Aspect ratio effects on revolving wings with Rossby number consideration

The Lift Effects of Chordwise Wing Deformation and Body Angle on Low-Speed Flying Butterflies

This work investigates the effects of body angle and wing deformation on the lift of free-flying butterflies. The flight kinematics were recorded using three high-speed cameras, and particle-image velocimetry (PIV) was used to analyze the transient flow field around the butterfly. Parametric studies via numerical simulations were also conducted to examine the force generation of the wing by fixing different body angles and amplifying the chordwise deformation. The results show that appropriately amplifying chordwise deformation enhances wing performance due to an increase in the strength of the vortex and a more stabilized attached vortex. The wing undergoes a significant chordwise deformation, which can generate a larger lift coefficient than that with a higher body angle, resulting in a 14% increase compared to a lower chordwise deformation and body angle. This effect is due to the leading-edge vortex attached to the curved wing, which alters the force from horizontal to vertical. It, therefore, produces more efficient lift during flight. These findings reveal that the chordwise deformation of the wing and the body angle could increase the lift of the butterfly. This work was inspired by real butterfly flight, and the results could provide valuable knowledge about lift generation for designing microaerial vehicles.

Decoupling wing-shape effects of wing-swept angle and aspect ratio on a forward-flying butterfly

The effect of wing shape on a forward-flying butterfly via decoupled factors of the wing-swept angle and the aspect ratio (AR) was investigated numerically. The wing-shape effect is a major concern in the design of a microaerial vehicle (MAV). In nature, the wing of a butterfly consists of partially overlapping forewing and hindwing; when the forewing sweeps forward or backward relative to the hindwing, the wing-swept angle and the AR of the entire wing simultaneously change. The effects of the wing-swept angle and AR on aerodynamics are coupled. To decouple their effects, we established wing-shape models with varied combinations of the wing-swept angle and AR based on the experimental measurement of two butterfly species (Papilio polytes and Kallima inachus) and developed a numerical simulation for analysis. In each model, the forewing and hindwing overlapped partially, constructing a single wing. Across the models, the wing-swept angle and AR of these single wings varied sequentially. The results show that, through our models, the effects of the wing-swept angle and AR were decoupled; both have distinct flow mechanisms and aerodynamic force trends and are consistent in the two butterfly species. For a fixed AR, a backward-swept wing increases lift and drag because of the enhanced attachment of the leading-edge vortex with increased strength of the wingtip vortex and the spanwise flow. For a fixed wing-swept angle, a small AR wing increases lift and decreases drag because of the large region of low pressure downstream and the wake-capture effect. Coupling these effects, the largest lift-to-drag ratio occurs for a forward-swept wing with the smallest AR. These results indicate that, in a flapping forward flight, sweeping a forewing forward relative to a hindwing is suitable for cruising. The flow mechanisms and decoupled and coupled effects of the wing-swept angle and the AR presented in this paper provide insight into the flight of a butterfly and the design of a MAV.

Capturing wake capture: a 2D numerical investigation into wing-wake interaction aerodynamics

A wing generating lift leaves behind a region of disturbed air in the form of a wake. For a hovering insect, the wings must return through the wake produced by the previous half-stroke and this can have significant effects on the aerodynamic performance. This paper numerically investigates 2D wings interacting with their own wake at Reynolds numbers of 10²and 10³, enabling an improved understanding of the underlying physics of the 'wake capture' aerodynamic mechanism of insect flight. We adopt a simple kinematic motion pattern comprised of a translational stroke motion followed by a complete stop to expose wake interaction effects. Representative stroke distance to chord ratios between 1.5 and 6.0 are considered, enabling different leading-edge vortex (LEV) attachment states. We also allow pitching rotation towards the end of stroke, leading to wake intercepting angles of 135°, 90°, and 45°, analogous to delayed, symmetric, and advanced pitching rotations of insect wings. It is shown that both vortex suction and jet flow impingement mechanisms can lead to either positive or negative effects depending on the LEV attachment state, and that stroke distances resulting in a detached/attached LEV lead to beneficial/detrimental wake interaction lift. Pitching rotation at the end of the stroke motion is found to induce a strong rotational trailing-edge vortex (RTEV). For advanced pitching, this RTEV serves to enable either a stronger flow impingement effect leading to positive wake interaction lift if the LEV is detached, or a less favourable vortex suction effect leading to negative wake interaction lift if the LEV is closely attached. The higher Reynolds number led to faster development of the wake vortices, but the primary wake interaction mechanisms remained the same for both Reynolds numbers.

The Aerodynamic Effect of an Alula-like Vortex Generator on a Revolving Wing

An alula is a small structure of feathers that prevents birds from stalling. In this study, the aerodynamic effect of an alula-like vortex generator (alula-VG) on a revolving wing was investigated using the PIV technique in a water tank. The alula-VG was mounted on a rectangular wing model at two spanwise positions. The wing model with a revolving motion was installed at different angles of attack, which included pre-stall and post-stall conditions. The velocity fields around the wing model with/without an alula-VG were measured and analyzed, including the vorticity contour, the circulation of vortex structures, and the corresponding sectional lift coefficient, which are used to explain the aerodynamic effect induced by an alula-VG. The lift-off and bursting of the leading-edge vortex (LEV) affect the magnitude of the chordwise circulation and the section lift coefficient. The results show that compared to an alula-VG mounted fixed wing model, the flow interactions among the alula-VG induced spanwise flow, the inertial force caused by the revolving motion, and the wing-tip vortex play important roles in the vortex bursting and the resultant aerodynamic performance. The effect of an alula-VG on a revolving wing depends on its spanwise position and the angle of attack of a wing model, which need to be properly matched.

Dynamic experimental rigs for investigation of insect wing aerodynamics

This paper provides a systematic and critical review of dynamic experimental rigs used for insect wing aerodynamics research. The goal is to facilitate meaningful comparison of data from existing rigs and provide insights for designers of new rigs. The scope extends from simple one degree of freedom rotary rigs to multi degrees of freedom rigs allowing various rotation and translation motions. Experimental methods are characterized using a consistent set of parameters that allows objective comparison of different approaches. A comprehensive catalogue is presented for the tested flow conditions (assessed through Reynolds number, Rossby number and advance ratio), wing morphologies (assessed through aspect ratio, planform shape and thickness to mean chord ratio) and kinematics (assessed through motion degrees of freedom). Links are made between the type of aerodynamic characteristics being studied and the type of experimental set-up used. Rig mechanical design considerations are assessed, and the aerodynamic measurements obtained from these rigs are discussed.

Wing Planform Effect on the Aerodynamics of Insect Wings

Simple Summary

This study aims to provide an improved understanding of the effect of wing planform shape on the aerodynamic performance of insect flapping wings. We focus our investigation on three planform parameters, namely aspect ratio, radial centroid location, and wing root offset, and their effect on the aerodynamic performance is characterised at a flow Reynolds number most relevant to small insects similar to fruit flies. We show that aspect ratio and root offset mainly influence the flow detachment area near the wingtip, whereas radial centroid location mainly influences the local flow evolution time on the wing surface. Overall, increasing the aspect ratio is beneficial to lift and efficiency up to a limit where flow detachment near the wing tip leads to less-favorable performance. Similarly, increasing the wing root offset leads to an increased flow detachment area near the wing tip, resulting in reduced lift coefficient, but the aerodynamic efficiency remains relatively unaffected by the root offset value for most aspect ratios. Finally, increasing the radial centroid location mainly increases the aerodynamic efficiency.

Abstract

This study investigates the effect of wing planform shape on the aerodynamic performance of insect wings by numerically solving the incompressible Navier-Stokes equations. We define the wing planforms using a beta-function distribution and employ kinematics representative of normal hovering flight. In particular, we use three primary parameters to describe the planform geometry: aspect ratio, radial centroid location, and wing root offset. The force coefficients, flow structures, and aerodynamic efficiency for different wing planforms at a Reynolds number of 100 are evaluated. It is found that the wing with the lowest aspect ratio of 1.5 results in the highest peaks of lift and drag coefficients during stroke reversals, whereas the higher aspect ratio wings produce higher lift and drag coefficients during mid half-stroke translation. For the wings considered, the leading-edge vortex detachment is found to be approximately at a location that is 3.5–5 mean chord lengths from the wing center of rotation for all aspect ratios and root offsets investigated. Consequently, the detachment area increases with the increase of aspect ratio and root offset, resulting in reduced aerodynamic coefficients. The radial centroid location is found to influence the local flow evolution time, and this results in earlier formation/detachment of the leading-edge vortex for wings with a smaller radial centroid location. Overall, the best performance, when considering both average lift coefficient and efficiency, is found at the intermediate aspect ratios of 4.5–6; increasing the centroid location mainly increases efficiency; and increasing the root offset leads to a decreased average lift coefficient whilst leading to relatively small variations in aerodynamic efficiency for most aspect ratios.

The relationship between body size and flight power output in the mango stem borer (Batocera rufomaculata)

Adult body size in insects can be influenced by environmental conditions during larval growth. The effect of such intraspecific variation in body mass on flight performance is poorly understood. In Batocera rufomaculata, a large tree boring beetle, adults emerging from larvae that developed in a dying host tree, and therefore, under nutrient-deprived diet conditions, are smaller but have an elevated long-distance flight capability compared to larger conspecifics that developed in viable host trees. The improved endurance for long-distance flight in the smaller individuals appears to contradict the interspecific trend in flying animals of a decrease in Cost of Transport (CoT) with increased body mass. To explore the relationship between intraspecific variation in body size and power expended during steady forward flight, we flew these beetles tethered in a wind tunnel and compared the flapping kinematics and power output of individuals varying in body mass (1-7 gr). Concurrently, we measured the forces the insects applied on the tether allowing us to evaluate the tethering effects and correct for them. From the flapping kinematics we estimated the mechanical power expended using a quasi-steady blade-element model. We found that muscle mass-specific power did not differ between small and large individuals flying at the same wind (flight) speed in the tunnel. Consequently, the CoT of B. rufomaculata does not vary with body mass. Such invariance of mass-specific power with body mass may aid the dispersal of smaller individuals from deteriorating host trees to new ones.

Enhanced lift and thrust via the translational motion between the thorax-abdomen node and the center of mass of a butterfly with a constructive abdominal oscillation

Butterflies fly with an abdomen oscillating relative to the thorax; the abdominal oscillation causes body parts to undulate translationally relative to the center of mass of a butterfly, which could generate a significant effect on flight. Based on experimental measurements, we created a numerical model to investigate this effect in a free-flying butterfly (Idea leuconoe). We fixed the motions of wing-flapping and thorax-pitching, and parametrized the abdominal oscillation by varied oscillating phase. To concentrate the analysis on translational dynamics, we used a motion of a thorax-abdomen node, a joint that the thorax and the abdomen rotate about, to express the translational motion of body parts relative to the center of mass. The results show that the abdominal oscillation enhances lift and thrust via the translational motion of the thorax-abdomen node relative to the center of mass. With the abdominal oscillating phase recorded from real butterflies, the abdominal oscillation causes the thorax-abdomen node to move downward relative to the center of mass in downstroke and move upward relative to the center of mass in upstroke. This constructive movement amplifies the wing-flapping speed relative to the center of mass, which enhances the angle of attack and the strength of leading- and trailing-edge vortices on the wings. The wings thereby generate increased values of instantaneous lift and thrust by 50.32% and 32.57% compared to the case of no abdominal oscillation. Natural butterflies are stated to utilize a particular phase offset of abdominal oscillation to fly. With comparing varied oscillating phases, only the abdominal oscillating phase recorded from natural butterflies produces the best constructive effect on the translational motion of thorax-abdomen node, which maximizes the lift and thrust generated on the wings. It clarifies that butterflies use this specific range of abdominal oscillating phase to regulate the translational motion between the thorax-abdomen node and the center of mass to enhance flight. Our work reveals the translational mechanism of the abdominal oscillation, which is as important as the thorax-pitching effect. The findings in this work provide insight into the flight of butterflies and the design of micro aerial vehicles.

Effects of phase lag on the hovering flight of damselfly and dragonfly

In this work we studied the differences in flight kinematics and aerodynamics that could relate to differences in wing morphologies of a dragonfly and a damselfly. The damselflies and dragonflies normally fly with the fore wing or hind wing in the lead, respectively. The wing of the damselfly is petiolate, which means that the wing root is narrower than that of the dragonfly. The influence of the biological morphology between the damselfly and the dragonfly on their hovering strategies is worthy of clarification. The flight motions of damselflies and dragonflies in hovering were recorded with two high-speed cameras; we analyzed the differences between their hovering motions using computational fluid dynamics. The distinct mechanisms of the hovering flight of damselflies (Matrona cyanoptera) and dragonflies (Neurothemis ramburii) with different phase lags between fore and hind wings were deduced. The results of a comparison of the differences of wing phases in hovering showed that the rotational effect has an important role in the aerodynamics; the interactions between fore and hind wings greatly affect their vortex structure and flight performance. The wake of a damselfly sheds smoothly because of slender petiolation; a vertical force is generated steadily during the stage of wing translation. Damselflies hover with a longer translational phase and a larger flapping amplitude. In contrast, the root vortex of a dragonfly impedes the shedding of wake vortices in the upstroke, which results in the loss of a vertical force; the dragonfly hence hovers with a large amplitude of wing rotation. These species of Odonata insects developed varied hovering strategies to fit their distinct biological morphologies.

On the lift-optimal aspect ratio of a revolving wing at low Reynolds number

Lentink & Dickinson (2009 J. Exp. Biol.212, 2705-2719. (doi:10.1242/jeb.022269)) showed that rotational acceleration stabilized the leading-edge vortex on revolving, low aspect ratio (AR) wings and hypothesized that a Rossby number of around 3, which is achieved during each half-stroke for a variety of hovering insects, seeds and birds, represents a convergent high-lift solution across a range of scales in nature. Subsequent work has verified that, in particular, the Coriolis acceleration plays a key role in LEV stabilization. Implicit in these results is that there exists an optimal AR for wings revolving about their root, because it is otherwise unclear why, apart from possible morphological reasons, the convergent solution would not occur for an even lower Rossby number. We perform direct numerical simulations of the flow past revolving wings where we vary the AR and Rossby numbers independently by displacing the wing root from the axis of rotation. We show that the optimal lift coefficient represents a compromise between competing trends with competing time scales where the coefficient of lift increases monotonically with AR, holding Rossby number constant, but decreases monotonically with Rossby number, when holding AR constant. For wings revolving about their root, this favours wings of AR between 3 and 4.

Scaling Bioinspired Mars Flight Vehicles for Hover

With the resurgent interest in landing humans on Mars, it is critical that our understanding of the Martian environment is complete and accurate. One way to improve our model of the red planet is through aerial surveillance, which provides information that augments the observations made by ground-based exploration and satellite imagery. Although the ultra-low-density Mars environment has previously stymied designs for achieving flight on Mars, bioinspired solutions for flapping wing flight can utilize the same high lift producing mechanisms employed by insects on Earth. Motivated by the current technologies for terrestrial flapping wing aerial vehicles on Earth, we seek solutions for a 5 gram bioinspired flapping wing aerial vehicle for flight on Mars. A zeroth-order method is proposed to determine approximate wing and kinematic values that generate bioinspired hover solutions. We demonstrate that a family of solutions exists for designs that are O(10¹) g, which are verified using a 3D Navier-Stokes solver. Our results show that unsteady lift enhancement mechanisms, such as delayed stall and rotational lift, are present in the bioinspired solution for a 5 g flapping wing vehicle hovering in Mars conditions, verifying that the zeroth-order method is a useful design tool. As a result, it is possible to design a family of bioinspired flapping wing robots for Mars by augmenting the adverse effects of the ultra-low density with large wings that exploit the advantages of unsteady lift enhancement mechanisms used by insects on Earth.

The leading-edge vortex on a rotating wing changes markedly beyond a certain central body size

Stable attachment of a leading-edge vortex (LEV) plays a key role in generating the high lift on rotating wings with a central body. The central body size can affect the LEV structure broadly in two ways. First, an overall change in the size changes the Reynolds number, which is known to have an influence on the LEV structure. Second, it may affect the Coriolis acceleration acting across the wing, depending on the wing-offset from the axis of rotation. To investigate this, the effects of Reynolds number and the wing-offset are independently studied for a rotating wing. The three-dimensional LEV structure is mapped using a scanning particle image velocimetry technique. The rapid acquisition of images and their correlation are carefully validated. The results presented in this paper show that the LEV structure changes mainly with the Reynolds number. The LEV-split is found to be only minimally affected by changing the central body radius in the range of small offsets, which interestingly includes the range for most insects. However, beyond this small offset range, the LEV-split is found to change dramatically.

The role of the leading edge vortex in lift augmentation of steadily revolving wings: a change in perspective

The presence of a stable leading edge vortex (LEV) on steadily revolving wings increases the maximum lift coefficient that can be generated from the wing and its role is important to understanding natural flyers and flapping wing vehicles. In this paper, the role of LEV in lift augmentation is discussed under two hypotheses referred to as 'additional lift' and 'absence of stall'. The 'additional lift' hypothesis represents the traditional view. It presumes that an additional suction/circulation from the LEV increases the lift above that of a potential flow solution. This behaviour may be represented through either the 'Polhamus leading edge suction' model or the so-called 'trapped vortex' model. The 'absence of stall' hypothesis is a more recent contender that presumes that the LEV prevents stall at high angles of attack where flow separation would normally occur. This behaviour is represented through the so-called 'normal force' model. We show that all three models can be written in the form of the same potential flow kernel with modifiers to account for the presence of a LEV. The modelling is built on previous work on quasi-steady models for hovering wings such that model parameters are determined from first principles, which allows a fair comparison between the models themselves, and the models and experimental data. We show that the two models which directly include the LEV as a lift generating component are built on a physical picture that does not represent the available experimental data. The simpler 'normal force' model, which does not explicitly model the LEV, performs best against data in the literature. We conclude that under steady conditions the LEV as an 'absence of stall' model/mechanism is the most satisfying explanation for observed aerodynamic behaviour.

Petiolate wings: effects on the leading-edge vortex in flapping flight

The wings of many insect species including crane flies and damselflies are petiolate (on stalks), with the wing planform beginning some distance away from the wing hinge, rather than at the hinge. The aerodynamic impact of flapping petiolate wings is relatively unknown, particularly on the formation of the lift-augmenting leading-edge vortex (LEV): a key flow structure exploited by many insects, birds and bats to enhance their lift coefficient. We investigated the aerodynamic implications of petiolation P using particle image velocimetry flow field measurements on an array of rectangular wings of aspect ratio 3 and petiolation values of P = 1-3. The wings were driven using a mechanical device, the 'Flapperatus', to produce highly repeatable insect-like kinematics. The wings maintained a constant Reynolds number of 1400 and dimensionless stroke amplitude Λ* (number of chords traversed by the wingtip) of 6.5 across all test cases. Our results showed that for more petiolate wings the LEV is generally larger, stronger in circulation, and covers a greater area of the wing surface, particularly at the mid-span and inboard locations early in the wing stroke cycle. In each case, the LEV was initially arch-like in form with its outboard end terminating in a focus-sink on the wing surface, before transitioning to become continuous with the tip vortex thereafter. In the second half of the wing stroke, more petiolate wings exhibit a more detached LEV, with detachment initiating at approximately 70% and 50% span for P = 1 and 3, respectively. As a consequence, lift coefficients based on the LEV are higher in the first half of the wing stroke for petiolate wings, but more comparable in the second half. Time-averaged LEV lift coefficients show a general rise with petiolation over the range tested.