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MunichSummerSchoolatUniversityofAppliedSciencesProf.KimA.Shollenberger
TheoryandApplica>onofGasTurbineSystems
PartI:IdealSha-PowerCycles
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OutlineforTheoryofGasTurbineSystems
Introduc6onI. IdealSha-PowerCyclesII. ActualShaBPowercyclesIII. CentrifugalFlowCompressorsIV. AxialandRadialFlowTurbinesV. Combus>onSystemsVI. PerformancePredic>on
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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.
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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
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Introduc>ontoGasTurbines
Usedtoproducemechanicalpowerbyexpandingahighenergygasacrossaturbinewithoutreciproca>ngmembers(suchasapiston/cylinderassembly),thustheyhavethefollowingadvantages:• Highpowerproduc=onfortheirsizeandweight• Highreliabilityduetoreducedrubbingmembers,fewbalancingproblems,andlowlubrica>ngoilconsump>on
• Simpleu>liza>onofmul=plefuels
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HistoryofWater/SteamTurbines
• Firstturbinesusedwaterastheworkingfluidtoproducehydro-electricpower;s>llasignificantcontributortoworld’senergyresources
• Steamturbinesintroducedaround1900;widelyusedforelectricitygenera>on(currentunitscanhaveover1GWofshaBpowerand40%efficiency)
• Steamturbineswerealsowidelyusedformarinepropulsionupun>lmid1970’s(whenmoreefficientdieselenginestookover)exceptfornuclear-poweredaircraBcarriersandsubmarines
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DisadvantagesofSteamTurbines
• Produc>onofhigh-pressurehigh-temperaturesteamrequiresbulkyandexpensivesteamgenera>ngequipment
• Hotgasesproducedinboilerornuclearreactorcorecanneverreachtheturbine;insteadanintermediatefluid,typicallysteam,flowsthroughtheturbine
• Satura>ontemperatureofsteam,evenathighpressures,limitsmaximumthermalefficiencytheore>callypossible
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HistoryofGasTurbines
• Seriousdevelopmentbeganinthe1940’s;mainlyonturbojetengineforaircraBpropulsion
• Significantuseforotherfields,includingelectricalpowerproduc>on,beganinthe1950’s
• Wideusetoday(currentunitscanhaveover0.5GWofshaBpowerand45%efficiency)hasbeendrivenbyimprovingtwomainperformancelimi>ngfactors:– Componentefficienciesthroughaerodynamicsresearch– Hightemperaturematerialsdevelopedthroughadvancesinmetallurgy
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GasTurbineCycles
Twomainclassifica>ons:1. ShaCPowerCyclesusedforlandbasedelectric
powergenera>on,marinepropulsion,mechanicaldrivesystems,processheat,compressedair,etc.
2. AircraCPropulsionCycleswhereperformancedependsonforwardspeedandal>tude
ThiscoursewillfocusonshaBpowercycles.
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ShaBPowerCycles
Twomainconfigura>ons:a. Opentotheatmosphere– Mostcommonforpowergenera>onandengines– Heataddi>ontypicallyinacombus>onchamber
b. Closedloop– Foundinnuclearpowerplants– Heataddi>onandheatrejec>ondonebyheatexchangersatconstantpressure
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OpenShaBPowerCycle
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OpenShaBPowerCycleOpera>on
1. Freshairisdrawnintothecompressorwherebothitspressureandtemperatureareincreased
2. Fuelismixedwithcompressedairatanappropriatefuel/airra>oandignitedinthecombus=onchambertoproducehighenergygases
3. Combus>onproductsareexpandedacrossaturbinetoalowerpressureandtemperaturewhichproducesshaCpowerthatisusedtooperatethecompressorandgenerateelectricity
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ClosedShaBPowerCycleReplacecombus>onchamberwithheatexchangerandcloseloopbyaddingasecondheatexchanger
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IdealCondi>onsforGasTurbines
Assumethefollowing:1. Compressionandexpansionprocessesare
reversibleandadiaba>c,thusisentropic2. Kine>cenergyandpoten>alenergychangesforgas
arenegligible3. Pressurelossesforgasarenegligible4. Idealgaswithconstantproper>esandcomposi>on
atconstantmassflowrate(steadyopera>on)5. “Complete”heattransfer(temperatureriseoncold
sideequalstemperaturedroponhotside)
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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.
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BraytonCycle
turbine
compressor heatexchanger
heatexchanger
Pressure(p)–SpecificVolume(v)Diagram
Temperature(T)-Entropy(s)Diagram
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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( )
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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
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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
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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
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CyclePerformance
Thermalefficiency-desiredpowerorworkrateoutputdividedbyrequiredheatinputNOTE:Bythe2ndLawofThermodynamicspowercyclemustrejectheattoproducework,thusηth<1.
ηth =!Wcycle !m!Qin !m
=!Q23 + !Q41!Q23
=1−!Qout!Qin
ηth =1−h4 − h1h3 − h2
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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( )
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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
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BraytonCycleNetWorkRate
ForfixedT1 = Tmin andT3 = Tmax ,networkratefirstincreaseswithpressurera>o,reachesmaximumatrp, opt,andthendecreases.
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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
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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
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Example#1Airentersthecompressorofanidealgasturbinesystemat100kPaand27°C.Thepressurera>ois5andthemaximumtemperatureis867°C.Foryourcalcula>onsusethecold-airstandardandlistanyaddi>onalassump>ons.a. SketchtheT-sdiagramforthiscycle.b. Calculatethethermalefficiency.c. Calculatethebackworkra>o.d. Calculatethespecificworkoutput.
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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
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NotesonBraytonCycle
• Effectofpressurera=oonefficiencycanbeobservedbyconsideringareasonT-sdiagram
• Maximumtemperature(T3)limitedbyturbineblades(approximately1750K)–oBencalledthe“metallurgicallimit”
• Minimumtemperature(T1)usuallyambient(approximately300K),thusnotconsideredanindependentvariable
• Tradeoffbetweenop>mumthermalefficiencyandmaximumworkoutput
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ImprovingGasTurbinePerformance
1. Regenera=on-useturbineexhausttopreheatairenteringcombustor
2. Reheat-reheatturbineexhaustandaddaddi>onalturbine(s)
3. Intercooling-coolcompressorexhaustandaddaddi>onalcompressor(s)
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Regenera>veGasTurbine
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BraytonCyclewithRegnera>on
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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( )
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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
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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
![Page 36: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/36.jpg)
Example#2Airentersthecompressorofanidealgasturbinesystemat100kPaand27°Cwithidealregenera=on.Thepressurera>ois5andthemaximumtemperatureis867°C.Foryourcalcula>onsusethecold-airstandardandlistanyaddi>onalassump>ons.a. SketchtheT-sdiagramforthiscycle.b. Calculatethethermalefficiency.c. Calculatethebackworkra>o.d. Calculatethespecificworkoutput.
![Page 37: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/37.jpg)
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.
![Page 38: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/38.jpg)
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.
![Page 39: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/39.jpg)
BraytonCyclewithReheat
• Excessairisusedforcombus>onbecauseoftemperaturelimitsimposedbyturbineblades
• Secondturbineusesexcessairandaddi>onalfuelformorecombus>on
• Foridealreheat(maximumworkrate)forfixedrpandT3 = Tb, pressurera>oacrosseachstagecanbeshowntobeequalwherepa=pb=pi: rp =
p2p1=
p3pa
⎛
⎝⎜
⎞
⎠⎟
2
=pbp4
⎛
⎝⎜
⎞
⎠⎟
2
![Page 40: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/40.jpg)
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⎡
⎣
⎢⎢
⎤
⎦
⎥⎥
![Page 41: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/41.jpg)
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( )
⎡
⎣⎢⎢
⎤
⎦⎥⎥
![Page 42: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/42.jpg)
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
![Page 43: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/43.jpg)
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( )
![Page 44: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/44.jpg)
Example#3Airentersthecompressorofanidealgasturbinesystemat100kPaand27°Cwithidealreheat.Thepressurera>ois5andthemaximumtemperatureis867°C.Foryourcalcula>onsusethecold-airstandardandlistanyaddi>onalassump>ons.a. SketchtheT-sdiagramforthiscycle.b. Calculatethethermalefficiency.c. Calculatethebackworkra>o.d. Calculatethespecificworkoutput.
![Page 45: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/45.jpg)
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
![Page 46: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/46.jpg)
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
![Page 47: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/47.jpg)
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.
![Page 48: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/48.jpg)
BraytonCyclewithIntercooling
• Lessworkisrequiredtocompressacoolgas• Compensatesforlowtemperaturelimitedbynature(examples:airoroceantemperature)
• Limiteduseinprac>cebecauserequiresbulkyequipmentandhugeamountsofcoolingwater
• Foridealintercooling(minimumworkrate)forfixedrpandT1 = Td, pressurera>oacrosseachstagecanbeshowntobeequalwherepa=pb=pi:
rp =p2p1=
pcp1
!
"#
$
%&
2
=p2pd
!
"#
$
%&
2
![Page 49: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/49.jpg)
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
![Page 50: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/50.jpg)
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( )
![Page 51: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/51.jpg)
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
![Page 52: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/52.jpg)
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
![Page 53: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/53.jpg)
GasTurbinewithRegenera>on,Reheat,andIntercooling
• Whilereheatandintercoolingaloneincreaseworkoutput,theyalsodecreasethermalefficiency:– Forreheat,needextraheatforhea>ngbetweenstagesandheatrejec>onathighertemperatures
– Forintercooling,needtoheatupmoreaBercompression
• However,reheatandintercoolingincreasethepoten>alforregenera>on;combined,theoveralleffectcanbeanincreaseinthethermalefficiency
![Page 54: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/54.jpg)
GasTurbinewithRegenera>on,Reheat,andIntercooling
![Page 55: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/55.jpg)
BraytonCyclewithRegenera>on,Reheat,andIntercooling
![Page 56: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/56.jpg)
Example#4Airentersthefirstcompressorstageofanidealgasturbinesystemwithidealregenera>on,reheat,andintercoolingat100kPaand27°C.Thepressurera>ois5acrossbothcompressorsandthemaximumtemperatureis867°C.Foryourcalcula>onsusethecold-airstandardandlistanyaddi>onalassump>ons.a. SketchtheT-sdiagramforthiscycle.b. Calculatethethermalefficiency.c. Calculatethebackworkra>o.d. Calculatethespecificworkoutput.
![Page 57: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/57.jpg)
EricsonCycle
• IdealcycleforgasturbineengineswithanefficiencyequaltotheCarnotefficiency
• Theore>callyaccomplishedinthelimitwhereregenera>onisusedwithaninfinitenumberofstagesofreheatandintercooling
![Page 58: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/58.jpg)
CombinedGasTurbine-VaporPowerCycle
Wasteheatfromgasturbinepowercycle(toppingcycle)isusedasheatinputforvaporpowercycle,thusthethermalefficiencybecomes:wheresubscriptgisforthegascycleandthesubscriptvisforthevaporcycle.
ηth =!Wg !mg + !Wv !mv
!Qin,g !mg
![Page 59: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/59.jpg)
CombinedBrayton-IdealVaporPowerCycle
![Page 60: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/60.jpg)
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
![Page 61: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/61.jpg)
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
![Page 62: Theory and Applicaon of Gas Turbine SystemsTheory and Applicaon of Gas Turbine Systems Part I: ... over 1 GW of sha power and 40% efficiency) ... depends on forward speed and al>tudekshollen/GasTurbine/Lecture_GT_Part_I.pdf ·](https://reader031.vdocuments.site/reader031/viewer/2022030400/5a6ff6f47f8b9ac0538b855c/html5/thumbnails/62.jpg)
GasTurbinesForAircraBPropulsion
S>lluseBraytoncyclewiththefollowingchanges:• Diffuserde-acceleratesincomingflowtozerovelocity(incomingflowhassignificantKE)
• Nozzleacceleratesexi>ngflowtosignificantKE
• TurbineworkproducedequalscompressorworkandminoraircraBpowerneeds
h1 = hair +Vair2
2
V5 ≈ 2 h4 − h5( )
h3 − h4 ≈ h2 − h1