WindPRO / PARK - EMD International AS.

Introduction to the Ainslie Wake Model (Eddy Viscosity Model)
D
M
= C
b =
8D
M
T
− 0.05 − (16C
3.56C
T
(1 − 0.5) D
M
T
− 0.5) A /1000
Other authors specify a boundary condition where the initiation position (downwind position) varies. In Lange
et al [4] reference to a study made by Vermeulen [5] is made. Vermeulen suggests that the near wake length is
modeled through contributions from ambient turbulence, rotor generated turbulence and shear generated
turbulence. The near wake length is divided into two regions; the first x h is modeled as:
x
h
= r
0
⎡⎛
dr ⎞
⎢⎜
⎟
⎢⎣
⎝ dx ⎠
2
a
⎛ dr ⎞
+ ⎜ ⎟
⎝ dx ⎠
2
λ
⎛ dr ⎞
+ ⎜ ⎟
⎝ dx ⎠
2
m
⎤
⎥
⎥⎦
−0.5
where r 0 is an ‘effective’ radius of an expanded rotor disc, = [ D / 2] ( m 1) / 2
D is the rotor diameter
C t the thrust coefficient
The different contributions in the equation above are calculated as:
⎛ dr ⎞
⎜ ⎟
⎝ dx ⎠
⎛ dr ⎞
⎜ ⎟
⎝ dx ⎠
⎛ dr ⎞
⎜ ⎟
⎝ dx ⎠
2
a
2
λ
2
m
⎧2.5I
+ 0.05
= ⎨
⎩5I
= 0.012Bλ
=
for I ≥ 0.02
for I < 0.02
r 0 + and m = 1 / 1− Ct
ambient turbulence
rotor generated turbulence
[(1
− m)
1.49 + m ]/ (9.76(1+
m)) shear - generated turbulence
where
I is the ambient turbulence intensity
B is the number of rotor blades
λ is the tip speed ratio
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