Environmental Engineering Reference
In-Depth Information
C
t
= 4
a F
(1 -
a
)
if
£
a
c
a
a
c
+ (1 - 2
a
c
)
a
C
t
= 4
F
if
>
a
c
a
(5-36)
a
c
³
1
/
3
The second equation is a linear extrapolation of the first from the junction point
a
=
a
c
. The
value of
a
c
should be equal or greater than 1/3 in order that the Betz Limit is not exceeded.
In summary, the set of equations used to determine the induced velocities in accordance with
strip theory is composed of Equations (5-23a), (5-32), (5-35), and (5-36).
Cascade Effects on Lift and Drag Coeficients
Lift and drag coefficients,
C
L
and
C
D
, are functions of the angle of attack, a, as follows:
C
L
=
C
L
[a ]
C
D
=
C
D
[a ]
a = f - b+ Da
c
(5-37)
where
Da
c
= cascade correction to angle of attack (rad)
At a given radial position on the blades, the circumference can be unrolled and represented as
a sequence or
cascade
of airfoils, as shown in Figure 5-14. An expression for the so-called
cascade correction
will be derived using the flow geometry shown in this figure. In the strip
theory developed to this point, we have used a
lifting line
approach, where the flow distor-
tions caused by the rotor width and blade thickness are ignored. Near the root of a thick
blade, however, flow distortion can be significant.
Figure 5-14. Cascade effects on angle of attack.
(a) Streamline displacement caused by
finite blade thickness (b) Streamline curvature caused by the finite blade width
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