Aeroelastic Wing Research Articles

LMI feasibility analysis of 2DOF NATA model

AbstractPresent paper shows the different types of tensor product model based linear matrix inequality controller design and feasibility analysis of two degrees of freedom aeroelastic wing section model. The tensor product models are based on reducing or removing the nonlinear behavior of the system and weighting functions. The linear matrix inequality based method results globally asymptotically stable system. The goal of the paper is to examine that selecting and varying the transformation space influences the feasibility of the linear matrix inequality based controller. The paper gives a comparison between the different tensor product models in terms of controller performance. The linear matrix inequality gives feasible solution for the controller design if the transformation space is selected adequately.

Free wake panel method simulations of a highly flexible wing in flutter and gusts

This paper presents low speed fluid structure interaction simulations of a highly flexible wing at various flow conditions, including flutter and excitation from sinusoidal gusts. Such wings are becoming more relevant in recent years, due to their potential for improving aerodynamics and reducing weight, while their flutter characteristics are particularly challenging to address, as the modal properties of the wings change as deflections increase. Calculations are based on time domain coupling of a geometrically exact beam structural model and a 3D free wake panel method, modeling the outer surface of the wing, which allow for nonlinear effects in terms of geometrical deformations and the flow at low computational cost. Static and aeroelastic wing deflections are in line with experimental data of the Pazy wing, which is a benchmark for highly flexible wings from Technion. Two flutter mechanisms are predicted within 1 to 3 m/s of the experimental range. An analysis of the flutter modes is performed, showing that the second torsion mode plays a role in flutter, something that had not been published before. Limit cycle oscillations are achieved and are shown to compare well with reference data, with the frequency being within 1% of the experimental value. Finally, results of gust simulations of the Pazy wing are compared to data from experiments and corrections for the wind tunnel measurements are proposed, which should facilitate future validation efforts. This work serves as a contribution to the Pazy wing dataset and is a step towards mid-fidelity simulations for more complex configurations.

Conceptual Design of a Robotic Ground-Aerial Vehicle with an Aeroelastic Wing Model for Mars Planetary Exploration

This paper presents the technical barriers and an analysis to advance the conceptual development of novel robotic ground-aerial vehicles (RGAVs) for exploration missions to Mars prior to human arrival and the establishment of a base. The concept for RGAVs for Mars planetary exploration is novel, and will require innovations that are at various stages of development or use by the aerospace community. The RGAV concept will utilize inflatable wing technology, which increases the flexibility of the wing, and thus the possibility of structural dynamic instabilities that must be studied in the context of the Martian atmosphere. An aeroelastic model for wing bending is proposed, which considers wind gusts where the change in wind direction is up to ±6° from the mean, and a turbulence intensity of up to 20%. Their effect on the bending displacement of a semi-elastic wing is quantified, resulting in a maximum wing tip displacement of 16.2 cm. Low-fidelity computational aerodynamic analysis is performed using OpenVSP (3.31.1, NASA, Washington, DC, USA) to compute mean aerodynamic loads during cruise conditions at a cruise Mach number of 0.70. Finally, a non-linear adaptive control system is proposed for the longitudinal aerial dynamics and a proportional integral derivative (PID) controller is outlined for the ground roving lateral dynamics.

Function Approximation Technique (FAT)-Based Adaptive Feedback Linearization Control for Nonlinear Aeroelastic Wing Models Considering Different Actuation Scenarios

Function Approximation Technique (FAT)-Based Adaptive Feedback Linearization Control for Nonlinear Aeroelastic Wing Models Considering Different Actuation Scenarios

Enhanced nonlinear state–space identification for efficient transonic aeroelastic predictions

Transonic aerodynamic systems exhibit strong nonlinearities due to various factors such as flow separations and shock wave oscillations. Thus, transonic aerodynamic modeling methods based on system identifications have attracted increasing attention. However, the dimensions of the models constructed via the current system identification methods are so high that it is difficult to predict transonic flutters and limit cycle oscillations simultaneously. This paper proposes an enhanced nonlinear state–space modeling method to identify a two-dimensional aerodynamic system in the transonic region. At first, the parsimonious linear model with modified inputs is identified by using the eigensystem realization algorithm. The model order is reduced by substituting the generalized displacement of the first-order mode (dominated by plunge) with its generalized velocity in the inputs. The polynomial functions are then used to represent the nonlinearities in the transonic aerodynamic systems. The polynomial functions do not contribute to the system linearization around the equilibrium such that the linear and nonlinear modeling stages are independent. The coefficients of these nonlinear terms are determined via nonlinear optimization. Finally, a nonlinear aerodynamic model is established and applied to aeroelastic applications. To demonstrate the accuracy and efficiency of this method, a two-dimensional, transonic aeroelastic wing with an NACA0012 profile is investigated. The simulation results show that the nonlinear state–space model with modified inputs improves the efficiency and accuracy of transonic aerodynamic nonlinear modeling. Moreover, the aerodynamic model coupled with the structural model can accurately predict the transonic flutter boundary and limit cycle oscillations.

Frequency-Domain Lifting-Line Aerodynamic Modelling for Wing Aeroelasticity

A frequency-domain lifting-line solution algorithm for the prediction of the unsteady aerodynamics of wings is presented. The Biot–Savart law is applied to determine the normalwash generated by the wake vorticity distribution, whereas steady and unsteady airfoil theories (Glauert’s and Theodorsen’s, respectively) are used to evaluate the sectional aerodynamic loads, namely the lift and pitching moment. The wake vorticity released at the trailing edge derives from the bound circulation through the Kutta condition and is convected downstream with the velocity of the undisturbed flow. The local bound circulation is obtained by the application of the Kutta–Joukowski theorem, extended to unsteady flows. Assuming a bending and torsion wing, this paper provides the aerodynamic matrix of the transfer functions, relating the generalised aerodynamic loads to the Lagrangian coordinates of the elastic deformation. Its rational approximation yields a reduced-order state-space aerodynamic model suitable for an aeroelastic stability analysis and control purposes. The numerical investigation examines the influence of both the wake shed/trailed vorticity modelling and different approximations of the Kutta–Joukowski theorem for unsteady flows on the aerodynamic transfer functions given by the developed frequency-domain lifting-line solver. The accuracy of the solver is assessed by comparison with the predictions obtained by a three-dimensional boundary-element-method solver for potential flows. It is shown that, at least for the frequency range considered, regardless of the approximation of the Kutta–Joukowski theorem applied, the formulation based on the Theodorsen theory provides predictions that are in very good agreement with the results from the boundary element method for a slender wing. This agreement worsens as the wing aspect ratio decreases. A lower level of accuracy is obtained by the application of the sectional loads given by the Glauert theory. In this case, the predictions are more sensitive to the approximation used to express the Kutta–Joukowski theorem for unsteady flows.

Enhancing Flight Envelope for a Nonlinear Aeroelastic Wing-Section Using Adaptive Fuzzy Sliding Mode Control Law

This paper presents an adaptive fuzzy sliding mode controller (AFSMC) for the control of a nonlinear aeroelastic wing section. The proposed controller estimates both the model dynamics of the system and the switching control of the sliding mode. Furthermore, the designed controller’s strategy is to enhance quality and ensure flight safety by providing additional damping to the already stable system and increasing the flight speed beyond the open-loop flutter speed. The aeroelastic system describes the plunge and pitch motions of the aircraft wing-section equipped with leading and trailing edge control surfaces. Additionally, the selected two-degree-of-freedom model includes structural stiffness nonlinearities and quasi-steady aerodynamics. The simulation results show the effectiveness of the proposed controller toward suppressing flutter and LCOs and reducing the vibrational level in the subcritical flight speed range. Additionally, the designed control strategy effectively controls and derives the state trajectories to the origin despite uncertainties and gust loads.

Uncertainty quantification of aeroelastic wings flutter using an optimized machine learning approach

This study outlines the flutter characteristics of aeroelastic wings under unsteady aerodynamic loading based on an efficient support vector machine assisted k-method. First, the aeroelastic wing flutter speed and flutter frequency are obtained using k-method. Then, the uncertain input parameters distribution is modeled by probability density functions. These parameters are propagated to the aeroelastic wing equations. The Monte Carlo simulation using 12 parallel logical threads is carried out to obtain the flutter speed and the flutter frequency distribution. An optimal robust surrogate model is trained by limited numbers of input and output using support vector machine. Monte Carlo simulation is also carried out in conjunction with the machine learning based k-method computational framework for obtaining the complete probabilistic description of flutter speed and flutter frequency. The coupled support vector regression based k-method is a novel approach that is first used in the aeroelastic wings flutter. The present method is found to reduce the computational time and cost significantly without compromising the accuracy of results.

Data-driven modeling of transonic unsteady flows and efficient analysis of fluid–structure stability

The reduced-order aerodynamic models constructed via the linear/nonlinear system identification methodologies cannot reveal the flow characteristics of the fluid–structure coupling system because the state variables of the reduced-order model do not explicitly represent fluidic properties. In this study, a data-driven modeling procedure is proposed to reconstruct a physics-based, reduced-order aerodynamic model. In the procedure, the transonic unsteady flows of concern are projected onto low-dimensional base vectors first via the proper orthogonal decomposition of pressure snapshots subject to a specific structural excitation. Then a state-space representation of the temporal coefficients of proper orthogonal decomposition modes subject to the structural excitation is established by using the dynamic mode decomposition with control. Finally, for the fluid–structure stability analysis, pressure snapshots are recovered from the coefficients of proper orthogonal decomposition, and aerodynamic forces are derived by integrating the pressure coefficients around the wing surface. The state vector in above-mentioned data-driven model has a clear sense in physics with regard to pressure distribution. To demonstrate the accuracy of the proposed procedure, a two-dimensional, transonic aeroelastic wing with an NACA0012 profile is studied. The unsteady aerodynamic forces, frequency responses of the reduced-order aerodynamic model, transonic flutter boundary, and flow characteristics at the flutter condition are predicted and compared with direct computational fluid dynamic simulations. The results show that the modeling procedure can accurately predict the transonic flutter boundary and flow characteristics.

Nonlinear aeroelastic stability analysis of a two-stage axially moving telescopic wing by using fully intrinsic equations

During the process of span extension for an aircraft wing equipped with a telescopic morphing mechanism, the wing aspect ratio increases, and hence, the geometrical nonlinearities might become more significant. In this regard, this paper aims to investigate the effect of structural nonlinearity on the aeroelasticity of span morphing wings using the exact fully intrinsic equations for the first time. Furthermore, the effects of various parameters such as thrust force, engine location, chord size, flight altitude, initial angle of attack, and overlapping mass on the aeroelasticity of the wing are studied. The applied aerodynamic loads in an incompressible flow regime are determined using Peters’ unsteady aerodynamic model. In order to check the stability of the system, first the resulting nonlinear partial differential equations are discretized by using the central finite difference method and then linearized about the static equilibrium. Finally, by obtaining the eigenvalues of the linearized system, the stability of the wing is evaluated. It is observed that by using the fully intrinsic equations, the instability of the axially moving telescopic wing can be determined more accurately. Moreover, the results show that the morphing length and overlapping mass have significant effects on the aeroelastic stability of the telescopic wing.

Efficient aeroelastic wing optimization through a compact aerofoil decomposition approach

Efficient optimization of an aeroelastic wing is presented through multi-disciplinary analysis using low-dimensional modal design variables. Much work in wing optimization has concentrated on high-fidelity surface control, therefore utilising often hundreds of design variables. However, whilst fine surface control can be useful, problems can arise such as large disparities in design variable values when planform variables are introduced, slow convergence speeds, and lack of compatibility with global algorithms. Therefore, the focus of this paper is to filter the design space of this problem to reduce the dimensionality and complexity of the problem. Orthogonal geometric design variables are derived in the geometric space via singular value decomposition. Orthogonality of design variables leads to a well-conditioned design space and ensures effective optimizer convergence. These variables are applied in a sectional fashion for fixed planform drag minimization of a flexible transonic wing, using a gradient-based optimizer. Shock-free solutions are demonstrated when optimizing a rigid wing, indicating suitability of the aerofoil modes for sectional-based wing optimization. However, it is shown that these wings have poor performance when subsequently deformed under flight loads, hence optimisation including full aeroelastic performance is performed. Encouragingly, shock-free solutions are again computed. Loading is shifted outboard, leading to increased tip deflection. Monotonic improvement in the objective function (drag) with increase in dimensionality is also proven. Furthermore, applying these sectional deformation modes globally across the wing with only 10 design variable leads to a 28% drag reduction, which is within 7 drag counts of when the modes are applied locally through 82 design variables. This therefore opens the possibility of introducing global optimization algorithms to high-fidelity aeroelastic wing optimization.

Adaptive wing aeroelasticity CFD analysis using artificial neural network (ANN)

Morphing wing technology has been part of the aviation industry since the time of the Wright Brothers. Wright Brothers used morphing wing for Wright flyer, and type of morphing wing used then was twisting the wing prepared with the help of bicycle tubes and cardboards. But to enhance the morphing wing technology and to produce more effective results aerodynamically, and increase lift performances and lower drag performances, better materials with better mechanism had to be used. This research is directed towards morphing a Supersonic aero elastic wing in Computational Fluid Dynamics (CFD) analysis using Artificial Neural Networks (ANN). Here a CFD analysis of National Advisory Committee for Aeronautics (NACA)0012 airfoil, made of a morphing material is done in the initial part. It has low and transonic regions of CFD analysis in the said airfoil. The problems persisting with the high speed aerodynamic CFD analysis is brought out in detail. Later part of the work is on designing of a self-trainable and multilayer Artificial Deep Neural Network and its programming using Python deep learning (Python Anaconda). It also explains how these Artificial Intelligence (AI) techniques help immensely in supersonic aerodynamic and aeroelastic analysis of the aerofoils. The data from designing the aerofoil and its CFD analysis will be used for training the deep neural networks, which is done by the Python code.

Effects of Unbalanced Lamination Parameters on the Static Aeroelasticity of a High Aspect Ratio Wing

In this paper, in order to understand the influence of the unbalanced coefficient of composite laminates on the static aeroelasticity of high aspect wings, a series of numerical simulation calculations were carried out, and this work wants to provide some reference for the structural design of aircraft. Considering the influence of geometric nonlinearity, the unidirectional fluid-solid coupling calculation method based on loose coupling is used to control the change of unbalanced coefficient of laminates on the basis of layering angle, layering thickness, and layering region, so as to observe the changes caused to the wings. The relationship between the unbalanced coefficient and the constant thickness layup and the variable thickness layup with 0° and ±45° layup angles was studied, respectively. Then, the layup angle of 90° was added to study the influence of the unbalanced coefficient on the static aeroelasticity of the wing structure with the change of the layup angle and the different choice of layup region. The results show that the deformation is the smallest when the unbalanced coefficient is 0.5, and the deformation trend is evenly distributed along both sides when the unbalanced coefficient is 0.5. When the unbalanced coefficient is changed, adding the 90° layup angle can significantly reduce the overall deformation of the wing and show different sensitivity characteristics to different layup areas. The increase of the unbalanced coefficient makes the chordal displacement gradually change from linear distribution to nonlinear distribution along the spread direction, and the displacement will gradually decrease.

A Parametric Study on the Aeroelasticity of Flared Hinge Folding Wingtips

This paper presents a parametric study on the aeroelasticity of cantilever wings equipped with Flared Hinge Folding Wingtips (FHFWTs). The finite element method is utilized to develop a computational, low-fidelity aeroelastic model. The wing structure is modelled using Euler–Bernoulli beam elements, and unsteady Theodorsen’s aerodynamic strip Theory is used for aerodynamic load predictions. The PK method is used to estimate the aeroelastic boundaries. The model is validated using three rectangular, cantilever wings whose properties are available in literature. Then, a rectangular, cantilever wing is used to study the effect of folding wingtips on the aeroelastic response and stability boundaries. Two scenarios are considered for the aeroelastic analysis. In the first scenario, the baseline, rectangular wing is split into inboard and outboard segments connected by a flared hinge that allows the outboard segment to fold. In the second scenario, a folding wingtip is added to the baseline wing. For both scenarios, the influence of fold angle, hinge-line angle (flare angle), hinge stiffness, tip mass and geometry are assessed. In addition, the load alleviation capability of FHFWT is evaluated when the wing encounters discrete (1-cosine) gusts. Finally, the hinge is assumed to exhibit cubic nonlinear behavior in torsion, and the effect of nonlinearity on the aeroelastic response is assessed and analyzed for three different cases.

Generalized composite noncertainty-equivalence adaptive control of a prototypical wing section with torsional nonlinearity

The paper presents a generalized composite noncertainty-equivalence adaptive control system for the control of a prototypical aeroelastic wing section using a single trailing-edge control surface. The plunge–pitch (two-degree-of-freedom) dynamics of this aeroelastic system include torsional pitch-axis nonlinearity. The open-loop system exhibits limit cycle oscillations beyond a critical free-stream velocity. It is assumed that parameters of the model are not known. The objective is to suppress the oscillatory responses of the system. Based on the immersion and invariance approach, a generalized composite noncertainty-equivalence adaptive (NCEA) control system for regulation of the pitch angle is designed. The control system consists of a control module and a composite parameter identifier—designed independently. The composite integral parameter estimation law is based on (1) the immersion and invariance (I&I) theory, (2) gradient-based adaptation algorithm, and (3) classical certainty-equivalence adaptive (CEA) update rule. Besides the composite integral component, the full parameter estimate also includes a judiciously chosen nonlinear algebraic function. This composite identifier inherits stronger stability properties. Using the Lyapunov analysis, asymptotic suppression of the limit cycle oscillations and the boundedness of system trajectories are established. Interestingly, in the closed-loop system including the composite update rule, there exist two attractive manifolds to which the system’s trajectories converge. Simulation results are presented which show the suppression of the oscillatory plunge displacement and pitch angle responses despite uncertainties in the model parameters. Furthermore, the performance and stability properties of this composite NCEA control system—including the gradient-based adaptation and the update rule of the CEA system—are better than the simple NCEA system.

Uncoupled method for static aeroelastic analysis

Fluid–structure interaction (FSI) analysis is often highly computationally expensive, making it infeasible to conduct iterative aeroelastic design studies or rigorous optimizations. This work develops a new method for aeroelastic analysis that can be more efficient in the determination of final structure/fluid equilibrium configurations, especially during design studies where attributes of a structure may be altered but those of the flow are unchanged. In this new scheme, referred to as the uncoupled static aeroelastic analysis method, the usual approach of performing fluid and structure analysis that increments in time in a coupled manner is replaced by many fully decoupled, and thus highly parallelizable, structural and fluid analyses. Surrogate modeling of results enables analytical determination of interpolation intersections between physical solution fields, such intersections being proposed as the solution to coupled FSI analysis. Since the fluid and structure result sets are calculated and stored separately, fluid results can be re-used without additional analysis when the structure considered is modified (e.g., as during a design study), enabling new solutions to be quickly obtained while avoiding the more expensive fluid evaluations. This new method is demonstrated herein on three examples: (1) a rigid baffle, (2) a cantilevered deformable baffle, and (3) an aeroelastic wing. For each, the solution found via the uncoupled method is shown to closely approximate the FSI solution. Parallelization of the evaluations required to generate data for the uncoupled method enables solutions to be obtained in significantly less time as compared to the coupled scheme.

Analysis of damping from vertical sloshing in a SDOF system

The effect of the sloshing motion of liquid in a tank on the vertical transient motion of a single degree of freedom system is investigated. Step release tests of a vertically vibrating structure, including a tank containing liquid, demonstrate that added damping from the sloshing motion depends upon the amount of fluid in the tank and the maximum acceleration. The maximum amount of damping was observed at a 50% fill level and the system showed three distinct response regimes during the transient decay, all related to different motions of the fluid. The first response regime, immediately at the start of the transient, is considered to be the most important to exploit for aircraft gust loads alleviation due to its dominant role in the overall energy dissipation balance. Further, to advance the understanding of the modelling and predictive capabilities, coupled fluid-structure models of two opposing levels of fidelity were developed and evaluated. Namely, smoothed particle hydrodynamics (SPH) and an equivalent mechanical model (EMM) based on a bouncing ball model were considered to represent the fluid motion in the tank during the experiment. Both models are shown to provide good predictive capability in the initial impacting sloshing mode while the subsequent flow regime can be predicted with the SPH model only. The findings in this paper open routes towards improved coupled fluid-structure models and their use in improved aeroelastic wing design.

Aeroelastic inverse: Estimation of aerodynamic loads during large amplitude limit cycle oscillations

This paper presents an algorithm to compute the aerodynamic forces and moments of an aeroelastic wing undergoing large amplitude heave and pitch limit cycle oscillations. The technique is based on inverting the equations of motion to solve for the lift and moment experienced by the wing. Bayesian inferencing is used to estimate the structural parameters of the system and generate credible intervals on the lift and moment calculations. The inversion technique is applied to study the affect of mass coupling on limit cycle oscillation amplitude. Examining the force, power, and energy of the system, the reasons for amplitude growth with wind speed can be determined. The results demonstrate that the influence of mass coupling on the pitch–heave difference is the driving factor in amplitude variation. The pitch–heave phase difference not only controls how much aerodynamic energy is transferred into the system but also how the aerodynamic energy is distributed between the degrees of freedom.

A smoothed particle hydrodynamics–peridynamics coupling strategy for modeling fluid–structure interaction problems

Fluid–structure interaction (FSI) is a multiphysics problem with diverse application scenarios ranging from the aeroelasticity of aircraft wings and the structural response of marine platforms, to blood circulation through aortic valves. Solving the FSI problems is challenging, predominantly because of the complex time-variant geometry in the fluid–structure interface. To alleviate the difficulties encountered by the grid-based methods in tracking and meshing the fluid–structure interface involving large deformation and structure failures, in this study, we propose a meshfree framework that couples smoothed particle hydrodynamics (SPH) with peridynamics (PD) for the numerical modeling of FSI problems. This SPH–PD framework involves a four-step partitioned coupling procedure, where the key point is utilizing the SPH moving ghost particles as a medium. An original data transfer scheme is developed based on the partnerships built between the SPH moving ghost particles and the PD particles. The structure failures are incorporated in the PD model by adopting a damage law of maximum bond stretch. The SPH–PD method is validated against existing experimental and numerical data. Through the use of this model, we successfully simulate the low-velocity fluid–structure impact and capture the large deformation with local failures.

Amplitude Annihilation in Wake-Influenced Aeroelastic Limit-Cycle Oscillations

This paper investigates the dynamics of a pitching and heaving aeroelastic wing undergoing large-amplitude limit-cycle oscillations influenced by a vortical wake from an upstream rectangular cylinder bluff body. The results show that under certain conditions, the limit cycle is annihilated. The conditions in which annihilation occurs are dependent on the limit-cycle frequency, bluff-body shedding frequency, and the magnitude of the mass coupling in the system. The low mass coupling configuration shows that vortical disturbances on the wing cause minor amplitude modulation until the shedding frequency is within a critical distance of the third harmonic of the limit-cycle oscillation frequency. Within this band, the amplitude modulations grow such that the pitch amplitude varies by up to 10 deg. When the mass coupling is increased and when the shedding frequency is within a critical distance of the third harmonic, the limit cycle is annihilated and the system returns to equilibrium. The annihilation phenomenon is caused by the addition of strong aerodynamic coupling between the vortex wake and the wing, influencing the limit-cycle kinematics such that the limit-cycle returns to the equilibrium position. The paper discusses both the kinematic and aerodynamic behaviors of wake-influenced aeroelastic limit-cycle annihilation.