Figure 6-1.. Prewhirl distribution patterns.

Euler work distributions at an impellerexit， with respect to the impellerwidth， are shown in Figure 6-14. From Figure6-14， the prewhirl distribution should be made not only from the relative Mach number at the inducer inletshroud radius， but also from Euler work distribution at the impeller exit.Uniform impeller exit flow conditions， considering the impellerlosses， are important factors in obtaining good compressor performance.
1mpeller
An impeller in a centrifugal compressor imparts energy to a fluid. The impeller consists of two basic components: (1) an inducer like an axial-flowrotor， and (2) the radial blades where energy is imparted by centrifugal force. Flow enters the impeller in the axial direction and leaves in the radial direc-tion. The velocity variations from hub to shroud resulting from these changes in flow directions complicate the design procedure for centrifugal compres-sors. C.H. Wu has presented the three-dimensional theory in an impeller， but it is difficult to solve for the flow in an impeller using the previous theory without certain simplified conditions. Others have dealt with it as a quasi-three-dimensional solution. It is composed oftwo solutions， one in themeridional surface (hub-to-shroud)， and the other in the stream surface of revolution (blade-to-blade). These surfaces are illustrated in Figure 6-15.
By the application of the previous method using a numerical solution tothe complex flow equations， it is possible to achieve impeller efficiencies of more than 90%. The actual flow phenomenon in an impeller is more com-plicated than the one calculated. One example of this complicated flow isshown in Figure 6-16. The stream lines observed in Figure 6-16 do notcross， but are actually in different planes observed near the shroud. Figure 6-17 shows the flow in the meridional plane with separation regions at the inducer section and at the exit.
Experimental studies of the flow within impeller passages have shown that the distribution of velocities on the blade surfaces are different from the distributions predicted theoretically. It is likely that the discrepancies between theoretical and experimental results are due to secondary flows from pressure losses and boundary-layer separation in the blade passages.High-performance impellers should be designed， when possible， with the aid of theoretical methods for determining the velocity distributions on the blade surfaces.

Figure 6-15. Two-dimensional surface for a flow analysis.

Figure 6-16. Flow map of impeller plane.
Examples of the theoretical velocity distributions in the impeller blades of a centrifugal compressor are shown in Figure 6-18. The blades should be designed to eliminate large decelerations or accelerations of flow in the impeller that lead to high losses and separation of the flow. Potential flow solutions predict the flow well in regions away from the blades where boundary-layer effects are negligible. In a centrifugal impeller the viscous shearing forces create a boundary layer with reduced kinetic energy. If thekinetic energy is reduced below a certain limit， the flow in this layer becomesstagnant， then it reverses.

1nducer
The function of an inducer is to increase the fluid's angular momentum without increasing its radius of rotation. In an inducer section the blades bend toward the direction of rotation as shown in Figure 6-19. The inducer is an axial rotor and changes the flow direction from the inlet flow angle tothe axial direction. It has the largest relative velocity in the impellerand， ifnot properly designed， can lead to choking conditions at its throat as shown in Figure 6-19.
There are three forms of inducer camber lines in the axial direction. Theseare circulararc， parabolicarc， and elliptical arc. Circular arc camber lines areused in compressors with low pressureratios， while the elliptical arc produces good performance at high pressure ratios where the flow has transonic mach numbers.
　
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