Flexible Airfoil Research Articles

Enhancing output characteristics of semi-active flapping airfoil energy capture device via flexible deformation strategy

ABSTRACT A concentrated-torsion flexible airfoil model is established to enhance the output characteristics of the flapping airfoil energy capture device in this work. The effect of the damping ratio C 2*, spring ratio K 2* of the torsion spring, and mass ratio M A * of the tail airfoil on the dynamic characteristics is investigated systematically. The numerical simulation results show that compared with the rigid airfoil, the time-averaged power coefficient and output efficiency of the optimized flexible airfoil (C 2* = 4, K 2* = 0.5, and M A * = 0.7) are increased by 91.85% and 63.45%, respectively. Remarkably, the output efficiency of the optimized flexible airfoil is 32.15%. The reason for the enhanced performance is that the passive deformation can ensure the airfoil generates a stronger vortex and delays the shedding of the vortex. In addition, the experimental test results (with a 36.29% performance enhancement) further demonstrate the effectiveness of using the concentrated-torsional flexible deformation strategy in enhancing the energy output characteristics of the flapping airfoil.

Experimental and numerical investigations to the aeroelastic response of flexible thin airfoil

The paper investigates the phenomenon of the aeroelastic response of flexible thin airfoils under various angles of attack (AOAs) and flow velocities through wind tunnel experiments and numerical simulations. The vibration modal characteristics are explored, including vibration frequencies, amplitudes, modal transition, and instantaneous characteristics. Vibration is directly measured using non-contact laser sensors, and the numerical model is appropriately configured to simulate the fluid–structure interaction (FSI) problem under large deformation. Experiments cover a range of AOAs (1°–20°) and incoming velocities (from 10 to 73 m/s), with dynamic responses measured using four laser sensors. Both average and instantaneous modal response features are analyzed, revealing multi-modal characteristics as velocity and AOA increase. The vibration mode transitions from pure bending to higher-order modes as incoming velocity increases. Specifically, at higher velocities and increased AOA, the high-order vibration component shifts from bending-torsional coupled mode to pure-torsional mode. Comparison of vibration frequencies between experimental measurements and finite element method simulations highlights significant shifts, particularly in the pure-torsional mode. Furthermore, employing commercial software ANSYS CFX and ANSYS Mechanical, a two-way three-dimensional FSI model successfully replicates flutter boundaries observed experimentally at 1° AOA and approximately incoming velocity 73 m/s. This FSI model is extended to simulate the multi-modal vibrations at 15° AOA, yielding insights into flow phenomena contributing to multi-modal vibration at this AOA. An explanation is provided for the multi-modal vibration phenomenon observed in the experiments based on the above insight. Finally, the differences between the experimental and numerical simulations are speculated upon.

Mechanical Behavior of Honeybee Forewing with Flexible Resilin Joints and Stripes.

The flexibility of insect wings should be considered in the design of bionic micro flapping-wing aircraft. The honeybee is an ideal biomimetic object because its wings are small and possess a concise vein pattern. In this paper, we focus on resilin, an important flexible factor in honeybees' forewings. Both resilin joints and resilin stripes are considered in the finite element model, and their mechanical behaviors are studied comprehensively. Resilin was found to increase the static deflections in chordwise and spanwise directions by 1.4 times and 1.9 times, respectively. In modal analysis, natural frequencies of the first bending and first torsional modes were found to be decreased significantly-especially the latter, which was reduced from 500 Hz to 217 Hz-in terms of resilin joints and stripes, closely approaching flapping frequency. As a result, the rotational angle amplitude in dynamic responses is remarkable, with an amplification ratio of about six. It was also found that resilin joints and stripes together lead to well-cambered sections and improve the stress concentrations in dynamic deformation. As resilin is widespread in insect wings, the study could help our understanding of the flexible mechanism of wing structure and inspire the development of flexible airfoils.

Fluid-structure interaction simulation for multi-body flexible morphing structures

The multi-body flexible morphing airfoil can improve the aerodynamic characteristics based on different flight missions continuously. Recently researches have focused on the unsteady aerodynamic characteristics of flexible wings under passive actuation. However, the unsteady aerodynamic characteristics with the fluid–structure interaction effects in the multi-body active actuation process of morphing airfoil deserve further investigation. In this paper, a fluid–structure coupled simulation method for multi-body flexible morphing airfoil with active actuation subsystem was investigated, and the aerodynamic characteristics during deformation were compared with different skin flexibility, flow field environment, actuation mode and actuation time. The numerical results show that for the steady aerodynamic, the skin flexibility can improve the stability efficiency. In the unsteady process, the change trend of the transient lift coefficient and pitching moment are consistent with those of the active drive characteristics, while the instantaneous lift-drag ratio coefficient is greatly affected by the driving mode and can be improved by increasing the driving duration.

Robust Algorithm Software for NACA 4-Digit Airfoil Shape Optimization Using the Adjoint Method

Optimizing the aerodynamic shape of an airfoil is a critical concern in the aviation industry. The introduction of flexible airfoils has allowed the shape of the airfoil to vary, depending on the flight conditions. Therefore, in this study, we propose an algorithm that is capable of robustly optimizing the shape of the airfoil based on variable parameters of the airfoil and flight conditions. The proposed algorithm can be understood as an optimization method, which employs the adjoint method, a powerful tool for estimating the sensitivity of the model output to the input in numerous studies. From an aerodynamic perspective, the development of shape geometry is a crucial step in airfoil development. The study used NACA-4 digit airfoils as input for the initial assumption and the range of shape change. The optimal shape was found using the proposed algorithm by defining one NACA profile as the initial value and another NACA profile as the limit for the optimized shape, considering the aerodynamic coefficients and flight conditions. However, morphing airfoils have certain deformation limitations. As an innovation in the algorithm, bounds were defined for the shape change during optimization so that the result can be constructed within the capabilities of the morphing wing. These bounds can be adjusted (depending on the capabilities of the airfoils). To validate the proposed algorithm, the study compared it with a previous flow solver for the same airfoil.

Influence of lengthways spacing and phase difference on traveling wave energy absorption characteristics of flexible airfoils in a diamond array

Under certain motion parameters, traveling wave motion can absorb energy from incoming flow. In addition to the geometric and motion parameters of each unit, the arrangement also has a great influence on the energy absorption efficiency of traveling wave bodies. Using NACA0012 airfoil as a two-dimensional simplified model, the influence of lengthways spacing and phase difference on energy absorption efficiency of airfoils in the diamond array is studied by numerical calculation in this paper. The results show that with the increase of the lengthways spacing between the midstream airfoils and the downstream airfoil, the transverse interference between the airfoils decreases gradually until disappear. Specifically, with the increase of lengthways spacing, the energy absorption efficiency of the midstream airfoils decreases first and then stays constant, while the downstream airfoil shows a simple harmonic fluctuation with decreasing amplitude. When there exists transverse interference in the array, the energy absorption efficiency of the midstream and downstream airfoils shows a simple harmonic fluctuation concerning the phase difference between the upstream airfoil and the downstream airfoil. When there is no transverse interference in the array, the energy absorption efficiency of the downstream airfoil is a simple harmonic fluctuation concerning the phase difference between the upstream airfoil and the downstream airfoil. Under the optimal arrangement, the energy absorption efficiency of the diamond array is 35% higher than that of a single traveling wave airfoil.

Experimental Study of Aerodynamic Characteristics of Partially Flexible NACA0012 Airfoil

In this study, aerodynamic characteristics of a NACA0012 airfoil section whose part of the skin of the upper surface was constructed of polydimethylsiloxane membrane (PDMS) were experimentally studied in a wind tunnel at a Reynolds number (based on the airfoil chord length) of . The aim of this concept is to take advantage of passive vibration of an elastic membrane in the air to enhance mixing, which energizes the flow near the blade surface. As a result, flow separation on blades can be delayed or even suppressed, widening the usable range of angles of attack for a general-purpose airfoil having a wide range of applications. During the experiment, the blade model was connected to a rotary table with an attached stepper motor, which allowed the angle of attack to vary. A two-component balance was used to measure the lift and drag forces on models, and a smoke-wire technique was adopted to visualize the flowfield around the tested airfoil. Influences of geometric parameters of the PDMS on the effectiveness of flow separation control over the airfoil were systematically analyzed. The results suggested that with the appropriate thickness and Young’s modulus the airfoil having the leading-edge membrane displayed better aerodynamic characteristics such as a delay in dynamic stall angle and higher lift-to-drag ratio at relatively large angles of attack compared to its conventional counterpart. As PDMS is an inexpensive, durable, and readily available material, the present study therefore provides a potentially feasible approach for passive flow separation control in numerous aeronautical and turbomachine applications.

Fluid–structure interaction of multi-body systems: Methodology and applications

We present a method for computing fluid–structure interaction problems for multi-body systems. The fluid flow equations are solved using a fractional-step method with the immersed boundary method proposed by Uhlmann (2005). The equations of the rigid bodies are solved using recursive algorithms proposed by Felis (2017). The two systems of equations are weakly coupled, so that the resulting method is cost-effective. The accuracy of the method is demonstrated by comparison with two- and three-dimensional cases from the literature: the flapping of a flexible airfoil, the self-propulsion of a plunging flexible plate, and the flapping of a flag in a free stream. As an illustration of the capabilities of the proposed method, two three-dimensional bio-inspired applications are presented: an extension to three dimensions of the plunging flexible plate and a simple model of spider ballooning.

Simulation of Aerodynamic Performances of Flexible Flapping Wing Airfoils

Compared with fixed wings, the flapping wing has a significant aerodynamic performance advantage at low speeds and low Reynolds numbers, which draws more and more attentions. But most previous studies focus on rigid flapping airfoils, the aerodynamic performances of flexible flapping airfoils are still unclear. A fluid-solid coupling model for the flexible elliptical airfoils was developed to analyze the flow field around the airfoil, the airfoil deformation and the aerodynamic characteristics of airfoils, at different wind speeds and attack angles. Compared with the rigid airfoil, the flexible airfoil can delay the shedding time of the wake vortex and reduce the oscillation frequency of the disturbance on the lift force. The flexible airfoil significantly suppresses the disturbance of the wake flow and reduces the oscillation amplitude of disturbance. Even, the airfoil disturbance oscillation can be completely eliminated at an appropriate Young’s modulus of the airfoil. These results provide a theoretical guidance for the design of soft aircraft.

Simulation For Aerodynamic Performance of flexible Flapping Wing Airfoil

Simulation For Aerodynamic Performance of flexible Flapping Wing Airfoil

Influence of Lengthways Spacing and Phase Difference on Traveling Wave Energy Absorption Characteristics of Flexible Airfoils in a Diamond Array

Influence of Lengthways Spacing and Phase Difference on Traveling Wave Energy Absorption Characteristics of Flexible Airfoils in a Diamond Array

Experimental investigation on effect of partial flexibility at low aspect ratio airfoil - Part II: Installation both on suction and pressure surface

In this experimental study, flow over NACA 4412 airfoil with flexible membrane mounted both on suction surface and pressure surface was investigated at Reynolds number of 5x104and different angles of attack. The smoke-wire visualization method was used for flow visualization to demonstrate flow phenomena as laminar separation bubble (LSB), leading edge separation and tip vortices. A constant temperature anemometer (CTA) was used for measuring flow over the partially flexible airfoil. Concerning the flow visualization, smoke-wire experiment was been conducted at z/c=0.1 and z/c=0.4. Besides, hot-wire experiment by means of CTA was employed to measure flow properties including values of velocity, turbulence statistics and Reynold stress over both uncontrolled and controlled airfoil. The results showed that partially flexible airfoil had several benefits compared with the uncontrolled airfoil. The results for this partially flexible airfoil were mainly lower size of LSB, higher stall angle of attack, ensuring more stable flow characteristics and more aerodynamic performance.

Influence of spanwise flexibility on steady and dynamic responses of airfoils vs hydrofoils.

There is growing interest in using lighter and more flexible foils with active and/or passive smart actuation mechanisms to increase efficiency and maneuverability. For efficient operations, airfoils and hydrofoils tend to have an effective aspect ratio greater than two, which permits spanwise flexibility depending on the choice of material and architectural design. The fluid density plays an important role in the steady and dynamic performance, including the governing hydroelastic instability mechanism. To understand the influence of spanwise flexibility, we examine the response of a rectangular cantilevered foil as a canonical proxy for more complex lift generating devices. This research aims to investigate the influence of key geometric, material, and flow parameters on the steady and dynamic responses of the spanwise flexible airfoils vs hydrofoils. The results are obtained using an inviscid frequency- and time-domain fluid-structure interaction model that accounts for flow-induced bend-twist coupling terms and are compared with inviscid theory results without the flow-induced bend-twist coupling terms. The results show that the flow-induced bend-twist coupling effects impact the natural frequencies and damping coefficients, and such effects grow with increasing fluid density and flow speed. Hence, the flow-induced bend-twist coupling effects are more critical for hydrofoils than airfoils, particularly for the twisting mode. Ignoring the flow-induced bend-twist coupling terms leads to an incorrect prediction of flutter speed and over-prediction of the damping, which is dangerous because the actual vibrations and dynamic load amplification may be higher than the prediction, which could lead to accelerated fatigue. The results demonstrate that flexible hydrofoils have much lower natural frequencies and higher damping coefficients than airfoils due to higher fluid inertial and damping forces, both of which are proportional to the fluid density. While all components of the fluid forces are proportional to the fluid density, the fluid damping forces grow with the velocity, and the fluid disturbing forces grow with velocity square. Therefore, divergence tends to be the governing instability mode for hydrofoils, while flutter is typically the governing instability mode for airfoils. The maximum aero/hydro-elastic bending and twisting deformations are limited by the corresponding reduced stable velocity to avoid divergence or flutter.

Propulsion and energy harvesting performances of a flexible thin airfoil undergoing forced heaving motion with passive pitching and deformation of small amplitude

The fluid–structure interaction in a foil undergoing prescribed heave with passive pitching and flexibility about any pivot is formulated in the linear inviscid limit using a quartic approximation for the deflection. The resulting system of three algebraic equations is valid for arbitrary mass and stiffness distributions of the foil. The small pitching and deformation amplitudes result linearly from two of the equations, while the third equation provides the force at the pivot point that generates the heaving motion, and hence the power input. This general formulation allows to analyze jointly both the propulsion and the energy harvesting problems for this class of flapping foils. In the first case, the thrust force is readily obtained from the prescribed heave and the resulting pitching and deformation, and consequently the propulsive efficiency once the power input is computed. In the second problem, the energy may be harvested by linear and/or torsional dampers at the pivot point, so that the efficiency of the system is readily computed once the pitch motion and the power input are obtained. Thus, the present work allows for a depth parametric survey and analysis of these two physical problems. The best performance is usually obtained around the first natural frequency of the fluid–structure system, which is obtained here by minimizing an algebraic function. The formulation is validated by reproducing some previous results for both problems, most of them obtained numerically for rigid foils and without the simplicity nor the richness in the parameter space of the present formulation. The parametric range for which flexibility maximizes the propulsion and the energy harvesting efficiencies in relation to an otherwise identical rigid-foil system is analyzed.

Aerodynamic periodicity of transient aerodynamic forces of flexible plunging airfoils

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.

Load alleviation of feather-inspired compliant airfoils for instantaneous flow control

Birds morph their wing shape to adjust to changing environments through muscle-activated morphing of the skeletal structure and passive morphing of the flexible skin and feathers. The role of feather morphing has not been well studied and its impact on aerodynamics is largely unknown. Here we investigate the aero-structural response of a flexible airfoil, designed with biologically accurate structural and material data from feathers, and compared the results to an equivalent rigid airfoil. Two coupled aero-structural models are developed and validated to simulate the response of a bioinspired flexible airfoil across a range of aerodynamic flight conditions. We found that the bioinspired flexible airfoil maintained lift at Reynolds numbers below 1.5 × 105, within the avian flight regime, performing similarly to its rigid counterpart. At greater Reynolds numbers, the flexible airfoil alleviated the lift force and experienced trailing edge tip displacement. Principal component analysis identified that the Reynolds number dominated this passive shape change which induced a decambering effect, although the angle of attack was found to effect the location of maximum camber. These results imply that birds or aircraft that have tailored chordwise flexible wings will respond like rigid wings while operating at low speeds, but will passively unload large lift forces while operating at high speeds.

Effect of partial flexibility over both upper and lower surfaces to flow over wind turbine airfoil

Fluid-structure interaction phenomena on NACA 4412 airfoil having membrane material which was partially mounted on both its suction and pressure surfaces were experimentally investigated in wind tunnel measurements. Different experiments including Digital Image Correlation, smoke-wire, force measurement, and hot-wire systems were conducted at varying angles of attack, α (0° to 24°), and different Reynolds numbers (Re = 2.5 × 104, 5 × 104 and 7.5 × 104). The controlled case gave benefits of up to 2 times in lift coefficient at lower angles of attack (α = 0° − 10°), at the same time drag coefficient decreased. Moreover, the partially flexible airfoil presented high power efficiencies at the pre-stall angles of attack (α = 0° − 10°). Using the flexibility caused the shear layer to approach, laminar separation bubble to suppress, and the wake region to shrunk, indicating the high lift force and less drag force production. The membrane vibrated and deformed due to the flow over the airfoil. Then, the membrane vibration caused the flow to trigger, which caused fluid–structure interaction to perform and the laminar separation bubble to shrink. The transition to turbulence formed earlier and these two flow phenomena moved towards upstream, resulting in having fewer flow fluctuations and increasing the flow stability. This ensures important advantages such as enhancement of aerodynamic performance, power efficiency, and decreasing vibration and noise for wind turbine blades.

Effect of flexibility on unsteady aerodynamics forces of a purely plunging airfoil

Introducing flexibility into the design of a vertically flapping wing is an effective way to enhance its aerodynamic performance. As less previous studies on the aerodynamics of vertically flapping flexible wings focused on the lift generated in a wide range of angle of attack·a 2D numerical simulation of a purely plunging flexible airfoil is employed using a loose fluid–structure interaction method. The aerodynamics of a fully flexible airfoil are firstly studied with the flexibility and angle of attack. To verify whether an airfoil could get aerodynamic benefit from the change in structure, partially flexible airfoil with rigid leading edge and flexible trailing edge were further considered. Results show that flexibility could always reduce airfoil drag while lift and lift efficiency both peak at moderate flexibility. When freestream velocity is constant, lift is maximized at a high angle of attack about 40° while this optimal angle of attack reduces to 15° in drag-balanced status. The airfoil drag reduction, lift augmentation as well as efficiency enhancement mainly attribute to the passive pitching other than the camber deformation. Partially deformed airfoil with the longest length of moderate flexible trailing edge can achieve the highest lift. This study may provide some guidance in the wing design of Micro Air Vehicle (MAV).

In-Flight Estimation of the Aerodynamics of Tethered Wings for Airborne Wind Energy

A new filtering approach is presented, able to estimate online the aerodynamic characteristics of tethered wings used in airborne wind energy systems. The approach is based on the extended Kalman filter (EKF) and on a representative model of the flight dynamics. The filter is fed with measurements available at the ground station, namely, the line angles and their rates, the traction force on the tether, and the wind speed and direction a few meters above the ground. Convergence and accuracy of the estimates are first evaluated through simulations. Then, the approach is demonstrated using extensive experimental data, collected during field tests with two small-scale prototypes built independently by different research groups and four different flexible airfoils (power kites), of both ram-air type and of leading-edge-inflated type. The experimental results show that the algorithm can effectively estimate both the state and the aerodynamic parameters of the wings, as well as the wind speed and direction at the wing's altitude, and makes it possible to analyze the kite aerodynamics during highly dynamical tethered flight.

A fully-coupled CFD/CSD computational approach for aeroelastic studies of helicopter blade-vortex interaction

Blade-vortex interaction (BVI) is one of the main sources of noise and vibrations in helicopters. The aeroelastic response of the blade, to BVI phenomenon, is one of the main factors affecting the helicopter's aerodynamic performance and stability. In the present research we developed and implemented a novel CFD-based, strong (two-way) time-domain coupling, mathematical model, for the numerical prediction of the aeroelastic response of the helicopter blade to BVI. Another novelty, of the fully coupled CFD/CSD approach, is that the fluid flow is solved using the large-eddy simulation (LES) approach. In the present research, the aeroelastic response of a symmetric NACA0012 airfoil to BVI is computed using a two-degree of freedom (2-DOF) mass/spring model. The numerical studies show that the blade-vortex offset distance, (h), plays a key role in the mechanism of BVI and therefore, it influences the aerodynamic coefficients. The computational studies show that the BVI phenomenon diminishes with the increase of the offset distance (h). Also, it was observed that the elastic nature of the airfoil acts as a damper and it diminishes the effect of BVI on the aerodynamic coefficients. Therefore, for a flexible airfoil, the lift coefficient exhibits a decay, at the instant of blade-vortex interaction, when compared with rigid airfoil.