Flexible Wing Model Research Articles

Analysis of additively manufactured flexible wing model

PurposeThis paper aims to assess the feasibility of additively manufactured wind tunnel models. The additively manufactured model was used to validate a computational framework allowing the evaluation of the performance of five wing models.Design/methodology/approachAn optimized fighter wing was additively manufactured and tested in a low-speed wind tunnel to obtain the aerodynamic coefficients and deflections at different speeds and angles of attack. The flexible wing model with optimized curvilinear spars and ribs was used to validate a finite element framework that was used to study the aeroelastic performance of five wing models. As a computationally efficient optimization method, homogenization-based topology optimization was used to generate four different lattice internal structures for the wing in this study. The efficiency of the spline-based optimization used for the spar-rib model and the lattice-based optimization used for the other four wings were compared.FindingsThe aerodynamic loads and displacements obtained experimentally and computationally were in good agreement, proving that additive manufacture can be used to create complex accurate models. The study also shows the efficiency of the homogenization-based topology optimization framework in generating designs with superior stiffness.Originality/valueTo the best of the authors’ knowledge, this is the first time a wing model with curvilinear spars and ribs was additively manufactured as a single piece and tested in a wind tunnel. This research also demonstrates the efficiency of homogenization-based topology optimization in generating enhanced models of different complexity.

Wing dynamic shape-sensing from fiber-optic strain data using the Kalman state estimator

A novel method for shape sensing based on strain data and the use of the Kalman state estimator is presented and studied experimentally. Several recent studies proposed different methods in which strain data, measured in optical fibers, can be used to estimate the deformed shape of a flexible wing. Fiber optic sensors typically provide accurate, high resolution, strain data, yielding detailed prediction of a wing's deformed shape. However, in real life applications there could be moments in which the strain data is imperfect (for example, due to saturation or temperature effects), corrupted, or missing. The current study proposes to use a Kalman state estimator that weighs in strain-data and simulation output of an aeroelastic plant model to estimate the wing deformations. The method is demonstrated with a flexible wing model that is excited by prescribed control surfaces deflection in a wind-tunnel test. Strains over the front and rear wing spars are measured by Fiber Bragg Grating sensors, embedded in two optical fibers, and used to estimate the wing deformations. The latter are compared to wing deformations measured by a motion recovery camera system. Results show the advantages of the use of the Kalman state estimator when the strain data is corrupted. Additionally, with this approach, wing's modal velocities are estimated together with the wing deformations, resulting in smooth and accurate modal velocities that are readily usable by the vehicle's control system.

Nonintrusive Experimental Aeroelastic Analysis of a Highly Flexible Wing

The aeroelastic response of the Delft–Pazy wing to steady and periodic unsteady inflow conditions is analyzed experimentally. The Delft–Pazy wing is a highly flexible wing model based on the benchmark Pazy wing (Avin, O., Raveh, D. E., Drachinsky, A., Ben-Shmuel, Y., and Tur, M., “Experimental Aeroelastic Benchmark of a Very Flexible Wing,” AIAA Journal, Vol. 60, No. 3, 2022, pp. 1745–1768) and exhibits wingtip displacements of more than 24% of the span in the present study. The nonintrusive measurements are performed with an integrated optical approach that provides combined measurements of the structural response of the wing and the unsteady flowfield around it. The aeroelastic loads acting on the wing are derived using physical models and validated against force balance measurements, showing a good agreement for all considered inflow conditions. The analysis of the aeroelastic response of the wing to the unsteady inflow produced by a gust generator shows that both structural and aerodynamic responses depend strongly on the frequency of the gust. The results of this study provide a characterization of the aeroelastic behavior of the Delft–Pazy wing and can serve as a reference for the development of novel and improved nonlinear aeroelastic simulation models.

Active flutter suppression for a flexible wing model with trailing-edge circulation control via reinforcement learning

Previous attempts at active flutter suppression have been based on driving the deflection of multiple pairs of discontinuous mechanical control surfaces. Here, we explore the effects of trailing-edge Circulation Control (CC) for flutter control on flexible wings. To avoid the problem that the nonlinear aeroelastic model is difficult to establish accurately, we trained a closed-loop control strategy based on the model-free deep reinforcement learning algorithm through aeroelastic wind tunnel testing. The results show that the strategy can intelligently select the appropriate jet intensity according to the real-time state of the flexible wing. The oscillation amplitude of flutter can be reduced by 92%. The air consumption required for unsteady CC to suppress flutter is reduced by 37% compared to steady CC. This study aims to provide an innovative control method and strategy for active flutter suppression of large aspect ratio flexible wings.

Computational aerodynamics of insect flight using volume penalization

The state-of-the-art of insect flight research using advanced computational fluid dynamics techniques on supercomputers is reviewed, focusing mostly on the work of the present authors. We present a brief historical overview, discuss numerical challenges and introduce the governing model equations. Two open source codes, one based on Fourier, the other based on wavelet representation, are succinctly presented and a mass-spring flexible wing model is described. Various illustrations of numerical simulations of flapping insects at low, intermediate and high Reynolds numbers are presented. The role of flexible wings, data-driven modeling and fluid–structure interaction issues are likewise discussed.

Flutter Tests of the Pazy Wing

The paper presents the flutter and limit-cycle oscillation (LCO) tests of the Pazy wing, a very flexible wing model designed to study aeroelastic phenomena associated with nonlinear geometry and provide data for nonlinear aeroelastic model validation. The Pazy wing model, analyses, and data from earlier aeroelastic tests are provided by Avin et al. (“Experimental Aeroelastic Benchmark of a Very Flexible Wing,” AIAA Journal, 2022, pp. 1–24). In the current study, three velocity sweeps were performed at different angles of attack (AoA), during which the wing entered and exited limit-cycle oscillations (LCO). A motion-recovery camera system and fiber-optics Bragg grating sensors were used to track the deformations and strains over the wingspan. The wing encountered LCO when the wingtip deformation was approximately 25% of the span. The onset velocity, frequency, and mode shape varied, depending on the test’s AoA. The paper first focuses on the onset of the oscillations, where the onset velocity and oscillation mode-shapes are analyzed. The paper then continues to investigate the LCO characteristics and the nonlinear behavior of the wing. The wing models and experimental data are publicly available through the Third Aeroelastic Prediction Workshop.**

Vibration control studies of a high-aspect-ratio wing with geometric nonlinearity

Many challenges of vibration problems due to structure nonlinearity are growing while high-aspect-ratio wings are being widely used. Feasible vibration control method is an effective way to decrease such challenges. At the beginning, a new high-aspect-ratio flexible wing model with swept-back angle and control surface was designed and manufactured. Numerical simulation was employed to find basic dynamic characteristics of the wing. Ground experiments could provide vibration test results of this wing. The numerical method of computational flutter velocity of the wing including geometric nonlinearity was applied to study this wing. Then the open-loop flutter dynamic pressure and the closed-loop flutter speed were compared, it is found that the control law designed by linear quadratic Gaussian theory can increase the flutter speed of the present geometric nonlinear wing model. The computational results of flutter vibration show that the geometric nonlinear flutter speed is lower than the linear flutter speed, and the change in torsional mode is the critical reason for the decrease in flutter speed. Both numerical and experimental method proposed in this paper could be applied to predict the approximate flutter effect of such complex elastic high-aspect-ratio wing via structural nonlinearity.

Experimental Aeroelastic Benchmark of a Very Flexible Wing

The paper presents the design, analyses, and testing of the Pazy wing, a very flexible wing model that was designed to study aeroelastic phenomena associated with geometrically nonlinear deflections and to provide data for validation of nonlinear aeroelastic simulation models. The Pazy wing is made of a main thin aluminum spar and a Nylon 12 printed ribs chassis providing the NACA0018 aerodynamic airfoil shape. The wing was covered entirely with a polyester film that serves as the skin. Static loading tests were used for model adaptation and to assure that the wing can deform to over 50% of its span without failing. Ground vibration tests were also used for model adaptation. Because there are uncertainties in the characteristics of the polyester skin under loads, both the static and ground vibration tests were used to asses the contribution of the skin to the wing’s stiffness and determine the stiffness bound with and without the skin. Wind-tunnel tests were conducted at conditions that lead to static and unsteady structural responses. The wing deformations were tracked by a motion recovery system, and the strains over the wingspan were recorded with a Bragg-grating fiber-optics system. In the static wind-tunnel tests, the aerodynamic loads were recorded by a force balance. The wind-tunnel tests included angle-of-attack sweeps in constant airspeed and velocity sweeps in fixed angle of attack. The largest wing-tip static deformation recorded in test was of 50% span. In the velocity-sweep tests, the wing showed strong oscillations at a velocity at which the wing-tip deformation was approximately 25% of the span and became stable again at higher speeds. The wing models and test data are publicly available through the 3rd Aeroelastic Prediction Workshop (https://nescacademy.nasa.gov/workshops/AePW3/public).

Geometrically nonlinear aeroelastic characteristics of highly flexible wing fabricated by additive manufacturing

Additive manufacturing technology has a potential to improve manufacturing costs and may help to achieve high-performance aerospace structures. One of the application candidates would be a wind tunnel wing model. A wing tunnel model requires sophisticated designs and precise fabrications for accurate experiments, which frequently increase manufacturing cost. In this paper, manufacturing accuracy and aeroelastic characteristics of an additively manufactured wing model are evaluated numerically and experimentally. The feasibility of such wings to use in wind tunnel tests is also demonstrated. In addition, a geometrically nonlinear aeroelastic analysis model, which have been developed in the previous study, is validated for static calculations by comparing with results of the wind tunnel test for the additively manufactured highly flexible wing model.

Aeroelastic Control and Estimation with a Minimal Nonlinear Modal Description

Modal-based nonlinear moving horizon estimation (MHE) and model predictive control (MPC) strategies for very flexible aeroelastic systems are presented. They are underpinned by an aeroelastic model built from a one-dimensional intrinsic (based on strains and velocities) description of geometrically nonlinear beams and an unsteady vortex lattice aerodynamic model. Construction of a nonlinear modal-based reduced-order model of the aeroelastic system, employing a state-space realization of the linearized aerodynamics around an arbitrary reference point, allows us to capture the main nonlinear geometrical couplings at a very low computational cost. Embedding this model in both MHE and MPC strategies, which solve the system continuous-time adjoints efficiently to compute sensitivities, lays the foundations for real-time estimation and control of highly flexible aeroelastic systems. Finally, the performance and versatility of the framework operating in the nonlinear regime are demonstrated on two very flexible-wing models, with notably different dynamics, and on two different control setups: a gust-load alleviation problem on a very high-aspect-ratio wing with slower dynamics, which involves substantial deflections; and flutter suppression on a flexible wing with significantly faster dynamics, where an unconventional nonlinear stabilization mechanism is unveiled.

Large Deformation Modeling of Wing-Like Structures Based on Support Vector Regression

Large flexible aircrafts produce large deformation during flight, leading to obvious geometric nonlinearities. Large deformation modeling is essential for modern aircraft design. Calculation of large deformation based on a full-order model often carries an unbearable computing burden. The reduced-order model (ROM) can be efficient in calculation but requires lots of test datasets. This study investigates support vector regression (SVR) to build a regression model to calculate the static large deformation of wing-like structures. The correlation coefficient (R) and root mean square error (RMSE) are used to evaluate the performance of the regression models. In contrast to the ROM that has been proposed, the regression model based on SVR requires far fewer training cases, with almost the same accuracy in this research. Meanwhile, comparison with another prediction model built based on random forest regression (RFR) has also been reported. The results reveal that the SVR algorithm has better accuracy on this issue. Finally, ground test results of a real large flexible wing model show that the regression model proposed here reaches a good agreement with measurement data under applied load. This work illustrates that the machine learning algorithm is an efficient and accurate way to predict large deformation of aircrafts.

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

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

A mass-spring fluid-structure interaction solver: Application to flexible revolving wings

The secret to the spectacular flight capabilities of flapping insects lies in their wings, which are often approximated as flat, rigid plates. Real wings are however delicate structures, composed of veins and membranes, and can undergo significant deformation. In the present work, we present detailed numerical simulations of such deformable wings. Our results are obtained with a fluid–structure interaction solver, coupling a mass–spring model for the flexible wing with a pseudo-spectral code solving the incompressible Navier–Stokes equations. We impose the no-slip boundary condition through the volume penalization method; the time-dependent complex geometry is then completely described by a mask function. This allows solving the governing equations of the fluid on a regular Cartesian grid. Our implementation for massively parallel computers allows us to perform high resolution computations with up to 500 million grid points. The mass–spring model uses a functional approach, thus modeling the different mechanical behaviors of the veins and the membranes of the wing. We perform a series of numerical simulations of a flexible revolving bumblebee wing at a Reynolds number Re=1800. In order to assess the influence of wing flexibility on the aerodynamics, we vary the elasticity parameters and study rigid, flexible and highly flexible wing models. Code validation is carried out by computing classical benchmarks.

Analytical sensitivity analysis of flexible aircraft with the unsteady vortex-lattice aerodynamic theory

The unsteady vortex-lattice method provides a medium-fidelity tool for calculation of low-speed aerodynamic loads based on the potential-flow theory. It has long been favored in research on the aeroelasticity and flight dynamics for flexible aircraft with high aspect ratios. However, the unsteady vortex-lattice method is established in the discrete time domain which brings difficulties to modeling aeroelastic system for stability analysis. An analytical aerodynamic sensitivity calculation scheme is developed in this paper to formulate the aeroelastic equations of motion with UVLM aerodynamics. A free wake model is used to simulate accurate vortex shedding and subsequent wake propagation. Using a small perturbation method, the aerodynamic governing equations are linearized around the equilibrium condition, where the analytical sensitivities can be derived. The surface spline interpolation algorithm is adopted to implement the structure-aerodynamic coupling. Both aerodynamic sensitivities with respect to structural motions and circulation strengths of vortices are obtained. In numerical studies, a time-marching transient response analysis scheme is used to obtain the distributed aerodynamic loads and structural deformations. Analytical sensitivity results are validated by the finite difference method. The proposed analytical sensitivity calculation framework is demonstrated to be applicable to commonly used beam-based flexible wing models, as well as the shell-based finite element models with higher fidelity. The derived sensitivity formulations and related numerical implementations can build the foundation for further studies on aeroelastic optimization and stability analysis.

Wing flexibility reduces the energetic requirements of insect flight

Flapping insect wings deform under aerodynamic as well as inertial-elastic forces. This deformation is thought to improve power economy and reduce the energetic costs of flight. However, many flapping wing models employ rigid body simplifications or demand excessive computational power, and are consequently unable to identify the influence of flexibility on flight energetics. Here, we derive a reduced-order model capable of estimating the driving torques and corresponding power of flapping, flexible insect wings. We validate this model by actuating a tobacco hornworm hawkmoth Manduca sexta (L.) forewing with a custom single-degree-of-freedom mechanical flapper. Our model predicts measured torques and instantaneous power with reasonable accuracy. Moreover, the flexible wing model predicts experimental trends that rigid body models cannot, which suggests compliance should not be neglected when considering flight dynamics at this scale. Next, we use our model to investigate flight energetics with realistic flapping kinematics. We find that when the natural frequency of the wing is roughly three times that of the flapping frequency, flexibility can reduce energy expenditures by almost 25% compared to a rigid wing if negative work is stored as potential energy and subsequently released to do positive work. The wing itself can store about 30% of the 1200 J of total energy required over a wingbeat. Peak potential energy storage occurs immediately before stroke reversal. We estimate that for a moth weighing 1.5–2.5 g, the peak instantaneous power required for flight is 75–125 W kg−1. However, these peak values are likely lower in natural insect flight, where the wing is able to exchange strain energy with the compliant thorax. Our findings highlight the importance of flexibility in flapping wing micro aerial vehicle design and suggest tuned flexibility can greatly improve vehicle efficiency.

Boundary feedback stabilization of a flexible wing model under unsteady aerodynamic loads

This paper addresses the boundary stabilization of a flexible wing model, both in bending and twisting displacements, under unsteady aerodynamic loads, and in presence of a store. The wing dynamics is captured by a distributed parameter system as a coupled Euler–Bernoulli and Timoshenko beam model. The problem is tackled in the framework of semigroup theory, and a Lyapunov-based stability analysis is carried out to assess that the system energy, as well as the bending and twisting displacements, decay exponentially to zero. The effectiveness of the proposed boundary control scheme is evaluated based on simulations.

Robust Switching Control and Subspace Identification for Flutter of Flexible Wing

Active flutter suppression and subspace identification for a flexible wing model using micro fiber composite actuator were experimentally studied in a low speed wind tunnel. NACA0006 thin airfoil model was used for the experimental object to verify the performance of identification algorithm and designed controller. The equation of the fluid, vibration, and piezoelectric coupled motion was theoretically analyzed and experimentally identified under the open‐loop and closed‐loop condition by subspace method for controller design. A robust pole placement algorithm in terms of linear matrix inequality that accommodates the model uncertainty caused by identification deviation and flow speed variation was utilized to stabilize the divergent aeroelastic system. For further enlarging the flutter envelope, additional controllers were designed subject to the models beyond the flutter speed. Wind speed was measured online as the decision parameter of switching between the controllers. To ensure the stability of arbitrary switching, Common Lyapunov function method was applied to design the robust pole placement controllers for different models to ensure that the closed‐loop system shared a common Lyapunov function. Wind tunnel result showed that the designed controllers could stabilize the time varying aeroelastic system over a wide range under arbitrary switching.

The effect of wing flexibility on sound generation of flapping wings

In this study, the unsteady flow and acoustic characteristics of a three-dimensional (3D) flapping wing model of a Tibicen linnei cicada in forward-flight are numerically investigated. A single cicada wing is modelled as a membrane with a prescribed motion reconstructed from high-speed videos of a live insect. The numerical solution takes a hydrodynamic/acoustic splitting approach: the flow field is solved with an incompressible Navier–Stokes flow solver based on an immersed boundary method, and the acoustic field is solved with linearized perturbed compressible equations. The 3D simulation allows for the examination of both the directivity and frequency compositions of the flapping wing sound in a full space. Along with the flexible wing model, a rigid wing model that is extracted from real motion is also simulated to investigate the effects of wing flexibility.The simulation results show that the flapping sound is directional; the dominant frequency varies around the wing. The first and second frequency harmonics show different radiation patterns in the rigid and flexible wing cases, which are demonstrated to be highly associated with wing kinematics and loadings. Furthermore, the rotation and deformation in the flexible wing is found to help lower the sound strength in all directions.

Aeroelastic Optimization Design for High-Aspect-Ratio Wings with Large Deformation

This paper presents a framework of aeroelastic optimization design for high-aspect-ratio wing with large deformation. A highly flexible wing model for wind tunnel test is optimized subjected to multiple aeroelastic constraints. Static aeroelastic analysis is carried out for the beamlike wing model, using a geometrically nonlinear beam formulation coupled with the nonplanar vortex lattice method. The flutter solutions are obtained using the P-K method based on the static equilibrium configuration. The corresponding unsteady aerodynamic forces are calculated by nonplanar doublet-lattice method. This paper obtains linear and nonlinear aeroelastic optimum results, respectively, by the ISIGHT optimization platform. In this optimization problem, parameters of beam cross section are chosen as the design variables to satisfy the displacement, flutter, and strength requirements, while minimizing wing weight. The results indicate that it is necessary to consider geometrical nonlinearity in aeroelastic optimization design. In addition, optimization strategies are explored to simplify the complex optimization process and reduce the computing time. Different criterion values are selected and studied for judging the effects of the simplified method on the computing time and the accuracy of results. In this way, the computing time is reduced by more than 30% on the premise of ensuring the accuracy.

Effects of wing flexibility on bumblebee propulsion

This study provides a comprehensive analysis of the effects of flexibility on bumblebee propulsion. The unusual stiffness distribution of bumblebee wings caused by the absence of veins on their outer one-third region is analyzed for the first time, with two flexible-wing models and one rigid-wing model tested in two-way Fluid-Structure Interactions (FSI) simulations. The two flexible-wing models are the uniform stiffness model in which the whole area (100%) of the wing is flexible and the reduced tip-stiffness model in which the tip region (30% of the total wing area) is more flexible than the rest of the wing. The rigid wing has been found to have the highest power economy (ratio of lift to input power), with the uniform- and reduced tip-stiffness wings being 7% and 15% less economical, respectively. The rigid wing produces drag, while both flexible-wing models produce thrust with a difference of approximately 3%. In forward flight, the positive thrust clearly highlights the importance of flexibility for the aerodynamic performance and propulsion of a bumblebee which will be unable to fly forward if its wings are modeled as rigid bodies.