Wind Energy

7
Models for Computer Simulation of Wind Flow
over Sparsely Forested Regions
J.C. Lopes da Costa, F.A. Castro and J.M. L.M. Palma
7.1 Introduction
Because of the flow complexity and wind power reduction, the regions near or
within forests have not been considered for wind park installation. However,
because of the shortage of good clear sites, this situation was reverted, adding
new motivation to the study of the wind flow over forested regions.
The so-called k − ε model, the standard in flow modelling of engineering
applications, has also appeared in atmospheric flow studies, circumventing the
limitations of simpler approaches [1]. However, in the case of canopy flows,
there are open questions on the actual performance of the k − ε compared
with lower order models, and the mathematical form of the additional terms
in the transport equations for the turbulence kinetic energy k and its rate of
dissipation ε [2].
7.2 Mathematical Models
The canopy models as in [4, 6] and a version of k − ε − v2 − f [3] are studied
over model forests. For sake of compactness, the model description will be
restricted to their differences from the standard versions, i.e. without the terms
accounting for the canopy. The reader may refer to the original publications
for a complete description of each of the models being used here.
The presence of the canopy requires an additional term in the momentum
equation accounting for the extra drag, and re-definition of the production
terms of k and ε in the transport equations, where additional terms Sk and
Sε will appear (Pk − ρε + Sk) and (C1ε/kPk − C2ρε2 /k + Sε). In case of
k −ε−v 2 −f turbulence model, the equation for f contains also an additional
Sk, Cf2(Pk + Sk)/k.
The terms Sk and Sε will read
Sk = 1
2 ραCD
�
βp
�
�U � �3 �
− βd �U � �
� k , (7.1)