Flexible Membrane Wing Research Articles

Multifidelity approach to the numerical aeroelastic simulation of flexible membrane wings

Due to their lightness, the capacity to adapt to the flow conditions, and the safety when operating near humans, the use of membrane-resistant structures has increased in fields as micro aerial vehicles and yachts sails. This work focuses on the computational methodology required for simulating the aeroelastic coupling of the structure with the incident wind flow. A semi-monocoque structure (composed of a main spar, a set of ribs, and an external membrane) inside a wind tunnel is simulated using two different methodologies. Firstly, a complete fluid-structure interaction is calculated by combining the finite element methodology for the solid and the unsteady Reynolds average Navier-Stokes computational fluid dynamics for the air, including nonlinear effects and prestress. Then, a low-fidelity model is applied, obtaining the linear aeroelastic eigenvalues and the temporal response of the wing. Both methodologies results are in agreement with estimating the transient mean deformation and flutter velocity. However, the modal analysis tends to overestimate the aeroelastic effects, as it calculates potential aerodynamics, predicting an instability velocity lower than that provided by the transient simulations.

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.

Coupled Dynamics of Steady Jet Flow Control for Flexible Membrane Wings

We present a steady jet-flow-based flow control of flexible membrane wings for the adaptive and efficient motion of bat-inspired drones in complex flight environments. A body-fitted variational computational aeroelastic framework is adopted for the modeling of fluid–structure interactions. High-momentum jet flows are injected from the leading edge and transported to the wake flows to alter the aerodynamic performance and the membrane vibration. The coupled dynamic effect of active jet flow control on membrane performance is systematically explored. While the results indicate that the current active flow control strategy performs well at low angles of attack, its effectiveness degrades at high angles of attack with large flow separation. To understand the coupling mechanism, the variations of the vortex patterns are examined by the proper orthogonal decomposition modes, and the fluid transport process is studied by the Lagrangian coherent structures. Two scaling relations that quantitatively connect the membrane deformation with the aerodynamic loads presented in our previous work are verified even when active jet flow control is applied. A unifying feedback loop that reveals the fluid–membrane coupling mechanism is proposed. These findings can facilitate the development of next-generation bio-inspired drones that incorporate smart sensing and intelligent control.

Aeroelastic characteristics of flexible membrane wings with ceiling effect

We present a numerical study to analyze the aeroelastic characteristics of two-dimensional flexible membrane wings subjected to the ceiling effect. A body-fitted variational aeroelastic solver based on the fully coupled Navier–Stokes and nonlinear structural equations is employed to model the coupled fluid-membrane system. The coupled dynamics and the aerodynamic performance of flexible membrane wings with ceiling effect are investigated in a parameter space of angle of attack and ceiling distance. The effect of ceiling distance on the aeroelastic characteristics is examined at pre-stall, near-stall, and stall conditions. The role of flexibility in the coupled system under near-ceiling conditions is investigated by comparing with its rigid flat and cambered counterparts. The effect of no-slip and perfect slip boundary conditions of the ceiling wall is compared to quantify the momentum transport influenced by the ceiling effect. The connection between the aerodynamic loads and the membrane deformation is constructed by two scaling relations presented in our previous studies. The results indicate that the aeroelastic characteristics of the flexible membrane wings under near-ceiling conditions are adjusted from three aspects, namely, (i) the gap to the ceiling, (ii) the wing flexibility, and (iii) the ceiling boundary condition. This study represents a step toward an improved understanding of the aeroelastic characteristics of flexible membrane wings under ceiling conditions with different boundary layer flows. These findings can facilitate the development of high-efficiency bio-inspired micro-air vehicles that have robust flight stability and can perform missions in confined spaces.

Unsteady Aeroelastic Characterization and Scaling Relations of Flexible Membrane Wings

We present a numerical study to characterize nonlinear unsteady aeroelastic interactions of two-dimensional flexible wings at high angles of attack. The coupled fluid–flexible wing system is solved by a body-fitted variational aeroelastic solver based on the fully coupled Navier–Stokes and nonlinear structural equations. Using the coupled fluid–structure analysis, this study is aimed to provide physical insight and correlations for the aeroelastic behavior of flexible wings in the parameter space of the angle of attack and the aeroelastic number. The phase diagrams of the aerodynamic performance are established to obtain the envelope curves of the optimal performance and determine the transition line of the drag variation. The effects of the angle of attack and the aeroelastic number on the aeroelastic behaviors are systematically examined. The time-averaged membrane deformation is positively correlated with a nondimensional number, the so-called Weber number. A new scaling relation is proposed based on the dynamic equilibrium between the aerodynamic force fluctuation and the combined inertia–elastic fluctuation. The unsteady aerodynamic force can be adjusted by manipulating the membrane vibration, the mass ratio, the Strouhal number, and the aeroelastic number. The numerical investigations provide design guidelines and have the potential to enhance the maneuverability and flight agility of micro air vehicles with flexible wing structures.

Modelling Aero-Structural Deformation of Flexible Membrane Kites

Airborne wind energy systems using flexible membrane wings have the advantages of a low weight, small packing volume, high mobility and rapid deployability. This paper investigates the aero-structural deformation of a leading edge inflatable kite for airborne wind energy harvesting. In the first step, a triangular two-plate representation of the wing is introduced, leading to an analytical description of the wing geometry depending on the symmetric actuation state. In the second step, this geometric constraint-based model is refined to a multi-segment wing representation using a particle system approach. Each wing segment consists of four point masses kept at a constant distance along the tubular frame by linear spring-damper elements. An empirical correlation is used to model the billowing of the wing’s trailing edge. The linear spring-damper elements also the model line segments of the bridle line system, with each connecting two point masses. Three line segments can also be connected by a pulley model. The aerodynamic force acting on each wing segment is determined individually using the lift equation with a constant lift coefficient. The particle system model can predict the symmetric deformation of the wing in response to a symmetric actuation of the bridle lines used for depowering the kite (i.e., changing the pitch angle). The model also reproduces the typical twist deformation of the wing in response to an asymmetric line actuation used for steering the kite. The simulated wing geometries are compared with photogrammetric information taken by the onboard video camera of the kite control unit, focusing on the wing during flight. The results demonstrate that a particle system model can accurately predict the geometry of a soft wing at a low computational cost, making it an ideal structural building block for the next generation of soft wing kite models.

An Aero-Structural Model for Ram-Air Kite Simulations

Similar to parafoils, ram-air kites are flexible membrane wings inflated by the apparent wind and supported by a bridle line system. A major challenge in estimating the performance of these wings using a computer model is the strong coupling between the airflow around the wing and the deformation of the membrane structure. In this paper, we introduce a staggered coupling scheme combining a structural finite element solver using a dynamic relaxation technique with a potential flow solver. The developed method proved numerically stable for determining the equilibrium shape of the wing under aerodynamic load and is thus suitable for performance measurement and load estimation. The method was validated with flight data provided by SkySails Power. Measured forces on the tether and steering belt of the robotic kite control pod showed good resemblance with the simulation results. As expected for a potential flow solver, the kite’s glide ratio was overestimated by 10–15%, and the measured tether elevation angle in a neutral flight scenario matched the simulations within 2 degrees. Based on the obtained results, it can be concluded that the proposed aero-structural model can be used for initial designs of ram-air kites with application to airborne wind energy.

Mode transition in fluid–structure interaction of piezoelectric membrane wings

Flow-induced vibrations can be utilized to harvest energy for micro-air vehicles (MAVs). A flexible membrane wing with an embedded piezoelectric energy harvester at an angle of attack of 12° and the Reynolds number (Re) of 8000 is studied by numerical simulations. An aero-electro-mechanical model is established to investigate the effect of the leading-edge (LE) and trailing-edge (TE) geometries on the fluid–structure interaction (FSI) modes, aerodynamic performance, and energy harvesting performance. A new correction method of structural frequency is proposed that it considers both the aerodynamic stiffness effect and the added mass effect corresponding to a specific FSI mode of interest. The results suggest that the mode transition accompanied by the performance changes is essentially caused by the FSI state transition, which is distinguished by the corrected structural frequency and the vortex shedding one. With the Fourier mode decomposition (FMD) method, the modes of membrane vibration and pressure fluctuation become clear. The LE geometry is found to affect the FSI state by influencing the leading-edge vortices, which further triggers the mode transition.

Aeroelastic characterisation of a bio-inspired flapping membrane wing

Natural fliers like bats exploit the complex fluid–structure interaction between their flexible membrane wings and the air with great ease. Yet, replicating and scaling the balance between the structural and fluid-dynamical parameters of unsteady membrane wings for engineering applications remains challenging. In this study, we introduce a novel bio-inspired membrane wing design and systematically investigate the fluid–structure interactions of flapping membrane wings. The membrane wing can passively camber, and its leading and trailing edges rotate with respect to the stroke plane. We find optimal combinations of the membrane properties and flapping kinematics that out-perform their rigid counterparts both in terms of increased stroke-average lift and efficiency, but the improvements are not persistent over the entire input parameter space. The lift and efficiency optima occur at different angles of attack and effective membrane stiffnesses which we characterise with the aeroelastic number. At optimal aeroelastic numbers, the membrane has a moderate camber between 15% and 20% and its leading and trailing edges align favourably with the flow. Higher camber at lower aeroelastic numbers leads to reduced aerodynamic performance due to negative angles of attack at the leading edge and an over-rotation of the trailing edge. Most of the performance gain of the membrane wings with respect to rigid wings is achieved in the second half of the stroke when the wing is decelerating. The stroke-maximum camber is reached around mid-stroke but is sustained during most of the remainder of the stroke which leads to an increase in lift and a reduction in power. Our results show that combining the effect of variable stiffness and angle of attack variation can significantly enhance the aerodynamic performance of membrane wings and has the potential to improve the control capabilities of micro air vehicles.

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 lift-enhancement 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.

Aeroelastic mode decomposition framework and mode selection mechanism in fluid–membrane interaction

In this study, we present a global Fourier mode decomposition framework for unsteady fluid–structure interaction. We apply the framework to isolate and extract the aeroelastic modes arising from a coupled three-dimensional fluid–membrane system. We investigate the frequency synchronization between the vortex shedding and the structural vibration via mode decomposition analysis. We explore the role of flexibility in the aeroelastic mode selection and perform a systematic comparison of flow features among a rigid flat wing, a rigid cambered wing and a flexible membrane. The camber effect can enlarge the pressure suction area on the membrane surface and suppress the turbulent intensity, compared to the rigid flat wing counterpart. With the aid of our mode decomposition technique, we find that the dominant structural mode exhibits a chordwise second and spanwise first mode at different angles of attack. The structural natural frequency corresponding to this mode is estimated using an approximate analytical formula. By examining the dominant frequency of the coupled system, we show that the dominant membrane vibration mode is selected via the frequency lock-in between the dominant vortex shedding frequency and the structural natural frequency. From the fluid modes and the mode energy spectra at α=20∘ and 25°, the aeroelastic modes corresponding to the non-integer frequency components lower than the dominant frequency are observed, which are associated with the bluff body vortex shedding instability. The non-periodic aeroelastic behaviors observed at higher angles of attack are related to the interaction between aeroelastic modes caused by the frequency lock-in and the bluff-body-like vortex shedding. Using the mode decomposition analysis, we suggest a feedback cycle for flexible membrane wings undergoing synchronized self-sustained vibration. This feedback cycle reveals that the dominant aeroelastic modes are selected through the mode and frequency synchronization during fluid–membrane interaction to exhibit similar modal shapes in the membrane vibration and the pressure pulsation.

Experimental analysis of fluid-structure interaction in flexible wings at low Reynolds number flows

PurposeThe purpose of this exhaustive experimental study is to investigate the fluid-structure interaction in the flexible membrane wings over a range of angles of attack for various Reynolds numbers.Design/methodology/approachIn this paper, an experimental study on fluid-structure interaction of flexible membrane wings was presented at Reynolds numbers of 2.5 × 104, 5 × 104 and 7.5 × 104. In the experimental studies, flow visualization, velocity and deformation measurements for flexible membrane wings were performed by the smoke-wire technique, multichannel constant temperature anemometer and digital image correlation system, respectively. All experimental results were combined and fluid-structure interaction was discussed.FindingsIn the flexible wings with the higher aspect ratio, higher vibration modes were noticed because the leading-edge separation was dominant at lower angles of attack. As both Reynolds number and the aspect ratio increased, the maximum membrane deformations increased and the vibrations became visible, secondary vibration modes were observed with growing the leading-edge vortices at moderate angles of attack. Moreover, in the graphs of the spectral analysis of the membrane displacement and the velocity; the dominant frequencies coincided because of the interaction of the flow over the wings and the membrane deformations.Originality/valueUnlike available literature, obtained results were presented comparatively using the sketches of the smoke-wire photographs with deformation measurement or turbulence statistics from the velocity measurements. In this study, fluid-structure interaction and leading-edge vortices of membrane wings were investigated in detail with increasing both Reynolds number and the aspect ratio.

Dynamic mode decomposition-based reconstructions for fluid–structure interactions: An application to membrane wings

Four data-driven low-order modeling approaches, Dynamic mode decomposition (DMD) and three other variations (optimal mode decomposition, total-least-squares DMD and high-order DMD), are used to capture the spatio-temporal evolution of fluid–structure interactions. These methods are applied to experimental data obtained in a flow over a flexible membrane wing and its elastic deformation. Spectral coherence indicates there exists an interaction between the flow and structural deformation at a single frequency for this problem (depending on the angle of attack and/or the presence of a ground). It is therefore an ideal dataset to assess the performance of the four different methods in terms of the relevant modes/frequencies and reconstruction of flow and structural deformation. We show that the four methods detect the same dominant frequency (within Fourier resolution) and qualitatively the same associated mode. However, the modes appear to be heavily damped or amplified preventing a successful flow and structure reconstruction (except when using high-order DMD). This problem persists even if the damping coefficients are set to 0 due to imprecision in the estimation of the dominant frequency. The reconstruction is assessed by means of the average correlation between the real and reconstructed fields corresponding to 0.42 and 0.85 for the fluid and membrane deformation respectively when using high-order DMD (and virtually 0 for the other three methods). Based on the analysis, we conclude that high-order DMD, particularly for when fluid and structural data are modeled simultaneously, is the most suitable method to generate linear low-order models for fluid–structure interaction problems. Further, we show that this modeling is not dependent on the relative energies of fluid and membrane deformation.

Fluid–structure interaction of a flexible membrane wing at a fixed angle of attack

Fluid–structure interaction of a flexible membrane wing was investigated experimentally at a fixed angle of attack (α = 14°). The Reynolds numbers (Re) based on the chord length of the membrane wing were 6 × 104, 6.6 × 104, and 8 × 104, respectively, which belong to low Reynolds numbers. Membrane deformations and the global flow fields around the membrane wing were measured synchronously with two-dimensional time-resolved particle image velocimetry. The membrane performs strongly periodic standing-wave vibration modes while interacting with the surrounding flow. Although the flow fields and membrane vibrations are coupled in all Re cases, it is newly discovered that, at Re = 6 × 104, the dominant frequency of the flow is around 9.1 Hz (Strouhal number St = 0.15) instead of the dominant membrane vibration frequency of 35.1 Hz (first-order vibration mode, St = 0.56). By tracking the Lagrangian coherent structures over the membrane, it is revealed that the vortical structures at Re = 6 × 104 are affected by the flow from both the leading- and trailing-edges. The frequency of 35.1 Hz in the power spectrum of flow is attributed to the successive shedding of leading-edge vortices coupled with membrane vibration, while the dominant frequency of flow field (9.1 Hz) is resulted from the interaction of strong trailing-edge reverse flow and the leading-edge separated flow, and the mechanism is explored. For higher Re cases (Re = 6.6 × 104 and 8 × 104), the membrane presents second- and third-order vibration modes separately. The dominant frequencies of the flow structure and membrane vibration are consistent, and the periodic shedding of leading-edge vortices is the main flow characteristic in both Re cases.

Validation of the quasi-steady performance model for pumping airborne wind energy systems

The quasi-steady performance model (QSM) has been developed specifically for pumping airborne wind energy systems using flexible membrane wings. In this study, we validate this model using a comprehensive set of flight data that includes 87 consecutive pumping cycles and is acquired with the development platform of Kitepower B.V. The aerodynamic properties of the kite are determined using onboard measurements of the relative flow velocity. We found that neglecting the vertical wind component and straightening and slacking motion of the tether lead to substantial errors in the kite velocity calculated using the system model. A reasonable agreement between the QSM simulations and flight data can be obtained by multiplying the kite’s drag coefficient by a fudge factor and thereby turning the QSM into a grey-box model. The model accuracy is statistically evaluated as opposed to only evaluating a single pumping cycle per system configuration as done in earlier research.

Aeroelasticity Validation Study for a Three-Dimensional Membrane Wing

The objective of this effort is to study the aeroelastic characteristics of a flexible membrane wing at different Reynolds numbers using direct numerical simulation and to investigate techniques to reduce the adverse effects of flow separation and unsteady aerodynamics. For the aeroelastic predictions, a first-principles-based approach is undertaken, where the flow solver is fully coupled with the structural dynamics solver. This approach is able to accurately and efficiently predict the unsteady aerodynamics, boundary-layer separation, lift and drag, and the stress and structural deformation of the flexible membrane wing. The focus of this paper is on the systematic validation of this coupled solver for a specific membrane configuration, where extensive experimental measurements are available. Comparisons between the present simulations and experiments are made for the following quantities: 1) mean membrane shape; 2) dominant membrane oscillating frequencies under various conditions; 3) flowfield visualizations; 4) instantaneous velocity field; 5) membrane displacement response to instantaneous flowfield; 6) use of rigid and flexible membranes; 7) distribution of mean velocity field; and 8) distribution of turbulence intensity. Comparisons of these quantities show the favorable agreement of the present prediction against measurement, and hence build a sound validation study for the coupled fluid–structure solver.

An experimental investigation of laminar separation bubble formation on flexible membrane wing

In this study, fluid–structure interaction over a flexible membrane wing with aspect ratio (AR) of 3 at low Reynolds numbers was investigated experimentally. Smoke wire flow visualization technique was performed for analyzing time-dependent behavior of flow over this flexible membrane wing. Furthermore, time dependent deformation of flexible membrane wing was measured. It was clearly seen that the value of membrane deformation increased with increasing angle of attack. Moreover, it was stated that the size of laminar separation bubble (LSB) changed with time due to the unsteady flow characteristics of membrane wing. The unsteady behavior over the flexible membrane wing caused different deformation modes to form at different angles of attack. For the flexible wings with higher aspect ratios, the LSB was more dominant in the membrane wings at low Re numbers, and caused the membrane vibration to increase based on the angle of attack which the LSB started to be overpowering.

Aerodynamic comparisons of flexible membrane micro air vehicle wings with cambered and flat frames

Flexible membrane wings at the micro air vehicle scale can experience improved lift/drag ratios, delays in stall, and decreased time-averaged flow separation when compared to rigid wings. This research examines the effect of frame camber on the aerodynamic characteristics of membrane wings. The frames for the wings were 3D printed using a polymer-based material. The membranes are silicone rubber. Tests were conducted at Re ∼50,000. Aerodynamic force and moment measurements were acquired at angles-of-attack varying from −4 to 24°. Additionally, digital image correlation data were acquired to assess time-averaged shapes of the membrane wings during wind tunnel tests. An in-house program was developed to average the deflection plots from the digital image correlation images and produce time-averaged shapes. Lifting-line theory based on the time-averaged shapes was then used to calculate theoretical lift and induced drag coefficients, showing that the time-average shape of the membrane under load contributes extensively to the aerodynamic performance. The results show that introducing camber to the frames of membrane wings increases aerodynamic efficiency.

On the fluid-structure interaction of flexible membrane wings for MAVs in and out of ground-effect

Wind tunnel experiments are conducted at a Reynolds number of Re=56,000, measuring rigid flat-plates and flexible membrane wings from free-flight into ground-effect conditions. Load cell measurements, digital image correlation and particle image velocimetry are applied in high-speed to resolve time-synchronised lift, drag and pitch oscillations simultaneously with membrane and flow dynamics. Proper orthogonal decomposition is applied on flow oscillations to determine their spatiotemporal evolution. Loads, membrane motions and flow dynamics are correlated to each other to investigate their underlying coupling physics. A membrane wing's ability of static cambering and dynamic membrane oscillations are found to be beneficial when the wing is in ground-effect, where the descent in height forces premature leading-edge vortex-shedding and drag increase. The dynamic motions of membrane wings help to exploit vortex-shedding dynamics from the leading-edge that ensures time-averaged reattached flow over the wing upper surface, resulting in further lift enhancement. Membrane wings show lag-free fluid-membrane coupling at peak-lift conditions. In post-stall conditions, the membrane is found to lag the flow dynamics, signalling the end of direct fluid-structure coupling.

Tendon-Sheath Mechanisms in Flexible Membrane Wing Mini-UAVs: Control and Performance

Flexible membrane wings (FMWs) are known for two inherent advantages, that is, adaptability to gusty airflow as the wings can flex according to the gust load to reduce the effective angle of attack and the ability to be folded for compact storage purposes. However, the maneuverability of UAV with FMWs is rather limited as it is impossible to install conventional ailerons. The maneuver relies only on the rudders. Some applications utilize torque rods to warp the wings, but this approach makes the FMW become unfoldable. In this research, we proposed the application of a tendon-sheath mechanism to manipulate the wing shape of UAV. Tendon-sheath mechanism is relatively flexible; thus, it can also be folded together with the wings. However, its severe nonlinearity in its dynamics makes the wing warping difficult to control. To compensate for the nonlinearity, a dedicated adaptive controller is designed and implemented. The proposed approach is validated experimentally in a wind tunnel facility with imitated gusty condition and subsequently tested in a real flight condition. The results demonstrate a stable and robust wing warping actuation, while the adaptive washout capability is also validated. Accurate wing warping is achieved and the UAV is easily controlled in a real flight test.