Wind Turbine Aerodynamics - Characteristic Parameters

Characteristic Parameters

Different wind turbines will come in different sizes. Then once the wind turbine is operating it will experience a wide range of conditions. This variability complicates the comparison of different types of turbines. To deal with this, nondimensionalization is applied to various qualities. One of the qualities of nondimensionalization is that when geometrically similar turbines will produce the same non-dimensional results, while because of other factors (difference in scale, wind properties) produce very different dimensional properties. This allows one to make comparisons between different turbines, while eliminating the effect of things like size and wind conditions from the comparison.

The coefficient of power is the most important variable in wind turbine aerodynamics. Buckingham π theorem can be applied to show that non-dimensional variable for power is given by the equation below. This equation is similar to efficiency, so values between 0 and less than one are typical. However this is not the exactly the same as efficiency so in practice some turbines can exhibit greater than unity power coefficients. In these circumstances one cannot conclude the first law of thermodynamics is violated because this is not an efficiency term by the strict definition of efficiency.

(CP)

where: is the coefficient of power, is the air density, A is the area of the wind turbine, finally V is the wind speed.

Equation (1) shows two important dependents. The first is the speed (U) that the machine is going at. The speed at the tip of the blade is usually used for this purpose, and is written as the product of the blade radius and the rotational speed of the wind (U=omega*r, where omega = rotational velocity in radians/second). This variable is nondimensionalized by the wind speed, to get the speed ratio:

(SpeedRatio)

The force vector is not straightforward, as stated earlier there are two types of aerodynamic forces, lift and drag. Accordingly there are two non-dimensional parameters. However both variables are non-dimensionalized in a similar way. The formula for lift is given below, the formula for drag is given after:

(CL)

(CD)

where: is the lift coefficient, is the drag coefficient, is the relative wind as experienced by the wind turbine blade, A is the area but may not be the same area used in the power non-dimensionalization of power.

The aerodynamic forces have a dependency on W, this speed is the relative speed and it is given by the equation below. Note that this is vector subtraction.

(RelativeSpeed)