Page 47 - Wind Energy Handbook

TURBULENCE 21

B
sin Æ ¼ v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (2:14)
u " !# 2
u
t u 2
ln þB
fz 0

2.6.3 Turbulence intensity

The turbulence intensity in the neutral atmosphere clearly depends on the surface
roughness. For the longitudinal component, the standard deviation ó u is approxi-
mately constant with height, so the turbulence intensity decreases with height.

More precisely, the relationship ó u 2:5u may be used to calculate the standard

deviation, with the friction velocity u calculated as in the previous section. More
recent work (ESDU, 1985) suggests a variation given by:
p
7:5ç(0:538 þ 0:09 ln(z=z 0 )) u
ó u ¼ (2:15)

1 þ 0:156 ln(u =fz 0 )
where

ç ¼ 1 6 fz=u (2:16)
p ¼ ç 16 (2:17)

This approximates to ó u ¼ 2:5u close to the ground, but gives larger values at
greater heights. The longitudinal turbulence intensity is then

I u ¼ ó u =U (2:18)

The lateral (v) and vertical (w) turbulence intensities are given (ESDU, 1985) by

ó v 4 ðz
I v ¼ ¼ I u 1 0:22 cos (2:19)
U 2h

ó w 4 ðz
I w ¼ ¼ I u 1 0:45 cos (2:20)
U 2h
Note that specific values of turbulence intensity for use in design calculations are
prescribed in some of the standards used for wind turbine design calculations, and
these may not always correspond with the above expressions. For example, the
Danish standard (DS472, 1992) specifies

I u ¼ 1:0= ln(z=z 0 ) (2:21)

with I v ¼ 0:8I u and I w ¼ 0:5I u . The IEC standard (IEC, 1999) gives

I u ¼ I 15 (a þ 15=U)=(a þ 1) (2:22)