Centrifugal Compressors Classes and comparisons between compressors AxialCentrifugalFunction Large...

Centrifugal Compressors• Classes and comparisons between compressors

FunctionCentrifugalAxial

Engine typeSmall engineLarge engine

Mass flow rate< 15 kg/sVery large (> 100 kg/s)

EfficiencyLow 86-87 %High 94 %

# of stagessmalllarge

Pressure ratio per stageHigh (5-7)Low (<1.5)

Pressure lossHigh for more than one stage

Low, thus allow using many stages

Fixing and manufacturing

easyNot easy

CostCheap, wider operating range

Very expensive

Centrifugal Compressors

Principle of Operation

Centrifugal compressors consist of stationary casing containing

a. Rotating impeller (imparts a high velocity of air),

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

c. Impeller may be single or double-sided


• Air 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• Work done and Pressure Rise:

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

• :

2C2wC

2rC

) ( , 2 speedtipimpellerUCconditionsidealAt r


• Velocity diagrams


• Considering unit mass of air:

• momentum equation

blades) ( vanesofnumber n

stanitz);by :sexperiment ( ;n

0.631

1 ;U

Cfactor Slip w2

2

22

1122

U Work

thus,,factor slip Utilizing

vanes)guide no of case ideal(for

0.0-T Work

;

rC

rCrCtorqueT

w

ww

2 U Work

thus,,

loss) frictional asenergy in losses to(due

factor,input power a Defining•


• With state 1 as inlet to rotor• “ 2 as exit from rotor• “ 3 as exit of diffuser • No energy addition in diffuser• Thus

)(13 oo TT

=

)(120 oTT

compressor theacross rise

re temperatustagnation :)( Where

)(

balanceEnergy

13

213

oo

oop

TT

UTTc

Centrifugal Compressors• Defining c as overall isentropic efficiency, then

overall stagnation pressure ratio is given by :

13

13

'

oo

oo

c TT

TT

11

'

'

1

131

1

3

1

3)(

o

ooco

o

o

o

o

T

TTT

T

T

P

P

121

11

13 1)(

1

op

c

o

ooc

Tc

u

T

TT

thus vanes,ofnumber increasing

by increased becan ;compressor ofcapacity work limitingfactor a :

compressorin capacity work limiting areboth

.rotor in (friction) less: ;diffuser androtor in )frictional ( lessboth presents

c

Centrifugal Compressors• Example 4.1• The following data are suggested as a basis for

the design of a single-sided centrifugal compressor:

• Power input factor = =1.04• Slip factor = 0.9• Rotational speed, N= 290 rev/s• Overall diameter of impeller, D=0.5m• Eye tip diameter=2re=De=0.3m• Eye root diameter, D1=2r1=0.15m• Air mass flow, m=9 kg/s• Inlet stagnation temperature To1= 295• Inlet stagnation pressure Po1 = 1.1 bar• Isentropic efficiency, c=0.78

Centrifugal Compressors• Requirements 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.


• (a) impeller tip speed

smU /5.4552905.0 • Temperature equivalent of the work done on unit mass flow of air, is

Kc

UTT

poo 193

10005.1

5.4559.004.13

22

13

23.4295

19378.01

)(1

5.31

1

13

1

3

o

ooc

o

o

T

TT

p

p

DNr*N**2 22 rU


• Power required=kWTTcm oop 1746193005.19)(

13

.

(b) to find the inlet angle it is necessary to determine the inlet velocity which in this case is axial;

11 e. . CCi a

.

inlet.at area flow theis A1 where

mequation continuity esatisfy thmust 11111 aa CAC

Since the density 1 depends upon C1and both are unknown, a trial and error process is required.

Centrifugal Compressors• Flow triangles• u2=455.5 m/s

• Assume axial flow• two unknown (,c) in one

equation but another relation is given by

21

2111111 4 ht ddCACm

po c

CTTand

RT

P

2

21

11

11 1

1

111

21

11 1

calculate thus,and,

2 get then Cget and

11

1

oo

po

T

T

p

pthen

c

cTTAssume

smru

smru

tt

hh

/ 273

,/5.136

11

11


• Note 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,

222

1 053.04

)15.03.0( mA

Based on stagnation conditions:

31 /30.1

295287.0

1001.1

1

1

1mkg

RT

p

o

oo


/131053.030.1

9

111 1

mA

mCC a

11 aCCSince ,the equivalent dynamic temperature is

3

1

11

5.3

11

1

21

1

2

3

221

/21.15.286287.0

100992.0

992.05.286/295

1.1

)/(

5.2865.82952

5.8201.0

31.1

10005.12

131

2

1

1

1

mkgRT

p

TT

pp

Kc

CTT

Kc

C

o

o

po

p


:

/140053.021.1

9

:

111

1

trialfinal

smA

mC

checkC

a

a

m/s 145= try 11CCa

equivalent dynamics temperature is

Kc

C

p

5.10201.0

45.1

10005.12

145

2

2

3

221


smA

mC

checkC

mkgRT

p

TT

pp

Kc

CTT

a

a

o

o

po

/143053.085.1

9

:

/185.15.284287.0

100968.0

968.05.284/295

1.1

)/(

5.2845.102952

11

3

1

11

5.3

11

1

21

1

1

1

1

1

1


• This 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:

smNDrN

The

ee /2732903.0 2 r

radius tipeyeimpeller at the , Uspeed, peripheral

e

e

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 CompressorsthusCa ,C choice theMaking 1r2

2

2

2 2 2 222

2

2 2

0.9 455.5 410 /

1.43 4.193.8

2 0.201

w

r w

p

C U m s

C CC K

c

mA

Cr

2 2

,

get , we need to get P

0.78, 0.22, 1/ 2 0.11

loss in the impeller 0.5(1 ) 0.11

0.89

c

c

x rotor

To

loss loss

the


1

5.35.3

1

13

1

2

1

2

(1

582.1295

19389.01

o

ooimp

o

o

o

o

T

TT

p

p

p

p

To calculate density at exit


2

'1'

2

2

22

2

2222

12

12

1

2

1

2

2

12

2

2

&

2

,

22

PTT

TT

T

T

p

p

togetP

Tc

CTthusT

assumeCC

uC

c

CC

c

C

oo

ooc

o

o

o

o

po

ar

p

r

p

thus get 2.

Centrifugal Compressors KTTbutTTpp oooo 488295193 //

3222

5.322

ceT

T

p

p

thereforeKc

CTT

oo

po

sin488

2.394

, ,2.3948.934882

5.31

22

22

2

22

2

3

2

22

2

5.3

22

2

222

/28.22.394287.0

10058.2

58.21.135.2 ,1.1

35.2488

2.394532.1

,)(

1

1

1

1

11

2

22

mkgRT

p

barppbut

p

ppp

p

p

asp

pget

p

p

p

p

p

p

o

oo

o

oo

o

oo

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

2

2

m 0.027614328.2

9

2

rC

mA

cmormD

Ab 76.1 0176.0

5.0

0276.0

Computational Design of a Centrifugal Compressor• PROGRAM MAIN • COMMON CP,R,GAMRAT• COMMON VECT(5000,500)• C• C• C 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 Compressor• C

• PI=22./7.• EPSI=1.05• SIGMA=0.9• RPM=305.• D0=0.6• DIT=0.4• DIR=0.15• FLOW=14• TO1=300• PO1=100.• EFFC=0.8• CP=1005• EFFIMP=0.89• GAMMA=1.4• R=0.287• GAMRAT=GAMMA/(GAMMA-1.)• U=PI*D0*RPM• TO13=EPSI*SIGMA*U*U/CP• PO13=(1.+EFFC*TO13/TO1)**GAMRAT• TO3=TO1+TO13• TO2=TO3• PO3=PO1*PO13• POWER=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 Compressor•C

• C1=100.• CALL SITER(C1,TO1,PO1,AI,FLOW)• C WRITE(6,12)C1,EPS,P1,T1,AI• C 12 FORMAT(2X,E13.3/4E13.4)• UE=PI*DIT*RPM• UR=PI*DIR*RPM• ALFAR=ATAN(C1/UR)*180./PI• ALFAT=ATAN(C1/UE)*180./PI• WRITE(6,24)• 24 FORMAT(8X,'ALFAT, ALFAR'/)• WRITE(6,13)ALFAT,ALFAR• 13 FORMAT(2X,2E13.3)• C• C Axial Depth CR=C1• CW=SIGMA*U• CSQ=CR*CR+CW*CW• PO2=PO1*(1.+EFFIMP*TO13/TO1)**GAMRAT• T2=TO2-CSQ/(2.*CP)• P2=PO2*(T2/TO2)**GAMRAT• RHO2=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 Compressor•C

• C CALL PERFORMANCE(POWER,TO1,PO1,EFFC,GAMRAT,CP)• STOP• END• C• SUBROUTINE SITER(C,TO,PO,A1,FLOW)• COMMON CP,R,GAMRAT• C WRITE(6,102)C,EPS,PO,TO,A1• RHO1=PO/(R*TO)• 10 C=FLOW/(RHO1*A1)• T=TO-C*C/(2.*CP)• P=PO*(T/TO)**GAMRAT• C• 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))/RHONEW• IF(EPS.LT.0.001)GO TO 20• RHO1=RHONEW• GO TO 10• 20 CONTINUE• WRITE(6,23)• WRITE(6,102)C,EPS,P,T,A1• 102 FORMAT(2X,5E13.4/)• Return• End

Computational Design of a Centrifugal Compressor

• SUBROUTINE PERFORMANCE(POWER,TO1,PO1,EFFC,GAMRAT,CP)• COMMON VECT(5000,500),WMAS(5000,500),BETA(5000,500),PI• FLOW=10.• DFLOW=FLOW/10.• WRITE(6,30)POWER,TO1,PO1,EFFC,GAMRAT,CP• 30 FORMAT(6E13.3)• DO 10 I=1,9• TO3=TO1+POWER*1000./FLOW/CP• PO3=PO1*(1.+EFFC*(TO3-TO1)/TO1)**GAMRAT• FLOW=FLOW-DFLOW• C WRITE(6,20)TO3,PO3• WRITE(6,20)FLOW,PO3/PO1• 20 FORMAT(2E13.3)• 10 CONTINUE• C • RETURN • END

Centrifugal Compressors• The 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=constant

• Cr: radial velocity will also decrease.

Centrifugal CompressorsExample 4.2Consider 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 space wd = 5 cmApproximate mean radius of diffuser throat, rm =0.033mDepth of diffuser passages dd 1.76Number of diffuser vanes nv 12Required 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 depth

(a)Consider 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,


smCw /34230.0

25.0410

2

The 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.

p

w

p c

CrC

c

C

22 thus,m/s, 97Cr2Try

22

222


• Ignoring 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

322

5.3

2

5.3

2

2

22

2

/77.21.425287.0

10038.3 ,38.31.107.3

07.3488

1.425582.1 ,

488

1.425

1.4259.62488 ,2

12

2

mkgbarp

p

p

p

p

KTc

CTT

oo

po

5.312 )582.1(/ oo PP

Centrifugal Compressors• Area 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

20332.0

0176.0*3.0**2

m

owr CC 16)342/9.97(tan)/(tan 1

221

2

Centrifugal Compressors• the throat width of the diffuser channels may

be found by a similar calculation for the flow at the assumed throat radius of 0.33m.

sm /31133.0

25.0410Cw2

Try Cr2= 83 m/s

32

2

5.3

2

2

2222

/96.25.436287.0

10071.3

71.31.137.3 ,37.3488

5.436582.1

5.4365.51488 ,5.51201.0

83.011.3

2

1

mkg

barpp

p

KTKc

C

o

p

Centrifugal Compressors• Area in radial direction=A (radial) = 2Db =0.0365

3.839

)(

22

2

2

rradi

r

r

CA

mCcheck

CGet

0

2

1- 15)( tan flow) ofdirection ( 2

C

Cr

cmwidth

throatofwidthbnA

mAA

th

rth

4.4

) ( *

0945.0sin 2

Centrifugal CompressorsCompressibility Effects• At the impeller inlet,( eye of the impeller), the relative

velocity is high and could be very close to sound values.

0.91.308/338/ 111 RTVM t

No problem at sea level conditions, however at high altitude ( aircraft engine), speed of sound decreases and we might have supersonic flow.

For example at 11000 m, T=217 K

supersonic 1.01.06/11 RTVM t


• we try to avoid this by having guide vanes and it is better to be variable in the case of change of conditions, such as altitude.

• By trial and error, the value of Ca can be determined from Ca and , C1t 9and C1t can be determined. Then

value V1t9can be determined which is smaller.=239 m/s.

82.0239

RT

M

For this design, the flow is subsonic at altitude. Trying

smCa /1501


• For 30 pre whirl• C1=150/cos30=173.2

mkgbarpc

CTT

p

/14.1,918.0 ,1.2802 1

2

101

239

56273149

/8630tan149.

149053.0*148.1

9 on,check

22

1

1

1

t

a

v

smCvel

C

7.01020*280*287.04.1

239

M


• In spite of the advantage, it has a disadvantage of reducing the pressure ratio of compressor.

2/)(

/

,/1

11

2013

1113

1

1

3

thaveragec

pc

oco

o

uuuu

cuCuT

whereTTP

P

ratio. pressurein reduction hence and

ofreduction tolead l which wil valuehasC130 a1 T


vanes)guidewithout (23.4example In this1

3 o

o

p

p

vanesguidewith 79.31

3 o

o

p

p

for details see text book

Centrifugal Compressors• Vaneless diffusers:• For vaneless diffuser, no problem, it can handle

supersonic flow while vaned diffuser can’t.• At the exit of the vaneless diffuser, C3=355,

M2=0.56<1.0, which is subsonic and is ok for vaned diffuser.

• Advantages of vane less diffuser:– Mach number M2 could be supersonic without – Vaneless space will eliminate any non-uniformity of

the flow coming out of the impeller ( jets and wakes).– This is good to avoid any problem in exciting the

vanes.– As a normal practice, no. of vanes in the diffuser is

less than impeller blades. • N (vanes)<N (impeller)

Centrifugal Compressors• Non-dimensional quantities for compressor

characteristics:• D=diameter, N=rpm, m=mass flow rate• po1=inlet pressure, po2=exit pressure• T01=inlet temperature, To2=exit temperature• N=no. of variables• M=basic dimensions• there are 7 variables, 3basic dimensions (M,L,T)• and terms 7-3=4.

11

1

112

11212

,

,,/,/

oo

o

oo

ooooo

T

N

P

TmcompressorsameFor

RT

ND

PD

RTmTTPP

Centrifugal Compressors Stall • Defined as the (aerodynamic stall) or the break-

away of the flow from the suction side of the blades. • A multi-staged compressor may operate safely with

one or more stages stalled and the rest of the stages unstalled . but performance is not optimum. Due to higher losses when the stall is formed.

Surge• Is a special fluctuation of mass flow rate in and out

of the engine. No running under this condition. • Surge is associated with a sudden drop in delivery

pressure and with violent aerodynamic pulsation which is transmitted throughout the whole machine.

Centrifugal Compressors Classes and comparisons between compressors AxialCentrifugalFunction Large...

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