Flapping Cycle Research Articles

A Stiffness-Adjusting Method to Improve Thrust Efficiency of a Two-Joint Robotic Fish

Fish are very efficient swimmers. In this paper, we studied a two degree-of-freedom (DOF) propeller that mimic fish caudal fin like locomotion. Kinematics modelling and hydrodynamic CFD analyses of the two DOF propellers were conducted. According to the CFD simulation, we show that negative power was generated within the flapping cycle, and wake flow at different instant was demonstrated. Based on the dynamic model, we compared the thrust efficiency under different stiffness control method. The results show that the thrust efficiency was enhanced under moderate stiffness control strategy.

Understanding undulatory locomotion in fishes using an inertia-compensated flapping foil robotic device

Recent advances in understanding fish locomotion with robotic devices have included the use of flapping foil robots that swim at a constant swimming speed. However, the speed of even steadily swimming live fishes is not constant because the fish center of mass oscillates axially throughout a tail beat cycle. In this paper, we couple a linear motor that produces controlled oscillations in the axial direction to a robotic flapping foil apparatus to model both axial and side to side oscillatory motions used by freely-swimming fishes. This experimental arrangement allows us to compensate for the substantial inertia of the carriage and motors that drive the oscillating foils. We identify a ‘critically-oscillated’ amplitude of axial motion at which the cyclic oscillations in axial locomotor force are greatly reduced throughout the flapping cycle. We studied the midline kinematics, power consumption and wake flow patterns of non-rigid foils with different lengths and flexural stiffnesses at a variety of axial oscillation amplitudes. We found that ‘critically-oscillated’ peak-to-peak axial amplitudes on the order of 1.0 mm and at the correct phase are sufficient to mimic center of mass motion, and that such amplitudes are similar to center of mass oscillations recorded for freely-swimming live fishes. Flow visualization revealed differences in wake flows of flexible foils between the ‘non-oscillated’ and ‘critically-oscillated’ states. Inertia-compensating methods provide a novel experimental approach for studying aquatic animal swimming, and allow instrumented robotic swimmers to display center of mass oscillations similar to those exhibited by freely-swimming fishes.

Aerodynamic implications of gull's drooped wing-tips

When in gliding flight, gulls are observed to adopt a drooped wing-tip configuration. This paper investigates whether this configuration might represent an aerodynamic optimum or if it is the result of constraints imposed by the gull's anatomy. A computational model was developed for the aerodynamic performance of a gull in gliding flight. This model was used in conjunction with both global and local optimizers to determine the most aerodynamically optimal configuration for cases where the gull was constrained to move its wing within its natural flapping cycle as well as when the wing had full freedom of motion. The results of this analysis determined the best wing configuration for a gull in gliding flight and demonstrated that such a configuration not only had the highest lift-to-drag ratio but also could be achieved within the constraints of the kinematics of the gull wing. These results are of interest outside studies of gulls, since the drooped wing-tip configuration could be relevant for new designs of small air vehicles.

An Automatical Matching Method Applied in Kinematics Measurement for the Flapping Rotary Wing

In this paper, a method to track marked points on the wings automatically to describe the wing kinematics in the coupled wing motion of flapping, pitching and rotating is introduced. The marked points on the surface of wings as tracking targets are determined, detected and matched by using digital image processing techniques. Three dimensions coordinates in marked points can be reconstructed by integrated 2D coordinates from multi-camera images and cameras calibration. By this method, it is shown in one flapping cycle, the trend of flapping angular speed various with time is approximate trapezoid function; the pitch angle changes rapidly; the rotation speed fast enhances 3.5 times as flapping frequency increase only 45%. It is possible aerodynamic effective can be improved remarkably.

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.

A bio-inspired study on tidal energy extraction with flexible flapping wings

Previous research on the flexible structure of flapping wings has shown an improved propulsion performance in comparison to rigid wings. However, not much is known about this function in terms of power efficiency modification for flapping wing energy devices. In order to study the role of the flexible wing deformation in the hydrodynamics of flapping wing energy devices, we computationally model the two-dimensional flexible single and twin flapping wings in operation under the energy extraction conditions with a large Reynolds number of 106. The flexible motion for the present study is predetermined based on a priori structural result which is different from a passive flexibility solution. Four different models are investigated with additional potential local distortions near the leading and trailing edges. Our simulation results show that the flexible structure of a wing is beneficial to enhance power efficiency by increasing the peaks of lift force over a flapping cycle, and tuning the phase shift between force and velocity to a favourable trend. Moreover, the impact of wing flexibility on efficiency is more profound at a low nominal effective angle of attack (AoA). At a typical flapping frequency f * = 0.15 and nominal effective AoA of 10°, a flexible integrated wing generates 7.68% higher efficiency than a rigid wing. An even higher increase, around six times that of a rigid wing, is achievable if the nominal effective AoA is reduced to zero degrees at feathering condition. This is very attractive for a semi-actuated flapping energy system, where energy input is needed to activate the pitching motion. The results from our dual-wing study found that a parallel twin-wing device can produce more power compared to a single wing due to the strong flow interaction between the two wings.

Comparison Study of Membrane Flapping Wing Based on Mooney-Rivlin Model and Linear Model

The maximum deformation and stress are compared based on Mooney-Rivlin Model and Linear Model for flapping wing. One flapping cycle was divided into twelve segments, and maximum deformation and stress were calculated in each segment. The results show that max deformation and stress all occur at the beginning of downstroke, the max deformation adopted Mooney-Rivlin model is 25 percent of the max deformation adopted the linear model, and the max stress adopted Mooney-Rivlin model is only 0.37 percent of the max stress adopted the linear model. Mooney-Rivlin Material is very suitable for the membrane flapping wing.

Characterization of the Mechanics of Compliant Wing Designs for Flapping-Wing Miniature Air Vehicles

Flapping-wing miniature air vehicles (MAVs) offer multiple performance benefits relative to fixed-wing and rotary-wing MAVs. This investigation focused on the problem of designing compliant wings for a flapping-wing MAV where only the spar configuration was varied to achieve improved performance. Because the computational tools needed for identifying the optimal spar configuration for highly compliant wing designs have yet to be developed, a new experimental methodology was developed to explore the effects of spar configuration on the wing performance. This technique optically characterized the wing deformations associated with a given spar configuration and used a customized test stand for measuring lift and thrust loads on the wings during flapping. This revealed that spar configurations achieving large and stable deformed volume during the flapping cycle provided the best combination of lift and thrust. The approach also included a sensitivity and reproducibility analysis on potential spar configurations. Results indicated that the wing shape and corresponding lift and thrust performance were very sensitive to slight changes in volume and 3-D shape associated with slight variations in the spar locations.

Numerical Simulation of Fully Passive Flapping Foil Power Generation

A fully passive flapping foil turbine was simulated using a two-dimensional Navier–Stokes solver with two-way fluid-structure interaction at a Reynolds number based on freestream flow and with a NACA 0012 foil. Both pitch angle and angle-of-attack control methodologies were investigated. Efficiencies of up to 30% based on the Betz criterion were found using pitch control, which is commensurate with values reported in the literature for prescribed motion studies. Nonsinusoidal foil pitching motions were found to be superior to sinusoidal motions. Efficiencies exceeding 41% were found using angle-of-attack control, and nonsinusoidal angle-of-attack profiles were found to be superior. The key to improving the efficiency of energy extraction from the flow is to control the timing of the formation and location of the leading-edge vortex at crucial times during the flapping cycle and the interaction of the vortex with the trailing edge. Simulations using Reynolds-averaged Navier–Stokes turbulence modeling suggest that the performance is maintained or only slightly reduced at .

Understanding Micro Air Vehicle Flapping-Wing Aerodynamics Using Force and Flowfield Measurements

Experimental studies were conducted by flapping a rigid rectangular wing with a mechanism that is capable of emulating complex insect wing kinematics, including figure-of-eight motions, in order to explore the fundamental unsteady flow on a flapping wing at micro-air-vehicle-scale Reynolds numbers. Force and moment measurements were obtained from a miniature six-component force transducer installed at the wing root. The wing was flapped in air and vacuum at the same frequency, and wing kinematics, and the resultant forces, were subtracted in order to obtain the pure aerodynamic forces. In the first part of this paper, the forces produced on the wing undergoing single-degree-of-freedom fixed-pitch pure flapping motions (no pitching or out-of-the-plane coning motions) were determined for a variety of pitch angles. The unsteady aerodynamic coefficients measured during these tests were almost six times the steady-state values measured in the wind tunnel. Flow visualization and particle image velocimetry tests were also conducted, which showed that the key reason for the force increase on the flapping wing is due to a strong leading-edge vortex for which the strength varied throughout the flapping cycle. In the second part of this paper, complete three-degree-of-freedom (flapping, pitching, and coning) insect wing kinematics were investigated for different pitching and coning variations. The aerodynamic forces obtained in these tests were compared with coefficients obtained from the single-degree-of-freedom flapping tests and wind-tunnel tests.

Formation of vortices and spanwise flow on an insect-like flapping wing throughout a flapping half cycle

AbstractThis paper presents an experimental investigation of the evolution of the leading-edge vortex and spanwise flow generated by an insect-like flapping-wing at a Reynolds number relevant to flapping-wing micro air vehicles (FMAVs) (Re = ~15,000). Experiments were accomplished with a first-of-its-kind flapping-wing apparatus. Dense pseudo-volumetric particle image velocimetry (PIV) measurements from 18% – 117% span were taken at 12 azimuthal positions throughout a flapping half cycle. Results revealed the formation of a primary leading-edge vortex (LEV) which saw an increase in size and spanwise flow (towards the tip) through its core as the wing swept from rest to the mid-stroke position where signs of vortex breakdown were observed. Beyond mid-stroke, spanwise flow decreased and the tip vortex grew in size and exhibited a reversal in its axial direction. At the end of the flapping half cycle, the primary LEV was still present over the wing surface, suggesting that the LEV remains attached to the wing throughout the entire flapping half cycle.

An Experimental Investigation into the Effect of Flap Angles for a Piezo-Driven Wing

This article presents a comparison of results from six degree of freedom force and moment measurements and Particle Image Velocimetry (PIV) data taken on the Air Force Institute of Technology's (AFIT) piezoelectrically actuated, biomimetically designed Hawkmoth, Manduca Sexta, class engineered wing, at varying amplitudes and flapping frequencies, for both trimmed and asymmetric flapping conditions to assess control moment changes. To preserve test specimen integrity, the wing was driven at a voltage amplitude 50% below the maximum necessary to achieve the maximal Hawkmoth total stroke angle. 86° and 65° stroke angles were achieved for the trimmed and asymmetric tests respectively. Flapping tests were performed at system structural resonance, and at ±10% off system resonance at a single amplitude, and PZT power consumption was calculated for each test condition. Two-dimensional PIV visualization measurements were taken transverse to the wing planform, recorded at the mid-span, for a single frequency and amplitude setting, for both trimmed and asymmetric flapping to correlate with the 6-DoF balance data. Linear velocity data was extracted from the 2-D PIV imagery at ± 1/2 and ±1 chord locations above and below the wing, and the mean velocities were calculated for four separate wing phases during the flap cycle. The mean forces developed during a flap cycle were approximated using a modification of the Rankine-Froude axial actuator disk model to calculate the transport of momentum flux as a measure of vertical thrust produced during a static hover flight condition. Values of vertical force calculated from the 2-D PIV measurements were within 20% of the 6-DOF force balance experiments. Power calculations confirmed flapping at system resonance required less power than at off resonance frequencies, which is a critical finding necessary for future vehicle design considerations.

Aerodynamic modelling of flapping flight using lifting line theory

PurposeThe purpose of the work is to design a flapping wing that generates net positive propulsive force and vertical force over a flapping cycle operating at a given freestream velocity. In addition, an optimal wing is designed based on the comparison of the force estimated from the quasi‐steady theory, with the wind‐tunnel experiments. Based on the designed wing configuration, a flapping wing ornithopter is fabricated.Design/methodology/approachThis paper presents a theoretical aerodynamic model of the design of an ornithopter with specific twist distribution that results generation of substantial net positive vertical force and thrust over a cycle at non‐zero advance ratio. The wing has a specific but different twist distribution during the downstroke and the upstroke that maintains the designed angle of attack during the strokes. The wing is divided into spanwise strips and Prandtl's lifting line theory is applied to estimate aerodynamic forces with the assumptions of quasi‐steady flow and the wings are without any dihedral or anhedral. Spanwise circulation distribution is obtained and hence lift is calculated. The lift is resolved along the freestream velocity and perpendicular to the freestream velocity to obtain vertical force and propulsive thrust force. Experiments are performed in a wind tunnel to find the forces generated in a flapping cycle which compares well with the theoretical estimation at low flying speeds.FindingsThe estimated aerodynamic force indicates whether the wing geometry and operating conditions are sufficient to carry the weight of the vehicle for a sustainable flight. The variation of the aerodynamic forces with varying flapping frequencies and freestream velocities has been illustrated and compared with experimental data that shows a reasonable match with the theoretical estimations. Based on the calculations a prototype has been fabricated and successfully flown.Research limitations/implicationsThe theory does not take into account the unsteady effects and estimates the aerodynamic forces at wing level condition. It doesn’t predict stall and ignores structural deformations due to aerodynamic loads. The airfoil section is only specified by the chord, zero lift angle of attack, lift slope, profile drag coefficient and angle of attack as given inputs. To fabricate a light weight wing that maintains a very accurate geometric twist and camber distribution as per the theoretical requirement is challenging.Practical implicationsUseful for designing ornithopter wing (preferably bigger) involving an unswept rigid spar with flapping and twisting.Originality/valueThe novelty of the present wing design is the appropriate spanwise geometric twisting about the leading edge spar.

Wing Kinematics Optimization for Hovering Micro Air Vehicles Using Calculus of Variation

The weight and power constraints imposed on flapping-wing micro air vehicles necessitate optimal design of the flapping kinematics. To date, the approach adopted for kinematics optimization has been to assume specific functions for the Euler angles describing the wing motion with respect to the body. Then, optimization is performed on the parameters of these functions. In another approach, a number of instants over the flapping cycle are selected, and optimization is performed on the magnitude of the Euler angles at these instants. This latter approach provides more freedom for the variations of the Euler angles rather than confining them to certain patterns. Yet, in both approaches, finite-dimensional optimization is adopted and, as such, additional constraints are imposed. Considering that the problem is an infinite-dimensional optimization problem, we use in this work the calculus of variations to obtain true optimality. The combination of the quasi-steady aerodynamics and the calculus of variations approach yields an upper bound for the flapping-wing aerodynamic performance. This bound can be used as a basis for evaluating the performance of any realistic design by assessing the degree of closeness between that design and the true optimal performance.

Stress Study of Membrane Flapping Wing Based on Mooney-Rivlin Model

The stress change of membrane flapping-wing aerial vehicle that used Moon-Rivlin model was calculated in one flapping cycle. One flapping cycle was divided into twelve segments, aerodynamic force and inertia force in each segment were calculated, the stress distribution could be gotten. The results show that: at the beginning of upstroke and at the beginning of downstroke, the stress of flapping-wing is maximum; the stress of downstroke near the flapping symmetry position is minimum, and the stress of upstroke near flapping symmetry position is another minimum peak stage.

Design, aerodynamics and autonomy of the DelFly

One of the major challenges in robotics is to develop a fly-like robot that can autonomously fly around in unknown environments. In this paper, we discuss the current state of the DelFly project, in which we follow a top-down approach to ever smaller and more autonomous ornithopters. The presented findings concerning the design, aerodynamics and autonomy of the DelFly illustrate some of the properties of the top-down approach, which allows the identification and resolution of issues that also play a role at smaller scales. A parametric variation of the wing stiffener layout produced a 5% more power-efficient wing. An experimental aerodynamic investigation revealed that this could be associated with an improved stiffness of the wing, while further providing evidence of the vortex development during the flap cycle. The presented experiments resulted in an improvement in the generated lift, allowing the inclusion of a yaw rate gyro, pressure sensor and microcontroller onboard the DelFly. The autonomy of the DelFly is expanded by achieving (1) an improved turning logic to obtain better vision-based obstacle avoidance performance in environments with varying texture and (2) successful onboard height control based on the pressure sensor.

Experimental Studies to Understand the Hover and Forward Flight Performance of a MAV-Scale Flapping Wing Concept

Systematic experimental studies were performed to understand the role of two key degrees of freedom, flapping and pitching, in aerodynamic performance of a flapping wing, in both hover and forward flight. Required flapping kinematics is prescribed mechanically, and dynamic pitching/twisting is obtained passively using inertial and aerodynamic forces. Forces produced by the wing are measured at the root using a six-component balance at different flapping frequencies, flapping/pitching amplitudes, and wind speeds. The results clearly show that maximum average thrust over a flap cycle in hover can be achieved using symmetric, high amplitude passive pitching. However, in forward flight, optimum aerodynamic performance (lift and propulsive thrust) is obtained using asymmetric wing pitching with low pitching amplitudes. Furthermore, dynamic twisting (obtained using flexible wings), instead of dynamic pitching, produces better performance in forward flight due to spanwise and temporal modulation of the wing pitch angle. Pure flapping (no pitching) of rigid wings in forward flight at high reduced frequencies and high pitch angles produces a threefold increase in lift coefficient over static values. Maximum average propulsive thrust over a flap cycle in forward flight is obtained using symmetric pitching. To produce high values of both, average lift and thrust, an asymmetry in kinematics along with pitching is required in forward flight. This can be achieved either through asymmetric pitching of rigid wings or dynamic twisting of torsionally flexible wings.

Kinematic control of aerodynamic forces on an inclined flapping wing with asymmetric strokes

In the present study, we conduct an experiment using a one-paired dynamically scaled model of an insect wing, to investigate how asymmetric strokes with different wing kinematic parameters are used to control the aerodynamics of a dragonfly-like inclined flapping wing in still fluid. The kinematic parameters considered are the angles of attack during the mid-downstroke (αmd) and mid-upstroke (αmu), and the duration (Δτ) and time of initiation (τp) of the pitching rotation. The present dragonfly-like inclined flapping wing has the aerodynamic mechanism of unsteady force generation similar to those of other insect wings in a horizontal stroke plane, but the detailed effect of the wing kinematics on the force control is different due to the asymmetric use of the angle of attack during the up- and downstrokes. For example, high αmd and low αmu produces larger vertical force with less aerodynamic power, and low αmd and high αmu is recommended for horizontal force (thrust) production. The pitching rotation also affects the aerodynamics of a flapping wing, but its dynamic rotational effect is much weaker than the effect from the kinematic change in the angle of attack caused by the pitching rotation. Thus, the influences of the duration and timing of pitching rotation for the present inclined flapping wing are found to be very different from those for a horizontal flapping wing. That is, for the inclined flapping motion, the advanced and delayed rotations produce smaller vertical forces than the symmetric one and the effect of pitching duration is very small. On the other hand, for a specific range of pitching rotation timing, delayed rotation requires less aerodynamic power than the symmetric rotation. As for the horizontal force, delayed rotation with low αmd and high αmu is recommended for long-duration flight owing to its high efficiency, and advanced rotation should be employed for hovering flight for nearly zero horizontal force. The present study suggests that manipulating the angle of attack during a flapping cycle is the most effective way to control the aerodynamic forces and corresponding power expenditure for a dragonfly-like inclined flapping wing.

Effect of Plasma-Based Control on Low-Reynolds-Number Flapping Airfoil Performance

Large-eddy simulation (LES) is employed to investigate the use of plasma-based actuation for the control of flapping motion of a wing section at low Reynolds number. The SD7003 airfoil section and imposed oscillatory motion of the investigation are representative of micro air vehicle (MAV) applications. Dielectric-barrier-discharge (DBD) plasma actuation is utilized to modify the transitional flow and improve aerodynamic performance. Solutions are obtained to the Navier-Stokes equations, that were augmented by source terms used to represent plasma-induced body forces imparted by the actuator on the fluid. A simple phenomenological model provided the body force resulting from the electric field generated by the plasma. The numerical method is based upon a high-fidelity time-implicit scheme, an implicit LES approach, and domain decomposition in order to perform calculations on a parallel computing platform. Solutions are obtained for combined periodic pitching and plunging motion about an 8 degree mean angle of attack at chordbased Reynolds numbers of 30,000 and 60,000. Baseline simulations without control are compared to cases employing plasma actuation in order to assess eects on performance. Comparison is also made with experimental data, and a grid resolution study is performed for validation purposes. Plasma-based control is able to mitigate, but not completely eliminate, the massive separation that occurs during the unsteady motion. It is shown that plasma actuation can reduce drag by 80% over the flapping cycle, and increase the lift to drag ratio by a factor of five.

Effects of pitching rotation on aerodynamics of tandem flapping wing sections of a hovering dragonfly

AbstractThis paper studies hovering capability of flapping two-dimensional tandem wing sections inspired by a real dragonfly wing configuration and kinematics. Based on unsteady numerical simulations, the dragonfly corrugated wings have been benchmarked against a flat wing in terms of the aerodynamic forces and flow structures generated during a flapping cycle. The timing of rotation at each stroke is studied by pitch rotation at three different rates, i.e., 80%, 60% and 40% of a flapping period. The results suggest that the longer time pitch rotation with the period of 80% of the overall flapping period is closer to the force calculations obtained of a balanced flight, that is, the mean vertical force supports the dragonfly weight of 0.754 g with a small difference of 0.92% and the mean horizontal force indicates negligible thrust. However, the corrugated wing performs aerodynamically differently from the flat plate with differences in and in by ±2.06% for the corrugated shape. The vorticity flow field for both wings have been recorded at some instants of flapping motions which give more explanation of such dissimilarity.