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Motivations Review of Vortex Model Tower Shadow Model Conclusion

TOWER SHADOW MODELIZATION WITH HELICOIDAL VORTEX METHOD Jean-Jacques Chattot University of California Davis OUTLINE. Motivations Review of Vortex Model Tower Shadow Model Conclusion. 45 th AIAA Aerospace Sciences Meeting and Exhibit

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Motivations Review of Vortex Model Tower Shadow Model Conclusion

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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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