Page 62 - Wind Energy Handbook
P. 62
36 THE WIND RESOURCE
Theoretical models capable of predicting turbulence levels in the wake are less
well developed. Quarton and Ainslie (1989) examined a number of different sets of
wake turbulence measurements, both in wind tunnels using small wind turbine
models or gauze simulators, and behind full-size turbines in the free stream. An
empirical formula for added turbulence I þ at a downstream distance x from the
turbine was found to give a good fit to the various measurements:
I
I þ ¼ 4:8C 0:7 0:68 (x=x n ) 0:57
T 0
where C T is the turbine thrust coefficient, I 0 the ambient turbulence intensity, and
x n the length of the near wake region. Here I 0 and I þ are expressed as percentages.
On the basis of further work, an improved expression was subsequently proposed
by Hassan (1992):
I þ ¼ 5:7C 0:7 0:68 (x=x n ) 0:96
I
T 0
The added turbulence is defined as the square root of the additional wind speed
variance normalized by the mean wind speed, i.e.,
q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
I þ ¼ I 2 wake I 2 0
where I wake is the total wake turbulence intensity, at any given downstream
distance.
The length of the near wake region, x n , is calculated according to Vermeulen
(1980) in terms of the rotor radius R and the thrust coefficient C T as
nr 0
x n ¼
dr
dx
where
r ffiffiffiffiffiffiffiffiffiffiffiffiffi
m þ 1
r 0 ¼ R
2
1
m ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 C T
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0:214 þ 0:144m(1 0:134 þ 0:124m)
n ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(1 0:214 þ 0:144m) 0:134 þ 0:124m
and dr=dx is the wake growth rate:
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2 2
dr dr dr dr
¼ þ þ
dx dx Æ dx m dx º
