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V2δδPr二 ρ r e (7-24)
.00 Gas Turbine Engineering Handbook
Using the simple radial equilibrium equation， the computation of the axial velocity distribution can be calculated. The accuracy of the techniques depends on how linear V2jr is with the radius.
e
This assumption is valid for low-performance compressors， but it does nothold well for the high-aspectratio， highly loaded stages where the effects of streamline curvature become significant. The radial acceleration of the meridional velocity and the pressure gradient in the radial direction must be considered. The radial gradient of static pressure for the highly curved streamline can be written
δP 二 ρ Ve 2 . ρV的 2cos . (7-25)δrr r句
where . is the angle of the streamline curvature with respect to the axial direction and r句 is the radius of curvature.
To determine the radius of curvature and the streamline slope accurately， the configuration of the streamline through the blade row must be known.The streamline configuration is a function of the annular passagearea， the camber and thicknessdistribution of theblade， and the flow angles at the inlet and outlet of the blade. Since there is no simple way to calculatethe effects of all the parameters， the techniques used to evaluate these radialaccelerations are empirical. By using iterativesolutions， a relationship can be obtained. The effect of high radial acceleration with high-aspect ratios can be negated by tapering the tip of the compressor inward so that the hub curvature is reduced.
Diffusion Factor
The diffusion factor first defined by Lieblien is a blade-loading criterion
D二 1 -W2 + Ve1 -Ve2 (7-26)
W12σW1
The diffusion factor should be less than .4 for the rotor tip and less than .6 for the rotor hub and the stator. The distribution of the diffusion factorthroughout the compressor is not properly defined.However， the efficiency is less in the later stages due to distortions of the radial velocity distributions in the blade rows. Experimental results indicate that even though efficiencyis less in the later stages， as long as the diffusion loading limits are notexceeded， the stage efficiencies remain relatively high.
The Incidence Rule
For low-speed airfoil design， the region of low-loss operation is generallyflat， and it is difficult to establish the precise value of the incidence angle that corresponds to the minimum loss as seen in Figure 7-22. Since the curvesare generally symmetrical， the minimum loss location was established at the middle of the low-loss range. The range is defined as the change in incidence angle corresponding to a rise in the loss coefficient equal to the minimum value.
The following method for calculation of the incidence angle is applicable to cambered airfoils. Work by NASA on the various cascades is the basis forthe technique. The incidence angle is a function of the blade camber， which is an indirect function of the air-turning angle
i二 ki0 +的. + 8的 (7-27)
where i0is the incidence angle for zero camber， and的 is the slope of the incidence angle variation with the air-turning angle (.). The zero-camber incidence angle is defined as a function of inlet air angle and solidity as seen in Figure 7-23 and the value of的 is given as a function of the inlet air angle and the solidity as seen in Figure 7-24.
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Figure 7-2.. Incidence angle for zero-camber airfoil.
Figure 7-24. .lope of incidence angle variation with air angle.
The incidence angle i0 is for a 10 blade thickness. For blades of other than 10.thickness， a correction factor Kis used， which is obtained from Figure 7-25.
The incidence angle now must be corrected for the Mach number effect (8的). The effect of the Mach number on incidence angle is shown in Figure 7-26. The incidence angle is not affected until a Mach number of .7 is reached.
The incidence angle is now fully defined. Thus， when the inlet and outletair angles and the inlet Mach number are known， the inlet blade angle can be computed in this manner.
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