Page 106 - Fluid Mechanics and Thermodynamics of Turbomachinery

Two-dimensional Cascades 87
the blade row with very little mixing with the mainstream flow. The wakes tend to
persist even where the blade rows of a turbomachine are very widely spaced.
A designer usually assumes that the blade rows of an axial-flow turbomachine
are sufficiently far apart that the flow is steady in both the stationary and rotating
frames of reference. The flow in a real machine, however, is unsteady both as a
result of the relative motion of the blade wakes between the blade rows and the
potential influence. In modern turbomachines, the spacing between the blade rows
is typically of the order of 1/4 to 1/2 of a blade chord. As attempts are made to
make turbomachines more compact and blade loadings are increased, then the levels
of unsteadiness will increase.
The earlier Russian results showed that the losses due to flow unsteadiness were
greater in turbomachines of high reaction and low Reynolds number. With such
designs, a larger proportion of the blade suction surface would have a laminar
boundary layer and would then exhibit a correspondingly greater profile loss as a
result of the wake-induced boundary layer transition.

Optimum space chord ratio of turbine blades (Zweifel)

It is worth pondering a little upon the effect of the space chord ratio in turbine
blade rows as this is a factor strongly affecting efficiency. Now if the spacing
between blades is made small, the fluid then tends to receive the maximum amount
of guidance from the blades, but the friction losses will be very large. On the
other hand, with the same blades spaced well apart, friction losses are small but,
because of poor fluid guidance, the losses resulting from flow separation are high.
These considerations led Zweifel (1945) to formulate his criterion for the optimum
space chord ratio of blading having large deflection angles. Essentially, Zweifel’s
criterion is simply that the ratio ( T ) of the actual to an “ideal” tangential blade
loading, has a certain constant value for minimum losses. The tangential blade loads
are obtained from the real and ideal pressure distributions on both blade surfaces,
as described below.
Figure 3.27 indicates a typical pressure distribution around one blade in a turbine
cascade, curves P and S corresponding to the pressure (or concave) side and suction
(convex) side respectively. The pressures are projected parallel to the cascade front
so that the area enclosed between the curves S and P represents the actual tangential
blade load per unit span,

Y D sc x .c y2 C c y1 /, (3.53)
cf. eqn. (3.3) for a compressor cascade.
It is instructive to examine the pressures along the blade surfaces. Assuming
1 2
incompressible flow the static inlet pressure is p 1 D p 0 c ; if losses are also
1
2
1 2
ignored the outlet static pressure p 2 D p 0 c . The pressure on the P side
2
2
remains high at first (p 0 being the maximum, attained only at the stagnation point),
then falls sharply to p 2 . On the S side there is a rapid decrease in static pressure
from the leading edge, but it may even rise again towards the trailing edge. The
closer the blade spacing s the smaller the load Y becomes (eqn. (3.53)). Conversely,
wide spacing implies an increased load with pressure rising on the P side and falling