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86 Fluid Mechanics, Thermodynamics of Turbomachinery

FIG. 3.26. Details near turbine cascade exit showing “throat” and suction-surface
curvature parameters.

where A t is the passage throat area and A n2 is the annulus area in the reference
plane downstream of the blades. If the annulus walls at the ends of the cascade
are not ﬂared then eqn. (3.52c) is the same as eqn. (3.52a). Between M 2 D 0.5 and
M 2 D 1.0 a linear variation of ˛ 2 can be reasonably assumed in the absence of any
other data.

Comparison of the proﬁle loss in a cascade and in a
turbine stage

The aerodynamic efﬁciency of an axial-ﬂow turbine is signiﬁcantly less than that
predicted from measurements made on equivalent cascades operating under steady
ﬂow conditions. The importance of ﬂow unsteadiness originating from the wakes
of a preceding blade row was studied by Lopatitiskii et al. (1969) who reported
that the rotor blade proﬁle loss was (depending on blade geometry and Reynolds
number) between two and four times greater than that for an equivalent cascade
operating with the same ﬂow. Hodson (1984) made an experimental investigation
of the rotor to stator interaction using a large-scale, low-speed turbine, comparing the
results with those of a rectilinear cascade of identical geometry. Both tunnels were
5
operated at a Reynolds number of 3.15 ð 10 . Hodson reported that the turbine
rotor midspan proﬁle loss was approximately 50 per cent higher than that of the
rectilinear cascade. Measurements of the shear stress showed that as a stator wake
is convected through a rotor blade passage, the laminar boundary layer on the
suction surface undergoes transition in the vicinity of the wake. The 50 per cent
increase in proﬁle loss was caused by the time-dependent transitional nature of the
boundary layers. The loss increase was largely independent of spacing between the
rotor and the stator.
In a turbine stage the interaction between the two rows can be split into two parts:
(a) the effects of the potential ﬂow; and (b) the effects due to wake interactions.
The effects of the potential inﬂuence extend upstream and downstream and decay
exponentially with a length scale typically of the order of the blade chord or pitch.
Some aspects of these decay effects are studied in Chapter 6 under the heading
“Actuator Disc Approach”. In contrast, blade wakes are convected downstream of

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