Wing In Forward Flight Research Articles

Investigation of the aerodynamic performance of the dragonfly-inspired tandem wings considering the coupling between the stroke plane and phase difference

The dragonfly's tandem wings can make full use of the interference of various spatial vortices to obtain efficient flight capability. The complex coupling among multiple motion parameters will have an important influence on the interference between the forewing (FW) and hindwing (HW). In this paper, the aerodynamic performance of the dragonfly-inspired tandem wings is analyzed using the Computational Fluid Dynamics (CFD) method considering the coupling effect of the stroke plane and phase difference. The variation of the force coefficient, vortex structure and aerodynamic efficiency of the tandem wings in forward flight are analyzed, respectively. The results show that the stroke plane angle affects the distribution of the leading edge vortex (LEV) and trailing edge vortex (TEV), which primarily controls the trend of horizontal force variation. The phase difference of tandem wings will change the fluctuation of the horizontal force coefficient curve by affecting the meeting time of the forewing and hindwing. However, with the increase of stroke plane angle, the fluctuation of aerodynamic coefficient caused by phase difference will decrease. The propulsion efficiency(η) and power loading(PL) can be improved through increasing the stroke plane angle and selecting a reasonable phase difference. The conclusion can provide theoretical guidance for the design of the dragonfly-inspired tandem flapping wing aircraft (DTFWA) and the choice of motion parameters.

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.

Flow interactions lead to self-organized flight formations disrupted by self-amplifying waves

Collectively locomoting animals are often viewed as analogous to states of matter in that group-level phenomena emerge from individual-level interactions. Applying this framework to fish schools and bird flocks must account for visco-inertial flows as mediators of the physical interactions. Motivated by linear flight formations, here we show that pairwise flow interactions tend to promote crystalline or lattice-like arrangements, but such order is disrupted by unstably growing positional waves. Using robotic experiments on “mock flocks” of flapping wings in forward flight, we find that followers tend to lock into position behind a leader, but larger groups display flow-induced oscillatory modes – “flonons” – that grow in amplitude down the group and cause collisions. Force measurements and applied perturbations inform a wake interaction model that explains the self-ordering as mediated by spring-like forces and the self-amplification of disturbances as a resonance cascade. We further show that larger groups may be stabilized by introducing variability among individuals, which induces positional disorder while suppressing flonon amplification. These results derive from generic features including locomotor-flow phasing and nonreciprocal interactions with memory, and hence these phenomena may arise more generally in macroscale, flow-mediated collectives.

Fluid–structure resonance in spanwise-flexible flapping wings

We report direct numerical simulations of the flow around a spanwise-flexible wing in forward flight. The simulations were performed at$Re=1000$for wings of aspect ratio 2 and 4 undergoing a heaving and pitching motion at Strouhal number$St_c\approx 0.5$. We have varied the effective stiffness of the wing$\varPi _1$while keeping the effective inertia constant,$\varPi _0=0.1$. It has been found that there is an optimal aerodynamic performance of the wing linked to a damped resonance phenomenon, that occurs when the imposed frequency of oscillation approaches the first natural frequency of the structure in the fluid,$\omega _{n,f}/\omega \approx 1$. In that situation, the time-averaged thrust is maximum, increasing by factor 2 with respect to the rigid case with an increase in propulsive efficiency of approximately 15 %. This enhanced aerodynamic performance results from the combination of larger effective angles of attack of the outboard wing sections and a delayed development of the leading edge vortex. With increasing flexibility beyond the resonant frequency, the aerodynamic performance drops significantly, in terms of both thrust production and propulsive efficiency. The cause of this drop lies in the increasing phase lag between the deflection of the wing and the heaving/pitching motion, which results in weaker leading edge vortices, negative effective angles of attack in the outboard sections of the wing, and drag generation in the first half of the stroke. Our results also show that flexible wings with the same$\omega _{n,f}/\omega$but different aspect ratio have the same aerodynamic performance, emphasizing the importance of the structural properties of the wing for its aerodynamic performance.

Unsteady aerodynamics of flapping bionic eagle wings in forward flight: An experimental and numerical study

The aerodynamic performance of fabricated eagle wing with the corrugated trailing edge was investigated experimentally and numerically in this study. In this respect, wings were designed by imitating the bionic eagle wing and fabricated using a 3D printer. Tests on the wings were performed in a wind tunnel for different bending deflection angles, flapping frequencies, angles of attack, and forward flight velocities. As the key parameters, lift and thrust forces, lift-to-drag and input power were compared between eagle wing and simplified wing. The results revealed that the eagle wing with the corrugated trailing edge led the lift force to be improved by 14% on average compared to the simplified wing, with the largest improvement of 45%. Further, the thrust force of a eagle wing was greater than that of the simplified wing (up to 21%). Also, the input power of the simplified wing mechanism was greater than that of the eagle wing. Numerical simulations were performed to study flow physics. After validating the numerical results against the experimental results, the lift and thrust force, lift-to-drag, pressure contours and vortex were compared between the eagle and simplified wings. The results of the numerical simulation revealed that lift-to-drag increased with for eagle wing with the corrugated trailing edge of eagle wing. the pressure difference between the upper and lower surfaces of the eagle wing was larger than that of the simplified wing; therefore, the lift force produced by the eagle wing was larger than that of the simplified wing.

Ground effect on the aerodynamics of a flapping wing in forward flight: an experimental study

PurposeGround effect is one of the important factors in the enhancement of wing aerodynamic performance. This study aims to investigate the aerodynamic forces and performance of a flapping wing with the bending deflection angel under the ground effect.Design/methodology/approachIn this study, the wing and flapping mechanism were designed and manufactured based on the seagull flight and then assembled. It is worth noting that this mechanism is capable of wing bending in the upstroke flight as big birds. Finally, the model was examined at bending deflection angles of 0° and 107° and different distances from the surface, flapping frequencies and velocities in forward flight in a wind tunnel.FindingsThe results revealed that the aerodynamic performance of flapping wings in forward flight improved due to the ground effect. The effect of the bending deflection mechanism on lift generation was escalated when the flapping wing was close to the surface, where the maximum power loading occurred.Practical implicationsFlapping wings have many different applications, such as maintenance, traffic control, pollution monitoring, meteorology and high-risk operations. Unlike fixed-wing micro aerial vehicles, flapping wings are capable of operating in very-low Reynolds-number flow regimes. On the other hand, ground effect poses positive impacts on the provision of aerodynamic forces in the take-off process.Originality/valueBending deflection in the flapping motion and ground effect are two influential factors in the enhancement of the aerodynamic performance of flapping wings. The combined effects of these two factors have not been studied yet, which is addressed in this study.

Effects of bore-hole design on the aerodynamics of a flapping rotary wing in forward flight

Inspired by the folding of wing area in bird flights, a bore-hole design has been introduced to hovering flapping rotary wings (FRWs) to reduce negative lift generation during upstrokes. However, the contribution of this novel concept to FRWs in forward flight is still unclear. Using numerical simulations, the effects of bore-hole design on the force generation and flow structures of FRWs at various advance ratios (J) and tilt angles of disk plane (β) are explained here. Our results show that the FRWs with bore-hole design can retain their lift enhancement within certain limits of J and β. Moreover, the lift enhancement is remarkable in upwind flapping cycles while becomes negligible in tailwind ones. Like hovering scenarios, the lift-enhancing mechanism in forward flight is characterized by the release of pressure difference on the hinge and the formation of a secondary leading-edge vortex (LEV), despite the distinct flow structures in upwind and tailwind conditions. It is further found that a positive incident angle is preferred for the formation of a strong shear layer above the hinge, therefore promoting the release of pressure difference. Besides the lift enhancement, the bore-hole design can also result in a decrease in revolving torque whereas the wind-frame drag is barely changed. According to our findings, following research considering the fluid-structure interaction of the hinge is suggested and the material and structure design of the hinge is crucial for future FRW MAVs.

Optimal thrust efficiency for a tandem wing in forward flight using varied hindwing kinematics of a damselfly

We reveal the hindwing kinematics of a damselfly that are optimal for the thrust efficiency, which is a major concern of a bio-inspired micro-aerial vehicle. The parameters of the hindwing kinematics include stroke-plane angle, rotational duration, and wing phase. We developed a numerical self-propulsion model to investigate the thrust efficiency. The correlation analysis and optimal analysis were used to investigate the relation between varied hindwing kinematics and thrust efficiency. The results show that the optimal wing kinematics of the hindwing occur at a large stroke-plane angle and a small rotational duration in which the thrust efficiency might increase up to 22% compared with the original motion of the hindwing. The stroke-plane angle is highly positively correlated with thrust efficiency, whereas the rotational duration is moderately negatively correlated; the wing phase has the least correlation. The flow-field analysis indicates that a large stroke-plane angle combined with a small rotational duration has a weak forewing–hindwing interaction, generating a small resulting force on the hindwing, but the force comprises a small negative horizontal force, which hence increases the thrust efficiency. In a flight strategy for a micro-aerial vehicle, a large stroke-plane angle combined with a small rotational duration yields an optimal thrust efficiency, which is suitable for a flight of long duration. A small stroke-plane angle combined with a large rotation is suitable for hovering flight because it leads to a large negative horizontal force and a small vertical force. This work hence provides insight into the design of a tandem-wing micro-aerial vehicle.

Unsteady aerodynamic analysis and effectiveness of bio-inspired flapping wings in V-formation flight

Several bird species have been observed to fly in V-formation, an arrangement which exploits aerodynamic features to allow the group to conserve energy when migrating over long distances without stopping and feeding. The use of such grouping arrangement and organized pattern has demonstrated longer endurance and less power consumption in comparison with single flights. In this work, a computationally efficient potential flow solver based on the unsteady vortex lattice method (UVLM) is employed to assess the aerodynamic performance of flapping wings in forward flight in terms of lift and thrust generation along with the propulsive efficiency. The UVLM has the capability to simulate incompressible and inviscid flows over moving thin wings where the separation lines are known a priori. A bio-inspired, albatross wing shape is considered and its aerodynamic performance in formation flights is compared against conventional elliptical and rectangular wing shapes. The aerodynamic analysis is carried out for different wing arrangements of 3-body and 5-body V-formations to determine the optimal spacing parameters leading to maximum propulsive efficiency. The simulation results reveal that, at the optimal formation angle and separation distance, the albatross-inspired wing shape produces the most lift over the flapping cycle, while the rectangular wing shape generates the most thrust over the flapping cycle. Furthermore, the optimal configuration in terms of propulsive efficiency is found to be a 5-body V-formation utilizing the albatross wing shape with a separation distance set to one-third of the span and a formation angle set to 139°. The present study provides guidance for the design of multi-flapping wing air vehicles based on the expected flight mission. The albatross wing shape is found to have superior capability in producing lift, while the elliptical wing shape is observed to consume less power. The rectangular wing shape is found to produce higher thrust and then can achieve faster forward motion.

Numerical analysis of the wing–wake interaction of tandem flapping wings in forward flight

Tandem flapping-wing micro aerial vehicles, which are inspired by dragonflies, are unique in that they have two pairs of wings, and this could increase their maneuverability during flight. In this study, a series of tandem flapping-wing arrangements were designed in polar coordinates, and the polar distance and polar angles of the hindwing were used as design variables. Such a consideration of variations in both the horizontal and vertical positions of the hindwing in the design of tandem-wing arrangements has the potential to elucidate new interaction mechanisms, leading to improvements in the aerodynamic characteristics of tandem flapping-wings. Two-dimensional numerical analyses of these arrangements were conducted. The results of these analyses showed that, compared with a single flapping wing, tandem wings can increase the lift coefficient by 78.1% with an appropriate arrangement, but decrease the lift coefficient by 51.6% with an inappropriate arrangement. The vorticity distributions for typical wing arrangements were examined to establish the effect of the design variables on the aerodynamic characteristics of the tandem wings in forward flight. Two types of wing–wake interaction mechanisms were revealed based on this analysis. Both of these interactions can significantly reduce the negative force during the upstroke, resulting in an increase in the time-averaged lift.

Aerodynamic investigation on shifted-back vertical stroke plane of flapping wing in forward flight

In order to properly understand aerodynamic characteristics in a flapping wing in forward flight, additional aerodynamic parameters apart from those in hover—an inclined stroke plane, a shifted-back stroke plane, and an advance ratio—must be comprehended in advance. This paper deals with the aerodynamic characteristics of a flapping wing in a shifted-back vertical stroke plane in freestream. A scaled-up robotic arm in a water towing tank was used to collect time-varying forces of a model flapping wing, and a semi-empirical quasi-steady aerodynamic model, which can decompose the forces into steady, quasi-steady, and unsteady components, was used to estimate the forces of the model flapping wing. It was found that the shifted-back stroke plane left a part of freestream as a non-perpendicular component, giving rise to a time-course change in the aerodynamic forces during the stroke. This also brought out two quasi-steady components (rotational and added-mass forces) apart from the steady one, even the wing moved with a constant stroke velocity. The aerodynamic model underestimated the actual forces of the model flapping wing even it can cover the increasingly distributed angle of attack of the vertical stroke plane with a blade element theory. The locations of the centers of pressure suggested a greater pressure gradient and an elongated leading-edge vortex along a wingspan than that of the estimation, which may explain the higher actual force in forward flight.

Unsteady aerodynamics of a micro flapping rotary wing in forward flight

Flapping rotary wing (FRW) is a promising wing layout applicable to micro air vehicles design due to its capability in high lift production. Previous aerodynamic investigations of FRW have mainly focused on hovering flight, while forward flight has been relatively ignored. Therefore, this numerical study aims to address the unsteady aerodynamics of FRW in forward flight based on a FRW configuration with a forward-tilted rotational plane. Results show that compared with hovering flight, forward flying FRW shows a rotational-cycle-averaged thrust and lift reduction and an enhanced rotating moment, all of which can be mainly ascribed to the changes in the aerodynamics on the retreating side. For FRW rotating at a specified rotational speed, the larger advance ratio and severe forward tilt of its rotational plane are both disadvantageous to thrust production and can lead to significant lift reduction. However, they are beneficial for rotational moment enhancement and conducive to FRW rotating at higher speeds, thereby further compensating for the losses in thrust and lift. By further taking a real FRW at near-zero rotating moment into consideration, high thrust and lift can be achieved at the same time in cases of high advance ratio and large rotational plane tilt angle due to fast passive rotating, which differs from flapping wing and rotary wing. These findings can expand our understanding of the unsteady aerodynamics of flapping wing with complex kinematics in forward flight and provide guidance to the design of an FRW micro air vehicle that is capable of forward flight.

Vortex topology of a pitching and rolling wing in forward flight

Vortex topology is analyzed from measurements of flow over a flat, rectangular plate with an aspect ratio of 2 which was articulated in pitch and roll, individually and simultaneously. The plate was immersed into a $$\text {Re} = 10,000$$ flow (based on chord length). Measurements were made using a 3D–3C plenoptic PIV system to allow for the study of complete vortex topology of the entire wing. The prominent focus is the early development of the leading-edge vortex (LEV) and resulting topology. The effect of the wing kinematics on the topology was explored through a parameter space involving multiple values of pitch rate and roll rate at pitch and roll angles up to $${50}^{\circ }$$ . Characterization and comparisons across the expansive data set are made possible through the use of a newly defined dimensionless parameter, $${\textit{k}_{\text {Rg}}}$$ . Termed the effective reduced pitch rate, $${\textit{k}_{\text {Rg}}}$$ , is a measure of the pitch rate that takes into account the relative rolling motion of the wing in addition to the pitching motion and freestream velocity. This study has found that for a purely pitching wing, increasing the reduced pitch rate $${\textit{k}}$$ delays the vortex evolution with respect to $$\alpha _\mathrm {eff}$$ . For a purely rolling wing, as the advance coefficient $${\textit{J}}$$ is increased, the vortex evolution is advanced with respect to nondimensionalized time and the bifurcation point of the LEV shifts inboard. For a pitching and rolling wing, the addition of roll stabilizes and delays the evolution of the LEV in both nondimensionalized time and effective angle of attack.

Effect of chordwise deformation on propulsive performance of flapping wings in forward flight

ABSTRACTLack of flexibility limits the performance enhancement of man-made flapping wing Micro Air Vehicles (MAVs). Active chordwise deformation (bending) is introduced into the flapping wing model at low Reynolds number of Re = 200 in the present study. The lattice Boltzmann method with immersed boundary is adopted in the numerical simulation. The effects of the bending amplitude, bending frequency and phase lag between bending and flapping on the propulsive performance are analysed. The numerical results show that all the chordwise deformation parameters including the bending amplitude, bending frequency and phase lag have a great influence on the flow field, Leading-Edge Vortex (LEV), Trailing-Edge Vortex (TEV) and previous Leading-Edge Vortex (pLEV) of the deformable flapping wing, which leads to the variation of the propulsive performance. With decreasing bending amplitude and increasing bending frequency, both the thrust and energy dissipation coefficients increase. The highest thrust coefficient and highest energy dissipation coefficient occur at a phase lag of 180°. On the other hand, strong dependence of the propulsive efficiency on the vortex tangle is found. The highest propulsive efficiency is obtained for the present model at a dimensionless bending amplitude of 0.2, bending frequency of 0.7Hz, and phase lag of 0°.

Numerical study of the sound generated by two tandem arranged wings in forward flight

The sound generated by two tandem arranged flexible wings in forward flight is numerically studied by using an immersed boundary method, at a Reynolds number of 100 and Mach number of 0.1. Three distinct cases are studied, encompassing a single wing and two tandem wings flapping in phase and out of phase. The sound generation of flapping wings is systematically studied by varying the wing flexibility (represented by the frequency ratio [Formula: see text]), structure-to-fluid mass ratio ([Formula: see text]), the phase difference (φ), and the gap ([Formula: see text]) between the two flapping wings. The results show that there is a direct correlation between the wing flexibility and sound generation for all cases considered. Specifically, for wings of low mass ratios ([Formula: see text]), an increase in flexibility resulted in a decrease in sound generation. For wings of high mass ratios ([Formula: see text]), an increase in flexibility resulted in higher sound output. The introduction of a second wing flapping in-phase resulted in an increase in aerodynamic features and sound generation, while the introduction of a second wing flapping out-of-phase experiences a decrease in sound output when compared to the in-phase case. In both cases, the effect of the wing flexibility on the sound production is similar to that of the single wing. An increase in flexibility is also found to have an impact on the plane of maximum sound pressure. For example, increasing flexibility resulted in a rotation of the plane of maximum sound pressure counter-clockwise relative to those at lower frequency ratios. Flexible wings with a structure-to-fluid mass ratio of unity and medium flexibility (i.e. [Formula: see text] and [Formula: see text]) are found to generate lower sound with high aerodynamic performance conserved.

The role of rotary motion on vortices in reverse flow

The physics of a rotary wing in forward flight are highly complex, particularly when flow separation is involved. The purpose of this work is to assess the role of three-dimensional (3-D) vortex dynamics, with a focus on Coriolis forces, in the evolution of vortices in the reverse flow region of a rotating wing. High-fidelity numerical simulations were performed to recreate the flow about a representative rotating wing in forward flight. A vorticity transport analysis was performed to quantify and compare the magnitudes of 2-D flow physics, vortex tilting and Coriolis effects in the resulting flow fields. Three-dimensional vortex dynamics was found to have a very small impact on the growth and behaviour of vortices in the reverse flow region; in fact, the rate of vortex growth was successfully modelled using a simple 2-D vortex method. The small role of 3-D physics was attributed to the Coriolis and vortex tilting terms being approximately equal and opposite to one another. This ultimately lead to vortex behaviour that more closely resembled a surging wing as opposed to a conventional rotating wing, a feature unique to the reverse flow region.

From flapping to heaving: A numerical study of wings in forward flight

Direct Numerical Simulations of the flow around a pair of flapping wings are presented. The wings are flying in forward flight at a Reynolds number Re=500, flapping at a reduced frequency k=1. Several values of the radius of flapping motion are considered, resulting in a database that shows a smooth transition from the wing rotating with respect to its inboard wingtip (flapping), to a vertical oscillation of the wing (heaving). In this transition from flapping to heaving, the spanwise-averaged effective angle of attack of the wing increases while the effect of the Coriolis and centripetal accelerations becomes weaker. The present database is analyzed in terms of the value and surface distribution of the aerodynamic forces, and in terms of 2D and 3D flow visualizations. While the former allows a decomposition of the force in pressure (i.e., the component of the force normal to the surface of the wing) and skin friction (i.e., tangential to the surface of the wing), the latter allows the identification of specific flow structures with the corresponding forces on the wing. It is found that the aerodynamic forces in the vertical direction (lift) tend to increase for wings moving with larger radius of flapping motion, becoming maximum for the heaving configuration. This is mostly due to the increase of the spanwise-averaged effective angle of attack of the wing with the radius of the flapping motion. Also, the local changes in the effective angle of attack have a strong effect on the structure of the leading edge vortex, resulting in changes in the distribution of suction along the span near the leading edge of the wing. The effect of the apparent accelerations is mostly felt on the spanwise position where the separation of the LEV occurs. On the other hand, the differences in the force in the streamwise direction (thrust/drag) between the configurations with different radius of flapping motion seems to be linked to the position of the stagnation point dividing the suction and pressure side boundary layers, which seems to be controlled by the local effective angle of attack. Finally, the results of the DNS are used to evaluate the performance of an unsteady panel method, and to explain its deficiencies.

An aerodynamic model for insect flapping wings in forward flight

This paper proposes a semi-empirical quasi-steady aerodynamic model of a flapping wing in forward flight. A total of 147 individual cases, which consisted of advance ratios J of 0 (hovering), 0.125, 0.25, 0.5, 0.75, 1 and ∞, and angles of attack α of −5 to 95° at intervals of 5°, were examined to extract the aerodynamic coefficients. The Polhamus leading-edge suction analogy and power functions were then employed to establish the aerodynamic model. In order to preserve the existing level of simplicity, KP and KV, the correction factors of the potential and vortex force models, were rebuilt as functions of J and α. The estimations were nearly identical to direct force/moment measurements which were obtained from both artificial and practical wingbeat motions of a hawkmoth. The model effectively compensated for the influences of J, particularly showing outstanding moment estimation capabilities. With this model, we found that using a lower value of α during the downstroke would be an effective strategy for generating adequate lift in forward flight. The rotational force and moment components had noticeable portions generating both thrust and counteract pitching moment during pronation. In the upstroke phase, the added mass component played a major role in generating thrust in forward flight. The proposed model would be useful for a better understanding of flight stability, control, and the dynamic characteristics of flapping wing flyers, and for designing flapping-wing micro air vehicles.

Flow interactions lead to orderly formations of flapping wings in forward flight

It has long been thought that birds and fish form into flocks and schools to take advantage of flows. It is now shown that flapping bodies not only move faster when grouped together but that the flows also help to arrange, or order, the members. This suggests that a school can be viewed as a ``swimming crystal'' of fish organized by flows.

The advance ratio effect on the lift augmentations of an insect-like flapping wing in forward flight

Time-varying force/moment measurements and digital particle image velocimetry (DPIV) were conducted to reveal the influence of an advance ratio$J$on an insect-like flapping wing. A scaled-up robotic model and a servo-driven towing tank were employed to investigate nine individual$J$cases –$J=0$(hovering), 0.0625, 0.1250, 0.1875, 0.25, 0.50, 0.75, 1.0 and$\infty$(gliding motion) – at a high Reynolds number ($Re\sim 10^{4}$). At$J\leqslant 0.25$, the aerodynamic forces slightly increased from those in hover ($J=0$). The centres of pressure in these cases were concentrated in the outboard section, and the leading-edge vortices (LEVs) grew more conically than those in hover. Spanwise cross-sectional DPIV indicated that the wings generated more balanced downwashes, which effectively supported the slight lift increments in this range. At$J>0.25$, a drastic force drop appeared as$J$increased. The DPIV results in the$J=0.5$case clearly showed a strong trailing-edge vortex on the outboard trailing edges encroaching into the upper surface, which had been occupied by the LEV for lower $J$. The LEV vorticity was noticeably weakened, and coherent substructures with substantial turbulence accompanied this vorticity. In the$J=1.0$case, such encroachment was extended to 50 % of the section, and the LEV outboard became significantly irregular. The near-wake structures also showed that the$J=1.0$case had the narrowest downwash area, with unstable root and tip vortices, which reflected considerable attenuation in the lift enhancements. It was of note that all of these vortical behaviours were clearly distinguishable from aspect ratio ($AR$) effects. The$J$even played a similar role to that of the$AR$in the Navier–Stokes equation. These findings clearly indicated that the$J$could be an independent quantity governing the overall vortical system and lift enhancing mechanism on a flapping wing of a flapping-wing micro air vehicle.