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

Effect of Hindwings on the Aerodynamics and Passive Dynamic Stability of a Hovering Hawkmoth

Insects are able to fly stably in the complex environment of the various gusts that occur in nature. In addition, many insects suffer wing damage in their lives, but many species of insects are capable of flying without their hindwings. Here, we evaluated the effect of hindwings on aerodynamics using a Navier-Stokes-based numerical model, and then the passive dynamic stability was evaluated by coupling the equation of motion in three degrees of freedom with the aerodynamic forces estimated by the CFD solver under large and small perturbation conditions. In terms of aerodynamic effects, the presence of the hindwings slightly reduces the efficiency for lift generation but enhances the partial LEV circulation and increases the downwash around the wing root. In terms of thrust, increasing the wing area around the hindwing region increases the thrust, and the relationship is almost proportional at the cycle-averaged value. The passive dynamic stability was not clearly affected by the presence of the hindwings, but the stability was slightly improved depending on the perturbation direction. These results may be useful for the integrated design of wing geometry and flight control systems in the development of flapping-winged micro air vehicles.

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.

A semi-empirical model of the aerodynamics of manoeuvring insect flight

Blade element modelling provides a quick analytical method for estimating the aerodynamic forces produced during insect flight, but such models have yet to be tested rigorously using kinematic data recorded from free-flying insects. This is largely because of the paucity of detailed free-flight kinematic data, but also because analytical limitations in existing blade element models mean that they cannot incorporate the complex three-dimensional movements of the wings and body that occur during insect flight. Here, we present a blade element model with empirically fitted aerodynamic force coefficients that incorporates the full three-dimensional wing kinematics of manoeuvring Eristalis hoverflies, including torsional deformation of their wings. The two free parameters were fitted to a large free-flight dataset comprising N = 26 541 wingbeats, and the fitted model captured approximately 80% of the variation in the stroke-averaged forces in the sagittal plane. We tested the robustness of the model by subsampling the data, and found little variation in the parameter estimates across subsamples comprising 10% of the flight sequences. The simplicity and generality of the model that we present is such that it can be readily applied to kinematic datasets from other insects, and also used for the study of insect flight dynamics.

Aerodynamic performance of flexible flapping wings deformed by slack angle

Wing flexibility is unavoidable for flapping wing flyers to ensure a lightweight body and for higher payload allowances on board. It also effectively minimizes the inertia force from high-frequency wingbeat motion. However, related studies that attempt to clarify the essence of wing flexibility remain insufficient. Here, a parametric study of a flexible wing was conducted as part of the effort to build an aerodynamic model and analyze its aerodynamic performance. The quasi-steady modeling was adopted with experimentally determined translational forces. These forces were determined from 84 flexible wing cases while varying the angle of attack at the wing rootα_rand the flexibility parameter, slack angleθ_S, with 19 additional rigid wing cases. This study foundα_rfor optimum lift generation to exceed 45° irrespective ofθ_S. The coefficient curves were well-fitted with a cubed-sine function. The model was rigorously validated with various wing kinematics, giving a good estimation of the experimental results. The estimated error was less than 5%, 6%, and 8% for the lift, drag, and moment, respectively, considering fast to moderate wing kinematics. The study was extended to analyze the pure aerodynamic performance of the flexible wing. The most suitable wing for a flapping-wing micro-aerial vehicle wing design with a simple vein structure was found to be the 5° slack-angled wing. The inference from this study further shows that a small amount of deformation is needed to increase the lift, as observed in natural flyers. Thus, wing deformation could allow living flyers to undertake less pitching motion in order to reduce the mechanical power and increase the efficiency of their wings.

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.

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.

Forewings match the formation of leading-edge vortices and dominate aerodynamic force production in revolving insect wings

In many flying insects, forewings and hindwings are coupled mechanically to achieve flapping flight synchronously while being driven by action of the forewings. How the forewings and hindwings as well as their morphologies contribute to aerodynamic force production and flight control remains unclear. Here we address the point that the forewings can produce most of the aerodynamic forces even with the hindwings removed through a computational fluid dynamic study of three revolving insect wing models, which are identical to the wing morphologies and Reynolds numbers of hawkmoth (Manduca sexta), bumblebee (Bombus ignitus) and fruitfly (Drosophila melanogaster). We find that the forewing morphologies match the formation of leading-edge vortices (LEV) and are responsible for generating sufficient lift forces at the mean angles of attack and the Reynolds numbers where the three representative insects fly. The LEV formation and pressure loading keep almost unchanged with the hindwing removed, and even lead to some improvement in power factor and aerodynamic efficiency. Moreover, our results indicate that the size and strength of the LEVs can be well quantified with introduction of a conical LEV angle, which varies remarkably with angles of attack and Reynolds numbers but within the forewing region while showing less sensitivity to the wing morphologies. This implies that the forewing morphology very likely plays a dominant role in achieving low-Reynolds number aerodynamic performance in natural flyers as well as in revolving and/or flapping micro air vehicles.

Coevolving advances in animal flight and aerial robotics

Our understanding of animal flight has inspired the design of new aerial robots with more effective flight capacities through the process of biomimetics and bioinspiration. The aerodynamic origin of the elevated performance of flying animals remains, however, poorly understood. In this themed issue, animal flight research and aerial robot development coalesce to offer a broader perspective on the current advances and future directions in these coevolving fields of research. Together, four reviews summarize and 14 reports contribute to our understanding of low Reynolds number flight. This area of applied aerodynamics research is challenging to dissect due to the complicated flow phenomena that include laminar–turbulent flow transition, laminar separation bubbles, delayed stall and nonlinear vortex dynamics. Our mechanistic understanding of low Reynolds number flight has perhaps been advanced most by the development of dynamically scaled robot models and new specialized wind tunnel facilities: in particular, the tiltable Lund flight tunnel for animal migration research and the recently developed AFAR hypobaric wind tunnel for high-altitude animal flight studies. These world-class facilities are now complemented with a specialized low Reynolds number wind tunnel for studying the effect of turbulence on animal and robot flight in much greater detail than previously possible. This is particular timely, because the study of flight in extremely laminar versus turbulent flow opens a new frontier in our understanding of animal flight. Advancing this new area will offer inspiration for developing more efficient high-altitude aerial robots and removes roadblocks for aerial robots operating in turbulent urban environments.