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.     

Application of digital particle image velocimetry to insect aerodynamics: measurement of the leading-edge vortex and near wake of a Hawkmoth

Some insects use leading-edge vortices to generate high lift forces, as has been inferred from qualitative smoke visualisations of the flow around their wings. Here we present the first Digital Particle Image Velocimetry (DPIV) data and quantitative analysis of an insect’s leading-edge vortex and near wake at two flight speeds. This allows us to describe objectively 2D slices through the flow field of a tethered Tobacco Hawkmoth (Manduca sexta). The near-field vortex wake appears to braodly resemble elliptical vortex loops. The presence of a leading-edge vortex towards the end of the downstroke is found to coincide with peak upward force production measured by a six-component force–moment balance. The topology of Manduca’s leading-edge vortex differs from that previously described because late in the downstroke, the structure extends continuously from wingtip across the thorax to the other wingtip.     

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.     

A flow control mechanism in wing flapping with stroke asymmetry during insect forward flight

A theoretical modeling approach as well as an unsteady analytical method is used to study aerodynamic characteristics of wing flapping with asymmetric stroke-cycles in connection with an oblique stroke plane during insect forward flight. It is revealed that the aerodynamic asymmetry between the downstroke and the upstroke due to stroke-asymmetrical flapping is a key to understand the flow physics of generation and modulation of the lift and the thrust. Predicted results for examples of given kinematics validate more specifically some viewpoints that the wing lift is more easily produced when the forward speed is higher and the thrust is harder, and the lift and the thrust are generated mainly during downstroke and upstroke, respectively. The effects of three controlling parameters, i.e. the angles of tilted stroke plane, the different downstroke duration ratios, and the different angles of attack in both down- and up-stroke, are further discussed. It is found that larger oblique angles of stroke planes generate larger thrust but smaller lift; larger downstroke duration ratios lead to larger thrust, while making little change in lift and input aerodynamic power; and again, a small increase of the angle of attack in downstroke or upstroke may cause remarkable changes in aerodynamic performance in the relevant stroke.The project supported by the National Natural Science Foundation of China (10072066, 90305009) and the Chinese Academy of Sciences (KJCX-SW-L04, KJCX2-SW-L2)The English text was polished by Ron Marshall.     

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。     

Aerodynamic forces and flow fields of a two-dimensional hovering wing

This paper reports the results of an experimental investigation on a two-dimensional (2-D) wing undergoing symmetric simple harmonic flapping motion. The purpose of this investigation is to study how flapping frequency (or Reynolds number) and angular amplitude affect aerodynamic force generation and the associated flow field during flapping for Reynolds number (Re) ranging from 663 to 2652, and angular amplitudes (α _A) of 30°, 45° and 60°. Our results support the findings of earlier studies that fluid inertia and leading edge vortices play dominant roles in the generation of aerodynamic forces. More importantly, time-resolved force coefficients during flapping are found to be more sensitive to changes in α _A than in Re. In fact, a subtle change in α _A may lead to considerable changes in the lift and drag coefficients, and there appears to be an optimal mean lift coefficient around α _A = 45°, at least for the range of flow parameters considered here. This optimal condition coincides with the development a reverse Karman Vortex street in the wake, which has a higher jet stream than a vortex dipole at α _A = 30° and a neutral wake structure at α _A = 60°. Although Re has less effect on temporal force coefficients and the associated wake structures, increasing Re tends to equalize mean lift coefficients (and also mean drag coefficients) during downstroke and upstroke, thus suggesting an increasing symmetry in the mean force generation between these strokes. Although the current study deals with a 2-D hovering motion only, the unique force characteristics observed here, particularly their strong dependence on α _A, may also occur in a three-dimensional hovering motion, and flying insects may well have taken advantage of these characteristics to help them to stay aloft and maneuver. An erratum to this article can be found at     

Flows around two airfoils performing fling and subsequent translation and translation and subsequent clap

The aerodynamic forces and flow structures of two airfoils performing “fling and subsequent translation“ and “translation and subsequent clap“ are studied by numerically solving the Navier-Stokes equations in moving overset grids. These motions are relevant to the flight of very small insects. The Reynolds number, based on the airfoil chord length c and the translation velocity U, is 17. It is shown that: (1) For two airfoils performing fling and subsequent translation, a large lift is generated both in the fling phase and in the early part of the translation phase. During the fling phase,a pair of leading edge vortices of large strength is generated; the generation of the vortex pair in a short period results in a large time rate of change of fluid impulse, which explains the large lift in this period. During the early part of the translation, the two leading edge vortices move with the airfoils;the relative movement of the vortices also results in a large time rate of change of fluid impulse, which explains the large lift in this part of motion. (In the later part of the translation, the vorticity in the vortices is diffused and convected into the wake.) The time averaged lift coefficient is approximately 2.4 times as large as that of a single airfoil performing a similar motion. (2) For two airfoils performing translation and subsequent clap, a large lift is generated in the clap phase. During the clap, a pair of trailing edge vortices of large strength are generated; again, the generation of the vortex pair in a short period (which results in a large time rate of change of fluid impulse) is responsible for the large lift in this period. The time averaged lift coefficient is approximately 1.6 times as large as that of a single airfoil performing a similar motion. (3) When the initial distance between the airfoils (in the case of clap, the final distance between the airfoils) varies from 0.1 to 0.2c, the lift on an airfoil decreases only slightly but the torque decreases greatly. When the distance is about lc， the interference effects between the two airfoils become very small.     

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.     

A study on the mechanism of high-lift generation by an airfoil in unsteady motion at low reynolds number

The aerodynamic force and flow structure of NACA 0012 airfoil performing an unsteady motion at low Reynolds number (Re=100) are calculated by solving Navier-Stokes equations. The motion consists of three parts: the first translation, rotation and the second translation in the direction opposite to the first. The rotation and the second translation in this motion are expected to represent the rotation and translation of the wing-section of a hovering insect. The flow structure is used in combination with the theory of vorticity dynamics to explain the generation of unsteady aerodynamic force in the motion. During the rotation, due to the creation of strong vortices in short time, large aerodynamic force is produced and the force is almost normal to the airfoil chord. During the second translation, large lift coefficient can be maintained for certain time period and , the lift coefficient averaged over four chord lengths of travel, is larger than 2 (the corresponding steady-state lift coefficient is only 0.9). The large lift coefficient is due to two effects. The first is the delayed shedding of the stall vortex. The second is that the vortices created during the airfoil rotation and in the near wake left by previous translation form a short “vortex street” in front of the airfoil and the “vortex street” induces a “wind”; against this “wind” the airfoil translates, increasing its relative speed. The above results provide insights to the understanding of the mechanism of high-lift generation by a hovering insect. The project supported by the National Natural Science Foundation of China (19725210)     

一种平行曲柄连杆扑翼机构的设计、优化与实现

提出了一种来自于昆虫结构启发的平 行曲柄连杆的扑翼机构. 该机构依靠两组平行布置的曲 柄连杆和连杆间的翼面控制机构实现, 既能够保证扑翼运动左右翼面的对称性, 又能够实现挥拍 攻角的调节和控制, 采用MATLAB的非线性优化工具对该扑翼机构进行了运动参数的 优化, 并设计制作了大比例的实物扑翼模型进行测力分析. 结果验证了这种扑 翼机构能够给出非定常高升力.     

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.     

Two- and three-dimensional numerical simulations of the clap–fling–sweep of hovering insects

The importance of three-dimensional effects for flapping wings is addressed by means of numerical simulation. In particular, the clap–fling–sweep mechanism is examined. The flow at the beginning of the downstroke is shown to be in reasonable agreement with the two-dimensional approximation. After the wings move farther than one chord length apart, three-dimensional effects become essential. Two values of the Reynolds number are considered. At Re=128, the spanwise flow from the wing roots to the wing tips is driven by the centrifugal forces acting on the mass of the fluid trapped in the recirculation bubble behind the wings. It removes the excess of vorticity and delays the periodic vortex shedding. At Re=1400, vortex breakdown occurs past the outer portion of the wings, and multiple vortex filaments are shed into the wake.     

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.     

Numerical simulation of flapping‐wing insect hovering flight at unsteady flow

A computational fluid dynamics (CFD) analysis was conducted to study the unsteady aerodynamics of a virtual flying bumblebee during hovering flight. The integrated geometry of bumblebee was established to define the shape of a three‐dimensional virtual bumblebee model with beating its wings, accurately mimicking the three‐dimensional movements of wings during hovering flight. The kinematics data of wings documented from the measurement to the bumblebee in normal hovering flight aided by the high‐speed video. The Navier–Stokes equations are solved numerically. The solution provides the flow and pressure fields, from which the aerodynamic forces and vorticity wake structure are obtained. Insights into the unsteady aerodynamic force generation process are gained from the force and flow‐structure information. The CFD analysis has established an overall understanding of the viscous and unsteady flow around the virtual flying bumblebee and of the time course of instantaneous force production, which reveals that hovering flight is dominated by the unsteady aerodynamics of both the instantaneous dynamics and also the past history of the wing. A coherent leading‐edge vortex with axial flow and the attached wingtip vortex and trailing edge vortex were detected. The leading edge vortex, wing tip vortex and trailing edge vortex, which caused by the pressure difference between the upper and the lower surface of wings. The axial flow, which include the spanwise flow and chordwise flow, is derived from the spanwise pressure gradient and chordwise pressure gradient, will stabilize the vortex and gives it a characteristic spiral conical shape. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

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.     

Investigation of flow field of clap and fling motion using immersed boundary coupled lattice Boltzmann method

This paper deals with the investigation of flow field due to clap and fling mechanism using immersed boundary coupled with lattice Boltzmann method. The lattice Boltzmann method (LBM), an alternative to Navier–Stokes solver, is used because of its simplicity and computational efficiency in solving complex moving boundary problems. Benchmark problems are simulated to validate the code, which is then used for simulating flow over two elliptic wing of aspect ratio 5 performing clap and fling flapping motion for different flow parameters such as Reynolds number (Re=75, 100, 150), advance ratio (J=10E−3.10E−2,0.2) and frequency (f=0.05 Hz, 0.25 Hz). Numerical simulation is able to capture typical low Reynolds number unsteady phenomena such as, ׳wake vortex wing interaction׳, ׳Kramer effect׳ and ׳delayed stall׳. The results are both qualitatively and quantitatively consistent with experimental observation. The parametric study involving different combinations of Re, f and J depict distinctly different aerodynamic performances providing physical insights into the flow physics. It is observed that a combination of low f, low J and high Re flow results in better aerodynamic performance. Pronounced lift enhancement via leading edge vortices are obtained in unsteady regime (J<1) compared to quasi-steady regime (J>1). The role of leading edge vortices in enhancing lift are investigated by studying the size and strength of these vortices for different flow conditions. For a given Re, the magnitude of maximum lift coefficient decreases with increasing f irrespective of the value of J; while the same is enhanced with the increasing Re.