Figure 6-1.. Velocity triangles.
Supposingconstant rotational speeds， noslip， and anaxialinlet， the velocity triangles are as shown in Figure 6-10. For the radialvane， the absolute tangential fluid velocity at the impeller exit is constant.even if the flow rate is increased or decreased.
Therefore，
H . U2V.. 82 . U2V82 . U2V.(6-3)
82
flow flow
decrease increase

For backward-curved vanes， the absolute tangential fluid velocity at the impeller exit increases with the reduction of flow rates and decreases with the increase in flow rate as shown in the following equation:
H . U2V.. U2V.(6-4)
82 > U2V82 <82
flow flow
decrease increase

For forward-curvedvanes， the absolute tangential fluid velocity at the impeller exit decreases with the reduction of flow rates and increases with the decrease in flow rate as shown in the following equation:
H . U2V.. 8< U2V82 > U2V.(6-5)
8
flow flow
decrease increase

1nlet Guide Vanes
The inlet guide vanes give circumferential velocity to the fluid at the inducer inlet. This function is called prewhirl. Figure 6-11 shows inducer inlet velocity diagrams with and without IGVs.
IGVs are installed directly in front of the induceror， where an axial entryis not possible， located radially in an intake duct.
A positive vane angle produces prewhirl in the direction of the impellerrotation， and a negative vane angle produces prewhirl in the opposite direc-tion. The disadvantage of positive prewhirl is that a positive inlet whirl velocity reduces the energy transfer. Since V81 is positive according to the Euler equation defined by
H二 1 [U1V81 U2V82 (6-6)Ac

For nonprewhirl (without IGVs axialentry)， V81 is equal to zero. Then the Euler work is H二 U2V82.
Withpositive prewhirl， the first term of the Euler equation remains H二 U1V81 U2V82Therefore， Euler work is reduced by the use of positiveprewhirl. On the other hand， negative prewhirl increases the energy transfer by the amount U1V81. This results in a larger pressure head being produced in the case of the negative prewhirl for the same impeller diameter and speed.
The positive prewhirl decreases the relative Mach number at the inducerinlet. However， negative prewhirl increases it. A relative Mach number is defined by
Mrel二 W1 (6-7)a1
where:
Mrel二 relative Mach number
W1二 relative velocity at an inducer inlet
a1二 sonic velocity at inducer inlet conditions

The purpose of installing the IGVs is to decrease the relative Mach number at the inducer-tip (impeller eye) inlet because the highest relative velocity at the inducer inlet is at the tip section. When the relative velocity is

Figure 6-12.Estimated effect of inlet prewhirl.(Rodgers， C. andShapiro，L.，""Design Considerations for High-Pressure-Ratio CentrifugalCompressors，"" ASME PaperNo.: 73-GT-31.)
close to the sonic velocity or greater thanit， a shock wave takes place in the inducer section. A shock wave produces shock loss and chokes the inducer. Figure 6-12 shows the effect of inlet prewhirl on compressor efficiency.
There are three kinds of prewhirl:
1.  Free-vortex prewhirl. This type is represented by r1V81二 constant with respect to the inducer inlet radius. This prewhirl distribution is shown in Figure 6-13. V81 is at a minimum at the inducer inletshroud radius. Therefore， it is not effective in decreasing the relative Mach number in this manner.

2.  Forced-vortex prewhirl. This type is shown as V81/r1二 constant. This prewhirl distribution is also shown in Figure 6-14. V81 is at a maximum atthe inducer inlet shroud radius， contributing to a decrease in the inlet relative Mach number.

3.  Control-vortex prewhirl. This type is represented by V81二 AR1 + B/r1， where A and B are constants. This equation shows the first type with A二0， B二 0， and the second type with B二0， A二 0.
　
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