ME 423 Chapter 4 Centrifugal Compressors Prof. Dr. O. Cahit ERALP

ME 423ME 423

Chapter 4Chapter 4Centrifugal CompressorsCentrifugal Compressors

Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP

Centrifugal CompressorsCentrifugal Compressors

4. CENTR4. CENTRIIFUGAL COMPRESSORSFUGAL COMPRESSORS

Attention was focused on the simple turbojet unit Attention was focused on the simple turbojet unit during the Second World Warduring the Second World War..

It was recognized that development time was critical It was recognized that development time was critical and much experience had been gained on theand much experience had been gained on the design design of small high – speed centrifugal compressors for of small high – speed centrifugal compressors for supercharging reciprocating engines.supercharging reciprocating engines.

As power requirements grew for aircrafts, it became As power requirements grew for aircrafts, it became clear that the axial flow compressor was more suitable clear that the axial flow compressor was more suitable large engines.large engines.

By theBy the late fifties, it became clear that smaller gas late fifties, it became clear that smaller gas turbines would have to use centrifugal compressors.turbines would have to use centrifugal compressors.


Advantages;Advantages; Primarily, suitable for handling small volume flows,Primarily, suitable for handling small volume flows, Shorter length than an equivalent axial compressor,Shorter length than an equivalent axial compressor, Better resistance to Better resistance to ““Foreign Object DamageForeign Object Damage”” (FOD), (FOD), Less susceptibility to loss of performance by build – up Less susceptibility to loss of performance by build – up

of deposits on blade surface,of deposits on blade surface, Ability to operate over a wider range of mass flowAbility to operate over a wider range of mass flowss at a at a

particular rotational speed. particular rotational speed.


A pressure ratio of around 4:1 can readily be obtained A pressure ratio of around 4:1 can readily be obtained from a single–stage compressor made of aluminium from a single–stage compressor made of aluminium alloys.alloys.

The advent of titanium alloys, permitting much higher The advent of titanium alloys, permitting much higher tip speeds, combined with advances in aerodynamics tip speeds, combined with advances in aerodynamics now permit pressure ratios of greater than 8:1 to be now permit pressure ratios of greater than 8:1 to be achieved in a single–stage.achieved in a single–stage.

When higher pressure ratios are required, the When higher pressure ratios are required, the centrifugal compressor may be used in conjunction centrifugal compressor may be used in conjunction with an axial flow compressor, or as a two–stage with an axial flow compressor, or as a two–stage centrifugal. centrifugal.


The centrifufal compressor consists essentially of a The centrifufal compressor consists essentially of a stationary casing containing a rotating impeller, which stationary casing containing a rotating impeller, which imparts a high velocity to the air and a number of fixed imparts a high velocity to the air and a number of fixed diverging passages in which the air is decelerated with diverging passages in which the air is decelerated with the consequent rise in static pressure. The part of the the consequent rise in static pressure. The part of the compressor containing the diverging passages is compressor containing the diverging passages is known as the known as the DiffuserDiffuser..

A increase ; V decrease A increase ; V decrease ⇨⇨ P increase P increase

4.1 PRINCIPLE OF OPERATION4.1 PRINCIPLE OF OPERATION



Impeller Eye Mean

Radius of Diffuser Throat

Width of Diffuser Channel

90° Bend taking air to combustion chambers

Vaneless Space

Diffuser Throat


Air is sucked into the impeller eye and whirled Air is sucked into the impeller eye and whirled around at a high speed by the values of the around at a high speed by the values of the impeller disc.impeller disc.

The static pressure of the air increases fromThe static pressure of the air increases from t the he eye to the tip because of the centrifugal effects.eye to the tip because of the centrifugal effects.

The remainder of the static pressure rise is The remainder of the static pressure rise is obtained in the diffuser, where high velocity air obtained in the diffuser, where high velocity air leaving the impeller tip is reduced.leaving the impeller tip is reduced.



The normal practice is to design the The normal practice is to design the compressor so that about half the pressure rise compressor so that about half the pressure rise occurs in the impeller and half in the diffuser.occurs in the impeller and half in the diffuser.

Shrouds have been used on Shrouds have been used on some some superchargers but not in GT practice. superchargers but not in GT practice.

It should be noted that straight radial vanes are It should be noted that straight radial vanes are normally used because the impellers are very normally used because the impellers are very highly streshighly stressseed.d.



Since no work is done on the air in the diffuser, the Since no work is done on the air in the diffuser, the energy absoenergy absorrbed by the compressor will be determined bed by the compressor will be determined by the conditions of air at the inlet and exit of the by the conditions of air at the inlet and exit of the impeller.impeller.

In the first iIn the first innstance it will be assumed that the air enters stance it will be assumed that the air enters tthhe impeller eye in the axial direction so that the initial e impeller eye in the axial direction so that the initial angular momentum of the air is zero.angular momentum of the air is zero.

4.2 WORK DONE & PRESSURE RISE4.2 WORK DONE & PRESSURE RISE



r1

r2

Eye Root

Ideal conditions at impeller tipV2 Vr2

VΘ2 =UV2 Vr2

Velocity relative to the impeller

VΘ2 < U

Eye Tipω (rad /s)


The axial portion of the vanes must be curved so that The axial portion of the vanes must be curved so that the air can pass smoothly into the eye. the air can pass smoothly into the eye.

The angle which the leading edge of a vane makes with The angle which the leading edge of a vane makes with the tangential direction the tangential direction ββ11 will be given by the relative will be given by the relative velocity of the air at inlet velocity of the air at inlet ww11..



VV22 : Absolute velocity with which the air leaves : Absolute velocity with which the air leaves

the impeller tip.the impeller tip.

VVθθ22 : Ta : Tanngential or whirl componentgential or whirl component

VVr2r2 : Radial velocity component : Radial velocity component

Under ideal conditions VUnder ideal conditions Vθθ22 = = UU



Due its inertia, the air trapped between the Due its inertia, the air trapped between the impeller vanes is reluctant to move around with impeller vanes is reluctant to move around with the impeller, and we have already noted that the impeller, and we have already noted that this results in a higher static pressure on the this results in a higher static pressure on the leading face of a vane than the trailing face.leading face of a vane than the trailing face.

It also prevents the air from acquiring a whirIt also prevents the air from acquiring a whir ll velocity equal to the impeller speed. This effect velocity equal to the impeller speed. This effect is known as is known as slipslip..



Thus, Thus, slipslip is, how far the whirl velocity at the impeller tip falls is, how far the whirl velocity at the impeller tip falls short of the tip speed.short of the tip speed.

This depends largely upon the number of vanes on the This depends largely upon the number of vanes on the impeller.impeller.

Greater the number of vanes, the smaller the slip.Greater the number of vanes, the smaller the slip.

VVθθ22 ⇒⇒ UU as as ## of vanes (n) of vanes (n) increase increase

Slip FactorSlip Factor ; ;

aan empn emprrical relationical relation;;


0.631

n

2V

U


For unit mass flow of air, the theoretical torque which isFor unit mass flow of air, the theoretical torque which is aapplied to the impeller : pplied to the impeller :

(theoretical torque/ (theoretical torque/ ṁṁ)) == VVθθ22rr22

Thus the work done on the air :Thus the work done on the air :

(W(Wdonedone))theortheor = V= Vθθ22rr22ΩΩ = V = Vθθ22U = U = σσUU22

Due to friction between the casing and the air carriedDue to friction between the casing and the air carried around by the vanes, and other losses which have a around by the vanes, and other losses which have a braking effect such as disc friction or braking effect such as disc friction or "windage“"windage“ ;;

the applied torque and therefore the actual work inputthe applied torque and therefore the actual work input is is greater than this theoretical value.greater than this theoretical value.



A A power input factorpower input factor ""ψψ" can be introduced to take " can be introduced to take account of this, so that the actual work done on the air account of this, so that the actual work done on the air becomesbecomes

Work done = Work done = ψψ σσ UU22

ψ ψ = 1.03 = 1.03 1.04 (typical value) 1.04 (typical value)

For an isentropic efficiency of For an isentropic efficiency of ηηcc;;

(T(T0303-T-T0101) = (T’) = (T’0303-T-T0101)/ )/ ηηcc


2

03 01 02 ap

UT T T T

C


Overall pressure ratio; Overall pressure ratio;

So:So:

ψψ and and σσ are neither independent of one another are neither independent of one another nor of nor of ηηcc

ψψ ⇨⇨ frictional loss frictional loss ⇨⇨ degraded into thermal degraded into thermal energy energy ⇨⇨ net effect is an increase in outlet T. net effect is an increase in outlet T.

ψψ decrease decrease ⇨⇨ ηη increase increase


1 103 03 03 01

01 01 01

1P T T T

P T T

2 103

01 01

1 c

p

P U

P T C


σσ should be as large as possible. It is limited since the should be as large as possible. It is limited since the number of vanes (n) is limited.number of vanes (n) is limited.

As n increases the solidity of the impeller eye increases, As n increases the solidity of the impeller eye increases, the effective flow area decreases, which causes an the effective flow area decreases, which causes an increase in frictioanal losses. increase in frictioanal losses.

So a suitable compromise must be found, and the So a suitable compromise must be found, and the present day practice is to use the number of vanes present day practice is to use the number of vanes which will give a slip factor of about 0.9.which will give a slip factor of about 0.9.

The other factor that influence the pressure ratio are the The other factor that influence the pressure ratio are the tip speed tip speed UU and the inlet temperature T and the inlet temperature T0101..

TT0101 depends on ambient conditions. depends on ambient conditions.



Centrifugal stresses in a rotating disc are proportional to Centrifugal stresses in a rotating disc are proportional to the square of rim speed.the square of rim speed.

For a single sides impeller of light alloy, U is limited to For a single sides impeller of light alloy, U is limited to about 460 m/s by the maximum allowable centrifugal about 460 m/s by the maximum allowable centrifugal stresses. Such a speed yields a pressure ratio of 4:1stresses. Such a speed yields a pressure ratio of 4:1..

Higher compression ratios mean more expensive Higher compression ratios mean more expensive materials such as titanium alloys.materials such as titanium alloys.



The problem of designing an efficient combustion The problem of designing an efficient combustion system is eased, if the velocity of the air entering system is eased, if the velocity of the air entering the combustion chamber is low.the combustion chamber is low.

It is therefore necessary to design the diffuser so It is therefore necessary to design the diffuser so that only a small part of the stagnation that only a small part of the stagnation temperature at the compressor outlet corresponds temperature at the compressor outlet corresponds to kinetic energy.to kinetic energy.

It is much more difficult to arrange for an efficient It is much more difficult to arrange for an efficient decdeceeleration of flow than an efficient acceleration. leration of flow than an efficient acceleration.

4.3. THE DIFFUSER


There is a natural tendency in a diffusing process, for air to There is a natural tendency in a diffusing process, for air to breakaway from the walls of the diverging passage, reverse breakaway from the walls of the diverging passage, reverse its direction and flow back in the direction of pressure its direction and flow back in the direction of pressure gradient.gradient.

If the divergence is too rapid, this may result in the If the divergence is too rapid, this may result in the formation of eddies with consequent transfer of some KE formation of eddies with consequent transfer of some KE into interinto internnal energy and a reduction in useful pressure rise.al energy and a reduction in useful pressure rise.

Experiments have showExperiments have shownn that the maximum permissible that the maximum permissible included angle of divergence of a rectangular channel with included angle of divergence of a rectangular channel with one pair of sides diverging is about one pair of sides diverging is about 11o. At angles greater At angles greater than this, the losses increase sharply.than this, the losses increase sharply.

4.3. THE DIFFUSER


Diffusing flows (declerating)Diffusing flows (declerating)

Expanding Flows (Accelerating)Expanding Flows (Accelerating)

The angle of the diffuser vanes at the leading edge must The angle of the diffuser vanes at the leading edge must be designed to suit the direction of absolute velocity of be designed to suit the direction of absolute velocity of the air at the radius of the leading edge, so that the air the air at the radius of the leading edge, so that the air will follow smoothly over the vanes.will follow smoothly over the vanes.

As there is always a radial gap between the impeller tip As there is always a radial gap between the impeller tip and the leading edges of the vanes, this direction will and the leading edges of the vanes, this direction will not be that the air leaves the impeller tip.not be that the air leaves the impeller tip.

4.3. THE DIFFUSER


To find the correct inlet angle for the diffuser vanes, theTo find the correct inlet angle for the diffuser vanes, the flow in the flow in the vaneless spacevaneless space must be considered. must be considered.

After the air leaves the impeller (neglecting friction)After the air leaves the impeller (neglecting friction)

AAnngular Momentum = Vgular Momentum = V r = constr = constantant

"in the vaneless Space“"in the vaneless Space“

VV decrease decreasess from the impeller tip to diffuser vane from the impeller tip to diffuser vaness

((asas r increase)r increase)

In accordance with the eqIn accordance with the equatiouation of continuityn of continuity;;

VVrr decrease decreasess with with the the increaseincrease in in r r..

The Net resultThe Net result :: V decrease V decreasess with increas with increasing ing rr..

4.3. THE DIFFUSER


When VWhen Vrr and V and V have been calculated at the radius of have been calculated at the radius of

the leading edges of diffuser vanes, then the direction of the leading edges of diffuser vanes, then the direction of the resultant velocity " V " can be found, hence the inlet the resultant velocity " V " can be found, hence the inlet angle of the vanes.angle of the vanes.

Once the Once the Number of VanesNumber of Vanes and the depth of the and the depth of the passage have been decided uponpassage have been decided upon,, the the throat width throat width can can be calculated to suit the mass flow required under given be calculated to suit the mass flow required under given conditions of T and P. conditions of T and P.

The Length of the Diffuser passages will be determined The Length of the Diffuser passages will be determined by by the maximum permissible the maximum permissible angleangle of divergence of divergence and the amount of diffusion required.and the amount of diffusion required.

4.3. THE DIFFUSER


After leaving the diffuser vanes, the air may be passed into After leaving the diffuser vanes, the air may be passed into a a VoluteVolute and hence to a single C and hence to a single Combustion ombustion CChamber hamber ""CCCC". For aircraft GT, each (or few) diffuser passage can ". For aircraft GT, each (or few) diffuser passage can be connected to a seperate "CC", or the stream could be be connected to a seperate "CC", or the stream could be fed fed iinto an "annular CC" surrounding the shaft connecting nto an "annular CC" surrounding the shaft connecting the Turbine compressor.the Turbine compressor.

4.3. THE DIFFUSER

Aθ

C.G.

_r

θ


We know that a breakdown of flow and excessive We know that a breakdown of flow and excessive pressure loss can be incurred if the velocity of a pressure loss can be incurred if the velocity of a compressible fluid relative to the surface over which it is compressible fluid relative to the surface over which it is moving reaches the moving reaches the speed of soundspeed of sound in the fluid. in the fluid.

When effort is made to obtain the maximum possible When effort is made to obtain the maximum possible mass flow from the smallest possible compressor (as in mass flow from the smallest possible compressor (as in aircraft practice), the air speeds are very high. It is of the aircraft practice), the air speeds are very high. It is of the utmost importance that the Mach numbers at certain utmost importance that the Mach numbers at certain points in the flow do not exceed the value beyond which points in the flow do not exceed the value beyond which the losses increase rapidly due to the formation of shock the losses increase rapidly due to the formation of shock waves.waves.

4.4. COMPRESSIBILITY EFFECTS


The The ““critical Mach numbercritical Mach number”” is usually less than unity is usually less than unity when calculated on the basis of the mean velocity of the when calculated on the basis of the mean velocity of the fluid relative to the boundary because the actual relative fluid relative to the boundary because the actual relative velocity near the surface of a curved boundary may be velocity near the surface of a curved boundary may be in access of the mean velocity. As a general rule, unless in access of the mean velocity. As a general rule, unless tests indicate otherwise, The Mach numbers are tests indicate otherwise, The Mach numbers are restricted to restricted to aabout bout 0.80.8..

At the intakeAt the intake,, the air is deflected through a certain angle the air is deflected through a certain angle before it passes into the radial channels on the impeller. before it passes into the radial channels on the impeller. There is always a tendency for the air to break away There is always a tendency for the air to break away from the convex face of the curved part of the impeller from the convex face of the curved part of the impeller vane. Here then is a point at which the Mach number vane. Here then is a point at which the Mach number will be extremely important.will be extremely important.



The Mach number is given byThe Mach number is given by::

Where TWhere T11 is the static temperature at the inlet. is the static temperature at the inlet.

4.4. COMPRESSIBILITY EFFECTS 1

1

1

WM

RT

W1

Breakaway commencing at rear shockwave



Fixed inlet guide vane

W1 V1

U1

V1

W1

Va1W1’

Angle of prewhirl


It is possible to reduce the relative velocity It is possible to reduce the relative velocity ww11 and hence and hence

the Mach number by introducing Prewhirl at the intake.the Mach number by introducing Prewhirl at the intake. This is achieved by allowing the air be drawn into the This is achieved by allowing the air be drawn into the

impeller eye over curved IGV's attached to the impeller eye over curved IGV's attached to the compressor casing, For the same axial velocity and compressor casing, For the same axial velocity and hence approximately the same mass flow, the relative hence approximately the same mass flow, the relative velocity is reduced as shown by the modified Velvelocity is reduced as shown by the modified Velocity ocity ..

This method of reducing Mach number, unfortunately This method of reducing Mach number, unfortunately reduces the work capacity of the compressor. reduces the work capacity of the compressor.



The air now has an initial whirl component VThe air now has an initial whirl component V11 so that, the so that, the

rate of change of angular momentum perrate of change of angular momentum per unit mass flow is unit mass flow is ::

H = VH = V22rr2 2 - V- V11rr11 if if VV11 is constant over the impeller eye.is constant over the impeller eye.

But the Mach number is only high at the tip of the eye. It is But the Mach number is only high at the tip of the eye. It is clearly preferable to vary the prewhirl, gradually reducing clearly preferable to vary the prewhirl, gradually reducing it from a maximum value at the tip, to zero at the root of it from a maximum value at the tip, to zero at the root of the eye. This may be done if the IGV are suitably twistedthe eye. This may be done if the IGV are suitably twisted..



Impeller Exit: Impeller Exit: It has been found that, as long as the radial velocity It has been found that, as long as the radial velocity

component is subsonic, component is subsonic, Mach numbers greater than 1Mach numbers greater than 1 can be used at the impeller without loss of efficiency.can be used at the impeller without loss of efficiency.

It appears that It appears that supersuperssonic diffusion can occur onic diffusion can occur without the formation of shock waves if it is carried without the formation of shock waves if it is carried out at constant angular momentum with vortex out at constant angular momentum with vortex motion in the vaneless space.motion in the vaneless space.

But if the Mach number at the leading edge of the But if the Mach number at the leading edge of the diffuser vanes are rather high, and it would probably be diffuser vanes are rather high, and it would probably be advisable to advisable to increase the radial wiincrease the radial widtdth of the h of the VANELESS SPACEVANELESS SPACE or the depth of the diffuser or the depth of the diffuser to to reduce the velocity at that radiusreduce the velocity at that radius..



HighHigh MM (at the (at the leadleadinging edge diffuse edge diffuser)r) is not desirable is not desirable because of air resonance considerations.because of air resonance considerations.

Static pressure differences around the circumference Static pressure differences around the circumference from due to locally high pressures at stagnation points. from due to locally high pressures at stagnation points. The danger is the instability created convectThe danger is the instability created convectss upstream upstream causing mechanical danger as well as spoiling the flow. causing mechanical danger as well as spoiling the flow. To take care of this the # of impeller vanes and diffuser To take care of this the # of impeller vanes and diffuser channels are selected properly.channels are selected properly.

Exciting frequency Exciting frequency ff [rpm [rpm,,# imp# impeller vanes eller vanes // # diffuser # diffuser vanesvanes] ] == aa natural frequency of impeller channels . natural frequency of impeller channels .

# diffuser channels are selected to be prime number# diffuser channels are selected to be prime number# impeller# impeller vanes vanes selected to be even number selected to be even number



As a result:As a result:

The Vaneless space bothThe Vaneless space both Decreases the danger of shock lossesDecreases the danger of shock losses Decrease the danger of excessive variations in static Decrease the danger of excessive variations in static

pressure due to Highpressure due to Higher Mer M near the impeller tip. near the impeller tip.







The performance of a compressor may be specified by The performance of a compressor may be specified by curves of delivery pressure and temperature (as a curves of delivery pressure and temperature (as a measure energy transfer) against mass flow for various measure energy transfer) against mass flow for various fixed values of rotational speeds. fixed values of rotational speeds.

These characteristics These characteristics ((¢¢)), however are dependent on , however are dependent on other variables such as conditions of pressure and other variables such as conditions of pressure and temperature at the entry of the compressor, and the temperature at the entry of the compressor, and the physical properties of the working medium. physical properties of the working medium.

Any attempt to allow for full variations of all these Any attempt to allow for full variations of all these quantities over the working range would involve an quantities over the working range would involve an excessive number of experiments, and make concise excessive number of experiments, and make concise presentation of the results impossible. presentation of the results impossible.

4.6. COMPRESSOR CHARACTERISTICS



Most of this complication may be eliminated by using the Most of this complication may be eliminated by using the technique of technique of ““Dimensional AnalysisDimensional Analysis”” by which the by which the variables involved may be combined to form a smaller variables involved may be combined to form a smaller number of more managable number of more managable "Dimensionless Groups“"Dimensionless Groups“

By Dimensional analysis the following groups may be By Dimensional analysis the following groups may be formedformed

0102 022

01 01 01 01

...,.. ...,... ...,..R TP T N D

mP T D P R T


When we are concerned with the performance of a When we are concerned with the performance of a machine of machine of Fixed SizeFixed Size, compressing a , compressing a Specified Gas, Specified Gas, RR and and DD in the above groups may be o in the above groups may be ommitted from the itted from the groups, Leaving Dimensional Groups such thatgroups, Leaving Dimensional Groups such that

If these are the variables affecting the performance, it is If these are the variables affecting the performance, it is only necessary to plot two sets of curves in order to only necessary to plot two sets of curves in order to describe the performance of a compressor (at a fixed describe the performance of a compressor (at a fixed speed) completely.speed) completely.


0102 02

01 01 01 01

...,.. ...,... ...,..TP T N

mP T P T


PP0202 /P /P0101 plotted plotted vsvs for fixed values of for fixed values of

TT0202/T/T0101 plotted plotted vs vs for fixed values offor fixed values of

from these 2 sets curves it is possible to construct from these 2 sets curves it is possible to construct isentropic efficiency isentropic efficiency curves at curves at constant speedconstant speed..


01

01

TmP

01

N

T

1

02 0102 01

02 01 02 01

/ 1

/ 1

P PT T

T T T T

01

01

TmP

01

N

T



2

5

4

3

1

0.6 0.8 1.0 1.20.40.20

0.6

0.8

0.7

1.0

0.9

Pressure Ratiopo2/po1

m√To1/po1

N/√To1

Relative toDesign Value

Surge Line

Locus of Points of Maximum Efficiency



2

5

4

3

1

0.6 0.8 1.0 1.20.40.20

Isentropic efficiencyηc %

m√To1/po1 (relative to design value)

0.6 0.7 0.8 0.9 1.0

N√To1/po1 (relative to design value)



CConsider what might be expected to occur when a valve onsider what might be expected to occur when a valve placed at the delivery line slowly operated. placed at the delivery line slowly operated.

TheoreticallyTheoreticallyA A :: Valve is shut; m =0; Valve is shut; m =0;

PP0202/P/P0101 pressure head (for the air trapped) pressure head (for the air trapped)B B :: and P and P0202/P/P0101 is maximum is maximum C C :: All the power is absorbed in overcoming internal friction All the power is absorbed in overcoming internal friction

resistance (hypothetical case)resistance (hypothetical case)In Actual CaseIn Actual Case

Point A could be obtained if desired but most of the curve Point A could be obtained if desired but most of the curve between A and B could not, owing to the phenomenbetween A and B could not, owing to the phenomenonon of of SURGINGSURGING..



Mass flow

Pre

ssu

re r

atio

A

DB

E

C0

1

Constantspeed curve

Theoretical Characteristics


SurgingSurging is associated with a sudden drop in delivery is associated with a sudden drop in delivery pressure and with violent aerodynamic pulsations which pressure and with violent aerodynamic pulsations which are transmitted throughout the whole machine.are transmitted throughout the whole machine.

If we suppose that the compressor is operating at some If we suppose that the compressor is operating at some point D onpoint D on the positive sloped part of the ¢ , then a the positive sloped part of the ¢ , then a decrease in mass flow will be accompanied by a fall in decrease in mass flow will be accompanied by a fall in delivery pressure.delivery pressure.

If the pressure of air downstream of the compressor If the pressure of air downstream of the compressor does not fall quickly enough the air will tend to reverse does not fall quickly enough the air will tend to reverse its direction and flow back in the direction of resulting its direction and flow back in the direction of resulting pressure gradient.pressure gradient.



When this occurs, the pressure ratio PWhen this occurs, the pressure ratio P0202/P/P0101 drops drops

rapidly. Meanwhile the pressure downstream of the rapidly. Meanwhile the pressure downstream of the compressor has fallen ascompressor has fallen as well, so that the compressor well, so that the compressor will now be able to pick up again to repeat the cycle of will now be able to pick up again to repeat the cycle of events which occur at high (!) frequency.events which occur at high (!) frequency.

RotatRotatiing Stallng Stall:: When there is any non-uniformity in the When there is any non-uniformity in the flow or geometry of the channels between blades or flow or geometry of the channels between blades or vanes, a breakdown in the flow in one channel (say vanes, a breakdown in the flow in one channel (say BB), ), cause the air to be deflected in such a way that channel cause the air to be deflected in such a way that channel CC receives fluid at a reduced angle of incidence. receives fluid at a reduced angle of incidence.



Channel Channel AA then stalls (air flow reduces) resulting in a then stalls (air flow reduces) resulting in a reduction of incidence to channel reduction of incidence to channel BB enabling the flow in enabling the flow in that channel to recover.that channel to recover.

Thus the stall propagates in a direction opposite to the Thus the stall propagates in a direction opposite to the blade rotation relative to the bblade rotation relative to the bllades, from channel to ades, from channel to channelchannel..

This results in aerodynamic vibrationsThis results in aerodynamic vibrations →→ fatigue failure. fatigue failure. PPassage blockage assage blockage →→ Loss of performance Loss of performance





Choking:Choking: On On theoretical ¢ curve, actually point theoretical ¢ curve, actually point CC can can not be reached, since some where beyond point not be reached, since some where beyond point EE the the flow will be flow will be choked.choked. ( (ii.e. maximum possible flow rate..e. maximum possible flow rate.))

The temperature ratio The temperature ratio ccurve will be similar to the one urve will be similar to the one for-pressure ratio sincefor-pressure ratio since

From PFrom P0202/P/P0101 and and TT0202//TT0101 one can plot one can plot c c vsvs


02 02

01 01

( , )cT P

fT P

01

01

m T

P


In some casesIn some cases equivalenequivalentt flow flow

and equivalenand equivalentt speed speed

are employed instead of the above are employed instead of the above

Here:Here:

GenerallyGenerally: : T Trefref = 288 = 288ooK PK Prefref = 1.013 bar = 1.013 bar (ISA) (ISA)


m

N

01 01,ref ref

T P

T P


Similar to compressor ¢ Turbine performance is Similar to compressor ¢ Turbine performance is expressed in terms of similar dimensionless (or expressed in terms of similar dimensionless (or dimensional) groupsdimensional) groups

Turbine performance is plots are given by plottingTurbine performance is plots are given by plotting

vs for variousvs for various

TURBINE CHARACTERISTICS

0303

04 03 03

, , ,m TP N

P P T

03

03

&m T

P

03

04

P

P 03

N

T


The efficiency plot is constant over a wide range of N and The efficiency plot is constant over a wide range of N and RT. This is because of the accelerating flow through the RT. This is because of the accelerating flow through the turbine bladturbine bladeses permit an operation over a wide range of permit an operation over a wide range of incidence without much loss.incidence without much loss.

The maximum The maximum corresponds to a corresponds to a choking condition at the existing pchoking condition at the existing prressure ratio. This essure ratio. This

choking might occur in the NGV nozzle (or sometimes at the choking might occur in the NGV nozzle (or sometimes at the outlet of the turbine depending on the design).outlet of the turbine depending on the design).

Even Even when when unchoked, the constant unchoked, the constant curves do curves do

not seperate very much. Especially for multistage turbinenot seperate very much. Especially for multistage turbines, s,

the the curves converge to a single one.curves converge to a single one.

This is very important esThis is very important esppecially for ecially for the the part load part load pperferformanceormance of a of a gas turbinegas turbine..


03 03/m T P

03/N T

03/N T




A centrifugal compressor which is fitted to an aircraft has A centrifugal compressor which is fitted to an aircraft has the following data;the following data;

Mass flow rate of airMass flow rate of air :: 6 kg/s6 kg/s Rotational speedRotational speed :: 15000 15000

rpmrpm Total pressure ratioTotal pressure ratio :: 4.04.0 Slip factor (σ)Slip factor (σ) :: 0.90.9 Power input factorPower input factor :: 1.041.04 Isentropic efficiencyIsentropic efficiency :: 0.820.82 Inner radius of impeller eyeInner radius of impeller eye :: 8 cm8 cm Outer radius of impeller eyeOuter radius of impeller eye :: 16 cm16 cm

Problem on Centrifugal Compressors


Ambient conditionsAmbient conditionsPPaa :: 0.3565 bar0.3565 bar

TTaa :: 236 K236 K Forward speed of the aircraftForward speed of the aircraft :: 240 m/s240 m/s Inlet prewhirl(constant for all radii)Inlet prewhirl(constant for all radii) :: 303000 At the impeller exit blades are straight βAt the impeller exit blades are straight β2v2v= 90= 9000 FIND:FIND:a) a) Maximum Mach No at the impeller inletMaximum Mach No at the impeller inletb) b) Maximum Mach No at the impeller inlet for no prewhirl.Maximum Mach No at the impeller inlet for no prewhirl. For both a and b sketch velocity trianglesFor both a and b sketch velocity trianglesc) c) The diameter of the impellerThe diameter of the impeller



d) d) Assume that meridional velocity is constant throughout Assume that meridional velocity is constant throughout the impeller,the impeller,

VVm1m1= V= Vm2m2 VVa1a1= V= Vr2r2

Find the impeller exit width bFind the impeller exit width b22, sketch velocity triangles., sketch velocity triangles.

e) e) If the diffuser inlet radius rIf the diffuser inlet radius r33= 1.2r= 1.2r22 and the width of the and the width of the vaneless space at the diffuser inlet is 2mm in excess of vaneless space at the diffuser inlet is 2mm in excess of impeller exit width, find the diffuser inlet Mach No.impeller exit width, find the diffuser inlet Mach No.



Solution :

b2

r2

b3

r1h

r1t

1

2

3

a)

2 2

01

240236 265

2 2010ac

ap

VT T K

c

/ 1 3.5

01 01 2651.5

236

k k

a a

P T

P T


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Documents

ME 423 Chapter 4 Centrifugal Compressors Prof. Dr. O. Cahit ERALP