Models, Data, and Methodology - On the Effect of Offshore Wind Farms on the Atmosphere and Ocean Dynamics - page 16

Fig. 3.1 Schema of actuator disc concept after Betz ( 1926b ), courtesy of Linde et al. (2014). Red
line marks rotor disc. For further details, please see text

1

A 0 v 1 v 2

T 0
T max ¼

2 ρ

v 2
v 1

c T ¼ ¼ ð Þ

1 3 : 1

1

A 0 v 1

2 ρ

The thrust coefficient c T is a parameter given for each wind turbine type by the
manufacturer s specifications, or it can be determined from field measurements.

The coefficient varies with the speed of wind. According to the definition of the
thrust coefficient, the rotor thrust equation (Eq. 3.1 ) only depends on the wind speed
of the undisturbed flow, the thrust coefficient, and the rotor area. The rotor area
depends on the rotor diameter and is easily calculated. But the undisturbed wind
speed has to be determined during model simulation.

'

1
2 ρ

1
2 c T ρ

T 0 ¼ A 0 v 1 v 2 A 0 v 1 ¼ c T T max ¼ ð 3 2 Þ

:

In METRAS, like in all mesoscale models, the horizontal grid size is typically
large, compared to the size of the wind turbine rotor. It means that for a single wind
turbine, the grid cell for the rotor and the reference position are the same. Also,
several wind turbines might be located within one single grid cell. Therefore, a
whole wind farm, like alpha ventus with 12 turbines, is only located within a few
adjacent grid cells. Therefore, the wind reduction of several wind turbines super-
poses one large wind wake in the model. To adapt that issue, the wind counts ratable
into affected grid box. That means a preprocessor mask consisted of an auxiliary
grid allows the calculation of one turbine within a relative bigger grid. Therefore, it
is necessary to determine the average reference wind speed for each wind farm in
METRAS. The reference wind speed is chosen over all grid cells containing the
wind farm itself. The area per grid cell covered by a rotor is defined as wind
turbine mask.
Multiplying Eq. ( 3.2 ) by the wind turbine mask and adding this term to the basic
momentum equation lead to the parameterization for wind turbines.