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90 Fluid Mechanics, Thermodynamics of Turbomachinery
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Problems

1. Experimental compressor cascade results suggest that the stalling lift coefficient of a
cascade blade may be expressed as

3
c 1
C L D 2.2
c 2
where c 1 and c 2 are the entry and exit velocities. Find the stalling inlet angle for a compressor
cascade of space chord ratio unity if the outlet air angle is 30 deg.
2. Show, for a turbine cascade, using the angle notation of Figure 3.27, that the lift
coefficient is
C L D 2.s/l/.tan ˛ 1 C tan ˛ 2 / cos ˛ m C C D tan ˛ m
1 1 2
where tan ˛ m D .tan ˛ 2 tan ˛ 1 / and C D D Drag/. c m l/.
2 2
0
A cascade of turbine nozzle vanes has a blade inlet angle ˛ D 0 deg, a blade outlet angle
1
0
˛ of 65.5 deg, a chord length l of 45 mm and an axial chord b of 32 mm. The flow entering
2
the blades is to have zero incidence and an estimate of the deviation angle based upon similar
cascades is that υ will be about 1.5 deg at low outlet Mach number. If the blade load ratio T
defined by eqn. (3.55) is to be 0.85, estimate a suitable space chord ratio for the cascade.
Determine the drag and lift coefficients for the cascade given that the profile loss coefficient
1
2
D p 0 /. c / D 0.035.
2 2
3. A compressor cascade is to be designed for the following conditions:
Nominal fluid outlet angle ˛ Ł D 30 deg
2
Cascade camber angle D 30 deg
Pitch/chord ratio s/l D 1.0
Circular arc camberline a/l D 0.5
Using Howell’s curves and his formula for nominal deviation, determine the nominal inci-
dence, the actual deviation for an incidence of C2.7 deg and the approximate lift coefficient
at this incidence.
4. A compressor cascade is built with blades of circular arc camber line, a space/chord
ratio of 1.1 and blade angles of 48 and 21 deg at inlet and outlet. Test data taken from
the cascade shows that at zero incidence (i D 0) the deviation υ D 8.2 deg and the total