Environmental Engineering Reference
In-Depth Information
which shows that 1/4 < a < 1/3 must hold. These losses as compared to Betz' ideal
limit are called swirl losses. Figure 5 shows the quantitative dependence. Two
other mechanisms have to be introduced, to model all effects shown in Fig. 3. They
are the so-called tip-losses and profi le-drag losses. An AD was defi ned as a com-
pact disk, formally having infi nitely many blades. To estimate the effect of a fi nite
number of blades, the two models are used. One is based on conformal mapping
of the fl ow around a stack of plates to that of a rotor with a fi nite number of blades
(given by Prandtl [42]) and the second is based on the theory of propeller fl ow of
Goldstein [24]. A recent investigation has been made by Sørensen and Okulov
[ 39 , 40 ]. Usually a reduction factor F is introduced to account for the decreasing
forces on the blade towards the tip:
2
( 12 )
F
=
arccos
exp{
f ,
}
p
with
BR r
1.
f
=
+
l
( 13 )
2
r
l as expressed by eqn 6.
Comparison with measurements by Shen et al. [55] resulted in a new empirical
tip-loss model for use in AD and CFD simulations. Recently Sharpe [53] has
revised the arguments of Glauert and extended them slightly. Mikkelsen et al. [ 38 ]
applied his numerical AD method to investigate this effect. His fi ndings were that
Glauert's optimum rotor
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
TSR
Betz
PP
Figure 5:
cc
as a function of TSR.
 
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