Flexible Wing Research Articles

Spring and Power in Hovering Ornithopters

Ornithopters are bird‐like flapping‐wing robots. Only small ornithopters can hover, with long endurance at hummingbird size. Could larger ornithopters be improved further to hover longer? This paper reviews and examines the drive and power of hovering ornithopters, and elastic means of energy or thrust boosters. While the rotation of flexible wings enhance the thrust generation, two‐winged ornithopters did not scale up well because of higher disk loading. In comparison, the X‐winged or multiple‐V‐winged ornithopters enjoy a lower disk loading by beating multiple wings slower, at a smaller stroke angle or a longer span. Further, the clap‐and‐fling interaction of V and X‐wings boosts the thrust generation. Future works can explore the wing flexibility and morphology change to improve the hoverability and flight agility of ornithopters.

Three-Dimensional Flutter Numerical Simulation of Wings in Heavy Gas and Transonic Flutter Similarity Law Correction Method

Wind tunnel testing is a crucial method for studying aircraft flutter. Using heavy gas as the wind tunnel medium can mitigate the escalating issue of test models being overweight as advanced aircraft develop. This paper employs an analytical method for numerical calculations of three-dimensional (3D) wing flutter based on fluid–structure interaction (FSI). Flutter calculations for the Goland wing are conducted, and the results in the air medium are consistent with the literature. In contrast, significant differences in flutter behavior are observed in the heavy gas R134a medium. Compared to air, when the model reaches a critical state in R134a, the incoming flow velocity is lower, the incoming flow density is approximately 3 to 5 times air, and the incoming flow dynamic pressure is about 1.1 to 1.2 times that of air. The correction of heavy gas flutter data is crucial for wind tunnel testing. This paper proposes a correction method based on the unsteady transonic flow similarity law proposed by Bendiksen under quasi-steady conditions. Attempts are made to revise relevant published wind tunnel tests and heavy gas flutter calculation results. The transonic flutter similarity law effectively explains the flutter similarity of rigid models in both heavy gas and air media. Still, it fails in cases with highly reduced frequencies and low mass ratios, such as those encountered with flexible wings.

Machine Learning‐Based Wind Classification by Wing Deformation in Biomimetic Flapping Robots: Biomimetic Flexible Structures Improve Wind Sensing

Flying animals such as insects and birds have strain receptors on their wings. The functions and information processing capabilities of these strain receptors, however, are largely unknown. Herein, the potential ability of wing strain sensors to detect wind direction in flapping flight is experimentally explored. Seven strain gauges are attached to the biomimetic wing shafts of flexible wings. The wings flap through an electric mechanism emulating hovering flight in a wind tunnel with gentle wind, and a convolutional neural network model for wind direction classification is developed. The results show that with only one strain gauge, accurate wind classification is achieved using segmented data of ≈1 flapping cycle. Even with segmented data of only 0.2 flapping cycles, wind classification can be achieved with all seven strain gauges. Moreover, the use of wing shafts improves the classification accuracy, especially with shorter segmented data. Additional flapping phase information does not substantially improve classification performance. These results suggest that hovering animals determine the wind direction via strain sensing, which is useful for flight control. The implementation of wing strain sensors in flapping‐wing aerial robots may improve flight control ability.

Experimental study on thermally induced vibration of flexible solar cell wing simulator

Abstract With the development of large spacecraft and satellite payloads, the power supply required is increasing, especially in space solar power stations, and the large flexible solar wing is an inevitable trend in the future. Due to their light weight and large area, flexible solar wings may face thermally induced vibration during orbit operation, which will lead to the degradation of spacecraft performance and even structural damage. In this paper, the test method of a flexible solar wing simulator is established, and the thermally induced vibration test of a flexible solar cell wing simulator is carried out. And vibration amplitude value is 25 and 9 microns with a frequency 0.56Hz.The characteristic of thermally induced vibration of flexible solar cell wing is given, which provides a basis for its thermally induced vibration suppression.

Hovering flapping wings with dynamic twist

The role of (active) dynamic wing twist on aerodynamic performance of three-dimensional hovering flapping flight is explored using numerical simulations. A variety of cases with different pitch angles and with (flexible wings) or without (rigid wings) dynamic twist are compared. The results show that changes in aerodynamic performance due to dynamic twist are comparable to those obtained without twist (rigid wing cases) by pitching the whole wing and that lift and lift-to-power ratio generally collapse onto a single curve when plotted as a function of the mid-stroke pitch angle at 2/3 wing radius. However, in some cases dynamic twist yields enhanced time-averaged efficiency. Using the force and power partitioning method, it is shown that this enhancement results from the absence of vortical structures near the wing root lower surface and to the presence of an extended leading edge vortex on the wing upper surface, when compared to the most efficient rigid wing case. These differences in flow topology lead to enhanced lift during the early phase of the strokes without changes in power consumption.

Iterative Learning Control for a Flexible Wing System Under Iteration-Varying Disturbances and References

Iterative Learning Control for a Flexible Wing System Under Iteration-Varying Disturbances and References

Analysis of the deformation of conical shells made by 4D Printing of composites

4D printing of composites (4DPC) is a technique that allows the manufacturing of composite structures to shape without the use of a complex-shaped mold. Instead, only a flat mold is utilized. This innovative technique has been employed to make composite leaf springs with performance comparable to metallic springs, omega stiffeners, and corrugated core for flexible wings. Recently, this technique was applied to fabricate composite conical shells. While experimental work has successfully demonstrated the transformation from flat to conical shape, the development of a numerical method to replicate this transformation is highly desirable. The availability of such method not only provides theoretical support for the experimental result, it also provides means to develop other shapes. The lay-up sequence for transforming flat to conical shapes involves curvilinear fibers. Most if not all finite elements currently available deal only with straight fibers (even though the boundaries of the element may be curved). The objective of this research is to examine the efficiency of the analysis for the deformation of composite from flat to curve made by 4DPC by special finite elements containing curved fibers. The developed finite elements were used to determine the shapes of conical shells made using multiple distinct lay-up sequences. The direction of bending in curvilinear fiber structures is significantly influenced by the orientation of the fibers. This highlights the critical role of fiber orientation and layer composition in achieving desired shapes in 4D printed composites.

Effect of wingtip-curve on aerodynamic performance in flapping flexible wings: rectangular versus hawkmoth-like

Effect of wingtip-curve on aerodynamic performance in flapping flexible wings: rectangular versus hawkmoth-like

Aerodynamics of a three-dimensionally deformed rigid wing

A flexible wing with a large aspect ratio emerges in many modern engineering applications (e.g. solar planes and super large wind turbine blades) and its interaction with incident flow differs markedly from conventional fluid–structure interactions (FSI), exhibiting frequently a large three-dimensional (3D) deformation. Yet, there is little information on how such deformation may change wing aerodynamics. This work investigates the aerodynamic performance of deformed and cantilever-supported NACA0012 rigid wings with an aspect ratio of 9, using ANSYS Fluent with the SST-κ-ω turbulence model at a chord-length-based Reynolds number Rec of 1.5 × 105. Numerical simulation is validated experimentally. The wing tip bending displacement is up to 4.14c, and the maximum twisted angle is up to 7°. The angle α of attack varies from 0° to 20° at mid span of the wing. It has been found that the torsional deformation can significantly advance the local flow separation, reattachment, bubble length, and transition from laminar to turbulence, resulting in a drop in the critical angle αcr of attack, at which the separation bubble size reaches the maximum. Accordingly, the lift and drag coefficients increase, as well as the bending and pitching-up moments, though the stall is advanced due to a change in local α. The tip vortex is also enhanced, inducing strong downwash postponing the separation bubble on the wing and resulting in redistributed force near the wing tip that increases markedly the local bending moment but decrease the local pitching-up moment. On the other hand, the bending deformation tends to produce an effect opposite to the torsion on the flow structure and causing little change in the lift coefficient, though reducing the induced drag and moments appreciably. With both deformations in place, the torsion overwhelms the bending in general in terms of its impact upon aerodynamics and flow structures, the latter acting to cancel at least partially the effect of the former.

Design and characterization of a wind-adaptable piezoelectric energy harvester utilizing a rigid-flexible compound blunt body

In response to the challenges posed by uncontrolled amplitude during galloping and narrow effective bandwidth during vortex-induced vibrations in current energy harvesters, a novel wind-adaptable piezoelectric energy harvester utilizing a rigid-flexible compound blunt body (W-APEH) is proposed. The rigid-flexible compound blunt body improves environmental adaptability and power generation capacity. During the transformation process of the rigid-flexible compound blunt body from a Y-shape to an r-shape, a vibration pattern changes from galloping to coupled vibration, then to vortex-induced vibration. The feasibility of the structure and principle of the W-APEH were proved through a series of simulations and experiments. The higher proportion of rigid wings within a blunt body increases the susceptibility to galloping. A larger windward angle will delay the occurrence of galloping in the W-APEH, shorten the time of coupled vibration, and reduce the output voltage. In the case of the flexible wing thickness remains below 0.3 mm, an increase in thickness leads to an extended galloping time, with vortex-induced vibrations occurring later. Specifically, the onset wind speed is only 3.5 m/s, and the working wind speed range is 5–21 m/s with appropriate structural dimensions. Furthermore, the W-APEH provides a maximum output power of 3.78 mW at an optimal load resistance of 250 kΩ.

On the role of wake-capture and resonance in spanwise-flexible flapping wings in tandem

Numerical simulations of the flow around spanwise-flexible flapping wings in tandem are reported, focusing on a thrust-generating configuration. Wings of aspect ratio 2 and 4 in forward flight undergo heaving and pitching motion following optimal 2D kinematics. The Reynolds number of the simulations is Re=1000. The effect of flexibility is explored by varying the effective stiffness of the wings, while the effective inertia is kept constant. The aerodynamic performance of the tandem system results from a combination of unsteady aerodynamics mechanisms, fluid–structure resonance, vortex–wing interactions (denoted wake capture in this study) and aerodynamic tailoring. It is found that the aerodynamic performance and structural behavior of forewings are dominated by a fluid–structural resonance. The maximum mean thrust for the forewings is obtained when the driving frequency approaches the first natural frequency of the structure, ωn,f/ω≈1, similarly to what is observed in isolated wings undergoing the same kinematics. On the other hand, hindwings show optimal performance in a broad region near ωn,f/ω≈2, and their aerodynamic performance seems to be dominated by wake–capture and aerodynamic–tailoring effects. The aerodynamic performance of the hindwings is dependent on the flexibility of the forewing, which impacts the intensity of the vortices shed into the wake and the resulting effective angle of attack (i.e., wake capture). The timing between the effective angle of attack and the pitching motion of the hindwing controls the generation of thrust (or drag) of each spanwise section of the hindwing (i.e., aerodynamic tayloring). A proof of concept study on the aerodynamic performance of systems made of wings with different flexibility suggests that they could outperform tandem systems with equally flexible wings. Thus, the optimal mixed–flexibility tandem system is composed by a resonant forewing, which maximizes the thrust generation of the forewing and the intensity of the vortices shed into the wake, and a hindwing whose flexibility must be tuned to maximize wake capture effects.

Systematic Experimental Evaluation of Aeroelastic Characteristics of a Highly Flexible Wing Demonstrator

This paper presents a comprehensive experimental analysis of the evolutionary modal characteristics of a highly flexible wing that exhibits bending–torsion coupling-driven instability. By implementing operational modal analysis on responses triggered by a combination of an external pulse-like stimulation and turbulence within the flow, this paper presents the airspeed-driven variations of the modal frequencies, damping ratios, and the underlying modal coupling behavior, leading to instability. This analysis is extended to varying the wing root pitch angles through which the effects of geometrical nonlinearity are exercised. Their effects are particularly noted on the hump feature of the airspeed-driven damping ratio locus of the mode responsible for instability. The decreasing critical damping ratio is shown to result in amplified turbulence-driven responses, which pose significant challenges to identification procedures by masking the visibility of other modes. Furthermore, through a novel technique used to analyze the modal coupling, the relative phase and magnitude properties of the coupled bending–torsion composition of the critical mode before and at flutter onset are evidenced experimentally. It is demonstrated that these relative participation measures provide a strong indication of the response content of the limit cycle oscillations that emerge after the flutter speed.

Design and investigation of flexible solar wing: In-plane dynamics

Space satellites are increasingly using flexible solar wings. The dynamic behavior of the flexible solar array in orbit, which is related to the service life, has not been fully studied. In this paper, a new flexible hinge design is proposed for connecting multiple solar arrays, and its influence on the in-plane nonlinear dynamic characteristics of the array is investigated. The novelty of this research lies in the exploration of the deformation mechanisms of these hinges, where a nonlinear static model is developed based on Hamilton principle to accurately predict stiffness properties. Since the nonlinearity of the hinge stiffness has a significant effect on the system response, the combination of complex dynamic frequency (CDF) method and the arc length method are applied to obtain the analytic solution of in-plane dynamic model. During the ground testing, diverse patterns of response are finally discovered, and nonlinear behaviors such as snap-through occurred. These results reveal that by adjusting hinge parameters, both the hinge stiffness and the resonance frequency of the flexible solar wing can be effectively modified. This research provides critical insights and guidance for enhancing the design of structural static margins, avoiding interference frequency bands, and improving system stability.

Observer based nonlinear robust control for a flexible wing with unknown time-varying output constraints

Observer based nonlinear robust control for a flexible wing with unknown time-varying output constraints

Static aeroelastic rolling of a highly flexible wing: Pazy wing with aileron

Static aeroelastic rolling of a highly flexible wing: Pazy wing with aileron

Innovative Skin Structures: Synthesis, Void Analysis, and Hysteresis Modeling of Zero Poisson’s Ratio Skin for Span Morphing Wing

This paper explores the use of carbon fiber-reinforced elastomeric skins for advancing flexible morphing wing technologies, highlighting exceptional 1D morphing capabilities. The study focuses on synthesizing a specially engineered elastomer-based skin with a zero Poisson’s ratio, achieved through precise formulation and fabrication onto unidirectional carbon fiber. Poisson’s ratio of the 1D skin is confirmed to be zero via image analysis. Micro-CT tomography evaluates carbon fiber quality and voids under varied prestretch conditions, revealing proportional increases in void sizes. X-ray tomography also provides insights into void distribution and morphology during pre- and post-cyclic stretching. The innovative approach enables seamless 1D morphing, achieving an impressive 200% stretch with a slight increase in actuation force and hysteresis loss percentage. Inspired by continuum mechanics, the proposed “Exp-ln-ln” framework accurately models the loading–unloading stretching of the skin. An extensive parametric investigation assesses key parameters, advancing fiber-reinforced elastomeric materials for aerospace morphing skins.

Impact of actuation and sensor measurement delays on stability of real-time hybrid aeroelastic simulation system

AbstractThis paper is focused on the stability of real-time hybrid aeroelastic simulation systems for flexible wings. In a hybrid aeroelastic simulation, a coupled aeroelastic system is ‘broken down’ into an aerodynamic simulation subsystem and a structural vibration testing subsystem. The coupling between structural dynamics and aerodynamics is achieved by real-time communication between the two subsystems. Real-time hybrid aeroelastic simulations can address the limitations associated with conventional aeroelastic testing performed within a wind tunnel or with pure computational aeroelastic simulation. However, as the coupling between structural dynamics and aerodynamics is completed through the real-time actuation and sensor measurement, their delays may inherently impact the performance of hybrid simulation system and subsequently alter the measured aeroelastic stability characteristics of the flexible wings. This study aims to quantify the impact of actuation and sensor measurement delays on the measured aeroelastic stability, e.g. the flutter boundary, of flexible wings during real-time hybrid simulations, especially when different aerodynamic models are implemented.

Effects Of Wing Elasticity On Tip Vortex: 3D Deformation And 2D3C Flow Field Measurements

As aircraft embrace broader applications, the flexible wing presents a promising avenue to enhance aircraft performance across a wide range of flight conditions. Although the aerodynamic benefits of wing deformation are widely recognized, the present understanding of the tip vortex is relatively limited. This work experimentally examines the effects of wing deformation on the tip vortex of a simplified aircraft model with two kinds of elastic wings and a rigid wing. The 3D deformations and 2D3C flow fields are measured using a synchronous measurement system, which includes the high accuracy deformation measurement (HADM) method and the stereoscopic particle image velocimetry (SPIV). It is shown that increased wing elasticity leads to greater bending, with the wing tip moving along the streamwise, vertically upward, and spanwise inward directions. These deformations are closely linked to aerodynamic forces and influence the tip vortex positions. The more elastic wing, EW2, exhibits the highest vortex core position, more than 0.5 times the length of the wing root, while the other one, EW1, shows the strongest vortex in the lift-increased regime. In the early wakes, the tip vortex of the elastic wing is elongated along the spanwise direction, resulting in an asymmetric shape. As it convects downstream, the vortex core disperses via viscous diffusion, resulting in a relatively more circular shape with decreased vorticity.

Wake interference effects on flow-induced vibration of flexible membrane wings

This work investigates the effect of wake interference on the nonlinear coupled dynamics and aerodynamic performance of flexible membrane wings at a moderate Reynolds number. A high-fidelity computational aeroelastic framework is employed to simulate the flow-induced vibration of flexible membrane wings in response to unsteady vortex wake flows produced by an upstream stationary circular cylinder. The coupled dynamics of the downstream membrane are investigated at different gap ratios, aeroelastic numbers, and offset distances. The variations in flow features, membrane responses, and frequency characteristics are analyzed to understand the wake interference effect on membrane aeroelasticity. The results indicate that the aerodynamic performance and flight stability of the downstream membrane are degraded under the wake interference effect. Four distinct flow regimes are classified for the cylinder–membrane configuration, namely (i) single body flow, (ii) co-shedding I, (iii) co-shedding II, and (iv) detached vortex-dominated vibration, respectively. The mode transition is found to build new frequency synchronization between the flexible membrane and its own surrounding flows, or the wake flows of the cylinder, to adjust the aerodynamic performance and membrane vibration. This study sheds new light on membrane aeroelasticity in response to wake flows and enhances understanding of the fluid–membrane coupling mechanism. These findings can facilitate the development of next-generation bio-inspired drones that have high flight efficiency and robust flight stability in gusty flows.

Analysis of fluid-structure coupling during the flapping of dragonfly hind wings under different flexible distributions

Abstract To investigate the influence of flexible distribution on the aerodynamic characteristics of a dragonfly hind wing during flapping flight, this study establishes a simplified plate model of the dragonfly hind wing based on the actual size, while neglecting the wrinkled microstructure. Six different flexible distribution patterns are proposed for the model. The overlapping grid technique is employed to achieve fluid-structure coupling calculations during the flapping motion of the dragonfly hind wing, by customizing the Young’s modulus in the solid region to represent different levels of flexibility. The results show that gradually increasing the flexibility along the chordwise direction of the dragonfly wing can induce a stronger leading-edge vortex during flapping, intensifying the accumulation of vorticity near the wingtip and resulting in a higher peak lift coefficient. The flexible wing has a positive impact on the formation and development of the trailing-edge vortex, leading to an increase in the thrust coefficient peak and time-averaged thrust coefficient of the dragonfly hind wing. Consequently, all aspects of the aerodynamic characteristics are significantly improved.