Wind energy I. Lesson 6. Wind turbines in general P2

Jarek Puczylowski - AG TWiSt / ForWind

Wind Energy lecture 02.12.2010 1

Jarek



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


variety of wind turbines

Wind Energy lecture 02.12.2010


different kinds of WECs

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wind turbine

horizontal axiswind turbine

vertical axiswind turbine



different kinds of WECs

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wind turbine

“drag” based wind turbines

“lift” based wind turbines



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drag force based wind turbines

What is drag?

wind velocity v



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What is drag?

wind velocity v

power of the wind

force acting on the body?



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What is drag?

wind velocity v

power of the wind




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What is drag?

wind velocity v

power of the wind


different shapes have different air resistances, i.e. different

drag coefficients cdcd = 0,34

cd = 1,33



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12

sphere

cd is dependent on shape and Re



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Persian windmill year 500-900 a.d.

How can we estimate the maximum power?



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v = const

cd = 1.1

power estimation of a persian windmill

tip speed ratio

cp

tip speed ratio

cp,max =0,16

tip speed ratio for drag force based wind turbines < 1



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lift force based wind turbines

airfoil design



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How does lift occur?

vup

vdown

FL



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How does lift occur?

vup

vdown

Bernoulli Equation(strong simplification of Navier-Stokes-Eq.,

i.e. no viscosity, stationary, novorticity)

1

2!u2

+ p = const

negative

FL



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How does lift occur?Bernoulli Equation

(strong simplification of Navier-Stokes-Eq., i.e. no viscosity, stationary, novorticity)

1

2!u2

+ p = const

negative

Pup

Pdown



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Why is vup larger than vdown?



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vup

vdown

starting vortex



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vup

vdown

starting vortex

angular momentumconservation

starting vortex



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vup

vdown

starting vortex

angular momentumconservation

starting vortex

wind velocity circulating vortex vup > vdown



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Forces acting on an airfoil



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Forces acting on an airfoil

FL = cL(Re,!) · 12"Au2

FD = cD(Re,!) · 12"Au2

Flift

Fdrag

F

cL = Lift coefficient

wind velocity v



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measuring lift (and drag) coefficients of airfoils

2 force sensors measure FL and FD

80 pressure sensors measure pressure distribution along the wall

wind velocity v



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measuring lift coefficients of airfoils

FL = cL(Re,!) · 12"Au2

2 force sensors measure FL and FD

80 pressure sensors measure pressure distribution along the wall



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measuring lift coefficients of airfoils



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Lift force based wind turbines

example:

Darrieus wind turbine



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wind velocity v

velocity due to rotation u

total velocity

FL

FD

tip speed ratio for Darrieus rotors > 3



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wind velocity v


total velocity

FL

FD

FD

FL



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wind velocity v


total velocity

FL

FD

FD

FL

FD



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wind velocity v


total velocity

FL

FD

FD

FL

FD

FD



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wind velocity v

FL

FD

FD

FL

FD

FD

0° assist rotation

180° assist rotation

90°oppose rotation

270°oppose rotation



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History of wind turbines

Denmark 1891



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Russia 1931



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USA 1942 - 50kW



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Germany 1942



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USA 1943 - 70kW



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UK 1956 - 100kW



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Denmark 1957 -200kW



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France 1958 - 800kW



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Germany 1982 - 3000kW

Education

Wind energy I. Lesson 6. Wind turbines in general P2