1. HELICOIDAL VORTEX MODEL FOR WIND TURBINE AEROELASTIC SIMULATION Jean-Jacques Chattot University of California Davis OUTLINE
Challenges in Wind Turbine Flows
The Analysis Problem and Simulation Tools
The Vortex Model
The Structural Model
Some Results
Conclusions
Fourth M.I.T. Conference
June 13-15, 2007

2. CHALLENGES IN WIND TURBINE FLOW ANALYSIS
Vortex Structure
- importance of maintaining vortex structure D
- free wake vs. prescribed wake models
High Incidence on Blades
- separated flows and 3-D viscous effects
Unsteady Effects
- yaw, tower interaction, earth boundary layer
Blade Flexibility

3. THE ANALYSIS PROBLEM AND SIMULATION TOOLS
Actuator Disk Theory (1-D Flow)
Empirical Dynamic Models (Aeroelasticity)
Vortex Models
- prescribed wake + equilibrium condition
- free wake
Euler/Navier-Stokes Codes
- 10 M grid points, still dissipates wake
- not practical for design
- expensive to couple with structural model
Hybrid Models

4. REVIEW OF VORTEX MODEL Goldstein Model Simplified Treatment of Wake
Rigid Wake Model
“Ultimate Wake” Equilibrium Condition
Base Helix Geometry Used for Steady and Unsteady Flows
Application of Biot-Savart Law
Blade Element Flow Conditions
2-D Viscous Polar

5. GOLDSTEIN MODEL
Vortex sheet constructed as perfect helix with variable pitch

6. SIMPLIFIED TREATMENT OF WAKE
No stream tube expansion, no sheet edge roll-up (second-order effects)
Vortex sheet constructed as perfect helix called the “base helix” corresponding to zero yaw

7. “ULTIMATE WAKE” EQUILIBRIUM CONDITION
Induced axial velocity from average power:

8. BASE HELIX GEOMETRY USED FOR STEADY AND UNSTEADY FLOWS
Vorticity is convected along the base helix, not the displaced helix, a first-order approximation

9. APPLICATION OF BIOT-SAVART LAW

10. BLADE ELEMENT FLOW CONDITIONS

11. 2-D VISCOUS POLAR S809 profile at Re=500,000 using XFOIL
+ linear extrapolation to

12. CONVECTION IN THE WAKE Mesh system: stretched mesh from blade
To x=1 where
Then constant steps to
Convection equation along vortex filament j:
Boundary condition

13. CONVECTION IN THE WAKE

14. ATTACHED/STALLED FLOWS
Blade working conditions: attached/stalled

15. RESULTS: STEADY FLOW
Power output comparison

16. RESULTS: YAWED FLOW
Time-averaged power versus velocity at different yaw angles
=5 deg
=10 deg
=20 deg
=30 deg

17. STRUCTURAL MODEL Blade Treated as a Nonhomogeneous Beam
Modal Decomposition (Bending and Torsion)
NREL Blades Structural Properties
Damping Estimated

18. NREL BLADES Structural Coefficients: - M’=5 kg/m - EIx=800,000 Nm2
- cfb=4
First Mode Frequency
- f1=7.28 Hz (vs Hz for NREL blade)

19. TIME AND SPACE APPROACHES
Typical Time Steps:
- Taero= s (1 deg azimuthal angle)
- Tstruc= s (with 21 points on blade)
Explicit Scheme
Large integration errors due to drifting
Implicit Scheme
Second-Order in time unstable
First-order not accurate enough
Modal Decomposition
Very accurate. Integration error only in source term

20. NREL ROOT FLAP BENDING MOMENT COMPARISON V=5 m/s, yaw=10 deg

21. TOWER SHADOW MODEL DOWNWIND CONFIGURATION

22. TOWER SHADOW MODEL
Model includes Wake Width and Velocity Deficit Profile, Ref: Coton et Al. 2002
Model Based on Wind Tunnel Measurements Ref: Snyder and Wentz ’81
Parameters selected:
Wake Width 2.5 Tower Radius, Velocity Deficit 30%

23. SOME RESULTS V=5 m/s, Yaw=0, 5, 10, 20 and 30 deg
Comparison With NREL Sequence B Data

24. RESULTS FOR ROOT FLAP BENDING MOMENT V=5 m/s, yaw=0 deg

25. RESULTS FOR ROOT FLAP BENDING MOMENT V=5 m/s, yaw=5 deg

26. RESULTS FOR ROOT FLAP BENDING MOMENT V=5 m/s, yaw=10 deg

27. RESULTS FOR ROOT FLAP BENDING MOMENT V=5 m/s, yaw=20 deg

28. RESULTS FOR ROOT FLAP BENDING MOMENT V=5 m/s, yaw=30 deg

29. NREL ROOT FLAP BENDING MOMENT COMPARISON V=10 m/s, yaw=0 deg

30. NREL ROOT FLAP BENDING MOMENT COMPARISON V=10 m/s, yaw=20 deg

31. NREL ROOT FLAP BENDING MOMENT COMPARISON V=12 m/s, yaw=0 deg

32. NREL ROOT FLAP BENDING MOMENT COMPARISON V=12 m/s, yaw=10 deg

33. NREL ROOT FLAP BENDING MOMENT COMPARISON V=12 m/s, yaw=30 deg

34. CONCLUSIONS
Stand-alone Navier-Stokes: too expensive, dissipates wake, cannot be used for design or aeroelasticity
Vortex Model: simple, efficient, can be used for design and aeroelasticity
Remaining discrepancies possibly due to tower motion

35. HYBRID APPROACH Use Best Capabilities of Physical Models
- Navier-Stokes for near-field viscous flow
- Vortex model for far-field inviscid wake
Couple Navier-Stokes with Vortex Model
- improved efficiency
- improved accuracy

36. HYBRID METHODOLOGY Navier-Stokes Vortex Method
Vortex Filament
Biot-Savart Law (discrete)
Boundary of
Navier-Stokes Zone
Converged for …
Bound Vortex
Fig. 1 Coupling Methodology

37. RECENT PUBLICATIONS
J.-J. Chattot, “Helicoidal vortex model for steady and unsteady flows”, Computers and Fluids, Special Issue, 35, : (2006).
S. H. Schmitz, J.-J. Chattot, “A coupled Navier-Stokes/Vortex-Panel solver for the numerical analysis of wind turbines”, Computers and Fluids, Special Issue, 35: (2006).
J. M. Hallissy, J.J. Chattot, “Validation of a helicoidal vortex model with the NREL unsteady aerodynamic experiment”, CFD Journal, Special Issue, 14: (2005).
S. H. Schmitz, J.-J. Chattot, “A parallelized coupled Navier-Stokes/Vortex-Panel solver”, Journal of Solar Energy Engineering, 127: (2005).
J.-J. Chattot, “Extension of a helicoidal vortex model to account for blade flexibility and tower interference”, Journal of Solar Energy Engineering, 128: (2006).
S. H. Schmitz, J.-J. Chattot, “Characterization of three-dimensional effects for the rotating and parked NREL phase VI wind turbine”, Journal of Solar Energy Engineering, 128: (2006).
J.-J. Chattot, “Helicoidal vortex model for wind turbine aeroelastic simulation”, Computers and Structures, to appear, 2007.

38. APPENDIX A UAE Sequence Q V=8 m/s Dpitch=18 deg CN at 80%

39. APPENDIX A UAE Sequence Q V=8 m/s Dpitch=18 deg CT at 80%

40. APPENDIX A UAE Sequence Q V=8 m/s Dpitch=18 deg

41. APPENDIX A UAE Sequence Q V=8 m/s Dpitch=18 deg

42. APPENDIX B Optimum Rotor R=63 m P=2 MW

43. APPENDIX B Optimum Rotor R=63 m P=2 MW

44. APPENDIX B Optimum Rotor R=63 m P=2 MW

45. APPENDIX B Optimum Rotor R=63 m P=2 MW

46. APPENDIX B Optimum Rotor R=63 m P=2 MW

47. APPENDIX B Optimum Rotor R=63 m P=2 MW

48. APPENDIX B Optimum Rotor R=63 m P=2 MW

49. APPENDIX C Homogeneous blade; First mode

50. APPENDIX C Homogeneous blade; Second mode

51. APPENDIX C Homogeneous blade; Third mode

52. APPENDIX C Nonhomogeneous blade; M’ distribution

53. APPENDIX C Nonhomog. blade; EIx distribution

54. APPENDIX C Nonhomogeneous blade; First mode

55. APPENDIX C Nonhomogeneous blade; Second mode

56. APPENDIX C Nonhomogeneous blade; Third mode

57. APPENDIX D: NONLINEAR TREATMENT
Discrete equations: If
Where

58. APPENDIX D: NONLINEAR TREATMENTIf
is the coefficient of artificial viscosity
Solved using Newton’s method