1. Wind Energy I
Wind-blade
interaction
consequences for design
Michael Hölling, WS 2010/2011 slide 1
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 / grid
Michael Hölling, WS 2010/2011 slide 2
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
2
Michael Hölling, WS 2010/2011 slide 3
4. Wind Energy I Lift and drag
Direct force measurements
FL
CL,F = 1
2 · ρ · v2 · A
Michael Hölling, WS 2010/2011 slide 4
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 L
Michael Hölling, WS 2010/2011 slide 5
6. Wind Energy I Lift and drag
Test section in wind tunnel
Michael Hölling, WS 2010/2011 slide 6
7. Wind Energy I Lift and drag
Test section in wind tunnel
Michael Hölling, WS 2010/2011 slide 7
8. Wind Energy I Lift and drag
Test section in wind tunnel
Michael Hölling, WS 2010/2011 slide 8
9. Wind Energy I Lift and drag
Test section in wind tunnel
Michael Hölling, WS 2010/2011 slide 9
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. Wind Energy I Lift and drag
cl cd
cd
cl
angle of attack α
Michael Hölling, WS 2010/2011 slide 11
12. Wind Energy I Lift and drag
cl (α)
Lift to drag ration: (α) =
cd (α)
1/ (α)
cl
angle of attack α
Michael Hölling, WS 2010/2011 slide 12
13. Wind Energy I Rotor blade design
http://www.ecogeneration.com.au
Michael Hölling, WS 2010/2011 slide 13
14. Wind Energy I Rotor blade design
http://www.ecogeneration.com.au
Michael Hölling, WS 2010/2011 slide 13
15. Wind Energy I Velocities at rotor blade
R urotR = ω R ures u2
β
uR
ures
u2
urot2 = ω r2 β
ur2
r ures u2
β
urot1 = ω r1 ur1
2
ω u2 = · u1
3
Michael Hölling, WS 2010/2011 slide 14
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. 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
2
Michael Hölling, WS 2010/2011 slide 16
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 res
Fres 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 res
Michael Hölling, WS 2010/2011 slide 17
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
dA
Michael Hölling, WS 2010/2011 slide 18
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 = dPBetz
Michael Hölling, WS 2010/2011 slide 19
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. 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 · urated
Michael Hölling, WS 2010/2011 slide 21
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 α
Michael Hölling, WS 2010/2011 slide 22
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. 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. 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. 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) ∝
r
Michael Hölling, WS 2010/2011 slide 26
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
r
Michael Hölling, WS 2010/2011 slide 27
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 rotation
Michael Hölling, WS 2010/2011 slide 28
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. Wind Energy I Blade optimization using Betz
Change of size and angle with increasing r
Michael Hölling, WS 2010/2011 slide 30
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 50
c(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. Wind Energy I Blade optimization using Betz
Real rotor blades
Michael Hölling, WS 2010/2011 slide 32
34. Wind Energy I Blade optimization using Betz
Modern design:
Michael Hölling, WS 2010/2011 slide 33
35. Wind Energy I Blade optimization using Betz
Modern design:
Enercon E-126
http://www.wind-energy-the-facts.org
Michael Hölling, WS 2010/2011 slide 33