Chapter 9- Vapor Power Systems - College of … Ideal Rankine Cycle An ideal Rankine cycle consists...
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1 Chapter 9: Vapor Power Systems Table of Contents Introduction ........................................................................................................................................ 2 Analyzing the Rankine Cycle ............................................................................................................... 4 Rankine Cycle Performance Parameters ............................................................................................ 5 Ideal Rankine Cycle ............................................................................................................................. 6 Example ........................................................................................................................................................ 7 Rankine Cycle Including Isentropic Efficiencies ................................................................................. 8 Example ........................................................................................................................................................ 9 Example ...................................................................................................................................................... 10 Rankine Cycle Improvements ........................................................................................................... 11 Example ...................................................................................................................................................... 12 Numerical Answers to Examples ...................................................................................................... 13
Transcript of Chapter 9- Vapor Power Systems - College of … Ideal Rankine Cycle An ideal Rankine cycle consists...
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Chapter9:VaporPowerSystems
TableofContents
Introduction........................................................................................................................................2
AnalyzingtheRankineCycle...............................................................................................................4
RankineCyclePerformanceParameters............................................................................................5
IdealRankineCycle.............................................................................................................................6Example........................................................................................................................................................7
RankineCycleIncludingIsentropicEfficiencies.................................................................................8Example........................................................................................................................................................9Example......................................................................................................................................................10
RankineCycleImprovements...........................................................................................................11Example......................................................................................................................................................12
NumericalAnswerstoExamples......................................................................................................13
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IntroductionVaporpowersystems,orvaporpowerplants,convertaprimaryenergysourceintoelectricitybyalternatelyvaporizingandcondensingaworkingfluid(usuallywater).TheRankinecycleisthebasicbuildingblockofvaporpowersystems.Theprimaryenergysource(e.g.,fossil-fuel,nuclear,solar,orgeothermal)supplies𝑄",theenergyneededtovaporizetheworkingfluidintheboiler.Theturbinepowershaftisconnectedtoanelectricgenerator,whichgeneratestheelectricitythatisthentransmittedanddistributedtoconsumersviatheelectricalgrid.
Forfossil-fueledvaporpowerplants,𝑄" issuppliedbycombustionofthefossilfuel(e.g.,coal).1
1(Moran,Shapiro,Boettner,&Bailey,2011)
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Fornuclearvaporpowerplants,𝑄" issuppliedbyacontrollednuclearreaction.2
Forsolarpowerplants,𝑄" issuppliedbycollectedandconcentratedsolarradiation.3
2(Moran,Shapiro,Boettner,&Bailey,2011)3(Moran,Shapiro,Boettner,&Bailey,2011)
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Forgeothermalpowerplants,𝑄" issuppliedbyhotwaterand/orsteamdrawnfrombelowtheearth’ssurface.Ofnote,theworkingfluidinageothermalpowerplantisanorganicsubstance,suchasisobutene,thathasalowerboilingpointthanwater.4
AnalyzingtheRankineCycleWewillanalyzethecomponentsoftheRankinecyclebyapplyingthe1stLawtoeachdeviceinthecycle(turbine,condenser,pump,boiler).Foralldeviceswewillassumesteadystate,steadyflow(SSSF),one-dimensional(1D)flow,uniformflow,andaquasiequilibriumprocess.Wewillalsoneglectanychangesinkineticandpotentialenergy.
4(Moran,Shapiro,Boettner,&Bailey,2011)
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Neglectingheattransferwiththesurroundings,therateatwhichworkisdevelopedperunitmassofvaporpassingthroughtheturbineis:
𝑊$%&'()* =𝑊$%&'()*
𝑚= ℎ. − ℎ0
Thesignof𝑊$%&'()* willbepositive,followingoursignconventionthatworkispositivewhenitisdonebythesystemandonthesurroundings.
Theonlyworkinteractionforthecondenserisflowwork.Therefore,therateatwhichheatistransferredperunitmassofvaporpassingthroughthecondenseris:
𝑄12)3*)4*& =𝑄12)3*)4*&
𝑚= ℎ5 − ℎ0 = −𝑄6
Thesignof𝑄12)3*)4*& willbenegative,followingoursignconventionthatheattransferispositivewhenheatistransferredtothesystemfromthesurroundings.
Neglectingheattransferwiththesurroundings,therateatwhichworkisdevelopedperunitmassofvaporpassingthroughthepumpis:
𝑊7%87 =𝑊7%87𝑚
= ℎ5 − ℎ9
Thesignof𝑊7%87willbenegative,followingoursignconventionforwork.
Theonlyworkinteractionfortheboilerisflowwork.Therefore,therateatwhichheatistransferredperunitmassofvaporpassingthroughtheboileris:
𝑄'2(:*& =𝑄'2(:*&𝑚
= ℎ. − ℎ9 = 𝑄"
Thesignof𝑄'2(:*& willbepositive,followingoursignconventionforheattransfer.
RankineCyclePerformanceParametersThethermalefficiencyoftheRankinecyclewillbeacomparisonofwhatweget(thenetworkofthecycle)towhatwehavetopay(theheatsuppliedtothecycle).
𝜂 =𝑊$%&'()* + 𝑊7%87
𝑄'2(:*&=
ℎ. − ℎ0 + ℎ5 − ℎ9ℎ. − ℎ9
= 1 +ℎ5 − ℎ0ℎ. − ℎ9
Thebackworkratiocomparestheworkrequiredbythepumptotheworkdevelopedbytheturbine.
𝑏𝑤𝑟 =𝑊7%87𝑊$%&'()*
=ℎ5 − ℎ9ℎ. − ℎ0
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IdealRankineCycleAnidealRankinecycleconsistsoffourreversibleprocesses.
Process1à2 Isentropicexpansionthroughtheturbinefromsaturatedvaportothecondenserpressure2à3 Constantpressureheatrejectionthroughthecondensertosaturatedliquid3à4 Isentropiccompressionthroughthepump4à1 Constantpressureheatadditionthroughtheboiler
Thepumpworkcanbeevaluatedusingthe1stLaworbyusingtheexpressionformechanicalworkforsteady-flowreversibleprocesses,wherechangesinkineticandpotentialenergyhavebeenneglected.
𝑊𝑚 &*A
= − 𝑣𝑑𝑝2%$
()
Thespecificvolumeofthefluidflowingthroughthepumpisapproximatelyconstant.Therefore,pumpworkcanbeapproximatedas:
𝑊7%87𝑚 &*A
≈ −𝑣5 𝑝9 − 𝑝5
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ExampleWateristheworkingfluidinanidealRankinecycle.Thecondenserpressureis6kPa.Theboilerpressureis10MPa.FindthethermalefficiencyofthecycleandcomparetoCarnotcycleefficiency.
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RankineCycleIncludingIsentropicEfficienciesAnalysisofanidealRankinecycleassumedallprocessesoperatedreversibly.WecanalsoanalyzeRankinecycleswhengivenisentropicefficienciesoftheturbineandofthepump.
ThethermalefficiencyofaRankinecycleincludingisentropicefficienciesoftheturbineandofthepumpcanbecalculatedby:
𝜂 =ℎ. − ℎ0 + ℎ5 − ℎ9
ℎ. − ℎ9=𝜂$%&'()* ℎ. − ℎ04 + ℎ5 − ℎ94
𝜂7%87ℎ. − ℎ9
=𝜂$%&'()* ℎ. − ℎ04 + 𝑣5 𝑝5 − 𝑝9𝜂7%87
ℎ. − ℎ9
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ExampleSteamistheworkingfluidinaRankinecycle.Superheatedvaporenterstheturbineat10MPa,480°C.Condenserpressureis6kPa.Theturbineandpumphaveisentropicefficienciesof80%and70%.Findtheheatadditionthroughtheboiler(kJ/kg),thethermalefficiencyofthecycle,andtheheatrejectionthroughthecondenser(kJ/kg).
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ExampleWateristheworkingfluidinaRankinecycle.Superheatedvaporenterstheturbineat10MPa,480°Cwithamassflowrateof7.8kg/sandexitsat8kPa.Theisentropicefficiencyoftheturbineis88%andtheisentropicefficiencyofthepumpis82%.FindthenetpowerdevelopedinkWandthethermalefficiencyofthecycle.
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RankineCycleImprovementsSuperheatandReheataretwooptionsforimprovingthethermalefficiencyofaRankinecycle.ARankinecyclewithsuperheatallowstheturbineinlettobesuperheatedvaporratherthansaturatedvapor.
ARankinecyclewithreheatincludesatwo-stageturbine.Steamexpandsthroughafirststageturbine(1à2),returnstotheboilertobereheated(2à3),andthenexpandsthroughthesecondstageoftheturbine(3à4)beforemovingthroughthecompressorandpump.
ThethermalefficiencyoftheRankinecyclewithreheatisagainacomparisonofwhatweget(thenetworkofthecycle)towhatwehavetopay(theheatsuppliedtothecycle).Forthis
𝜂 =ℎ. − ℎ0 + ℎ5 − ℎ9 + ℎF − ℎG
ℎ. − ℎG + ℎ5 − ℎ0
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ExampleSteamat10MPa,600°Centersthefirst-stageturbineofanidealRankinecyclewithreheat.Steamleavesthereheatsectionoftheboilerat500°C.Thecondenserpressureis6kPa.Thequalityattheexitofthesecond-stageturbineis90%.FindthethermalefficiencyofthecycleandcompareittotheCarnotefficiency.
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NumericalAnswerstoExamplesPage Answer(s)7 38.5%,47.1%9 3155kJ/kg,32.8%,2120kJ/kg10 7800kW,32%12 52.5%,64.5%
