Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

160 Fluid Mechanics, Thermodynamics of Turbomachinery
their effects on performance are being actively pursued in many countries. Horlock
(2000) has reviewed several approaches to end-wall blockage in axial compressors, i.e.
Khalid et al. (1999), Smith (1970), Horlock and Perkins (1974). One conclusion drawn
was that Smith’s original data showed that axial blockage was strongly dependent on
tip clearance and stage pressure rise. Although the other approaches can give the probable
increase in blockage across a clearance row they are unable to predict the absolute
blockage levels. Horlock maintained that this information can be found only from data
such as Smith’s, although he conceded that it was possible that full computational fluid
dynamics calculations might provide reasonable answers.
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 -0.5deg. The blade height–chord ratio is 2.0 and the
work done factor can be taken as 0.86 when the mean radius relative incidence (i -
i*)/e* is 0.4 (the operating point).
For this operating condition, determine
(i) the nominal incidence i* and nominal deflection e*;
(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.
The density at entrance to the stage is 3.5kg/m 3 and the mean radius blade speed is
242m/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 notation
used for flow angles is the same as for Figure 5.2. For blade angles, b¢ is therefore
used instead of a¢ for the sake of consistency.
Solution. (i) The nominal deviation is found using eqns. (3.39) and (3.40). With the
camber q = b1¢ -b 2¢=44.5° - (-0.5°) = 45° and the space chord ratio, s/l = 0.9, then
But
The nominal deflection e* = 0.8 max and, from Figure 3.12, e max = 37.5°. Thus, e* = 30°
and the nominal incidence is