# 5 Centrifugal Compressors

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Centrifugal CompressorsClasses and comparisons between compressors

Centrifugal CompressorsPrinciple of Operation

Centrifugal compressors consist of stationary casing containing

Rotating impeller (imparts a high velocity of air),

Fixed diverging passage (The air is decelerated with rise in static pressure).

Impeller may be single or double-sided

Centrifugal CompressorsAir is sucked into the impeller eye and whirled at high speed by the vanes of the impeller disc. The static pressure increases from eye to tip.Remainder of static pressure rise occurs in diffusers.Normally half of pressure rise occurs in the impeller and 50% in diffuser.Some stagnation pressure loss occurs.

Centrifugal Compressors

Centrifugal CompressorsWork done and Pressure Rise:

Absolute velocity of air at impeller tip.tangential or whirl componentradial component.

is the angle given by the direction of the relative velocity at inlet V1. Also this is the angle of leading edge of the vane with tangential direction.

Slip phenomenon: air trapped between the impeller vanes does not move with the impeller, thus air acquire whirl (Cw) velocity at the tip which is less than u.

:

Centrifugal Compressors

Centrifugal CompressorsVelocity diagrams

Centrifugal CompressorsConsidering unit mass of air: momentum equation

Centrifugal CompressorsWith state 1 as inlet to rotor 2 as exit from rotor 3 as exit of diffuser No energy addition in diffuserThus =

Centrifugal CompressorsDefining c as overall isentropic efficiency, then overall stagnation pressure ratio is given by :

Centrifugal CompressorsExample 4.1The following data are suggested as a basis for the design of a single-sided centrifugal compressor:Power input factor = =1.04Slip factor = 0.9Rotational speed, N= 290 rev/sOverall diameter of impeller, D=0.5mEye tip diameter=2re=De=0.3mEye root diameter, D1=2r1=0.15mAir mass flow, m=9 kg/sInlet stagnation temperature To1= 295Inlet stagnation pressure Po1 = 1.1 barIsentropic efficiency, c=0.78

Centrifugal CompressorsRequirements are (a) to determine the pressure ratio of the compressor and the power required to drive it assuming that the velocity of the air at inlet is axial. (b) to calculate the inlet angle of the impeller vanes at the root and tip of the radii of the eyes, assuming that the axial inlet velocity is constant across the eye annulus; and(c) to estimate the axial depth of the impeller channels at the periphery of the impeller.

Centrifugal Compressors(a) impeller tip speed Temperature equivalent of the work done on unit mass flow of air, is

Centrifugal Compressors

Power required=(b) to find the inlet angle it is necessary to determine the inlet velocity which in this case is axial; . Since the density 1 depends upon C1and both are unknown, a trial and error process is required.

Centrifugal CompressorsFlow trianglesu2=455.5 m/s

Assume axial flowtwo unknown (,c) in one equation but another relation is given by

Centrifugal CompressorsNote this is normal to design for an axial velocity of about 150 m/s, this providing a suitable compromise between high flow per unit frontal area and frictional losses in the intake. Annulus area of impeller eye, Based on stagnation conditions:

Centrifugal Compressors, the equivalent dynamic temperature is

Centrifugal Compressorsequivalent dynamics temperature is

Centrifugal Compressors

Centrifugal CompressorsThis is a good agreement and a further trial using Ca1=143 m/s is unnecessary because a small change in C has little effect upon . For this reason, it is more accurate to use the final value 143 m/s, rather than the mean of 145 m/s ( the trial value) and 143 m/s. The vane angles can now be calculated as follows: and at eye root radius =136.5 m/s,

Centrifugal Compressors at root=tan-1(143/136.5)=46.33, at tip =tan-1143/273=27.65(c) the shape of the impeller channel between eye and tip is very much a matter of trial and error.

The aim is to obtain as uniform a change of flow velocity up the channel as possible, avoiding local decelerations up the trailing face of the vane.

To estimate the density at the impeller tip, the static pressure and temperature are found by calculating the absolute velocity at this and using it in conjunction with the stagnation pressure which is calculated from the assumed loss up to this point.

Centrifugal Compressors

Centrifugal CompressorsTo calculate density at exit

Centrifugal Compressorsthus get 2.

Centrifugal Compressors

Centrifugal CompressorsThe required area of cross-section of flow in the radial direction at the impeller tip is

Computational Design of a Centrifugal Compressor PROGRAM MAIN COMMON CP,R,GAMRATCOMMON VECT(5000,500)CCC OPEN(30,FILE='D:\Dif\GRIDG.RES') OPEN(5,FILE='C:\CALCULATIONS\Data_PyT10_6.1mps_D50mmFdn.txt') OPEN(6,FILE='C:\CALCULATIONS\OUT.txt') OPEN(7,FILE='C:\CALCULATIONS\output data for drawings.txt') OPEN(8,FILE='C:\CALCULATIONS\OUT2.txt') C OPEN(30,FILE='C:\Dif\GRIDG.RES') C OPEN(6,FILE='C:\Dif\Conv 1\GRIDG.OUT') C OPEN(5,FILE='C:\dif\Conv 1\GRIDG.DAT') C OPEN(30,FILE='C:\Dif\Conv 1\GRIDG.RES',FORM='UNFORMATTED') C OPEN(6,FILE='C:\Dif\GRIDG.OUT') C OPEN(5,FILE='C:\dif\GRIDG.DAT') C OPEN(6,FILE='D:\Dif\GRIDG.OUT') C OPEN(5,FILE='D:\dif\GRIDG.DAT')

Computational Design of a Centrifugal CompressorCPI=22./7.EPSI=1.05SIGMA=0.9RPM=305.D0=0.6DIT=0.4DIR=0.15FLOW=14TO1=300PO1=100.EFFC=0.8CP=1005EFFIMP=0.89 GAMMA=1.4R=0.287GAMRAT=GAMMA/(GAMMA-1.)U=PI*D0*RPMTO13=EPSI*SIGMA*U*U/CPPO13=(1.+EFFC*TO13/TO1)**GAMRATTO3=TO1+TO13TO2=TO3PO3=PO1*PO13POWER=FLOW*CP*TO13/1000.WRITE(6,11)POWER,TO13,U,PO13 11 FORMAT(2X,'POWER=',E13.4,/2X,'TO13=',E13.5/2X,'U=',E13.5/3X, 1'Press ratio=',E13.4//)AI=PI*(DIT**2-DIR**2)/4.

Computational Design of a Centrifugal CompressorCC1=100. CALL SITER(C1,TO1,PO1,AI,FLOW)CWRITE(6,12)C1,EPS,P1,T1,AIC 12 FORMAT(2X,E13.3/4E13.4) UE=PI*DIT*RPMUR=PI*DIR*RPMALFAR=ATAN(C1/UR)*180./PIALFAT=ATAN(C1/UE)*180./PIWRITE(6,24) 24 FORMAT(8X,'ALFAT, ALFAR'/) WRITE(6,13)ALFAT,ALFAR 13 FORMAT(2X,2E13.3)CC Axial DepthCR=C1CW=SIGMA*UCSQ=CR*CR+CW*CWPO2=PO1*(1.+EFFIMP*TO13/TO1)**GAMRATT2=TO2-CSQ/(2.*CP)P2=PO2*(T2/TO2)**GAMRATRHO2=P2/(R*T2)A2=FLOW/(RHO2*CR)AXDEPTH=A2/(PI*D0)WRITE(6,17)AXDEPTH 17 FORMAT(//10X,'Axial Depth= ', 10X, E13.5)

Computational Design of a Centrifugal CompressorC

C CALL PERFORMANCE(POWER,TO1,PO1,EFFC,GAMRAT,CP)STOP ENDCSUBROUTINE SITER(C,TO,PO,A1,FLOW) COMMON CP,R,GAMRATC WRITE(6,102)C,EPS,PO,TO,A1RHO1=PO/(R*TO) 10 C=FLOW/(RHO1*A1) T=TO-C*C/(2.*CP)P=PO*(T/TO)**GAMRATC 23 FORMAT(7X,'C',18x,'EPS',8X,'P',8X,'T',15X,'A1'/)C WRITE(6,102)C,EPS,P,T,A1 RHONEW=P/(R*T)EPS=ABS((RHONEW-RHO1))/RHONEWIF(EPS.LT.0.001)GO TO 20RHO1=RHONEWGO TO 10 20 CONTINUE WRITE(6,23)WRITE(6,102)C,EPS,P,T,A1 102 FORMAT(2X,5E13.4/)ReturnEnd

Computational Design of a Centrifugal CompressorSUBROUTINE PERFORMANCE(POWER,TO1,PO1,EFFC,GAMRAT,CP)COMMON VECT(5000,500),WMAS(5000,500),BETA(5000,500),PIFLOW=10.DFLOW=FLOW/10. WRITE(6,30)POWER,TO1,PO1,EFFC,GAMRAT,CP 30FORMAT(6E13.3)DO 10 I=1,9TO3=TO1+POWER*1000./FLOW/CPPO3=PO1*(1.+EFFC*(TO3-TO1)/TO1)**GAMRATFLOW=FLOW-DFLOWCWRITE(6,20)TO3,PO3WRITE(6,20)FLOW,PO3/PO1 20FORMAT(2E13.3) 10 CONTINUEC RETURN END

Centrifugal CompressorsThe Diffuser:In the case of gas turbine, the air should exit the diffuser and enters the combustion chamber at minimum velocity.

Thus, design of diffuser requires that only a small part of strengthening temperature is K.E. normally u=90m/s at exit of the compressor. rapid divergence is not recommended optimum angle is 7.0.

Neglecting losses, thus, angular momentum r C=constantCr: radial velocity will also decrease.

Centrifugal CompressorsExample 4.2 Consider the design of a diffuser for the compressor dealt with in the previous example. The following additional data will be assumed: Radial width of vaneless spacewd = 5 cm Approximate mean radius of diffuser throat, rm =0.033mDepth of diffuser passages dd1.76 Number of diffuser vanesnv12 Required are (a) the inlet angle of the diffuser vanes and (b) the throat width of the diffuser passages which are assumed to be of constant depthConsider conditions at the radius of the diffuser vane leading edges, at r2=0.25+0.05=0.3m. Since in the vaneless space r Cw =constant for constant angular momentum,

Centrifugal CompressorsThe radial component of velocity can be found by trial and error. The iteration may be started by assuming that the temperature equivalent of the resultant velocity is that corresponding to the whirl velocity, but only the final trial is given here.

Centrifugal CompressorsIgnoring any additional loss between the impeller tip and diffuser vane leading edges at 0.3m radius, the stagnation pressure will be that calculated for the impeller tip, namely it will be that given by

Centrifugal CompressorsArea of cross-section of flow in radial

Check on Cr2:

Cr2=Taking Cr as 97.9 m/s, the angle of the diffuser vane leading edge for zero incidence should be