Wind turbines and Betz Law

WIND TURBINES AND BETZ LAW
Efficiency of wind turbines is limited to 59%.

Engineers and other rational people know either by education or intuition and logic that a wind turbine cannot absorb all the energy from an airstream. All types of turbines rotate only reluctantly because their rotating shaft in turn has to push magnets through coils to generate an electric current. The electrons (electricity) possess inertia so they don’t move from zero to a considerable speed through the wire without resistance.

The wind turbine absorbs the kinetic energy (energy of motion) from the wind which rotates it. In effect the wind, having given up some of its kinetic energy, its speed, has to leave the aft side of the turbine traveling slower than it entered. To travel slower it has to fan out somewhat to a larger diameter.

To slow and deviate the trajectory of even some of the air is a balancing act because, if the air leaves the turbine at the same speed it entered, no power is absorbed from the air. The air rotates the turbine but it is also affected by the turbines resistance to it, i.e., the air is slowed. Conversely, if the air leaves too slowly a raised pressure impulse within the air mass travels in reverse direction to the flow direction, back through the turbine and impedes the speed of the entering flow so less power than optimum is absorbed from the airstream.

Betz' law says that you can only convert less than 16/27 (or 59%) of the kinetic energy in the wind to mechanical energy using a wind turbine.

Betz' law was first formulated by the German Physicist Albert Betz in 1919. His book "Wind-Energie" published in 1926 gives a good account of the knowledge of wind energy and wind turbines.

In addition, the above mentioned resistance means the turbine blades will not turn as fast as the wind wants to push them. Therefore the blades may stall which further reduces their efficiency. Obviously there can be better designs than others which maximize efficiency.

While according to Betz Law the maximum efficiency is limited to 59%, at present the best wind turbines have a top efficiency of around 45%. That leaves a potential possible increase of around 31% over existing before the theoretical limit of 59% is reached.

It is unlikely that this present max efficiency of 45% will be increased by more than a slight margin since computerized fluid dynamics analysis (CFD) has rung about the last few % out of the existing conventional airfoils and wind turbine blades.

Now many new types of wind turbines are being invented and produced to attempt to increase the efficiency over the present 45% max. Some do not look at all like conventional Horizontal Axis Wind Turbines (in the industry, called a HAWT).

But keep in mind Betz Law! The principles still apply to all types of wind turbines. 59% efficiency is approximately it.

CFD analysis and the human brain cannot improve conventional wings and wind turbine blades further simply because these airfoils possess inherent limitations.

However some human brains long ago worked out how to greatly improve an airfoils lifting capacity.

A flap under the trailing edge called a Gurney Flap improves lift. But by far the best way to improve lift is by applying the COANDA form of CIRCULATION CONTROL.

This generates three times the lift by the wind turbine blade. This is performed regularly by us, NASA, Office of Naval Research, Georgia Tech Research Institute among others. In Australia this work has been conducted by Professor Ahmed Noor at University of New South Wales.

Three times lift does not mean 300 % increase in efficiency. To produce the effect has a penalty called “parasitic losses” When these are deducted from the result you still end up with a massive increase in lift that results in a very large part of the allowable 31% efficiency increase and that takes it far closer to the max 59% efficiency predicted by Betz Law.

Apart from the less effective Gurney Flap, there is no other way, full stop, to increase the efficiency of wind turbine blades by such a massive amount. Non technical decision makers need to know this. Present wind turbine installations obviously must proceed. But the next generation of wind turbines, employing Coanda Circulation Control should be now in the planning stages.

To understand it more, please read “Lift and the Coanda Effect” and Chanin’s thesis, based on work done in the NASA Ames 80 X 40 feet wind tunnel.