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CentrifugalCompressor Performance
Calculating the performance of a centrifugal compressor in both design and off-design conditions requires a knowledge of various losses encountered in a centrifugal compressor.
The accurate calculation and proper evaluation of losses within a centri-fugal compressor is as important as the calculation of the blade-loading para-meters. If the proper parameters are not controlled， efficiency decreases. The evaluation of various losses is a combination of experimental results and theory.The losses are divided into two groups: (1) losses encountered in the rotor， and
(2) losses encountered in the stator.
A loss is usually expressed as a loss of heat or enthalpy. A convenient way to express them is in a nondimensional manner with reference to the exit blade speed. The theoretical total head available (.tot) is equal to the head available from the energy equation
.th二 U12 (U2V82 U1V81)(6-16)2
plus the head， which is lost because of disc friction ( ..df) and resulting from any recirculation (..rc) of the air back into the rotor from the diffuser
.tot二 .th + ..df + ..rc (6-17)
The adiabatic head that is actually available at the rotor discharge is equal to the theoretical head minus the heat from the shock in the rotor (..sh)， the inducer loss (..in)， the blade loadings ( ..bl)， the clearance between the rotor and the shroud (..c)， and the viscous losses encountered in the flow passage (..sf)
.ia二 .th ..in ..sh ..bl ..c ..sf (6-18)
Therefore， the adiabatic efficiency in the impeller is
.imp二 .ia (6-19).tot
The calculation of the overall stage efficiency must also include lossesencountered in the diffuser. Thus， the overall actual adiabatic head attained will be the actual adiabatic head of the impeller minus the head losses encountered in the diffuser from wake caused by the impeller blade (..w)， the loss of part of the kinetic head at the exit of the diffuser (..ed)， and the loss of head from frictional forces (..osf) encountered in the vaned or vaneless diffuser space
.oa二 .ia ..w ..ed ..osf (6-20)
The overall adiabatic efficiency in an impeller is given by the following relationship:
.ov二 .oa (6-21).tot
The individual losses can now be computed. These losses are broken upinto two categories: (1) losses in the rotor， and (2) losses in the diffuser.
.otor Losses
Rotor losses are divided into the following categories:
Shock in rotor losses. This loss is due to shock occurring at the rotor inlet. The inlet of the rotor blades should be wedgelike to sustain a weakobliqueshock， and then gradually expanded to the blade thickness to avoidanother shock. If the blades areblunt， a bow shock will result， causing the flow to detach from the blade wall and the loss to be higher.
1ncidence loss.At off-design conditions， flow enters the inducer at anincidence angle that is either positive or negative， as shown in Figure 6-31. A positive incidence angle causes a reduction in flow. Fluid approaching a blade at an incidence angle suffers an instantaneous change of velocity at the blade inlet to comply with the blade inlet angle. Separation of the blade can create a loss associated with this phenomenon.
Disc friction loss. This loss results from frictional torque on the back surface of the rotor as seen in Figure 6-32. This loss is the same for a given
Figure 6-.1. Inlet velocity triangles at nonzero incidents.
size disc whether it is used for a radial-inflow compressor or a radial-inflowturbine. Losses in the seals， bearings， and gear box are also lumped in withthisloss， and the entire loss can be called an external loss. Unless the gap isof the magnitude of the boundarylayer， the effect of the gap size is negli-gible. The disc friction in a housing is less than that on a free disc due to theexistence of a ..core，'' which rotates at half the angular velocity.
Diffusion-blading loss. This loss develops because of negative velocity gradients in the boundary layer. Deceleration of the flow increases the boundary layer and gives rise to separation of the flow. The adverse pressure gradient that a compressor normally works against increases the chances of separation and causes significant loss.
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