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For flapping micro-air vehicles, periodical aerodynamics in every plunging period is always desired in the design of aircraft controlling system. During the periodic plunges of rigid airfoil, either periodical or non-periodical aerodynamic forces can be generated. Real airfoils are usually flexible so that the effect of flexibility on unsteady characteristics of aerodynamic periodicity should be considered. In this study, a fluid structure interaction analysis is employed to systematically investigate the aerodynamic periodicity of a periodically plunging flexible airfoil. The influences of several dimensionless kinematic and structural parameters on aerodynamic periodicity are investigated. The results show that the aerodynamic periodicity of plunging flexible airfoil qualitatively resembles that of rigid airfoil as the mechanisms contributing to aerodynamic periodicity are kept for airfoil with various flexibilities. However, aerodynamic periodicity at small plunging amplitude and high Reynolds number can be improved as airfoil becomes medium flexible but worsened as airfoil is very flexible. The reason is that the deformation of the airfoil changes the strength and structure of the nearby vortices, thereby leading to weak vortex–vortex and vortex–airfoil interactions. The extent of improvement in aerodynamic periodicity is also found significantly influenced by incoming velocity.

The Flapping Rotary Wing (FRW) is a micro air vehicle wing layout coupling flapping, pitching, and rotating motions. It can gain benefits in high lift from a fast passive rotating motion, which is tightly related to the passive pitching motion directly caused by wing flexible deformation. Therefore, flexible deformation is crucial for the wing kinematics and aerodynamic performance of an FRW. In this paper, we explored the effect of flexibility on wing kinematics and aerodynamics on the basis of a mechanical FRW model. A photogrammetric method was adopted to capture motion images according to which wing orientations and deformations were reconstructed. Corresponding aerodynamic force was computed using computational fluid dynamic method, and wing kinematics and deformations were used as simulation inputs. The experimental measurements presented the real orientation and deformation pattern of a real FRW. The wing passive deformation of a high-intensity FRW was found to be mainly caused by inertial force, and a linear positive spanwise twist was observed in the FRW. The effects of wing deformation on aerodynamic force production and the underlying mechanism were addressed. Results showed that lift augment, rotating moment enhancement, and power efficiency improvement can be achieved when a wing becomes flexible. Wing spanwise twist mainly accounts for these changes in aerodynamics, and increment in spanwise twist could further contributes to aerodynamic improvement.

In order to effectively improve vehicle riding comfort, handling stability, and realize vibration energy recovery, a new kind of electromagnetic linear hybrid active suspension (EMLHAS) integrated with linear motor and solenoid valve shock absorber is put forward. Firstly, for the analysis of the suspension performance, a quarter dynamic model of EMLHAS is established. At the same time, the mathematical models of a linear motor, including the active state and energy-regenerative state, are found. The correctness of mathematical models for the linear motor in the active and energy-regenerative states is verified by means of characteristic tests. Moreover, the velocity characteristic tests of solenoid valve shock absorber are carried out to determine its mathematical polynomial model in the semiactive state. Then, a new kind of multimode endocrine composite skyhook-groundhook control strategy is proposed. The suspension motion is divided into four modes according to the driving conditions of the vehicle. An endocrine control with long feedback and short feedback is combined with the skyhook-groundhook control. The control laws of the skyhook-groundhook controller and endocrine controller are, respectively, designed. Finally, the simulation analysis of suspension dynamic performance and energy-regenerative characteristic is done. The results show the control effect of endocrine composite skyhook-groundhook control is better than that of skyhook-groundhook control, which improves vehicle riding comfort and handling stability. Moreover, part of vibration energy is recovered.

The mechanisms of leading-edge vortex (LEV) formation and its stable attachment to revolving wings depend highly on Reynolds number ( $\textit {Re}$ ). In this study, using numerical methods, we examined the $\textit {Re}$ dependence of LEV formation dynamics and stability on revolving wings with $\textit {Re}$ ranging from 10 to 5000. Our results show that the duration of the LEV formation period and its steady-state intensity both reduce significantly as $\textit {Re}$ decreases from 1000 to 10. Moreover, the primary mechanisms contributing to LEV stability can vary at different $\textit {Re}$ levels. At $\textit {Re} , the LEV stability is mainly driven by viscous diffusion. At $200 , the LEV is maintained by two distinct vortex-tilting-based mechanisms, i.e. the planetary vorticity tilting and the radial–tangential vorticity balance. At $\textit {Re}>1000$ , the radial–tangential vorticity balance becomes the primary contributor to LEV stability, in addition to secondary contributions from tip-ward vorticity convection, vortex compression and planetary vorticity tilting. It is further shown that the regions of tip-ward vorticity convection and tip-ward pressure gradient almost overlap at high $\textit {Re}$ . In addition, the contribution of planetary vorticity tilting in LEV stability is $\textit {Re}$ -independent. This work provides novel insights into the various mechanisms, in particular those of vortex tilting, in driving the LEV formation and stability on low- $\textit {Re}$ revolving wings.

At low Reynolds numbers, revolving wings become less efficient in generating lift for hovering flight due to the increasing adverse viscous effects. Flying insects use reciprocating revolving wings...

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.

Recently, a novel concept of flapping Micro-Air-Vehicles (FMAVs) with four wings has been proposed, which potentially utilizes the clap-and-fling effect for lift enhancement and agile maneuvers through an adjustment of wing kinematics. However, the application of the clap-and-fling effect in the four-winged FMAVs is underexplored and the dynamic stability is still unclear. In this paper, aerodynamics and flight dynamic stability of the four-winged FMAVs are studied experimentally and numerically. Results show that the clap-and-fling effect is observed when the flapping frequency is above 18 Hz. Due to the clap-and-fling effect, the lift generation and aerodynamic efficiency are both improved, which is mainly attributed to the fling phase. Further studies show that the clap-and-fling effect becomes weaker as the wing root spacing increases and is almost absent at a wing root spacing of 1.73 chord length. In addition, a wing with an aspect ratio of 3 can increase both lift generation and efficiency due to the clap-and-fling effect. Finally, according to the dynamic stability analysis of the four-winged FMAV, the divergence speed of the lateral oscillation mode is about 4 times faster than that of the longitudinal oscillation mode. Our results can provide guidance on the design and control of four-winged FMAVs.

Reducing weight and increasing lift have been an important goal of using flapping wing micro air vehicles (FWMAVs). However, FWMAVs with mechanisms to limit the angle of attack (α) artificially by active force cannot meet specific requirements. This study applies a bioinspired model that passively imitates insects’ pitching wings to resolve this problem. In this bionic passive pitching model, the wing root is equivalent to a torsional spring.αobtained by solving the coupled dynamic equation is similar to that of insects and exhibits a unique characteristic with two oscillated peaks during the middle of the upstroke/downstroke under the interaction of aerodynamic, torsional, and inertial moments. Excess rigidity or flexibility deteriorates the aerodynamic force and efficiency of the passive pitching wing. With appropriate torsional stiffness, passive pitching can maintain a high efficiency while enhancing the average lift by 10% than active pitching. This observation corresponds to a clear enhancement in instantaneous force and a more concentrated leading edge vortex. This phenomenon can be attributed to a vorticity moment whose component in the lift direction grows at a rapid speed. A novel bionic control strategy of this model is also proposed. Similar to the rest angle in insects, the rest angle of the model is adjusted to generate a yaw moment around the wing root without losing lift, which can assist to change the attitude and trajectory of a FWMAV during flight. These findings may guide us to deal with various conditions and requirements of FWMAV designs and applications.

Flapping rotary wing is a novel aerodynamic configuration proposed in recent years for micro air vehicles. To understand the aerodynamic characteristics of this wing layout, a computational fluid d...

The micro Flapping Rotary Wing (FRW) concept inspired by insects was proposed recently. Its aerodynamic performance is highly related to wing pitching and rotational motions. Therefore, the effect of wing pitching kinematics and rotational speed on unsteady aerodynamic forces and power consumption of a FRW in hovering flight is further studied in this paper using computational fluid dynamics method. Considering a fixed pitching amplitude (i.e., 80°), the vertical force of FRW increases with the downstroke angle of attack and is enhanced by high wing rotational speed. However, a high downstroke angle of attack is not beneficial for acquiring high rotational speed, in which peak vertical force at balance status (i.e., average rotational moment equals zero.) is only acquired at a comparatively small negative downstroke angle of attack. The releasing constraint of pitching amplitude, high rotational speed and enhanced balanced vertical force can be acquired by selecting small pitching amplitude despite high power consumption. To confirm which wing layout is more power efficient for a certain vertical force requirement, the power consumed by FRW is compared with the Rotary Wing (RW) and the Flapping Wing (FW) while considering two angle of attack strategies without the Reynolds number (Re) constraint. FRW and RW are the most power efficient layouts when the target vertical force is produced at an angle of attack that corresponds to the maximum vertical force coefficient and power efficiency, respectively. However, RW is the most power efficient layout overall despite its insufficient vertical force production capability under a certain Re.

Lightweight design is key to high efficiency and long durability of micro air vehicle (MAV), while it will inevitably reduce the stiffness of the structures and affect the motion of the mechanism. In this study, an elastodynamic model for flapping-wing MAV (FMAV) is established to unveil the effect of elastic deformation of transmission mechanism on the flapping motion. Based on kineto-elastostatic analysis, an elastodynamic model of the transmission mechanism is built, which reveals that the inertial force of the transmission mechanism for typical FMAV is much smaller than the force transmitted. Thus, the inertial force can be ignored, and analytical formula between the deformation of transmission mechanism and the flapping angle is derived. Finite element method (FEM) simulations are conducted to validate the analytical formula, and the results show that the flapping angle obtained from the analytical formula matches well with FEM simulations. The proposed elastodynamic model and analytical formula will provide theoretical guidance for designing and optimizing FMAV with desired transmission mechanism and flapping motion.

Passive wing pitching is a hypothesis in insect flight, and it is used widely by most flapping-wing micro air vehicles (FWMAVs). This study analyzes the flight control of hovering model fruit fly and FWMAV with passive pitching wings. The longitudinal and lateral control derivatives are obtained by numerical simulation of the fluid dynamic equations coupled with the torsional spring passive pitching system. In contrast to active pitching wings, some of the control derivatives are remarkably changed by passive pitching wings, such asZΦ(vertical force produced by unit stroke amplitude),Zf(vertical force produced by unit flapping frequency), andMψ0(pitching moment produced by unit rest angle). For example, increasing flapping frequency does not lead to an evident increase in lift and may even have a reverse effect. Therefore, the flight control of FWMAV with passive pitching wings should be treated with caution. For wings pitching passively with a torsional spring at the root, the differential change of the angle of attack in the downstroke and upstroke (αdand αu) could be achieved by modulation of the rest angle alone; however, the equal change in αdand αumay require an otherwise manipulation of the elastic coefficient. Results in this study provide guidelines for the design of FWMAVs in evaluating the effects of different control inputs correctly and formulating a cost-effective control scheme.

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.

A novel design of a micro air vehicle with flapping rotary wings was recently proposed. In this paper, the investigation is focused on aerodynamic enhancement of a bore-hole and an elastic cover added onto an intact flapping rotary wing. The aerodynamic force and the pitching motion of the perforated wing are both acquired in experiments. In comparison with an intact wing, a typical perforated wing shows a significant decrement in negative lift and thus a higher mean lift. As a supporting process, the computational fluid dynamics method is then employed to analyze the flow around the wing and the hole, and thereby make clear the underlying physical mechanism. It is found the hole opens due to the cover deflection in a passive manner and produces a secondary starting vortex on the wing lower surface of the cover during upstrokes. Together with the tip vortex around the lateral edges of the cover, the resulting vortex significantly reduces the magnitude of the negative lift, and thus explains the mean-lift enhancement in a flapping cycle. Additionally, the mean-lift enhancement correlates with the geometric parameters of the hole. An increment up to 40% in maximum mean lift is identified for a perforated wing in comparison with an intact wing. These results indicate that a bore-hole design could be a promising approach to enhance the aerodynamic lift of a flapping rotary wing.

Leading-edge vortex (LEV) is a hallmark of insect flight that forms and remains stably attached on high angle-of-attack (AoA), low aspect ratio (AR) wings undergoing revolving or flapping motion. Despite the efforts on explaining the stability of LEV when it reaches steady state in revolving wings, its formation process remains largely underexplored. Here, we investigate the LEV formation on a revolving wing (AoA = 45°, AR = 4 and Re = 1500), starting with a constant acceleration in the first chord (c) length of travel and then rotating at a constant velocity. The ‘Shake-the-box’ (STB) Lagrangian particle tracking velocimetry (PTV) system together with a volumetric patching process were performed to reconstruct the entire time-resolved flow field. Results show that LEV reaches steady state after approximately 4c of travel, within which its formation can be separated into three stages. In the first stage, a conical LEV structure begins to form with a tangential downstream convection of (negative) radial shear vorticity. In the second stage, the radial vorticity within the LEV is further convected downwards by the developed downwash, which limits its growth, whereas vorticity stretching increases the LEV strength. In the third stage, vorticity tilting and spanwise convection reduce the LEV strength at its rear end next to the trailing edge and, therefore, preventing it from growing. Our results suggest that insect wings with AR ~ 4, Re ~ 103 and flapping amplitude between 2c and 4c may barely or even not reach the steady state of LEV, indicating an indispensable role of transient LEV dynamics in understanding insect flight.

In conventional Micro-Air-Vehicle design inspired by insects, the periodical motion of flapping airfoil usually leads to generation of a periodical aerodynamic force. However, recent studies indicate that time courses of aerodynamic force and flow structure of a flapping airfoil may be non-periodical even though the airfoil undergoes a periodical motion. In this paper, a computational fluid dynamics analysis is employed to investigate the effects of some dimensionless variables, such as Reynolds number, plunging amplitude, advance ratio, and angle of attack, on the periodicity of the flow around a flapping airfoil. The governing equations in an inertial frame of reference are solved to obtain unsteady flow structure and aerodynamic behaviors of the airfoil. It is found in the results that the periodicity of the flow and aerodynamics is greatly dependent on Reynolds number and plunging amplitude. Under given conditions, the product of these two variables may be utilized as a criterion parameter to judge whether the time course of the flow is periodical or not. In addition, a new mechanism that accounts for the non-periodical flow is revealed to explain the flow of airfoil with pre-stall angle of attack.

Both the transient formation and the stable attachment of leading-edge vortex (LEV) contribute to the high lift generation of an insect wing when it revolves at high angles of attack. In this study, we examined the LEV formation and the transient lift generation on a revolving wing with Reynolds number at 1500 and aspect ratio at 3, using combined computational and experimental methods. The wing started from stationary with a constant angular acceleration within a prescribed chord length of travel at its radius of gyration (i.e. λ a ), ranging from 0.25 to 2, and then revolved at a constant velocity. Our results showed that the rate of LEV development saturated when λ a 1 , resulting in a minimum chord length of travel of 2.5 to arrive at a steady LEV. This minimum travel distance agreed well with the prediction based on the vortex formation criterion proposed in other vortex generators. On the other hand, the instantaneous lift generation was strongly dependent on the instantaneous wing velocity and acceleration and therefore exhibited no saturation as λ a decreases, which is seen in the LEV formation. The lift generation was attributed to the evolution of tangential vorticity according to the vortex impulse theory. Finally, the instantaneous volume-averaged LEV circulation at different angles of attack scaled well with the instantaneous velocity normal to the leading edge.

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.

Due to adverse viscous effects, revolving wings suffer universally from low efficiency at low Reynolds number (Re). By reciprocating wing revolving motion, natural flyers flying at low Re successfully exploit unsteady effects to augment force production and efficiency. Here we investigate the aerodynamics of an alternative, i.e., a revolving wing with concomitant unsteady pitching and vertical flapping perturbations (a pitching-flapping-perturbed revolving wing). The current work builds upon a previous study on flapping-perturbed revolving wings (FP-RWs) and focuses on combined effects of pitching-flapping perturbation on force generation and vortex behaviors. The results show that, compared with a FR-RW, pitching motion further (1) reduces the external driving torque for rotating at 0° angle of attack (α0) and (2) enhances lift and leads to a self-rotating equilibrium at α0 = 20°. The power loading of a revolving wing at α0 = 20° can be improved using pitching-flapping perturbations with large pitching amplitude but small Strouhal number. Additionally, an advanced pitching improves the reduction of external driving torque, whereas a delayed pitching weakens both the lift enhancement and the reduction of external driving torque. Further analysis shows that pitching effects can be mainly decomposed into the Leading-Edge-Vortex (LEV)-mediated pressure component and geometric projection component, together they determine the force performance. LEV circulation is found to be determined by the instantaneous effective angle of attack but could be affected asymmetrically between upstroke and downstroke depending on the nominal angle of attack. Pitching-flapping perturbation thus can potentially inspire novel mechanisms to improve the aerodynamic performance of rotary wing micro air vehicles.

The longitudinal steady-state control for going from hovering to small speed flight of a model insect is studied, using the method of computational fluid dynamics to compute the aerodynamic derivatives and the techniques based on the linear theories of stability and control for determining the non-zero equilibrium points. Morphological and certain kinematical data of droneflies are used for the model insect. A change in the mean stroke angle \({(\delta \bar {\phi})}\) results in a horizontal forward or backward flight; a change in the stroke amplitude (δΦ) or a equal change in the down- and upstroke angles of attack (δα1) results in a vertical climb or decent; a proper combination of \({\delta \bar {\phi}}\) and δΦ controls (or \({\delta \bar {\phi}}\) and δα1 controls) can give a flight of any (small) speed in any desired direction.

The effect of the wake of previous strokes on the aerodynamic forces of a flapping model insect wing is studied using the method of computational fluid dynamics. The wake effect is isolated by comparing the forces and flows of the starting stroke (when the wake has not developed) with those of a later stroke (when the wake has developed). The following has been shown. (1) The wake effect may increase or decrease the lift and drag at the beginning of a half-stroke (downstroke or upstroke), depending on the wing kinematics at stroke reversal. The reason for this is that at the beginning of the half-stroke, the wing ``impinges'' on the spanwise vorticity generated by the wing during stroke reversal and the distribution of the vorticity is sensitive to the wing kinematics at stroke reversal. (2) The wake effect decreases the lift and increases the drag in the rest part of the half-stroke. This is because the wing moves in a downwash field induced by previous half-stroke's starting vortex, tip vortices and attached leading edge vortex (these vortices form a downwash producing vortex ring). (3) The wake effect decreases the mean lift by 6%–18% (depending on wing kinematics at stroke reversal) and slightly increases the mean drag. Therefore, it is detrimental to the aerodynamic performance of the flapping wing.

Aerodynamic forces and power requirements in forward flight in a bumblebee (Bombus terrestris) were studied using the method of computational fluid dynamics. Actual wing kinematic data of free flight were used in the study (the speed ranges from 0 m/s to 4.5 m/s; advance ratio ranges from 0–0.66). The bumblebee employs the delayed stall mechanism and the fast pitching-up rotation mechanism to produce vertical force and thrust. The leading-edge vortex does not shed in the translatory phase of the half-strokes and is much more concentrated than that of the fruit fly in a previous study. At hovering and low-speed flight, the vertical force is produced by both the half-strokes and is contributed by wing lift; at medium and high speeds, the vertical force is mainly produced during the downstroke and is contributed by both wing lift and wing drag. At all speeds the thrust is mainly produced in the upstroke and is contributed by wing drag. The power requirement at low to medium speeds is not very different from that of hovering and is relatively large at the highest speed (advance ratio 0.66), i.e. the power curve is J-shaped. Except at the highest flight speed, storing energy elastically can save power up to 20%–30%. At the highest speed, because of the large increase of aerodynamic torque and the slight decrease of inertial torque (due to the smaller stroke amplitude and stroke frequency used), the power requirement is dominated by aerodynamic power and the effect of elastic storage of energy on power requirement is limited.