Aerodynamic Force Generation Research Articles

Aerodynamic analysis of complex flapping motions based on free-flight biological data

The wings of birds contain complex morphing mechanisms that enable them to perform remarkable aerial maneuvers. Wing morphing is often described using five wingbeat motion parameters: flapping, bending, folding, sweeping, and twisting. However, the specific impact of these motions on the aerodynamic performance of wings throughout the wingbeat cycle, and their potential to inform engineering applications, remains insufficiently explored. To bridge this gap and better incorporate the properties of coupled motions into the design of biomimetic aircraft, we present a numerical investigation of four flapping-based coupled motions during different flight phases (i.e. take-off, level flight, and landing) using a pigeon-like airfoil model. The wingbeat motion data for these four coupled motions were based on real flying pigeons and divided into: flap-bending, flap-folding, flap-sweeping, and flap-twisting. We used computational fluid dynamic simulations to study the effects of these coupled motions on the flow field, generation of transient aerodynamic forces, and work done by different motions on flapping. It was found that, first, the flap-bending motion causes unstable changes in the effective angle of attack (AoA), which affects the attachment of the leading-edge vortex (LEV), thereby producing more lift at smaller bending angles. Next, the flap-folding motion causes the LEV to attach to the wing earlier and regulates the detachment of vortices. Significant changes in the folding angle are used to influence lift generation and the flap-sweeping motion has minimal effect on the flow field structure across the three flight phases. Finally, flap-twisting motion leads to notable changes in the effective AoA, allowing for dynamic adjustments to control aerodynamics at different stroke stages, resulting in less drag during take-off and more drag during landing. This study enhances the understanding of the aerodynamic performance of bird with coupled motions in different flight phases and provides theoretical guidance for the design of bionic flapping-wing aircraft with multi-degree-of-freedom wings.

Aerodynamic Characteristics of Cruciform Parachute with an Asymmetric Configuration of Ropes

In this study, an aerodynamic control scheme was proposed based on an asymmetric configuration of the ropes of a cruciform parachute to provide the lateral aerodynamic control forces required for it. Wind tunnel tests were conducted to confirm that this scheme could generate a lateral aerodynamic force for the cruciform parachute that was approximately 24% of the axial force. The deployment of a cruciform parachute under a subsonic flow regime was simulated by coupling the lattice Boltzmann method with a structural model. The shape of the canopy obtained from the coupled calculations was in good agreement with that determined based on the results of the wind tunnel test. The results of both showed that the cruciform parachute tilted along the direction of the shortened ropes under the combined action of the asymmetric configuration and incoming flow. This led to a difference in the lateral pressure on the canopy that led to the generation of lateral aerodynamic forces, which were linearly related to the reduced length of the ropes, and increased as their length decreased.

Aerodynamics of a flapping wing with stroke deviation in forward flight

In this paper, we numerically studied the effect of stroke deviation on the aerodynamic performance of the three-dimensional flapping wing in forward flight at a low Reynolds number. Six deviation motion patterns with different stroke deviation amplitudes were investigated. The results show that the distinct patterns exert a substantial influence on the aerodynamic forces of the flapping wing, with a more pronounced effect at higher values of deviation amplitude. For most patterns, stroke deviation enhances either lift or thrust performance unilaterally. The maximum lift and thrust of the wing with deviation motion can be 37% and 35% larger than that of the wing without deviation motion. A detailed analysis of typical flow characteristics underscores the pivotal role of deviation motion in aerodynamic force generation. Finally, two artificially created innovative deviation motion patterns are proposed, which exhibit an exceptional capacity to augment thrust by up to 123% or enhance comprehensive aerodynamic performance significantly. These findings establish a theoretical foundation for designing high-performance flapping-wing micro-air vehicles.

Effects of blood-feeding on mosquitoes hovering kinematics and aerodynamics

Mosquitoes exhibit a distinctive and remarkable flight pattern, flapping their wings at a high frequency with relatively small stroke amplitude. However, until recently, the underlying aerodynamic mechanisms have remained unclear. Furthermore, there is a lack of understanding about their flight behaviors after blood-feeding and the corresponding aerodynamic characteristics. This study aims to explore this uncharted area, conducts experiments to acquire kinematic and morphological data and numerical simulations to obtain three-dimensional flow characteristic. Further analysis uncovers several key findings. Both before and after blood-feeding hovering exhibit a similar flapping wing pattern, characterized by downstroke and upstroke with three stages of each half stroke. After blood-feeding, there are significant increases in stroke amplitude, mid-downstroke duration, velocity, and flip angles. Additionally, body pitch, stroke plane tilt, and Reynolds number experience increments. In hovering, mosquitoes balance vertical force with weight, with substantial peaks observed in each stage, particularly during the mid-stroke. After blood-feeding, the vertical force experiences a 3.3-fold increase, with the majority of the increase occurring during the mid-downstroke. The study identifies three unsteady mechanisms for aerodynamic force generation without blood-feeding hovering, namely, added-mass force, delayed stall, and fast-pitching-up rotation. These mechanisms persist after blood-feeding, with a greater reliance on delayed stall to support increased weight.

A numerical study on the aerodynamic effects of dynamic twisting on forward flight flapping wings

To better understand the secret of natural flying vertebrates such as how humming-birds twist their wings to achieve superb flight ability, we presented a numerical investigation of dynamic twisting based on a hummingbird-like flapping wing model. Computational fluid dynamic simulations were performed to examine the effects of dynamic twisting on the unsteady flow field, the generation of instantaneous aerodynamic forces, and the time-averaged aerodynamic performance. This research reveals the details of leading-edge vortices (LEVs) and the underlying mechanisms behind the positive effects of wing torsion. The results demonstrated that wing torsion can effectively maintain the favorable distribution of effective angle of attack along the wing spanwise, resulting in a higher time-averaged thrust and vertical force. Further, the proper parameters of dynamic twisting can also improve the propulsive efficiency in forward flight. Dynamic twisting also showed a superior ability in controlling the airflow separation over the wing surface and maintaining the stability of the LEV. The amplitudes of effective angle of attack associated with the highest peak thrust and the maximum thrust-to-power at different advanced ratios were also explored, and it was found that the amplitudes decrease with increasing advanced ratio. To improve the efficiency during larger advanced ratio, specific modifications to the pitching of the wing were proposed in this work. The research in this paper has promising implications for the bio-inspired flapping wing.

Influence of posture during gliding flight in the flying lizard Draco volans

The agamid lizards of the genus Draco are undoubtedly the most renown reptilian gliders, using their rib-supported patagial wings as lifting surfaces while airborne. Recent investigations into these reptiles highlighted the role of body posture during gliding, however, the aerodynamics of postural changes in Draco remain unclear. Here, we examine the aerodynamics and gliding performances of Draco volans using a numerical approach focusing on three postural changes: wing expansion, body camber, and limb positioning. To this aim, we conducted 70 three-dimensional steady-state computational fluid dynamics simulations of gliding flight and 240 two-dimensional glide trajectory calculations. Our results demonstrate that while airborne, D. volans generates a separated turbulent boundary layer over its wings characterized by a large recirculation cell that is kept attached to the wing surface by interaction with wing–tip vortices, increasing lift generation. This lift generating mechanism may be controlled by changing wing expansion and shape to modulate the generation of aerodynamic force. Furthermore, our trajectory simulations highlight the influence of body camber and orientation on glide range. This sheds light on how D. volans controls its gliding performance, and conforms to the observation that these animals plan their glide paths prior to take off. Lastly, D. volans is mostly neutral in pitch and highly maneuverable, similar to other vertebrate gliders. The numerical study presented here thus provides a better understanding of the lift generating mechanism and the influence of postural changes in flight in this emblematic animal and will facilitate the study of gliding flight in analogous gliding reptiles for which direct observations are unavailable.

Experimental Analyses of Aerodynamic Force Generation and Wing Motion Associated with a Single-motor-driven Butterfly-inspired Flapping-wing Robot

Experimental Analyses of Aerodynamic Force Generation and Wing Motion Associated with a Single-motor-driven Butterfly-inspired Flapping-wing Robot

An experimental study of the aerodynamic performance of a maple wing model at low Reynolds numbers

Maple seeds are widely known for their autorotation and may achieve remarkably long-distance flights owing to their unique wing morphology. These features suggest the adaptability of the blades to wind turbines and air vehicles. However, the effects of these morphological features on aerodynamic force generation are still poorly understood. An enlarged replica of a sample 3D maple wing was produced using additive manufacturing. Direct force experiments were conducted in a low-speed wind tunnel using a two-component force balance to obtain the lift and drag coefficients of the model wing. The polar curves of the wing were obtained for three different Re numbers by repeating the experiments over a wide angle of attack range of -50 to 50°. The best aerodynamic performance is obtained at 18° and -12° attack angles for positive and negative angles, respectively, regardless of the Re number. This preliminary study shows that maple seed can be mimicked in the design of propellers and wind-turbine blades.

Correlations between flexural stiffness, wingbeat frequency and aerodynamic force generation in hovering insect flight

We report a direct relationship between wing flexural stiffness, wingbeat frequency, and mean aerodynamic force generation based on the wing morphological database for various insect species in hovering flight condition. Proposed correlations have shown the potential to predict the minimum aerodynamic force generation in flapping wings for a given flapping frequency with reasonable accuracy. The robustness of these correlations is demonstrated by validating them against the available experimental data for the various artificial flapping-wing configurations. These regression models can be used as first-order design tools which will save computational and experimental time while developing flapping-wing drones.

Quasi three-dimensional deformable blade element and unsteady vortex lattice reduced-order modeling of fluid–structure interaction in flapping wings

Flapping, flexible insect wings deform under inertial and fluid loading. Deformation influences aerodynamic force generation and sensorimotor control, and is thus important to insect flight mechanics. Conventional flapping wing fluid–structure interaction models provide detailed information about wing deformation and the surrounding flow structure, but are impractical in parameter studies due to their considerable computational demands. Here, we develop two quasi three-dimensional reduced-order models (ROMs) capable of describing the propulsive forces/moments and deformation profiles of flexible wings. The first is based on deformable blade element theory (DBET) and the second is based on the unsteady vortex lattice method (UVLM). Both rely on a modal-truncation based structural solver. We apply each model to estimate the aeromechanics of a thin, flapping flat plate with a rigid leading edge, and compare ROM findings to those produced by a coupled fluid dynamics/finite element computational solver. The ROMs predict wing deformation with good accuracy even for relatively large deformations of 25% of the chord length. Aerodynamic loading normal to the wing's rotation plane is well captured by the ROMs, though model errors are larger for in-plane loading. We then perform a parameter sweep to understand how wing flexibility and mass affect peak deflection, mean lift and average power. All models indicate that flexible wings produce less lift but require lower average power to flap. Importantly, these studies highlight the computational efficiency of the ROMs—compared to the convention modeling approach, the UVLM and DBET ROMs solve 4 and 6 orders of magnitude faster, respectively.

Investigation of chordwise functionally graded flexural rigidity in flapping wings using a two-dimensional pitch–plunge model

Insect wings are heterogeneous structures, with flexural rigidity varying one to two orders of magnitude over the wing surface. This heterogeneity influences the deformation the flapping wing experiences during flight. However, it is not well understood how this flexural rigidity gradient affects wing performance. Here, we develop a simplified 2D model of a flapping wing as a pitching, plunging airfoil using the assumed mode method and unsteady vortex lattice method to model the structural and fluid dynamics, respectively. We conduct parameter studies to explore how variable flexural rigidity affects mean lift production, power consumption and the forces required to flap the wing. We find that there is an optimal flexural rigidity distribution that maximizes lift production; this distribution generally corresponds to a 3:1 ratio between the wing’s flapping and natural frequencies, though the ratio is sensitive to flapping kinematics. For hovering flight, the optimized flexible wing produces 20% more lift and requires 15% less power compared to a rigid wing but needs 20% higher forces to flap. Even when flapping kinematics deviate from those observed during hover, the flexible wing outperforms the rigid wing in terms of aerodynamic force generation and power across a wide range of flexural rigidity gradients. Peak force requirements and power consumption are inversely proportional with respect to flexural rigidity gradient, which may present a trade-off between insect muscle size and energy storage requirements. The model developed in this work can be used to efficiently investigate other spatially variant morphological or material wing features moving forward.

Preliminary design of bionic flapping wing vehicle

This paper deals with the preliminary design of bionic flapping wing vehicle. The design is driven by its requirement and objective namely the maximum weight should be less than 0.5 kg with 1.5 m wingspan. In the conceptual design, the wing planform, wing structures and system of flapping mechanism will be considered to find the initial configuration and then continued the sizing of the flapping vehicle. The analysis of designed flapping vehicle is increasingly complex due to firstly the generation of time-dependent aerodynamic forces and moments from unsteady flow around the flapping wing, secondly, flexible wing structure which generates higher thrust may cause a structure failure and thirdly, a flapping mechanism system generating differential flapping motion for the vehicle maneuver. The aerodynamic analysis for given flapping motion model is carried out using Computational Fluid Dynamics method based the solution of unsteady Reynold Averaged Navier-Stokes equations and the structure analysis is conducted with the input of aerodynamic loads using Finite Element method to find critical stresses that may cause a structure failure. As a solution of differential flapping two controlled servos are used. The architecture of electrical system is made to analysis of the distribution of data signal and power. The flight maneuver is achieved by changes in flapping frequency and sweeping angle. The selection of system components is performed by considering weight constraint. The flight maneuver is achieved by changes in flapping frequency and sweeping angle. The wing platform has elliptical shape with airfoil maximum camber of 6% chord at a quarter chord. The outer body and wing are made of foam laminated by glass fibre with the foam density of 0.045 g/cm3. The horizontal tail is made of mylar film with density of 1.38 g/cm3 and its area of 168.3 cm2. As simulated results, the amount of total lift is 4.18 Newton generated at 6 Hz flapping frequency.

Mechanism of aerodynamic force generation concerning train vibration in tunnel (LES of large-scale flow structure around simplified train model)

Mechanism of aerodynamic force generation concerning train vibration in tunnel (LES of large-scale flow structure around simplified train model)

A flight mechanics-based justification of the unique range of Strouhal numbers for avian cruising flight

In this paper, analytical expressions for cycle-averaged aerodynamic forces generated by flapping wings are derived using a force model and flapping kinematics suitable for the forward flight of avian creatures. A strip theory-based formulation is proposed and the analytical expressions are found as functions of the amplitude of twist profile, mean twist angle, the flow separation point on the upper surfaces of the wings, and Strouhal number. Numerical results are obtained for a rectangular planform as well as for a representative avian wing planform. Utilizing these results, it is shown that there exists a narrow Strouhal number range where cycle-averaged net thrust, lift, and lift to drag ratio are optimal for a given flow pattern over the upper surfaces of the wings. This narrow Strouhal number range, found to be between 0.1 and 0.3, corresponds to the cruising range for a large number of avian creatures, as documented in current literature. An explanation, based on force constraints and local optimization in aerodynamic force generation, is provided for the unique range of Strouhal numbers utilized in avian cruising flight. The results and the approach outlined in the paper can be utilized to design efficient bio-inspired flapping vehicles.

Aerodynamic performance of a bristled wing of a very small insect

Aerodynamic force generation capacity of the wing of a miniature beetle Paratuposa placentis is evaluated using a combined experimental and numerical approach. The wing has a peculiar shape reminiscent of a bird feather, often found in the smallest insects. Aerodynamic force coefficients are determined from a dynamically scaled force measurement experiment with rotating bristled and membrane wing models in a glycerin tank. Subsequently, they are used as numerical validation data for computational fluid dynamics simulations using an adaptive Navier–Stokes solver. The latter provides access to important flow properties such as leakiness and permeability. It is found that, in the considered biologically relevant regimes, the bristled wing functions as a less than 50% leaky paddle, and it produces between 66 and 96% of the aerodynamic drag force of an equivalent membrane wing. The discrepancy increases with increasing Reynolds number. It is shown that about half of the aerodynamic normal force exerted on a bristled wing is due to viscous shear stress. The paddling effectiveness factor is proposed as a measure of aerodynamic efficiency.Graphic abstract

Effect of corrugation on the aerodynamic performance of three-dimensional flapping wings

The effect of corrugation implemented in cambered wings on the aerodynamic performance of three-dimensional flapping-wings was studied. For the first time, the measured wing kinematics of a hover-capable tailless flapping-wing micro air vehicle, which is called KUBeetle, was employed for all wing profiles. The forces and flow structures were obtained using the computational fluid dynamics (CFD) method via the commercial software ANSYS-Fluent. Different corrugation heights of 0 (non-corrugated), 3%, and 6% of local chord length were considered. For each corrugation height, the effect of corrugation near leading and trailing edges were also investigated. For A-group wings in which the corrugation was placed over all of the chord, the lift and drag increased, compared to the non-corrugated profile in downstroke. However, during upstroke when the stroke direction is reversed, the corrugation profiles reversed upside down, causing reduction in lift and drag. Meanwhile, for P-group wings in which 20% chord length near the leading edge and trailing edge were non-corrugated, forces decreased slightly in both the down- and up-strokes. Especially, the characteristics of aerodynamic force generation including lift-to-drag ratio of the P-group wing with a corrugation height of 3% of local chord length was very close to those of the non-corrugated cambered wing. Since wing corrugation is expected to stiffen the membrane wing, this particular wing may replace the current wing removing vein structures, which can contribute to lighter weight and lower power consumption to overcome inertial force at the stroke reversals.

The role of effective angle of attack in hovering pitching-flapping-perturbed revolving wings at low Reynolds number

Since the performance of revolving wings is limited at a low Reynolds number (Re), the pitching-flapping-perturbed revolving wing (PFP-RW) is proposed as an approach for an augmentation of lift and efficiency. However, the underlying physics of the effective angle of attack (αe) in aerodynamic force generation is underexplored. Here, as a follow-up of our previous study [L. Chen et al., “Unsteady aerodynamics of a pitching-flapping-perturbed revolving wing at low Reynolds number,” Phys. Fluids 30, 051903 (2018)], we further investigate the role of αe in aerodynamic force generation and the corresponding leading-edge vortex (LEV) behaviors of a hovering PFP-RW at Re = 1500. Results show that the efficiency of a PFP-RW with sinusoidal flapping motion can be improved by a sinusoidal modulation of the αe profile while retaining the αe amplitude. Instead of the αe amplitude, if the flapping amplitude is fixed during the sinusoidal modulation of the αe profile, the lift of a PFP-RW is significantly enhanced despite a slight reduction in efficiency. For PFP-RWs with different pitching-flapping perturbations but an identical αe profile, a general trend of resultant-velocity-normalized lift and drag coefficients in the wind frame is predominantly retained, except for the deviations during the late downstroke. The breakdown of the general trend is attributed to the wing-LEV interaction, the effect of which is not reflected by the instantaneous resultant velocity. For PFP-RWs with small-amplitude sinusoidal αe profiles, the variation of pitching-flapping perturbations can further lead to novel LEV behaviors, e.g., a dual-LEV structure, during its formation. Our findings can provide guidance for the control of pitching-flapping perturbations on PFP-RWs.

Effects of timing and magnitude of wing stroke-plane tilt on the escape maneuverability of flapping wing

Hummingbirds perform a variety of agile maneuvers, and one of them is the escape maneuver, in which the birds can steer away from threats using only 3–4 wingbeats in less than 150 ms. A distinct kinematic feature that enables the escape maneuver is the rapid backward tilt of the wing stroke plane at the beginning of the maneuver. This feature results in a simultaneous nose-up pitching and backward acceleration. In this work, we investigated how the magnitude and timing of the wing stroke-plane tilt (relative to the phase of flapping cycle) affected the generation of backward thrust, lift, and pitching moment and therefore the maneuverability of escape flight. Investigations were performed using experiments on dynamically scaled robotic wings and computational fluid dynamic simulation based on a simplified harmonic wing stroke and rotation kinematics at Re = 1000 and hummingbird wing kinematics at Re ≈ 10 000. Results showed that the wing stroke-plane tilt timing exerted a strong influence on the aerodynamic force generation. Independent of the tilt magnitude, the averaged backward thrust and pitching moment were maximized when the stroke plane tilt occurred near the end of the half strokes (e.g., upstroke and downstroke). Relative to the other timings of stroke-plane tilt, the ‘optimal’ timings led to a maximal backward tilt of the total aerodynamic force during the wing upstroke; hence, the backward thrust and nose-up pitching moment increased. The ‘optimal’ timings found in this work were in good agreement with those identified in the escape maneuvers of four species of hummingbirds. Therefore, hummingbirds may use a similar strategy in the beginning of their escape maneuver.

Scaling of the performance of insect-inspired passive-pitching flapping wings.

Flapping flight using passive pitch regulation is a commonly used mode of thrust and lift generation in insects and has been widely emulated in flying vehicles because it allows for simple implementation of the complex kinematics associated with flapping wing systems. Although robotic flight employing passive pitching to regulate angle of attack has been previously demonstrated, there does not exist a comprehensive understanding of the effectiveness of this mode of aerodynamic force generation, nor a method to accurately predict its performance over a range of relevant scales. Here, we present such scaling laws, incorporating aerodynamic, inertial and structural elements of the flapping-wing system, validating the theoretical considerations using a mechanical model which is tested for a linear elastic hinge and near-sinusoidal stroke kinematics over a range of scales, hinge stiffnesses and flapping frequencies. We find that suitably defined dimensionless parameters, including the Reynolds number, Re, the Cauchy number, Ch, and a newly defined 'inertial-elastic' number, IE, can reliably predict the kinematic and aerodynamic performance of the system. Our results also reveal a consistent dependency of pitching kinematics on these dimensionless parameters, providing a connection between lift coefficient and kinematic features such as angle of attack and wing rotation.

Experimental Study on Forewing–Hindwing Phasing in Hovering and Forward Flapping Flight

The effects of the phase difference between fore- and hindwings are experimentally investigated on the aerodynamic force, aerodynamic efficiency, and longitudinal control forces for tandem flapping wings in hovering and forward flight. The aerodynamic force and power are measured using a dynamically scaled mechanical model in a water tunnel at a Reynolds number of 7660–11,400. The experimental results indicate that a tandem configuration, except in-phase motion, is detrimental to the generation of vertical and horizontal aerodynamic forces in hovering and slow forward flight; whereas the vertical force is enhanced in out-of-phase motion when the hindwing leads the forewing in faster forward flight. In-phase motion has the largest aerodynamic efficiency of all the phase differences in hovering and forward flight, which does not correspond to the phase difference that dragonflies use in hovering and forward flight. In contrast, a shift in the phase difference in the range of 45–180 deg (hindwing leads forewing) does not change the total vertical or horizontal force but largely and monotonically changes the pitching moment about the body caused by the force difference between the fore- and hindwings in hovering and forward flight, which corresponds to the fact that dragonflies use antiphase motion in hovering and out-of-phase motion of 50–130 deg in forward flight.