Wind energy I. Lesson 7. Wind blade interaction

Wind Energy I

Wind-blade
interaction
consequences for design

Michael Hölling, WS 2010/2011 slide 1

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


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



Direct force measurements

FL
CL,F = 1
2 · ρ · v2 · A



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



Test section in wind tunnel



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 / °



cl cd

cd

cl

angle of attack α



cl (α)
Lift to drag ration: (α) =
cd (α)

1/ (α)
cl

angle of attack α


Wind Energy I Rotor blade design

http://www.ecogeneration.com.au


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


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]


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

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


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


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


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=?


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


Rotor blade design depends on cl(α), chosen for a good ε(α)

1/ (α)
cl

angle of attack α


Influence of λ and z:

Key words:

Stability !

minimizing costs !


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]

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]

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



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


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



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]



Change of size and angle with increasing r



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]



Real rotor blades


Modern design:


Modern design:
Enercon E-126

http://www.wind-energy-the-facts.org


Wind energy I. Lesson 7. Wind blade interaction

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Wind energy I. Lesson 7. Wind blade interaction