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