Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

Two-dimensional Cascades 73
FIG. 3.14. Variation in profile loss with incidence for typical turbine blades (adapted
from Ainley 1948).
surface boundary layers, viz. surface velocity distribution, blade Reynolds number, inlet
Mach number, free-stream turbulence and unsteadiness, and surface roughness. From
the analysis of experimental data several correlation methods have been evolved which
enable the first-order behaviour of the blade losses and limiting fluid deflection to be
predicted with sufficient accuracy for engineering purposes.
LIEBLEIN. The correlation of Lieblein (1959), NASA (1965) is based on the experimental
observation that a large amount of velocity diffusion on blade surfaces tends to
produce thick boundary layers and eventual flow separation. Lieblein states the general
hypothesis that in the region of minimum loss, the wake thickness, and consequently
the magnitude of the loss in total pressure, is proportional to the diffusion in velocity
on the suction surface of the blade in that region. The hypothesis is based on the consideration
that the boundary layer on the suction surface of conventional compressor
blades contributes the largest share of the blade wake. Therefore, the suction-surface
velocity distribution becomes the main factor in determining the total pressure loss.
Figure 3.15 shows a typical velocity distribution derived from surface pressure measurements
on a compressor cascade blade in the region of minimum loss. The diffusion
in velocity may be expressed as the ratio of maximum suction-surface velocity to
outlet velocity, c max,s/c2. Lieblein found a correlation between the diffusion ratio cmax,s/c2
and the wake momentum thickness to chord ratio, q2/l at the reference incidence (midpoint
of working range) for American NACA 65-(A10) and British C.4 circular-arc
blades. The wake momentum thickness, with the parameters of the flow model in Figure
3.16 is defined as