PLANT DESIGN AND ENERGY PRODUCTION ESTIMATION - Wind Resource Assessment: A Practical Guide to Developing a Wind Project - page 248

Here D 0 is the rotor diameter (in meters), k is the decay constant, and x is the distance
downstream from the rotor (expressed in rotor diameters). The speed deficit v (as a

fraction of the free-stream speed) is assumed to be constant across the width and is
given by the equation,

δ

D 0
D

2

1

δ v ( x ) = ( 1 − − C t ) (16.8)

( x )

In this equation, C t is the thrust coefficient of the turbine, a parameter that represents
the amount of force generated by the rotor against the wind. Along with the turbine
power curve, C t is specified by the manufacturer and varies with speed.
A key question in wake modeling is how the wakes of successive downstream
turbines combine with one another. In the Park model, the incident wind speed at a
downwind turbine is the free-stream wind speed minus the wake deficit calculated by
Equation 16.8, multiplied by the fractional overlap between downwind turbine's rotor
and the upwind turbine's wake cross section (Fig. 16-7). Where there are several
upstream wind turbines with overlapping wakes, the incident speed is assumed to
equal the free-stream speed minus the largest single wake deficit.
Modified Park differs from Park in two ways. One is how the overlap with an
upwind wake is calculated: in modified Park, the area of overlap is represented by a
rectangle. The other is that the wake generated by a wake-affected turbine is the same
as if the turbine were in the free-stream except that its thrust coefficient, C t , is cal-
culated using the incident wind speed for that turbine. In general, these modifications
produce a smaller wake loss than that estimated by Park. Where there is a choice,
modified Park is generally used.
The only parameter that needs to be defined when running the Park or modified
Park model is the wake decay constant. This typically ranges in value from 0.04

(a) (b)

D 1

overlap

overlap

D 0

Method 1 Method 2

X 01

Figure 16-7. (a) Plan view of a turbine wake of initial width D 0 expanding with distance
downstream and intersecting the rotor of a second turbine. (b) Two methods of calculating
the area of overlap between the wake and the second turbine. The first is that implemented
in the Park model, the second is that implemented in the modified Park model. Source: AWS
Truepower.