hau, e.. wind turbines – fundamentals, technologies, application, economics. 2nd

8/18/2019 HAU, E.. Wind Turbines – Fundamentals, Technologies, Application, Economics. 2nd

1/37

Overview of lectures in this series

1. Introduction and motors (Oct. 3)

2. Motors and generators (Oct. 10)

3. Distribution and use of electricity (Oct. 17)

4.

The wind (Oct. 24)5. Heat engines 1 (Oct. 31)

6. Heat engines 2 (Nov. 7)

7. Nuclear generation (Nov. 14)

8. Solar power – thermal and electric (Nov. 21)9. Fuel cells (Dec. 5)

10. Summary, Consumption and the future (Dec. 12)

http://kicp.uchicago.edu/~switzer/


2/37

C O M P T O N L E C T U R E 4 : O C T O B E R 2 4 , 2 0 0 9E R I C S W I T Z E R

The Wind

"In the beginning, being encouraged by one who is into aviation, I have

applied to the insects the laws of resistance for air, and I reached, with

Mr. Sainte-Lague, the conclusion that their flight is impossible.” -- Le Vol Des Insects (Hermann and Cle, Paris, 1934) August Magnan


3/37

Resources

! Wind Turbine Fundamentals, Technologies, Application, Economics by E. Hau, Springer

!

“Annual Report on U.S. Wind Power Installation,

Cost, and Performance Trends: 2007” (EERE/DOE Wiser and Bolinger)


4/37

What is wind?

! Air: 78% nitrogen, 21%oxygen + other trace gas

! Mean velocity ~1000mph

! Collision rate: few GHz

! In what sense is the airstill, then?


5/37

What is wind?

!

Wind is a mass flow

10 mph wind through a door frame = 18 pounds per second.


6/37

Intuition about the wind

!

The wind embodies energy: you can use it to turnmechanical devices which do work. (On a farm, it

may pump water – lifting a mass through some

height)! The wind can produce a force – you know this from

trying to stand in a gale.


7/37

A catching device


8/37

A catching device: power

Power is energy per time:

Power embodied: Area A swept and

velocity cubed.

P ~ Watts and v ~ m/s


9/37

A catching device: force

Force induced: Area A swept,

velocity squared and a dragcoefficient Cd (depends on the

object the wind hits)

F ~ Newtons and v ~ m/s


10/37

Hand out the window


11/37

Drag-type windmill

A 9th century Persian-style drag windmill

Can not spin faster

than the wind!


12/37

A hand against the wind?

Mills of La Mancha Image: wikipedia


13/37

Generators – why not use the wind?

!

Connection to lec. 1-3:

! A changing magnetic flux induces a voltage(Faraday’s induction)

Flux = area*magnetic field (B)*cos(angle)


14/37

A modern turbine

Image: wikipedia


15/37

Lift-type windmill


16/37

Airfoils: lift, drag and stall


17/37

Resultant lift


18/37

Forces on the Turbine

Wind Turbines Fundamentals, Technologies, Application, Economics E. Hau, Springer

Can spin faster

than the wind.

Horizontal axis wind turbine

(HAWT)

Need to yaw to

wind.


19/37

A hypothetical generator: failure


20/37

Idealized flow around a turbine

The same mass of air must flow through each of these surfaces.

Recall: Flow rate is A ! v

Analogy: a river


21/37

The Betz efficiency

Take ratio of extracted to input wind power (an efficiency):

Energy: drives v out to zero Mass flow: likes v out

Maximum efficiency at v out/v in=1/3.


22/37

The real world: turbines are big

Images: wikipedia


23/37

Bird deaths in Denmark

Image: Sustainable Energy Without All the Hot Air MacKay


24/37

Conversion Efficiency



25/37

Extended momentum theory

Some of the energy of incoming wind goes into a rotating wake

Total efficiency depends on how fast the blades turn.

Also: tip vortices



26/37

Efficiency as a function of tip speed


Tip speed ratio:

Speed at blade tipdivided by incoming

wind speed.

At low tip speed

ratio, losses from wake.

A high tip speed,

losses from airfoil

drag.

4th blade buys ~1-2% power


27/37

Power control


Small rotors without

blade pitch controlcan exploit a passive

stall, where the angleof attach naturally

reaches stall above

some threshold windspeed. Can also yawout of the wind,“furling”.


28/37

Power curve

Cut in

Rated Cut-out

Pitch control



29/37

Wind speed distributions


gusts


30/37

The graded annual power



31/37

What is a typical turbine?

Annual Report on U.S. Wind Power Installation, Cost, and Performance Trends: 2007(EERE/DOE Wiser and Bolinger)


32/37

Some statistics

Annual Report on U.S. Wind Power Installation, Cost, and Performance Trends: 2007(EERE/DOE Wiser and Bolinger)


33/37

Net energy flows

32% eff.

2 5 %

e f f

.


34/37

Something to be optimistic about

NCEP


35/37

The potential of wind

!

173,000 TW incident solar power

! 121,000 TW to the Earth’s surface

! 3,600 TW into wind

!

1200 TW at < 1 km above surface

! 400 TW on land, 50 TW surface

! 2 TW sane

!

Of order 10 TW needed! This is highly optimistic!

"Fundamentals of Renewable Energy Processes” A. V. da Rosa, IPCC 2001


36/37

Conclusions

!

Wind is a flow of mass and embodies power ~ v 3

! Either drag (historical) or lift (modern) can be used

! There is a fundamental (Betz) limit to the efficiency

!

Moreover, there are limits to how much power youeven want to extract!

!

Turbines have a standard power curve

! Wind speeds vary and imply a graded annual power


37/37

My other car is a sphere: lecture 6

Image: wikipedia

hau, e.. wind turbines – fundamentals, technologies, application, economics. 2nd

Documents