Environmental Engineering Reference
In-Depth Information
Figure 2-15. Typical planform of a HAWT rotor blade.
The vertical scale is magniied
for clarity. [Grifin 2001].
The aerodynamically active length of this blade is assumed to extend from 25 percent of span
to the tip. The
mean radius
is deined as the radius that divides the active low area into two
equal areas. With these assumptions in mind, the aspect ratio of this sample blade is calcu-
lated to be 33.3, as follows:
1 + (
R
0
/
R
)
2
2
(2-19a)
R
M
/
R
=
= 0.729
c
(
R
0
/
R
= 0.729)
R
c
M
/
R
=
= 0.045
by interpolation
(2-19b)
2 (1 -
R
0
/
R
)
c
M
/
R
=
1.500
(2-19c)
m
=
0.045
= 33.3
Aerodynamic force data are usually measured in a wind tunnel using sub-scale models
that extend from wall to wall, eliminating any airlow around the ends of the model. These
models are said to have an
ininite aspect ratio
, and the force coeficients obtained are re-
ferred to as
two-dimensional
. Mathematical models were developed for modifying two-
dimensional coeficients to represent the aerodynamic behavior of inite-length airfoils, not
only in the attached regime [Jacobs and Abbott 1932] but also in the far-stall regime [Viterna
and Corrigan 1981]. These early model equations are given in Chapter 6.
Previous models of airfoil lift and drag coeficients have recently been updated and ex-
tended to include effects of
airfoil thickness
in addition to the effects of angle of attack, aspect
ratio, and stall [Spera 2008]. Figures 2-16(a) and (b) illustrate these updated models. Lift
and drag behavior in the attached and stall-development regimes, where forces are airfoil-
contour dependent, are represented by one set of equations in the reference, labeled
pre-stall
.
A second set of equations are labeled
post-stall
and represents behavior in the deep-stall
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