Aeroelasticity : Complexities and Challenges in Rotary–Wing

Vehicles

C. VenkatesanIIT Kanpur

AEROELASTICITY

Study of fluid and structure interaction

Applicable for•Civil Structures•Ships, Offshore Structures•Aero Structures

More specifically used to address issues related to flying vehicles

CIVIL STRUCTURES

• Tall chimney/Buildings

• Bridges

• Overhead cables

• Flow through pipes (head exchanger)

• Aircraft (Wings, control surface)

• Rockets (Panels, control surface)

• Helicopters (Rotor blades, rotor/

fuselage system)

• Gas Turbines (Blades)

AEROSPACE STRUCTURES

BASIC INGREDIENTS

A-E Static AeroelasticityA-I Flight MechanicsE-I Mechanical Vibrations /Structural Dynamics

E

A

I

C

Aerodynamics

Elasticity Inertia

Control

A-E-I Dynamic AeroelasticityA-E-I-C Aero-Servo-Elasticity

AEROELASTIC PROBLEMS

• Static aeroelasticity– Divergence– Control effectiveness /

reversal– Wing deformation

• Dynamic aeroelasticity– Dynamic response

(Gust, landing)– Flutter

MATHEMATICAL FORM

tXXXFKXXCXM ,,,

LINEAR/ NONLINEAR/ TIME INVARIANT/ TIME VARIANT

COMPLEXITIES IN- STRUCTURAL MODELING- AERODYNAMIC MODELING

FORM OF BASIC EQUATION

STRUCTURAL COMPLEXITYDISTRIBUTED PARAMETER FUSELAGE (INFINITE DOF)

FE DISCRETISATION (FEW THOUSAND DOF)

MODEL TRANSFORMATION WITH TRUNCATED NUMBER OF MODES

DYNAMIC ANALYSIS IN MODAL SPACE

GEOMETRIC NONLINEARITY: LARGE DEFORMATIONMATERIAL NONLINEARITY: ELASTOMERS

FUSELAGE STRUCTURAL DYNAMIC MODEL-----------------------------------------------------------------------------

HIGH MODAL DENSITY: CLOSELY PLACED MODAL FREQUENCIES (20 MODES WITHIN 3Hz – 30Hz)

Mode 1: 3.51HzMode 2: 4.15Hz

Mode 3: 5.35HzMode 4: 12.05Hz

AERODYNAMIC COMPLEXITY

UNSTEADY AERODYNAMICS

- SUBSONIC, TRANSONIC, SUPERSONIC- 3-DIMENSIONAL EFFECTS

ATTACHED FLOW/ SEPARATED FLOW

INTRODUCTION-----------------------------------------------------------------------

-• Since the First Successful Flight of Truly Operational, Mechanically Simple and Controllable Helicopter by Sikorsky (1939-42)

- Continued R&D Efforts to Improve Helicopter By

Incorporating New Technological Developments As and When Matured and Available

• Composites• Automatic Flight Control Systems• Noise and Vibration Control • Advances in Fundamental Understanding of Rotor/ Fuselage Dynamics, and Aerodynamics

HELICOPTER: AEROELASTICIAN’S VIEW

AERODYNAMICS - COMPLEX WAKE - BVI - ROTOR/FUSELAGE

DYNAMICS - BLADE MODES - FUSELAGE MODES - STRUCTURAL COUPLING - HIGH MODAL DENSITY

R&D EFFORTS --------------------------------------------------------------------------------

• INTENSELY PURSUED BY ACADEMIA AND INDUSTRY

• CONSIDERABLE PROGRESS IN THE PAST 40 YEARS

• STILL SEVERAL DISCREPANCIES EXIST BETWEEN THEORY AND EXPERIMENT

• MODEL TESTS AND FLIGHT MEASUREMENTS PROVIDE DATA FOR CORRELATION

• IMPROVE UNDERSTANDING OF THE PHYSICS OF THE PROBLEM

• MODIFY, DEVELOP SUITABLE MATHEMATICAL MODELS

HELICOPTER DYNAMICS --------------------------------------------------------------------------

CLASSIFICATION OF PROBLEMS

- ISOLATED ROTOR BLADE AEROELASTICITY (COUPLED FLAP-LAG-TORSION-AXIAL MODES)

- COUPLED ROTOR-FUSELAGE DYNAMICS

ROTOR BLADE MODEL-----------------------------------------------------------------------------

LONG-SLENDER-TWISTED BEAMS UNDERGOING IN-PLANE BENDING (LAG), OUT-OF-PLANE BENDING (FLAP),TORSION AND AXIAL DEFORMATIONS

ROTOR BLADE MODELING-----------------------------------------------------------------------------

xi

zi

yi

k j •

•

w

vuix

FIRST MODEL 1958(Houbolts&Brooks)

SUBSTANTIAL WORKAFTER 1970

FINITE DEFORMATION MODEL

Aerodynamics in Forward Flight 0 180deg.

180 360 deg.

Advancing side : High velocity Low angle of attack Retreating side : Low velocity High angle of attack Blade stall occurs in the retreating region.

Advancing Side i.e.,

Retreating side i.e.,sin VrV

Sources of unsteadiness in Helicopter rotor blade

A)

B)

C)

Unsteady Motion of Airfoil

sinTV r R v

1tan P

T

VV

eff

2 2T PV V V

Velocity Components Velocity distribution and effective angle of attack :

Unsteady motion + High angle of attack DYNAMIC STALL

wRwRVp cos

COUPLED ROTOR-FUSELAGE DYNAMICS--------------------------------------------------------------------------------

• VEHICLE DYNAMICS (FLYING AND HANDLING QUALITIES)- FUSELAGE RIGID BODY- BLADE FLAP DYNAMICS (DOMINANT)- FREQUENCY RANGE 0.3Hz – 1.5Hz

• AEROMECHANICAL INSTABILITIES (GROUND/ AIR RESONANCE)- FUSELAGE RIGID BODY- BLADE LAG DYNAMICS (DOMINANT)- FREQUENCY RANGE 2Hz – 5Hz

• HELICOPTER VIBRATION- FLEXIBLE FUSELAGE- FLAP-LAG-TORSION MODES - FREQUENCY RANGE (ABOVE 10Hz)

GROUND RESONANCE

(a) Collective (b) Cosine cyclic (c) Sine cyclic (d) Alternating

ROTOR MODES vs BLADE MOTION--------------------------------------------------------------------------------

SHIFT OF ROTOR SYSTEM C.G FROM CENTRE IN CYCLIC MODES

AS THE BLADES ROTATE, MOVEMENT OF ROTOR C.G CAUSES CHURNING MOTION TO HELICOPTER

GROUND RESONANCE--------------------------------------------------------------------------------

• BLADES: FLAP, LAG

• FUSELAGE: PITCH, ROLL

• BLADE MOTION IN ROTATING FRAME

• FUSELAGE MOTION IN NON-ROTATING FRAME

GROUND RESONANCE STABILITY ANALYSIS

--------------------------------------------------------------------------------

• LINEARISED STABILITY EQUATIONS

0 qKqCqM

INERTIA, STRUCTURAL, AERODYNAMICEFFECTS INCLUDED IN MASS, DAMPINGAND STIFFNESS MATRICES

{q} – ROTOR/FUSELAGE/ INFLOW DOF

EIGENVALUES S=i

- MODAL DAMPING (NEGATIVE STABLE; POSITIVE UNSTABLE) - MODAL FREQUENCY

GROUND RESONANCE STABILITY: EXPERIMENT{BOUSMAN, US ARMY RES. & TECH. LAB (1981)}

--------------------------------------------------------------------------------

BLADE ATTACHMENTTEST SETUP

SEVERAL BLADE CONFIGURATIONS TESTEDCONF-1: NON-ROTATING NATURAL FREQ: F0=3.13Hz L0=6.70HzCONF-4: NON-ROTATING NATURAL FREQ: F0=6.63Hz L0=6.73Hz

_____ Uniform Inflow Δ o Experiment

, H

z

, RPM

MODAL FREQUENCY CORRELATION (CONF.-1){UNIFORM INFLOW MODEL}

--------------------------------------------------------------------------------

ROLL

PITCH

, RPM

, H

z______ Uniform Inflow Δ o Experiment

MODAL FREQUENCY CORRELATION (CONF.-4){UNIFORM INFLOW MODEL}

--------------------------------------------------------------------------------

ROLL

PITCH-FLAP

______ Perturbation Inflow - - - - - Dynamic Inflow Δ o Experiment

, RPM

, H

z

MODAL FREQUENCY CORRELATION (CONF.-4){TIME VARYING INFLOW MODEL}

--------------------------------------------------------------------------------

REMARKS--------------------------------------------------------------------------------

CORRELATION STUDY TAUGHT THE LESSON:

• A GOOD (OR ADEQUATE) ANALYTICAL MODEL FOR ONE ROTOR CONFIGURATION MAY NOT BE ADEQUATE FOR OTHER ROTOR CONFIGURATIONS

REMINDS THE PROVERB

WHAT IS GOOD FOR THE GOOSE, IS NOT GOOD FOR THE GANDER

FLIGHT DATA

1 5.250Hz .736E+3 NM

2 4.450 .573E+3

3 5.100 .547E+3

4 4.650 .506E+3

5 4.100 .320E+3

6 4.950 .278E+3

7 0.200 .276E+3

8 4.850 .270E+3

9 3.950 .210E+3

10 4.250 .164E+3

PWR SPECTRUM Ch A

moment

Time signal

Freq. contents

Lift coefficient

Moment coefficient

Drag coefficient

DYNAMIC STALL

Courtesy: Principles of Helicopter Aerodynamics G.J.Leishmann

Unsteady Aerodynamic Coefficients k=0.03 k=0.05 k=0.1Reduced freq.

• Response of 2-D airfoil undergoing pitching and heaving in a pulsating flow is analysed

• The pitching motion and oncoming flow velocity are taken as

0

0

0

0

12 ; 6

113 / sec; 45.2 / sec22.83 / sec (3.63 )

o o

Sin t

V V V Sin t

V m V mrad Hz

2-D Airfoil response simulating cross-section of a rotor blade

RESPONSE STUDY

HEAVE RESPONSEC.G location

Response

Frequency content

Phase plane plots

Effect of initial condition

Liaponov Exponent

0% 3% 5%

TORSIONAL RESPONSEC.G. Location

Response

Frequency content

Phase plane plots

Effect of initial condition

Liaponov Exponent

0% 3% 5%

CONCLUDING REMARKS------------------------------------------------------------------------------

• SEVERAL ISSUES STILL NOT UNDERSTOOD FULLY

• CONTINUED RESEARCH TO IMPROVE HELICOPTER PERFORMANCE

• VERY FERTILE FIELD FOR CHALLENGING RESEARCH

THANK YOU