Computational aerodynamics of low Reynolds number plunging,pitching and flexible wings for MAV applications

Micro air vehicles （MAV＇s） have the potential to revolutionize our sensing and information gathering capabilities in environmental monitoring and homeland security areas. Due to the MAV＇s＇ small size, flight regime, and modes of operation, significant scientific advancement will be needed to create this revolutionary capability. Aerodynamics, structural dynamics, and flight dynamics of natural flyers intersects with some of the richest problems in MAV＇s, inclu- ding massively unsteady three-dimensional separation, transition in boundary layers and shear layers, vortical flows and bluff body flows, unsteady flight environment, aeroelasticity, and nonlinear and adaptive control are just a few examples. A challenge is that the scaling of both fluid dynamics and structural dynamics between smaller natural flyer and practical flying hardware/lab experiment （larger dimension） is fundamentally difficult. In this paper, we offer an overview of the challenges and issues, along with sample results illustrating some of the efforts made from a computational modeling angle.

Propulsion Performance of Spanwise Flexible Wing Using Unsteady Panel Method

In this paper, the propulsion performance of a spanwise flexible oscillating wing, which is broadly similar to the undulation of a fin fluke, is investigated. The geometry of the fluke underwent three prescribed harmonic oscillating motions simultaneously while surging with constant velocity. The effect of deflection phase angle, flexibility parameter, and wing tip deflection amplitude on thrust coefficient and swimming efficiency was studied. A low-order unsteady panel method coupled with a time stepping algorithm for free wake alignment is implemented in a computer program to estimate the propulsion efficiency of lifting bodies. A novel approach is introduced to evaluate the singular integrals of line vortices by using an adaptive mollifier function. This method is an efficient way to accelerate computational speed by reducing the order of problem from R^3 to body boundaries. Results present the significant effect of phase angle on the propulsion characteristics of oscillating fluke.

Gust response of an elasto-flexible morphing wing using fluid–structure interaction simulations

Small and micro unmanned aircraft are the focus of scientific interest due to their wide range of applications.They often operate in a highly unstable flight environment where the application of new morphing wing technologies offers the opportunity to improve flight characteristics.The investigated concept comprises port and starboard adjustable wings,and an adaptive elastoflexible membrane serves as the lifting surface.The focus is on the benefits of the deforming membrane during the impact of a one-minus-cosine type gust.At a low Reynolds number of Re=264000,the morphing wing model is investigated numerically by unsteady fluid-structure interaction simulations.First,the numerical results are validated by experimental data from force and moment,flow field,and deformation measurements.Second,with the rigid wing as the baseline,the flexible case is investigated,focusing on the advantages of the elastic membrane.For all configurations studied,the maximum amplitude of the lift coefficient under gust load shows good agreement between the experimental and numerical results.During the decay of the gust,they differ more the higher the aspect ratio of the wing.When considering the flow field,the main differences are due to the separation behavior on the upper side of the wing.The flow reattaches earlier in the experiments than in the simulations,which explains the higher lift values observed in the former.Only at one intermediate configuration does the lift amplitude of the rigid configuration exceeds that of the flexible by about 12%,with the elastic membrane resulting in a smaller and more uniform peak load,which is also evident in the wing loading and hence in the root bending moment.

Effects of wing deformation on aerodynamic performance of a revolving insect wing

Flexible wings of insects and bio-inspired micro air vehicles generally deform remarkably during flapping flight owing to aerodynamic and inertial forces,which is of highly nonlinear fluid-structure interaction（FSI）problems.To elucidate the novel mechanisms associated with flexible wing aerodynamics in the low Reynolds number regime,we have built up a FSI model of a hawkmoth wing undergoing revolving and made an investigation on the effects of flexible wing deformation on aerodynamic performance of the revolving wing model.To take into account the characteristics of flapping wing kinematics we designed a kinematic model for the revolving wing in two-fold：acceleration and steady rotation,which are based on hovering wing kinematics of hawkmoth,Manduca sexta.Our results show that both aerodynamic and inertial forces demonstrate a pronounced increase during acceleration phase,which results in a significant wing deformation.While the aerodynamic force turns to reduce after the wing acceleration terminates due to the burst and detachment of leading-edge vortices（LEVs）,the dynamic wing deformation seem to delay the burst of LEVs and hence to augment the aerodynamic force during and even after the acceleration.During the phase of steady rotation,the flexible wing model generates more ver-tical force at higher angles of attack（40°–60°）but less horizontal force than those of a rigid wing model.This is because the wing twist in spanwise owing to aerodynamic forces results in a reduction in the effective angle of attack at wing tip,which leads to enhancing the aerodynamics performance by increasing the vertical force while reducing the horizontal force.Moreover,our results point out the importance of the fluid-structure interaction in evaluating flexible wing aerodynamics：the wing deformation does play a significant role in enhancing the aerodynamic performances but works differently during acceleration and steady rotation,which is mainly induced by inertial force in acceleration but by aerodynamic forces in steady rotation.

Aerodynamic Analysis and Simulation of Flapping Wing Aerial Vehicles on Hovering

In order to design and verify control algorithms for flapping wing aerial vehicles(FWAVs),calculation models of the translational force,rotational force and virtual mass force were established with the basis on the modified quasi-steady aerodynamic theory and high lift mechanisms of insect flight.The simulation results show that the rotational force and virtual mass force can be ignored in the hovering FWAVs with simple harmonic motions in a cycle.The effects of the wing deformation on aerodynamic forces were investigated by regarding the maximum rotational angle of wingtip as a reference variable.The simulation results also show that the average lift coefficient increases and drag coefficient decreases with the increase of the maximum rotational angle of wingtip in the range of 0-90°.

Resonance mechanism of flapping wing based on fluid structure interaction simulation

Certain insect species have been observed to exploit the resonance mechanism of their wings.In order to achieve resonance and optimize aerodynamic performance,the conventional approach is to set the flapping frequency of flexible wings based on the Traditional Structural Modal(TSM)analysis.However,there exists controversy among researchers regarding the relationship between frequency and aerodynamic performance.Recognizing that the structural response of wings can be influenced by the surrounding air vibrations,an analysis known as Acoustic Structure Interaction Modal(ASIM)is introduced to calculate the resonant frequency.In this study,Fluid Structure Interaction(FSI)simulations are employed to investigate the aerodynamic performance of flapping wings at modal frequencies derived from both TSM and ASIM analyses.The performance is evaluated for various mass ratios and frequency ratios,and the findings indicate that the deformation and changes in vortex structure exhibit similarities at mass ratios that yield the highest aerodynamic performance.Notably,the flapping frequency associated with the maximum time-averaged vertical force coefficient at each mass ratio closely aligns with the ASIM frequency,as does the frequency corresponding to maximum efficiency.Thus,the ASIM analysis can provide an effective means for predicting the optimal flapping frequency for flexible wings.Furthermore,it enables the prediction that flexible wings with varying mass ratios will exhibit similar deformation and vortex structure changes.This paper offers a fresh perspective on the ongoing debate concerning the resonance mechanism of Flexible Flapping Wings(FFWs)and proposes an effective methodology for predicting their aerodynamic performance.

Flexible Wing Kinematics of a Free-Flying Beetle （Rhinoceros Beetle Trypoxylus Dichotomus）

Detailed 3-Dimensional （3D） wing kinematics was experimentally presented in free flight of a beetle, Trypoxylus dichotomus, which has a pair of elytra （forewings） and flexible hind wings. The kinematic parameters such as the wing tip trajectory, angle of attack and camber deformation were obtained from a 3D reconstruction technique that involves the use of two synchronized high-speed cameras to digitize various points marked on the wings. Our data showed outstanding characteristics of deformation and flexibility of the beetle＇s hind wing compared with other measured insects, especially in the chordwise and spanwise directions during flapping motion. The hind wing produced 16% maximum positive camber deformation during the downstroke. It also experienced twisted shape showing large variation of the angle of attack from the root to the tip during the upstroke.

Experimental investigations of a full model with adaptive elasto-flexible membrane wings

The morphing wing concept aims to constantly adapt the aerodynamics to different flight stages.The wing is able to adapt to different flight conditions by an adjustable Aspect Ratio(AR)and sweep.A high AR configuration provides high aerodynamic efficiency,while a low AR configuration,with highly swept wings offers a good maneuverability.Additionally,the flexible membrane allows the wing surface to stretch and contract in-plane as well as the airfoil to adapt to different aerodynamic loads.In the context of this work,the aerodynamic characteristics of a full model with form-adaptive elasto-flexible membrane wings are investigated experimentally.The focus is on the high-lift regime and on the analysis of the aerodynamic coefficients as well as their sensitivities.Especially,the lateral aerodynamic derivatives at asymmetric wing positions are of interest.

Time-domain nonlinear aeroelastic analysis and wind tunnel test of a flexible wing using strain-based beam formulation

A theoretical formulation for time-domain nonlinear aeroelastic analysis of a flexible wing model is presented and validated by wind tunnel tests. A strain-based beam model for nonlinear structural analysis is combined with the Unsteady Vortex Lattice Method(UVLM) to form the complete framework for aeroelastic analysis. The nonlinear second-order differential equations are solved by an implicit time integration scheme that incorporates a Newton-Raphson sub-iteration technique. An advanced fiber optic sensing technique is firstly used in a wind tunnel for measuring large structural deformations. In the theoretical study, the nonlinear flutter boundary is determined by analyzing the transient response about the nonlinear static equilibrium with a series of flow velocities. The gust responses of the wing model at various gust frequencies are also studied. Comparisons of the theoretical and experimental results show that the proposed method is suitable for determining the nonlinear flutter boundary and simulating the gust response of flexible wings in the time domain.

Regularities between kinematic and aerodynamic characteristics of flexible membrane wing

The kinematic characteristics of flexible membrane wing have vital influences on its aerodynamic characteristics. To deeply explore the regularities between them, time-resolved aerodynamic forces and deformations at different aeroelastic parameters and angles of attack(α) were measured synchronously by wind tunnel experiments. The membrane motion can be mainly divided into two states at α > 0° with various lift-enhancement regularities: Deformed-Steady State(DSS)at pre-stall, and Dynamic Balance State(DBS) at around stall and post-stall. Besides, the mean camber, maximum vibration amplitude, and lift coefficient almost reach their maxima simultaneously within the DBS region. By introducing momentum coefficient Cμ of membrane vibration, positive correlation among amplitude, momentum and lift is successfully established, and the liftenhancement mechanism of membrane vibration is revealed. Moreover, it is newly and surprisingly found that at different vibration modes, the maximum vibration amplitude and root mean square of vibration velocity present positive and linear correlation with different slopes, and their chordwise locations are basically consistent. Therefore, novel ideas for active control of flexible wing are proposed: by controlling the vibration amplitude, frequency, and mode, while selecting the specific chordwise locations for intensive excitation, Cμ can be efficiently increased. Ultimately, the aerodynamic performance will be improved.

Experimental Investigation of Flexible Hawkmoth-like Wings on the Wing-wake Interaction in Hovering Flight

To study wing-wake interaction for various wing flexibilities, force measurements and digital particle image velocimetry were carried out on flapping hawkmoth-like wings in a water tank. Wing thickness was employed as a design variable for the wing flexi- bility distributions. Abrupt flap-down and phase delay in flexible wings influenced the behaviors of the Leading-Edge Vortex （LEV） and Trailing-Edge Vortex （TEV）, generated by the previous stroke. While the rigid wing exhibited a detached LEV at the end of the stroke, wing with specific flexibilities obtained attached LEVs. The attached LEVs induced a relatively rapid flow toward the wing surface as a result of encountering the TEV, and the flow caused a higher lift peak. On the other hand, the wings with larger wing deformations generated distinctive changes in LEV and TEV behaviors. The flap-down helped the TEV form closer to the wing surface, and it thus caused a downwash rather than wing-wake interaction. Furthermore, the most flexible wing had a newly-formed pair of LEVs above the wing during the wing reversal, thereby being not able to generate the wing-wake interaction. These results help to understand the different vortex structures generated by flexible wings during the wing reversal and the corresponding effects of wing-wake interaction.

THE FLEXIBLE HYDROFOIL WING FLOAT

The Flexible Hydrofoil Wing Float(Fhwf)is a new device for lifting the headline of a trawl.It is made from Superior Grade canvas.Part of the structure is cut away at the leading edge to form a water intake.The flow of seawater inflates the canvas into a shape similar to that of an aircraft wing,thus generating lift.Sea trials have been conducted on practical wing floats suitable for full scale fishing gear.Model tests have been conducted in a wind tunnel.At low attack angles,the lift coefficient(C_L)is 0.32,the lift to drag ratio(G_L/C_d)is 5 and the mo- ment ccefficient(C(?))is positive Better results are obtained when netting is placed below the model float,compared with the float in isolation.The wing float has many advantages compared with conventional lifting devices.It may be used at any depth.Large net mouth openings may be achieved at high speeds.It is cheap,simple to install and to handle.Spare wing floats may be folded for storage and do not require much space.

Control-oriented modeling of a high-aspect-ratio flying wing with coupled flight dynamics

The flight-structural dynamics of a high-aspect-ratio wing challenge the flight control design.This paper develops a reduced model of coupled dynamics with stability consideration.The structural dynamics are formulated with dihedrals,and the central loads drive the deformation.The control-oriented model with essential coupled dynamics is formulated.Modal sensitivity anal-ysis and input–output pairing are performed to identify the control structure.Besides,an example of flight control design is provided to discuss the necessity of considering structural dynamics in controller design.Analytical coupled flight dynamics provide a system-theoretic approach for sta-bility and facilitate model-based control techniques.Simulation results reveal the characteristics of flight-structural coupled dynamics and demonstrate that the influence of flexible modes should be considered in control design,especially in lateral dynamics.

Effects of wing flexibility on aerodynamic performance of an aircraft model

The low-speed wind tunnel experiment is carried out on a simplified aircraft model to explore the influence of wing flexibility on the aircraft aerodynamic performance.The investigation involves the measurements of force,membrane deformation and velocity field at Reynolds number of 5.4×10^(4)-1.1×10^(5).In the lift curves,two peaks are observed.The first peak,corresponding to the stall,is sensitive to the wing flexibility much more than the second peak,which nearly keeps constant.For the optimal case,in comparison with the rigid wing model,the delayed stall of nearly5°is achieved,and the relative lift increment is about 90%.It is revealed that the lift enhanced region corresponds to the larger deformation and stronger vibration,which leads to stronger flow mixing near the flexible wing surface.Thereby,the leading-edge separation is suppressed,and the aerodynamic performance is improved significantly.Furthermore,the effects of sweep angle and Reynolds number on the aerodynamic characteristics of flexible wing are also presented.

In-plane corrugated cosine honeycomb for 1D morphing skin and its application on variable camber wing

A novel 0-Poisson＇s ratio cosine honeycomb support structure of flexible skin is proposed. Mechanical model of the structure is analyzed with the energy method, finite element method （FEM） and experiments have been performed to validate the theoretical model. The in-plane characteristics of the cosine honeycomb are compared with accordion honeycomb through analytical models and experiments. Finally, the application of the cosine honeycomb on a variable camber wing is studied. Studies show that mechanical model agrees well with results of FEM and experiments. The transverse non-dimensional elastic modulus of the cosine honeycomb increases （decreases） when the wavelength or the wall width increases （decreases）, or when the amplitude decreases （increases）. Compared with accordion honeycomb, the transverse non-dimensional elastic modulus of the cosine honeycomb is smaller, which means the driving force is smaller and the power consumption is less during deformation. In addition, the cosine honeycomb can satisfy the deform- ing requirements of the variable camber wing.

Influence of membrane wing active deformation on the aerodynamic performance of an aircraft model

The aerodynamic performance of a simplified aircraft model with a pair of actively deformed membrane wings is investigated experimentally in this work. The active deformation is achieved with Macro fiber composite(MFC) actuators, which are attached to the upper surface of the wings and occupied 13.7% of the wing surface area. Wind tunnel experiments are conducted to evaluate the influence of membrane active deformation on the aerodynamic performance of the aircraft. The results show that the membrane deforms and vibrates under the actuation which can effectively suppress the leading-edge separation and facilitate the reattachment. Therefore, compared with the rigid wing model, the lift coefficient of the actively deformed membrane wing model is enhanced remarkably from the angle of attack of 7° to 22°. The stall angle is delayed by 2°, and a maximum lift coefficient enhancement of 32.5% is reached, which shows a wide potential application in improving the aerodynamic performance of modern aircraft.

Aerodynamic performance of the flexibility of corrugated dragonfly wings in flapping flight

At low Reynolds numbers,the variable flexibility of flapping insect wings is considered essential in improving the favorable aerodynamic forces.To further explore whether significant aerodynamic coupling exists between the microstructure and passive flexible deformation,this paper proposes three technical comparison airfoils:a corrugated wing with deformation,a symmetric flat plate wing with deformation,and a corrugated wing without deformation.Based on STAR-CCM+software,this paper numerically solves the Navier-Stokes equations using the fluid-structure interaction method.The results show that the aerodynamic performance of the flexible corrugated wing is better than that of the rigid corrugated wing,and its lift and thrust are both improved to a certain extent,and the thrust efficiency of the flexible corrugated wing is significantly higher than that of the flexible flat plate.Although the thrust is improved,a part of the lift is lost,and as the flapping amplitude increases past 35°,the disparity gradually increases.A comparison of the flexible technical airfoils shows that the corrugated structure promotes thrust and retards lift,which is closely related to the formation and dissipation of strong vortex rings during the downstroke phase.On the premise of maintaining typical flapping without falling,dragonflies can fly with skillful efficiency by adjusting the way they flap their wings.The results of this work provide new insight into the formation and role of thrust in flapping maneuvering flight and provide a specific reference for developing new bionic flapping-wing aircraft.

Stream Surface Theory of Bird-like Flapping Flight

Through analyzing the motion characteristics of bird-like flapping flight, it is considered that the wing angular acceleration is equal to zero at the point of maximum angular speed. Thus, the flapping flight is equivalent to a uniform rotating motion which can be analyzed by using the stream surface theory of turbomachinery during a micro period of time. In this article, the N-S equations of the motion are expanded in a non-orthogonal curvilinear coordinate system, and simplified on stream surfaces of the flapping flight model. By using stream function me- thod, the three-dimensional unsteady flow equations are simplified as a two-order partial differential equation with variable coefficients eventually and the equation＇s iterative solving method on S1 and $2 stream surfaces of the flapping flight model is presented. Through expanding the relatively steady equations of flapping flight at an arbitrary time point of a stroke on meridional plane of the flapping flight model, it can use a relatively steady mo- tion to approximate the real flapping flight at that time point, and analyze the flow stability influenced by the wing＇s flexibility. It can be seen that the wing flexibility is related to the higher pressurization capacity and the flow stability, and the pressurization capacity of flexible wing is proportional to the angular speed, angular distor- tion rate and radius square.