Thin Airfoil Research Articles

Investigation of the decisive factor for the effectiveness of biomimetic protuberances during the stall process

This study investigates the influence of leading-edge protuberances (LEP) on the stall process of airfoils to identify the decisive factor in the effectiveness of LEPs. Owing to its clearly defined three-dimensional structure, an LEP introduces uncertainties into its effects on the stall angle of attack and the lift coefficient curve. This poses a challenge for several airfoils when universal stall control strategies are adopted. These problems were studied by classifying 12 symmetrical baseline airfoil types based on their blade thicknesses under the condition of Re = 180 000. These include thin airfoil stalls (TS), leading-edge stalls (LS), and a combination of leading-edge and trailing-edge stalls (CS). Two representative airfoils from each category were selected to study single-protuberance airfoils. The distribution of the suction surface momentum and evolution of the spanwise vortices revealed that the streamwise vortices induced by the LEP resulted in an attached flow. However, the impact of these flow patterns varies depending on the type of airfoil used. The TS and LS airfoils experienced an increase in the stall angle and maximum lift coefficient, resulting in an overall improvement in the airfoil performance. The CS airfoils are the most heavily influenced, experiencing a decrease in the maximum lift coefficient and exhibiting phenomena such as a one-sided stall and step-by-step stall. Finally, this paper proposes for the first time that the main factor influencing the different effects of protuberances is the stall type of the airfoil. This new knowledge can serve as a valuable reference for the implementation of protuberances in practical mechanical applications.

Performance potential of fully-passive airborne wind energy system based on flapping airfoil

In the field of renewable energy, high-altitude wind energy emerges as a promising source, particularly at altitudes (>300 m) where conventional wind turbines cannot reach. Currently, the Airborne Wind Energy System (AWES) stands as the major technology for high-altitude wind energy harvesting, but confronts challenges including increasing performance enhancement, system robustness, and cost reduction. In response to these challenges, we developed a fully-passive AWES that employs a self-excited flapping airfoil to efficiently transfer wind energy to the ground. We study and optimize this fully-passive AWES with fluid-structure interaction method in a numerical wind tunnel, achieving a notable power coefficient of 1.17 and efficiency of 20 % with an average tether angle near 30°. We find that a thin airfoil with a slight camber near the leading edge outperforms other profiles. Increasing the pitching axis distance, the imbalance distance, the spring stiffness, and the pitching moment of inertia can improve the energy harvesting performance, but decreased the system robustness. We offer essential guidelines for setting initial parameters of the AWES, facilitating the design and deployment of this innovative technology. This work underscore that the fully-passive AWES is capable of realizing high-altitude wind energy harvesting with simplified structure and outstanding energy-harvesting performance.

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.

Theory of the momentum source method for synthetic turbulence

The interaction between turbulence and blade leading edges is known to have a significant impact on the aerodynamic and aeroacoustic performance of propellers. In addition to directly simulating turbulence, synthetic turbulence, such as the momentum source method, has been developed as a popular method for studying this interaction process in computational fluid dynamics and computational aeroacoustics. However, it is found that for non-periodic disturbances, although the induced velocity field is divergence-free, spurious noise may be generated in the source region and contaminate simulation results. To address this issue, the present work proposes adding a correction term so that the divergence-free condition is satisfied globally and the unwanted acoustic waves are suppressed, as an extension to our previous work for time-periodic gusts [H. Jiang, Phys. Fluids 35, 096115 (2023)]. The strength of the proposed approach lies in its simplicity, flexibility, and generality. First, it derives explicit source terms, which are straightforward for numerical implementations, to generate unsteady flow fluctuations. Second, the sources can be added inside the computational domain, saving computational costs for turbulence convection and being compatible with most existing boundary conditions. Third, the proposed method can obtain analytical expressions for the needed momentum source of the Navier–Stokes equation subject to any desired isotropic or anisotropic divergence-free turbulence fields. The method has been verified by examples of synthesizing harmonic gusts, Gaussian eddies, and random turbulence. The synthetic velocity results characterized by different spectral components are directly compared to target velocity fields, verifying the proposed approach and showing its capability. Parameters that influence the distribution of added sources are systematically investigated to identify an optimal combination for different scenarios. Finally, the model is employed to evaluate the aerodynamic interaction between an incoming turbulence and a thin airfoil. The obtained results exhibit good correspondence with analytical solutions.

Lift tailoring on unsteady airfoils with leading-edge vortex shedding using an inverse aerodynamic approach

In this paper, we present a physics-informed approach to tailor the lift profile of an unsteady airfoil through the execution of an appropriate maneuver. In previous research, a low-order aerodynamic model based on the unsteady thin airfoil theory was developed for predicting the flowfield and loads on airfoils undergoing arbitrary motions. The theory was phenomenologically augmented using the concept of leading edge suction parameter (LESP) to incorporate the capability to predict intermittent leading edge vortex (LEV) shedding. The criticality of LESP was used to predict the onset and termination of LEV shedding and thus model the effect of LEVs on the flowfield and loads for a prescribed motion. In the current work, an inverse aerodynamic formulation is developed based on this framework for tackling the inverse problem: to obtain the motion kinematics required for generating a prescribed lift profile for an airfoil operating in the dynamic-stall regime. The LEV-modeling capability of the aerodynamic model enables the motion-design algorithm to take into account the effect of complex phenomena, such as dynamic stall and LEV shedding, which are not taken into account in previous research approaches. Several case studies are presented to demonstrate various scenarios such as lift tracking using pitching and heaving motions, lift cancellation during unsteady motion, and the generation of a given lift profile using two equivalent motions. The kinematic profiles generated by the inverse formulation are also simulated using a high-fidelity unsteady computational fluid dynamics solver to validate the predictions.

Direct numerical simulations of an airfoil undergoing dynamic stall at different background disturbance levels

Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude free stream disturbances is investigated using direct numerical simulations. The flow is practically indistinguishable from clean inflow simulations in the literature for turbulence intensities at the leading edge of ${Tu} = 0.02\,\%$ . At slightly higher turbulence intensities of ${Tu} = 0.05\,\%$ , the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex (DSV). This phenomenon is considered in more detail by analysing its appearance in an ensemble of simulations comprising statistically independent realisations of the flow, thus proving its statistical relevance. In order to extract the transient dynamics of the vortex shedding, the classical proper orthogonal decomposition method is generalised to include time in the energy measure and applied to the time-resolved simulation data of incipient dynamic stall. Using this technique, the dominant transient spatiotemporally correlated features are distilled and the wave train of the vortex shedding prior to the emergence of the main DSV is reconstructed from the flow data exhibiting dynamics of large-scale coherent growth and decay within the turbulent boundary layer.

Fluidic undulation effects on carangiform swimmers propelled by internal active bending moments

With different shapes and material properties, fish all achieve undulatory swimming gait under the action of internal active muscle stimulation and external fluid forces. Such locomotion can be decomposed into deformation affected by internal and external forces in the body frame and overall translation and rotation solely determined by fluid forces. In order to revisit the undulatory swimming gait, we investigate the hydrodynamic performance of two-dimensional flexible carangiform swimmers with varying stiffnesses and thicknesses, which are driven by the active internal bending moments, and employ the complex orthogonal decomposition and Fourier decomposition methods to quantitatively measure and analyze the proportion of undulation. It is found that standing wave deformation characteristics are prominently observed along fish-like bodies with high stiffness, whereas traveling wave characteristics are more evident in bodies with lower stiffness. The self-propelled fish body demonstrates lateral oscillation and rotation around its center of mass, namely, the heaving and pitching movement, particularly in specimens with high stiffness. The present analysis shows that the heaving and pitching locomotion induced by the fluid significantly increase the traveling wave proportion by modulating the amplitude and phase of the left and right traveling waves viewed in forward frame. We called it fluidic undulation effects (FUE), which is different from the undulation of body deformation. This effect is more pronounced for large stiffnesses and thin airfoils. The standing wave deformation observed with a large stiffness transforms into a traveling wave propulsion pattern, with its traveling wave index even slightly surpassing that of a small-stiffness pattern. Although the efficiency of the standing wave deformation is low, it facilitates a faster forward speed (body lengths per stroke). The positive impact of the FUE on the swimming performance is also confirmed by restricting the recoil motions of the lateral translation and rotation of the body. Furthermore, we observe that there is no undulatory swimming gait that has both the highest energy efficiency and the highest speed.

Comparative Assessment on Unsteady Aerodynamics of Thin and Thick Airfoils Subjected to Pitching Motion

This article presents the comparison between the unsteady flow characteristics of thick (t/c ≥ 6%) and thin (t/c ≤ 6%) airfoils performing pitching motion at Reynolds number Re = 3.6 × 10 5 . For the analysis, the considered airfoils are NACA 0012 as thick and symmetric airfoil and GOE 417A as thin and highly cambered airfoil. The analysis in this study is restricted to only two airfoils because from the preliminary investigations, similar aerodynamic characteristics with slight variation in their flow field development under same conditions were observed. The influence of reduced frequency, pitching amplitude and mean angle of attack on the airfoil’s aerodynamic performance in terms of instantaneous force coefficients is thoroughly investigated. Further, the flow surrounding the airfoils is also investigated. It is noticed that the aforementioned parameters substantially affect the instantaneous force coefficients (both qualitatively and quantitatively). Under certain conditions, the formation of reverse Karman vortex street was observed indicating airfoil’s thrust force generation. It must be noted that the conditions where the thrust force generation occurs for thick and symmetric airfoils like NACA 0012 are quite different from that of thin and cambered airfoils like GOE 417A. Additionally, a drastic change in the flow field around the airfoils is observed under similar conditions. For NACA 0012 airfoil, the formation and convection of the Leading Edge Vortex (LEV) under certain conditions has detrimental effects on its aerodynamic characteristics as it encourages early flow separation. However, the same cannot be true for thin and highly cambered airfoils like GOE 417A. Under the similar conditions with negligible variation, the LEV contributes toward providing extra suction over the GOE 417A airfoil’s suction side. This significantly improves airfoil’s aerodynamic characteristics.

Nonisothermal analysis of two uniform boundary layer shear flows

AbstractThe heat transfer phenomenon on the multiphase flows plays an imperative role in several biological and industrial processes, like the oil production industries, catalytic reactors, energy losses in several thermal systems, energy storage, paper manufacture, and heat exchanger systems. Therefore, this study scrutinized the heat transfer characteristic between two uniform boundary layer shear flows with different strengths flowing in the same direction. This problem involves the simulation of the convergence of boundary layers with varying shear strengths. The nonlinear differential system is scrutinized and converted into dimensionless ordinary differential equations by employing appropriate dimensionless variables. The resulting set of highly nonlinear ordinary differential equations is resolved numerically utilizing the Matlab solver “bvp4c.” The resulting numerical solutions are used to construct graphs that illustrate and elucidate the impact of numerous physical parameters on flow patterns. For both fluids, results for the Nusselt number and shear stress are also presented graphically for various parameters. The acquired results demonstrate that the velocity profile upsurges for both upper and lower fluids by enhancing the shear parameter. Furthermore, the number of streamlines is enhanced by augmenting the values of the viscosities ratio parameter. The present problem applies to the trailing edge flow over a thin airfoil with camber.

An Improved Approach for Reducing the Dimensionality of Wing Aerodynamic Optimization Considering Longitudinal Stability

The wing aerodynamic shape optimization is a typical high-dimensional problem with numerous independent design variables. Researching methods to reduce the dimensionality of optimization from the perspective of aerodynamic characteristics is necessary. One traditional aerodynamic-based approach decouples the wing’s camber and thickness according to the thin airfoil theory, but it has limitations due to unclear application scope and effectiveness. This paper proposes an improved approach that determines the values of certain thickness variables based on a data-driven aerodynamic characteristics model before optimization, which considers longitudinal stability. By reducing the number of design variables, the dimensionality of optimization is decreased effectively. The derivation of the improved approach is accomplished through the design of experiments, parametric modeling, computational fluid dynamics, and sensitivity analysis. The effectiveness of the improved approach is validated by applying it to the aerodynamic optimization of an ONERA-M6 wing in subsonic flow based on the surrogate-based optimization algorithm. The results demonstrate that the improved approach significantly accelerates the optimization process while maintaining global effectiveness.

Static Aeroelastic Research of Supersonic Wing

The thin airfoil design and the supersonic flight condition make the aeroelastic deformation have an important effect on the aerodynamic characteristics of the supersonic aircraft. In this paper, a supersonic Unmanned Aerial Vehicle (UAV) wing is taken as the research object, and the static aeroelastic weak coupling calculation method (CFD/CSD) is used to carry out the modification of the aerodynamic coefficient of the wing. The analysis results show that the aeroelastic deformation reduces the lift coefficient, and the pitch moment produces a head-up increment. At the same time, the aerodynamic focus of the wing moves forward, which reduces the static stability margin of the aircraft. The influence of aeroelastic deformation on aerodynamic characteristics increases with increasing Mach number.

Impact of Aerodynamic Modeling Assumptions on Flutter Speeds of Vertical-Axis Wind Turbines

Theodorsen’s unsteady aerodynamic theory has been used extensively in flutter speed prediction of wind turbine blades. In this study, three key assumptions of Theodorsen theory (thin airfoil, flat wake, and small angle of attack) have been revisited, and all three assumptions have been addressed in combination to obtain new lift and moment equations that are subsequently applied in flutter calculations for full-scale vertical-axis wind turbine (VAWT) rotors, not just of an individual airfoil or blade. Furthermore, edgewise aerodynamics terms are added to the lift and moment equations to include their effects on flutter speeds. The newly obtained equations were implemented in the OWENS (Offshore Wind ENergy Simulation) toolkit, which is an FEM (Finite Element Method)-based toolkit for aeroelastic analysis of VAWTs. The effect of modifying each of these assumptions has been studied for the flutter RPM prediction of three primary modes of flutter of VAWTs: propeller, butterfly, and tower modes. For the land-based case, the most change was observed for the flutter RPM of the propeller mode, with a maximum increase of 2.62% for the two-bladed UTD 5 MW VAWT case. For the floating offshore case, the primary flutter modes (tower and platform pitch) were not significantly affected.

Numerical study of inflow turbulence distortion and noise for airfoils

In this work, the interaction of grid-generated turbulence with airfoils of different thicknesses, namely, a National Advisory Committee for Aeronautics (NACA) 0008 and a NACA 0018, is investigated, leading to a deeper understanding of the influence of the airfoil geometry on the near-field flow and on the far-field pressure fluctuations. Experimentally validated lattice-Boltzmann simulations are used to analyze the flow properties in the leading-edge (LE) vicinity. The analysis of the velocity fluctuations near the LE shows that momentum is transferred from the streamwise to the transverse velocity for the NACA 0008 airfoil interacting with a large turbulence length scale. This mechanism changes with the increase in the airfoil thickness because the inflow turbulence length scale becomes comparable to the airfoil thickness in the LE region, resulting in a higher concentration of vortices near the LE oriented in the transverse direction, creating high-velocity fluctuations in the spanwise direction. The near- and far-field pressure fluctuations are analyzed to understand the impact of the inflow turbulence distortion on these parameters and the limitations of analytical methods for real airfoils. Results show that the wall-pressure fluctuations are affected by the turbulence distortion in the LE region. Thick airfoils have noise directivity patterns significantly different compared to the Amiet predictions for higher frequencies, radiating higher noise levels upstream of the LE than the thin airfoil. This is likely associated with a drastic change in the pressure fluctuation distribution near the airfoil LE region, attributed to the change in the distortion of the vortical structures in the LE area.

Influence of the Blunt Trailing-Edge Thickness on the Aerodynamic Characteristics of the Very Thick Airfoil

In this paper, the NWT600 airfoil with a thickness ratio of 60% is taken as the research object. The aerodynamic performance of the airfoil is analyzed by experiments and numerical simulations. The results simulated by various turbulence models used in the 2D steady-state RANS method are compared, including the Spalart–Allmaras model, k-ω SST model, k-ε realizable model, and Reynolds stress (linear pressure-strain) model. The influence of blunt trailing-edge thickness on aerodynamic characteristics is studied by adding thickness symmetrically. The results show that even under the low subsonic flow with a Mach number of 0.149, the airflow is prone to severe separation. The aerodynamic performance of the airfoil is very different from that of the conventional thin airfoil. Although the 2D steady-state RANS models overestimate the pressure on the surface of the airfoil in most cases, it is qualitatively acceptable to predict the pressure distribution of the very thick airfoil. Numerical results simulated by the Reynolds stress model are in the best agreement with the experimental data. It is also found that symmetrically thickening the trailing edge effectively improves the maximum lift coefficient and reduces the drag coefficient at a small angle of attack.

Exact momentum sources for gust injection in flow simulations

Vortical gusts are unsteady flow disturbances that can affect the aerodynamic performance and stability of aircraft. Generating realistic vortical gusts in flow simulations is challenging due to the complexity and diversity of turbulence characteristics. This paper introduces a novel framework for creating vortical gusts in flow simulations using momentum sources. The method can manipulate the incoming flow with any desired divergence-free velocity perturbation at any location and avoid unwanted acoustic waves in the meanwhile. It starts from a linearized incompressible momentum equation without viscous effects. The equation has a frequency-domain representation, which is an ordinary differential equation and easy to solve. Then, several conditions are imposed to determine unknown coefficients. Expressions of source terms producing one-dimensional and two-dimensional gusts are obtained. The generated velocity field is compared to the specified gust and shows outstanding agreement. Several parameters that affect the distribution of added sources are systematically studied to find a combination that can provide optimal performance in various scenarios. Finally, the model is used to assess the aerodynamic interaction of a vortical gust and thin airfoils. The results agree well with the analytical solutions provided by the Sears model.

Study on Airfoils and Aerodynamics of High-Speed Aircraft Propeller

To boost the aerodynamics of high-speed aircraft propellers, the lift-to-drag (L/D) ratio variation law and the Mach number contour distribution of flat-convex airfoil NACA4412, supercritical airfoil RAE2822 and thin airfoil at a high Reynolds number NACA65206 at different Mach numbers (Ma) and angles of attack (AoA) are investigated through computational fluid dynamics (CFD). After analyzing the lift and drag characteristics of the three airfoils, NACA65206 is selected to design a high-speed aircraft propeller. Then the flow field of the designed propeller is simulated through CFD, and its aerodynamic performance is calculated. The results show that NACA65206 exhibits a higher L/D ratio and gentler stall if the Mach number increases from 0.5 to 0.9. The designed propeller with NACA65206 is found to have propulsive efficiency exceeding 80% at Mach 0.6 in flight, and the value is over 75% when the Mach number in flight is 0.7. These values suggest that the high-speed aircraft propeller designed with a thin airfoil and a large back-swept angle exhibits satisfactory propulsive efficiency.

Wall-pressure spectra, spanwise correlation, and far-field noise measurements of a NACA 0008 airfoil under uniform and turbulent inflows

This paper discusses unique measurements of wall-pressure fluctuations (WPFs), spanwise correlation length, and far-field noise of a NACA 0008 airfoil subjected to uniform, non-turbulent and turbulent inflows. From these measurements, the near-field characteristics of trailing-edge (TE) and leading-edge (LE) noise of a thin airfoil are analyzed. The competing nature of the LE and TE noise mechanisms of an airfoil subjected to a turbulent inflow is also investigated. Experiments were performed in the Aeroacoustic Wind Tunnel of the University of Twente for a chord-based Reynolds number ranging from 3.2×105 to 9×105 for a uniform inflow and a rod-generated turbulent inflow with a turbulence intensity of approximately 18%. The effective angles of attack ranged from -5∘ to 5∘. Measurements of the boundary layer at the TE, the WPFs along the chord and span, and the far-field radiated noise were performed. For the uniform inflow case, laminar-boundary-layer noise, turbulent-boundary-layer (TBL) noise, and blunt TE noise sources are identified. The far-field noise spectrum presents similar components in the frequency domain as the WPF spectrum and the spanwise correlation length at the TE. The angle of attack mainly affects the WPF spectrum and spanwise correlation length for chord-based Strouhal numbers St<10. The angle of attack slightly affects the TE noise with a maximum variation of 3 dB for 10<St<60. For the turbulent inflow case, it is observed that the turbulence significantly affects the WPFs and spanwise correlation length along the chord, increasing considerably compared to the case of uniform inflow. The highest WPF spectral level and the larger spanwise correlation length occur at positions close to the LE. The results show that the turbulent inflow yields a higher WPF spectral level and larger spanwise correlation length at the TE, resulting in higher levels of TE noise. However, LE noise is still the dominant noise source for St<25.2. For higher frequencies, the TE noise level is expected to become higher than the LE noise level.

Unsteady Propulsion of a Two-Dimensional Flapping Thin Airfoil in a Pulsating Stream

The cruising velocity of animals, or robotic vehicles, that use flapping wings or fins to propel themselves is not constant but oscillates around a mean value with an amplitude usually much smaller than the mean, and a frequency that typically doubles the flapping frequency. Quantifying the effect that these velocity fluctuations may have on the propulsion of a flapping and oscillating airfoil is of great relevance to properly modeling the self-propelled performance of these animals or robotic vehicles. This is the objective of the present work, where the force and moment that an oscillating stream exerts on a two-dimensional pitching and heaving airfoil are obtained analytically using the vortical impulse theory in the linear potential flow limit. The thrust force of the flapping airfoil in a pulsating stream in this limit is obtained here for the first time. The lift force and moment derived here contain new terms in relation to the pioneering work by Greenberg (1947), which are shown quantitatively unimportant. The theoretical results obtained here are compared with existing computational data for flapping foils immersed in a stream with velocity oscillating sinusoidally about a mean value.

Geometrically nonlinear effects in wing aeroelastic dynamics at large deflections

This paper investigates geometrically nonlinear effects due to nonlinear kinematics and follower aerodynamics in the aeroelastic dynamics of a very flexible wing. The test case is the Pazy wing, a benchmark wing model for geometrically nonlinear aeroelastic studies involving large deflections in low-speed flow. The work builds on a low-order model of the wing composed of a geometrically nonlinear beam coupled with potential flow thin airfoil theory. Nonfollower aerodynamics underestimates static deflections by up to 10%, whereas linear kinematics overestimates them by up to 50%. At low static deflections, the wing hump mode flutter mechanism is driven by three-dimensional unsteady aerodynamic effects. As static deflections increase, the flutter onset and offset speeds are driven by curvature effects that can only be captured by nonlinear kinematics, which reduce the natural frequencies associated with torsion and in-plane bending motions. Follower aerodynamics shrinks the hump mode instability region and shifts it to 1–4% lower flow speeds with no change in the flutter frequency, the qualitative trends, and the amplitude of limit-cycle oscillations. Overall, nonlinear kinematics is the primary geometrical nonlinearity influencing the wing aeroelastic behavior: the modal and stability scenarios with and without follower aerodynamics collapse onto the same curves when presented as functions of the tip deflection. However, geometrical nonlinearities alone miss the subcritical nature of the hump mode flutter mechanism, which is attributed to aerodynamic stall and its interaction with large deflections. This work expands the growing literature on the aeroelastic dynamics of very flexible wings and will ease future studies considering aerodynamic nonlinear effects.

The effect of airfoil elasticity on quasistatic aerodynamics and divergence

Shape-morphing airfoils are of interest due to their benefits for aerodynamic efficiency and commonly involve chordwise elasticity of the airfoil. We aim to examine the influence of chordwise elasticity on the aerodynamic properties and stability in the quasistatic limit. We model a shape-morphing airfoil as two, rear and front, Euler–Bernoulli beams connected to a rigid support at an arbitrary location along its chord. This setup is mounted on a torsion spring and is exposed to a uniform flow. We model aerodynamic forces acting on the wing via thin airfoil theory and obtain the solution of the elastic deflection via regular asymptotic expansions. Then, we substitute this result into the moment balance equation to find the rotation angle. This procedure allows us to examine the influence of chord-wise elasticity on the lift, aerodynamic center, twist angle, and the onset of divergence. We examine these results in terms of the elastic axis location and the dimensionless ratio between aerodynamic moment to bending stiffness. The lift curve slope is smaller than 2π up to the hinge location of about 0.53 chord and is greater than 2π elsewhere. The chord-wise elasticity moves the aerodynamic center forwards and increases the twist angle. In addition, chord-wise elasticity is found to increase the onset of divergence relative to the rigid case. Moreover, unlike the rigid case, divergence also exists for hinges in the front quarter chord. Finally, we present several possible cases of an actuated airfoil validated by numerical simulations.