ME 423 ME 423 Chapter 5 Chapter 5 Axial Flow Compressors Axial Flow Compressors Prof. Dr. O. Cahit ERALP Prof. Dr. O. Cahit ERALP
Jan 11, 2016
ME 423ME 423
Chapter 5Chapter 5Axial Flow CompressorsAxial Flow Compressors
Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Subsonic compressorsSubsonic compressors will be considered here as will be considered here as supersonic compressors have not proceeded beyond supersonic compressors have not proceeded beyond experimental stage.experimental stage.
A Comparison ofA Comparison of
Axial Flow Axial Flow CCompressors and Turbinesompressors and Turbines
TurbineTurbine :-:- Accelerating flow - Successive pressure drops Accelerating flow - Successive pressure drops and consequent reductions in enthalpy being converted and consequent reductions in enthalpy being converted into kinetic energy into kinetic energy
A1>A2 A1>A2 ⇨⇨ converging passages converging passages
Chapter 5 Axial Flow Compressors
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Axial Flow CompressorsAxial Flow Compressors
A Comparison ofA Comparison of Axial Flow Compressors and TurbinesAxial Flow Compressors and Turbines
Compressor :-Compressor :- Decelerating flow - Pressure rises are Decelerating flow - Pressure rises are obtained through successive stages of diffusing obtained through successive stages of diffusing passages with consequent reduction in velocity. passages with consequent reduction in velocity.
A1<A2 A1<A2 ⇨⇨ diverging passages diverging passages PProblems of compressors & turbines are differentroblems of compressors & turbines are different
in in compressorscompressors - aerodynamic problems - aerodynamic problems
in in turbines turbines - problems due to entry temperature and - problems due to entry temperature and heat-transfer.heat-transfer.
Boundary Layers -Boundary Layers - regions of low momentum air where regions of low momentum air where viscous effects dviscous effects doominate over inertial effects.minate over inertial effects.
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Axial Flow CompressorsAxial Flow Compressors
A Comparison ofA Comparison of Axial Flow Compressors and TurbinesAxial Flow Compressors and Turbines
Boundary layers are far less happy in a compressive flowBoundary layers are far less happy in a compressive flow.. BL in a compressor operate in an unfavourable pressure BL in a compressor operate in an unfavourable pressure gradient [(+) 've ; p increase ]gradient [(+) 've ; p increase ]
BL in a turbine operate in a favourable pressure gradientBL in a turbine operate in a favourable pressure gradient [ [ (-)'ve ; p decrease. ](-)'ve ; p decrease. ]
This is the reason why a single stage turbine can create This is the reason why a single stage turbine can create enough power to drive a number of stages of compressor.enough power to drive a number of stages of compressor.
Bend thin plates and stick them behind each other forming Bend thin plates and stick them behind each other forming a stationary a stationary cascade of bladescascade of blades..
Let the flow be directed towards the inletLet the flow be directed towards the inlet ofof this this cascade cascade of bladesof blades without any without any incidenceincidence..
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Axial Flow CompressorsAxial Flow Compressors
A Comparison ofA Comparison of Axial Flow Compressors and TurbinesAxial Flow Compressors and Turbines
As As AA22 > A > A11 in subsonic flow (incompressible) in subsonic flow (incompressible)
WW22 < W < W11 && PP22 > P > P11
This is no more than a subsonic diffuser This is no more than a subsonic diffuser
To carryTo carry a mechanical load a mechanical load,, somesome thickness is required. thickness is required.
If M < 0.3 If M < 0.3 incompressible incompressible
i.e. i.e. thus thus
1 2
P W P W2 22
1 121
212
P0 0 2
2
2
112 2
1WWPP ..
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Axial Flow CompressorsAxial Flow Compressors
A Comparison ofA Comparison of Axial Flow Compressors and TurbinesAxial Flow Compressors and Turbines
Clearly the outlet velocity WClearly the outlet velocity W22 cannot decrease beyond a cannot decrease beyond a certain level (cannot be zero)certain level (cannot be zero) (or W (or W22 ≠≠ 0) 0)
p Wp W1122 (since W (since W22 is fixed by the lower limit) is fixed by the lower limit)
One should design the compressor at the highest inlet One should design the compressor at the highest inlet velocity velocity
But the But the losses losses ⇨⇨ PPoo αα W W1122
αα 1/ 1/ pp
Stage pressure ratio is limited and the number of stages Stage pressure ratio is limited and the number of stages are determined accordinglyare determined accordingly (single stage or multistage)(single stage or multistage)
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Axial Flow CompressorsAxial Flow Compressors
A Comparison ofA Comparison of Axial Flow Compressors and TurbinesAxial Flow Compressors and Turbines
Due to the contractionDue to the contraction,, the flow initially accelerates the flow initially accelerates pressure drops (favourable to BL)pressure drops (favourable to BL) ( A( A11 > A > A11' )' )
then then
The amount of pressure rise between 1' to 2 is larger The amount of pressure rise between 1' to 2 is larger than that of 1 to 2than that of 1 to 2..
i.e more diffusion the limit of Wi.e more diffusion the limit of Wmaxmax is than of sonic limit. is than of sonic limit.
More diffusion means less efficiencyMore diffusion means less efficiency i.e why we prefer compressor bi.e why we prefer compressor bllades ades to be to be as thin as as thin as possible.possible.
W
W
W
Wmax
2
1
2
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Axial Flow CompressorsAxial Flow Compressors
A Comparison ofA Comparison of Axial Flow Compressors and TurbinesAxial Flow Compressors and Turbines
The more the (camber)The more the (camber),, the more is the adverse pressure the more is the adverse pressure gradientgradient,, then seperation occurs earlier. then seperation occurs earlier.
The sepThe sepeerraated flow leaves the blade at an unwanted ted flow leaves the blade at an unwanted angle and unsteady situation.angle and unsteady situation.
All these problems in compressor cascades are due to All these problems in compressor cascades are due to Boundary layers.Boundary layers.
TurbineTurbine problems are completely different since we want problems are completely different since we want the pressure to drop along the flow direction.the pressure to drop along the flow direction.
The flow is a high "h" enthalpy or high temperature, high The flow is a high "h" enthalpy or high temperature, high pressure (to low T low P) flow. pressure (to low T low P) flow.
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Axial Flow CompressorsAxial Flow Compressors
A Comparison ofA Comparison of Axial Flow Compressors and TurbinesAxial Flow Compressors and Turbines
The blades are such that minimum c/s area occurs at the The blades are such that minimum c/s area occurs at the trailing edge of the blades trailing edge of the blades which is which is called the throat.called the throat.
The flow area should contract continuously all the way The flow area should contract continuously all the way along the balong the bllades in order not to have an adverse ades in order not to have an adverse pressure gradient BL along the row. pressure gradient BL along the row.
Even an instantaneous discontinuity in the contraction of Even an instantaneous discontinuity in the contraction of the passage results in a locally seperated BL, thus the passage results in a locally seperated BL, thus increased turbulence. increased turbulence.
This might happen due to simplified manufacture for This might happen due to simplified manufacture for curvatures such as two circles.curvatures such as two circles.
This results in extremely high heat transfer coefficientThis results in extremely high heat transfer coefficient, , thus the blade will not last 10 minutes. thus the blade will not last 10 minutes.
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Axial Flow CompressorsAxial Flow Compressors
A Comparison ofA Comparison of Axial Flow Compressors and TurbinesAxial Flow Compressors and Turbines
For the For the Axial Compressors and turbines Axial Compressors and turbines the basic the basic components are components are rotors and statorsrotors and stators, the former carrying , the former carrying the rotating blades and the latter the stationary rows the rotating blades and the latter the stationary rows which serve to recover the pressure rise from the kinetic which serve to recover the pressure rise from the kinetic energy imparted to the fluid by the rotor blades as in energy imparted to the fluid by the rotor blades as in compressors and/or to redirect the flow into an angle compressors and/or to redirect the flow into an angle suitable for entry to the next row of moving blades.suitable for entry to the next row of moving blades.
A A compressor stagecompressor stage is composed of a is composed of a rotor followed rotor followed by a statorby a stator, where as a , where as a turbine stageturbine stage is composed of is composed of a a stator followed by a rotor .stator followed by a rotor .
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
A Comparison ofA Comparison of Axial Flow Compressors and TurbinesAxial Flow Compressors and Turbines
In CompressorsIn Compressors
It is usual to provide a row of stator blades –It is usual to provide a row of stator blades –Inlet Guide Inlet Guide Vanes (IGV's)Vanes (IGV's) at the upstream of the first stage. These at the upstream of the first stage. These direct the axially approaching flow correctly into the first direct the axially approaching flow correctly into the first row of rotor blades. Thus deflect the flow from axial row of rotor blades. Thus deflect the flow from axial direction to off-axial direction. IGV's are turbine type of direction to off-axial direction. IGV's are turbine type of blades.blades.
Two forms of Two forms of rotor constructionrotor construction is used is used
Drum typeDrum type-suitable for industrial applications-suitable for industrial applications
Disc typeDisc type - suitable for aircraft applications low weight, - suitable for aircraft applications low weight, high cost)high cost)
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Axial Flow CompressorsAxial Flow Compressors
A Comparison ofA Comparison of Axial Flow Compressors and TurbinesAxial Flow Compressors and Turbines
Another important constructional detail is the contraction Another important constructional detail is the contraction of the flow annulus from the low the high pressure end of of the flow annulus from the low the high pressure end of the compressor. the compressor.
This is necessary to maintain a reasonably constant axial This is necessary to maintain a reasonably constant axial velocity along. most compressors are designed on the velocity along. most compressors are designed on the basis of constbasis of constantant axial velocity because of the axial velocity because of the simplsimpliification in design procedure. One could have a fication in design procedure. One could have a rising hub or rising hub or a a falling shroud in compressors.falling shroud in compressors.
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Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
Basic principle : Acceleration of the working fluid followed Basic principle : Acceleration of the working fluid followed by diffusion to convert the acquired kinetic energy into a by diffusion to convert the acquired kinetic energy into a pressure rise. pressure rise.
The flow is considered as occuring in the tangential plane The flow is considered as occuring in the tangential plane at the mean blade height where the blade peripheral at the mean blade height where the blade peripheral velocity is u.velocity is u.
When the annulus is unrolled, since the blade C/S When the annulus is unrolled, since the blade C/S changes from Hub to Tip, one C/S is chosen changes from Hub to Tip, one C/S is chosen (e(e..gg.. at mid blade height) at mid blade height) and a series of constant C/S aerofoils result.and a series of constant C/S aerofoils result.
These are called a These are called a 2-D cascade of aerofoils2-D cascade of aerofoils..
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Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
A semi-A semi- cascade can be produced if the cascade end cascade can be produced if the cascade end boundary effects are eliminated (The flow in the channels boundary effects are eliminated (The flow in the channels are not aware of what happens at the ends)are not aware of what happens at the ends)
TheThe aerodynamics of a cascade repeat aerodynamics of a cascade repeatss itself with a itself with a periodicity of periodicity of ss (pitch). (pitch).
As the flow is going through the cascade, the end wall BL As the flow is going through the cascade, the end wall BL grows in thickness, thus the axial velocity grows.grows in thickness, thus the axial velocity grows.
TTo take care of thiso take care of this,, BL BL is is sucksucked;ed; or a large " or a large "Aspect RatioAspect Ratio" " cascade where the effect of end wall BL is less observedcascade where the effect of end wall BL is less observed, is used, is used.. v-absolute velocity v-absolute velocity w-relative velocity w-relative velocity u- peripheral blade velocityu- peripheral blade velocity
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Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
On the rotor, turn your head into the wind, and the On the rotor, turn your head into the wind, and the drought you feel is the relative velocity drought you feel is the relative velocity ww
Connect the absolute velocity vectors (Connect the absolute velocity vectors (u and vu and v) together ) together arrow-head to arrow-head, the tails became the relative arrow-head to arrow-head, the tails became the relative velocity vector (velocity vector (ww) )
WW22< W< W11 PP22 > P > P11 across the rotor across the rotor
across the statoracross the statorV V V1 3 2 P P3 2
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Axial Flow CompressorsAxial Flow Compressors
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Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
From the velocity trianglesFrom the velocity trianglesU/VU/Vaa= tan = tan 11 + tan + tan 11 (5.1)(5.1)U/VU/Vaa= tan = tan 22 + tan + tan 22 (5.2)(5.2)
The axial velocity VThe axial velocity Vaa is assumed to be constant throughout is assumed to be constant throughout the stage.the stage.
The work absorbed by the stage, from the consideration of The work absorbed by the stage, from the consideration of the"the"change of angular momentumchange of angular momentum", in terms of work done ", in terms of work done per unit mass flow rate or specific work input isper unit mass flow rate or specific work input is::
(5.3 , 5.4)(5.3 , 5.4)
oror (5.5)(5.5)
W U V V UVa.
( ) (tan tan ) 2 1 2 1
V U W U Va 2 2 2 tan
W UVa.
(tan tan ) 1 2
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Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
Vθ2 – Vθ1
Vθ2
Vθ1U
Va
exit
W2
V1
inletβ1 α1
V2
α2
β2
Combined Velocity Triangle for Axial Compressor Stage
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Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
The The input energyinput energy is absorbed is absorbed usefully tousefully to increase p increase p and vand v and and waste fully to increase Twaste fully to increase T (frictional losses) (frictional losses)
regardless of losses (efficiency)regardless of losses (efficiency) the whole input = the whole input = TTosos
If VIf V11 = V = V33
(5.6)(5.6)
In actual fact the stage temperature rise will be In actual fact the stage temperature rise will be lessless than than this owing to 3D effects in the compressor annulus this owing to 3D effects in the compressor annulus (growing end wall B/L)(growing end wall B/L)
T TUV
Cos sa
p (tan tan ) 1 2
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Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
Analysis of experimental results has shown that it is Analysis of experimental results has shown that it is necessary to multiply the results given by equation 5.6 by necessary to multiply the results given by equation 5.6 by the so called the so called work done factorwork done factor which is a number < 1 which is a number < 1
λλ = Actual work absorbing capacity /= Actual work absorbing capacity / Ideal work absorbing capacityIdeal work absorbing capacity
The explanation of this is based on the fact that the radial The explanation of this is based on the fact that the radial distribution of axial velocity is not constant across the distribution of axial velocity is not constant across the annulus but becomes increasingly peaky as the flow annulus but becomes increasingly peaky as the flow proceeds as shown in the figure.proceeds as shown in the figure.
From eFrom eqqn. 5.1 :n. 5.1 : VVaa tan tan 11 = U- V = U- Vaatan tan 11
SubstSubstituteitute into 5.5 : into 5.5 :
sincesince 11 & & 11 are fixed are fixed while Vwhile Vaa increase then increase then ww decrease decrease
21 tantan
.
aaVVUUW
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Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
From eFrom eqqn. 5.1 :n. 5.1 : VVaa tan tan 11 = U- V = U- Vaatan tan 11
SubstSubstituteitute into 5.5 : into 5.5 :
sincesince 11 & & 11 are fixed are fixed while Vwhile Vaa increase then increase then ww decrease decrease
21 tantan
.
aaVVUUW
Va Va
Va meanVa mean
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Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
If the compressor has been designed for a constant radial If the compressor has been designed for a constant radial distribution of Vdistribution of Vaa, the effect of an increase in V, the effect of an increase in Vaa in the in the central region will be to reduce the work capacity of central region will be to reduce the work capacity of blading in that area.blading in that area.
This reduction however should be compensated by This reduction however should be compensated by increases in the regions of the root and tip of the blading increases in the regions of the root and tip of the blading because of the reductions in Vbecause of the reductions in Vaa at these parts of the at these parts of the annulus. Unfortunately this is not the case sinceannulus. Unfortunately this is not the case since;; Influence of BL's on the annulus wallsInfluence of BL's on the annulus walls Blade tip clearancesBlade tip clearanceshas an adverse effect on this compensation and the net has an adverse effect on this compensation and the net
result is a loss in total work capresult is a loss in total work capaacity)city)
.W .W = Actual amount of work which can be supplied to = Actual amount of work which can be supplied to the the stage.stage.
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Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Elementary Theory For Axial Flow CompressorsElementary Theory For Axial Flow Compressors
Actual stage temperature rise :Actual stage temperature rise :
The pressure ratio: The pressure ratio:
ss= stage isentropic efficiency= stage isentropic efficiency
TCUVosp
a (tan tan )1 2
1
1
1
o
oss
s T
TR
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Axial Flow CompressorsAxial Flow Compressors
Degree of ReactionDegree of Reaction
== static pressure rise across the rotorstatic pressure rise across the rotor //
/ / static pressurestatic pressure rise across the whole stagerise across the whole stage
It is also a measure of how much of the total pressure It is also a measure of how much of the total pressure rise across the stage occurs in the rotor.rise across the stage occurs in the rotor.
Since CSince Cpp doesn't vary much across a stage, doesn't vary much across a stage, will be will be
equal to the corresponding temperature rises.equal to the corresponding temperature rises.
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Axial Flow CompressorsAxial Flow Compressors
Degree of ReactionDegree of Reaction
TTRR = Temperature rise across the rotor = Temperature rise across the rotor
TTSTST = Temperature rise across the stator = Temperature rise across the stator
TTSS = Stage temp = Stage temp.. Rise Rise
Assuming Assuming =1.0 =1.0
)tan(tan)tan(tan
)(.
1221
aa
spSTRp
UVUV
TCTTCW
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Axial Flow CompressorsAxial Flow Compressors
Degree of ReactionDegree of Reaction
The steady flow energy eqn :The steady flow energy eqn :
with eqn (5.8) :with eqn (5.8) :
ButBut
sincesince
W C T V Vp R
.( )
1
2 22
12
C T UV V Vp R a (tan tan ) ( ) 2 1 22
121
2
V Va2 2 sec V Va1 1 sec
C T UV Vp R a a (tan tan ) (sec sec ) 2 12 2
22
11
2
C T UV Vp R a a (tan tan ) (tan tan ) 2 12 2
22
11
2
sec tan2 2 1
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Axial Flow CompressorsAxial Flow Compressors
Degree of ReactionDegree of Reaction
(5.9)(5.9)
UV V
UV
V
U
a a
a
a(tan tan ) (tan tan )
(tan tan )(tan tan )
2 12 2
22
1
2 12 1
12 1
2
21 2 1 2
U
Va tan tan tan tan
12
21 2
VU
UV
a
a( tan tan )
V
Ua
2 1 2(tan tan )
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Axial Flow CompressorsAxial Flow Compressors
Degree of ReactionDegree of Reaction
For 50% reaction which is a wide practice (For 50% reaction which is a wide practice (=0.50)=0.50)
from eqfrom equatiouations 5.1ns 5.1 & 5.2& 5.2
⇨⇨ 11 == 22 , , 22 == 11
since Vsince V11=V=V33 11 == 33 (for repe (for repeatingating stages) stages)
For For ⇨⇨ symmetrical blading symmetrical blading
11 == 22 == 33 , , 11 == 22
0 502 1 2. (tan tan ) V
Ua tan tan 1 2
U
Vatan tan 1 2 tan tan 1 2
V V Va 1 1 3 3cos cos
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Axial Flow CompressorsAxial Flow Compressors
Degree of ReactionDegree of Reaction
EEqn 5.9 is derived for qn 5.9 is derived for =1=1
Actually Actually will differ from 50% slightly because of the will differ from 50% slightly because of the influence of influence of ;;
but still will be called but still will be called symmetricalsymmetrical blading. blading.
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Axial Flow CompressorsAxial Flow Compressors
33DD Flow Flow
Up to here the analysis has been confined to a 2Up to here the analysis has been confined to a 2DD flow flow basis at one particular radial position in the annulus ; basis at one particular radial position in the annulus ; which is usually chosen to be "at the mean blade height" which is usually chosen to be "at the mean blade height" Before considering its extension to cover the whole blade Before considering its extension to cover the whole blade height , attention must be given to some basic principles height , attention must be given to some basic principles of 3of 3DD flow. flow.
For high H/T ratio For high H/T ratio 2 2DD assumption is reasonable assumption is reasonable
Low H/T ratio Low H/T ratio Radial flow components should be Radial flow components should be considered.considered.
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Axial Flow CompressorsAxial Flow Compressors
33DD Flow Flow
Assumption Assumption Any radial flow within the annulus occurs only while Any radial flow within the annulus occurs only while
the fluid is passing through the blade rows. The flow in the fluid is passing through the blade rows. The flow in the gaps between successive blade rows will be in the gaps between successive blade rows will be in Radial EquilibriumRadial Equilibrium..
Basic Assumption VBasic Assumption V r =0 at the entry and exit of a r =0 at the entry and exit of a blade row.blade row.
A commonly used design method is based on this A commonly used design method is based on this principle and an equation is set up to fulfill the principle and an equation is set up to fulfill the requirement that radial pressure forces must act on requirement that radial pressure forces must act on the air elements in order to provide the necessary the air elements in order to provide the necessary radial acceleration associated with the peripheral radial acceleration associated with the peripheral velocity component Vvelocity component V..
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Axial Flow CompressorsAxial Flow Compressors
33DD Flow Flow
p+dp
p
dθ
r
dr
Vθ
p+dp/2p+dp/2
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Axial Flow CompressorsAxial Flow Compressors
33DD Flow Flow
From the figure the force balance in radial direction i.e From the figure the force balance in radial direction i.e pressure forces = centrifugal forces Vpressure forces = centrifugal forces Vrr =0 =0
Here Here for for small small
Cancelling dq through the eqn and neglecting 2Cancelling dq through the eqn and neglecting 2ndnd orderterms such as dpdr.orderterms such as dpdr.
(Radial Equilibrium Condition)(Radial Equilibrium Condition)
( )( ) ( )p dp r dr d prd pdpdrd
rdrdV
r 2
2 2
2
sin( ) 2 2
1 2
dp
dr
V
r
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Axial Flow CompressorsAxial Flow Compressors
Radial Equilibrium ConditionRadial Equilibrium Condition
The Radial equilibrium equation may be used:The Radial equilibrium equation may be used:
to determine Vto determine Vaa (r) once V (r) once V(r) is chosen(r) is chosen (design or(design or
indirect problem)indirect problem)
to determine Vto determine Vaa (r), V (r), V (r) produced by a selected (r) produced by a selected
blade shape i.e. a (r) (Direct problem)blade shape i.e. a (r) (Direct problem)
The stagnation enthalpy "hThe stagnation enthalpy "h00" at any radius r" at any radius r
sincesince
h hV
C T V Vp a0
22 2
2
1
2 ( )
C TP
p 1
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Axial Flow CompressorsAxial Flow Compressors
Radial Equilibrium ConditionRadial Equilibrium Condition
Differentiating wrt. r we haveDifferentiating wrt. r we have
Lets assume that the change in pressure across the Lets assume that the change in pressure across the annulus is small and the isentropic relation can be used. annulus is small and the isentropic relation can be used.
ii.e .e =const=const.. is valid with little error. is valid with little error.
In differential formIn differential form OROR substituting into the previous relationsubstituting into the previous relation;;
hP
V Va02 2
1
1
2
( )
dhdr
dPdr
P ddr
VdVdr
VdVdra
a021
1
P
ddr
P
0ddr
P
0
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Axial Flow CompressorsAxial Flow Compressors
Radial Equilibrium ConditionRadial Equilibrium Condition
Introducing the Introducing the Radial EquilibriumRadial Equilibrium condition condition
Apart from the regions near the walls of the annulus the Apart from the regions near the walls of the annulus the stagnation enthalpy (and Tstagnation enthalpy (and Too) is uniform across the ) is uniform across the
annulus at the entry to the blade rows.annulus at the entry to the blade rows.
Thus Thus
in any plane between a pair of blade rows.in any plane between a pair of blade rows.
dh
drVdV
drVdV
dr
V
raa0
2
dh
dr0 0
VdV
drVdV
dr
V
raa
2
0
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Axial Flow CompressorsAxial Flow Compressors
Radial Equilibrium ConditionRadial Equilibrium Condition
A special case may now be considered in whichA special case may now be considered in which VVaa=const=const.. is maintained across the annulus, so that is maintained across the annulus, so that
OR OR
Integrating this gives:Integrating this gives: OROR
Thus the whirl velocity component of the flow varies Thus the whirl velocity component of the flow varies inversely with the radius.inversely with the radius.
This is the This is the Free Vortex Free Vortex condition.condition.
dV
dr
V
r
dV
Vdrr
ln lnV r const V r const
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Radial Equilibrium ConditionRadial Equilibrium Condition
The The Free Vortex Radial Equilibrium is Satisfied by:Free Vortex Radial Equilibrium is Satisfied by:
Constant specific work input dhConstant specific work input dhoo/dr = 0/dr = 0
Constant axial velocity at all radii i.e. dVConstant axial velocity at all radii i.e. dVaa/dr =0/dr =0
Free Vortex variation of whirl velocity (VFree Vortex variation of whirl velocity (Vr =const)r =const)
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Radial Equilibrium ConditionRadial Equilibrium Condition
There is no reason why the specific work input should notThere is no reason why the specific work input should not
be varied with radius i.e.be varied with radius i.e. . . It would then be It would then be
necessarynecessary to choose a radial variation of one of the other to choose a radial variation of one of the other variables say Vvariables say Vaa (r) and determine the variation of V (r) and determine the variation of V with with r to satisfy the radial equilibrium. Thus in general a r to satisfy the radial equilibrium. Thus in general a design can be based on arbitrarily choosen radial design can be based on arbitrarily choosen radial distributions of any two variables and the appropriate distributions of any two variables and the appropriate variation of the third can be determined by using the variation of the third can be determined by using the equationequation
Note:Note: or any other variable may be used instead ofor any other variable may be used instead of
dh
dr0 0
dh
drVdV
drVdV
dr
V
raa0
2
d
dr
dV
dr
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow CompressorsMethod of
DesignWork
Variationswith radius
ho(r)
Tangentialvelocity
Distibution Vθ(r)
Axial velocitydistribution
withRadius Va(r)
Reactiondistribution with
Radius Λ(r)
RadialEquilib.
Remarks
ATwo-Dimensional
Supposedconstant
Supposed constant Supposed constant
Supposed constant
Ignored All variations of flow with radius are ignoredMethod for: high H/T stages
BFree Vortex
Constant Vθr = constant Constant Incresed with radius
Yes Limited by high rotor root deflection(approx. const. stator defl.)
C Constant Reaction (without equilibrium)
Supposedconstant
Vθ = ar ± b/r Supposed constant
Supposed constant
Ignored Λ and work distr. will NOT be const. since true variation in Va is not considered
D Constant Reaction
Constant Vθ = ar ± b/r From radial equilib.
Constant Yes Logical design methodHighly twisted blades
EHalf Vortex
Supposedconstant
Arithmetic meanof free vortex andconst. reaction dist.
Supposed constant
Not far from const.
Ignored Λ and work distr. will NOTbe const. since true variationin Va is not considered
FConstant α2
Supposedconstant
Fixed by conditionVθ2 = cost.
[stator entry]Vθ1 = a – b/r
[rotor entry]
Supposed constant
Not far from const.
Ignored Widely used but itsperformance and advantagesnot widely understood
G Forced Vortex
Increaseswith r2
Vθ α r From radial equilib.
Varies with radius Yes Rarely used
HExponential
Constant Vθ = a ± b/r From radial equilib.
Varies with radius Yes A logicl design method
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Axial Flow CompressorsAxial Flow Compressors
Blade DesignBlade Design
Having determined the air angle distributions to give the Having determined the air angle distributions to give the required stage work it is now necessary to convert these required stage work it is now necessary to convert these into blade angle distributions from which the correct into blade angle distributions from which the correct geometry of the blade forms may be determined.geometry of the blade forms may be determined.
Air Angles Air Angles Blade angles Blade angles Blade Geometry Blade Geometry
The common practice is to use the results of the wind The common practice is to use the results of the wind tunnel tests to determine the blade shapes to give the tunnel tests to determine the blade shapes to give the required air angles. The aim of the cascade testing is to required air angles. The aim of the cascade testing is to determine the required angles fordetermine the required angles for
Maximum mean deflectionMaximum mean deflection
Minimum mean total head loss.Minimum mean total head loss.
= 1
2
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Axial Flow CompressorsAxial Flow Compressors
Blade DesignBlade Designββ1v1v,,αα1v1v = Blade inlet angle = Blade inlet angle
ββ2v2v,,αα2v2v = Blade outlet angle = Blade outlet angle
ββ11, , αα11 = Air inlet angle = Air inlet angle
ββ22, , αα2 2 = Air outlet angle = Air outlet angle
WW11,V,V11 = Air inlet velocity = Air inlet velocity
WW22,V,V22 = Air outlet velocity = Air outlet velocity
s = pitchs = pitchc = chordc = chord
θθ = camber = = camber = αα1v1v – – αα2v2v
ξξ = stagger = 0.5( = stagger = 0.5(αα1v1v + + αα2v2v) )
єє = deflection = = deflection = αα11 – – αα22
i = incidence = i = incidence = αα11 - - αα1v1v
δδ = deviation = = deviation = αα22 – – αα2v2v
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Axial Flow CompressorsAxial Flow Compressors
Blade DesignBlade Design
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Blade DesignBlade Design
The loss in non-dimensional form The loss in non-dimensional form ww = =
It is desirable to avoid numbers with common multiples It is desirable to avoid numbers with common multiples for the bfor the bllades in successive rows to reduce the likelihood ades in successive rows to reduce the likelihood of introducing resonant frequencies.of introducing resonant frequencies.
The common practice is to choose an The common practice is to choose an even number for even number for the stator blades and a prime number for the rotor the stator blades and a prime number for the rotor blades.blades.
The bladeThe blade outlet angle outlet angle ““2v2v”” can not be determined from can not be determined from the air outlet angle the air outlet angle ““22”” until the deviation angle until the deviation angle ““”” has been determined.has been determined.
P P
V
01 02
121
2
2 2v
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Axial Flow CompressorsAxial Flow Compressors
β2 α2
nr prime
ns even
β1
ε = β1 – β2
β2
ε*
s/c
s
c
h h/c
know how ≈ 3
rm
nn = 2πrm/snumber of
blades
Des. Defl.Curve
recalculate s/c , h/c
Design Procedure
Blade DesignBlade Design
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Axial Flow CompressorsAxial Flow Compressors
Blade DesignBlade Design
Ideally the mean direction of the air leaving the cascade Ideally the mean direction of the air leaving the cascade would be that of the outlet angle is of the bladeswould be that of the outlet angle is of the blades..
BBut in practice it is found that there is a deviation which is ut in practice it is found that there is a deviation which is due to the reluctance of the air to turn through the full due to the reluctance of the air to turn through the full angle required by the shape of the blade.angle required by the shape of the blade.
EmpEmpiirical equations are employed to estimate rical equations are employed to estimate ..
wherewhere : :
where "a" = the distance to the point of maximum camber where "a" = the distance to the point of maximum camber from the leading edge.from the leading edge.
If the camber arc is circular If the camber arc is circular ((22 a/ca/c)) = = 11
m sc
ma
c 0 23
20 1
502 2. ( ) . ( )
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Blade DesignBlade Design
Using the values of Using the values of ““c, c, 1v1v, , 2v2v, , ““ ; ; it is possible to it is possible to
construct the circular arc camberconstruct the circular arc camber line of the blade around line of the blade around which an aerofoil section can be built up.which an aerofoil section can be built up.
This method can now be applied to a selected number of This method can now be applied to a selected number of points along the blade length to get a complete picture of points along the blade length to get a complete picture of the blade form.the blade form.
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation ooff Stage PerformanceStage Performance
After the completion of stage design it will now be After the completion of stage design it will now be necessary to check over the performance, particularly in necessary to check over the performance, particularly in regard to the efficiency which for a given work input will regard to the efficiency which for a given work input will completely govern the final pressure ratio. completely govern the final pressure ratio.
This efficiency is dependent of the total This efficiency is dependent of the total pressure dpressure drop for rop for each of the blade rows comprising the stage and in order each of the blade rows comprising the stage and in order to evaluate these quantities it will be necessary to revert to evaluate these quantities it will be necessary to revert the loss the loss mmeasurements in cascade tests.easurements in cascade tests.
Lift and profile drag coefficients Lift and profile drag coefficients CCLL and and CCDPDP can be can be obtained from measured values of mean loss obtained from measured values of mean loss ww..
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation ooff Stage PerformanceStage Performance
The static pressure rise across the blades is given by The static pressure rise across the blades is given by (incompressible assumption)(incompressible assumption)
P P P P V P V 2 1 02 22
01 121
212
( ) ( )
P V V P P 1
2 12
22
02 01( ) ( ) P P02 01
P Va 1
22 2
12
2 (tan tan )
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation ooff Stage PerformanceStage Performance
Assuming Assuming VVaa == VVa1a1 == VVa2a2;;
The axial force per unit length of each blade is = s The axial force per unit length of each blade is = s PP
From the consideration of momentum changes the forces From the consideration of momentum changes the forces acting along ethe cascade is given byacting along ethe cascade is given by
FF = s = s VVaa
change in tangent velocity component along the cascadechange in tangent velocity component along the cascade
FF = s= sVVaa *V *Vaa (tan (tan11 -- tantan2)2)
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation ooff Stage PerformanceStage Performance
The coefficients CThe coefficients CLL and C and CDPDP are based on arbitrarily are based on arbitrarily
defined vector mean velocity Vdefined vector mean velocity Vmm,,
where where
D =D = Drag force along vector mean velocity Drag force along vector mean velocity
L =L = Lift force perpendicular to vector mean velocity Lift force perpendicular to vector mean velocity
V Vm a m sec
tan (tan tan ) m 1
2 1 2
D V cCm Dp1
22 L V cCm L
1
22
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation ooff Stage PerformanceStage Performance
After some manipulationsAfter some manipulations
CCDPDP and C and CLL can be evaluated if a can be evaluated if a HowellHowell like curve is like curve is
known from cascade test results and known from cascade test results and
Csc V
Dpm
( )cos
cos
1
2 12
3
21
Csc
CL m Dp m 2 1 2tan tan cos tan
1 1
2 1
1 1 2
1
2
v
m
i *
tan (tan tan )
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation of of Stage PerformanceStage Performance
CDP
CL
İncidence i degrees
Dra
g co
effic
ient
CD
P Lift
coe
ffic
ient
CL
0.075
-10 -5 0 5 10
0
0.5
1.0
1.5
0.025
0.050
-15-200
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation of of Stage PerformanceStage Performance
Using the values of Using the values of from cascade test from cascade test
results for known values of (s/c); Cresults for known values of (s/c); CDPDP and C and CLL can be plotted can be plotted
against incidence.against incidence.
Since the value of CSince the value of Cpp tan tan mm in C in CLL equation is negligibly small, it equation is negligibly small, it
is usual to use a more convenient theoretical value of Cis usual to use a more convenient theoretical value of CLL given given
byby
In which the effect of profile drag is ignored. Using this formula, In which the effect of profile drag is ignored. Using this formula, curves of Ccurves of CLL can be plotted for nominal (or design) conditions to can be plotted for nominal (or design) conditions to
correspond with the curves of deflection. These curves are again correspond with the curves of deflection. These curves are again plotted against plotted against 22 for fixed values of s/c for fixed values of s/c
12 1
2V
CscL m
2 1 2tan tan cos
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation of of Stage PerformanceStage Performance
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation of of Stage PerformanceStage Performance
Before applying these coefficients to the blade rows of Before applying these coefficients to the blade rows of the compressor stage two additional factors must be the compressor stage two additional factors must be taken into account.taken into account.
Annulus DragAnnulus Drag: Drag effects due to the walls of the : Drag effects due to the walls of the Compressor annulus = Compressor annulus = CCDADA
CCDADA = 0.02 (s/h) = 0.02 (s/h)
Secondry LossesSecondry Losses: Due to the trailing vortices and tip : Due to the trailing vortices and tip ccllearances earances = C= CDSDS The following emprical relations can be The following emprical relations can be usedused
CCDSDS = 0.018 = 0.018 CCLL22
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation of of Stage PerformanceStage Performance
The overall Drag Coefficient is given byThe overall Drag Coefficient is given by
ProfileProfile + annulus + secondary+ annulus + secondary
(the annular cascade C(the annular cascade CDPDP is replaced by C is replaced by CDD) thus) thus
This enables the loss coefficientThis enables the loss coefficient for the blade for the blade row to be determined.row to be determined.
C C C CD DP DA DS
Csc V
Dm
1
2 12
3
21
cos
cos
12 1
2V
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation of of Stage PerformanceStage Performance
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation of of Stage PerformanceStage Performance
The theoretical pressure rise (i.e The theoretical pressure rise (i.e ww =0) =0)
Efficiency of the blade rowEfficiency of the blade row
P V Vth a a 1
2
1
22 2
12
22 2
12
2 (tan tan ) (sec sec )
P
V
th
a12
12 2
1
22
21
sec
sec
sec
P
V
th12
1
12
21
22
cos
cos
thth
th th
PP
V
P
V
1
12
12
12
12
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation of of Stage PerformanceStage Performance
For a case where For a case where = 50 % Rotor and stator rows are = 50 % Rotor and stator rows are similar thus this calculation carried at design diameter similar thus this calculation carried at design diameter can be applied to the whole stagecan be applied to the whole stage
forfor = = 1/21/2
stage efficiencystage efficiency
bl ‘
ssP P
P P
P
P
T
T
2 1
2 1
2
1 1
1
1 2( )
s
is‘
act
TT
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation of of Stage PerformanceStage Performance
thenthen
expanding and neglecting 2expanding and neglecting 2ndnd order terms; order terms;
forforT K
T K
so
o
20
4001
PP
TT
‘s2
1 1
11
2
bl ‘
ss
s
PP
PP
TT
TT
21
21
1
1
1
1
1
1
12
1
12
1
bl s
ss
TT
11
1 41
1
( )
bl s
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Axial Flow CompressorsAxial Flow Compressors
Calculation Calculation of of Stage PerformanceStage Performance
For cases other than 50 % reaction at the design For cases other than 50 % reaction at the design diameter an approximate stage efficiency is given bydiameter an approximate stage efficiency is given by
If If far removed from 50% far removed from 50%
s blR bl-ST 1
2
s bl-R bl-ST 1
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Axial Flow CompressorsAxial Flow Compressors
Summary of the Design ProcedureSummary of the Design Procedure
Assume Assume Ts and at the design radius Ts and at the design radius Calculate the air Calculate the air anglesangles
Applying chosen design condition (Free Vortex, Constant Applying chosen design condition (Free Vortex, Constant Reaction etc) Calculate air angles at all radiiReaction etc) Calculate air angles at all radii
Results of Cascade Tests Results of Cascade Tests Blade shapes (Blade Blade shapes (Blade angles)angles) C CDD and C and CLL
Calculate Calculate ηηss and and RRss
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Overall PerformanceOverall Performance
Assuming thatAssuming that ηηs s = = ηη∞∞
((ηη constant through all compressor stages), constant through all compressor stages), for a compressor consisting of N similar stages, each with for a compressor consisting of N similar stages, each with ηηs s = = ηη∞∞
R is the “R is the “Overall Pressure RatioOverall Pressure Ratio”” where where ;;
RN TTos
o
nn
11
1
nn s
1 1 1
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Axial Flow CompressorsAxial Flow Compressors
Overall PerformanceOverall Performance
Although the use of polytropic law gives a rapid means of Although the use of polytropic law gives a rapid means of estimating the overall performance of a multistage estimating the overall performance of a multistage compressor, it is necessary in practice to make a step by compressor, it is necessary in practice to make a step by step final performance calculation.step final performance calculation.
Latest blade manufacturing technology allows different Latest blade manufacturing technology allows different blade shapes for different rows.blade shapes for different rows.
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Compressibility EffectsCompressibility Effects
High air velocities between the blades effects the High air velocities between the blades effects the compressor performancecompressor performance..
Critical MachCritical Mach numbernumber MMcc is defined such that at entry is defined such that at entry velocities lower than thisvelocities lower than this;; the performance of the c the performance of the caascade scade differs very little from that at low speeds. Above this differs very little from that at low speeds. Above this losses begin to show a marked increase.losses begin to show a marked increase.
Maximum Mach Number is Maximum Mach Number is defined as thedefined as the air speed at air speed at which losses cancel the pressure risewhich losses cancel the pressure rise..
FFor a typical low speed cascade Mor a typical low speed cascade Mcc = 0.7 M = 0.7 Mmm =0.85 =0.85
Increased Mach number also narrows the operating Increased Mach number also narrows the operating range of incidence leading to poor performance at off range of incidence leading to poor performance at off design conditions.design conditions.
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Compressibility EffectsCompressibility Effects
In the sketch the variations in Mach # across the annulus In the sketch the variations in Mach # across the annulus is shown for Free Vortex and constant reaction blading. is shown for Free Vortex and constant reaction blading. Free Vortex blading shown large Mach number variations Free Vortex blading shown large Mach number variations which extreme care should be taken.which extreme care should be taken.
Since the velocity of sound in air increases with Since the velocity of sound in air increases with increasing temperature the Mach numbers will decrease increasing temperature the Mach numbers will decrease through the compressor due to the progressively through the compressor due to the progressively increasing temperature.increasing temperature.
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Compressibility EffectsCompressibility Effects
Not to suffer from compressibNot to suffer from compressibiility effects in early stages lity effects in early stages one mighone mightt use constant reaction design if no other use constant reaction design if no other precaprecauution can be taken.tion can be taken.
Transonic stages where the flow is actually supersonic Transonic stages where the flow is actually supersonic over a part of the blade height can now be designed over a part of the blade height can now be designed utilizing very thin and special shaped blades. One utilizing very thin and special shaped blades. One advantage is eliminating IGVadvantage is eliminating IGV’’s less noise. s less noise.
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Some Deductions from the Compressor Some Deductions from the Compressor CharacteristicsCharacteristics The overall compressor characteristic is composed of the The overall compressor characteristic is composed of the
stage characteristics stacked.stage characteristics stacked.
The mass flow through the compressor is controlled by The mass flow through the compressor is controlled by the choking of various stages in some cases early the choking of various stages in some cases early stages, in the others the rear stagesstages, in the others the rear stages..
If the axial flow compressor is designed for constant axial If the axial flow compressor is designed for constant axial velocity throughoutvelocity throughout ; ; the annulus area must decrease the annulus area must decrease along due to the increasing density.along due to the increasing density.
The annulus area for each stage is determined for the The annulus area for each stage is determined for the design condition. At any other operating conditon the design condition. At any other operating conditon the design point calculated area will result in a variation of design point calculated area will result in a variation of axial velocityaxial velocity..
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Axial Flow CompressorsAxial Flow Compressors
Some Deductions from the Compressor Some Deductions from the Compressor CharacteristicsCharacteristics
When the compressor is run at When the compressor is run at a speed lower than a speed lower than designdesign, , T and RT and Rcc are reduced than the are reduced than the densitydensity at the at the rear stages will be lower than the design value.rear stages will be lower than the design value.
As a result the axial velocity at the rear stages will As a result the axial velocity at the rear stages will increase, eventually choking will occurincrease, eventually choking will occur..
Thus Thus at low speedsat low speeds mm is determined by the is determined by the choking of choking of the rear stages.the rear stages. As the speed is increased density of the As the speed is increased density of the rear stages increases (V decrease) thus gets unchoked.rear stages increases (V decrease) thus gets unchoked.
At veryAt very high speeds choking will occur at the inlethigh speeds choking will occur at the inlet. . The vertical line of constant speed is due to choking at The vertical line of constant speed is due to choking at the inlet of the compressor.the inlet of the compressor.
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Axial Flow CompressorsAxial Flow Compressors
Some Deductions from the Compressor Some Deductions from the Compressor CharacteristicsCharacteristics
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Some Deductions from the Compressor Some Deductions from the Compressor CharacteristicsCharacteristics
A A B B
At the design speed if we consider the moving of At the design speed if we consider the moving of operating point from A to B. operating point from A to B.
At point B (on the surge line), the density at the At point B (on the surge line), the density at the compressor exit will be increased due to the compressor compressor exit will be increased due to the compressor exit will be increased due to the increase in delivery exit will be increased due to the increase in delivery pressure; also pressure; also ṁṁ is slightly reduced. is slightly reduced.
Axial velocity in the last stage is reduced incidence in the Axial velocity in the last stage is reduced incidence in the last stage is increased. Rotor blades are expected to last stage is increased. Rotor blades are expected to stall from the last stagesstall from the last stages..
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Axial Flow CompressorsAxial Flow Compressors
Some Deductions from the Compressor Some Deductions from the Compressor CharacteristicsCharacteristics
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Some Deductions from the Compressor Some Deductions from the Compressor CharacteristicsCharacteristics
AA C C
ṁṁ falls rapidly falls rapidly ; ; VVaa at the inlet decrease at the inlet decreases,s, incidence of incidence of the first stage increasethe first stage increases.s. But the incidence of the later But the incidence of the later stages decrease due to the increase of Vstages decrease due to the increase of Vaa (due to lower (due to lower pressure and density). At low speeds surging is probably pressure and density). At low speeds surging is probably due to first stages stalling. due to first stages stalling.
At conditions far removed from surge At conditions far removed from surge RR is very low is very low high high VVaa large decrease in incidence large decrease in incidence result in stall in result in stall in negative incidence negative incidence very low very low ηηcc
Me 423 Spring 2006Me 423 Spring 2006 Prof. Dr. O. Cahit ERALPProf. Dr. O. Cahit ERALP
Axial Flow CompressorsAxial Flow Compressors
Some Deductions from the Compressor Some Deductions from the Compressor CharacteristicsCharacteristics
At high pressure operation At high pressure operation Blow-offBlow-off at an intermediate at an intermediate stage (wasteful). Incidence can be maintained at design stage (wasteful). Incidence can be maintained at design value by increasing the speed of last stage (HPC) and value by increasing the speed of last stage (HPC) and decreasing the speed of first stage (LPC)decreasing the speed of first stage (LPC);;
Two spools are mechanically independent but Two spools are mechanically independent but aerodynamically coaerodynamically couupled.pled.