NewLecture8 Centrifugal Compressors

8/12/2019 NewLecture8 Centrifugal Compressors

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Module (6)

Centrifugal Compressor Stage

Prof. Dr: Aida Abdel Hafiz


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Centrifugal type of compressor is suitable for low specificspeed. Higher pressure ratio and lower mass flow

applications.

Performance-wise the centrifugal compressor is lessefficient (3-5%) than the axial type.

However, a much higher pressure ratio(4) per stage.

Single piece impeller and a wide range of stable operation aresome of the attractive aspects of this type.

Centrifugal compressorsare used in large refrigeration unitspetrochemical plants and large variety of other industrialapplications. In aircraft applications it is only used for smallturbo-prop engines.

Introduction


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Lesson (1)

Main

Components ofCentrifugal

Compressor Stage


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1- Elements of a Centrifugal Compressor

Stage

Figures (1 & 2) show the principal elements of a

centrifugal compressor stage.


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Fig. (1) Element of a centrifugal compressor stage.


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The flow enters a three-dimensional impeller through anaccelerating nozzle and a row of inlet guide vanes(IGVs).

The inlet nozzleaccelerates the flow from its initial conditions(at station i) to the entry of the inlet guide vanes.

The IGVs direct the flow in the desired direction at the entry

(station 1) of the impeller.

The impeller, through its blades, transfers the shaft work tothe fluid and increases its energy level. It can be made in onepiece consisting of both the inducer section and a largelyradial portion.

The inducer receives the flow between the hub and tipdiameters (dh, dt) of the impeller eye and passes it on to theradial portion of the impeller blades.


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The flow approaching the impeller may be with or withoutswirl.

The inducer section can be looked upon as an axialcompressor rotor placed upstream of the radial impeller. Insome designs this is made separately and then mounted onthe shaft along with radial impeller.

In a great majority of centrifugal compressors the impeller hasstraight radial blades after the inducer section.

At high speeds, the impeller blades are subjected to highstresses which tend to straighten a curved impeller blade.Therefore, the choice of rail straight blades is more sound for

higher peripheral speeds.

However, in fan and blower applications,on account of therelatively lower speeds, backward and forward-swept impellerblades are also used.


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Unlike axial machines, the hub diameter of the radial

impellers varies from the entry to the exit. The tips of theblades can be shrouded to prevent leakage, butmanufacturing and other problems of the shroudedimpellers have kept them open in most applications.

The impeller discharges the flow to the diffuserthrough a vaneless space, Fig. (2).

Here the static pressure or the fluid rises further on

account of the deceleration of the flow. The diffuser maybe merely a vaneless space or may consist of a bladering a shown in Fig. (2). For high performance, the designof the diffuser is as important as that of the impeller.


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Fig. (2) A centrifugal compressor stage.


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The flow at the periphery of thediffuser is collected by a spiralcasing known as the volutewhichdischarge it through the deliverypipe.

Figure (3) shows a centrifugalimpeller with blade located only in

the radial section betweendiameters d1and d2. To prevent highdiffusion ratio of the flow, theimpeller blades are invariablynarrower at a larger diameter (b2 90)with zero swirl at the entry. Itmay be observed that such blades have large fluiddeflection and give c2 >u2. This increases the workcapacity of the impeller and the pressure rise across it.

This configuration is unsuitable for higher speedsin compressor practice and leads to higher losses.However, for fan applications such blades are used in

multi vane or drum-type centrifugal blowers.


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Fig. (8) Entry and exit velocity triangles for forward swept blades

(2> 90) with zero swirl at entry.

forward-swept blades(2> 90)with zero swirl at the entry


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2.1 Stage Work

In a centrifugal compressor the peripheral velocities atthe impeller entry and exit are u1and u2respectively.Therefore, the specific work or the energy transfer is

W= u2c2u1c1 (12)


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In this equation, if c1 is positive, Figs (5, 6 & 7) theterm u1c1 is subtractive. Therefore, the work andpressure rise in the stage are relatively lower. Thesequantities are increased by reducing c1to zero Fig. (4)or making it negative.

In the absence of inlet guide vanes, c1=0. Thiscondition will be assumed throughout in this chapterunless mentioned otherwise.

Therefore, Eq (12) gives

W= u2c2 (13)


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The flow coefficient at the impeller exit is defined as

(14)

2

r22

u

c

therefore,

(15))cot-(1uW 222

2

Substituting from Eq (7)

W= u2(u2cr2cot 2)


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If f2 and 2are the actual values, the work given by Eq

(15) is the actual work in the stage.

The work is also given by the following from of Euler'sequation:

(16))(2

1)(

2

1)(

2

1 21

2

2

2

2

2

1

2

1

2

2 uuwwccW

For a radial tipped impeller with zero swirl (whirl) atthe entry1=90, 2=90-and Eqs. (13 & 15) reduce to

(17)2

2uW


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2.2 Pressure Coefficient

The head, pressure or loading coefficient isdefined before. As in the earlier chapter, here also it isdefined by

(18)

22uw


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This gives, in a dimensionless form, a measure of the

pressure raising capacities of various types ofcentrifugal impellers of different sizes running atdifferent speeds. Eq (13 & 15) give

(19 a)

(19 b)

2

2

u

c

)cot-(1w 22For zero entry swirl and no slip

for radial-tipped blades give =1


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Fig. (9) Performance characteristics of different types of

centrifugal impellers (c1=0, =1).

stable characteristics.

unstable


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Stage Pressure Rise


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2.3 Stage Pressure Rise The static pressure rise in a centrifugal compressor stage occurs in the

impeller, diffuser and the volute.

The pressure rise across the impelleris due to both the diffusion ofthe relative velocity vector w1 to w2 and the change in thecentrifugal energy.

The static pressure rise across the diffuser and volute (if any)occurs simply due to the energy transformation processes accompaniedby a significant deceleration of the flow. The initial kinetic energy(at the entry of the diffuser) is supplied by the impeller.

In this section the pressure rise (or pressure ratio) across the state isfirst determined for an isentropic process.

For small values of the stage pressure rise (as in axial stages andcentrifugal fans), the flow can be assumed to be incompressible.

for isentropic process


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(20)

)cot-(1uwhp1

2222oo

)cot-(1up 22

2

2o

Substituting from Eq (19 b)

(21)up22o

for isentropic process.


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However, the pressure rise in a centrifugal compressorstage is high and the change in the density of the fluidacross the stage is considerable.

Therefore, in most application, the flow is notincompressible.

The pressure ratio for compressible flowassuming to beperfect gasis obtained by


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)T-(Tchw o1o2spo

1)-T

T(Tcw

o1

o2so1p

(22)1]-)[(pTw

1-

roo1

pc

Substituting from Eq (15)

)cot-(1u1]-)[(pTc 222

2

1-

roo1p


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The rearrangement yields

(23)

(24)

u)cot-(11

p

pp

1-

1

22

22o1

o2ro

opTc

u1p 1-

1

22

ro

opTc


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Lesson (3)

Enthalpy-Entropy diagram


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3- Enthalpy-Entropy diagram

Figure (10) shows an enthalpy-entropy diagram for acentrifugal compressor stage, Figs. (1&2).

Flow process occurring in the accelerating nozzle (i-1),

impeller (1-2), diffuser (2-3) and the volute (3-4) aredepicted with values of static and stagnation pressures andenthalpies.

The flow, both in the inlet nozzle and guide vanes is

accelerating from static pressure pi. On account of thelosses and increase in the entropy the stagnation pressureloss is poi-po1, but the stagnation enthalpy remainsconstant:


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Fig. (10) h-s diagram for flow through

a centrifugal compressor stage.

accelerating nozzle i-1

impeller 1-2

diffuser2-3

the volute 3-4


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(25 a)

(25 b)

(26)

1ooi hh

211

2ii

c2

1hc

2

1h

o4sso3sso2s ppp


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(27)

(28)

(29)

ssossoso hhh 432

2111 2

1whh relo

2222 2

1whh relo


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The corresponding stagnation pressures are po1rel and

po2rel.

Static pressure rise in the diffuser and the volute

occurs during the processes 2-3 and 3-4, respectively.The stagnation enthalpy remains constant fromstation 2 to 4 but the stagnation pressure decreasesprogressively.


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The actual energy transfer (work) appears as the change inthe stagnation enthalpy. Therefore, from Eq. (16)

)(2

1)(

2

1)(

2

1 21

22

22

21

21

2212

uuwwcchhw ooa

(30)

(31)

432 ooo hhh

432 oos ppp


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This when rearranged gives

(32 a)

(32 b)

0)u(u2

1)w(w

2

1)h(h 21

22

21

2212

21o1rel

22o2rel u

2

1hu

2

1h

This relation is also shown on the h-s diagram, Fig. (10).


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Stage Efficiency


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3-1 Stage Efficiency

The actual work input to the stage is

(33 a)

For a perfect gas,

(33 b)

)cot-(1u)( 222214 oopa TTcw

)cot-(1u 222214 ooa hhw


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The ideal work between the same static pressures p1

and p4is

(34 a)

(34 b)

)( 1414 ossopossos TTchhw

)1T

T(Tcw

1o

ss4o1ops

]1)[(

1

1 )pTcw roops


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The last relation in Eq. (35) is valid for incompressibleflow assuming c4=c4ss

The ideal and actual values of the stage work areshown in Fig. (10).

The total-to-total efficiency of the stage can now bedefined by

Here the stagnation pressure ratio

(35)1o

4o

1o

ss4oro

pp

ppp


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(36 a)

(36 b)

1o4o

1oss4o

a

sst

hhhh

ww

)cot-(1u

)(

2222

14 ossopst

TTc

(36 c)

)cot-(1u

])1)p[(Tc

2222

1

ro1opst


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This equation yields the pressure ratio of the stage forthe given initial state of the gas and values of u2, 2,and 2.

(37)

1

1

22

22

u

)cot-1(1

opstro Tcp


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Degree of Reaction


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3-2 Degree of Reaction

A large proportion of energy in the gas at the impellerexit is in the form of kinetic energy.

This is converted into static pressure rise in the diffuserand volute casing.

The division of static pressure rise in the stage betweenthe impeller and stationary diffusion passages isdetermined by the degree of reaction.

This can be defined either in terms of pressure rise or

increase in enthalpy in the impeller and the stationarydiffusing passages.

Expressions for the degree of reaction in this section arederived from the following definition.


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stagein theenthalpystagnationinChange

impellerin theenthalpystaticinChangeR

(38)

o1o2

12

h-h

h-hR


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From Eq. (32 a)

(39))uw(2

1)wu(2

1hh 21

22

22

2212

For zero swirl at the entry (c1=0)

(40)22o1o2 cuhh

Therefore Eqs (39) and (40) when put into Eq (38) give

(41)

22

21

22

22

22

cu2

)uw()wu(R


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(42)22r

21r

21

21

cc)uw(

2222

22

2r2

222

2r2

22

cc2uuc)c(ucw

(43)2r2

2222

22

22

c-cc2uw-u

With inducer blades and zero entry swirl

(c1=0)

c1 =cx1=c r2


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Equations (42 & 43), when used in Eq. (41) give

(43 a)

2

2

2

11

u

cR

Substituting from Eq. (7) and rearranging

(43 b) 22cot2

1

2

1R


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Equation (43 b) is plotted in Fig. (11).

The degree of reactionof the radial-tipped impeller(2=90) remains constant at all values of the flow

coefficient.

Reaction increases with flow coefficient forbackward-swept impeller blades (

2 90) as shown.

From Eq. (19 a)


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Fig. (11) Variation of degree of reaction with flow coefficient for

various values of impeller exit air angle.


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(44 a)

(44 b)

21

1R

R)-2(1

the higher the degree of reaction, the lower is the stage pressurecoefficient and vice versa.


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Fig. (12) Variation of pressure coefficient with degree of reaction.

The backward-swept impeller blade give a higher degree of reaction ad a

lower pressure coefficient compared to the radial and forward-swept

blades.


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4- Slip Factor

The actual velocity profiles at the impeller exit due toreal flow behavior are shown in Figs. (13 & 14). Theenergy transfer occurring in the impellercorresponding to these velocity profiles is less than theone that would have been obtained with one-dimensional flow.


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Fig. (13) Meridional velocity distribution at the impeller exit.


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Fig. (14) Vane-to vane velocity distribution at theimpeller exit.

Slip

The relative eddymentioned earliercauses the flow inthe impellerpassages to derivefrom the bladeangle (2) at the exitto an angle ('2), thedifference beinglarger for a larger

blade pitch orsmaller number ofimpeller blades.

Velocityprofile


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Slip On account of the

aforementioned effects,the apex of the actual

velocity triangle at theimpeller exit is shifted

away (opposite to thedirection of rotation)from the apex of theideal velocity triangle asshown in Fig. (15) Thisphenomenon is knownas slip and the shift ofthe apex is the slip

velocity (cx). It may be

seen that, on account ofthe slip, the whirlcomponent is reduced

which in turn decreasesthe energy transfer andthe pressure developed.

Fig. (15) Exit velocity triangles with and without slip.

the slip velocity (cx)


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(45)

(46)

2

'2

c

c

2'22s )c(1ccc

Therefore, the slip velocity is given by

Slip Factor

The ratio of the actual and ideal values of the whirlcomponents at the exit is known as slip factor ( )


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The expression for the actual work done, pressureratio and stage efficiency expressed function to the slipfactor, from Eqs. (13 & 15).

(47))cot(1ucucuw 22222

2222

Stage efficiency f(slip factor)


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(48)

(49)

)cot-(1u

]1)[(

2222

1

1

m

)pTc roopst

m

1

1

22

22

u)cot-1(1

op

stroTc

p

Similarly Eqs (36 c & 37) are modified to

The methods of determining slip factors have been suggested by various investigators.

Stage efficiencyf(slip factor)


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Substituting for r from Eq. (50)

(51)22s sin

zrc

However, u2= r

2. therefore,

(52)

22s sinuz

c


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For a radial-tipped blade impeller (2=90), slip factorcan be predicted by

Where Z is the number of blades

the slip factor increases with the number of impellerblades

(55))

z

(1


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Lesson (4)

Design of Diffuser& Volute Casing


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5- Diffuser

The static pressure of the gas at the impeller exit isfurther raised by passing it through a diffuser locatedaround the impeller periphery.

The absolute velocity (c2) of the gas at the impeller exitis high which is reduced to a lower velocity (c3) in thediffuser as show in the enthalpy -entropy diagram Fig.

(10).


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The amount of deceleration and the staticpressure rise (p3-p2) in the diffuser depend on thedegree of reaction and the efficiency of thediffusion process.

An efficient diffuser must have minimum losses(po2-po3), maximum efficiency and maximum

recovery coefficient.


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5-1 Vaneless Diffuser

As the name indicates, the gas in a vanelessdiffuser is diffused in the vaneless apace around theimpeller before it leaves the stage through a volutecasing. In some applications the volute casing is

omitted.

The gas in the vaneless diffuser gains static pressurerise due to the diffusion process from a smaller

diameter (d2) to a larger diameter (d3).

The corresponding areas of cross-sections in the radialdirection are:


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(60)

22222br2bdA

(61)

33333 br2bdA


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Such a flow in the vaneless space is a free vortex flow

in which the angular momentum remains constant.The condition gives

(62)

3322 crcr


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The continuity equation at the entry and exit sectionsof the vaneless diffuser gives

(63)

3r332r22 AcAc

(64))br(2c)br(2c 33r3322r22

(65)

3r3332r222 bcrbcr


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For a small pressure rise across the diffuser, 2=3.

therefore

(66)

3r332r22 bcrbcr

For a constant width (parallel wall) diffuser b2=b3

(67)

crcr r33r22

The absolute velocity at the diffuser exit is given by


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The absolute velocity at the diffuser exit is given by

Equations (62), (67) & ( 68 ) yield

(68) 22

2

3

22

2

2

r2

2

3

22

3

2

r3

2

3

c

r

rcc

r

rccc

69)

r

r

c

c

c

c

c

c

3

2

2

3

2r

3r

2

3

This relation further gives

(70)

c

ctan

c

ctan

3

3r1

2

2r132

Thi i i lid l f i ibl fl


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This equation is valid only for incompressible flowthrough a constant width diffuser.

Equation (69) clearly shows that the diffusion isdirectly proportional to the diameter ratio (d3/d2).

This leads to a relatively large sized diffuserwhich is

a serious disadvantage of the vaneless type.

In some cases the overall diameter of the compressormay be impractically large. This is a serious limitation

which prohibits the use of vaneless diffusers inaeronautical applications.


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Besides this, the vaneless diffuser has a lower

efficiency and can be used only for a smallpressure rise.

However, for industrial applications, where large-sized

compressors are acceptable, the vaneless diffuser iseconomical and provides a wider range of operation.Besides this, it does not suffer from blade stalling andshock waves.


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6-2 Vaned diffuser

For a higher pressure ratio across the radial diffuser, thediffusion process has to be achieved across a relativelyshorter radial distance.

This requires the application of vanes which providegreater guidance to the flow in the diffusing passages.

Diffuser blade rings can be fabricated from sheet metal

or cast in cambered and uncambered shapes of uniformthickness, Figs. (17 & 18).

Figure (19)shows a diffuser ring made up of camberedaerofoil blades.


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To avoid separation of flow, the divergence of thediffuser blade passages in the vaned diffuser ring canbe kept small by employing a large number of vanes.However, this can lead to higher friction losses.

Thus an optimum number of diffuser vanes mustbe employed.


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The divergence of the flow passages must not

exceed 12.

The flow leaving the impeller has jets and wakes.When such a flow enters a large number of diffuser

passages, the quality of flow entering different diffuserblade passages differs widely and some of the bladesmay experience flow separation leading to rotatingstall and poor performance. To avoid such a possibility,

it is safer to provide a smaller number of diffuserblades than of the impeller.


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In some designs the number of diffuser blades iskept one-third of the number of impeller blades.

This arrangement provides a diffuser passage withflows from a number of impeller blade channels. Thus

the nature of the flow entering various diffuserpassages does not differ significantly.


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Another methods to prevent steep velocity

gradients at the diffuser entryis to provide a small(0.05 -0.1 d2) vaneless space between the impellerexit and the diffuser entry as shown in Fig. (20).

This allows the non-uniform impeller flowto mixout and enter the diffuser with less steep velocityprofiles.


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Besides this the absolute velocity (Mach number) of

the flow is reduced at the diffuser entry. This is a greatadvantage, specially if the absolute Mach number atthe impeller exit is greater than unity. The supersonicflow at the impeller exit is decelerated in this vaneless

space at constant angular momentum without shock.

Every diffusers blades ring is designed for given flowconditions at the entry at which optimum performance

is obtained. Therefore, at of-design operations thediffuser will give poor performance on account ofmismatching of the flow.


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In this respect a vaneless diffuser or a vaneddiffuser with aerofoil blades, Fig. (19) is better.

For some applications it is possible to providemovable diffuser blades whose directions can beadjusted to suit the changed conditions at the

entry.

In some designs for industrial applications, a vanelessdiffuser supplies the air of gas direct to the scroll

casing, whereas for aeronautical applications, varioussectors of the vanes diffuser are connected to separatecombustion chambers placed around the main shaft.


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Fig. (17) Diffuser ring with straightcambered blades.

Vaned Diffuser

Fig. (18) Diffuser ring with straight(uncambered) flat blades.


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Fig. (19) Diffuser ring with cambered aerofoil blades.


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5-3 Area Ratio Figure (20)shows a vanelessdiverging wall diffuser. Theside walls have a divergenceangle of 2. The area ratio of

such a diffuser in the radialdirection is

(

71

)22

33

2

3r bd

bd

A

A

A

Fig. (20) Radial diffuser passage with diverging walls.

Th i di l i i b


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The semi-divergence angle is given by

(72)

)r-r2(bbtan

2323

(73)

tan)d-d(tan)r-r(2bb 232323

(74)

2

23

2

3

b

bb1

b

b

(75)

222

3

2

23

2

3

d/b

tan1

d

d1tan

b

bb1

b

b

33tan

1d

1d

A


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(76)222

3

2

3r

d/b1

d1

dA

For parallel walls ( tan =0), this gives

2

3r

d

dA (77)

the area ratio of a diffuser can be increases by:


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the area ratio of a diffuser can be increases by:

Increasing the diameter ratio d3/d2

Increasing the width ratio, b3/b2

Decreasing the leading edge vane angle, 2

Various combinations of all the above.

Some typical values of these parameters are:

d3/d2=1.4 to 1.8

Ar= A3/A2=2.5 to 3

2=10 to 20 b3/b2=0.025-0.1

max= 5


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The higher diffuser efficiency can be achieved if the

following points are considered at the time of design:

1- The diffuser entrance blade angle must be such that air

impinges on it with a small angle of attack. 2- The flow passage area must be large enough to handle

the air and it must expand within certain maximumreasonable limits.

3- Sudden changes in flow are to be avoided.

6- Volute casing


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6 Volute casing

The volute or scroll casing collects and guidesthefollow from the diffuser or the impeller (in the absenceof a diffuser).

The flow is finally discharged from the volute throughthe delivery pipe. For high pressure centrifugalcompressors or blowers, the gas from the impeller isdischarged through a vaned diffuser, whereas for low

pressure fans and blowers, the impeller flow isinvariably collected directly by the volute since adiffuser is not required because of the relatively lowpressures.


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Figs. (22)show a volute casing along with the impeller,diffuser and vaneless spaces. The volute base circle

radius (r3) is a little larger (1.05 to 1.10 times thediffuser or impeller radius) than the impeller ordiffuser exit radius.

The vaneless space before volute decreases the non-uniformities and turbulence of flow entering thevolute as well as noise level.

Some degree of diffusion in the volute passage is alsoachieved in some designs, while others operate atconstant static pressure.


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Fig. (22) Scroll or volute casing of centrifugal machine.


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Different cross-sectionsare employed for the volutepassage as shown in Fig. (24).

The rectangular section is simple and convenientwhenthe volute casing is fabricated from sheet metal bywelding the curved wall to the two parallel side walls.

While the rectangular section is very common incentrifugal blowers, the circular section is widely used

in compressor practice.


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Fig. (24) Different cross-section of the volute passage.

Two most widely used methods of volute design are discussed below.


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Lesson (5)

Stage Losses

7- Stage losses


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7- Stage losses

The power supplied to the centrifugal compressor stage is the power

input at the coupling less the mechanical losses on account of thebearing, seal; and disc friction.

The aerodynamic losses occurring in the stage during the flow processfrom its entry to exit are taken into account by the stage efficiency.

These losses result from fluid friction, separation, circulatory motionand shock wave formations.

They lead to an increase in entropy and a decrease in stagnationpressure. The disc friction loss, through aerodynamic in nature, isconsidered along with the other shaft losses.


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The nature of flow and losses occurring in centrifugal compressorstages is considerably different from those in axial compressor stages

on account of different configurations of flow passages in the twotypes.

The centrifugal stages, on account of the relatively longer flow passagesand greater turning of the flow, suffer higher losses compared to theaxial type. This explains the generally lower values of the efficiency ofthe centrifugal stages compared to the axial type.

In this section different losses have been described separately on thebasis of their different nature. The components of the stage in whichthey occur have been mentioned where necessary.

The losses in centrifugal compressors can be also


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The losses in centrifugal compressors can be alsodivided into external and internal losses.

External losses include bearing friction, disk friction,shroud/casing friction, leakage, and external recirculationlosses.

Internal lossesare caused by the boundary layers on theblade (both suction and pressure side) and on the hub wall,by blade wakes, by corner and tip vortices, by possibleshocks (oblique or normal) and by recirculations within

the channel.

This classification is not always precise, and at timesdifferent authors present different groupings.

Th t f l b di id d t t l


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The type of losses can be divided to rotor lossesand stator losses as the following

7-1 Rotor Losses

Can be divided into:

1- Friction loss or profile loss. 2- Incidence loss.

3- Shock loss.

4- Impeller entry loss.

5- Tip clearance loss or leakage loss.

6- Disc friction loss or windage loss.

7- Diffusion and blade loading loss.

7 1 1 F i i l fil l


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7-1-1 Friction loss or profile loss

A major portion of the losses is due to fluid in stationaryand rotating blade passages. The flow except in theaccelerating nozzle and the inlet guide vanes is throughoutdecelerating.

Therefore, the thickening boundary layer separates wherethe adverse pressure gradient is too steep. This leads toadditional losses on account of stalling and wasteful

expenditure of energy in vortices.


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Losses due to friction depend on the friction factor,passage length and the square of the fluid velocity.Therefore, a stage with relatively longer impeller, diffuserand volute passages, and higher fluid velocities show poorperformance.


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Friction losses in the acceleration nozzle and inletguide vanes are relatively much smaller.

On account of high velocities and the decelerationsthat follow at the leading edges of the inducer and thediffuser blades, shock waves (if present) causeadditional losses. They can cause separation of the

boundary layers leading to higher losses.


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7-1-2 Incidence loss

At off-design conditions,flow enters the inducer atan incidence angle that is either positive or negative, asshown in Fig. (26).A positive incidence angle causes a

reduction in f low.

Fluid approaching a blade at an incidence angle suffersan instantaneous change of velocity at the blade inletto comply with the blade inlet angle.

Separation of the blade can create a loss associatedwith this phenomenon.


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Fig. (26) Inlet velocity triangles at non-zero incidents.

7-1-3 Impeller entry losses


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7 1 3 Impeller entry losses

In higher-pressure centrifugal compressors the radial-tipped impeller blades extend into the axial portion.Thus the incoming flow is efficiently guided from theaxial to the radial direction. However, in centrifugal

blowers with relatively lower pressure rise, the impellerblades are located only in the radial portion. Here theflow enters axially and turns radially

In this process the fluid suffers losses similar to thosein a bend. These losses depend on the inlet absolutevelocity but are small compared to other losses.

7 1 4 Sh k l


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7-1-4 Shock losses Additional losses that occur in a row of blades in a centrifugal

compressor stage on account of incidence are conventionally known asshock losses. The change of incidence itself very frequently resultsfrom the operation of the stage away from the design f low conditions.

During the off-design conditions the flow at the entry of the impeller

and diffuser blades approaches them with some degree of incidence.For instance, Fig. (27) depicts off-design velocity triangles at the entryof the inducer blades.

At the same rotational speed, the reduced flow rate introduces positiveincidence whereas negative incidence results from increased flow rate.Large incidences (especially positive), lead to flow separation, stallingand surge.


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Fig. (27) Entry velocity triangles at off-design operation.


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Fig. (29) Typical variation shock losses with incidence.

l l l k l


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7-1-5 Tip clearance loss or leakage loss

The gap between the blade and the shrouded inducedleakage flow across the gap.

The leakage flow arises due to a pressure differencebetween the two surfaces of the blade at the tip. Thetwo most critical parameters controlling themagnitude of the leakage flow are blade clearance

height and the blade loading (local pressure differencebetween the pressure and the suction surface). Fig.(30),


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Fig. (30) Leakage affecting clearance loss.

7 1 6 Disc friction loss or windage loss


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7-1-6 Disc friction loss or windage loss

This loss results from frictional torque on the backsurface of the rotor as seen in Fig. (31). This loss is thesame for given sizes disc whether it is used for a radial-

inflow compressor.

Losses in the seals, bearings, and gearbox are alsolumped in with this loss, and the entire loss can be

called an external loss.


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Fig. (31) Secondary flow at the back of an impeller.


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Occasionally, some author described the disc frictionlosses as external loss. These losses are those, whichgive, rise to an increase in impeller discharge

stagnation enthalpy and corresponding increase inpressure.

7 2 Stator losses


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7-2 Stator losses

Can be divided into:

1- Recirculating loss.

2- Wake mixing loss.

3- Vaned diffuser loss.

4- Vaneless diffuser loss.

5- Exit loss.

6- Scroll loss.


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Lesson (6)

PerformanceCharacteristics

8- Performance characteristics


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8- Performance characteristics The performance characteristics of a centrifugal compressor or a

blower at a given speed can be plotted in terms of the following

quantities:

Figure (32) shows the theoretical and actual performance

characteristics (- plot) for a centrifugal stage. The actual

characteristic is obtained by deducting the stage losses from the

theoretical head or pressure coefficient.

Therefore, the nature of the actual characteristic depends on the

manner in which he stage losses vary with the operating parameters.Friction and shock losses effect the performance significantly.


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Fig. (32) Losses and performance characteristic of a

centrifugal compressor stage.


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Losses are complex phenomena and as discussed hereare a function of many factors, including inletconditions, pressure ratios, blade angles, and flow.

Figure (33) shows the losses distributed in a typicalcentrifugal stage of pressure ratio below 2:1 withbackward-curved blades.

This figure is only a guideline.


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Fig. (33) Losses in a centrifugal compressor.


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Thank You

NewLecture8 Centrifugal Compressors

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