Page 186 - Fluid Mechanics and Thermodynamics of Turbomachinery

Axial-flow Compressors and Fans 167
3. Each stage of an axial flow compressor is of 0.5 reaction, has the same mean blade speed
and the same flow outlet angle of 30 deg relative to the blades. The mean flow coefficient is
constant for all stages at 0.5. At entry to the first stage the stagnation temperature is 278 K,
2
the stagnation pressure 101.3 kPa, the static pressure is 87.3 kPa and the flow area 0.372 m .
Using compressible flow analysis determine the axial velocity and the mass flow rate.
Determine also the shaft power needed to drive the compressor when there are 6 stages
and the mechanical efficiency is 0.99.
4. A sixteen-stage axial flow compressor is to have a pressure ratio of 6.3. Tests have
shown that a stage total-to-total efficiency of 0.9 can be obtained for each of the first six
stages and 0.89 for each of the remaining ten stages. Assuming constant work done in each
stage and similar stages find the compressor overall total-to-total efficiency. For a mass
flow rate of 40 kg/s determine the power required by the compressor. Assume an inlet total
temperature of 288 K.
5. At a particular operating condition an axial flow compressor has a reaction of 0.6, a
2
flow coefficient of 0.5 and a stage loading, defined as h 0 /U of 0.35. If the flow exit angles
for each blade row may be assumed to remain unchanged when the mass flow is throttled,
determine the reaction of the stage and the stage loading when the air flow is reduced by
10% at constant blade speed. Sketch the velocity triangles for the two conditions.
Comment upon the likely behaviour of the flow when further reductions in air mass flow
are made.
6. The proposed design of a compressor rotor blade row is for 59 blades with a circular
arc camber line. At the mean radius of 0.254 m the blades are specified with a camber
of 30 deg, a stagger of 40 deg and a chord length of 30 mm. Determine, using Howell’s
correlation method, the nominal outlet angle, the nominal deviation and the nominal inlet
angle. The tangent difference approximation, proposed by Howell for nominal conditions
Ł
(0 6 ˛ 6 40 ° ), can be used:
2
Ł
tan ˛ Ł tan ˛ D 1.55/.1 C 1.5 s/l/.
1 2
Determine the nominal lift coefficient given that the blade drag coefficient C D D 0.017.
Using the data for relative deflection given in Figure 3.17, determine the flow outlet
angle and lift coefficient when the incidence i D 1.8 deg. Assume that the drag coefficient is
unchanged from the previous value.
7. The preliminary design of an axial flow compressor is to be based upon a simplified
consideration of the mean diameter conditions. Suppose that the stage characteristics of a
repeating stage of such a design are as follows:
Stagnation temperature rise 25 ° C
Reaction ratio 0.6
Flow coefficient 0.5
Blade speed 275 m/s

The gas compressed is air with a specific heat at constant pressure of 1.005 kJ/(kg ° C).
Assuming constant axial velocity across the stage and equal absolute velocities at inlet and
outlet, determine the relative flow angles for the rotor.
Physical limitations for this compressor dictate that the space/chord ratio is unity at the
mean diameter. Using Howell’s correlation method, determine a suitable camber at the mid-
height of the rotor blades given that the incidence angle is zero. Use the tangent difference
approximation:
Ł
tan ˇ Ł tan ˇ D 1.55/.1 C 1.5 s/l/
1 2