Showing papers on "Flapping published in 2011"

Flapping and Bending Bodies Interacting with Fluid Flows

Abstract: The flapping or bending of a flexible planar structure in a surrounding fluid flow, which includes the flapping of flags and the self-streamlining of flexible bodies, constitutes a central problem in the field of fluid-body interactions. Here we review recent, highly detailed experiments that reveal new nonlinear phenomena in these systems, as well as advances in theoretical understanding, resulting in large part from the rapid development of new simulation methods that fully capture the mutual coupling of fluids and flexible solids.

Effects of Flexibility on the Aerodynamic Performance of Flapping Wings

Abstract: Effects of chordwise, spanwise, and isotropic flexibility on the force generation and propulsive efficiency of flapping wings are elucidated. For a moving body immersed in viscous fluid, different types of forces, as a function of the Reynolds number, reduced frequency (k), and Strouhal number (St), acting on the moving body are identified based on a scaling argument. In particular, at the Reynolds number regime of O(10 3 - 10 4 ) and the reduced frequency of O(1), the added mass force, related to the acceleration of the wing, is important. Based on the order of magnitude and energy balance arguments, a relationship between the propulsive force and the maximum relative wing tip deformation parameter (γ) is established. The parameter depends on the density ratio, St, k, natural and flapping frequency ratio, and flapping amplitude. The lift generation, and the propulsive efficiency can be deduced by the same scaling procedures. It seems that the maximum propulsive force is obtained when flapping near the resonance, whereas the optimal propulsive efficiency is reached when flapping at about half of the natural frequency; both are supported by the reported studies. The established scaling relationships can offer direct guidance for MAV design and performance analysis.

Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance

Abstract: Saving energy and enhancing performance are secular preoccupations shared by both nature and human beings. In animal locomotion, flapping flyers or swimmers rely on the flexibility of their wings or body to passively increase their efficiency using an appropriate cycle of storing and releasing elastic energy. Despite the convergence of many observations pointing out this feature, the underlying mechanisms explaining how the elastic nature of the wings is related to propulsive efficiency remain unclear. Here we use an experiment with a self-propelled simplified insect model allowing to show how wing compliance governs the performance of flapping flyers. Reducing the description of the flapping wing to a forced oscillator model, we pinpoint different nonlinear effects that can account for the observed behavior—in particular a set of cubic nonlinearities coming from the clamped-free beam equation used to model the wing and a quadratic damping term representing the fluid drag associated to the fast flapping motion. In contrast to what has been repeatedly suggested in the literature, we show that flapping flyers optimize their performance not by especially looking for resonance to achieve larger flapping amplitudes with less effort, but by tuning the temporal evolution of the wing shape (i.e., the phase dynamics in the oscillator model) to optimize the aerodynamics.

Translational and Rotational Damping of Flapping Flight and Its Dynamics and Stability at Hovering

Abstract: Body movements of flying insects change their effective wing kinematics and, therefore, influence aerodynamic force and torque production. It was found that substantial aerodynamic damping is produced by flapping wings through a passive mechanism termed “flapping countertorque” during fast yaw turns. We expand this study to include the aerodynamic damping that is produced by flapping wings during body translations and rotations with respect to all its six principal axes-roll, pitch, yaw, forward/backward, sideways, and heave. Analytical models were derived by the use of a quasi-steady aerodynamic model and blade-element analysis by the incorporation of the effective changes of wing kinematics that are caused by body motion. We found that aerodynamic damping, in all these cases, is linearly dependent on the body translational and angular velocities and increases with wing-stroke amplitude and frequency. Based on these analytical models, we calculated the stability derivatives that are associated with the linearized flight dynamics at hover and derived a complete 6-degree-of-freedom (6-DOF) dynamic model. The model was then used to estimate the flight dynamics and stability of four different species of flying insects as case studies. The analytical model that is developed in this paper is important to study the flight dynamics and passive stability of flying animals, as well as to develop flapping-wing micro air vehicles (MAVs) with stable and maneuverable flight, which is achieved through passive dynamic stability and active flight control.

Aerodynamic performance of a hovering hawkmoth with flexible wings: a computational approach

Abstract: Insect wings are deformable structures that change shape passively and dynamically owing to inertial and aerodynamic forces during flight. It is still unclear how the three-dimensional and passive change of wing kinematics owing to inherent wing flexibility contributes to unsteady aerodynamics and energetics in insect flapping flight. Here, we perform a systematic fluid-structure interaction based analysis on the aerodynamic performance of a hovering hawkmoth, Manduca, with an integrated computational model of a hovering insect with rigid and flexible wings. Aerodynamic performance of flapping wings with passive deformation or prescribed deformation is evaluated in terms of aerodynamic force, power and efficiency. Our results reveal that wing flexibility can increase downwash in wake and hence aerodynamic force: first, a dynamic wing bending is observed, which delays the breakdown of leading edge vortex near the wing tip, responsible for augmenting the aerodynamic force-production; second, a combination of the dynamic change of wing bending and twist favourably modifies the wing kinematics in the distal area, which leads to the aerodynamic force enhancement immediately before stroke reversal. Moreover, an increase in hovering efficiency of the flexible wing is achieved as a result of the wing twist. An extensive study of wing stiffness effect on aerodynamic performance is further conducted through a tuning of Young's modulus and thickness, indicating that insect wing structures may be optimized not only in terms of aerodynamic performance but also dependent on many factors, such as the wing strength, the circulation capability of wing veins and the control of wing movements.

Aerodynamics of a bio-inspired flexible flapping-wing micro air vehicle

Abstract: MAVs (micro air vehicles) with a maximal dimension of 15 cm and nominal flight speeds of around 10 m s⁻¹, operate in a Reynolds number regime of 10⁵ or lower, in which most natural flyers including insects, bats and birds fly. Furthermore, due to their light weight and low flight speed, the MAVs' flight characteristics are substantially affected by environmental factors such as wind gust. Like natural flyers, the wing structures of MAVs are often flexible and tend to deform during flight. Consequently, the aero/fluid and structural dynamics of these flyers are closely linked to each other, making the entire flight vehicle difficult to analyze. We have recently developed a hummingbird-inspired, flapping flexible wing MAV with a weight of 2.4-3.0 g and a wingspan of 10-12 cm. In this study, we carry out an integrated study of the flexible wing aerodynamics of this flapping MAV by combining an in-house computational fluid dynamic (CFD) method and wind tunnel experiments. A CFD model that has a realistic wing planform and can mimic realistic flexible wing kinematics is established, which provides a quantitative prediction of unsteady aerodynamics of the four-winged MAV in terms of vortex and wake structures and their relationship with aerodynamic force generation. Wind tunnel experiments further confirm the effectiveness of the clap and fling mechanism employed in this bio-inspired MAV as well as the importance of the wing flexibility in designing small flapping-wing MAVs.

Effect of Flexural and Torsional Wing Flexibility on Lift Generation in Hoverfly Flight

Abstract: Synopsis The effect of wing flexibility in hoverflies was investigated using an at-scale mechanical model. Unlike dynamically-scaled models, an at-scale model can include all phenomena related to motion and deformation of the wing during flapping. For this purpose, an at-scale polymer wing mimicking a hoverfly was fabricated using a custom micromolding process. The wing has venation and corrugation profiles which mimic those of a hoverfly wing and the measured flexural stiffness of the artificial wing is comparable to that of the natural wing. To emulate the torsional flexibility at the wing-body joint, a discrete flexure hinge was created. A range of flexure stiffnesses was chosen to match the torsional stiffness of pronation and supination in a hoverfly wing. The polymer wing was compared with a rigid, flat, carbon-fiber wing using a flapping mechanism driven by a piezoelectric actuator. Both wings exhibited passive rotation around the wing hinge; however, these rotations were reduced in the case of the compliant polymer wing due to chordwise deformations during flapping which caused a reduced effective angle of attack. Maximum lift was achieved when the stiffness of the hinge was similar to that of a hoverfly in both wing cases and the magnitude of measured lift is sufficient for hovering; the maximum lift achieved by the single polymer and carbon-fiber wings was 5.9 � 10 2 mN and 6.9 � 10 2 mN, respectively. These results suggest that hoverflies could exploit intrinsic compliances to generate desired motions of the wing and that, for the same flapping motions, a rigid wing could be more suitable for producing large lift.

Effects of flexibility on the aerodynamic performance of flapping wings

Abstract: Effects of chordwise, spanwise, and isotropic flexibility on the force generation and propulsive efficiency of flapping wings are elucidated. For a moving body immersed in viscous fluid, different types of forces, as a function of the Reynolds number, reduced frequency (k), and Strouhal number (St), acting on the moving body are identified based on a scaling argument. In particular, at the Reynolds number regime of O(10 3 - 10 4 ) and the reduced frequency of O(1), the added mass force, related to the acceleration of the wing, is important. Based on the order of magnitude and energy balance arguments, a relationship between the propulsive force and the maximum relative wing tip deformation parameter (γ) is established. The parameter depends on the density ratio, St, k, natural and flapping frequency ratio, and flapping amplitude. The lift generation, and the propulsive efficiency can be deduced by the same scaling procedures. It seems that the maximum propulsive force is obtained when flapping near the resonance, whereas the optimal propulsive efficiency is reached when flapping at about half of the natural frequency; both are supported by the reported studies. The established scaling relationships can offer direct guidance for MAV design and performance analysis.

Elastic deformation and energy loss of flapping fly wings.

Abstract: During flight, the wings of many insects undergo considerable shape changes in spanwise and chordwise directions. We determined the origin of spanwise wing deformation by combining measurements on segmental wing stiffness of the blowfly Calliphora vicina in the ventral and dorsal directions with numerical modelling of instantaneous aerodynamic and inertial forces within the stroke cycle using a two-dimensional unsteady blade elementary approach. We completed this approach by an experimental study on the wing's rotational axis during stroke reversal. The wing's local flexural stiffness ranges from 30 to 40 nN m2 near the root, whereas the distal wing parts are highly compliant (0.6 to 2.2 nN m2). Local bending moments during wing flapping peak near the wing root at the beginning of each half stroke due to both aerodynamic and inertial forces, producing a maximum wing tip deflection of up to 46 deg. Blowfly wings store up to 2.30 μJ elastic potential energy that converts into a mean wing deformation power of 27.3 μW. This value equates to approximately 5.9 and 2.3% of the inertial and aerodynamic power requirements for flight in this animal, respectively. Wing elasticity measurements suggest that approximately 20% or 0.46 μJ of elastic potential energy cannot be recovered within each half stroke. Local strain energy increases from tip to root, matching the distribution of the wing's elastic protein resilin, whereas local strain energy density varies little in the spanwise direction. This study demonstrates a source of mechanical energy loss in fly flight owing to spanwise wing bending at the stroke reversals, even in cases in which aerodynamic power exceeds inertial power. Despite lower stiffness estimates, our findings are widely consistent with previous stiffness measurements on insect wings but highlight the relationship between local flexural stiffness, wing deformation power and energy expenditure in flapping insect wings. * c : wing chord ![Graphic][1] : mean wing chord D : drag parallel with local stream E : wing loading energy EI : flexural stiffness EPE : elastic potential energy F a : total aerodynamic force F acc : added mass reaction force F a,h : horizontal component of total aerodynamic force F a,n : aerodynamic force normal to wing chord F a,v : vertical component of total aerodynamic force F i : total inertia F i,h : inertia in the horizontal due to wing translation and rotation ![Graphic][2] : inertia in the horizontal due to wing translation ![Graphic][3] : inertia in the horizontal due to wing rotation F i,n : total inertia normal to wing chord F i,v : inertia in the vertical due to wing rotation F m : Magnus force F m,n : Magnus force normal to wing chord F n : total force normal to wing chord (vector sum of F a,n, : F m,n and F i,n) h : wing thickness k : combined wing spring constant from root to r l : distance of m w from rotational axis L : lift normal with local stream m w : wing mass of blade element M : local wing bending moment n : number of wing blade starting at wing root P acc : total inertial power for wing flapping P aero : total aerodynamic power for wing flapping r : distance from wing root r′ : blade position R : wing length SED : strain energy density t : time v : normal velocity of wing element computational w : width of wing blade α : geometrical angle of attack with respect to vertical αg : geometrical angle of attack with respect to horizontal ![Graphic][4] : angular velocity of wing rotation ![Graphic][5] : angular acceleration of wing rotation β : added mass coefficient δ : wing deflection ρ : air density e : elasticity ϕ : wing stroke angle ![Graphic][6] : angular velocity of wing translation ![Graphic][7] : angular acceleration [1]: /embed/inline-graphic-9.gif [2]: /embed/inline-graphic-10.gif [3]: /embed/inline-graphic-11.gif [4]: /embed/inline-graphic-12.gif [5]: /embed/inline-graphic-13.gif [6]: /embed/inline-graphic-14.gif [7]: /embed/inline-graphic-15.gif

Actuator disk model and span efficiency of flapping flight in bats based on time-resolved PIV measurements

Abstract: All animals flap their wings in powered flight to provide both lift and thrust, yet few human-engineered designs do so. When combined with flexible wing surfaces, the resulting unsteady fluid flows and interactions in flapping flight can be complex to describe, understand, and model. Here, a simple modified actuator disk is used in a quasi-steady description of the net aerodynamic lift forces on several species of bat whose wakes are measured with time-resolved PIV. The model appears to capture the time-averaged and instantaneous lift forces on the wings and body, and could be used as basis for comparing flapping flight efficiency of different animal species and micro air vehicle designs.

A wing-assisted running robot and implications for avian flight evolution.

Abstract: DASH+Wings is a small hexapedal winged robot that uses flapping wings to increase its locomotion capabilities. To examine the effects of flapping wings, multiple experimental controls for the same locomotor platform are provided by wing removal, by the use of inertially similar lateral spars, and by passive rather than actively flapping wings. We used accelerometers and high-speed cameras to measure the performance of this hybrid robot in both horizontal running and while ascending inclines. To examine consequences of wing flapping for aerial performance, we measured lift and drag forces on the robot at constant airspeeds and body orientations in a wind tunnel; we also determined equilibrium glide performance in free flight. The addition of flapping wings increased the maximum horizontal running speed from 0.68 to 1.29 m s⁻¹, and also increased the maximum incline angle of ascent from 5.6° to 16.9°. Free flight measurements show a decrease of 10.3° in equilibrium glide slope between the flapping and gliding robot. In air, flapping improved the mean lift:drag ratio of the robot compared to gliding at all measured body orientations and airspeeds. Low-amplitude wing flapping thus provides advantages in both cursorial and aerial locomotion. We note that current support for the diverse theories of avian flight origins derive from limited fossil evidence, the adult behavior of extant flying birds, and developmental stages of already volant taxa. By contrast, addition of wings to a cursorial robot allows direct evaluation of the consequences of wing flapping for locomotor performance in both running and flying.

Effect of wing–wake interaction on aerodynamic force generation on a 2D flapping wing

Abstract: This paper is motivated by the works of Dickinson et al. (Science 284:1954–1960, 1999) and Sun and Tang (J Exp Biol 205:55–70, 2002) which provided two different perspectives on the influence of wing–wake interaction (or wake capture) on lift generation during flapping motion. Dickinson et al. (Science 284:1954–1960, 1999) hypothesize that wake capture is responsible for the additional lift generated at the early phase of each stroke, while Sun and Tang (J Exp Biol 205:55–70, 2002) believe otherwise. Here, we take a more fundamental approach to study the effect of wing–wake interaction on the aerodynamic force generation by carrying out simultaneous force and flow field measurements on a two-dimensional wing subjected to two different types of motion. In one of the motions, the wing at a fixed angle of attack was made to follow a motion profile described by “acceleration-constant velocity-deceleration”. Here, the wing was first linearly accelerated from rest to a predetermined maximum velocity and remains at that speed for set duration before linearly decelerating to a stop. The acceleration and deceleration phase each accounted for only 10% of the stroke, and the stroke covered a total distance of three chord lengths. In another motion, the wing was subjected to the same above-mentioned movement, but in a back and forth manner over twenty strokes. Results show that there are two possible outcomes of wing–wake interaction. The first outcome occurs when the wing encounters a pair of counter-rotating wake vortices on the reverse stroke, and the induced velocity of these vortices impinges directly on the windward side of the wing, resulting in a higher oncoming flow to the wing, which translates into a higher lift. Another outcome is when the wing encounters one vortex on the reverse stroke, and the close proximity of this vortex to the windward surface of the wing, coupled with the vortex suction effect (caused by low pressure region at the center of the vortex), causes the net force on the wing to decrease momentarily. These results suggest that wing–wake interaction does not always lead to lift enhancement, and it can also cause lift reduction. As to which outcome prevails depend very much on the flapping motion and the timing of the reverse stroke.

Structural dynamics and aerodynamics measurements of biologically inspired flexible flapping wings

Abstract: Flapping wing flight as seen in hummingbirds and insects poses an interesting unsteady aerodynamic problem: coupling of wing kinematics, structural dynamics and aerodynamics. There have been numerous studies on the kinematics and aerodynamics in both experimental and computational cases with both natural and artificial wings. These studies tend to ignore wing flexibility; however, observation in nature affirms that passive wing deformation is predominant and may be crucial to the aerodynamic performance. This paper presents a multidisciplinary experimental endeavor in correlating a flapping micro air vehicle wing's aeroelasticity and thrust production, by quantifying and comparing overall thrust, structural deformation and airflow of six pairs of hummingbird-shaped membrane wings of different properties. The results show that for a specific spatial distribution of flexibility, there is an effective frequency range in thrust production. The wing deformation at the thrust-productive frequencies indicates the importance of flexibility: both bending and twisting motion can interact with aerodynamic loads to enhance wing performance under certain conditions, such as the deformation phase and amplitude. By measuring structural deformations under the same aerodynamic conditions, beneficial effects of passive wing deformation can be observed from the visualized airflow and averaged thrust. The measurements and their presentation enable observation and understanding of the required structural properties for a thrust effective flapping wing. The intended passive responses of the different wings follow a particular pattern in correlation to their aerodynamic performance. Consequently, both the experimental technique and data analysis method can lead to further studies to determine the design principles for micro air vehicle flapping wings.

Numerical study of flow characteristics behind a stationary circular cylinder with a flapping plate

Abstract: The laminar flow over a stationary circular cylinder with a flapping plate is simulated in this study to investigate the flow characteristics by using our recently developed boundary condition-enforced immersed boundary-lattice Boltzmann method [Wu and Shu, J. Comput. Phys. 228, 1963 (2009); Wu et al., Int. J. Numer. Methods Fluids 62, 327 (2010); Wu and Shu, Comm. Comp. Phys. 7, 793 (2010)]. The purpose of this work is to study the flow control behind a bluff body by an alternative way different from the rotationally oscillating motion. The idea is in fact from the tadpole locomotion, where the bluff head-body is modeled by a circular cylinder, and the thin tail is simplified by a rigid plate with flapping motion. In this work, only the laminar flow is considered and thus the Reynolds number is chosen as 100. Similar to the case of rotationally oscillating cylinder, the flow wake behind the cylinder and flapping plate is strongly affected by the flapping amplitude and frequency of plate. On the other han...

Flight mechanics of a tailless articulated wing aircraft

Abstract: This paper investigates the flight mechanics of a micro aerial vehicle without a vertical tail in an effort to reverse-engineer the agility of avian flight. The key to stability and control of such a tailless aircraft lies in the ability to control the incidence angles and dihedral angles of both wings independently. The dihedral angles can be varied symmetrically on both wings to control aircraft speed independently of the angle of attack and flight path angle, while asymmetric dihedral can be used to control yaw in the absence of a vertical stabilizer. It is shown that wing dihedral angles alone can effectively regulate sideslip during rapid turns and generate a wide range of equilibrium turn rates while maintaining a constant flight speed and regulating sideslip. Numerical continuation and bifurcation analysis are used to compute trim states and assess their stability. This paper lays the foundation for design and stability analysis of a flapping wing aircraft that can switch rapidly from flapping to gliding flight for agile manoeuvring in a constrained environment.

Longitudinal Flight Dynamics of Bioinspired Ornithopter Considering Fluid-Structure Interaction

Abstract: This paper addresses the flapping frequency-dependent trim flight characteristics of a bioinspired ornithopter. An integrative ornithopter flight simulator including a modal-based flexible multibody dynamics solver, a semiempirical reduced-order flapping-wing aerodynamic model, and their loosely coupled fluid―structure interaction are used to numerically simulate the ornithopter flight characteristics. The effect of the fluid―structure interaction of the main wing is quantitatively examined by comparing the wing deformations in both spanwise and chordwise directions, with and without aerodynamic loadings, and it shows that the fluid―structure interaction created a particular phase delay between the imposed wing motion and the aeroelastic response of the main wing and tail wing. The trimmed level flight conditions of the ornithopter model are found to satisfy the weak convergence criteria, which signifies that the longitudinal flight state variables of ornithopters need to be bounded and that the mean value of the variables are converged to the finite values. Unlike conventional fixed-wing aerial vehicles, the longitudinal flight state variables, such as forward flight speed, body pitch attitude, and tail-wing angle of attack in trimmed level flight, showed stable limit-cycle oscillatory behaviors with the flapping frequency as the dominant oscillating frequency. The mean body pitch attitude and tail-wing angle, and the root-mean-square value of the body pitch attitude, decreased as the flapping frequency increased. In addition, the mean forward flight speed is found to almost linearly increase with the flapping frequency.

An experimental study of the unsteady vortex structures in the wake of a root-fixed flapping wing

Abstract: An experimental study was conducted to characterize the evolution of the unsteady vortex structures in the wake of a root-fixed flapping wing with the wing size, stroke amplitude, and flapping frequency within the range of insect characteristics for the development of novel insect-sized nano-air-vehicles (NAVs). The experiments were conducted in a low-speed wing tunnel with a miniaturized piezoelectric wing (i.e., chord length, C = 12.7 mm) flapping at a frequency of 60 Hz (i.e., f = 60 Hz). The non-dimensional parameters of the flapping wing are chord Reynolds number of Re = 1,200, reduced frequency of k = 3.5, and non-dimensional flapping amplitude at wingtip h = A/C = 1.35. The corresponding Strouhal number (Str) is 0.33, which is well within the optimal range of 0.2 < Str < 0.4 used by flying insects and birds and swimming fishes for locomotion. A digital particle image velocimetry (PIV) system was used to achieve phased-locked and time-averaged flow field measurements to quantify the transient behavior of the wake vortices in relation to the positions of the flapping wing during the upstroke and down stroke flapping cycles. The characteristics of the wake vortex structures in the chordwise cross planes at different wingspan locations were compared quantitatively to elucidate underlying physics for a better understanding of the unsteady aerodynamics of flapping flight and to explore/optimize design paradigms for the development of novel insect-sized, flapping-wing-based NAVs.

Optimal Hovering Kinematics of Flapping Wings for Micro Air Vehicles

Abstract: This paper presents theoretical and experimental analyses of insect flapping mechanics and aerodynamics, with the aim of developing flapping-wing micro air vehicles. A model of an insect thorax flapping mechanism is developed that includes a quasi-steady aerodynamic model. Computer simulations of the thorax model show insectlike wing kinematics, including passive wing rotation at the end of the stroke. These kinematics are perturbed in a sequence of experiments using a robotic flapping-wing device to determine optimal hovering kinematics. Experiments are supported with numerical optimization based on the aerodynamic model. Apart from optimal kinematics, this study shows negative aerodynamic power required during wing rotation, which explains passive wing rotation at the end of the stroke.

Effect of flapping kinematics on the mean lift of an insect-like flapping wing:

Abstract: An experimental investigation of the effects of varying flapping kinematics on the mean lift produced by an insect-like flapping wing in hover is presented. This was performed with application to flapping-wing micro-air vehicles (FMAVs) in mind. Experiments were accomplished with a first-of-its-kind mechanical flapping-wing apparatus capable of reproducing a wide range of insect-like wing motions in air on the FMAV scale (~150 mm wingspan). This apparatus gives an insect-like wing the three controllable degrees of freedom required to produce the three separate motions necessary for mimicking an insect-like flapping-wing trajectory: sweeping (side to side), plunging (up and down), and pitching (angle of attack variation). Lift was measured via a force balance while the following kinematic parameters were varied: flapping frequency (f ), angle of attack at mid-stroke (αmid), timing of pitch reversal with stroke reversal (rotation phase), stroke amplitude (Φ), and plunge amplitude (Θ). Results revealed that ...

Cross sectional geometry of the forelimb skeleton and flight mode in pelecaniform birds.

Abstract: Avian wing elements have been shown to experience both dorsoventral bending and torsional loads during flapping flight. However, not all birds use continuous flapping as a primary flight strategy. The pelecaniforms exhibit extraordinary diversity in flight mode, utilizing flapping, flap-gliding, and soaring. Here we (1) characterize the cross-sectional geometry of the three main wing bone (humerus, ulna, carpometacarpus), (2) use elements of beam theory to estimate resistance to loading, and (3) examine patterns of variation in hypothesized loading resistance relative to flight and diving mode in 16 species of pelecaniform birds. Patterns emerge that are common to all species, as well as some characteristics that are flight- and diving-mode specific. In all birds examined, the distal most wing segment (carpometacarpus) is the most elliptical (relatively high I(max) /I(min) ) at mid-shaft, suggesting a shape optimized to resist bending loads in a dorsoventral direction. As primary flight feathers attach at an oblique angle relative to the long axis of the carpometacarpus, they are likely responsible for inducing bending of this element during flight. Moreover, among flight modes examined the flapping group (cormorants) exhibits more elliptical humeri and carpometacarpi than other flight modes, perhaps pertaining to the higher frequency of bending loads in these elements. The soaring birds (pelicans and gannets) exhibit wing elements with near-circular cross-sections and higher polar moments of area than in the flap and flap-gliding birds, suggesting shapes optimized to offer increased resistance to torsional loads. This analysis of cross-sectional geometry has enhanced our interpretation of how the wing elements are being loaded and ultimately how they are being used during normal activities.

Aerodynamics of a Bio-inspired Flexible Flapping Wing Micro Air Vehicle

Abstract: MAVs (micro air vehicles) with a maximal dimension of 15 cm and nominal flight speeds around 10 m/s, normally operate in a Reynolds number regime of 105 or lower, in which most natural flyers including insects, bats and birds fly. Like such natural flyers, the wing structures of MAVs are often flexible and tend to deform by aerodynamic and inertial forces during flight. Consequently, the aero/fluid and structural dynamics of these flyers are closely linked to each other, making the entire flight vehicle difficult to analyze. We have recently developed a hummingbird-inspired, flapping flexible wing MAV with a weight of 2.4 - 3.0 gf and a wingspan of 10 - 12 cm. In this study, we carry out an integrated study of the flexible wing aerodynamics of this flapping MAV by means of an in-house computational fluid dynamic (CFD) solver. A CFD model that has a realistic wing planform and can mimic realistic flexible wing kinematics measured by a high-speed camera filming system is established, which provides a quantitative prediction of unsteady aerodynamics of the four-winged MAV in terms of vortex and wake structures and their relationship with aerodynamic force generation. The CFD-based results show that a leading edge vortex (LEV) and hence a strong negative pressure region are generated on the wings during half stroke. As observed in insect flapping flight, This LEV likely plays a crucial role in the lift and/or thrust force-production in the MAV flight.

Vortex Visualization in Ultra Low Reynolds Number Insect Flight

Abstract: We present the visual analysis of a biologically inspired CFD simulation of the deformable flapping wings of a dragonfly as it takes off and begins to maneuver, using vortex detection and integration-based flow lines. The additional seed placement and perceptual challenges introduced by having multiple dynamically deforming objects in the highly unsteady 3D flow domain are addressed. A brief overview of the high speed photogrammetry setup used to capture the dragonfly takeoff, parametric surfaces used for wing reconstruction, CFD solver and underlying flapping flight theory is presented to clarify the importance of several unsteady flight mechanisms, such as the leading edge vortex, that are captured visually. A novel interactive seed placement method is used to simplify the generation of seed curves that stay in the vicinity of relevant flow phenomena as they move with the flapping wings. This method allows a user to define and evaluate the quality of a seed's trajectory over time while working with a single time step. The seed curves are then used to place particles, streamlines and generalized streak lines. The novel concept of flowing seeds is also introduced in order to add visual context about the instantaneous vector fields surrounding smoothly animate streak lines. Tests show this method to be particularly effective at visually capturing vortices that move quickly or that exist for a very brief period of time. In addition, an automatic camera animation method is used to address occlusion issues caused when animating the immersed wing boundaries alongside many geometric flow lines. Each visualization method is presented at multiple time steps during the up-stroke and down-stroke to highlight the formation, attachment and shedding of the leading edge vortices in pairs of wings. Also, the visualizations show evidence of wake capture at stroke reversal which suggests the existence of previously unknown unsteady lift generation mechanisms that are unique to quad wing insects.

The motion of kelp blades and the surface renewal model

Abstract: We consider how the flapping of kelp blades may enhance the flux of nutrients to a blade, by stripping away the diffusive sub-layer and renewing the fluid at the blade surface. The surface renewal model explains the degree of flux enhancement observed in previous studies under different flow and flapping conditions. We measured the motion of real kelp blades of Laminaria saccharina, Macrocystis pyrifera, and Nereocystis luetkeana under unidirectional current in a laboratory flume. Observed flapping frequencies coupled with the renewal model, suggest that the flapping of blades in the field has the potential to significantly enhance flux to the blade surface at low current speed, but has little effect on flux at high current speeds.

Modulation of leading edge vorticity and aerodynamic forces in flexible flapping wings.

Abstract: In diverse biological flight systems, the leading edge vortex has been implicated as a flow feature of key importance in the generation of flight forces. Unlike fixed wings, flapping wings can translate at higher angles of attack without stalling because their leading edge vorticity is more stable than the corresponding fixed wing case. Hence, the leading edge vorticity has often been suggested as the primary determinant of the high forces generated by flapping wings. To test this hypothesis, it is necessary to modulate the size and strength of the leading edge vorticity independently of the gross kinematics while simultaneously monitoring the forces generated by the wing. In a recent study, we observed that forces generated by wings with flexible trailing margins showed a direct dependence on the flexural stiffness of the wing. Based on that study, we hypothesized that trailing edge flexion directly influences leading edge vorticity, and thereby the magnitude of aerodynamic forces on the flexible flapping wings. To test this hypothesis, we visualized the flows on wings of varying flexural stiffness using a custom 2D digital particle image velocimetry system, while simultaneously monitoring the magnitude of the aerodynamic forces. Our data show that as flexion decreases, the magnitude of the leading edge vorticity increases and enhances aerodynamic forces, thus confirming that the leading edge vortex is indeed a key feature for aerodynamic force generation in flapping flight. The data shown here thus support the hypothesis that camber influences instantaneous aerodynamic forces through modulation of the leading edge vorticity.

Flexible flapping systems: computational investigations into fluid-structure interactions

Abstract: In the present work, the authors examine two computational approaches that can be used to study flexible flapping systems. For illustration, a fully coupled interaction of a fluid system with a flapping profile performing harmonic flapping kinematics is studied. In one approach, the fluid model is based on the Navier-Stokes equations for viscous incompressible flow, where all spatio-temporal scales are directly resolved by means of Direct Numerical Simulations (DNS). In the other approach, the fluid model is an inviscid, potential flow model, based on the unsteady vortex lattice method (UVLM). In the UVLM model, the focus is on vortex structures and the fluid dynamics is treated as a vortex kinematics problem, whereas with the DNS model, one is able to form a more detailed picture of the flapping physics. The UVLM based approach, although coarse from a modeling standpoint, is computationally inexpensive compared to the DNS based approach. This comparative study is motivated by the hypothesis that flapping related phenomena are primarily determined by vortex interactions and viscous effects play a secondary role, which could mean that a UVLM based approach could be suitable for design purposes and/or used as a predictive tool. In most of the cases studied, the UVLM based approach produces a good approximation. Apart from aerodynamic load comparisons, features of the system dynamics generated by using the two computational approaches are also compared. The authors also discuss limitations of both approaches.

Flight Dynamic Stability of a Flapping Wing Micro Air Vehicle in Hover

Abstract: This paper discusses a methodology of analyzing the flight dynamic stability of a flapping wing Micro Air Vehicle (MAV) in hover. The flexible flapping wings are modeled by a strain-based geometrically nonlinear beam formulation, coupled with an empirical aerodynamic formulation for load calculation on the wings surfaces. Wing flapping kinematics is described using a set of Euler angles. Nonlinear equations of motion for the body frame attached to the vehicle are used to complete the coupled aeroelastic and flight dynamic formulation. All these formulations are implemented in an integrated numerical framework. To evaluate the flight dynamic stability of the hovering flapping wing MAV, the coupled nonlinear governing equations are linearized, and the transition matrix over a wing flapping cycle is determined. By taking advantage of the periodic hovering condition, the stability analysis is performed based on the transition matrix in the Floquet theory. Longitudinal and lateral stabilities of a flapping wing MAV in hover is explored with the impact of different wing rigidity and inertia.