Aeroelasticity : Complexities and Challenges in Rotary–Wing Vehicles

1. Aeroelasticity : Complexities and Challenges in Rotary–Wing Vehicles C. Venkatesan IIT Kanpur

2. 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

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

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

5. A C E I 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

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

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

8. 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

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

10. AERODYNAMIC COMPLEXITY UNSTEADY AERODYNAMICS - SUBSONIC, TRANSONIC, SUPERSONIC - 3-DIMENSIONAL EFFECTS ATTACHED FLOW/ SEPARATED FLOW

11. 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

12. HELICOPTER: AEROELASTICIAN’S VIEW AERODYNAMICS - COMPLEX WAKE - BVI - ROTOR/FUSELAGE DYNAMICS - BLADE MODES - FUSELAGE MODES - STRUCTURAL COUPLING - HIGH MODAL DENSITY

13. 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

14. HELICOPTER DYNAMICS -------------------------------------------------------------------------- CLASSIFICATION OF PROBLEMS - ISOLATED ROTOR BLADE AEROELASTICITY (COUPLED FLAP-LAG-TORSION-AXIAL MODES) - COUPLED ROTOR-FUSELAGE DYNAMICS

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

16. ROTOR BLADE MODELING ----------------------------------------------------------------------------- FIRST MODEL 1958 (Houbolts&Brooks) SUBSTANTIAL WORK AFTER 1970 FINITE DEFORMATION MODEL

17. 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.

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

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

20. 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)

21. GROUND RESONANCE

22. (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

23.   GROUND RESONANCE -------------------------------------------------------------------------------- • BLADES: FLAP, LAG • FUSELAGE: PITCH, ROLL • BLADE MOTION IN ROTATING FRAME • FUSELAGE MOTION IN NON-ROTATING FRAME

24.   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

25. BLADE ATTACHMENT TEST SETUP GROUND RESONANCE STABILITY: EXPERIMENT {BOUSMAN, US ARMY RES. & TECH. LAB (1981)} -------------------------------------------------------------------------------- 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

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

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

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

29. 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

30. FLIGHT DATA Freq. contents PWR SPECTRUM Ch A moment Time signal

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

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

33. 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

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

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

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