Wind Turbines Deflect the Wind
Wind turbine in stream tube The image on the previous page on the energy in the wind is a bit simplified. In reality, a wind turbine will deflect the wind, even before the wind reaches the rotor plane. This means that we will never be able to capture all of the energy in the wind using a wind turbine. We will discuss this later, when we get to Betz' Law.
In the image above we have the wind coming from the right, and we use a device to capture part of the kinetic energy in the wind. (In this case we use a three bladed rotor, but it could be some other mechanical device).
The Stream Tube
The wind turbine rotor must obviously slow down the wind as it captures its kinetic energy and converts it into rotational energy. This means that the wind will be moving more slowly to the left of the rotor than to the right of the rotor.
Since the amount of air entering through the swept rotor area from the right (every second) must be the same as the amount of air leaving the rotor area to the left, the air will have to occupy a larger cross section (diameter) behind the rotor plane.
In the image above we have illustrated this by showing an imaginary tube, a so called stream tube around the wind turbine rotor. The stream tube shows how the slow moving wind to the left in the picture will occupy a large volume behind the rotor.
The wind will not be slowed down to its final speed immediately behind the rotor plane. The slowdown will happen gradually behind the rotor, until the speed becomes almost constant.
The Air Pressure Distribution in Front of and Behind the Rotor
Air pressure graph The graph to the left shows the air pressure plotted vertically, while the horizontal axis indicates the distance from the rotor plane. The wind is coming from the right, and the rotor is in the middle of the graph.
As the wind approaches the rotor from the right, the air pressure increases gradually, since the rotor acts as a barrier to the wind. Note, that the air pressure will drop immediately behind the rotor plane (to the left). It then gradually increases to the normal air pressure level in the area.
What Happens Farther Downstream?
If we move farther downstream the turbulence in the wind will cause the slow wind behind the rotor to mix with the faster moving wind from the surrounding area. The wind shade behind the rotor will therefore gradually diminish as we move away from the turbine. We will discus this further on the page about the park effect.
Why not a Cylindrical Stream Tube?
Now, you may object that a turbine would be rotating, even if we placed it within a normal, cylindrical tube, like the one below. Why do we insist that the stream tube is bottle-shaped? Turbine within a cylindrical tube Of course you would be right that the turbine rotor could turn if it were placed in a large glass tube like the one above, but let us consider what happens:
The wind to the left of the rotor moves with a lower speed than the wind to the right of the rotor. But at the same time we know that the volume of air entering the tube from the right each second must be the same as the volume of air leaving the tube to the left. We can therefore deduce that if we have some obstacle to the wind (in this case our rotor) within the tube, then some of the air coming from the right must be deflected from entering the tube (due to the high air pressure in the right ende of the tube).
So, the cylindrical tube is not an accurate picture of what happens to the wind when it meets a wind turbine. This picture at the top of the page is the correct picture.
© Copyright 1997-2003 Danish Wind Industry Association
Updated 1 June 2003
http://www.windpower.org/en/tour/wres/tube.htm
Please wait...