Flapping Wing Aerodynamics Research Articles

Leading-edge curvature effect on aerodynamic performance of flapping wings in hover and forward flight

This study investigates the role of leading-edge (LE) curvature in flapping wing aerodynamics considering hovering and forward flight conditions. A scaled-up robotic model is towed along its longitudinal axis by a rack gear carriage system. The forward velocity of the robotic model is changed by varying the advance ratio J from 0 (hovering) to 1.0. The study reveals that the LE curvature has insignificant influence on the cycle-average aerodynamic lift and drag. However, the time-history lift coefficient shows that the curvature can enhance the lift around the middle of downstroke. This enhanced lift is reduced from 5% to 1.2% as J changed from 0 to 1.0. Further flow examinations reveal that the LE curvature is beneficial by enhancing circulation only at the outboard wing sections. The enhanced outboard circulation is found to emanate from the less stretched leading-edge vortices (LEVs), weakened trailing-edge vortices (TEVs), and the coherent merging of the tip vortices (TVs) with the minor LEVs as observed from the phase-lock planar digital particle image velocimetry measurements. The far-wake observation shows that the LE curvature enhances the vorticity within the TV, helping to reduce the overall flow fluctuations in the far field. These findings can be extended to explain the predominantly straight LE wing shape with a small amount of curvature only observed near the wing tip for flapping fliers with Re from 103 to 104.

The Functions of Phasic Wing-Tip Folding on Flapping-Wing Aerodynamics.

Insects produce a variety of highly acrobatic maneuvers in flight owing to their ability to achieve various wing-stroke trajectories. Among them, beetles can quickly change their flight velocities and make agile turns. In this work, we report a newly discovered phasic wing-tip-folding phenomenon and its aerodynamic basis in beetles. The wings' flapping trajectories and aerodynamic forces of the tethered flying beetles were recorded simultaneously via motion capture cameras and a force sensor, respectively. The results verified that phasic active spanwise-folding and deployment (PASFD) can exist during flapping flight. The folding of the wing-tips of beetles significantly decreased aerodynamic forces without any changes in flapping frequency. Specifically, compared with no-folding-and-deployment wings, the lift and forward thrust generated by bilateral-folding-and-deployment wings reduced by 52.2% and 63.0%, respectively. Moreover, unilateral-folding-and-deployment flapping flight was found, which produced a lateral force (8.65 mN). Therefore, a micro-flapping-wing mechanism with PASFD was then designed, fabricated, and tested in a motion capture and force measurement system to validate its phasic folding functions and aerodynamic performance under different operating frequencies. The results successfully demonstrated a significant decrease in flight forces. This work provides valuable insights for the development of flapping-wing micro-air-vehicles with high maneuverability.

Influence of Area Distribution Along the Span Direction on Flapping Wing Aerodynamics in Hover Based on Numerical Modeling Analysis

Influence of Area Distribution Along the Span Direction on Flapping Wing Aerodynamics in Hover Based on Numerical Modeling Analysis

Bio-inspired Flapping Wing Aerodynamics: A Review

Bio-inspired Flapping Wing Aerodynamics: A Review

Dynamics modeling and experiment validation for piezoelectric-transmission-wing system

Aiming at the challenge of predicting the dynamic behavior of the flapping wing in the piezoelectric-transmission-wing (PTW) wingbeat system, a lumped-parameter model coupling piezoelectric structural mechanics and flapping-wing aerodynamics is proposed to address the challenge caused by the fluid-structure interaction (FSI). Firstly, a model describing the piezoelectric mechanical response is established, which has the ability to better predict the mechanical response of the piezoelectric actuator under high electric field and low-frequency driving conditions. In order to verify the validity and accuracy, tip deflection, stiffness and blocking force experiments as well as data comparisons are performed to substantiate the findings. Secondly, a comprehensive and reasonable lumped-parameter dynamic model is constructed based on the analysis of the transmission mechanics based on pseudo-rigid-body theory and the improved aerodynamic modeling of the wing, along with the aforementioned piezoelectric mechanical modeling. Thirdly, simulation and dynamic response experiments of the wingbeat system are carried out. Results show that the simulation data are in good agreement with the experimental values, which indicates the accuracy of the model in predicting the dynamic behavior of the flapping wing powered by the piezoelectric actuator. Moreover, some interesting phenomena such as the pitch oscillation of the wing and the dependence of the flapping motion on the driving frequency have been demonstrated in the simulation and the wingbeat experiment, respectively. The research findings of this article offer three types of assistance: (1) providing a parameter design method for piezoelectric actuators to achieve the desired mechanical response; (2) predicting and explaining the dynamic behavior of the PTW wingbeat system; and (3) providing a theoretical foundation for the parameter design and optimization of the wing-actuator pairing in the flapping wing system.

A Neural Network Approach to Estimate Transient Aerodynamic Properties of a Flapping Wing System

Understanding the causal impacts among various parameters is essential for designing micro aerial vehicles (MAVs). The simulation of computational fluid dynamics (CFD) provides us with a technique to calculate aerodynamic forces precisely. However, even a single result regularly takes considerable computational time. Machine learning, due to the advance in computer hardware, shows another approach that can speed up the analysis process. In this study, we introduce an artificial neural network (ANN) framework to predict the transient aerodynamic forces and the corresponding energy consumption. Instead of considering the whole transient changes of each parameter as inputs, we utilised the technique of Fourier transform to simplify the ANN structure for minimising the computation cost. Furthermore, two typical activation functions, rectified linear unit (ReLU) and sigmoid, were attempted to build the network. The validity of the method was further examined by comparing it with CFD simulation. The result shows that both functions are able to provide highly accurate estimations that can be implemented for model construction under this framework. Consequently, this novel approach makes it possible to reduce the complexity of analysis, study the flapping wing aerodynamics and enable a more efficient way to optimise parameters.

The function of pitching in Beetle's flight revealed by insect-wearable backpack

The study of insect flight orientation is important for investigating flapping-wing aerodynamics and designing bioinspired micro air vehicles (MAVs). Pitch orientation plays a vital role in flight control, which has been explored less than directional control. In this study, the role of pitching maneuvers in flight was revealed by mounting an insect-wearable backpack on a beetle, which transformed the live insect into a bioelectronic device. The flight status of the cyborg beetle in a large chamber was recorded wirelessly. Accordingly, the pitch angle and forward acceleration showed a strong linear relationship. The coupling of pitch angle and forward acceleration was due to a tilted net aerodynamic force and the induced air drag. Moreover, the left and right subalar muscles of the beetle, a pair of major flight muscles, were electrically stimulated in free flight on demand to pitch up the beetle's body. We demonstrated that the induced nose-up movements were effective for decelerating the beetle in air. The flight orientation findings from the flying cyborgs would inspire a new approach to the study of flapping-wing flight and control of flapping-wing MAVs.

State-space aerodynamic model reveals high force control authority and predictability in flapping flight.

Flying animals resort to fast, large-degree-of-freedom motion of flapping wings, a key feature that distinguishes them from rotary or fixed-winged robotic fliers with limited motion of aerodynamic surfaces. However, flapping-wing aerodynamics are characterized by highly unsteady and three-dimensional flows difficult to model or control, and accurate aerodynamic force predictions often rely on expensive computational or experimental methods. Here, we developed a computationally efficient and data-driven state-space model to dynamically map wing kinematics to aerodynamic forces/moments. This model was trained and tested with a total of 548 different flapping-wing motions and surpassed the accuracy and generality of the existing quasi-steady models. This model used 12 states to capture the unsteady and nonlinear fluid effects pertinent to force generation without explicit information of fluid flows. We also provided a comprehensive assessment of the control authority of key wing kinematic variables and found that instantaneous aerodynamic forces/moments were largely predictable by the wing motion history within a half-stroke cycle. Furthermore, the angle of attack, normal acceleration and pitching motion had the strongest effects on the aerodynamic force/moment generation. Our results show that flapping flight inherently offers high force control authority and predictability, which can be key to developing agile and stable aerial fliers.

Roles of wing flexibility and kinematics in flapping wing aerodynamics

Insects are excellent fliers because of their ability to generate precise wing kinematics and deform their wings for the sufficient production of unsteady aerodynamic forces. Most of the previous studies on the effects of wing kinematics on the aerodynamics have been limited to the use of rigid wings, and leaves the contribution of wing flexibility unknown. Here, an experiment was conducted to investigate the effect of varied sweep duration and timing of rotation on the unsteady aerodynamic characteristics of hovering flexible and rigid wings at Re of 104. This study found that the forces generated by the flexible wing showed a conspicuous phase delay, which was more sensitive to the change in sweep duration than the timing of rotation. The transient negative lift associated with rigid wings undergoing delayed and advanced wing rotations totally disappeared in the flexible case. A digital particle image velocimetry (DPIV) measurement at the middle of stroke revealed a slight difference in the vortical structures surrounding the two wings in terms of proximity to the shed trailing-edge vortices (TEVs). Also, the linearly twisted nature of the flexible wing caused the coherent leading-edge vortex (LEV) to be stabilized throughout the wingspan. This increased the radial limit of the delayed stall from 3.6c in the rigid wing to 4.8c in the flexible wing. In general, the flexible wing with symmetric and delayed wing rotations generated the higher efficiency. The corresponding net force vectors were tilted in an almost vertical direction in comparison to the rigid wing. This is an indication that natural fliers adopt specific wing kinematics in addition to their wing deformation for the upward titling of their net force vector, which will significantly enhance their aerodynamic performance.

Recent progress in flexibility effects on wing aerodynamics and acoustics

Since the theoretical aeroelasticity for flapping-wing aerodynamics was introduced in the 1920s, the effects of flexibility on aeroelasticity have been paid more attention to aerodynamic design. In recent years, the trait of the wing flexibility is applied for small-scale wings of biomimetic flyers including micro air vehicles and mini unmanned aerial vehicles. Until now, the aerodynamic performance and great agility of these flyers, which are beneficially used for military missions and other civilian applications, have been improved through surrogate flapping wings with the favorable effects of the flexibility. As per the aeroelasticity principle for the forward flying, the chordwise flexibility of an elastic flapping wing can generate thrust and lift redistributions, whereas the spanwise flexibility can result in variations of the angle of attack and the shift of phase along the wingspan direction. Consequently, all vortices generated by the flapping wing i.e. (1) leading-edge vortices, (2) tip vortices, and (3) trailing-edge vortices are blended supportively, thereby improving the aerodynamic performance and agility. Hence, the growth of research and development of the aerodynamic performance and agility for these flyers under the influence of flexible wings increases through experimental and computational studies dynamically and rapidly. This review aims to highlight the important role of the flexibility in the recent progress in wing aerodynamics of these flyers through several wing models done by famous groups of experts in this field. In addition, this review includes the acoustics of the wings under the flexibility effects which is considered as a new key for better flyer design and improvement. A comprehensive understanding of the integrated aerodynamics and acoustics under the wing flexibility is, therefore, needed.

Effects of flapping wing kinematics on the aeroacoustics of hovering flight

Despite the recent interest in flapping wing aerodynamics, the aerodynamic sound generation mechanism of a flapping wing is inadequately understood. In this paper, the interplay between the wing motion, resulting unsteady aerodynamics, and aeroacoustics of a flapping wing flyer is investigated. The wing motion is varied in terms of the flapping amplitude, pitching amplitude, and the phase difference between flap and pitch. The unsteady flow around the flapping wing is numerically calculated using a well-validated Navier-Stokes equation solver. Acoustic pressures are computed using the Ffowcs-Williams-Hawkings equation in a three-dimensional space at varying distances from the wing. Two main sound generation mechanisms are found. The flapping motion induces the highest sound pressure level (SPL) in the stroke plane. Furthermore, the SPL peaks under the wing due to the wake induced by lift generation. Effective motions, generating the highest lift and lowest SPL, are found when the flap and pitch amplitudes are high and when the pitch rotation is delayed with respect to flap. These results suggest that the delayed rotations observed for small hovering insects may aim to minimize sound production rather than maximize lift generation.

Quasi-Steady versus Navier–Stokes Solutions of Flapping Wing Aerodynamics

Various tools have been developed to model the aerodynamics of flapping wings. In particular, quasi-steady models, which are considerably faster and easier to solve than the Navier–Stokes equations, are often utilized in the study of flight dynamics of flapping wing flyers. However, the accuracy of the quasi-steady models has not been properly documented. The objective of this study is to assess the accuracy of a quasi-steady model by comparing the resulting aerodynamic forces against three-dimensional (3D) Navier–Stokes solutions. The same wing motion is prescribed at a fruit fly scale. The pitching amplitude, axis, and duration are varied. Comparison of the aerodynamic force coefficients suggests that the quasi-steady model shows significant discrepancies under extreme pitching motions, i.e., the pitching motion is large, quick, and occurs about the leading or trailing edge. The differences are as large as 1.7 in the cycle-averaged lift coefficient. The quasi-steady model performs well when the kinematics are mild, i.e., the pitching motion is small, long, and occurs near the mid-chord with a small difference in the lift coefficient of 0.01. Our analysis suggests that the main source for the error is the inaccuracy of the rotational lift term and the inability to model the wing-wake interaction in the quasi-steady model.

Influence of thickness on performance characteristics of non-sinusoidal plunging motion of symmetric airfoil

For the past few decades flapping wing aerodynamics has attracted a great deal of research interest from both the aeronautical and biological communities pertaining to the development of MAVs. The objective of this study is to examine and understand the effect of non-dimensional plunge amplitude and reduced frequency on propulsive performance of NACA 4-digit airfoil series and to examine the performance characteristics of square plunge motion and trapezoidal plunge motion. Two dimensional flow simulations around plunging symmetric aerofoils were performed using FLUENT. The simulations were carried out at Reynolds number of 20000 using incompressible laminar, NS solver. The reduced frequency (k) was varied from 0.5–5 and the plunging amplitude (h) was varied from 0.25–1.5. The plunging motions to the aerofoils were provided through UDFs. The effect of variation of k and h on the thrust coefficient (CT), power-input coefficient (CP) and propulsive efficiency (η) is studied. CT value is maximum for square plunge profile for all the airfoils. However, for a given value of h, with the increase in k, CT increases with increasing thickness of the airfoil and reaches a maximum value for airfoil thickness of NACA0018 and then starts decreasing. With varying h and k, it was observed that the propulsive efficiency reached a peak value and the peak shifts to higher h and k with increasing airfoil thickness. From the above study, it was concluded that airfoil thickness played a major part in influencing the thrust generation at low Strouhal number. However, at high Strouhal numbers airfoils showed diverse trends with respect to thrust generation. Sinusoidal plunging motion was more efficient but generated less thrust when compared to square and trapezoidal plunging motions.

Numerical Simulation of a Flapping Micro Aerial Vehicle Through Wing Deformation Capture

Three-dimensional numerical simulations of a four-wing flapping micro aerial vehicle (FMAV) with actual experimentally captured wing membrane kinematics have been performed using an immersed boundary method Navier–Stokes finite volume solver. To successfully simulate the clap and fling motion involving the wing intersection, the numerical solver has been specifically modified to use a newly improved interpolation template searching algorithm to prevent divergence. Reasonable agreement was found between the numerical and experimental results, with the first and second force peaks from the experimental results well captured by the simulations, which was not possible in the past. Moreover, a “V-shaped linked” vortex was observed, which was similar to the vortical structures found in other experiments and simulations. A wing drag analysis showed that the drag magnitude of the clap and fling configuration was about 2.5 times that of the single-wing configuration. Visualizations of the flowfields through pressure contours and vortical isosurfaces led to a better understanding of the underlying flapping-wing aerodynamics. The ability to accurately simulate the FMAV with flexible wings opened up many opportunities for further FMAV design-related problems.

Numerical Study on Thrust Generation in an Airfoil Undergoing Nonsinusoidal Plunging Motion

AbstractFor the last few decades, an extensive research has been focused on flapping-wing aerodynamics to understand the generation of thrust due to pitching and plunging motions of an airfoil. How...

Fluid-structure interaction enhances the aerodynamic performance of flapping wings: a computational study

Insect wings change its shape passively by the aerodynamic and inertial forces when flapping, which can greatly affect its aerodynamic performances. In order to confirm the importance of the fluid-structure interaction in flapping wing aerodynamics, we performed computational fluid-structure interaction analyses of a hovering hawkmoth with ‘virtual’ vacuum conditions that can adjust the effect of the aerodynamic force on the deformation of flapping wings. It is turned out that the large part of the wing deformation, such as the wing twist, is induced by the inertial force as reported previously, but the adjustment of the wing deformation by the aerodynamic force can greatly affect the kinematics and the aerodynamics of flapping wings. While the wing deformation, regardless of the contribution of the aerodynamic force, can increase the aerodynamic power, force and efficiency of flapping wings, the wing deformation adjusted in response to the unsteady aerodynamics of flapping wings can further enhance the aerodynamic performance. These results not only reveal the influence of the wing deformation on the aerodynamic performance of flapping wings, but also point out the great importance of the fluid-structure interaction in the aerodynamics of insect flight and the design of bio-inspired micro aerial vehicles.

Achieving hover equilibrium in free flight with a flexible flapping wing

Recent discoveries in the fields of flapping wing aerodynamics and fluid–structure interaction have demonstrated that flexible wings can generate more lift than rigid wings. However, the implications of wing flexibility on the flight dynamics of flapping wing flyers is still an open research question. The main difficulty is that the free flight of flapping flyers with flexible wings is a result of the dynamic balance between unsteady aerodynamics, fluid–structure interaction, and flight dynamics. This study presents a fully coupled three-way flight simulator that solves the two-dimensional Navier–Stokes equations, tightly coupled to the Euler–Bernoulli beam equations of the wing and the nonlinear multi-body equations of motion for the dynamics at the fruit fly scale. A novel trim algorithm is used to determine the hover equilibrium in the longitudinal plane. The control inputs, i.e. the flapping amplitude, stroke plane angle, and flapping offset angle as well as the initial conditions are determined that effectively eliminate average body accelerations to less than 3% of gravitational acceleration. The resulting hover equilibrium control parameters flapping amplitude, stroke plane angle and the total power required agree well with the biological observation of fruit flies. Body oscillations in hovering free flight affect the flexible response of the wing compared to prescribed body motion without oscillation. The affected wing motion reduces the lift coefficient by up to 8.7% for the stiffest wing, necessitating slightly different control inputs to achieve trim. Finally, the power required to achieve hover equilibrium is 32%–94% lower for flexible wings than for rigid wings that are actively rotated to match the same passive pitch schedule.

Experimental Investigation of Aerodynamics of Feather-Covered Flapping Wing.

Avian flight has an outstanding performance than the manmade flapping wing MAVs. Considering that the feather is light and strong, a new type of the flapping wing was designed and made, whose skeleton is carbon fiber rods and covered by goose feathers as the skin. Its aerodynamics is tested by experiments and can be compared with conventional artificial flapping wings made of carbon fiber rods as the skeleton and polyester membrane as the skin. The results showed that the feathered wing could generate more lift than the membrane wing in the same flapping kinematics because the feathered wing can have slots between feathers in an upstroke process, which can mainly reduce the negative lift. At the same time, the power consumption also decreased significantly, due to the decrease in the fluctuating range of the periodic lift curve, which reduced the offset consumption of lift. At the same time, the thrusts generated by the feather wing and the membrane wing are similar with each other, which increases with the increase of flapping frequency. In general, the aerodynamic performances of the feather wing are superior to that of the membrane wings.

Three-Dimensional Flow Field Investigations of Flapping Wing Aerodynamics

Three-dimensional unsteady flow fields of a flapping, low-aspect-ratio wing have been investigated by means of highly resolved tomographic particle image velocimetry (Tomo-PIV) measurements and computational fluid dynamics (CFD). Furthermore, force measurements have been carried out. Tomo-PIV was applied to the flow above a flat plate wing during the downstroke. High spatial resolution and large volume thickness could be achieved by using sensitive sCMOS cameras and a traversing setup. The CFD calculations covered the complete period of motion. The analysis of the vortex-dominated flow fields provides a deeper understanding of vortex interaction and three-dimensionality of low Reynolds number ( and ) flows. Two different Strouhal numbers ( and ) are considered and their effects on the development of a leading edge and tip vortex are discussed. The PIV results show instantaneous flow fields after a leading edge separation that are dominated by small-scale turbulent vortex structures. The presented CFD approach is able to predict these vortices by using highly resolved meshes. Coarser grids compare well with the phase-averaged experimental flow fields, which feature multiple large-scale leading edge vortices developing during the downstroke. Turbulent effects decrease for the lower Reynolds number. Force and moment hystereses as well as large-scale leading edge vortice circulation, calculated from the PIV results, increase with increasing Strouhal number. Vortex breakdown of the wing tip vortex can be observed during the downstroke in the experimental data.

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.