Aeroelasticity : Complexities and Challenges in Rotary

1
Aeroelasticity Complexities and Challenges in
RotaryWing Vehicles

• C. Venkatesan
• IIT Kanpur

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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

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CIVIL STRUCTURES

• Tall chimney/Buildings
• Bridges
• Overhead cables
• Flow through pipes (head exchanger)

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AEROSPACE STRUCTURES

• Aircraft
• (Wings, control surface)
• Rockets
• (Panels, control surface)
• Helicopters
• (Rotor blades, rotor/ fuselage system)
• Gas Turbines (Blades)

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BASIC INGREDIENTS
Aerodynamics
Control

• A-E Static Aeroelasticity
• A-I Flight Mechanics
• E-I Mechanical Vibrations
• /Structural Dynamics

Inertia
Elasticity
A-E-I Dynamic Aeroelasticity A-E-I-C
Aero-Servo-Elasticity
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AEROELASTIC PROBLEMS

• Static aeroelasticity
• Divergence
• Control effectiveness / reversal
• Wing deformation
• Dynamic aeroelasticity
• Dynamic response (Gust, landing)
• Flutter

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MATHEMATICAL FORM
FORM OF BASIC EQUATION
LINEAR/ NONLINEAR/ TIME INVARIANT/ TIME
VARIANT COMPLEXITIES IN - STRUCTURAL
MODELING - AERODYNAMIC MODELING
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STRUCTURAL COMPLEXITY
DISTRIBUTED PARAMETER FUSELAGE (INFINITE DOF)
FE DISCRETISATION (FEW THOUSAND DOF)
MODEL TRANSFORMATION WITH TRUNCATED NUMBER OF
MODES
DYNAMIC ANALYSIS IN MODAL SPACE
GEOMETRIC NONLINEARITY LARGE DEFORMATION MATERIAL
NONLINEARITY ELASTOMERS
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FUSELAGE STRUCTURAL DYNAMIC MODEL ----------------
--------------------------------------------------
-----------

HIGH MODAL DENSITY CLOSELY PLACED MODAL
FREQUENCIES (20 MODES WITHIN 3Hz 30Hz)
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AERODYNAMIC COMPLEXITY
UNSTEADY AERODYNAMICS - SUBSONIC, TRANSONIC,
SUPERSONIC - 3-DIMENSIONAL EFFECTS ATTACHED
FLOW/ SEPARATED FLOW
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INTRODUCTION -------------------------------------
-----------------------------------
Since the First Successful Flight of Truly
Operational, Mechanically Simple and
Controllable Helicopter by Sikorsky
(1939-42) - Continued RD 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
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HELICOPTER AEROELASTICIANS VIEW
AERODYNAMICS - COMPLEX WAKE - BVI
- ROTOR/FUSELAGE
DYNAMICS - BLADE MODES - FUSELAGE MODES
- STRUCTURAL COUPLING - HIGH MODAL DENSITY
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RD 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


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HELICOPTER DYNAMICS -----------------------------
---------------------------------------------
CLASSIFICATION OF PROBLEMS - ISOLATED ROTOR
BLADE AEROELASTICITY (COUPLED
FLAP-LAG-TORSION-AXIAL MODES) - COUPLED
ROTOR-FUSELAGE DYNAMICS
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ROTOR BLADE MODEL --------------------------------
---------------------------------------------
LONG-SLENDER-TWISTED BEAMS UNDERGOING IN-PLANE
BENDING (LAG), OUT-OF-PLANE BENDING
(FLAP), TORSION AND AXIAL DEFORMATIONS

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ROTOR BLADE MODELING -----------------------------
------------------------------------------------
FIRST MODEL 1958 (HouboltsBrooks) SUBSTANTIAL
WORK AFTER 1970

FINITE DEFORMATION MODEL
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Aerodynamics in Forward Flight

• Advancing Side i.e.,
• Retreating side i.e.,

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

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Unsteady Motion of Airfoil

• Sources of unsteadiness in Helicopter rotor blade
• A)
• B)
• C)

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Velocity Components

• Velocity distribution and effective angle of
  attack

• Unsteady motion High angle of attack ? DYNAMIC
  STALL

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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)


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

BLADES FLAP, LAG FUSELAGE PITCH, ROLL
BLADE MOTION IN ROTATING FRAME FUSELAGE
MOTION IN NON-ROTATING FRAME

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GROUND RESONANCE STABILITY ANALYSIS --------------
--------------------------------------------------
----------------
LINEARISED STABILITY EQUATIONS

• INERTIA, STRUCTURAL, AERODYNAMIC
• EFFECTS INCLUDED IN MASS, DAMPING
• AND STIFFNESS MATRICES
• q ROTOR/FUSELAGE/ INFLOW DOF
• EIGENVALUES S??i?
• - MODAL DAMPING (NEGATIVE STABLE POSITIVE
  UNSTABLE)
• ? - MODAL FREQUENCY

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GROUND RESONANCE STABILITY EXPERIMENT BOUSMAN,
US ARMY RES. TECH. LAB (1981) -----------------
--------------------------------------------------
-------------

SEVERAL BLADE CONFIGURATIONS TESTED CONF-1
NON-ROTATING NATURAL FREQ ?F03.13Hz
?L06.70Hz CONF-4 NON-ROTATING NATURAL FREQ
?F06.63Hz ?L06.73Hz

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MODAL FREQUENCY CORRELATION (CONF.-1) UNIFORM
INFLOW MODEL ------------------------------------
--------------------------------------------
ROLL
PITCH
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MODAL FREQUENCY CORRELATION (CONF.-4) UNIFORM
INFLOW MODEL ------------------------------------
--------------------------------------------
ROLL
PITCH-FLAP
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MODAL FREQUENCY CORRELATION (CONF.-4) TIME
VARYING INFLOW MODEL ----------------------------
--------------------------------------------------
--
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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
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FLIGHT DATA
Freq. contents
PWR SPECTRUM Ch A
1 5.250Hz .736E3 NM
2 4.450 .573E3
3 5.100 .547E3
4 4.650 .506E3
5 4.100 .320E3
6 4.950 .278E3
7 0.200 .276E3
8 4.850 .270E3
9 3.950 .210E3
10 4.250 .164E3
moment
Time signal
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DYNAMIC STALL

• Lift coefficient

• Moment coefficient

• Drag coefficient

Courtesy Principles of Helicopter Aerodynamics
G.J.Leishmann
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Unsteady Aerodynamic Coefficients
Reduced freq.
k0.03 k0.05
k0.1
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RESPONSE STUDY

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

• 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

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HEAVE RESPONSE
C.G location Response Frequency
content Phase plane plots Effect of initial
condition Liaponov Exponent
0 3 5
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TORSIONAL RESPONSE
0 3 5
C.G. Location Response Frequency
content Phase plane plots Effect of initial
condition Liaponov Exponent
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CONCLUDING REMARKS -------------------------------
-----------------------------------------------
SEVERAL ISSUES STILL NOT UNDERSTOOD FULLY
CONTINUED RESEARCH TO IMPROVE HELICOPTER
PERFORMANCE VERY FERTILE FIELD FOR CHALLENGING
RESEARCH
THANK YOU