FLUTTER ANALYSIS OF AGARD WING445.6

HARIKRISHNAN.R(10610101011)MUTHUVEL.J(10610101029)RICHARD FRANKLIN.K(10610101702) PROJECT GUIDE: BALAN

JAYA ENGINEERING COLLEGEDEPATRMENT OF AERONAUTICAL ENGINEERING

The aeroelastic phenomenon named flutter is usually the worst situation in real flight conditions. Flutter can be a

problem with any aircraft design and we prefer to predict and modify the critical flutter speed of an aircraft before an incident occurs. We can accurately predict flutter speed and flutter frequency with analysis programs.we are going to analyze the flutter behavior of the AGARD wing 445.6 and material we are going to select is aluminium alloy. Here we have undertaken the coupling method for predicting the flutter behavior of wing model. The two main parameters we are going to concern are flutter frequency and flutter velocity. We are going to couple the three analysis namely, Modal Analysis for predicting natural frequencies, Aerodynamic analysis calculating the lift force, Structural Analysis for calculating deformation of the wing at different angels.

ABSTRACT

Introduction * aeroelsticity * collar’s triangle * flutter Literature review Design methodology Design proposal Reference

Table of contents

Aeroelasticity can be defined as a science which studies the interaction between inertial forces, aerodynamic forces and elastic forces.

The aeroelastic problems can be classified by means of a modified Collar triangle.

Flutter is defined as the dynamic instability of an elastic body in an airstream it is caused by the unsteady aerodynamic forces generated from elastic deformations of the structure

Introduction

Collar’s triangle

Flutter is an unstable oscillation which can lead to destruction. Flutter can occur on fixed surfaces, such as the wing or the stabilizer, as well as on control surfaces such as the aileron or the elevator for instance.

FLUTTER

Flutter analysis methods

Fully coupled algorithmsThe complete system involving fluid and structure solver is embedded into a unique code. For this case an iterative solution is carried out at each time Step

Strongly coupled algorithmsThese algorithms contain sufficient interaction between the two codes such that the stability of the system is at least equal to that of the least stable code

Weakly coupled algorithmsThese systems usually consist of two separate programs which are connected to each other through a defined interface. Coupling between the two codes is done once for each time step

WING FLUTTER ANALYSIS WITH AN UNCOUPLED METHOD-KAVUKCUOGLU, KORAY,

SUPERSONIC FLUTTER AND POST- FLUTTER CONTROL OF AN AIRCRAFT WING SECTION. -Piergiovanni MARZOCCA, Liviu LIVRESCU, Walter A. SILVA

FLUTTER IN THE SKY-Charbel Farhat STATUS OF UNSTEADY AERODYNAMIC

PREDICTION FOR FLUTTER OF HIGHPERFORMANCE AIRCRAFT-Rudy Yurkovich

Literature review

The software we have handled is CFD (CFX) for Aerodynamical Analysis, CSD for Structural analysis, both softwares belongs to the ANSYS Software package. The three analysis namely

Modal analysis Structural analysis Aerodynamic analysis

Design methodology

Flutter Modeling of a One-Degree-of-Freedom System : The very basic approach to flutter problem is

modeling of a rigid airfoil of unit Span. The airfoil is assumed to be hinged at the leading edge by a torsional spring

Flutter modeling

The stiffness constant of the torsional spring is denoted by Ka, α is the AOA (Angle of Attack), The equation of motion for this system is

Where, Iα- moment of inertia about leading edge My-aerodynamic moment at leading edgeThe oscillation of the airfoil is assumed to be harmonic

oscillation with a frequency of ω, amplitude α and time t,

Flutter Modeling of a Two-Degree-of-Freedom System:The system consists of a rigid airfoil of unit span as in the previous case but in addition to torsional motion,

formulation,

Where,Qh and Qα are aerodynamic force in the vertical direction and aerodynamic moment about the aerodynamic center,m is the mass per unit span,Iα is the mass moment of inertia,Sα is the static mass moment per unit span,ѡh is the uncoupled natural bending frequency, ѡα is the uncoupled natural torsional frequency,

P-K Method: In this method, the flutter problem is formulated by

forced response analysis equations and solved as an eigenvalue problem. The aerodynamic forces are formulated as a function of time, displacement, velocity and acceleration of the structure.

Where,the mass matrix by [M], stiffness matrix by [K] anddisplacement by {q}

COUPLED CFD-CSD METHODS:Coupled CFD-CSD method requires the solution of aeroelasticequations at each time step. In order to calculate the structural deformation of the structure under aerodynamic loading, model equations are used

Where,ζ is the structural damping coefficientQi flutter frequencyωi modal frequency

STRUCTURAL DESIGN OF AGARD 445.6 WING SPECIFICATIONS: Sweep back angle - 45° Taper ratio - 0.66 Cross-section Airfoil - NACA 65004 Root Chord Length - 1.83 ft Tip Chord Length - 1.208 ft Aspect Ratio(semi) - 1.65 Wing Span (semi) - 2.5 ft

AIRFOIL CHARACTERISTICS:The cross section of the AGARD Wing is of the airfoil profile ofNACA 65A-004.

Root coordinate Tip coordinate

x y x y

1.83 0 1.208 0

1.826316 5.52E-05 1.205568 3.64E-05

1.815296 0.000243 1.198293 0.000161

1.797026 0.000627 1.186234 0.000414

1.771655 0.001297 1.169486 0.000856

1.739387 0.002347 1.148185 0.00155

1.700481 0.003854 1.122503 0.002544

1.655251 0.005841 1.092646 0.003856

1.60406 0.008214 1.058855 0.005422

1.547322 0.010951 1.021402 0.007229

1.485493 0.013987 0.980588 0.009233

1.419071 0.017226 0.936742 0.011371

1.34859 0.020562 0.890217 0.013573

1.274618 0.023885 0.841387 0.015767

1.197751 0.027077 0.790646 0.017874

1.118607 0.03002 0.738403 0.019817

1.037823 0.032588 0.685077 0.021511

0.956051 0.034616 0.631098 0.02285

0.873949 0.035943 0.576902 0.023726

0.792177 0.036544 0.522923 0.024123

0.711393 0.036511 0.469597 0.024101

0.632249 0.035932 0.417354 0.023719

0.555382 0.034901 0.366613 0.023039

0.48141 0.033466 0.317783 0.022091

0.410929 0.031668 0.271258 0.020904

0.344507 0.029549 0.227412 0.019505

0.282678 0.027155 0.186598 0.017925

0.22594 0.02456 0.149145 0.016213

0.174749 0.021771 0.115354 0.014371

0.129519 0.018859 0.085497 0.012449

0.090613 0.015911 0.059815 0.010503

0.058345 0.013019 0.038514 0.008594

0.032974 0.010242 0.021766 0.006761

0.014704 0.007227 0.009707 0.004771

0.003684 0.003777 0.002432 0.002493

0 0 0 0

0.003684 0.00378 0.002432 0.00249

0.014704 -0.00723 0.009707 -0.00477

0.032974 -0.01024 0.021766 -0.00676

0.058345 -0.01302 0.038514 -0.00859

0.090613 -0.01591 0.059815 -0.0105

0.129519 -0.01886 0.085497 -0.01245

0.174749 -0.02177 0.115354 -0.01437

0.22594 -0.02456 0.149145 -0.01621

0.282678 -0.02715 0.186598 -0.01792

0.344507 -0.02955 0.227412 -0.01951

0.410929 -0.03167 0.271258 -0.0209

0.48141 -0.03347 0.317783 -0.02209

0.555382 -0.0349 0.366613 -0.02304

0.632249 -0.03593 0.417354 -0.02372

0.711393 -0.03651 0.469597 -0.0241

0.792177 -0.03654 0.522923 -0.02412

0.873949 -0.03594 0.576902 -0.02373

0.956051 -0.03462 0.631098 -0.02285

1.037823 -0.03259 0.685077 -0.02151

1.118607 -0.03002 0.738403 -0.01982

1.197751 -0.02708 0.790646 -0.01787

1.274618 -0.02388 0.841387 -0.01577

1.34859 -0.02056 0.890217 -0.01357

1.419071 -0.01723 0.936742 -0.01137

1.485493 -0.01399 0.980588 -0.00923

1.547322 -0.01095 1.021402 -0.00723

1.60406 -0.00821 1.058855 -0.00542

1.655251 -0.00584 1.092646 -0.00386

1.700481 -0.00385 1.122503 -0.00254

1.739387 -0.00235 1.148185 -0.00155

1.771655 -0.0013 1.169486 -0.00086

1.797026 -0.00063 1.186234 -0.00041

1.815296 -0.00024 1.198293 -0.00016

1.826316 -5.50E-05 1.205568 -3.60E-05

1.83 0 1.208 0

Airfoil cordinates

Airfoil profile at tip:

AIRFOIL PROFILE

airfoil profile at root:

Bisplinghoff R. L., Ashley H., Halfman R. L., Aeroelasticty, 1957, Addison-Wesley Publishing Company.

Theodorsen T., ―General Theory of Aerodynamic Instability and the Mechanism of Flutter, NACA Report 496, 1935

Ashley H., Zartarian G., ―Piston Theory – A New Aerodynamic Tool for the Aeroelastician, Twenty-Fourth Annual Meeting, IAS, New York, January 23-26,1956

Lee-Rausch, E. M., Batina, J. T., ―Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics, AIAA-93-3476, 1993

References