How a Wind Turbine Works

The secret of wind power

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Abstract


We explain how the flow of air around the rotor blades of a wind turbine creates a lift force, which turns the rotor around its axis and drives a generator of electric energy.


Rotor Blade Acts Like a Wing

The rotor blade of a wind turbine acts like a wing and generates a lift force L and a drag force D, with L turning the rotor around a (usually horisontal) axis and thereby driving a generator of electricity. The rotor is similar to a propeller but the action is inverted: A propeller delivers forward thrust at the expense of torsion of the propeller axis, while a wind turbine delivers torsion from incoming wind (negative thrust). 
The energy produced by a wind turbine scales with the lift L and the rotational velocity of the rotor. It is
desirable to have large L with large lift/drag ratio L/D, because the drag D is limited by the incoming wind pressure.

There is a lot of mystery surrounding the generation of lift and drag of a wing, which is propagated into
mysteries of how a wind turbine works, as show in e.g. The Wind Turbine delivering the usual incorrect explanation of the generation of lift:

  • ...the air flow over the rear side must have a higher velocity…Greater velocity produces a  pressure drop on the rear side of the blade, and it is this pressure drop that produces the lift. 

But the mystery is uncovered in the Knol  Why It Is Possible to Fly leading to also an explanation of Why a Propeller Gives Thrust. 
From this basis we can understand how a wind turbine works: In order to have large lift L with L/D > 10, the angle of attack should be between 10 and 15, which requires a variable pitch increasing with the distance to the rotor axis, since the apparent wind direction changes with the same distance. This can be seen in the left figure below, which also shows that the chord length decreases with the distance to the axis.
 

                                  Wind turbine park, rotor with generator and blade design.


Lift and Drag of a Wing

Mechanism

Below we give a shortcut to the action of wing, with the flow seen as perturbation of zero lift/drag potential flow arising from a mechanism of instability at rear separation, which modifies the pressure distribution so as to give both lift and drag. Notice that large lift comes from suction on the leeward surface resulting from the fact the flow does not separate on the crest. This is because the fluid (air or water) has very small viscosity which means that the boundary layer is turbulent with small skin friction closely approximated by the slip boundary condition of potential flow. Slightly viscous flow with laminar boundary layer separates on the crest and gives poor lift.
 

Sideview of velocity and pressure, and topview of streamwise vorticity of Naca0012 wing at aoa = 14. Observe the turbulent streamwise vorticity emanating from top separation, as sketched above. Computed solution of the Navier-Stokes equations with slip boundary condition [1].


Principle of action of a wing: Potential flow (upper left) with zero lift/drag modified by low-pressure counter-rotating rolls of streamwise vorticity from instability mechanism at separation (upper right), switching the pressure on rear wing (bottom) to give both lift and drag (H high, L low pressure).

 Lift/Drag Ratio L/D

Lift, drag and lift/drag ratio for a sail (left) and Naca0012 wing (right)  as function of aoa.

We see (larger figs) that for a symmetric airlfoil like a Naca0012, L ~ 2.5 is maximal for aoa = 20 with L/D ~ 3 small, while for unsymmetric airfoil like a sail, L/D > 6 for aoa = 20 at maximal lift. This means that a sail works efficiently at maximal lift for aoa = 20, while a symmetric airfoil has a satisfactory L/D only for aoa < 15 with non-maximal lift (as discussed in more detail in Why It Is Possible to Sail). A propeller normally is rather thin and is more similar to a sail than a symmetric airfoil.

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