Post on 30-Jun-2015
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Wind Energy I
Michael Hölling, WS 2010/2011 slide 1
Wind-blade interaction
consequences for design
Wind Energy I
slideMichael Hölling, WS 2010/2011 2
Class content
4 Wind power
5 Wind turbines in general 6 Wind - blades
interaction
7 Π-theorem
8 Wind turbine characterization
9 Control strategies
10 Generator
11 Electrics / grid
3 Wind field characterization
2 Wind measurements
Wind Energy I
slideMichael Hölling, WS 2010/2011 3
Lift and drag
α
Fl
Fd
Fl = cl(!) · 12
· " · A · u2
Fd = cd(!) · 12
· " · A · u2
Lift force:
Drag force:
with
c
dru
Fres
A = c · dr
Wind Energy I
slideMichael Hölling, WS 2010/2011 4
Lift and drag
CL,F =FL
12 · ! · v2 · A
Direct force measurements
Wind Energy I
slideMichael Hölling, WS 2010/2011 5
Lift and drag
Pressure measurements
CL,p =pp ! ps12 · ! · v2
· L
c · "
the so called Althaus factor η corrects for the finite length of L
Wind Energy I
slideMichael Hölling, WS 2010/2011 6
Test section in wind tunnel
Lift and drag
Wind Energy I
slideMichael Hölling, WS 2010/2011 7
Lift and drag
Test section in wind tunnel
Wind Energy I
slideMichael Hölling, WS 2010/2011 8
Lift and drag
Test section in wind tunnel
Wind Energy I
slideMichael Hölling, WS 2010/2011 9
Lift and drag
Test section in wind tunnel
Wind Energy I
slideMichael Hölling, WS 2010/2011 10
Lift and drag
−5 0 5 10 15 20 25−0.2
0
0.2
0.4
0.6
0.8
1
1.2
AoA α / °
c L / 1
force measurementwall pressure measurementreference Althaus
Lift coefficient for laminar inflow condition
Wind Energy I
slideMichael Hölling, WS 2010/2011 11
Lift and drag
cl
cl cd
cd
angle of attack α
Wind Energy I
slideMichael Hölling, WS 2010/2011
angle of attack α
1/!(
")
c l
12
Lift and drag
!(") =cl(")cd(")
Lift to drag ration:
Wind Energy I
slideMichael Hölling, WS 2010/2011 13
Rotor blade design
http://www.ecogeneration.com.au
Wind Energy I
slideMichael Hölling, WS 2010/2011 13
Rotor blade design
http://www.ecogeneration.com.au
Wind Energy I
slideMichael Hölling, WS 2010/2011 14
Velocities at rotor blade
ω
r
R
urot1 = ω r1
urot2 = ω r2
urotR = ω R
u2 =23
· u1
uR
u2ures
β
ur2
u2ures
β
ur1
u2ures
β
Wind Energy I
slideMichael Hölling, WS 2010/2011 15
Velocities at rotor blade
ures(r) =
!"23u1
#2
+ (! · r)2
0 10 20 30 40 500
20
40
60
80
r [m]
ure
s [
m/s
]
ures
Wind Energy I
slideMichael Hölling, WS 2010/2011 16
Forces at rotor blade
β
u2
ures
urot
α
ω
Fl
Fd
plane of rotation
.Fres
Fl =12
· ! · A · cl(") · u2res
Fd =12
· ! · A · cd(") · u2res
Wind Energy I
slideMichael Hölling, WS 2010/2011 17
Forces at rotor blade
Force component in direction of rotation
.
β
α
u2
ures
urot
ω
Fl
Fd
Fres
plane of rotation
β
Fdrot = !12
· ! · A · cd(") · u2res · cos(#)
β Flrot =12
· ! · A · cl(") · u2res · sin(#)
Frot =12
· ! · A · u2res · [cl(") · sin(#)! cd(") · cos(#)]
Wind Energy I
slideMichael Hölling, WS 2010/2011 18
Blade optimization using Betz
Maximal extractable power based on Betz
r
dr
For the whole plane:
PBetz =1627
· 12
· ! · u31 · (" · R2)
For a ring-segment:
dPBetz =1627
· 12
· ! · u31 · (2 · " · r · dr! "# $
dA
)
Wind Energy I
slideMichael Hölling, WS 2010/2011 19
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:
dProt = z · 12
· ! · c(r) · dr! "# $dA
·u2res · cl(") · sin(#) · urot(r)! "# $
!·r
This should be equal to dPBetz for an optimum design:
dProt = dPBetz
Wind Energy I
slideMichael Hölling, WS 2010/2011 20
Blade optimization using Betz
After all the calculations the chord length can be determined by:
c(r) =1z
· 2 · ! · R
cl(")· 89
· 1
# ·!
#2 ·"
rR
#2 + 49
What is the right choice for:R = ?cl(α) = ?z = ?λ = ?
Wind Energy I
slideMichael Hölling, WS 2010/2011 21
Blade optimization using Betz
Rotor radius R determines the maximum extractable power from the wind and is linked to the power of the generator !
Prated =12
· ! · cp · " · R2! "# $
A
·u3rated
R =
!2 · Prated
! · cp · " · u3rated
Wind Energy I
slideMichael Hölling, WS 2010/2011 22
Blade optimization using Betz
Rotor blade design depends on cl(α), chosen for a good ε(α)
angle of attack α
1/!(
")
c l
Wind Energy I
slideMichael Hölling, WS 2010/2011 23
Blade optimization using Betz
Influence of λ and z:
Key words:
Stability !
minimizing costs !
Wind Energy I
slideMichael Hölling, WS 2010/2011 24
Blade optimization using Betz
After all the calculations the chord length can be determined by:
c(r) =1z
· 2 · ! · R
cl(")· 89
· 1
# ·!
#2 ·"
rR
#2 + 49
0 10 20 30 40 500
2
4
6
8
10
12
14
16
18
20
r [m]
c(r
) [m
]
c(r)
cl(!) = 1! = 7
z = 3With:
R = 50m
Wind Energy I
slideMichael Hölling, WS 2010/2011 25
Blade optimization using Betz
Good approximation for c(r) for λ > 3 and r > 15% R :
c(r) ! 1z
· 2 · ! · R
cl(")· 89
· 1#2 ·
!rR
"
0 10 20 30 40 500
2
4
6
8
10
12
14
16
18
20
r [m]
c(r
) [m
]
c(r)c(r) approx
Wind Energy I
slideMichael Hölling, WS 2010/2011 26
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) !
tc
! t(r) " 1r
c(r)t(r)
= const.
Wind Energy I
slideMichael Hölling, WS 2010/2011 27
How does the angle of attack α change with increasing r ?
Blade optimization using Betz
uR
u2ures
β
ur2
u2ures
β
ur1
u2ures
β
r
β changes with:
tan(!) =u2
urot
! ! = arctan!
23
· R
" · r
"
Wind Energy I
slideMichael Hölling, WS 2010/2011 28
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 !
plane of rotation
β ures
urot
α
ω
.
γ! = " ! #
Wind Energy I
slideMichael Hölling, WS 2010/2011 29
Blade optimization using Betz
! = 7
For:
R = 50m
! = 3!
0 10 20 30 40 500
10
20
30
40
50
60
70
80
r [m]
an
gle
[°]
!"
Wind Energy I
slideMichael Hölling, WS 2010/2011 30
Blade optimization using Betz
Change of size and angle with increasing r
Wind Energy I
slideMichael Hölling, WS 2010/2011 31
Blade optimization using Betz
0 10 20 30 40 500
10
20
30
40
50
60
70
80
r [m]
angle
[°]
!"
0 10 20 30 40 500
2
4
6
8
10
12
14
16
18
20
r [m]
c(r
) [m
]
c(r)
Real rotor blades often start their profile at 15% of the rotor radius
Wind Energy I
slideMichael Hölling, WS 2010/2011 32
Blade optimization using Betz
Real rotor blades
Wind Energy I
slideMichael Hölling, WS 2010/2011 33
Modern design:
Blade optimization using Betz
Wind Energy I
slideMichael Hölling, WS 2010/2011 33
Modern design:
Blade optimization using Betz
http://www.wind-energy-the-facts.org
Enercon E-126