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 More specifically used to address issues related to flying vehicles

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

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

BASIC INGREDIENTS A-E Static Aeroelasticity A-I Flight Mechanics Aerodynamics Control E A I C A-E Static Aeroelasticity A-I Flight Mechanics E-I Mechanical Vibrations /Structural Dynamics Elasticity Inertia A-E-I Dynamic Aeroelasticity A-E-I-C Aero-Servo-Elasticity

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

MATHEMATICAL FORM FORM OF BASIC EQUATION LINEAR/ NONLINEAR/ TIME INVARIANT/ TIME VARIANT COMPLEXITIES IN - STRUCTURAL MODELING - AERODYNAMIC MODELING

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

FUSELAGE STRUCTURAL DYNAMIC MODEL ----------------------------------------------------------------------------- Mode 1: 3.51Hz Mode 2: 4.15Hz Mode 3: 5.35Hz Mode 4: 12.05Hz HIGH MODAL DENSITY: CLOSELY PLACED MODAL FREQUENCIES (20 MODES WITHIN 3Hz – 30Hz)

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 ----------------------------------------------------------------------------- FIRST MODEL 1958 (Houbolts&Brooks) SUBSTANTIAL WORK AFTER 1970 FINITE DEFORMATION MODEL

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.

Unsteady Motion of Airfoil Sources of unsteadiness in Helicopter rotor blade A) B) C)

Velocity Components Velocity distribution and effective angle of attack : Unsteady motion + High angle of attack  DYNAMIC STALL

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) - BLADE LAG DYNAMICS (DOMINANT) - FREQUENCY RANGE 2Hz – 5Hz • HELICOPTER VIBRATION - FLEXIBLE FUSELAGE - FLAP-LAG-TORSION MODES - FREQUENCY RANGE (ABOVE 10Hz)

GROUND RESONANCE

ROTOR MODES vs BLADE MOTION -------------------------------------------------------------------------------- (a) Collective (b) Cosine cyclic (c) Sine cyclic (d) Alternating 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 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

GROUND RESONANCE STABILITY: EXPERIMENT {BOUSMAN, US ARMY RES. & TECH. LAB (1981)} -------------------------------------------------------------------------------- TEST SETUP BLADE ATTACHMENT SEVERAL BLADE CONFIGURATIONS TESTED CONF-1: NON-ROTATING NATURAL FREQ: F0=3.13Hz L0=6.70Hz CONF-4: NON-ROTATING NATURAL FREQ: F0=6.63Hz L0=6.73Hz

MODAL FREQUENCY CORRELATION (CONF.-1) {UNIFORM INFLOW MODEL} -------------------------------------------------------------------------------- _____ Uniform Inflow Δ o Experiment , Hz , RPM ROLL PITCH

MODAL FREQUENCY CORRELATION (CONF.-4) {UNIFORM INFLOW MODEL} -------------------------------------------------------------------------------- , RPM , Hz ______ Uniform Inflow Δ o  Experiment ROLL PITCH-FLAP

MODAL FREQUENCY CORRELATION (CONF.-4) {TIME VARYING INFLOW MODEL} -------------------------------------------------------------------------------- ______ Perturbation Inflow - - - - - Dynamic Inflow Δ o  Experiment , RPM , Hz

WHAT IS GOOD FOR THE GOOSE, IS NOT GOOD FOR THE GANDER 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 Freq. contents Time signal moment PWR SPECTRUM Ch A 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 moment Time signal

DYNAMIC STALL Lift coefficient Moment coefficient Drag coefficient Courtesy: Principles of Helicopter Aerodynamics G.J.Leishmann

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

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

HEAVE RESPONSE 0% 3% 5% C.G location Response Frequency content Phase plane plots Effect of initial condition Liaponov Exponent 0% 3% 5%

TORSIONAL RESPONSE 0% 3% 5% Frequency content Phase plane plots 0% 3% 5% C.G. Location Response Frequency content Phase plane plots Effect of initial condition Liaponov Exponent

CONCLUDING REMARKS ------------------------------------------------------------------------------ • SEVERAL ISSUES STILL NOT UNDERSTOOD FULLY • CONTINUED RESEARCH TO IMPROVE HELICOPTER PERFORMANCE • VERY FERTILE FIELD FOR CHALLENGING RESEARCH THANK YOU