Flapping Wing Aerodynamics Research Articles

Using adjoint-based optimization to study kinematics and deformation of flapping wings

The study of flapping-wing aerodynamics faces a large control space with different wing kinematics and deformation. The adjoint-based approach, by solving an inverse problem to obtain simultaneously the sensitivity with respect to all control parameters, has a computational cost independent of the number of control parameters and becomes an efficient tool for the study of problems with a large control space. However, the adjoint equation is typically formulated in a fixed fluid domain. In a continuous formulation, a moving boundary or morphing domain results in inconsistency in the definition of an arbitrary perturbation at the boundary, which leads to ambiguousness and difficulty in the adjoint formulation if control parameters are related to boundary changes (e.g. the control of wing kinematics and dynamic deformation). The unsteady mapping function, as a traditional way to deal with moving boundaries, can in principle be a remedy for this situation. However, the derivation is often too complex to be feasible, even for simple problems. Part of the complexity comes from the unnecessary mapping of the interior mesh, while only mapping of the boundary is needed here. Non-cylindrical calculus, on the other hand, provides a boundary mapping and considers the rest of domain as an arbitrary extension from the boundary. Using non-cylindrical calculus to handle moving boundaries makes the derivation of the adjoint formulation much easier and also provides a simpler final formulation. The new adjoint-based optimization approach is validated for accuracy and efficiency by a well-defined case where a rigid plate plunges normally to an incoming flow. Then, the approach is applied for the optimization of drag reduction and propulsive efficiency of first a rigid plate and then a flexible plate which both flap with plunging and pitching motions against an incoming flow. For the rigid plate, the phase delay between pitching and plunging is the control and considered as both a constant (i.e. a single parameter) and a time-varying function (i.e. multiple parameters). The comparison between its arbitrary initial status and the two optimal solutions (with a single parameter or multiple parameters) reveals the mechanism and control strategy to reach the maximum thrust performance or propulsive efficiency. Essentially, the control is trying to benefit from both lift-induced thrust and viscous drag (by reducing it), and the viscous drag plays a dominant role in the optimization of efficiency. For the flexible plate, the control includes the amplitude and phase delay of the pitching motion and the leading eigenmodes to characterize the deformation. It is clear that flexibility brings about substantial improvement in both thrust performance and propulsive efficiency. Finally, the adjoint-based approach is extended to a three-dimensional study of a rectangular plate in hovering motion for lift performance. Both rigid and flexible cases are considered. The adjoint-based algorithm finds an optimal hovering motion with advanced rotation which has a large leading-edge vortex and strong downwash for lift benefit, and the introduction of flexibility enhances the wake capturing mechanism and generates a stronger downwash to push the lift coefficient higher.

Three-dimensional simulation for fast forward flight of a calliope hummingbird

We present a computational study of flapping-wing aerodynamics of a calliope hummingbird (Selasphorus calliope) during fast forward flight. Three-dimensional wing kinematics were incorporated into the model by extracting time-dependent wing position from high-speed videos of the bird flying in a wind tunnel at 8.3 m s−1. The advance ratio, i.e. the ratio between flight speed and average wingtip speed, is around one. An immersed-boundary method was used to simulate flow around the wings and bird body. The result shows that both downstroke and upstroke in a wingbeat cycle produce significant thrust for the bird to overcome drag on the body, and such thrust production comes at price of negative lift induced during upstroke. This feature might be shared with bats, while being distinct from insects and other birds, including closely related swifts.

Aerodynamic Analysis of Flexible Flapping Wing Micro Aerial Vehicle Using Quasi-Steady Approach

In recent times flexible flapping-wing aerodynamics has generated a great deal of interest and is the topic of contemporary research because of its potential application in micro aerial vehicles (MAVs). The prominent features of MAVs include low Reynolds Number, changing the camber of flapping wings, development of related mechanisms, study of the suitability airfoil shape selection and other parameters. Generally, low Reynolds Number is similar to that of an insect or a bird (103–105). The primary goal of this project work is to perform CFD analysis on flexible flapping wing MAVs in order to estimate the lift and drag by using engineering methods such as quasi-steady approach. From the wind tunnel data, 3-D deformation is obtained. For CFD analysis, two types of quasi-steady methods are considered. The first method is to slice the wing section chord-wise and span wise at multiple regions, frame by frame, and obtain the 2-D corrugated camber section for each frame. This 2-D corrugated camber is analysed using CFD techniques and all the individual 2-D corrugated camber results are summed up frame by frame, to obtain the total lift and drag for one wing beat. The second method is to consider the 3D wing in entirety and perform the CFD analysis to obtain the lift and drag for five wing beat.

Flapping wing aerodynamics: from insects to vertebrates.

More than a million insects and approximately 11,000 vertebrates utilize flapping wings to fly. However, flapping flight has only been studied in a few of these species, so many challenges remain in understanding this form of locomotion. Five key aerodynamic mechanisms have been identified for insect flight. Among these is the leading edge vortex, which is a convergent solution to avoid stall for insects, bats and birds. The roles of the other mechanisms - added mass, clap and fling, rotational circulation and wing-wake interactions - have not yet been thoroughly studied in the context of vertebrate flight. Further challenges to understanding bat and bird flight are posed by the complex, dynamic wing morphologies of these species and the more turbulent airflow generated by their wings compared with that observed during insect flight. Nevertheless, three dimensionless numbers that combine key flow, morphological and kinematic parameters - the Reynolds number, Rossby number and advance ratio - govern flapping wing aerodynamics for both insects and vertebrates. These numbers can thus be used to organize an integrative framework for studying and comparing animal flapping flight. Here, we provide a roadmap for developing such a framework, highlighting the aerodynamic mechanisms that remain to be quantified and compared across species. Ultimately, incorporating complex flight maneuvers, environmental effects and developmental stages into this framework will also be essential to advancing our understanding of the biomechanics, movement ecology and evolution of animal flight.

A CFD-informed quasi-steady model of flapping wing aerodynamics.

Aerodynamic performance and agility during flapping flight are determined by the combination of wing shape and kinematics. The degree of morphological and kinematic optimisation is unknown and depends upon a large parameter space. Aimed at providing an accurate and computationally inexpensive modelling tool for flapping-wing aerodynamics, we propose a novel CFD (computational fluid dynamics)-informed quasi-steady model (CIQSM), which assumes that the aerodynamic forces on a flapping wing can be decomposed into the quasi-steady forces and parameterised based on CFD results. Using least-squares fitting, we determine a set of proportional coefficients for the quasi-steady model relating wing kinematics to instantaneous aerodynamic force and torque; we calculate power with the product of quasi-steady torques and angular velocity. With the quasi-steady model fully and independently parameterised on the basis of high-fidelity CFD modelling, it is capable of predicting flapping-wing aerodynamic forces and power more accurately than the conventional blade element model (BEM) does. The improvement can be attributed to, for instance, taking into account the effects of the induced downwash and the wing tip vortex on the force generation and power consumption. Our model is validated by comparing the aerodynamics of a CFD model and the present quasi-steady model using the example case of a hovering hawkmoth. It demonstrates that the CIQSM outperforms the conventional BEM while remaining computationally cheap, and hence can be an effective tool for revealing the mechanisms of optimization and control of kinematics and morphology in flapping-wing flight for both bio-flyers and unmanned air systems.

Numerical study of tandem flapping wing aerodynamics in both two and three dimensions

In this paper we extend our previous two-dimensional tandem wing study to three-dimensions. In our previous study we found that vortex interactions highly depend on the phase lag angle and spacing between the forewing and hindwing. In this paper the effect of phase lag angle between the fore and hind wings on the wing–wing interactions, force production, and efficiency of the hindwing was studied for three different phase lag angles, 0°, 90° and 180°. The spacing used between the forewing and hindwing was one chord. A single frequency sinusoidal pitch–plunge motion was used at a Strouhal number of 0.3 and a Reynolds number of 200. The aspect ratio of the three dimensional wing was two. The simulations were based on the incompressible Navier–Stokes equations, discretized on overlapping grids. The wing motions were prescribed by a series of composed transformation matrices. A moving overlapping grid technique will be used to handle the moving boundary problems. It was found that the three dimensional cases exhibited a spanwise variation in the LEV structure and a weaker LEV formation at midspan compared to the two-dimensional cases with the same kinematics. The spanwise variation resulted in weaker vortex interactions between the fore and hind wing than predicted by the two dimensional study.

The influence of wing morphology on the three-dimensional flow patterns of a flapping wing at bird scale

The effect of airfoil design parameters, such as airfoil thickness and camber, are well understood in steady-state aerodynamics. But this knowledge cannot be readily applied to the flapping flight in insects and birds: flow visualizations and computational analyses of flapping flight have identified that in many cases, a leading-edge vortex (LEV) contributes substantially to the generation of aerodynamic force. In flapping flight, very high angles of attack and partly separated flow are common features. Therefore, it is expected that airfoil design parameters affect flapping wing aerodynamics differently. Existing studies have focused on force measurements, which do not provide sufficient insight into the dominant flow features. To analyse the influence of wing morphology in slow-speed bird flight, the time-resolved three-dimensional flow field around different flapping wing models in translational motion at a Reynolds number of$22\,000<\mathit{Re}<26\,000$was studied. The effect of several Strouhal numbers ($0.2<\mathit{St}<0.4$), camber and thickness on the flow morphology and on the circulation was analysed. A strong LEV was found on all wing types at high$\mathit{St}$. The vortex is stronger on thin wings and enhances the total circulation. Airfoil camber decreases the strength of the LEV, but increases the total bound circulation at the same time, due to an increase of the ‘conventional’ bound circulation at the inner half of the wing. The results provide new insights into the influence of airfoil shape on the LEV and force generation at low$\mathit{Re}$. They contribute to a better understanding of the geometry of vertebrate wings, which seem to be optimized to benefit from LEVs in slow-speed flight.

Space–time computational analysis of MAV flapping-wing aerodynamics with wing clapping

Computational analysis of flapping-wing aerodynamics with wing clapping was one of the classes of computations targeted in introducing the space---time (ST) interface-tracking method with topology ...

Effects of aspect ratio on flapping wing aerodynamics in animal flight

Morphology as well as kinematics is a critical determinant of performance in flapping flight. To understand the effects of the structural traits on aerodynamics of bio-flyers, three rectangular wings with aspect ratios (AR) of 1, 2, and 4 performing hovering-like sinusoidal kinematics at wingtip based Reynolds number of 5 300 are experimentally investigated. Flow structures on sectional cuts along the wing span are compared. Stronger K-H instability is found on the leading edge vortex of wings with higher aspect ratios. Vortex bursting only appears on the outer spanwise locations of high-aspect-ratio wings. The vortex bursting on high-aspect-ratio wings is perhaps one of the reasons why bio-flyers normally have low-aspect-ratio wings. Quantitative analysis exhibits larger dimensionless circulation of the leading edge vortex (LEV) over higher aspect ratio wings except when vortex bursting happens. The average dimensionless circulation of AR1 and AR2 along the span almost equals the dimensionless circulation at the 50% span. The flow structure and the circulation analysis show that the sinusoidal kinematics suppresses breakdown of the LEV compared with simplified flapping kinematics used in similar studies. The Reynolds number effect results on AR4 show that in the current Re range, the overall flow structure is not sensitive to Reynolds number.

Sequentially-coupled space–time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV

We present a sequentially-coupled space---time (ST) computational fluid---structure interaction (FSI) analysis of flapping-wing aerodynamics of a micro aerial vehicle (MAV). The wing motion and deformation data, whether prescribed fully or partially, is from an actual locust, extracted from high-speed, multi-camera video recordings of the locust in a wind tunnel. The core computational FSI technology is based on the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) formulation. This is supplemented with using NURBS basis functions in temporal representation of the wing and mesh motion, and in remeshing. Here we use the version of the DSD/SST formulation derived in conjunction with the variational multiscale (VMS) method, and this version is called "DSD/SST-VMST." The structural mechanics computations are based on the Kirchhoff---Love shell model. The sequential-coupling technique is applicable to some classes of FSI problems, especially those with temporally-periodic behavior. We show that it performs well in FSI computations of the flapping-wing aerodynamics we consider here. In addition to the straight-flight case, we analyze cases where the MAV body has rolling, pitching, or rolling and pitching motion. We study how all these influence the lift and thrust.

Space–time interface-tracking with topology change (ST-TC)

To address the computational challenges associated with contact between moving interfaces, such as those in cardiovascular fluid–structure interaction (FSI), parachute FSI, and flapping-wing aerodynamics, we introduce a space–time (ST) interface-tracking method that can deal with topology change (TC). In cardiovascular FSI, our primary target is heart valves. The method is a new version of the deforming-spatial-domain/stabilized space–time (DSD/SST) method, and we call it ST-TC. It includes a master–slave system that maintains the connectivity of the “parent” mesh when there is contact between the moving interfaces. It is an efficient, practical alternative to using unstructured ST meshes, but without giving up on the accurate representation of the interface or consistent representation of the interface motion. We explain the method with conceptual examples and present 2D test computations with models representative of the classes of problems we are targeting.

Experimental and Computational Modeling of the Kinematics and Aerodynamics of Flapping Wing

High-speed videography is used in measuring the kinematic and deformation parameters of the flapping wing. Based on these data, a theoretical analysis of the underlying physics is performed using computational fluid dynamics simulations. The time varying of the pitching angle in the chordwise directions exhibits a significant second harmonic. Results suggest the mechanics of membrane deformations during a flapping cycle is analogous to the buckling of a bistable structure. Noticeably, with an increase in the freestream speed, the downstroke duration increases. The solution to the three-dimensional fluid dynamics problem is constructed using two-dimensional solutions obtained for several sections of the wing by the improved discrete vortex method. The inertial component is dominant in the normal force coefficient, and hence, added mass is the main mechanism in aerodynamic force production for the studied problem. A normal component of the acceleration of the wing’s trailing edge taken with a negative sign is introduced as a kinematic parameter that is essential in flapping-wing aerodynamics. The results show a satisfactory agreement in trends of the acceleration and force coefficients. From the analysis of kinematical changes, it follows that synchronization of acceleration and of the pitching angle is important for achieving maximum values of the vertical force coefficients.

Active and passive stabilization of body pitch in insect flight

Flying insects have evolved sophisticated sensory–motor systems, and here we argue that such systems are used to keep upright against intrinsic flight instabilities. We describe a theory that predicts the instability growth rate in body pitch from flapping-wing aerodynamics and reveals two ways of achieving balanced flight: active control with sufficiently rapid reactions and passive stabilization with high body drag. By glueing magnets to fruit flies and perturbing their flight using magnetic impulses, we show that these insects employ active control that is indeed fast relative to the instability. Moreover, we find that fruit flies with their control sensors disabled can keep upright if high-drag fibres are also attached to their bodies, an observation consistent with our prediction for the passive stability condition. Finally, we extend this framework to unify the control strategies used by hovering animals and also furnish criteria for achieving pitch stability in flapping-wing robots.

Wing performance and 3-D vortical structure formation in flapping flight

Numerical simulations of the three-dimensional flow around a modelled insect wing were performed to investigate the performance in flapping flight and to provide insight into the vortex dynamics and associated force generation. Different parameters relevant for three-dimensional flapping wing aerodynamics have been studied, notably the angle of attack in mid-stroke, the Rossby number, the Reynolds number and the stroke kinematic pattern. A parametric study has been made for these parameters, notably for the hovering flight regime. The leading-edge vortex is confirmed to be important for the gain in lift, it being larger and more stable at angles of attack larger than about 30°. At smaller angles of attack, the leading-edge vortex development is insufficient to increase the lift, instead the lift decreases. It is observed that the trend of the force development over the cycle and the effect of the angle of attack is similar for revolving and translating wings. However, a flapping wing motion with a revolving character has an important lift-enhancing effect, at a small penalty of drag. Although the variations in lift and drag with Reynolds number are found to be larger at lower Rossby numbers, the lift-enhancing effect of the revolving wing appears not strongly dependent on Reynolds number. Application of a ‘trapezoidal angle of attack’ pattern with increased angular rotation at stroke reversal showed a significant performance increase. It was further shown how the variation in lift and drag can be significantly influenced by introducing deviation in the stroke pattern. A comparison between the three-dimensional simulations and two-dimensional simulations (for forward flight conditions) displayed similar trends with respect to the influence of the angle of attack. However, the latter do not account for finite wing and tip vortex effects which were found to have an important impact on the LEV development.

Unsteady Aerodynamics of Flapping Wing of a Bird

The unsteady flow behavior and time-dependent aerodynamic characteristics of the flapping motion of a bird’s wing were investigated using a computational method. During flapping, aerodynamic interactions between bird wing surfaces and surrounding flow may occur, generating local time-dependent flow changes in the flow field and aerodynamic load of birds. To study the effect of flapping speed on unsteady aerodynamic load, two kinds of computational simulations were carried out, namely a quasi-steady and an unsteady simulation. To mimic the movement of the down-stroke and the upstroke of a bird, the flapping path accorded to a sinus function, with the wing attitude changing in dihedral angle and time. The computations of time-dependent viscous flow were based on the solution of the Reynolds Averaged Navier-Stokes equations by applying the k- e turbulence model. In addition, the discretization for the computational domain around the model used multi-block structured grid to provide more accuracy in capturing viscous flow, especially in the vicinity of the wing and body surfaces, to obtain a proper wing-body geometry model. For this research, the seagull bird was chosen, which has high aspect ratio wings with pointed wing-tips and a high camber wing section. The results include mesh movement, velocity contours as well as aerodynamic coefficients of the flapping motion of the bird at various flapping frequencies.

Design and Manufacturing of Biologically Inspired Micro Aerial Vehicle Wings Using Rapid Prototyping

Micro Aerial Vehicles (MAVs) are an emerging class of uninhabited aerial vehicle (UAV). Their reduced scale (maximum dimension of approximately 150 mm) provides advantages in terms of advanced mission capabilities, such as wildlife monitoring and urban search and rescue. This introduces the design challenge of flying efficiently at very low Reynolds numbers (e.g. Re<10000). To date, three basic MAV design concepts have been developed: fixed, rotary and flapping wings. Each approach has been met with limited success due to gust stability, flight control and propulsive efficiency. The design of both fixed and rotary wing aircraft is relatively mature, whereas flapping wing design is in its infancy and therefore its viability cannot yet be assessed. Nonetheless flapping wing MAVs have the potential to offer advantages such as stealth, manoeuvrability, and improved propulsive efficiencies. This paper focuses on the challenging problem of the manufacture and testing of flapping wings for MAVs. A review of the current state of flapping wing aerodynamics, manufacturing, and wing structures is provided. A detailed assessment of the aerodynamic performance of flexible MAV-scale wings was carried out. Aerodynamic force measurements were collected using a spin rig to assess the effect of design details on lift generation. It was found that a simple three-vein wing structure manufactured using a fused filament fabrication 3D printer could produce lift forces close to those of natural insect wings. The lift and stall performance was found to be sensitive to chordwise stiffness by testing wings without veins. These results demonstrate that it is possible to produce low cost biologically inspired wings with aerodynamic performance equal to or better than natural wings – a critical step on the path to a functional and practical flapping wing MAV.

Fluid Structure Interaction of Unsteady Aerodynamics of Flapping Wing at Low Reynolds Number

Wing flexibility controls the aerodynamic-force generation of flapping-wing flyers. As the wing flaps through the air, it is subjected to both aerodynamic force acting on the surface of the wing and inertial force due to the acceleration or deceleration of the wing’s mass. The interaction between these inertial-elastic and aerodynamic forces resulted in wing deformation. To study the effects of skin flexibility and wing deformation on the aerodynamic performance of a flapping wing, fluid flow and structural analyses (two-way fluid structure interaction) are implemented in real-time application through the Multi-Physics Code Coupling Interface, using FLUENT and ABAQUS solvers. The different bending stiffness ratios are highlighted at 2,489; 159 and 1, which correspond to rigid, flexible, and highly flexible cases, respectively. In the present research, wing flexibility is investigated at low Reynolds number (Re^9,000) and reduced frequency (k=1.92). To validate the numerical model, an experimental study was conducted, and the result of the mean aerodynamic lift and drag coefficient showed good agreement. The time-averaged aerodynamic performances, such as mean lift coefficient, drag coefficient, and lift-to- drag ratio, revealed that the aerodynamic performance of flapping wings increases with the increase in flexibility.

Computer modeling techniques for flapping-wing aerodynamics of a locust

We present an overview of the special computer modeling techniques we have developed recently for flapping-wing aerodynamics of a locust. The wing motion and deformation data is from an actual locust, extracted from high-speed, multi-camera video recordings of the locust in a wind tunnel. The special techniques have been developed around our core computational technique, which is the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation. Here we use the version of the DSD/SST formulation derived in conjunction with the variational multiscale (VMS) method, and this version is called “DSD/SST-VMST.” The special techniques are based on using, in the space–time flow computations, NURBS basis functions for the temporal representation of the motion and deformation of the locust wings. Temporal NURBS basis functions are used also in representation of the motion of the volume meshes computed and in remeshing. In this special-issue paper, we present a condensed version of the material from [1], concentrating on the flapping-motion modeling and computations, and also a temporal-order study from [2].

Flapping wing aerodynamics of a numerical biological flyer model in hovering flight

Flapping flyers showcase excellent flight performances under many flight environments. In particular, hovering is a miracle of insects that can be seen for most of sizes of flying insects. Understanding of sizing or Reynolds numbers effects in hovering flights on the aerodynamics is not only of interest to the micro-air-vehicle ommunity but also of importance to comparative morphologists. In this study, a computational study of such size effects on insect hovering aerodynamics is conducted, which is performed using an integrated numerical framework consisting of the modeling of realistic wing-body morphology, the modeling of flapping-wing and body kinematics, and an in-house Navier–Stokes solver. Computational results of four typical insects in hovering flight including a thrips, a fruitfly, a honeybee, and a hawkmoth over a wide range of Reynolds numbers from O(101) to O(104) are presented. Furthermore the correlation among the near-and far-field flow features, the aerodynamic force production, and the wing kinematics is highlighted.

Space–time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle

We present a detailed computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle (MAV). The computational techniques used include the Deforming-Spatial-Domain/Stabilized Space---Time (DSD/SST) formulation, which serves as the core computational technique. The DSD/SST formulation is a moving-mesh technique, and in the computations reported here we use the space---time version of the residual-based variational multiscale (VMS) method, which is called "DSD/ SST-VMST." The motion and deformation of the wings are based on data extracted from the high-speed, multi-camera video recordings of a locust in a wind tunnel. A set of special space---time techniques are also used in the computations in conjunction with the DSD/SST method. The special techniques are based on using, in the space---time flow computations, NURBS basis functions for the temporal representation of the motion and deformation of the wings and for the mesh moving and remeshing. The computational analysis starts with the computation of the base case, and includes computations with increased temporal and spatial resolutions compared to the base case. In increasing the temporal resolution, we separately test increasing the temporal order, the number of temporal subdivisions, and the frequency of remeshing. In terms of the spatial resolution, we separately test increasing the wing-mesh refinement in the normal and tangential directions and changing the way node connectivities are handled at the wingtips. The computational analysis also includes using different combinations of wing configurations for the MAV and investigating the beneficial and disruptive interactions between the wings and the role of wing camber and twist.