Environmental Engineering Reference
In-Depth Information
power coefficient of 15.0, compared with 0.3 for the drag device. Thus, lift devices can quite
readily produce 50 times the power per unit of projected area than that produced by drag de-
vices. Moreover, operating a lifting device at velocities well in excess of the wind velocity is
easily achieved by rotating machines. It is further noted that the maximum power coefficient
of any rotary machine using drag is also less than (4/27)
C
D,max
based on the projected area of
the drag elements.
With the superiority of the lifting translator established, the concept of placing lifting
surfaces on a rotating machine to form a turbine is seen to be an obvious method of convert-
ing wind energy to useful work.
Performance Parameters
The
power performance
of a wind turbine can be expressed in dimensionless form in two
ways. First, for a fixed wind speed, the
power coefficient
,
C
P
, and the
tip-speed ratio
, l, are
used. The power coefficient is defined in Equation (5-2), in which
A
P
is now the projected
area of the
moving rotor
(called the
swept area
) and the tip-speed ratio is
l =
v U
max
=
R
W
/
/
)
(5-6)
where
l = tip-speed ratio
R
= maximum rotor radius (m)
W = rotor speed (rad/s)
The power in the Equation (5-2) can be either the rotor output, in which case we have the
rotor power coefficient
,
C
P
,
r
, or the system output power, in which case we have the
system
power coefficient
,
C
P
,
s
. The difference between these two outputs is the power-train and
electrical equipment losses.
The second dimensionless form for expressing performance is for a fixed rotor angular
speed, in which the
advance ratio
,
J
, and a
rotor speed power coefficient
,
K
P
are used. These
parameters are defined by
U
R
W
=
1
l
/
J
=
U v
min
=
)
(5-7a)
0.5 r
R
3
W
3
A
=
C
P
P
(5-7b)
K
P
=
l
3
As before,
K
P
can be given for the rotor or for the entire system.
Figures 5-5 and 5-6 illustrate
C
P
,
r
as a function of l and
K
P
,
r
as a function of
J
for a
typical HAWT operating at fixed pitch. Operating points A, B, C, and D are shown in both
figures. The left-hand side of Figure 5-5 (ABC) is controlled by
blade stall
. Local
angles of
attack
(angles between the relative wind and the blade
chord line
) are relatively large as point
A is approached. Changes in blade
pitch angle
have a great effect on power output along
segment ABC. The right-hand side of Figure 5-5 (CD) is controlled by drag, particularly
skin
friction
, because the angles of attack are small as point D is approached.
The plot of
K
p
versus
J
is a dimensionless plot of
power vs. wind speed
, or a
power
curve
, at fixed rotor speed and blade pitch. Note that maximum power, B, does not occur at
the maximum power coefficient point, C. At fixed pitch, maximum power occurs in the stall
region when the lift coefficient is near its peak value over much of the blade.
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