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MunichSummerSchoolatUniversityofAppliedSciencesProf.KimA.Shollenberger
TheoryandApplica>onofGasTurbineSystems
PartI:IdealSha-PowerCycles
OutlineforTheoryofGasTurbineSystems
Introduc6onI. IdealSha-PowerCyclesII. ActualShaBPowercyclesIII. CentrifugalFlowCompressorsIV. AxialandRadialFlowTurbinesV. Combus>onSystemsVI. PerformancePredic>on
References1. Moran,MJandHNShappiro,FundamentalsofEngineering
Thermodynamics,8thedi>on,JohnWiley&Sons,2014.2. Munson,BR,Young,DF,andTFOkiishi,Fundamentalsof
FluidMechanics,7thedi>on,JohnWiley&Sons,Inc.,2013.3. SaravanamuZoo,HIH,Rogers,GFC,Cohen,H,andP
Straznicky,GasTurbineTheory,6thedi>on,Pren>ceHall(PearsonEduca>onLTD),2009.
4. Boyce,MP,GasTurbineEngineeringHandbook,4rdedi>on,Elsevier(BuZerworthHeinemann),2012.
heat transfer rates specific entropyT temperaturev specific volumeV velocityV volume
work ratez elevationρ density
BasicNomenclaturecp specificheatat
constantpressurecv specificheatat
constantvolumeĖ energy rateg gravitation accelerationh specific enthalpyk specific heats ratio
mass flowratep pressure
!Q
!W
!m
Introduc>ontoGasTurbines
Usedtoproducemechanicalpowerbyexpandingahighenergygasacrossaturbinewithoutreciproca>ngmembers(suchasapiston/cylinderassembly),thustheyhavethefollowingadvantages:• Highpowerproduc=onfortheirsizeandweight• Highreliabilityduetoreducedrubbingmembers,fewbalancingproblems,andlowlubrica>ngoilconsump>on
• Simpleu>liza>onofmul=plefuels
HistoryofWater/SteamTurbines
• Firstturbinesusedwaterastheworkingfluidtoproducehydro-electricpower;s>llasignificantcontributortoworld’senergyresources
• Steamturbinesintroducedaround1900;widelyusedforelectricitygenera>on(currentunitscanhaveover1GWofshaBpowerand40%efficiency)
• Steamturbineswerealsowidelyusedformarinepropulsionupun>lmid1970’s(whenmoreefficientdieselenginestookover)exceptfornuclear-poweredaircraBcarriersandsubmarines
DisadvantagesofSteamTurbines
• Produc>onofhigh-pressurehigh-temperaturesteamrequiresbulkyandexpensivesteamgenera>ngequipment
• Hotgasesproducedinboilerornuclearreactorcorecanneverreachtheturbine;insteadanintermediatefluid,typicallysteam,flowsthroughtheturbine
• Satura>ontemperatureofsteam,evenathighpressures,limitsmaximumthermalefficiencytheore>callypossible
HistoryofGasTurbines
• Seriousdevelopmentbeganinthe1940’s;mainlyonturbojetengineforaircraBpropulsion
• Significantuseforotherfields,includingelectricalpowerproduc>on,beganinthe1950’s
• Wideusetoday(currentunitscanhaveover0.5GWofshaBpowerand45%efficiency)hasbeendrivenbyimprovingtwomainperformancelimi>ngfactors:– Componentefficienciesthroughaerodynamicsresearch– Hightemperaturematerialsdevelopedthroughadvancesinmetallurgy
GasTurbineCycles
Twomainclassifica>ons:1. ShaCPowerCyclesusedforlandbasedelectric
powergenera>on,marinepropulsion,mechanicaldrivesystems,processheat,compressedair,etc.
2. AircraCPropulsionCycleswhereperformancedependsonforwardspeedandal>tude
ThiscoursewillfocusonshaBpowercycles.
ShaBPowerCycles
Twomainconfigura>ons:a. Opentotheatmosphere– Mostcommonforpowergenera>onandengines– Heataddi>ontypicallyinacombus>onchamber
b. Closedloop– Foundinnuclearpowerplants– Heataddi>onandheatrejec>ondonebyheatexchangersatconstantpressure
OpenShaBPowerCycle
OpenShaBPowerCycleOpera>on
1. Freshairisdrawnintothecompressorwherebothitspressureandtemperatureareincreased
2. Fuelismixedwithcompressedairatanappropriatefuel/airra>oandignitedinthecombus=onchambertoproducehighenergygases
3. Combus>onproductsareexpandedacrossaturbinetoalowerpressureandtemperaturewhichproducesshaCpowerthatisusedtooperatethecompressorandgenerateelectricity
ClosedShaBPowerCycleReplacecombus>onchamberwithheatexchangerandcloseloopbyaddingasecondheatexchanger
IdealCondi>onsforGasTurbines
Assumethefollowing:1. Compressionandexpansionprocessesare
reversibleandadiaba>c,thusisentropic2. Kine>cenergyandpoten>alenergychangesforgas
arenegligible3. Pressurelossesforgasarenegligible4. Idealgaswithconstantproper>esandcomposi>on
atconstantmassflowrate(steadyopera>on)5. “Complete”heattransfer(temperatureriseoncold
sideequalstemperaturedroponhotside)
IdealGasPowerCycle(AlsoCalledBraytonorJouleCycle)
NamedaBeranAmericanengineer,GeorgeBrayton,whoproposedthecycleforareciproca>ngoilburningenginearound1870Process1-2:isentropiccompression(compressor)Process2-3:constantpressureheataddi>onProcess3-4:isentropicexpansion(turbine)Process4-1:constantpressureheatrejec>onNOTE:For“idealcycle”thatassumes“constantworkingfluid,”openandclosedcyclesarethesame.
BraytonCycle
turbine
compressor heatexchanger
heatexchanger
Pressure(p)–SpecificVolume(v)Diagram
Temperature(T)-Entropy(s)Diagram
1stLawofThermodynamics
Forcontrolvolume(CV)withinletat(1)andoutletat(2):
Forsteadystateandwherechangesinkine>cenergy(KE)andpoten>alenergy(PE)negligible:
NOTE:Signconven>onisheattransferintotheCVandworkoutoftheCVareposi>ve,thusnega>vesignabove
dEcv
dt= !Qcv − !Wcv + !m h1 − h2( )+V1
2 −V22
2+ g z1 − z2( )
"
#$
%
&'
0 = !Qcv − !Wcv + !m h1 − h2( )
Process 1stLawAnalysis Descrip6on Symbols
1-2 compressorworkratein
2-3 heataddi>on
3-4 turbineworkrateout
4-1 heatrejec>on
1stLawofThermodynamicsAnalysis
!W12 = !m h1 − h2( )
!Q23 = !m h3 − h2( )
!W34 = !m h3 − h4( )
!Q41 = !m h1 − h4( )
!Qin = !Q23
!Wt = !W34
!Qout = − !Q41
!Wc = − !W12
BraytonCycleAnalysis
Networkrateforcycle:
Netheattransferforcycle:
NOTE:Asexpectedforaclosedcycle:
!Wcycle = !W12 + !W34 = − !Wc + !Wt = !m h1 − h2 + h3 − h4( )
!Qcycle = !Q23 + !Q41 = !Qin − !Qout = !m h3 − h2 + h1 − h4( )
!Wcycle = !Qcycle
ProcessDefini>ons
BackWorkRa=o–ra>oofcompressorworkinputtoturbineworkoutputCompressorPressureRa=o–ra>ooftheexitandinletpressuresforthecompressor
NOTE:ForBraytoncycle
bwr =!Wc !m!Wt !m
=!W12
!W34
=h2 − h1h3 − h4
rp =p2p1
p2p1=p3p4
CyclePerformance
Thermalefficiency-desiredpowerorworkrateoutputdividedbyrequiredheatinputNOTE:Bythe2ndLawofThermodynamicspowercyclemustrejectheattoproducework,thusηth<1.
ηth =!Wcycle !m!Qin !m
=!Q23 + !Q41!Q23
=1−!Qout!Qin
ηth =1−h4 − h1h3 − h2
ColdAir-StandardAnalysis
Foridealgaswithconstantspecificheats:Useisentropicrela>onshipforProcess1-2and3-4:
T2T1=
p2p1
!
"#
$
%&
k−1( ) k
= rpk−1( ) k
T4T3=
p4p3
!
"#
$
%&
k−1( ) k
=1
rpk−1( ) k =
T1T2
h1 − h2 = cp T1 −T2( )
ColdAir-StandardAnalysisforCycleSpecificWorkOutput
Recallcycleworkratefromearlier:
Calculateop>mumrpformaximumusing:
!Wcycle = !m h1 − h2 + h3 − h4( ) = !m cp T1 1−T2T1
"
#$
%
&'+T3 1−
T4T3
"
#$
%
&'
(
)*
+
,-
!Wcycle
!m cp T1= 1− rp
k−1( ) k"#
$%+T3T11− 1
rpk−1( ) k
"
#&&
$
%''
∂ !Wcycle ∂rp = 0
rp, optk−1( ) k = T3 T1
BraytonCycleNetWorkRate
ForfixedT1 = Tmin andT3 = Tmax ,networkratefirstincreaseswithpressurera>o,reachesmaximumatrp, opt,andthendecreases.
ColdAir-StandardAnalysisforBackWorkRa>o
Recallfromearlier:NOTE:Minimizecompressorversusturbineworkbydecreasingcompressortemperatures(T1andT2)andincreasingturbinetemperatures(T3andT4)
bwr = h2 − h1h3 − h4
=cp T2 −T1( )cp T3 −T4( )
=T1 T2 T1 −1( )T4 T3 T4 −1( )
bwr = T1T4=T2T3=T1T3rpk−1( ) k
Cold-AirStandardAnalysisforThermalEfficiency
Recallfromearlier:NOTE:Efficiencyincreaseswithpressurera>o.
ηth =1−h4 − h1h3 − h2
=1−cp T4 −T1( )cp T3 −T2( )
=1−T1 T4 T1 −1( )T2 T3 T2 −1( )
ηth =1−T1T2
=1− T4T3
=1− 1rpk−1( ) k
Example#1Airentersthecompressorofanidealgasturbinesystemat100kPaand27°C.Thepressurera>ois5andthemaximumtemperatureis867°C.Foryourcalcula>onsusethecold-airstandardandlistanyaddi>onalassump>ons.a. SketchtheT-sdiagramforthiscycle.b. Calculatethethermalefficiency.c. Calculatethebackworkra>o.d. Calculatethespecificworkoutput.
BraytonCyclePerformance
0.0
0.2
0.4
0.6
0.8
0%
20%
40%
60%
80%
0 5 10 15 20 25 30
Specific Work O
utputTher
mal
Effi
cien
cy
Pressure Ratio
k = 1.4, T1 = 300 K, T3 = 1000 K
typical pressure ratios for gas- turbine engines
NotesonBraytonCycle
• Effectofpressurera=oonefficiencycanbeobservedbyconsideringareasonT-sdiagram
• Maximumtemperature(T3)limitedbyturbineblades(approximately1750K)–oBencalledthe“metallurgicallimit”
• Minimumtemperature(T1)usuallyambient(approximately300K),thusnotconsideredanindependentvariable
• Tradeoffbetweenop>mumthermalefficiencyandmaximumworkoutput
ImprovingGasTurbinePerformance
1. Regenera=on-useturbineexhausttopreheatairenteringcombustor
2. Reheat-reheatturbineexhaustandaddaddi>onalturbine(s)
3. Intercooling-coolcompressorexhaustandaddaddi>onalcompressor(s)
Regenera>veGasTurbine
BraytonCyclewithRegnera>on
BraytonCyclewithRegenera>on
• TurbineexhaustatState(4)isusedtopreheatairfromState(2)toState(x)beforeenteringcombustor
• Reducesheataddi>on:• Reducesheatrejec>on:• Addi>onalheatexchangerincreasescapitalcosts• Canincreasethermalefficiencyatlowerrp
!Qin = !Qx3 < !Q23
!Qout = !Qy1 < !Q41
ηth =!Wcycle !m!Qin !m
=!W12 + !W34!Qx3
=h1 − h2( )+ h3 − h4( )
h3 − hx( )
RegeneratorPerformance
RegeneratorEffec=veness–ra>oofactualtomaximumtheore>calenthalpyincrease
IdealRegenerator–foraheatexchangerwithinfinitearea:ηreg=100%,Tx=T4,Ty=T2,andNOTE:Specificworkoutputandbwrareunchanged.
ηreg =actual heat transfer
maximum heat transfer=hx − h2
h4 − h2
!Q2 x = − !Q4y
BraytonCyclewithRegenera>onThermalEfficiency
Forcoldair-standardanalysis:Foranidealregenerator:
NOTE: Forrp=1,ηthequals Carnotefficiency
ηth =h1 − h2( )+ h3 − h4( )
h3 − hx( )=1−
T2 −T1( )+ T4 −Tx( )T3 −Tx( )
ηth =1−T2 1−T1 T2( )T3 1−T4 T3( )
=1− T1T3
"
#$
%
&'T2T1
"
#$
%
&'
ηth =1−T1T3
"
#$
%
&'rp
k−1( )/k
Example#2Airentersthecompressorofanidealgasturbinesystemat100kPaand27°Cwithidealregenera=on.Thepressurera>ois5andthemaximumtemperatureis867°C.Foryourcalcula>onsusethecold-airstandardandlistanyaddi>onalassump>ons.a. SketchtheT-sdiagramforthiscycle.b. Calculatethethermalefficiency.c. Calculatethebackworkra>o.d. Calculatethespecificworkoutput.
0%
20%
40%
60%
80%
0 5 10 15 20 25 30
Ther
mal
Effi
cien
cy
Pressure Ratio
k = 1.4
T3 / T1 = 5T3 / T1 = 4T3 / T1 = 3T3 / T1 = 2Simple Cycle
ComparisonofThermalEfficiencyforBraytonCyclewithRegenera>on
NOTE:Curvesstopatsimplecyclebecauseaddi>onalregenera>onheattransferisnotpossible.
BraytonCyclewithReheatUsername: Kim ShollenbergerBook: Fundamentals of Engineering Thermodynamics, 8th Edition. No part of any book may be reproduced or transmitted in any form by any means without the publisher's prior written permission. Use (other than pursuant to the qualified fair use privilege) in violation of the law or these Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law.
BraytonCyclewithReheat
• Excessairisusedforcombus>onbecauseoftemperaturelimitsimposedbyturbineblades
• Secondturbineusesexcessairandaddi>onalfuelformorecombus>on
• Foridealreheat(maximumworkrate)forfixedrpandT3 = Tb, pressurera>oacrosseachstagecanbeshowntobeequalwherepa=pb=pi: rp =
p2p1=
p3pa
⎛
⎝⎜
⎞
⎠⎟
2
=pbp4
⎛
⎝⎜
⎞
⎠⎟
2
BraytonCyclewithReheatSpecificWorkOutput
Forcoldair-standardanalysis:
!Wcycle = !m h1 − h2( )+ !m h3 − ha( )+ !m hb − h4( )
!Wcycle
!m cp T1= 1− T2
T1
⎛
⎝⎜
⎞
⎠⎟+
T3T11− Ta
T3
⎛
⎝⎜
⎞
⎠⎟+
TbT11− T4
Tb
⎛
⎝⎜
⎞
⎠⎟
!Wcycle
!m cp T1= 1− rp
k−1( ) k⎡⎣
⎤⎦+T3T12− pi
p3
⎛
⎝⎜
⎞
⎠⎟
k−1( ) k
−p4pi
⎛
⎝⎜
⎞
⎠⎟
k−1( ) k⎡
⎣
⎢⎢
⎤
⎦
⎥⎥
BraytonCyclewithReheatSpecificWorkOutput,cont.
Determinepiforidealreheatusing
∂ !Wcycle ∂ pi = 0
T3T1
−k −1k
⎛
⎝⎜
⎞
⎠⎟pip3
⎛
⎝⎜
⎞
⎠⎟
−1 k1p3
⎛
⎝⎜
⎞
⎠⎟−
k −1k
⎛
⎝⎜
⎞
⎠⎟p4pi
⎛
⎝⎜
⎞
⎠⎟
−1 k
−p4pi2
⎛
⎝⎜
⎞
⎠⎟
⎡
⎣⎢⎢
⎤
⎦⎥⎥= 0
pip3
⎛
⎝⎜
⎞
⎠⎟
−1 kpip3
⎛
⎝⎜
⎞
⎠⎟=
p4pi
⎛
⎝⎜
⎞
⎠⎟
−1 kp4pi
⎛
⎝⎜
⎞
⎠⎟ →
pip3=p4pi= rp
!Wcycle
!m cp T1= 1− rp
k−1( ) k⎡⎣
⎤⎦+ 2
T3T11− 1
rpk−1( ) 2 k( )
⎡
⎣⎢⎢
⎤
⎦⎥⎥
BraytonCyclewithReheatSpecificWorkOutput,cont.
Calculateop>mumrpformaximumusing
−k −1k
⎛
⎝⎜
⎞
⎠⎟ rp
−1 k − 2 T3T1
⎛
⎝⎜
⎞
⎠⎟ −
k −12k
⎛
⎝⎜
⎞
⎠⎟ rp
1−3k( ) 2 k( ) = 0
rp, opt3 k−1( ) 2k( ) =
T3T1
∂ !Wcycle ∂rp = 0
∂∂rp
1− rpk−1( ) k⎡
⎣⎤⎦+ 2
T3T1
⎛
⎝⎜
⎞
⎠⎟∂∂rp
1− 1rpk−1( ) 2 k( )
⎡
⎣⎢⎢
⎤
⎦⎥⎥= 0
BraytonCyclewithReheatThermalEfficiency
Forcoldairstandardanalysis:Foridealreheat:
ηth =1−1 rp
k−1( )/ 2k( ) − T1 T3( )2− T1 T3( )rp
k−1( )/k −1 rpk−1( )/ 2k( )
ηth =h1 − h2( )+ h3 − ha( )+ hb − h4( )
h3 − h2( )+ hb − ha( )=1−
T4 −T1( )T3 −T2( )+ Tb −Ta( )
Example#3Airentersthecompressorofanidealgasturbinesystemat100kPaand27°Cwithidealreheat.Thepressurera>ois5andthemaximumtemperatureis867°C.Foryourcalcula>onsusethecold-airstandardandlistanyaddi>onalassump>ons.a. SketchtheT-sdiagramforthiscycle.b. Calculatethethermalefficiency.c. Calculatethebackworkra>o.d. Calculatethespecificworkoutput.
ComparisonofSpecificWorkOutputforBraytonCyclewithReheat
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20 25 30
Spec
ific
Wor
k O
utpu
t
Pressure Ratio
k = 1.4, T1 = 300 K, T3 = 1000 K
Reheat CycleSimple Cycle
ComparisonofThermalEfficiencyforBraytonCyclewithReheat
0%
20%
40%
60%
80%
0 5 10 15 20 25 30
Ther
mal
Effi
cien
cy
Pressure Ratio
k = 1.4
Simple CycleT3 / T1 = 20T3 / T1 = 6T3 / T1 = 4T3 / T1 = 3
BraytonCyclewithIntercooling
2704601 2015/07/10 75.128.66.176
Username: Kim ShollenbergerBook: Fundamentals of Engineering Thermodynamics, 8th Edition. No part of any book may be reproduced or transmitted in any form by any means without the publisher's prior written permission. Use (other than pursuant to the qualified fair use privilege) in violation of the law or these Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law.
2704601 2015/07/10 75.128.66.176
Username: Kim ShollenbergerBook: Fundamentals of Engineering Thermodynamics, 8th Edition. No part of any book may be reproduced or transmitted in any form by any means without the publisher's prior written permission. Use (other than pursuant to the qualified fair use privilege) in violation of the law or these Terms of Service is prohibited. Violators will be prosecuted to the full extent of the law.
BraytonCyclewithIntercooling
• Lessworkisrequiredtocompressacoolgas• Compensatesforlowtemperaturelimitedbynature(examples:airoroceantemperature)
• Limiteduseinprac>cebecauserequiresbulkyequipmentandhugeamountsofcoolingwater
• Foridealintercooling(minimumworkrate)forfixedrpandT1 = Td, pressurera>oacrosseachstagecanbeshowntobeequalwherepa=pb=pi:
rp =p2p1=
pcp1
!
"#
$
%&
2
=p2pd
!
"#
$
%&
2
BraytonCyclewithIntercoolingSpecificWorkOutput
Forcoldair-standardanalysis:Foridealintercooling:
!Wcycle = !m h1 − hc( )+ !m hd − h2( )+ !m h3 − h4( )
!Wcycle
!m cp T1= 2 1− rp
k−1( ) 2 k( )"#
$%+T3T11− 1
rpk−1( ) k
"
#&&
$
%''
!Wcycle
!m cp T1= 1− Tc
T1
"
#$
%
&'+
TdT11− T2
Td
"
#$
%
&'+
T3T11− T4
T3
"
#$
%
&'
rp, opt3 k+1( ) 2k( ) = T3 T1
BraytonCyclewithIntercoolingThermalEfficiency
Forcoldairstandardanalysis:Foridealintercooling:
ηth =1−1 rp
k−1( )/k + T1 T3( ) rpk−1( )/ 2k( ) − 2"
#$%
1− T1 T3( ) rpk−1( )/k
ηth =h1 − hc( )+ hd − h2( )+ h3 − h4( )
h3 − h2( )=1−
T4 −T1( )+ hc − hd( )T3 −T2( )
ComparisonofSpecificWorkOutputforBraytonCyclewithIntercooling
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 5 10 15 20 25 30
Spec
ific
Wor
k O
utpu
t
Pressure Ratio
k = 1.4, T1 = 300 K, T3 = 1000 K
IntercoolingSimple Cycle
ComparisonofThermalEfficiencyforBraytonCyclewithIntercooling
0%
20%
40%
60%
80%
0 5 10 15 20 25 30
Ther
mal
Effi
cien
cy
Pressure Ratio
k = 1.4
Simple CycleT3 / T1 = 20T3 / T1 = 6T3 / T1 = 4T3 / T1 = 3
GasTurbinewithRegenera>on,Reheat,andIntercooling
• Whilereheatandintercoolingaloneincreaseworkoutput,theyalsodecreasethermalefficiency:– Forreheat,needextraheatforhea>ngbetweenstagesandheatrejec>onathighertemperatures
– Forintercooling,needtoheatupmoreaBercompression
• However,reheatandintercoolingincreasethepoten>alforregenera>on;combined,theoveralleffectcanbeanincreaseinthethermalefficiency
GasTurbinewithRegenera>on,Reheat,andIntercooling
BraytonCyclewithRegenera>on,Reheat,andIntercooling
Example#4Airentersthefirstcompressorstageofanidealgasturbinesystemwithidealregenera>on,reheat,andintercoolingat100kPaand27°C.Thepressurera>ois5acrossbothcompressorsandthemaximumtemperatureis867°C.Foryourcalcula>onsusethecold-airstandardandlistanyaddi>onalassump>ons.a. SketchtheT-sdiagramforthiscycle.b. Calculatethethermalefficiency.c. Calculatethebackworkra>o.d. Calculatethespecificworkoutput.
EricsonCycle
• IdealcycleforgasturbineengineswithanefficiencyequaltotheCarnotefficiency
• Theore>callyaccomplishedinthelimitwhereregenera>onisusedwithaninfinitenumberofstagesofreheatandintercooling
CombinedGasTurbine-VaporPowerCycle
Wasteheatfromgasturbinepowercycle(toppingcycle)isusedasheatinputforvaporpowercycle,thusthethermalefficiencybecomes:wheresubscriptgisforthegascycleandthesubscriptvisforthevaporcycle.
ηth =!Wg !mg + !Wv !mv
!Qin,g !mg
CombinedBrayton-IdealVaporPowerCycle
CombinedBrayton-IdealVaporPowerCycleAnalysis
1stLawCVanalysisofheatexchangerbetweencycles(assumeadiaba>c,negligibleKEandPE)Subs>tuteintothermalefficiencyandreducetoget:NOTE:Thermalefficiencyistypicallymuchhigherthanthermalefficiencyofgascyclealone.
0 = !mg h8 − h9( )+ !mv h2 − h3( ) → !mg !mv = h8 − h9( ) h3 − h2( )
ηth =ηth,g +h8 − h9h7 − h6
"
#$
%
&'ηth,v
CombinedBrayton-IdealVaporPowerCycleAnalysis,Cont.
Forcoldairstandard:• Ideally,T9wouldbeaslowaspossiblesuchthatT9=T5,then
(T8-T9)wouldbeapproximatelythesameas(T7-T6)andηthwouldbethesumofthetwoindividualcycles
• Inprac>ce,ηthisgenerallyhigherthaneithercyclewouldhaveindividuallybecauseofbothhightemperatureheataddi>onandlowtemperatureheatrejec>on
• Efficienciesofover60%arecurrentlyobtainedbymoderncombinedplantstoday
ηth =ηth,g +T8 −T9T7 −T6
"
#$
%
&'ηth,v
GasTurbinesForAircraBPropulsion
S>lluseBraytoncyclewiththefollowingchanges:• Diffuserde-acceleratesincomingflowtozerovelocity(incomingflowhassignificantKE)
• Nozzleacceleratesexi>ngflowtosignificantKE
• TurbineworkproducedequalscompressorworkandminoraircraBpowerneeds
h1 = hair +Vair2
2
V5 ≈ 2 h4 − h5( )
h3 − h4 ≈ h2 − h1
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