aeroelasticity : complexities and challenges in rotary–wing vehicles
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Aeroelasticity : Complexities and Challenges in Rotary–Wing Vehicles. C. Venkatesan IIT Kanpur. AEROELASTICITY. Study of fluid and structure interaction Applicable for Civil Structures Ships, Offshore Structures Aero Structures - PowerPoint PPT PresentationTRANSCRIPT
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Aeroelasticity : Complexities and Challenges in Rotary–Wing
Vehicles
C. VenkatesanIIT 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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• Aircraft (Wings, control surface)
• Rockets (Panels, control surface)
• Helicopters (Rotor blades, rotor/
fuselage system)
• Gas Turbines (Blades)
AEROSPACE STRUCTURES
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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
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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
tXXXFKXXCXM ,,,
LINEAR/ NONLINEAR/ TIME INVARIANT/ TIME VARIANT
COMPLEXITIES IN- STRUCTURAL MODELING- AERODYNAMIC MODELING
FORM OF BASIC EQUATION
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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
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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
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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 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
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HELICOPTER: AEROELASTICIAN’S VIEW
AERODYNAMICS - COMPLEX WAKE - BVI - ROTOR/FUSELAGE
DYNAMICS - BLADE MODES - FUSELAGE MODES - STRUCTURAL COUPLING - HIGH MODAL DENSITY
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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
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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-----------------------------------------------------------------------------
xi
zi
yi
k j •
•
w
vuix
FIRST MODEL 1958(Houbolts&Brooks)
SUBSTANTIAL WORKAFTER 1970
FINITE DEFORMATION MODEL
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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
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Sources of unsteadiness in Helicopter rotor blade
A)
B)
C)
Unsteady Motion of Airfoil
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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
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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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(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
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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
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
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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
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_____ Uniform Inflow Δ o Experiment
, H
z
, RPM
MODAL FREQUENCY CORRELATION (CONF.-1){UNIFORM INFLOW MODEL}
--------------------------------------------------------------------------------
ROLL
PITCH
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, RPM
, H
z______ Uniform Inflow Δ o Experiment
MODAL FREQUENCY CORRELATION (CONF.-4){UNIFORM INFLOW MODEL}
--------------------------------------------------------------------------------
ROLL
PITCH-FLAP
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______ Perturbation Inflow - - - - - Dynamic Inflow Δ o Experiment
, RPM
, H
z
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
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
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Lift coefficient
Moment coefficient
Drag coefficient
DYNAMIC STALL
Courtesy: Principles of Helicopter Aerodynamics G.J.Leishmann
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Unsteady Aerodynamic Coefficients k=0.03 k=0.05 k=0.1Reduced freq.
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• 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
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HEAVE RESPONSEC.G location
Response
Frequency content
Phase plane plots
Effect of initial condition
Liaponov Exponent
0% 3% 5%
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TORSIONAL RESPONSEC.G. Location
Response
Frequency content
Phase plane plots
Effect of initial condition
Liaponov Exponent
0% 3% 5%
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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