3. Outline
- variety of wind turbines / classification
- drag coefficient and drag force (example: Persian Windmill)
- aerodynamics of an airfoil
- lift coefficient and lift force (example: Darrieus Rotor)
- history of wind turbines
Wind Energy lecture 02.12.2010 3
5. Jarek Puczylowski - AG TWiSt /
ForWind
different kinds of WECs
horizontal axis
wind turbine
wind turbine
vertical axis
wind turbine
Wind Energy lecture 02.12.2010 5
6. Jarek Puczylowski - AG TWiSt /
ForWind
different kinds of WECs
“drag” based
wind turbines
wind turbine
“lift” based
wind turbines
Wind Energy lecture 02.12.2010 6
7. Jarek Puczylowski - AG TWiSt /
ForWind
drag force based wind turbines
What is drag?
wind velocity v
Wind Energy lecture 02.12.2010 7
8. Jarek Puczylowski - AG TWiSt /
ForWind
drag force based wind turbines
power of the wind
What is drag?
force acting on the body?
wind velocity v
Wind Energy lecture 02.12.2010 8
9. Jarek Puczylowski - AG TWiSt /
ForWind
drag force based wind turbines
power of the wind
What is drag?
force acting on the body?
wind velocity v
Wind Energy lecture 02.12.2010 9
10. Jarek Puczylowski - AG TWiSt /
ForWind
drag force based wind turbines
power of the wind
What is drag?
force acting on the body?
different shapes have different
air resistances, i.e. different
wind velocity v cd = 0,34 drag coefficients cd
cd = 1,33
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12. Jarek Puczylowski - AG TWiSt /
ForWind
cd is dependent on shape and Re
sphere
Wind Energy lecture 02.12.2010 12
13. Jarek Puczylowski - AG TWiSt /
ForWind
drag force based wind turbines
Persian windmill
year 500-900 a.d.
How can we estimate the
maximum power?
Wind Energy lecture 02.12.2010 13
14. Jarek Puczylowski - AG TWiSt /
ForWind
drag force based wind turbines
power estimation of a
persian windmill
v = const
cp
cd = 1.1
cp,max =0,16
tip speed ratio
tip speed ratio
tip speed ratio for drag force
based wind turbines < 1
Wind Energy lecture 02.12.2010 14
15. Jarek Puczylowski - AG TWiSt /
ForWind
drag force based wind turbines
Wind Energy lecture 02.12.2010 15
16. Jarek Puczylowski - AG TWiSt /
ForWind
lift force based wind turbines
airfoil design
Wind Energy lecture 02.12.2010 16
17. Jarek Puczylowski - AG TWiSt /
ForWind
lift force based wind turbines
How does lift occur?
FL
vup
vdown
Wind Energy lecture 02.12.2010 17
18. Jarek Puczylowski - AG TWiSt /
ForWind
lift force based wind turbines
Bernoulli Equation
(strong simplification of Navier-Stokes-Eq.,
How does lift occur? i.e. no viscosity, stationary, novorticity)
1 2
FL 2
ρu + p = const
vup
vdown
negative
Wind Energy lecture 02.12.2010 18
19. Jarek Puczylowski - AG TWiSt /
ForWind
lift force based wind turbines
Bernoulli Equation
(strong simplification of Navier-Stokes-Eq.,
How does lift occur? i.e. no viscosity, stationary, novorticity)
1 2
ρu + p = const
2
Pup
Pdown negative
Wind Energy lecture 02.12.2010 19
20. Jarek Puczylowski - AG TWiSt /
ForWind
Why is vup larger than vdown?
Wind Energy lecture 02.12.2010 20
21. Jarek Puczylowski - AG TWiSt /
ForWind
Why is vup larger than vdown?
vup starting vortex
vdown
Wind Energy lecture 02.12.2010 21
22. Jarek Puczylowski - AG TWiSt /
ForWind
Why is vup larger than vdown?
angular momentum
conservation
starting vortex
vup starting vortex
vdown
Wind Energy lecture 02.12.2010 22
23. Jarek Puczylowski - AG TWiSt /
ForWind
Why is vup larger than vdown?
angular momentum
conservation
starting vortex
vup starting vortex
wind velocity circulating vortex vup > vdown
vdown
Wind Energy lecture 02.12.2010 23
24. Jarek Puczylowski - AG TWiSt /
ForWind
Forces acting on an airfoil
Wind Energy lecture 02.12.2010 24
25. Jarek Puczylowski - AG TWiSt /
ForWind
Forces acting on an airfoil
Flift F
wind velocity v Fdrag
1
FD = cD (Re, α) · ρAu 2
2
1
FL = cL (Re, α) · ρAu 2 cL = Lift coefficient
2
Wind Energy lecture 02.12.2010 25
26. Jarek Puczylowski - AG TWiSt /
ForWind
measuring lift (and drag) coefficients of airfoils
2 force sensors measure FL and FD
wind velocity v
80 pressure sensors measure
pressure distribution along the wall
Wind Energy lecture 02.12.2010 26
27. Jarek Puczylowski - AG TWiSt /
ForWind
measuring lift coefficients of airfoils
2 force sensors measure FL and FD
80 pressure sensors measure
pressure distribution along the wall
1
FL = cL (Re, α) · ρAu2
2
Wind Energy lecture 02.12.2010 27
28. Jarek Puczylowski - AG TWiSt /
ForWind
measuring lift coefficients of airfoils
Wind Energy lecture 02.12.2010 28
29. Jarek Puczylowski - AG TWiSt /
ForWind
Lift force based wind turbines
example:
Darrieus
wind turbine
Wind Energy lecture 02.12.2010 29
30. Jarek Puczylowski - AG TWiSt /
ForWind
wind velocity v
tip speed ratio for
Darrieus rotors > 3
total velocity
velocity due to FD
rotation u
FL
Wind Energy lecture 02.12.2010 30
31. Jarek Puczylowski - AG TWiSt /
ForWind
wind velocity v
total velocity
velocity due to FD
rotation u
FL
FD
FL
Wind Energy lecture 02.12.2010 31
32. Jarek Puczylowski - AG TWiSt /
ForWind
wind velocity v
total velocity
velocity due to FD
rotation u
FL FD
FD
FL
Wind Energy lecture 02.12.2010 32
33. Jarek Puczylowski - AG TWiSt /
ForWind
wind velocity v
total velocity
velocity due to FD
rotation u
FL FD
FD
FD
FL
Wind Energy lecture 02.12.2010 33