Wind Energy

U mean / U ref
1
0.9
0.8
0.7
49 Modelling Wind Turbine Wakes with a Porosity Concept 267
0.6
X = 2D
X = 4D
X = 6D
X = 9D
X = 12D
0.5
−1.5 −1 −0.5 0 0.5
X = 15D
1 1.5
r/D
I u / I u0
3
2.5
2
1.5
1
−1.5 −1 −0.5 0 0.5 1 1.5
Fig. 49.1. Streamwise velocity and turbulence intensity downstream of a porous
disc
Figure 49.1 presents results for a 100 mm-diameter disc made of mesh 6 at
different downstream locations. The near-wake area, characterized by an annular
shear layer and an annular turbulence intensity distribution, is well
defined and ends up at x/D = 4, where the two shear layers start collapsing.
The deduced axial flow induction factor is a =0.18. The far wake starts at
x/D = 9, from where the mean velocity and turbulence intensity profiles are
self-similar. At x/D = 9, the turbulence intensity is locally three times higher
than the freestream turbulence intensity Iu0.
Tests on the influence of the porosity level on the velocity and turbulence
distributions show that one can totally control the velocity deficit, and so the
shear-generated turbulence, using the appropriate mesh porosity level. Tests
on the mesh cell size for a fixed porosity level (65%) illustrate that when the
ratio between the mesh cell size and the disc diameter is smaller than 0.05,
the velocity distribution is independent of the mesh. If this ratio is respected,
it is also independent of the disc size.
49.4 Results for Shear Freestream Conditions
A wind farm was built with 9 square-arranged porous discs made of mesh
6 mounted on masts (Fig. 49.2). The masts spacing is ∆x = ∆y = 3D.
Figure 49.3 shows the mean velocity distributions 3D downstream of the first,
the second and the third row of porous discs. The black circle shows the disc
circumference. Classical features of the wind turbine wakes are found [4]. As
expected, the velocity deficit is located lower than the disc centre, due to the
ground effect. The velocity deficit increases between the first and the second
row, but stays constant between the second and the third one, although the
wake extend is still growing. Figure 49.4 shows the turbulence intensity distributions
at the same locations. It is worth to notice that, after three rows,
the turbulence intensity can locally reach 26%, due to the combination of the
r/D