Modified PARK model

This is a simple model of the wake that is based on the same algorithm used in PARK [4] [5].

Model initialisation

This two-dimensional model uses the momentum theory to predict the initial profile from the thrust coefficient assuming a rectangular wind speed profile, and that the wake expands linearly behind the rotor. The figure below outlines the flow field used by the model.

Flow field used in the Modified PARK model to calculate the wind turbine output

Wake development

The downstream wind speed is calculated using the following equation:

$$U_{w}\ = \ U_{i}\left\lbrack 1 - \left( 1 - \sqrt{1 - C_{t}} \right)\left( \frac{D}{D + 2kx} \right)^{2} \right\rbrack$$

Here U_i is the axial wind speed incident on the turbine, C_t is the thrust coefficient and k is the wake decay constant that can be defined by the following expression [5]:

$$k\ = \ \frac{A}{ln(h/z_{0})}$$

where “A” is a constant equal to 0.5, h is the turbine hub height and z₀ the surface roughness length.

The parameter k is set at the same value for all wind directions. This assumes that there is no significant variation in surface roughness length over the site and the surrounding area.