wind energy i. lesson 7. wind blade interaction

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


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


Lift and drag

CL,F =FL

12 · ! · v2 · A

Direct force measurements

Wind Energy I


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


Test section in wind tunnel

Lift and drag

Wind Energy I


Lift and drag


Wind Energy I


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


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


Rotor blade design

http://www.ecogeneration.com.au



Wind Energy I


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


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


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


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


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



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



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



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



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

angle of attack α

1/!(

")

c l

Wind Energy I



Influence of λ and z:

Key words:

Stability !

minimizing costs !

Wind Energy I



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



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



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


How does the angle of attack α change with increasing r ?


uR

u2ures

β

ur2

u2ures

β

ur1

u2ures

β

r

β changes with:

tan(!) =u2

urot

! ! = arctan!

23

· R

" · r

"

Wind Energy I



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



! = 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



Change of size and angle with increasing r

Wind Energy I



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



Real rotor blades

Wind Energy I


Modern design:


Wind Energy I


Modern design:


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

Enercon E-126



wind energy i. lesson 7. wind blade interaction

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