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coefficient for low aspect ratios (which is not predicted by Equations (6-3)), and that the
same situation ( i.e. , a lower separated-lift coefficient) persists as the angle of attack
increases beyond the stall point.
Post-Stall Modeling of Lift and Drag Coefficients
As previously noted, the airfoils in fixed-pitch rotors (used in stall-controlled HAWTs
and most VAWTs) will operate over all three of the flow regimes in Figure 6-2. In order
to accurately predict the peak power of a fixed-pitch rotor, it is particularly important to
know the details of lift and drag behavior in the high lift/stall development regime. An
empirical model for modifying two-dimensional airfoil data in all three regimes to more
accurately represent wind turbine rotor behavior has been developed by Viterna and
Corrigan [1981]. This model is based on the following three assumptions:
--
In the attached flow regime, Equations (6-3) adequately model end effects in
terms of the blade aspect ratio, and no tip- or hub-loss models are needed.
--
In the high-lift/stall-development regime, the torque force (sometimes called
the suction force ) on the element, acting in the plane of rotation, does not
decrease with increasing angle of attack; rather, it is independent of angle of
attack.
--
In the flat-plate/fully-stalled regime, the dominant parameter is the maximum
value of the drag coefficient, and this is determined by the blade aspect ratio.
The equations which implement these assumptions in the Viterna-Corrigan post-stall model
are as follows:
a³a S :
sin2a + K L cos 2 a
sina
C L = C D ,max
2
(6-4a)
C D = C D ,max sin 2 a + K D cos a
(6-4b)
sin a S
cos 2 a S
K L = ( C L , S - C D ,max sin a S cos a S )
(6-4c)
K D = C D , S - C D ,max sin 2 a S
cos a S
(6-4d)
m £ 50 : C D ,max = 1.11 + 0.018 m
m > 50 : C D ,max = 2.01
(6-4e)
where
C D,max = maximum drag coefficient in the fully-stalled regime
To illustrate the application of Equations (6-3) and (6-4), Viterna and Corrigan [1981]
analyzed the power output of the historic Gedser wind turbine, shown in Figure 3-1. The
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