弯度非定常变化时,曲线在弯度递增区和递减区之间存在明显的迟滞效应,而且随着变形速率的增加,这种迟滞也越明显。流场显示结果表明,这种小St数下出现的流动迟滞是由于弯度变形导致的流动分离的分离点相对机翼运动迟滞所造成的。这说明弯度变化时,分离流场结构的响应时间尺度与弯度变化周期相当,也揭示了该条件下机翼弯度变化对流动的抑制作用主要是通过改变分离区的大小来实现的。     

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.