Page 117 - Fluid Mechanics and Thermodynamics of Turbomachinery

98 Fluid Mechanics, Thermodynamics of Turbomachinery

FIG. 4.3. Soderberg’s correlation of turbine blade loss coefficient with fluid deflection
(adapted from Horlock (1960).

made for Soderberg’s correlation that, although based on relatively few parameters,
it is of comparable accuracy with the best of the other methods.
Soderberg found that for the optimum space chord ratio, turbine blade losses
(with “full admission” to the complete annulus) could be correlated with space-
chord ratio, blade aspect ratio, blade thickness chord ratio and Reynolds number.
Soderberg used Zweifel’s criterion (see Chapter 3) to obtain the optimum space-
chord ratio of turbine cascades based upon the cascade geometry. Zweifel suggested
that the aerodynamic load coefficient T should be approximately 0.8. Following
the notation of Figure 4.1

2
T D 0.8 D 2.s/b/.tan ˛ 1 C tan ˛ 2 / cos ˛ 2 . .4.11/

The optimum space chord ratio may be obtained from eqn. (4.11) for specified
values of ˛ 1 and ˛ 2 .
For turbine blade rows operating at this load coefficient, with a Reynolds number
5
of 10 and aspect ratio H/b D blade height/axial chord) of 3, the “nominal” loss
Ł
coefficient is a simple function of the fluid deflection angle D ˛ 1 C ˛ 2 , for
Ł
a given thickness chord ratio .t max /l/. Values of are drawn in Figure 4.3 as
a function of deflection , for several ratios of t max /l. A frequently used analyt-
ical simplification of this correlation (for t max /l D 0.2/, which is useful in initial
performance calculations, is

2
Ł
D 0.04 C 0.06 . (4.12)
100
This expression fits Soderberg’s curve (for t max /l D 0.2/ quite well for 5 120 ° ,
but is less accurate at higher deflections. For turbine rows operating at zero inci-
dence, which is the basis of Soderberg’s correlation, the fluid deflection is little
different from the blading deflection since, for turbine cascades, deviations are