Aeroelastic Problems Research Articles

Stochastic collocation method for secondary bifurcation of a nonlinear aeroelastic system

A stochastic collocation method is proposed to investigate the secondary bifurcation of a two-dimensional aeroelastic system with structural nonlinearity represented by cubic restoring forces, and uncertainties expressed by random parameters in the cubic stiffness coefficient and in the initial pitch angle. The accuracy of the stochastic collocation method is improved by incorporating higher order schemes, such as piecewise cubic interpolation and piecewise cubic spline interpolation, instead of a piecewise linear interpolation formula. For an aeroelastic problem with the uncertainty expressed by a time dependent combination of five random variables, an efficient collocation method is developed using a sparse grid approach with a dimension adaptive strategy. Numerical simulations are carried out to demonstrate the effectiveness of the proposed method for long term computation and discontinuous problems.

Reduced Order Models Using Generalized Eigenanalysis

This article discusses the use of generalized eigenanalysis to extract reduced order models from the linearization of structural and aeroelastic problems written in differential-algebraic form. These problems may arise from multi-body analysis and in general from mixed approaches, where a high degree of generality and modelling flexibility are sought. A method based on a shift technique is proposed, that allows to exploit the regularity of the matrix pencil resulting from the linearization of differential-algebraic problems. Alternatively, the generalized Schur decomposition, or QZ decomposition, is directly used to select a cluster of eigenvalues related to the dynamic states. The two approaches are used to reduce the model to ordinary differential in state-space form. The two methods are applied to simple numerical problems, highlighting their robustness and versatility compared to other techniques. They are also applied to numerical models of a high-altitude long endurance aircraft obtained using a free general-purpose multi-body solver and a dedicated mixed variational solver.

Design of Adjoint-Based Laws for Wing Flutter Control

An airplane, by its nature of being, is constructed so that it is as light as possible. The structural design is guided by static and dynamic factors. The more stringent constraints on the structural design are due to dynamic loads, caused by aero-elastic interactions. One of the most commonly encountered problems in aeroelasticity is flutter, a term that is used to recognize the transfer of energy from unsteady aerodynamics associated with the surrounding fluid to the wing structure, resulting in rapidly divergent behaviour. If flutter can be controlled at cruise speeds, we can design lighter wings and consequently more efficient airplanes. It is therefore, in the aircraft designer’s best interest to design innovative ways in which flutter can be controlled without making the resulting structure too heavy. There are three important choices to make while designing active control strategies for suppressing flutter. The first is the choice of actuator. In this paper, the actuators we use are jets in the walls through which there is a small mass flow, either by way of blowing or suction. The second is to define a clear control objective. Finally, we need to design a control law that will make suitable state measurements and drive the actuators so that the desired control objective is achieved. The concept of Active Flow Control is fast gaining popularity in Fluid Mechanics circles. Indeed, it is important to realize that adding or removing fluid at the wing surface is equivalent to effecting a shape modification. Flow control using surface jets should, in principle, have an effect very similar to that of morphing surfaces. The capability to directly alter the flow field offers a huge realm of possibilities. Seifert, Theofilis and Joslin categorize the problems that are amenable to using Active Flow Control:

A multifidelity approach for the construction of explicit decision boundaries: application to aeroelasticity

This paper presents a multifidelity approach for the construction of explicit decision boundaries (constraints or limit-state functions) using support vector machines. A lower fidelity model is used to select specific samples to construct the decision boundary corresponding to a higher fidelity model. This selection is based on two schemes. The first scheme selects samples within an envelope constructed from the lower fidelity model. The second technique is based on the detection of regions of inconsistencies between the lower and the higher fidelity decision boundaries. The approach is applied to analytical examples as well as an aeroelasticity problem for the construction of a nonlinear flutter boundary.

THE WING-BODY AEROELASTIC ANALYSES USING THE INVERSE DESIGN METHOD

Flutter phenomenon is one of the most dangerous problems in aeroelasticity. When it occurs, the aircraft structure can fail in a few second. In recent aeroelastic research, computational fluid dynamics (CFD) techniques become important means to predict the aeroelastic unstable responses accurately. Among various flow equations like Navier-Stokes, Euler, full potential and so forth, the transonic small disturbance (TSD) theory is widely recognized as one of the most efficient theories. However, the small disturbance assumption limits the applicable range of the TSD theory to the thin wings. For a missile which usually has small aspect ratio wings, the influence of body aerodynamics on the wing surface may be significant. Thus, the flutter stability including the body effect should be verified. In this research an inverse design method is used to complement the aerodynamic deficiency derived from the fuselage. MGM (modified Garabedian-McFadden) inverse design method is used to optimize the aerodynamic field of a full aircraft model. Furthermore, the present TSD aeroelastic analyses do not require the grid regeneration process. The MGM inverse design method converges faster than other conventional aerodynamic theories. Consequently, the inverse designed aeroelastic analyses show that the flutter stability has been lowered by the body effect.

Panel flutter analysis of general laminated composite plates

The problem of nonlinear aeroelasticity of a general laminated composite plate in supersonic air flow is examined. The classical plate theory along with the von-Karman nonlinear strains is used for structural modeling, and linear piston theory is used for aerodynamic modeling. The coupled partial differential equations of motion are derived by use of Hamilton’s principle and Galerkin’s method is used to reduce the governing equations to a system of nonlinear ordinary differential equations in time, which are then solved by a direct numerical integration method. Effects of in-plane force, static pressure differential, fiber orientation and aerodynamic damping on the nonlinear aeroelastic behavior of the plate are studied. Results show that the fiber orientation has significant effect on dynamic behavior of the plate and the asymmetric properties, changes the behavior of the limit cycle oscillation.

Reliability-Based Design Optimization of Nonlinear Aeroelasticity Problems

This paper introduces a methodology for the reliability-based design optimization (RBDO) of nonlinear aeroelastic problems. It is based on the construction of explicit flutter and subcritical limit cycle oscillations (LCO) boundaries in terms of the design variables. The boundaries, generated using a Support Vector Machine (SVM), can then be used to efficiently evaluate probabilities of failure and solve an RBDO problem. Test results are presented demonstrating the construction of flutter boundaries as well as LCO boundaries for problems with structural nonlinearities. The solution of an example of RBDO problem is also provided.

Numerical investigation on the aeroelastic behavior of an airship with hull-fin configuration

Numerical investigation was conducted on an airship of hull-fin configuration for aerodynamic and aeroelastic characteristics in three-dimensional viscous flows. The mathematical model was built and the corresponding numerical code was developed for the fluid-structure interaction problem. The governing equations of the viscous flow with LL-Low Reynolds modified model were solved by the standard SIMPLE algorithm based on the finite volume method. A fluid-structure coupled method was employed to solve the nonlinear aeroelasticity problem for the airship. The computational results of the viscous flow are in good agreement with the experimental measurements. The simulation on the aeroelastic behavior of the airship in a trimmed flight reveals the effect of structure flexibility on the aerodynamic performance.

Aerodynamic instability of a bridge deck section model: Linear and nonlinear approach to force modeling

The aerodynamic behavior of a bridge deck section model with a simple single-box shape was characterized in wind tunnel. At large nose-up mean angles of attack, a torsional instability arises, outlining a situation in which nonlinear aeroelastic effects may be critical. Such condition represents an interesting case to develop and validate nonlinear models for the aeroelastic problem. The experimental campaign allowed both to characterize the aerodynamic forces using forced motion tests and to study the aeroelastic behavior of the section model, when excited by actively generated turbulent wind. These aeroelastic tests are used to validate a numerical time-domain model for aerodynamic forces that takes into account the nonlinearities due to the reduced velocity and to the amplitude of the instantaneous angle of incidence. Results are critically analyzed and compared with those obtained with a linear model.

Numerical simulation of beam unloading from elastic linkages in a plane-parallel medium flow

The process of profile unloading from elastic linkages in a plane-parallel flow of an incompressible medium is examined. The beam model of profile deformation is used. The parameters of the transient mode under different pause durations between linkage breaks are determined. The procedure permitting the solution of the connected problem of aeroelasticity by means of the vortex elements method used to determine the nonstationary aerodynamic loads is verified and the results of the verification are given.

The Aerodynamic Behaviour of the Deck of Stonecutters Bridge, Hong Kong

Stonecutters Bridge currently under construction in Hong Kong, with a main span of 1018 m, will become one of the longest span cable-stayed bridges in the world on its completion at the end of 2009. The design of the bridge deck contains a number of interesting aerodynamic features including the streamlined steel twin box-girder deck structure and the associated guide vanes installed at the underside of the deck. A bridge of this span will be subject to a variety of wind-induced vibration problems, including vortex-induced response, buffeting response and flutter instability. This, coupled with the extreme typhoon wind climate in Hong Kong, necessitated extensive aerodynamic investigations to address the above-mentioned aeroelastic problems. This paper gives a summary of the investigations concerning the deck of the bridge.

A Simple Analytical Approach to the Aeroelastic Stability Problem of Long-Span Cable-Stayed Bridges

This paper deals with the aeroelastic stability problem of long-span cable-stayed bridges under an approaching crosswind flow. Starting from a continuous model of the fan-shaped bridge scheme with both H- or A-shaped towers, critical states of the coupled wind-structure system are identified by means of a variational formulation, accounting for torsional and flexural (vertical and lateral) bridge oscillations. The overall bridge dynamics is described by introducing simple mechanical systems with equivalent stiffness properties and, under the assumption of a prevailing truss-like bridge behavior, analytical estimates for dominant stiffness contributions are proposed. Several case studies are discussed and comparisons with experimental evidences as well as with available analytical and numerical results are presented. The proposed simplified approach proves to be consistent and effective for successfully capturing the main wind-bridge interaction mechanisms, and it could be considered as a useful engineering tool for the aeroelastic stability analysis of long-span cable-stayed bridges.

FLEXURAL OSCILLATIONS OF FLEXIBLE AIRFOILS IN SUBSONIC COMPRESSIBLE FLOWS

This paper presents simple and efficient analytical solutions for unsteady subsonic compressible flows past flexible airfoils executing low frequency oscillations. These analytical solutions are obtained with a method using velocity singularities related to the airfoil leading edge and ridges. The method has been validated for the pitching and plunging oscillations of the rigid airfoils by comparison with results based on Jordan’s data for compressible flows and by comparison with the solutions obtained by Theodorsen, Postel & Leppert and Mateescu & Abdo for incompressible flows. The method has been applied to obtain efficient analytical solutions for the flexural oscillations of airfoils in compressible flows, which can be efficiently used in solving aeroelastic problems. Professor Carafoli’s contributions to the aerodynamics of airfoils and wings Starting from 1924, in Paris, Elie Carafoli made significant contributions to the aerodynamic studies of wings and airfoils, included in Aerodynamics of airplane wings [5], Theory of lifting airfoils [6], in which he presented the aerodynamics of airfoils with rounded trailing edge, named later Carafoli airfoils, Influence of ailerons on the aerodynamic characteristics of lifting surfaces [7], and in Experimental studies on monoplane wings [8]. After 1928, he continued his research and academic activity in Romania, bringing new contributions to the aerodynamics of wings and airfoils in incompressible flows, which were mostly included in Aerodynamics [9], book also translated from Romanian into German and Russian. After 1950, Elie Carafoli developed a special interest for compressible flows and published High Speed Aerodynamics [10], initially in Romanian and then translated in English. He made, together with his collaborators, important contributions on the aerodynamics of wings and airfoils in supersonic flows, most of them included in the monograph Wing Theory in Supersonic Flow [11] published by Pergamon Press, to which the present author also collaborated. INCAS BULLETIN No. 2/ 2009 51 DOI: 10.13111/2066-8201.2009.1.2.11 For his outstanding achievements in aerodynamics, Elie Carafoli received very numerous international distinctions and awards, such as Diploma “Paul Tisandier” of the International Aeronautical Federation, Gauss Medal attributed yearly to the best scientist in the world by the Scientific Society Braunschweig, Germany, Apollo 11 Medal, Tsiolkovski Medal and many others distinctions which can not be listed here due to the space limitation. Elie Carafoli was one of the few Honorary Fellows of the Royal Aeronautical Society, Great Britain, and one of the first members of the International Academy of Astronautics (proposed by Theodor von Karman), and he was elected first Vice-President and then President of the International Astronautic Federation. In Romania, Carafoli was elected member of the Romanian Academy in 1948, and later named President of the Technical Sciences Section of the Academy, and he received the greatest Romanian medals, prizes and awards. One of the important realizations of Academician Carafoli was the foundation in 1949 of a research institute of the Romanian Academy, known as the Institute of Fluid Mechanics, which is presently named the National Institute for Aerospace Research “Elie Carafoli”. This institute contributed to the scientific formation of numerous former students and collaborators of Professor Carafoli, who distinguished themselves by contributions in aerodynamics and other related aerospace domains. Many of the former students and collaborators of Professor Carafoli became professors at their turn in Romania, as well as in other countries, such as Canada, France, Germany and United States of America, to name only a few. The present author had the privilege to study Aerodynamics with Professor Carafoli, who was also the Ph. D. supervisor, and to be his close collaborator for more than two decades. He is indebted to Professor Carafoli for many research advices, which materialized not only in many publications resulted from their direct scientific collaboration, but also in his further research and academic activity, first in Romania, and since 1982 in Canada. This author, together with his Masters’ and Ph. D. students, aims to continue the best scientific tradition of Professor Carafoli, with new contributions to the aerodynamics of wings and airfoils in steady and unsteady flows in incompressible, compressible subsonic and supersonic regimes and at low Reynolds numbers, in addition to other contributions in related aerospace domains (a few selected examples from the last ten years are included in references [20–37, 43].

Green functions for boundary value problems about divergence of elongated plate

AbstractBucking of a thin flexible elongated plate in supersonic gas flow along Ox‐axis, compressed or extended by boundary stresses at the edges x = 0 and x = 1 is governed by a boundary value problem for nonlinear ordinary integro‐differential equation with two bifurcation parameters: external stress and Mach number. On two examples of boundary conditions Bw″(0) = 0, w‴(0) = 0, w(1) = 0, w′(1) = 0 and B′ w(0) = 0, w′(0) = 0, w″(1) = 0, w‴(1) = 0. Green functions for the linearized problems are constructed. Arising technical difficulties are overcoming with the aid of the bifurcation curves representation through the roots of relevant characteristic equations. In the known literature [1] marked, that Green functions for aeroelasticity problems were not constructed. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Computational aeroelastic studies of a generic hypersonic vehicle

AbstractThe hypersonic aeroelastic problem of a generic hypersonic vehicle having a lifting-body type fuselage and canted fins is studied using third order piston theory and Euler aerodynamics. Computational aeroelastic response results are used to obtain frequency and damping characteristics, and compared with those from piston theory solutions for a variety of flight conditions. Aeroelastic behavior is studied for the range of 2·5 < M < 28, at altitudes ranging from 10,000ft to 80,000ft. Because of the significant computational resources required, a study on optimal mesh selection was first carried out for use with Euler aerodynamics. The three dimensional flow effects captured using Euler aerodynamics was found to lead to significantly higher flutter boundaries when compared to those based on nonlinear piston theory. The results presented here illustrate some of the more important three dimensional effects that can be encountered in hypersonic aeroelasticity of complex configurations.

A study on vortex-induced vibration of supertall buildings in acrosswind

SUMMARY Modern tall buildings using innovative structural systems and high-strength materials tend to be slender and lightly damped. Hence, they are vulnerable to the dynamic action of wind. Crosswind excitation on tall buildings can result in aeroelastic problems. Vortex-induced vibration (VIV) is the prime problem in self-excited vibration of the flexible structures, and it should be especially observed in order to avoid the ultimate limit state in the design stage. In order to predict the vortex-induced response of a supertall building in China with the single-degree-of-freedom (SDOF) mathematical model, wind tunnel tests were carried out with an improved aeroelastic model according to the similitude. The measured top acceleration of the structure showed that VIV was quite significant at some wind speeds and should be considered in the design. Based on the experimental data, the aerodynamic parameters were determined and the characteristics of VIV were investigated in some details. The time history of acceleration at the lock-in wind speed was then obtained using the Runge–Kutta method with the SDOF model. The numerical results are in accordance with the measurements. Copyright © 2009 John Wiley & Sons, Ltd.

Efficient Aeroelastic Analysis Method Including Inverse Design for Body Effects

EROELASTICITY is the research field of studying theinteractionbetweenthestructuraldynamicsandaerodynamics.It deals with the complex coupled phenomena of aircraft in extremeflightconditionsinthedesignstageofaircraftdevelopment.Amongthe aeroelastic problems, flutter phenomenon is the most dangerousone. Furthermore, if the aircraft flies in the transonic range, theaerodynamiccomplexityresultingfromshockwaveoscillation,flowseparation, and so forth, dramatically increases. Therefore, theinvestigation of nonlinear aerodynamics based on computationalfluid dynamics (CFD) has become important in recent aeroelasticanalysis. An aeroelastic examination using an efficient unsteadyaerodynamic analysis with the transonic small-disturbance (TSD)equation, which has been widely recognized as one of the mostefficient CFD-based approaches, has especially strong computa-tional advantages in many different types of parametric studies,because TSD code does not require CFD grid regeneration but onlychangesinwingsurfaceslopeduetostructuralmotiononafixed-gridsystem [1]. Based on these advantages, full-span aircraft have beenstudied.Inanactiveway,thefuselageisusuallyrepresentedbyaboxwithin the embedded multigrid. Instead of the former method, theCFD-basedaeroelasticanalysisofacomplexfull-spanaircraftmodelhasbeenperformedbyYooetal.[2]assumingthattheaerodynamicsof a wing are not influenced by the body shape. This assumption ismeaningful from an aeroelastic point of view, because the main partof lift and flexibility is contributed by the wing. Nevertheless, thefuselage can distort the aerodynamic small-disturbance pressure onthewingsurface, and it is necessary to investigate the bodyeffect influtter analysis [3].Tocomputeapressureperturbationduetothefuselage,aninversedesign method is applied in this research. A typical inverse designmethodismainlyusedtoautomaticallyoptimizetheairfoilgeometrytothelevelofanadequatetargetpressure.Thereareseveralkindsofinverse design methods, such as the MGM (modified Garabedian–McFadden) method [4], defection correction method [5], spring-analogy traction method [6], free-form deformation method, and soon. Among them, the MGM method is simple and easy to adoptbecauseitusesonlyoneauxiliaryequationtoobtainthetargetairfoilshape.ThissimplicitycanbeeffectivefortheCFD-basedaeroelasticanalysis problems, which need a tremendous computing time. TheMGM method assumes that the pressure difference between targetandbaselineairfoilsisafunctionofsurfacedisplacementanditsfirstandsecondderivatives.TheMGMauxiliaryequationregardstherateof change in surface slope as a pseudotime term and iterates until itconverges to zero.Figure1showstheflowchartofinversedesignprocedure.Aswiththe other CFD analysis process, the grid is generated first. Next, thesteadyaerodynamicsareanalyzed.Thenthepressuredistributiononawingsurfaceiscomparedwiththetargetpressuredistribution.Iftheresidualtermisnotzero,allthestepsarerepeated.However,themainadvantage is in the loop. Unlike other CFD codes, the TSD-basedaeroelastic code does not require grid regeneration for every step. Itproceeds with information on surface slope variation.In this study, an efficient aeroelastic analysis method includingbody aerodynamics is introduced. First, TSD theory and aeroelasticequation are explained briefly. Next, the MGM inverse designmethodisusedtomodifytheaerodynamicforcetoincludethebodyeffect.Insequence,thevalidationoftheMGMmethodisgiven.Thenthewing-bodymodelisselectedasanumericalexample.Finally,themodified aeroelastic analysis follows.

Aeroservoelastic Analysis for Transonic Missile Based on Computational Fluid Dynamics

Aeroservoelastic Analysis for Transonic Missile Based on Computational Fluid Dynamics

Adjoint-Based Sensitivity Formulation for Fully Coupled Unsteady Aeroelasticity Problems

A method to compute sensitivities for use in gradient-based shape optimization applied to unsteady aeroelasticity problems is presented. The method takes into account the coupling between all three fundamental aspects of computational aeroelasticity: namely, unsteady flow equations, time-varying structural response to aerodynamic loads, and dynamic meshes that accommodate geometric deformations. The devised method provides discretely exact sensitivities of time-integrated and non-time-integrated objective functions with respect to design variables that control the shape of geometry. The algorithm is formulated in a general manner and can be readily extended to coupled multidisciplinary problems involving any number of disciplines. The algorithm is applied to a simple two-dimensional flutter model to demonstrate the proof of concept.

Application of the modified reduced-order aerodynamics modelling approach to aeroelastic analysis

This study presents the application of the Proposed Modified Reduced-Order Aerodynamics Modelling approach for aeroelastic analysis based on the boundary element method (BEM) as a novel approach. The used BEM has the capability to capture the thickness effect and geometric complexity of a general three-dimensional model. In this approach the reduced-order aerodynamic model is defined through the eigenvalue problem of unsteady flow based on the unknown wake singularities. Based on the used aerodynamic model an explicit algebraic form of the aeroelastic equations is derived that reduces computational efforts and complexity. This special feature enables us to determine the aeroelastic instability directly via eigenanalysis of the aeroelastic problem. The eigenanalysis and reduced-order modelling of unsteady flow over a NACA 0012 airfoil are performed as an example and the results are compared with those obtained from conventional reduced-order modelling (CROM) method. The obtained results demonstrate the accuracy and superior efficiency of the present method over the CROM method. The method was then applied to the aeroelastic analyses of a typical section, in order to show the procedure of driving the explicit algebraic form. Furthermore, to illustrate the capability of the method in the handling of the three-dimensional problems, aeroelastic results for a wing are presented and compared with the results of the Theodorsen's aerodynamic theory.