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Wind energy I. Lesson 7. Wind blade interaction

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Wind energy I. Lesson 7. Wind blade interaction

  1. 1. Wind Energy I Wind-blade interaction consequences for designMichael Hölling, WS 2010/2011 slide 1
  2. 2. Wind Energy I Class content 5 Wind turbines in 6 Wind - blades general 2 Wind measurements interaction 7 Π-theorem 8 Wind turbine characterization 3 Wind field 9 Control strategies characterization 10 Generator 4 Wind power 11 Electrics / gridMichael Hölling, WS 2010/2011 slide 2
  3. 3. Wind Energy I Lift and drag Fl Fres c Fd u α dr 1 Lift force: Fl = cl (α) · · ρ · A · u 2 2 with A = c · dr 1 Drag force: Fd = cd (α) · · ρ · A · u 2 2Michael Hölling, WS 2010/2011 slide 3
  4. 4. Wind Energy I Lift and drag Direct force measurements FL CL,F = 1 2 · ρ · v2 · AMichael Hölling, WS 2010/2011 slide 4
  5. 5. Wind Energy I Lift and drag Pressure measurements pp − ps L CL,p = 1 · 2 · ρ · v2 c · η the so called Althaus factor η corrects for the finite length of LMichael Hölling, WS 2010/2011 slide 5
  6. 6. Wind Energy I Lift and drag Test section in wind tunnelMichael Hölling, WS 2010/2011 slide 6
  7. 7. Wind Energy I Lift and drag Test section in wind tunnelMichael Hölling, WS 2010/2011 slide 7
  8. 8. Wind Energy I Lift and drag Test section in wind tunnelMichael Hölling, WS 2010/2011 slide 8
  9. 9. Wind Energy I Lift and drag Test section in wind tunnelMichael Hölling, WS 2010/2011 slide 9
  10. 10. Wind Energy I Lift and drag Lift coefficient for laminar inflow condition 1.2 1 0.8 0.6 c /1 L 0.4 0.2 force measurement 0 wall pressure measurement reference Althaus −0.2 −5 0 5 10 15 20 25 AoA α / °Michael Hölling, WS 2010/2011 slide 10
  11. 11. Wind Energy I Lift and drag cl cd cd cl angle of attack αMichael Hölling, WS 2010/2011 slide 11
  12. 12. Wind Energy I Lift and drag cl (α) Lift to drag ration: (α) = cd (α) 1/ (α) cl angle of attack αMichael Hölling, WS 2010/2011 slide 12
  13. 13. Wind Energy I Rotor blade design http://www.ecogeneration.com.auMichael Hölling, WS 2010/2011 slide 13
  14. 14. Wind Energy I Rotor blade design http://www.ecogeneration.com.auMichael Hölling, WS 2010/2011 slide 13
  15. 15. Wind Energy I Velocities at rotor blade R urotR = ω R ures u2 β uR ures u2 urot2 = ω r2 β ur2r ures u2 β urot1 = ω r1 ur1 2 ω u2 = · u1 3Michael Hölling, WS 2010/2011 slide 14
  16. 16. Wind Energy I Velocities at rotor blade 2 2 ures (r) = u1 + (ω · r)2 3 80 ures 60 ures [m/s] 40 20 0 0 10 20 30 40 50 r [m]Michael Hölling, WS 2010/2011 slide 15
  17. 17. Wind Energy I Forces at rotor blade plane of rotation u2 urot β ures Fl Fres α . Fd ω 1 Fl = · ρ · A · cl (α) · u2 2 res 1 Fd = · ρ · A · cd (α) · ures 2 2Michael Hölling, WS 2010/2011 slide 16
  18. 18. Wind Energy I Forces at rotor blade Force component in direction of rotation u2 plane of rotation urot β ures Fl β 1 Flrot = · ρ · A · cl (α) · u2 · sin(β) 2 resFres α . 1 Fd Fdrot = − · ρ · A · cd (α) · u2 · cos(β) 2 res ω β 1 Frot = · ρ · A · u2 · [cl (α) · sin(β) − cd (α) · cos(β)] 2 resMichael Hölling, WS 2010/2011 slide 17
  19. 19. Wind Energy I Blade optimization using Betz Maximal extractable power based on Betz For the whole plane: 16 1 PBetz = · · ρ · u1 · (π · R ) 3 2 27 2 dr For a ring-segment: r 16 1 dPBetz = · · ρ · u3 · (2 · π · r · dr) 27 2 1 dAMichael Hölling, WS 2010/2011 slide 18
  20. 20. Wind Energy I Blade optimization using Betz The design of the blade should achieve this dPBetz for each ring- segment !!! The mechanical power that can be converted by the segments dA of z rotor blades is given by: 1 dProt = z · · ρ · c(r) · dr ·ures · cl (α) · sin(β) · urot (r) 2 2 dA ω·r This should be equal to dPBetz for an optimum design: dProt = dPBetzMichael Hölling, WS 2010/2011 slide 19
  21. 21. Wind Energy I Blade optimization using Betz After all the calculations the chord length can be determined by: 1 2·π·R 8 1 c(r) = · · · z cl (α) 9 2· r 2+ 4 λ· λ R 9 What is the right choice for: R=? cl(α) = ? z=? λ=?Michael Hölling, WS 2010/2011 slide 20
  22. 22. Wind Energy I Blade optimization using Betz Rotor radius R determines the maximum extractable power from the wind and is linked to the power of the generator ! 1 Prated = · ρ · cp · π · R ·urated 2 3 2 A 2 · Prated R= 3 ρ · cp · π · uratedMichael Hölling, WS 2010/2011 slide 21
  23. 23. Wind Energy I Blade optimization using Betz Rotor blade design depends on cl(α), chosen for a good ε(α) 1/ (α) cl angle of attack αMichael Hölling, WS 2010/2011 slide 22
  24. 24. Wind Energy I Blade optimization using Betz Influence of λ and z: Key words: Stability ! minimizing costs !Michael Hölling, WS 2010/2011 slide 23
  25. 25. Wind Energy I Blade optimization using Betz After all the calculations the chord length can be determined by: 1 2·π·R 8 1 c(r) = · · · z cl (α) 9 2· r 2+ 4 λ· λ R 9 20 18 c(r)With: 16 14 z=3 12 c(r) [m] cl (α) = 1 10 8 λ=7 6 R = 50m 4 2 0 0 10 20 30 40 50 r [m]Michael Hölling, WS 2010/2011 slide 24
  26. 26. Wind Energy I Blade optimization using Betz Good approximation for c(r) for λ > 3 and r > 15% R : 1 2·π·R 8 1 c(r) ≈ · · · 2 z cl (α) 9 λ · r R 20 18 c(r) 16 c(r) approx 14 12 c(r) [m] 10 8 6 4 2 0 0 10 20 30 40 50 r [m]Michael Hölling, WS 2010/2011 slide 25
  27. 27. Wind Energy I Blade optimization using Betz To keep the ratio of chord length to thickness constant, this decaying behavior is also valid for the thickness t(r) ! t c c(r) = const. t(r) 1 ⇒ t(r) ∝ rMichael Hölling, WS 2010/2011 slide 26
  28. 28. Wind Energy I Blade optimization using Betz How does the angle of attack α change with increasing r ? ures u2 β changes with: β uR u2 tan(β) = urot ures u2 2 R β ⇒ β = arctan · ur2 3 λ·r ures u2 β ur1 rMichael Hölling, WS 2010/2011 slide 27
  29. 29. Wind Energy I Blade optimization using Betz This change in β has to accounted for to keep α constant --> mounting angle γ to plane of rotation changes with r ! urot β ures γ α γ =β−α . ω plane of rotationMichael Hölling, WS 2010/2011 slide 28
  30. 30. Wind Energy I Blade optimization using Betz For: α=3 ◦ 80 λ=7 70 ! " R = 50m 60 angle [°] 50 40 30 20 10 0 0 10 20 30 40 50 r [m]Michael Hölling, WS 2010/2011 slide 29
  31. 31. Wind Energy I Blade optimization using Betz Change of size and angle with increasing rMichael Hölling, WS 2010/2011 slide 30
  32. 32. Wind Energy I Blade optimization using Betz Real rotor blades often start their profile at 15% of the rotor radius 20 80 18 c(r) 70 ! 16 " 60 14 angle [°] 12 50c(r) [m] 10 40 8 30 6 20 4 2 10 0 0 0 10 20 30 40 50 0 10 20 30 40 50 r [m] r [m] Michael Hölling, WS 2010/2011 slide 31
  33. 33. Wind Energy I Blade optimization using Betz Real rotor bladesMichael Hölling, WS 2010/2011 slide 32
  34. 34. Wind Energy I Blade optimization using Betz Modern design:Michael Hölling, WS 2010/2011 slide 33
  35. 35. Wind Energy I Blade optimization using Betz Modern design: Enercon E-126 http://www.wind-energy-the-facts.orgMichael Hölling, WS 2010/2011 slide 33

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