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166 Fluid Mechanics, Thermodynamics of Turbomachinery
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Problems

(Note: In questions 1 to 4 and 8 take R D 287 J/(kg ° C) and
D 1.4.)
1. An axial flow compressor is required to deliver 50 kg/s of air at a stagnation pressure
of 500 kPa. At inlet to the first stage the stagnation pressure is 100 kPa and the stagnation
temperature is 23 ° C. The hub and tip diameters at this location are 0.436 m and 0.728 m. At
the mean radius, which is constant through all stages of the compressor, the reaction is 0.50
and the absolute air angle at stator exit is 28.8 deg for all stages. The speed of the rotor is
8000 rev/min. Determine the number of similar stages needed assuming that the polytropic
efficiency is 0.89 and that the axial velocity at the mean radius is constant through the stages
and equal to 1.05 times the average axial velocity.
2. Derive an expression for the degree of reaction of an axial compressor stage in terms
of the flow angles relative to the rotor and the flow coefficient.
Data obtained from early cascade tests suggested that the limit of efficient working of an
axial-flow compressor stage occurred when

(i) a relative Mach number of 0.7 on the rotor is reached;
(ii) the flow coefficient is 0.5;
(iii) the relative flow angle at rotor outlet is 30 deg measured from the axial direction;
(iv) the stage reaction is 50%.
Find the limiting stagnation temperature rise which would be obtained in the first stage
of an axial compressor working under the above conditions and compressing air at an inlet
stagnation temperature of 289 K. Assume the axial velocity is constant across the stage.