Leakage. Fluid flow from one side of a blade to the other side is referred to as leakage. Leakage reduces the energy transfer from impeller to fluid and decreases the exit velocity angle.
Number of vanes.The greater the number of vanes， the lower the vaneloading， and the closer the fluid follows the vanes. With higher vane load-ings， the flow tends to group up on the pressure surfaces and introduces a velocity gradient at the exit.
Vane thickness. Because of manufacturing problems and physicalnecessity， impeller vanes are thick. When fluid exits the impeller， the vanesno longer contain theflow， and the velocity is immediately slowed. Becauseit is the meridional velocity that decreases， both the relative and absolutevelocities decrease， changing the exit angle of the fluid.
A backward-curved impeller blade combines all these effects. The exit velocity triangle for this impeller with the different slip phenomenon changes is shown in Figure 6-25. This triangle shows that actual operating conditions are far removed from the projected design condition.
Several empirical equations have been derived for the slip factor (see Figure 6-26). These empirical equations are limited. Two of the more common slip factors are presented here.
Stodola Slip Factor
The second Helmholtz law states that the vorticity of a frictionless fluiddoes not change with time.Hence， if the flow at the inlet to an impeller isirrotational， the absolute flow must remain irrotational throughout the impeller. As the impeller has an angular velocity ω， the fluid must have an angular velocity.. relative to the impeller. This fluid motion is called therelative eddy. If there were no flow through the impeller， the fluid in the
Figure 6-25. Effect on exit velocity triangles by various parameters.
Figure 6-26. Various slip factors as a function of the flow coefficient.
impeller channels would rotate with an angular velocity equal and opposite to the impeller's angular velocity.
To approximate theflow， Stodola's theory assumes that the slip is due to the relative eddy. The relative eddy is considered as a rotation of a cylinder of fluid at the end of the blade passage at an angular velocity of.ωabout its own axis. The Stodola slip factor is given by
μ二 1王 1 sin .2 (6-10)
z V凡2 cot .2
U2
where:
.2二 the blade angle
z二 the number of blades
V凡2二 the meridional velocity
U2二 blade tip speed.
Calculations using this equation have been found to be lower than experi-mental values.
Stanitz Slip Factor
Stanitz calculated blade-to-blade solutions for eight impellers andconcluded that for the range of conditions covered by thesolutions， U is a function of the number of blades (z)， and the blade exit angle ( .2)is approximately the same whether the flow is compressible or incompressible
1 μ二 10.63王 1 W凡2 (6-11)
z cot .2
U2
Stanitz's solutions were for王/4 <.2<王/ 2. This equation compares well with experimental results for radial or near-radial blades.
Diffusers
Diffusing passages have always played a vital role in obtaining good performance from turbomachines. Their role is to recover the maximum possible kinetic energy leaving the impeller with a minimum loss in total pressure. The efficiency of centrifugal compressor components has been steadily improved by advancing their performance.However， significant further improvement in efficiency will be gained only by improving thepressure recovery characteristics of the diffusing elements of these machines， since these elements have the lowest efficiency.
The performance characteristics of a diffuser are complicated functions ofdiffusergeometry， inlet flow conditions， and exit flow conditions. Figure 6-27 shows typical diffusers classified by their geometry. The selection of anoptimum channel diffuser for a particular task is difficult， since it must be chosen from an almost infinite number of cross-sectional shapes and wall configurations. In radial and mixed-flow compressors the requirement of high performance and compactness leads to the use of vaned diffusers as shown in Figure 6-28. Figure 6-28 also shows the flow regime of a vane-island diffuser.
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