1. WIND TURBINE FLOW ANALYSIS Jean-Jacques Chattot University of California Davis OUTLINE
Challenges in Wind Turbine Flows
The Analysis Problem and Simulation Tools
The Vortex Model
The Hybrid Approach
Conclusion
GGAM Mini-Conference
Saturday, March 31, 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. CHALLENGES IN WIND TURBINE FLOW ANALYSIS

4. 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

5. 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

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

7. 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

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

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

10. APPLICATION OF BIOT-SAVART LAW

11. BLADE ELEMENT FLOW CONDITIONS

12. 2-D VISCOUS POLAR S809 profile at Re=500,000 using XFOIL
+ linear extrapolation to

13. NONLINEAR TREATMENT
Discrete equations: If
Where

14. NONLINEAR TREATMENT If is the coefficient of artificial viscosity
Solved using Newton’s method

15. 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

16. CONVECTION IN THE WAKE

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

18. RESULTS: STEADY FLOW
Power output comparison

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

20. 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

21. 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

22. 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.

23. CONCLUSIONS Vortex Model: simple, efficient, can be used for design
Stand-alone Navier-Stokes: too expensive, dissipates wake, cannot be used for design
Hybrid Model: takes best of both models to create most efficient and reliable simulation tool
Next Frontier: aeroelasticity and multidisciplinary design

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

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

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

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

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

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

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

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

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

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

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

35. APPENDIX C Homogeneous blade; First mode

36. APPENDIX C Homogeneous blade; Second mode

37. APPENDIX C Homogeneous blade; Third mode

38. APPENDIX C Nonhomogeneous blade; M’ distribution

39. APPENDIX C Nonhomog. blade; EIx distribution

40. APPENDIX C Nonhomogeneous blade; First mode

41. APPENDIX C Nonhomogeneous blade; Second mode

42. APPENDIX C Nonhomogeneous blade; Third mode

43. TOWER SHADOW MODEL DOWNWIND CONFIGURATION