Wind powerPart 3: Technology

San Jose State UniversityFX Rongère

February 2009

Wind Turbine Aerodynamics

Energy balance over the stream tube

Inlet: index 1Outlet: index 2Turbine: index T

).( AAAA

AA

AA

AOpen

khmWQdt

dE

Betz’s Simplified Approach

The turbine is perfect: there is no internal entropy generation

AA

AA A

A

Open

smT

Q

dt

dS.

0.

AA

A sm

0.

AA

A hm

Then, when air considered as an incompressible fluid:

Betz’s Simplified Approach

Energy balance equation is reduced to:

In addition, we assume that the wind speed stay axial through the turbine:

Balance of Forces:

2122.2

1. vvmWT

TT vAvAvAm ...... 2211

T

A

TT vFAdvFT

.... The power of the torque absorb by the turbine is equal to the power taken from the air flow

Momentum equation on the system:

A

AA

AA

open

vmFdt

vd.

.

Betz’s Simplified Approach

Then:

21. vvmF

And:

21

22

2121

.2

1

.2

1...

vvv

vvmvvvm

T

T

Introducing a the interference factor:

1

1

v

vva T

Betz’s Simplified Approach

Then:

231

211

22

21

22

21

1.....2

.1..4.2

1..1..

.2

1....

2

1.

aaAvW

vaaAavW

vvAvvvmW

TT

TT

TTT

The power absorbed by the turbine is maximum if:

windwindTMaxT WWAv

aaW

.59.0

27

16.

2..1..4

312

,

Betz’s Simplified Approach

31

01.4.3

0

2

a

aa

da

Wd T

Then

Betz’s law

12

1

.31

.32

vv

vvT

Other factors

Other factors limit the performance of wind turbinesWake rotationAerodynamic dragFinite number of blades and

interaction between themBlade tip losses

Wake rotation In fact, the air is rotating downstream the rotor

by reaction to the torque applied to the rotor

Maximum conversion rate with wake rotation: Glauert’s law

To characterize this effect we introduce: Angular velocity of the rotor : ΩT

Angular velocity imparted to the flow: ω Angular induction factor: a’ = ω/2ΩT

Axial interference factor:

Blade tip speed : λ = ΩTR/v1

We can then show that the transfer power is maximum if:

1

1

v

vva T

14

31'

a

aa

Then the maximum conversion rate is given by the following equation:

With a(λ) defined by:

Betz’s law corresponds to: and:

Maximum conversion rate with wake rotation: Glauert’s law

dxx

xxx

W

WCp

a

Wind

MaxT

Max

)(

25.2

,

31

)41()21()1(24

a

aa

31

141 22

3

1a

Optimal Interference FactorGlauert's model

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 2 4 6 8 10

Blade tip ratio

Inte

rfer

ence

Fac

tor

(a)

By drawing CpMax we can show that: Larger is the blade tip ratio higher is the conversion rate For blade tip ratio greater than 4 conversion rate is close

to Betz’s law The optimal axial interference factor is close to 1/3 for

large enough blade tip ratio

Maximum conversion rate with wake rotation: Glauert’s law

λ

Optimal Coversion RateGlauert's model

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10

Blade tip ratio

Co

nve

rsio

n r

ate

λ

Angular induction factor

Aerodynamic drag The aerodynamics of a blade is defined by:

lcv

DC

lcv

LC

D

L

...21

...21

2

2

L: Lift force

v: Wind speed on the blade

c: Chord of the blade

D: Drag force

l: Span of the bladeα: Angle of attack

Lift and Drag

Lift and Drag are related:

• Lift transfers power

• Drag generates losses

•Bearings•Viscous Friction•Noise

• About 10 -15% of aerodynamic inefficiencies

Design optimization

Blade shape may be optimized using laboratory test and numerical modeling See: Wind Energy, Explained by J.F.

Manwell, J.G. McGowan and A.L.Rogers, John Wiley, 2002, for detailed explanations

See also: Riso DTU – National Laboratory for Renewable Energy http://www.risoe.dtu.dk/

Interaction between blades

Blade tip speed is limited by the interaction between the blades. Typically, if the rotation is too fast (λ>λMax) then the flow for each is perturbed by the previous one

Conversion rate WMax/WWind

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5 6

Blade Tip Speed

Con

vers

ion r

ate

Multiblade Wind pump

Three Blade Wind Turbine

Two Blade Wind Turbine

Vertical axis Wind Turbine (Darrieus)

λ

Blade tip losses Local rotating airflow at the tip of the blades due to the

difference of pressure between the faces of the blades Similar to aircraft wings

Thesis at DTU has shown a gain of 1.65% but with an increase in thrust of 0.65%

Performance glider with wingletsWingtip loss of Boeing 737

Source: Mads Døssing Vortex Lattice Modelling of Winglets on Wind Turbine Blades Risø-R-1621(EN) Aug. 2007

Actual Wind Turbine Conversion Rate

Example: Liberty of Clipper Windpower

Power curve

Actual Turbine Conversion rate

Power curve and Conversion rate

GE 1.5S

-200.00

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

1600.00

0.00 5.00 10.00 15.00 20.00 25.00 30.00

Wind Speed (m/s)

Po

wer

(kW

)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Series2

Series1

Optimization Parameters

Theoretical Power CurveConversion rate: .35

-100

0

100

200

300

400

500

0 5 10 15 20 25 30

Wind speed (m/s)

Pow

er (W

/m2)

Cut in

Cut out

Efficiency

Max Power

Generated Energy Generated Energy = Wind Speed Distribution x Turbine Power

CurveCapacity Factor

0

100

200

300

400

500

0 5 10 15 20 25

Wind Speed (m/s)

Win

d T

urbi

ne P

ower

(k

W/m

2)

0%

2%

4%

6%

8%

10%

Win

d P

roba

bilit

y

Capacity Factor

Lower Capacity factor allows higher energy capture Generally preferred CF is between 30% and 40%

5 12% 33% 4% 0% 89%5.5 16% 33% 3% 0% 82%6 20% 32% 2% 0% 76%

6.5 24% 30% 1% 0% 68%7 28% 29% 1% 0% 60%

7.5 32% 27% 1% 0% 50%8 36% 25% 1% 0% 45%

8.5 40% 23% 0% 0% 38%9 44% 22% 0% 0% 33%

Energy after Cut out

Energy at max eff

Average Wind Speed

Capacity Factor

Captured Energy/ Wind

Energy before cut-in

Eff 0.35Max Power 400 W/ m2Cut-in 4 m/ sCut-out 25 m/ s

Characteristics of the tested turbine

hoursPowerMax

EnergyGeneratedAnnualCF

760,8..

Wind Turbine Optimization

0%

10%

20%

30%

40%

50%

5 6 7 8 9

Average Wind Speed (m/s)

0%

20%

40%

60%

80%

100%

Capacity Factor

Captured Energy/ Wind Energy

Energy at max eff

Wind Turbine Optimization

Conv. Rate 0.35Max Power 400 W/ m2Cut-in 4 m/ sCut-out 25 m/ s

0

50

100

150

200

250

0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24

00.010.020.030.040.050.060.070.080.090.1

Annual Wind Turbine Energy

Annual Wind Energy (kWh/ m2)

Pdf

Wind and Power Distribution

Wind Turbine Optimization

0

20

40

60

80

100

120

140

0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24

Wind Speed (m/s)

Ann

ual E

nerg

y (K

Wh/

m2)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Annual Wind Turbine Energy

Annual Wind Energy (kWh/ m2)

Pdf

vm = 6 m/ s

CF=24%Captured Energy =33%

Conv. Rate 0.35Max Power 400 W/ m2Cut-in 4 m/ sCut-out 25 m/ s

0

50

100

150

200

250

0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24

00.010.020.030.040.050.060.070.080.090.1

Annual Wind Turbine Energy

Annual Wind Energy (kWh/ m2)

Pdf

Wind and Power Distribution

Wind Turbine Optimization

0

50

100

150

200

250

300

350

0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24

Wind Speed (m/s)

Ann

ual E

nerg

y (K

Wh/

m2)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Annual Wind TurbineEnergy

Annual Wind Energy(kWh/ m2)

Pdf

vm = 9m/s

CF=44%Captured Energy =22%

Conv. Rate 0.35Max Power 400 W/ m2Cut-in 4 m/ sCut-out 25 m/ s

0

50

100

150

200

250

0 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24

00.010.020.030.040.050.060.070.080.090.1

Annual Wind Turbine Energy

Annual Wind Energy (kWh/ m2)

Pdf

Companies to follow GE: www.ge.com Clipper Windpower: www.clipperwind.com Vestas: www.vestas.com Repower: www.repower.com Gamesa: www.gamesa.com Suzlon: www.suzlon.com Mitsubishi: www.mitsubishi.com