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Tower Shadow Modelization with Helicoidal Vortex Method

Explore tower shadow effects on wind turbine blades using simplified vortex models. Discuss wake models, blade element conditions, and tower interference. See results and conclusions from studied configurations.

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Tower Shadow Modelization with Helicoidal Vortex Method

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  1. TOWER SHADOW MODELIZATION WITH HELICOIDAL VORTEX METHODJean-Jacques ChattotUniversity of California DavisOUTLINE • Motivations • Review of Vortex Model • Tower Shadow Model • Conclusion 45th AIAA Aerospace Sciences Meeting and Exhibit 26th ASME Wind Energy Symposium, Reno, NV, Jan.8-11, 2007

  2. MOTIVATIONS • Take Advantage of Model Simplicity and Efficiency for Analysis of Unsteady Effects with Impact on Blade Fatigue Life and Acoustic Signature - Include Tower Interference Model (Upwind 2006) - Include Tower Shadow Model (Downwind 2007)

  3. 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

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

  5. 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

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

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

  8. APPLICATION OF BIOT-SAVART LAW

  9. BLADE ELEMENT FLOW CONDITIONS

  10. 2-D VISCOUS POLAR S809 profile at Re=500,000 using XFOIL + linear extrapolation to

  11. FLEXIBLE BLADE MODEL • Blade Treated as a Nonhomogeneous Beam • Modal Decomposition (Bending and Torsion) • NREL Blades Structural Properties • Damping Estimated

  12. TOWER SHADOW MODELDOWNWIND CONFIGURATION

  13. 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%

  14. SIMPLIFIED MODEL • LINE OF DOUBLETSPERTURBATION POTENTIAL • If |Y’|>2.5 a, Outside Wake, Use Where: • If |Y’|<2.5 a, Inside Wake:

  15. RESULTS • V=5 m/s, Yaw=0, 5, 10, 20 and 30 deg • V=7 m/s, Yaw=0, 5, 10 and 20 deg • V=10 m/s, Yaw=0, 5, 10 and 20 deg • V=12 m/s, Yaw=0, 10 and 30 deg • Comparison With NREL Sequence B Data

  16. RESULTS FOR ROOT FLAP BENDING MOMENTV=5 m/s, yaw=0 deg

  17. RESULTS FOR ROOT FLAP BENDING MOMENTV=5 m/s, yaw=5 deg

  18. RESULTS FOR ROOT FLAP BENDING MOMENTV=5 m/s, yaw=10 deg

  19. RESULTS FOR ROOT FLAP BENDING MOMENTV=5 m/s, yaw=20 deg

  20. RESULTS FOR ROOT FLAP BENDING MOMENTV=5 m/s, yaw=30 deg

  21. EFFECT OF ROTOR INDUCED VELOCITY ON WAKEV=5 m/s, yaw=30 deg

  22. RESULTS FOR ROOT FLAP BENDING MOMENTV=5 m/s, yaw=30 deg

  23. NREL ROOT FLAP BENDING MOMENT COMPARISONV=7 m/s, yaw=0 deg

  24. NREL ROOT FLAP BENDING MOMENT COMPARISONV=7 m/s, yaw=5 deg

  25. NREL ROOT FLAP BENDING MOMENT COMPARISONV=7 m/s, yaw=10 deg

  26. NREL ROOT FLAP BENDING MOMENT COMPARISONV=7 m/s, yaw=20 deg

  27. NREL ROOT FLAP BENDING MOMENT COMPARISONV=10 m/s, yaw=0 deg

  28. NREL ROOT FLAP BENDING MOMENT COMPARISONV=10 m/s, yaw=5 deg

  29. NREL ROOT FLAP BENDING MOMENT COMPARISONV=10 m/s, yaw=10 deg

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

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

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

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

  34. CONCLUSIONS • Simple model for tower shadow easy to implement • Good results obtained for “downwind” configuration • Some remaining unsteady effects possibly due to tower motion • Vortex Model proves very efficient and versatile

  35. APPENDIX AUAE Sequence QV=8 m/s Dpitch=18 deg CN at 80%

  36. APPENDIX AUAE Sequence QV=8 m/s Dpitch=18 deg CT at 80%

  37. APPENDIX AUAE Sequence QV=8 m/s Dpitch=18 deg

  38. APPENDIX AUAE Sequence QV=8 m/s Dpitch=18 deg

  39. APPENDIX BOptimum Rotor R=63 m P=2 MW

  40. APPENDIX BOptimum Rotor R=63 m P=2 MW

  41. APPENDIX BOptimum Rotor R=63 m P=2 MW

  42. APPENDIX BOptimum Rotor R=63 m P=2 MW

  43. APPENDIX BOptimum Rotor R=63 m P=2 MW

  44. APPENDIX BOptimum Rotor R=63 m P=2 MW

  45. APPENDIX BOptimum Rotor R=63 m P=2 MW

  46. APPENDIX CHomogeneous blade; First mode

  47. APPENDIX CHomogeneous blade; Second mode

  48. APPENDIX CHomogeneous blade; Third mode

  49. APPENDIX CNonhomogeneous blade; M’ distribution

  50. APPENDIX CNonhomog. blade; EIx distribution

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