The Aerodynamics Of The Wind Turbine – Part 2

WIND TURBINE BLADES BEHAVE IN THE SAME WAY

Returning to the wind turbine blade, just as in the situation for the cyclist, we can observe the aerodynamic and force diagrams in two different situations,

when the wind turbine is stationary and when it is running at a normal operational speed. We will use as an example the cross section near the blade tip of a Bonus 450 kW Mk III operating in a wind speed ÒvÒ of 10 m/s.

When the rotor is stationary, as shown in drawing (A) below, the wind

has a direction towards the blade, at a right angle to the plane of rotation, which is the area swept by the rotor during the rotation of the blades. The wind speed of 10 m/s will produce a wind pressure of 80 N/m2 of blade surface, just like the effect on our cyclist. The wind pressure is roughly in the same direction as the wind and is also roughly perpendicular to the flat side of the blade profile.

The part of the wind pressure blowing in the direction of the rotor shaft attempts to bend the blades and tower, while the smaller part of the wind pressure blowing in the direction of the rotation of the blades produces a torque that attempts to start the wind turbine.

Once the turbine is in operation and the rotor is turning, as is shown in the center diagram (B), the blade encounters a head wind from its own forward movement in exactly the same way as the cyclist does. The strength of head wind ÒuÓ at any specific place on the blade depends partly on just how fast the wind turbine blade is rotating, and partly how far out on the blade one is from the shaft.

In our example, at the normal operating speed of 30 rpm, the head wind ÒuÓ near the tip of the 450 kW wind turbine is about 50 m/s.

The ÒmeteorologicalÓ wind ÒvÓ of 10 m/s will thus give a resulting wind over the profile of about 51 m/s.

This resulting wind will have an effect on the blade surface with a force of 1500 N/m2. The force ÒFÓ will not be in the direction of the resulting wind, but almost at a right angle to the resulting wind.

In the drawing on the right (C) the force of the wind pressure ÒFÓ is again split up into a component in the direction of rotation and another component at a right angle to this direction. The force ÒFaÓ at a right angle to the plane of rotation attempts to bend the blade back against the tower, while the force ÒFdÓ points in the direction of rotation and provides the driving torque.

We may notice two very important differences between the forces on the blade in these two different situations and forces on the cyclist in the two corresponding situations. One difference is that the forces on the blade become very large during rotation.

If vector arrows illustrating the forces in the diagrams were drawn in a scale that was indicative of the sizes of the different forces, then these vector arrows of a wind turbine in operation would have been 20 times the size of the vector arrows of the same wind turbine at rest.

This large difference is due to the resulting wind speed of 51 m/s striking a blade during operation, many times the wind speed of 10 m/s when the wind turbine is at rest. Just like the cyclist, the blade encounters head wind resulting from its own movement,however head wind is of far greater importance on a wind turbine blade than for a cyclist in motion.

The other important difference between a wind turbine blade and a cyclist is that the force on the blade is almost at a right angle to the resulting wind striking the profile. This force is known as the lift and also produces a small resistance or drag.

The direction of this lift force is of great importance. A cyclist only feels the wind resistance as a burden, requiring him to push down extra hard on the pedals. However with a wind turbine blade this extra wind resistance will act as a kind of power booster, at least in the normal blade rotational speed range.

The reason for this difference is due to the blades streamlined profile, which behaves aerodynamically completely differently as compared to the irregular shaped profile of a man on a bicycle. The wind turbine blade experiences

Experiences both lift and drag, while a cyclist only experiences drag.

LIFT

Lift is primary due to the physical phenomena known as BernoulliÕs Law. This physical law states that when the speed of an air flow over a surface is increased the pressure will then drop. This law is counter to what most people experience from walking or cycling in a head wind, where normally one feels that the pressure increases when the wind also increases. This is also true when one sees an air flow blowing directly against a surface, but it is not the case when air is flowing over a surface.

One can easily convince oneself that this is so by making a small experiment. Take two small pieces of paper and bend them slightly in the middle. Then hold them as shown in the diagram and blow in between them. The speed of the air is higher in between these two pieces of paper than outside (where of course the air speed is about zero), so therefore the pressure inside is lower and according to BernoulliÕs Law the papers will be sucked in towards each other. One would expect that they would be blown away from each other, but in reality the opposite occurs.

This is an interesting little experiment, that clearly demonstrates a physical phenomenon that has a completely different result than what one would expect. Just try for yourself and see.

The aerodynamic profile is formed with a rear side, that is much more curved than the front side facing the wind. Two portions of air molecules side by side in the air flow moving towards the profile at point A will separate and pass around the profile and will once again be side by side at point B after passing the profileÕs trailing edge. As the rear side is more curved than the front side on a wind turbine blade, this means that the air flowing over the rear side has to travel a longer distance from point A to B than the air flowing over the front side.

Therefore this air flow over the rear side must have a higher velocity if these two different portions of air shall be reunited at point B. Greater velocity produces a pressure drop on the rear side of the blade, and it is this pressure drop that produces the lift. The highest speed is obtained at the rounded front edge of the blade.

The blade is almost sucked forward by the pressure drop resulting from this greater front edge speed. There is also a contribution resultingfrom a small over-pressure on the front side of the blade.

Compared to an idling blade the aerodynamic forces on the blade under operational conditions are very large. Most wind turbine owners have surely noticed these forces during a start-up in good wind conditions. The wind turbine will start to rotate very slowly at first, but as it gathers speed it begins to accelerate faster and faster. The change from slow to fast acceleration is a sign that the bladeÕs aerodynamic shape comes into play, and that the lift greatly increases when the blade meets the head wind of its own movement.

The fast acceleration, near the wind turbineÕs operational rotational speed places great demands on the electrical cut-in system that must Òcapture and engage Ò the wind turbine without releasing excessive peak electrical loads to the grid.