Aeroelastic Problems Research Articles

The interaction between flutter and buffet in transonic flow

This paper presents a kind of nodal-shaped oscillation that is caused by the interaction between flutter and buffet in transonic flow. This response differs from the common limit cycle oscillation that appears in transonic aeroelastic problems. The benchmark active controls technology model with the NACA0012 airfoil is used as the research model. First, both buffet and flutter cases are computed through unsteady Reynolds-averaged Navier–Stokes method and are validated by experimental data. Second, the interaction is found to occur beyond the flutter onset velocity at Mach 0.71. When the pitching angle of a fluttering structure exceeds the buffet onset angle, the high-frequency aerodynamic loads induced by transonic buffet destroy the original flutter model, and then the amplitude of the structure motion decays. When the structural pitching angle is less than the buffet onset angle, the buffet disappears and flutter occurs again. As the process repeats itself, the transonic aeroelastic system displays a nodal-shaped oscillation (divergent–damping–divergent–damping oscillation). Finally, the mechanism of the interaction is discussed by analyzing the energy transportation between the flow and the structure in one cycle of nodal-shaped oscillation, and by observing the variation in the phase-angle difference between the plunging and pitching displacements. In this way, this research provides a new approach to understand flutter suppression.

A Teaching Experience: Aeroelasticity and the Finite Element Method

The aeroelastic modelling of aircraft structures is a fundamental area for the students of Aerospace Engineering Degree. This subject has a strongly multidisciplinary character and involves other several subjects like mechanics, vibrations, aerodynamics, structural analysis. Consequently, the students find stimulating the challenge of merging their knowledge at different areas. In this paper, a teaching experience on the solution of the aeroelastic problem of a 3D-wing through six different computer tasks is presented. The main objective is to attempt a relatively complex problem using a simple version of the Finite Element Method with only four degrees of freedom. The students begin creating the shape functions of the discrete model and finish solving the flutter instability problem.

Time dependent adjoint-based optimization for coupled fluid–structure problems

A formulation for sensitivity analysis of fully coupled time-dependent aeroelastic problems is given in this paper. Both forward sensitivity and adjoint sensitivity formulations are derived that correspond to analogues of the fully coupled non-linear aeroelastic analysis problem. Both sensitivity analysis formulations make use of the same iterative disciplinary solution techniques used for analysis, and make use of an analogous coupling strategy. The information passed between fluid and structural solvers is dimensionally equivalent in all cases, enabling the use of the same data structures for analysis, forward and adjoint problems. The fully coupled adjoint formulation is then used to perform rotor blade design optimization for a four bladed HART2 rotor in hover conditions started impulsively from rest. The effect of time step size and mesh resolution on optimization results is investigated.

Recent developments on refined theories for beams with applications

This paper is a review of the most influential approaches to developing beam models that have been proposed over the last few decades. Essentially, primary attention has been paid to isotropic structures while a few extensions to composites have been given for the sake of completeness. Classical models - Da Vinci, Euler-Bernoulli, and Timoshenko - are described first. All those approaches that are aimed at the improvement of classical theories are then presented by considering the following main techniques: shear correction factors, warping functions, Saint-Venant based solutions and decomposition methods, variational asymptotic methods, the Generalized Beam Theory and the Carrera Unified Formulation (CUF). Special attention has been paid to the latter by carrying out a detailed review of the applications of 1D CUF and by giving numerical examples of static, dynamic and aeroelastic problems. Deep and thin-walled structures have been considered for aerospace, mechanical and civil engineering applications. Furthermore, a brief overview of two recently introduced methods, namely the mixed axiomatic/asymptotic approach and the component-wise approach, has been provided together with numerical assessments. The review presented in this paper shows that the development of advanced beam models is still extremely appealing, due to the computational efficiency of beams compared to 2D and 3D structural models. Although most of the techniques that have recently been developed are focused on a given number of applications, 1D CUF offers the breakthrough advantage of being able to deal with a vast variety of structural problems with no need for ad hoc formulations, including problems that can notoriously be dealt with exclusively by means of 2D or 3D models, such as complete aircraft wings, civil engineering constructions, as well as multiscale and wave propagation analyses. Moreover, 1D CUF leads to a complete 3D geometrical and material modeling with no need of artificial reference axes/surfaces, reduced constitutive equations or homogenization techniques

Numerical Algorithms for Solving One Type of Singular Integro-Differential Equation Containing Derivatives of the Time Delay States

This study presents numerical algorithms for solving a class of equations that partly consists of derivatives of the unknown state at previous certain times, as well as an integro-differential term containing a weakly singular kernel. These equations are types of integro-differential equation of the second kind and were originally obtained from an aeroelasticity problem. One of the main contributions of this study is to propose numerical algorithms that do not involve transforming the original equation into the corresponding Volterra equation, but still enable the numerical solution of the original equation to be determined. The feasibility of the proposed numerical algorithm is demonstrated by applying examples in measuring the maximum errors with exact solutions at every computed nodes and calculating the corresponding numerical rates of convergence thereafter.

MEASUREMENTS OF FLUTTER DERIVATIVES OF A BRIDGE DECK SECTIONAL MODEL

Aeroelastic phenomena should be considered during the design phase of long span bridges. One of the aeroelastic problems is flutter, the dynamic instability that may cause structural failure at a wind speed called the flutter speed. The prediction of flutter speed of a bridge needs a thorough modelling of bridge stiffness, inertias, and especially its unsteady aerodynamic forces. The potential flow theory is not applicable to calculate unsteady aerodynamics of oscillating bridges due to their non-streamlined complex geometry, and the non-avoidable flow separation. For these reasons, a semi empirical model proposed by Scanlan is used to describe unsteady aerodynamic forces on an oscillating bridge deck. In this model, relation between unsteady aerodynamic forces and motion of the bridge is modelled using parameters known as flutter derivatives. The values of flutter derivatives can be identified from the free vibration responses of an elastic bridge at several wind-speeds. This paper presents wind tunnel tests and flutter derivatives identification of a sectional aeroelastic bridge model. Modified Ibrahim Time Domain method was applied to identify the eigenvalues and eigenvectors of the model at each wind speed, from which the flutter derivatives can be calculated. The results show that the measurement procedure is able produce flutter derivatives, which are in good agreement with those obtained by other researchers.

LCO Flutter Analysis on Coir Pressed Mat Fibre/Epoxy Composites Plate

The effects of aspect ratio and fiber-epoxy weight ratio of coir fibre/epoxy composite wing idealized as flat plate on flutter speed were preliminary studied in this current research to investigate the aeroelastic response on natural fiber composite material. The usage of natural material such as coir fiber reinforced composite might become possible solutions in future since it offers lower weight, cost reduction, and preservation of the environment factor compared to presence structures like conventional glass or carbon fiber as the reinforcement for composites. For this work, the analysis of coir fiber on aeroelastic problem will be preliminary investigated to establish related data to be served, especially in the aerospace research areas. The research began with the existing raw untreated coir fiber, which was in the form of pressed mat and originally in random oriented fiber forms, were set in the composite preparation process by simple hand-lay-up and compression moulding method under the room temperature and also controlled pressure conditions. Specimen with different aspect ratios (5, 6 and 7) with 25% wt fiber reinforcement composite was installed in the wind tunnel for subsonic experimental aeroelastic test. The result shows that the plates with lower aspect ratio have higher flutter speed.

Staggered Approach for Fluid-Structure Interaction Phenomena of an AGARD 445.6 Wing Using Commercial CFD/CSM Software

This paper presents the development of an efficient time-marching simulation technology for fluid-structure interaction applications using commercial computational fluid dynamics (CFD) and computational solid mechanics (CSM) software and in-house modules. By splitting the multidisciplinary coupling problem into three major analysis fields (the fluid field, the structure field, and the moving mesh pseudofield) one can solve each field using already available and validated software and the coupling between the different analysis fields can be accomplished by in-house software (FORTRAN and C codes). This simulation technology is able to predict both unsteady interaction phenomena and nonlinear aeroelastic problems in reasonable time, taking advantage of a high-performance computing network. Commercial CFD software was used to solve the Navier-Stokes equations and the chosen turbulence models of the fluid field while the structural field was solved using commercial CSM software. The transfer of information from the fluid field to the structural field and vice versa is computed by an in-house interpolation module, which reduces the user interaction to a minimum initialization. The third field, the moving mesh, was solved with another in-house code, which employs the spring network analogy and the elastic material analogy. The advancement of the solution is controlled by means of FORTRAN and C codes that manage the run/wait conditions of software modules based on the staggered procedures proposed in previous research. The proposed aeroelastic simulation technology was validated with the experimental data available for the advisory group for aerospace research and development (AGARD) 445.6 standard aeroelastic configuration for dynamic response at subsonic and transonic free stream Mach numbers.

Efficient reduced-order modeling of unsteady aerodynamics robust to flight parameter variations

In this study, a computational fluid dynamics (CFD) based reduced-order modeling (ROM) approach robust to flight parameter variations is presented. The approach, which uses Kriging surrogates and recurrence frameworks together for unsteady aerodynamic loads predictions, does not need to reconstruct the ROM with flight parameters changes. To illustrate the approach, the aeroelastic problem of a NACA 64A010 airfoil undergoing pitching and plunging motions at zero mean angle of attack is studied. The results predicted via the proposed approach agree well with those obtained via the high-fidelity CFD solver over the selected range of Mach numbers.

Stabilization of High-Dimensional Harmonic Balance Solvers Using Time Spectral Viscosity

We investigate the application of a temporal spectral viscosity operator to eliminate aliasing errors associated with the high-dimensional harmonic balance technique, which is an efficient method for modeling nonlinear time-periodic problems. Previous studies have shown that aliasing errors resulting from the discrete Fourier transformation may slow down convergence, trigger a nonlinear instability, or lead to nonphysical solutions. A temporal spectral viscosity operator, similar to that used for pseudospectral methods, is introduced. The temporal spectral viscosity is added to the high-frequency modes of the solution to eliminate aliasing errors so as to ensure the convergence to the physical solution. The implementation of the technique is straightforward and can be incorporated into the high-dimensional harmonic balance solver as a matrix product operator. The accuracy and effectiveness of the modified method is demonstrated for different test cases including a Duffing oscillator and unsteady flow about an oscillating circular cylinder. Finally, the temporal spectral viscosity is applied to a turbomachinery aeroelasticity problem to investigate the effect of added dissipation on the accuracy of unsteady solutions.

Investigation on transonic flutter active auppression with CFD-Based ROMs

The calculation of accurate unsteady aerodynamic forces is critical in the analysis of aeroelastic problems, however the efficiency is low because of high computational costs of the computational fluid dynamics (CFD) portion. Additionally, direct integrated CFD and computational structural dynamics (CSD) technique is unsuitable for the analysis of ASE and the flutter active suppression in state-space form. A reduced-order model (ROM) based on Volterra series was developed using CFD calculation and used to predict the flutter coupled with the structure. The closed-loop control systems designed by the sliding mode control (SMC) and linear quadratic Gaussian (LQG) control were constructed with ROM/CSD to suppress the AGARD 445.6 wing flutter. The detailed implementation of the two control approaches is presented, and the flutter suppression effectiveness is discussed and compared. The results indicate that SMC method can make the controlled object response decay to the stable equilibrium more rapidly and has better control effects than the LQG control.

Experimental benchmark of a free plunging wing with imposed flap oscillations

The validation of fluid–structure interaction solvers is difficult since there is a lack of experimental data. Therefore, in this work an aeroelastic experiment is presented. The focus is on the temporal coupling between fluid and structure dynamics. Issues in the spatial coupling are eliminated by using a rigid wing. The wing, with a harmonically actuated 0.2c trailing edge flap, has a degree of freedom in the plunge (vertical) direction. The wing has a chord of 0.5m and is suspended with springs. The wing motion is constrained by a vertical rail system.For simplicity attached flow is desired and therefore the set angle of attack is α=0°. The Reynolds number is approximately Re=700000 and the flap deflects over a range of about ±2°. The damped natural frequency of the structure expressed as a reduced frequency is about k=0.194 and measurements are performed for reduced flap frequencies ranging from k=0.1 to k=0.3. Displacements and time dependent aerodynamic forces are measured and for k=0.198 2-D PIV measurements are performed. The planar PIV measurements are used to intrinsically determine the unsteady loads using Noca׳s method.As expected the aeroelastic problem shows similarities with a viscously damped mass–damper–spring, meaning the maximum excursion of the wing is found near the system eigenfrequency. The lift is dominated by the flap motion and the effective angle of attack due to the motion introduces phase shifts of the lift signal with respect to the flap phase angle.The experiment has been set up and executed with the necessary precision, but small ambiguities are found in the lift and drag disqualifying the data for validation. Nevertheless the data set provides a clear insight into typical loads and motions and can be used for comparative studies. It can also be used to (re)design future experiments to improve the quality of the data to the desired level of accuracy for validation.

Computational aeroelastic investigation of a transonic limit-cycle-oscillation experiment at a transport aircraft wing model

Aeroelastic measurements of a three-dimensional wing model, the so-called Aerostabil wing, were conducted in the Transonic Windtunnel Göttingen. This clean, backward-swept wing allowed the experimental investigation of limit cycle oscillations in a certain transonic parameter range. In this paper, a detailed insight into the observed physical phenomena, especially the measured limit cycle oscillations, is presented by means of CFD–CSM coupled simulations. These simulations on the basis of a detailed structural finite element model reveal the specific properties of the Aerostabil wing and furthermore allow investigating the unstable behavior of this windtunnel model for transonic flow settings. The aerodynamic characteristics include a two-shock system and large flow separation areas, further increasing the complexity of the aeroelastic problem. A structural single degree-of-freedom system is used for the prediction of the experimental stability range and the limit cycle oscillation investigations. Due to the good agreement of simulation and experiment the limit cycle oscillations can be explained by means of nonlinear aerodynamic effects.

Aeroelastic Topology Optimization of Blade-Stiffened Panels

Metallic blade-stiffened panels are optimized for various eigenvalue metrics of interest to the aerospace community. This is done via solid isotropic material with penalization-based topology optimization: the stiffeners are discretized into finite elements, and each element is assigned a design variable, which may vary from 0 (void) to 1 (solid). A known issue with eigenvalue-based optimization is discontinuities due to mode switching, which may be avoided through a series of eigenvalue separation constraints, or (more challenging, but less restrictive) a bound method with mode tracking. Both methods are demonstrated to obtain optimal stiffener topologies for panel buckling, but only the former is used for aeroelastic panel-flutter problems. Satisfactory flutter optimal results are obtained, but the work concludes with a discussion of the challenges associated with the use of a bound method for aeroelastic problems, with specific complications posed by the advent of hump modes.

Reduced-Order Aeroelastic Models for Dynamics of Maneuvering Flexible Aircraft

This paper investigates the model reduction, using balanced realizations, of the unsteady aerodynamics of maneuvering flexible aircraft. The aeroelastic response of the vehicle, which may be subject to large wing deformations at trimmed flight, is captured by coupling a displacement-based flexible-body dynamics formulation with an aerodynamic model based on the unsteady vortex lattice method. Consistent linearization of the aeroelastic problem allows the projection of the structural degrees of freedom on a few vibration modes of the unconstrained vehicle but preserves all couplings between the rigid and elastic motions and permits the vehicle flight dynamics to have arbitrarily large angular velocities. The high-order aerodynamic system, which defines the mapping between the small number of generalized coordinates and unsteady aerodynamic loads, is then reduced using the balanced truncation method. Numerical studies on a representative high-altitude, long-endurance aircraft show a very substantial reduction in model size, by up to three orders of magnitude, that leads to model orders (and computational cost) similar to those in conventional frequency-based methods but with higher modeling fidelity to compute maneuver and gust loads. Closed-loop results for a cantilever wing finally demonstrate the application of this approach in the synthesis of a robust stability augmentation system.

A Semi-discretized Numerical Method for Solving One Type of Singular Integro-differential Equation Containing Derivatives of the Possible Delay States

This studypresents a numerical method for solving a class of equations that partly consists of two derivatives of the unknown state, namely the first derivative at the moment and the second derivative at a previous certain time, as well as an integro-differential term containing a weakly singular kernel. These equations are types of integro-differential equation of the second kind and were originally obtained from an aeroelasticity problem. In an integrable condition, the precise solutions of this class of equations can be obtained by transforming the equations into equations similar to the Volterra integral equations of the second kind with delay. The main contribution of this study is to propose a semi-discretized numerical methodthat does not involve transforming the original equation into the corresponding Volterra equation, but still enables the numerical solution of the original equation to be determined. The feasibility of the proposed numerical method is demonstrated by applying examples in measuring the maximum errors with exact solutions and comparing graphs of the numerical and exact solutions.

A Study on Fluid Self-Excited Flutter and Forced Response of Turbomachinery Rotor Blade

Complex mode and single mode approach analyses are individually developed to predict blade flutter and forced response. These analyses provide a system approach for predicting potential aeroelastic problems of blades. The flow field properties of a blade are analyzed as aero input and combined with a finite element model to calculate the unsteady aero damping of the blade surface. Forcing function generators, including inlet and distortions, are provided to calculate the forced response of turbomachinery blading. The structural dynamic characteristics are obtained based on the blade mode shape obtained by using the finite element model. These approaches can provide turbine engine manufacturers, cogenerators, gas turbine generators, microturbine generators, and engine manufacturers with an analysis system to remedy existing flutter and forced response methods. The findings of this study can be widely applied to fans, compressors, energy turbine power plants, electricity, and cost saving analyses.

Numerical Calculation of Effect of Elastic Deformation on Aerodynamic Characteristics of a Rocket

The application and workflow of Computational Fluid Dynamics (CFD)/Computational Structure Dynamics (CSD) on solving the static aeroelastic problem of a slender rocket are introduced. To predict static aeroelastic behavior accurately, two-way coupling and inertia relief methods are used to calculate the static deformations and aerodynamic characteristics of the deformed rocket. The aerodynamic coefficients of rigid rocket are computed firstly and compared with the experimental data, which verified the accuracy of CFD output. The results of the analysis for elastic rocket in the nonspinning and spinning states are compared with the rigid ones. The results highlight that the rocket deformation aspects are decided by the normal force distribution along the rocket length. Rocket deformation becomes larger with increasing the flight angle of attack. Drag and lift force coefficients decrease and pitching moment coefficients increase due to rocket deformations, center of pressure location forwards, and stability of the rockets decreases. Accordingly, the flight trajectory may be affected by the change of these aerodynamic coefficients and stability.

Recent advance in nonlinear aeroelastic analysis and control of the aircraft

A review on the recent advance in nonlinear aeroelasticity of the aircraft is presented in this paper. The nonlinear aeroelastic problems are divided into three types based on different research objects, namely the two dimensional airfoil, the wing, and the full aircraft. Different nonlinearities encountered in aeroelastic systems are discussed firstly, where the emphases is placed on new nonlinear model to describe tested nonlinear relationship. Research techniques, especially new theoretical methods and aeroelastic flutter control methods are investigated in detail. The route to chaos and the cause of chaotic motion of two-dimensional aeroelastic system are summarized. Various structural modeling methods for the high-aspect-ratio wing with geometric nonlinearity are discussed. Accordingly, aerodynamic modeling approaches have been developed for the aeroelastic modeling of nonlinear high-aspect-ratio wings. Nonlinear aeroelasticity about high-altitude long-endurance (HALE) and fight aircrafts are studied separately. Finally, conclusions and the challenges of the development in nonlinear aeroelasticity are concluded. Nonlinear aeroelastic problems of morphing wing, energy harvesting, and flapping aircrafts are proposed as new directions in the future.

A new frequency domain based approach for a nonlinear aeroelasticity analysis

In this paper, a new frequency-domain based approach for the investigation of aeroelasticity problems is introduced that is capable of handling both linear and nonlinear problems. This approach is based on coupling a conceptual method used in a structural dynamic analysis and an optimum equivalent linear frequency response function (OELF). Additionally, a new criterion for determining the flutter speed and the instability of nonlinear systems is introduced that is based on the condition number of the aeroelastic matrices. Due to the global nature of the condition number, the new criterion proves to be efficient and simple to use. To examine the efficiency of the new technique, a two-dimensional nonlinear airfoil with an unsteady aerodynamic model is considered.