Physics of Wind Parks - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 132

number of blades, and blade aerodynamics. The far wake is the region beyond the
near wake, where modelling the actual rotor is less important (Vermeer et al 2003 ).
The wake velocity deficit, the downwind decay rate of the wake, and the added
turbulence intensity within the far wake with respect to downwind distance behind
wind turbines are largely determined by two factors: the turbine's thrust coefficient
[see Eq. ( 6.13 ) and Fig. 6.2 ] and the ambient atmospheric turbulence [often
characterized by the parameter 'turbulence intensity', see Eq. ( 3.10 )]. The initial
velocity deficit depends on the amount of momentum extracted by the turbine from
the ambient flow. Thus, this deficit is a function of the turbine's thrust coefficient.
Turbine thrust coefficients are generally highest at low wind speeds around the cut-
in wind speed and decrease with increasing wind speed. They approach to very
low values above the rated wind speed of the turbine. Nevertheless, published data
on wake deficits have often been analyzed as a function of wind speed rather than
thrust coefficient. Wake measurement data generally verify that deficits are highest
at low wind speeds and lowest at high wind speeds (Elliot 1991 ). Vermeer et al
( 2003 ) give the following relation for the distance-dependent relative velocity
deficit in the far wake:

n

Du
u h

¼ u h0 u h
u h

D
s

¼ A ð 6 : 1 Þ

where u h is the wind speed at hub height, D is the rotor diameter, s is the distance
from the turbine, and A and n are constants. A depends on the turbine thrust
coefficient and increases with it. A varies between 1 and 3 while n takes values
between 0.75 and 1.25 and principally depends on the ambient turbulence
intensity. The WAsP model (Troen and Petersen 1989 ) uses a similar approach
(Barthelmie and Jensen 2010 ):

2

¼ 1

p

u h
u h0

D
D þ ks

1 C t

ð 6 : 2 Þ

with the turbine thrust coefficient C t (see ( 6.13 ) and Fig. 6.2 ) and the wake decay
coefficient k. k = 0.04 is typical for offshore conditions (Barthelmie and Jensen
2010 ) while 0.075 is the default value in WAsP (Barthelmie et al ( 2004 ).
The added turbulence intensity in the wake decreases more slowly than the
velocity deficit. Vermeer et al ( 2003 ) give three empirical formulae from three
different sources which describe the measured data quite well. According to
Quarton ( 1989 ) the added turbulence intensity decreases as:

q

I 2 I 2 1

0 : 57

s N
s

¼ 4 : 8C 0 : T I 0 : 68 DI ¼ ð 6 : 3 Þ

1

where I ? is the undisturbed turbulence intensity, C T is the thrust coefficient, and s N
is the length of the near wake which is between one and three rotor diameters. The
width of the wake is proportional to the one third power of the rotor diameter (see
Frandsen et al 2006 for more details):