Effects of mass and chordwise flexibility on 2D self-propelled flapping wings

A self-propelled flexible flapping wing 2D numerical model undergoing a combined pitching and heaving motion is presented. Since such freely moving foil experiences zero net thrust, a definition of efficiency for this kind of problem is proposed and discussed against other formulations found in the literature. It is also shown that the deviation motion of wings such as that found in natural flyers is likely a consequence of the fluid–structure dynamics of the wings. The passive deviation motion observed in numerical simulations is either a consequence of a feathering mechanism referred to as rigid feathering or of the inertial displacement caused by the wing deformation. The effects of flexibility on the performance of the wing are also presented. It is found that flexibility may significantly enhance the efficiency in pressure-driven deformation cases. The rigid feathering mechanism is found to have an effect similar to that of the feathering caused by wing flexibility on the performances of pressure-driven deformation cases.     

Force production and asymmetric deformation of a flexible flapping wing in forward flight

Insect wings usually are flexible and deform significantly under the combined inertial and aerodynamic load. To study the effect of wing flexibility on both lift and thrust production in forward flight, a two-dimensional numerical simulation is employed to compute the fluid–structure interaction of an elastic wing section translating in an inclined stroke plane while pitching around its leading ledge. The effects of the wing stiffness, mass ratio, stroke plane angle, and flight speed are considered. The results show that the passive pitching due to wing deformation can significantly increase thrust while either maintaining lift at the same level or increasing it simultaneously. Another important finding is that even though the wing structure and actuation kinematics are symmetric, chordwise deformation of the wing shows a larger magnitude during upstroke than during downstroke. The asymmetry is more pronounced when the wing has a low mass ratio so that the fluid-induced deformation is significant. Such an aerodynamic cause may serve as an additional mechanism for the asymmetric deformation pattern observed in real insects.     

柔性扑翼的气动特性研究

以往扑翼的气动力计算研究都很少考虑扑翼的柔性,而在鸟的扑翼动作中,在外加气动力和鸟自身的扑动力作用下,扑翼的柔性变形相当大。本文在原有匀速刚性模型的基础上,提出考虑了扑翼扑动速率变化和形状变化的扑翼分析模型,使之更接近鸟翼柔性扑动真实情况。通过计算分析气动特性发现,控制适当的话,柔性变形能大大改善扑翼的气动性能。本文通过模拟鸟扑翼的柔性运动,计算了时柔性扑翼气动力以及平均升力系数和平均推力系数随着扑动角、倾斜角等参数变化的情况,从而从气动的角度解释了为什么鸟在不同的飞行阶段扑翼规律各不相同,并为柔性扑翼飞行器的设计提供了理论依据。     

Numerical simulation of a flapping four-wing micro-aerial vehicle

A three-dimensional numerical simulation of a four-wing (two wings on each side, one on top of another) flapping micro-aerial vehicle (FMAV), known as the Delfly micro, is performed using an immersed boundary method Navier–Stokes finite volume solver at Reynolds numbers of 5500 (forward flight condition). The objective of the present investigation is to gain an insight to the aerodynamics of flapping wing biplane configuration, by making an analysis on a geometry that is simplified, yet captures the major aspects of the wing behavior. The fractional step method is used to solve the Navier–Stokes equations. Results show that in comparison to the Delfly II flapping kinematics (a similar FMAV configuration but smaller flapping stroke angles), the Delfly-Micro flapping kinematics provides more thrust while maintaining the same efficiency. The Delfly-Micro biplane configuration generates more lift than expected when the inclination angle increases, due to the formation of a uniform leading edge vortex. Estimates of the lift produced in the forward flight conditions confirm that in the current design, the MAV is able to sustain forward flight. The potential effect of wing flexibility on the aerodynamic performance in the biplane configuration context is investigated through prescribed flexibility in the simulations. Increasing the wing׳ spanwise flexibility increases thrust but increasing chordwise flexibility causes thrust to first increase and then decrease. Moreover, combining both spanwise and chordwise flexibility outperforms cases with only either spanwise or chordwise flexibility.     

Three-dimensional effects on the translational locomotion of a passive heaving wing

This study was carried out on a three-dimensional wing with a freedom in translational direction under a prescribed up and down heaving motion. The investigation focused on how the system kinematics and structural parameters affect the dynamic response of a wing with a relatively small span length. The induced wing motion is a result of the system stability breakdown, which has only been observed by previous researches in the two-dimensional case. The results obtained indicate that the evolution of the wing locomotion is controlled not only by the flapping frequency but also influenced by the system inertia as well as the wing aspect ratio and density ratio. Moreover, initial perturbation effect on wings flexibility plays a role in the evolution development.     

Influence of wing flexibility on the aerodynamic performance of a tethered flapping bumblebee

The sophisticated structures of flapping insect wings make it challenging to study the role of wing flexibility in insect flight. In this study, a mass-spring system is used to model wing structural dynamics as a thin, flexible membrane supported by a network of veins. The vein mechanical properties can be estimated based on their diameters and the Young's modulus of cuticle. In order to analyze the effect of wing flexibility, the Young's modulus is varied to make a comparison between two different wing models that we refer to as flexible and highly flexible. The wing models are coupled with a pseudo-spectral code solving the incompressible Navier–Stokes equations, allowing us to investigate the influence of wing deformation on the aerodynamic efficiency of a tethered flapping bumblebee. Compared to the bumblebee model with rigid wings, the one with flexible wings flies more efficiently, characterized by a larger lift-to-power ratio.     

Experimental study of wings undergoing active root flapping and pitching

This paper presents the results of experiments carried out on mechanical wings undergoing active root flapping and pitching in the wind tunnel. The objective of the work is to investigate the effect of the pitch angle oscillations and wing profile on the aerodynamic forces generated by the wings. The experiments were repeated for a different reduced frequency, airspeed, flapping and pitching kinematics, geometric angle of attack and wing sections (one symmetric and two cambered airfoils). A specially designed mechanical flapper was used, modelled on large migrating birds. It is shown that, under pitch leading conditions, good thrust generation can be obtained at a wide range of Strouhal numbers if the pitch angle oscillation is adjusted accordingly. Consequently, high thrust was measured at both the lowest and highest tested Strouhal numbers. Furthermore, the work demonstrates that the aerodynamic forces can be sensitive to the Reynolds number, depending on the camber of the wings. Under pitch lagging conditions, where the effective angle of attack amplitude is highest, the symmetric wing was affected by the Reynolds number, generating less thrust at the lowest tested Reynolds value. In contrast, under pure flapping conditions, where the effective angle of attack amplitude was lower but still significant, it was the cambered wings that demonstrated Reynolds sensitivity.     

Experimental study on interaction of aerodynamics with flexible wings of flapping vehicles in hovering and cruise flight

Flapping wings are promising lift and thrust generators, especially for very low Reynolds numbers. To investigate aeroelastic effects of flexible wings (specifically, wing’s twisting stiffness) on hovering and cruising aerodynamic performance, a flapping-wing system and an experimental setup were designed and built. This system measures the unsteady aerodynamic and inertial forces, power usage, and angular speed of the flapping wing motion for different flapping frequencies and for various wings with different chordwise flexibility. Aerodynamic performance of the vehicle for both no wind (hovering) and cruise condition was investigated. Results show how elastic deformations caused by interaction of inertial and aerodynamic forces with the flexible structure may affect specific power consumption. This information was used here to find a more suitable structural design. The best selected design in our tests performs up to 30% better than others (i.e., less energy consumption for the same lift or thrust generation). This measured aerodynamic information could also be used as a benchmarking data for unsteady flow solvers.     

Experimental investigation of the effect of chordwise flexibility on the aerodynamics of flapping wings in hovering flight

Ornithopters or mechanical birds produce aerodynamic lift and thrust through the flapping motion of their wings. Here, we use an experimental apparatus to investigate the effects of a wing's twisting stiffness on the generated thrust force and the power required at different flapping frequencies. A flapping wing system and an experimental set-up were designed to measure the unsteady aerodynamic and inertial forces, power usage and angular speed of the flapping wing motion. A data acquisition system was set-up to record important data with the appropriate sampling frequency. The aerodynamic performance of the vehicle under hovering (i.e., no wind) conditions was investigated. The lift and thrust that were produced were measured for different flapping frequencies and for various wings with different chordwise flexibilities. The results show the manner in which the elastic deformation and inertial flapping forces affect the dynamical behavior of the wing. It is shown that the generalization of the actuator disk theory is, at most, only valid for rigid wings, and for flexible wings, the power P varies by a power of about 1.0  of the thrust T. This aerodynamic information can also be used as benchmark data for unsteady flow solvers.     

Effects of camber angle on aerodynamic performance of flapping-wing micro air vehicle

This study investigates the unsteady aerodynamic characteristics of the cambered wings of a flapping-wing micro air vehicle (FW-MAV) in hover. A three-dimensional fluid–structure interaction solver is developed for a realistic modeling of large-deforming wing structure and geometry. Cross-validation is conducted against the experimental results obtained also in the present study to establish more accurate analyses of cambered wings. An investigation is carried out on the unsteady vortex structures around the wings caused by the passive twisting motion. A parametric study is then conducted to evaluate the aerodynamic performance with respect to the camber angle at three different flapping frequencies including normal operating conditions. The camber angles producing the largest thrust and highest propulsive efficiency are estimated at each flapping frequency, and their effects on aerodynamic performance are analyzed in terms of the stroke phase. The timing and magnitude of the passive twisting motion, which are dependent on the camber angle at the operating frequency, greatly affects the unsteady vortex structure. Consequently, the camber angle designed at the operating frequency plays a key role in enhancing the aerodynamic performance of FW-MAVs.     

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.     

扑翼柔性及其对气动特性的影响

以往对扑翼气动特性的研究基本上都是基于简单的匀速刚性模型,但是通过大量观察不同飞鸟的扑翼动作发现,该模型与鸟翼的实际扑动还有很大差别。鸟翼不但上扑段和下扑段所需时间不同,而且在扑动过程中,鸟翼的形状无论沿弦向或展向都存在着相当大的柔性变形。本文在原有匀速刚性模型的基础上,加入了扑动速率变化和形状变化的影响,得出新的变速柔性扑翼分析模型,使之更接近鸟翼柔性扑动的真实情况。通过对比计算发现,柔性变形对扑翼的升力与推力都有着显著影响,如果控制得当,柔性变形能大大改善扑翼的气动性能。     

Numerical analysis on transitions and symmetry-breaking in the wake of a flapping foil

Flying and marine animals often use flapping wings or tails to generate thrust. In this paper, we will use the simplest flapping model with a sinusoidal pitching motion over a range of frequency and amplitude to investigate the mechanism of thrust generation. Previous work focuses on the Karman vortex street and the reversed Karman vortex street but the transition between two states remains unknown. The present numerical simulation provides a complete scenario of flow patterns from the Karman vortex street to reversed Karman vortex street via aligned vortices and the ultimate state is the deflected Karman vortex street, as the parameters of flapping motions change. The results are in agreement with the previous experiment. We make further discussion on the relationship of the observed states with drag and thrust coefficients and explore the mechanism of enhanced thrust generation using flapping motions.     

A simulation-based study on longitudinal gust response of flexible flapping wings

Winged animals such as insects are capable of flying and surviving in an unsteady and unpredictable aerial environment. They generate and control aerodynamic forces by flapping their flexible wings. While the dynamic shape changes of their flapping wings are known to enhance the efficiency of their flight, they can also affect the stability of a flapping wing flyer under unpredictable disturbances by responding to the sudden changes of aerodynamic forces on the wing. In order to test the hypothesis, the gust response of flexible flapping wings is investigated numerically with a specific focus on the passive maintenance of aerodynamic forces by the wing flexibility. The computational model is based on a dynamic flight simulator that can incorporate the realistic morphology, the kinematics, the structural dynamics, the aerodynamics and the fluid–structure interactions of a hovering hawkmoth. The longitudinal gusts are imposed against the tethered model of a hovering hawkmoth with flexible flapping wings. It is found that the aerodynamic forces on the flapping wings are affected by the gust, because of the increase or decrease in relative wingtip velocity or kinematic angle of attack. The passive shape change of flexible wings can, however, reduce the changes in the magnitude and direction of aerodynamic forces by the gusts from various directions, except for the downward gust. Such adaptive response of the flexible structure to stabilise the attitude can be classified into the mechanical feedback, which works passively with minimal delay, and is of great importance to the design of bio-inspired flapping wings for micro-air vehicles.     

VISCOELASTIC CONSTITUTIVE MODEL RELATED TO DEFORMATION OF INSECT WING UNDER LOADING IN FLAPPING MOTION

Flexible insect wings deform passively under the periodic loading during napping flight. The wing flexibility is considered as one of the specific mechanisms on improving insect flight performance. The constitutive relation of the insect wing material plays a key role on the wing deformation, but has not been clearly understood yet. A viscoelastic constitutive relation model was established based on the stress relaxation experiment of a dragonfly wing (in vitro). This model was examined by the finite element analysis of the dynamic deformation response for a model insect wing under the action of the periodical inertial force in flapping. It is revealed that the viscoelastic constitutive relation is rational to characterize the biomaterial property of insect wings in contrast to the elastic one. The amplitude and form of the passive viscoelastic deformation of the wing is evidently dependent on the viscous parameters in the constitutive relation.     

Bond graph modeling of a typical flapping wing micro-air-vehicle with the elastic articulated wings

In the present research, a new comprehensive model of a flexible articulated flapping wing robot using the bond graph approach is presented. The flapping kinematics of a two-section wing is introduced via the bond graph based approach on a hybrid mechanism providing amplitude and phase characteristics. The aerodynamic quasi-steady approach equipped with stall correlation is utilized according to the reduced flapping frequency and the angle of attack ranges. The local flow velocity and the wing position are calculated in both wing and body coordinates taking into account rotation and translation of the wing different parts. Estimation of the effective angle of attack is performed by calculating the instantaneous torque distribution on both wing sections. Aeroelastic modeling is employed in which the wing structure is assumed as an elastic Euler–Bernoulli beam at the leading edge with three linear torsional modes. In this novel integrated bond graph model, computation of the performance indices including the average lift and thrust, consumed and produced powers by flapping and mechanical efficiency are presented. Due to existence of the numerous geometric and kinematic parameters in articulated flexible flapping wing, such a model is essential for design and optimization. Consequently, an example of a typical parametric study and the results validation are carried out. It is indicated that the sensitivity of the bird performance to relative change in design variables would increase for out of phase flapping, second part stiffness, flapping amplitude, frequency and velocity respectively. It is interesting that by employing the reverse-phase flapping which is possible only via articulated wings, the maximum efficiency could be achieved. In addition, it is shown that adjusting the wing torsional stiffness is a crucial item in design of passive flapping robots. The key advantage of the two-section flapping wing is depicted as the controlling capability of the angle of attack in the outer part of the wing. Finally, the improved version of the bird is being addressed by approximately 15% progress in propulsive efficiency.

     

Role of wing morphing in thrust generation

In this paper, we investigate the role of morphing on flight dynamics of two birds by simulating the flow over rigid and morphing wings that have the characteristics of two different birds, namely the Giant Petrel and Dove Prion. The simulation of a flapping rigid wing shows that the root of the wing should be placed at a specific angle of attack in order to generate enough lift to balance the weight of the bird. However, in this case the generated thrust is either very small, or even negative, depending on the wing shape. Further, results show that morphing of the wing enables a significant increase in the thrust and propulsive efficiency. This indicates that the birds actually utilize some sort of active wing twisting and bending to produce enough thrust. This study should facilitate better guidance for the design of flapping air vehicles.     

Measurement of Thrust and Lift Forces Associated With Drag of Compliant Flapping Wing for Micro Air Vehicles Using a New Test Stand Design

Compliant wing designs have the potential of improving flapping wing Micro-Air Vehicles (MAVs). Designing compliant wings requires a detailed understanding of the effect of compliance on the generation of thrust and lift forces. The low force and high-frequency measurements associated with these forces necessitated a new versatile test stand design that uses a 250 g load cell along with a rigid linear air bearing to minimize friction and the dynamic behavior of the test stand while isolating only the stationary thrust or lift force associated with drag generated by the wing. Moreover, this stand is relatively inexpensive and hence can be easily utilized by wing designers to optimize the wing compliance and shape. The frequency response of the wing is accurately resolved, along with wing compliance on the thrust and lift profiles. The effects of the thrust and lift force generated as a function of flapping frequency were also determined. A semi-empirical aerodynamic model of the thrust and lift generated by the flapping wing MAV on the new test stand was developed and used to evaluate the measurements. This model accounted for the drag force and the effects of the wing compliance. There was good correlation between the model predictions and experimental measurements. Also, the increase in average thrust due to increased wing compliance was experimentally quantified for the first time using the new test stand. Thus, our measurements for the first time reveal the detrimental influence of excessive compliance on drag forces during high frequency operation. In addition, we were also able to observe the useful effect of compliance on the generation of extra thrust at the beginning and end of upstrokes and downstrokes of the flapping motion.     

Comparative Analysis of the Characteristics of the Vortex Wake behind a Flapping Wing Performing Oscillations of Different Types

The wake characteristics of a custom-designed airfoil performing pitching oscillations, heaving oscillations, and a combination of pitch and heave oscillations are compared in this study. The influence of flapping parameters are investigated at a constant Reynolds number Re\(_{c} = 2640\) and is presented for the Strouhal numbers based on the oscillation amplitude, St_A, varying in the \(0.1 \leqslant {\text{S}}{{{\text{t}}}_{A}} \leqslant 0.4\) range. The generation of vorticity above and below the airfoil depends on the airfoil’s initial direction of motion and remains the same for all types of flapping oscillations investigated. The evolution of the leading-edge and trailing-edge vortices is presented. The heaving oscillations of the airfoil are found to have a greater influence on the characteristics of the leading edge vortex. The wake behind the combined pitch-heave oscillations appears to be governed by pitching oscillations below \({\text{S}}{{{\text{t}}}_{A}} = 0.24\), whereas it is driven by heaving oscillations above \({\text{S}}{{{\text{t}}}_{A}} = 0.24\). The force computations indicate that the mere existence of the reverse von Kármán street is not sufficient to develop the thrust on the airfoil. The periodic component of velocity fluctuations significantly influences the wake characteristics. The anisotropic stress field developed around the airfoil due to the periodic fluctuations of the velocity is presented. The coherent structures developed in the wake are identified using the proper orthogonal decomposition and a qualitative comparison of the structures for different flapping oscillations is presented. The energy transfer from the flapping airfoil to the fluid for different flapping oscillations is highest for heaving oscillations followed by combined pitch-heave oscillations and pitching oscillations.