Page 187 - Fluid Mechanics and Thermodynamics of Turbomachinery

168 Fluid Mechanics, Thermodynamics of Turbomachinery
for nominal conditions and the data of Figure 3.17 for finding the design deflection. (Hint.
Use several trial values of to complete the solution.)
8. Air enters an axial flow compressor with a stagnation pressure and temperature of
100 kPa and 293 K, leaving at a stagnation pressure of 600 kPa. The hub and tip diameters
at entry to the first stage are 0.3 m and 0.5 m. The flow Mach number after the inlet guide
vanes is 0.7 at the mean diameter. At this diameter, which can be assumed constant for all
the compressor stages, the reaction is 50%, the axial velocity to mean blade speed ratio is
0.6 and the absolute flow angle is 30 deg at the exit from all stators. The type of blading used
for this compressor is designated “free-vortex” the axial velocity is constant for each stage.
Assuming isentropic flow through the inlet guide vanes and a small stage efficiency of
0.88, determine:
(1) the air velocity at exit from the IGVs at the mean radius;
(2) the air mass flow and rotational speed of the compressor;
(3) the specific work done in each stage;
(4) the overall efficiency of the compressor;
(5) the number of compressor stages required and the power needed to drive the compressor;
(6) consider the implications of rounding the number of stages to an integer value if the
pressure ratio must be maintained at 6 for the same values of blade speed and flow
coefficient.
NB. In the following problems on axial-flow fans the medium is air for which the density is
3
taken to be 1.2 kg/m .
9. (a) The volume flow rate through an axial-flow fan fitted with inlet guide vanes is
3
2.5 m /s and the rotational speed of the rotor is 2604 rev/min. The rotor blade tip radius is
23 cm and the root radius is 10 cm. Given that the stage static pressure increase is 325 Pa
and the blade element efficiency is 0.80, determine the angle of the flow leaving the guide
vanes at the tip, mean and root radii.
(b) A diffuser is fitted at exit to the fan with an area ratio of 2.5 and an effectiveness of
0.82. Determine the overall increase in static pressure and the air velocity at diffuser exit.
10. The rotational speed of a four-bladed axial-flow fan is 2900 rev/min. At the mean
radius of 16.5 cm the rotor blades operate at C L D 0.8 with C D D 0.045. The inlet guide
vanes produce a flow angle of 20 ° to the axial direction and the axial velocity through the
stage is constant at 20 m/s.
For the mean radius, determine:
(1) the rotor relative flow angles;
(2) the stage efficiency;
(3) the rotor static pressure increase;
(4) the size of the blade chord needed for this duty.
11. A diffuser is fitted to the axial fan in the previous problem which has an efficiency
of 70% and an area ratio of 2.4. Assuming that the flow at entry to the diffuser is uniform
and axial in direction, and the losses in the entry section and the guide vanes are negligible,
determine:
(1) the static pressure rise and the pressure recovery factor of the diffuser;
(2) the loss in total pressure in the diffuser;
(3) the overall efficiency of the fan and diffuser.