Page 93 - Wind Energy Handbook

BREAKDOWN OF THE MOMENTUM THEORY 67

2
C Tl
1.5
C T mom
1
C
T emp
0.5
C
T exp
0
a
T
-0.5
0 0.2 0.4 0.6 0.8 1 1.2
a
Figure 3.16 Comparison of Theoretical and Measured Values of C T

blade circulation, there is no circulation present in the case of the circular plate.
Circulation would cause a small pressure drop similar to that given by the
momentum theory because it would be determined by the very low axial velocity of
the flow which actually permeates the disc.

3.6.3 Empirical determination of thrust coefficient

A suitable straight line through the experimental points would appear to be
possible, although Glauert proposed a parabolic curve, and provides an empirical
solution to the problem of the thrust on a heavily loaded turbine (a rotor operating
at a high value of the axial flow induction factor).
Most authors assume that the entire thrust on the rotor disc causes axial
momentum change. Therefore, for the empirical line to be useful it must be
assumed that it applies not only to the whole rotor but also to each separate stream-
tube. Let C 1 be the empirical value of C t when a ¼ 1. Then, as the straight line must
be a tangent to the momentum theory parabola at the transition point, the equation
for the line is
p ffiffiffiffiffiffiffiffi
C T ¼ C T1 4( C T1 1)(1 a) (3:55)

and the value of a at the transition point is

1 p ffiffiffiffiffiffiffiffi
a T ¼ 1 C T1 (3:56)
2
By inspection of Figure 3.16, C T1 must lie between 1.6 and 2; C T1 ¼ 1:816 would
appear to be the best fit to the experimental data of Figure 3.16, whereas Wilson and
Lissaman (1974) favour the lower value of C T1 ¼ 1:6. Glauert fits a parabolic curve
to the data giving much higher values of C T1 at high values of a but he was