Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

Two-dimensional Cascades 77
FIG. 3.18. Variation of nominal deflection with nominal outlet angle for several
space–chord ratios (adapted from Howell 1945a and 1945b).
important that an accurate estimate is made of it. Re-examining Figure 3.11, it will be
observed that the fluid receives its maximum guidance on the pressure side of the
cascade channel and that this diminishes almost linearly towards the suction side of the
channel.
Howell used an empirical rule to relate nominal deviation d* to the camber and
space–chord ratio,
(3.39)
where n 1 – 2 for compressor cascades and n 1 for compressor inlet guide vanes.
The value of m depends upon the shape of the camber line and the blade setting. For
a compressor cascade (i.e. diffusing flow),
(3.40a)
where a is the distance of maximum camber from the leading edge. For the inlet guide
vanes, which are essentially turbine nozzles (i.e. accelerating flow),
(3.40b)
EXAMPLE 3.1. A compressor cascade has a space–chord ratio of unity and blade inlet
and outlet angles of 50deg and 20deg respectively. If the blade camber line is a circular
arc (i.e. a/l = 50%) and the cascade is designed to operate at Howell’s nominal
condition, determine the fluid deflection, incidence and ideal lift coefficient at the
design point.
Solution. The camber, q = a¢ 1 - a¢2 = 30deg. As a first approximation put a* 2
= 20deg in eqn. (3.40) to give m = 0.27 and, using eqn. (3.39), d* = 0.27 ¥ 30 =
8.1deg. As a better approximation put a* 2 = 28.1deg in eqn. (3.40) giving m = 0.2862
and d* = 8.6 deg. Thus, a* 2 = 28.6deg is sufficiently accurate.