Page 171 - Fluid Mechanics and Thermodynamics of Turbomachinery

152 Fluid Mechanics, Thermodynamics of Turbomachinery
the annulus walls. An inspection of this figure shows also that the excess total
temperature near the end walls increases in magnitude and extent as the flow
passes through the compressor. Work on methods of predicting annulus wall
boundary layers in turbomachines and their effects on performance are being
actively pursued in many countries. Although rather beyond the scope of this
textbook, it may be worth mentioning two papers for students wishing to advance
their studies further. Mellor and Balsa (1972) offer a mathematical flow model
based on the pitchwise-averaged turbulent equations of motion for predicting axial
flow compressor performance whilst Daneshyar et al. (1972) review and compare
different existing methods for predicting the growth of annulus wall boundary layers
in turbomachines.
EXAMPLE 5.2. The last stage of an axial flow compressor has a reaction of 50%
at the design operating point. The cascade characteristics, which correspond to each
row at the mean radius of the stage, are shown in Figure 3.12. These apply to a
cascade of circular arc camber line blades at a space chord ratio 0.9, a blade inlet
angle of 44.5 deg and a blade outlet angle of 0.5 deg. The blade height chord
ratio is 2.0 and the work done factor can be taken as 0.86 when the mean radius
Ł
Ł
relative incidence .i i //ε is 0.4 (the operating point).
For this operating condition, determine
Ł
Ł
(i) the nominal incidence i and nominal deflection ε ;
(ii) the inlet and outlet flow angles for the rotor;
(iii) the flow coefficient and stage loading factor;
(iv) the rotor lift coefficient;
(v) the overall drag coefficient of each row;
(vi) the stage efficiency.
3
The density at entrance to the stage is 3.5 kg/m and the mean radius blade
speed is 242 m/s. Assuming the density across the stage is constant and ignoring
compressibility effects, estimate the stage pressure rise.
In the solution given below the relative flow onto the rotor is considered. The
0
notation used for flow angles is the same as for Figure 5.2. For blade angles, ˇ is
0
therefore used instead of ˛ for the sake of consistency.
Solution. (i) The nominal deviation is found using eqns. (3.39) and (3.40). With
0
the camber D ˇ 0 ˇ D 44.5 ° . 0.5 ° / D 45 ° and the space/chord ratio, s/l D
1 2
0.9, then
Ł
Ł
υ D [0.23 C ˇ /500] .s/l/ 1/2
2
0
Ł
Ł
But ˇ D υ C ˇ D υ Ł 0.5
2 2
Ł
Ł
0
∴ υ D [0.23 C .υ C ˇ //500] ð 45 ð .0.9/ 1/2
2
Ł
D [0.229 C υ /500] ð 42.69 D 9.776 C 0.0854 υ Ł
Ł
∴ υ D 10.69 °
Ł
Ł
0
∴ ˇ D υ C ˇ D 10.69 0.5
2 2
' 10.2 °