Page 63 - Wind Energy Handbook

TURBULENCE IN COMPLEX TERRAIN 37

where

dr
¼ 2:5I 0 þ 0:005
dx Æ
is the growth rate contribution due to ambient turbulence,
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
dr ð 1 mÞ 1:49 þ m
¼
dx m (1 þ m)9:76

is the contribution due to shear-generated turbulence, and

dr
¼ 0:012Bº
dx º
is the contribution due to mechanical turbulence, where B is the number of blades
and º is the tip speed ratio.
Deep inside a wind farm, the reduction in wind speed and the increase in
turbulence intensity are the result of the superposition of wakes from many upwind
turbines. Frandsen and Thøgersen (1999) propose a model based on the geostrophic
drag law which takes into account the additional ‘surface roughness’ caused by the
turbines themselves. This leads to a formula for added turbulence above hub
height:
0:36
I þþ ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 þ 0:2 s 1 s=C T

where s 1 and s are the inter-turbine spacings, normalized by rotor diameter, within
a row and between rows. Since this does not apply below hub height, the average
added turbulence intensity I þ is then calculated as
q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
I þ ¼ 1 I 0 þ I þ I 2
2 0 þþ
However, no consensus has yet emerged on a sufficiently well-validated formula
for turbulence intensity within a wind farm for use in wind turbine design
calculations.

2.11 Turbulence in Complex Terrain

Predicting the turbulence intensity and spectrum at a given point within an area of
complex terrain is not straightforward. Hilly terrain upwind of the site in question
will lead to generally higher turbulence levels, and some authors have suggested
that this can be calculated from a ‘regional roughness length’ which takes the
topography into account as well as the surface roughness (Tieleman, 1992). On the