engineering science the life behind an internal combustion

ENGINEERING SCIENCE

LECTURE NOTES

The Life Behind anInternal Combustion EngineBY HAZEL WEE LING, ST HILDA’S COLLEGE, 2015–2019AND SHAUN TANG, UNIVERSITY COLLEGE, 2012–2016

The internal combustion engine ranks as one of the most important inventions ever made, providing controllable power from a truly portable unit since 1859. In this class, we will look at the theoretical thermodynamic cycles behind these machines – using knowledge of the First Law for a closed system – and at how real engines work.

EngineeringScience HazelWeeLing&ShaunTang

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FirstLawforOpenSystemsIntroductionManythermodynamicmachinesmaybemodelledasopensystems.TheFirstLawofthermodynamics

forclosedsystemsisnotreadilyapplicabletosuchmachines,sowemustrecastitintoanewform,the

steadyflowenergyequation.Wewillalsomeetanewproperty,enthalpy,whichisparticularlyuseful

forthesecalculations.

SteadyFlowinOpenSystemsSteadyFlowEnergyEquationForaclosedsystemtheFirstLawstates

whereUistheinternalenergyofthesystemduetothermalmotionofthe

molecules.WecanextendthisconcepttoincludethetotalenergyEofthesystem,comprisinginternal,gravitationalandgrosskineticenergy,sothat

where

z=heightaboveanarbitrarylevelm

c=bulkvelocityofthefluidms-1.

ThusgzJkg-1(orkJkg-1)isthepotentialenergyperunitmass,and1/2c2Jkg

-1(orkJkg

-1)isthegross

kineticenergyperunitmass.Usuallyinclosedsystemstheinitialandfinalvaluesofzareequal,andthe

valuesofcarezero,sothatthetotalenergyEisthesameastheinternalenergyU.

Consideranopensystemwithasteadymassflowm˙kgs-1intoandoutofthe

systemboundary,asillustratedbelow.Theheatflowrateintothesystemis


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Nowconsiderwhathappensduringonesecond.AnelementoffluidAispushed

intothesystem,andanelementoffluidBisexpelledasshowninthefigure.The

systemboundarycanbeanalysedasaclosedsystembutwithamovingboundary.TheFirstLawforaclosedsystemgives


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Enthalpy


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NegligibletermsintheSFEE

Workinareversiblesteadyflowprocess


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istheareaunderap–vcurve,betweenthecurveandthevaxisoffigure(a).Nowp1v1andp2v2arethetworectanglesinfigure(b),sothattheshaftworkws

isgivenbyminustheareabetweenthecurveandthepaxisoffigure(c),oranalyticallyby

Steadyflowdevices

Compressor

Acompressororpumpisadeviceforincreasingthepressureofafluid,illustratedschematicallyinthe

figureabove.Thetermcompressorisgenerallyusedforgases,andthetermpumpisusedforliquids.

Inacentrifugalcompressorarotatingimpellerflingsthefluidradiallyoutward,thusincreasingits

pressure.Inanaxialcompressor,thefluidispushedbybladesonarotatingwheelthroughstationary

bladesintoasmallerspace.Areciprocatingcompressoroperatesinadifferentfashion.

Consideracompressorwhichtakesfluidatpressurep1anddeliversitatpressurep2wherep2>p1.Ifweassumethat

_thecompressorisadiabatic

_kineticandpotentialenergychangesarenegligible


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Turbine

Aturbineisadeviceforextractingworkfromahighpressurefluid,illustratedschematicallyinthe

figureabove.Thebasicprincipleisthatthefluidexpandsthroughstationarynozzlesorbladesand

impactsagainstbladesmountedonarotatingwheel.Thisprocesscanberepeatedmanytimesin

stages.Ateachstagethefluidlosessomeofitsoriginalpressure.Commonexamplesarethesteam

turbineandthegasturbine.

Consideraturbinewhichtakesfluidatpressurep1andexhaustsitatpressurep2wherep1>p2.Ifweassumethat

_theturbineisadiabatic

_kineticandpotentialenergychangesarenegligible


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Example1:

Problem:Asteadyflowpumpcompressesliquidwaterat20oCfrom0.0233barto100bar,asshownschematicallyin

figure7.13.Thepumpisreversible.Calculatetheworkrequiredperkgofwater.Ifthepumpisalsoadiabatic,calculatethe

changeinspecificenthalpyofthewater.

Solution:Liquidwaterisalmostincompressible,soonthep–vdiagramoffigure7.14thelinefrom1to2isalmostvertical.

Atlowtemperaturesthespecificvolumeofwateriseffectivelyconstantandequaltov=1lkg-1=10

-3m

3kg

-1.Iftheprocessisreversible,thentheshaftworkis


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Example2:

Problem:Aboilertakesinwateratapproximately20

ocand100bar,heatsittoboilingtemperature,

vaporisesit,andsuperheatsthesteamto500oC,asshowninthefigurebelow.Theboileroperatesat

constantpressure,soonthep–vdiagram,theline2to3ishorizontal.Calculatetheheatinputperkg

offluid.


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Example3:

Problem:Steamat5000Cand100barispassedthroughanadiabaticturbineandexhaustsata

pressureof0.0233barandadrynessfractionof0.8,asshowninthefigure.Calculatetheshaftwork

producedbytheturbineperkgoffluid.


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Onthep–vdiagram,thelineformsagentlecurvefrom3to4.Fromthepreviousexample,h3=3374.6kJkg

-1.Wecanwriteh4as

Example4:

Problem:Wetsteamat0.0233baranddryness0.8iscondensedtogivesaturatedwaterat200C,as

illustratedinfigureabove.Calculatetheheatreleasedbythecondensationperkgoffluid.

Solution:Thewetsteamiscondensedinacondenser.Typicallythewetsteamimpactsagainstasurface

cooledbycoldwater.Noshaftworkisdone,sows=0,


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Onthep–vdiagram,thelinefrom3to4ishorizontal.Fromthepreviousexamples,h4=2047.3kJkg-1andh5=83.9kJkg-1.Notethatthesaturationpressureat200Cis0.0233bar.Hence

CyclesRankineCycleItwillbeobviousthatthelastfourexamplesdescribeprocesseswhichcanbejoinedtoformacycle.Thiscycle,calledtheRankinecycle,isillustratedinthefigurebelow,andisthebasisofmostelectrical

generatingstations,suchastheDidcotpowerstation.Itconvertsheatintowork.


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Rankinecycleonap-vdiagramItisusefultorepresenttheRankinecycleonap–vdiagramasinthefigureabove.Labeltheend

pointsofeachprocessclearlyandmarkarrowstoshowthedirectionofthecycle.Notethearrowsgo

clockwisearoundthecycle.Theprocessesare1→2feedpump,2→3boiler,3→4turbineand4→1

condenser.Notethatintheboilerandthecondenser,thepressureremainsconstant.Thefeedpump

lineisalmostverticalasthespecificvolumevdecreasesonlyslightlyfrom1→2.Point1liesonthe

saturatedliquidline,point2isinthesubcooledregion,point3inthesuperheatregion,andpoint4

insidethesaturatedliquidandvapourregion.

Internalcombustionengines

IntroductionTheinternalcombustionengine,initstwocommonforms,thespark-ignitionengineandthe

compression-ignitionorDieselengine,mustrankasoneofthemostimportantinventionsevermade,

providingcontrollablepowerfromatrulyportableunit.Inthischapterwewilllookatthetheoretical

cyclesbehindthesemachines,usingourknowledgeoftheFirstLawforaclosedsystem,andalsoat

howrealengineswork.

IdealisedCycles(AirStandardCycles)WhenweconsideredtheRankinecycle,theworkingfluidateverypointinthecyclewassteam,or

water,apuresubstance.Thesamewatersimplywentaroundandaroundthecycle,undergoingeach

processinturn,inaclosedsystem.Theinternalcombustionengineisratherdifferent.

Thespark-ignitionenginedrawsairfromtheatmosphereintoachamber,mixesitwithfuel,

compressesthefuel-airmixture,ignitesitwithaspark,allowstheresultinghotgasestoexpandanddo

work,thenexpelsthegasesintotheatmosphere.

Thecompression-ignitionengineisverysimilarexceptthattheairaloneis

compressed,afterwhichthefuelisinjected,ignitingspontaneously.Thustherearetwofeatureswhich

areimmediatelyapparent.

- Theinternalcombustionengineisnotstrictlyaclosedsystem,asairisdrawninandlater

expelled,alongwithcombustionproducts.True,thatsameaircouldeventuallybedrawnintotheengineagain,makingitacycleasillustratedinthefigurebelow,butthisisstretchingthe

definitionsomewhat.

- Theworkingfluidisnotapuresubstance,andinfactchangesconsiderablyinitscomposition

andthermalproperties,fromprocesstoprocess.Furthermore,themassofworkingfluid

containedwithintheenginevarieswithtime.Thecombustionprocessinarealengineisnotthe

simplestoichiometricequationyouhaveseeninthelastchapter,butisverycomplicated,with


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theformationofmanyotherproducts,suchasoxidesofnitrogenduetothehightemperatures,

andhydrocarbonsduetoprematurequenchingofthecombustionontherelativelycold

chamberwalls.

Tosimplifytheanalysisoftheinternalcombustionengine,weusetheairstandardcycle,inwhichtheworkingfluidisassumedtobeair,whichcirculateswithintheengineasinatrueclosedsystem.This

givesagoodfirstapproximation,becausetheprincipalconstituentofairisN2,whichremains

unchangedduringthecycle(exceptfortheformationofsmallamountsofNOandNO2).

InternalcombustionengineOttoCycleTheOttocycleisanairstandardcycleapproximatingthespark-ignitionengine

cycle.Therearefourprocesses,asillustratedinthefigureabove.

- 1→2representsreversibleadiabaticcompressionoftheair,requiringworkWin,frompressure

p1andvolumeV1top2andV2- 2→3representstheadditionofheatQintotheairatconstantvolumeV2=V3,raisingthe

pressuretop3- 3→4representsreversibleadiabaticexpansionoftheair,producingworkWout,topressure

p4andvolumeV4=V1- 4→1representstherejectionofheatQoutfromtheairatconstantvolumeV4=V1,reducing

thepressuretop1.

FromtheFirstLaw,wecanrelatetheworkandheattermsby


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Butthecompressionandexpansionprocesses,1→2and3→4,areboth

reversibleandadiabatic,soiftheairbehavesasanidealgas,canberepresentedby


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DieselCycleTheDieselcycleisanairstandardcycleapproximatingthecompression-ignition

enginecycle.Therearefourprocesses,asillustratedinthefigurebelow.


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GasTurbineEnginesIntroductionThegasturbineenginehasrevolutionisedairtravelwithitsamazingpowerto

weightratio.Inthischapterwewilllookatthetheoreticalcyclebehindthegas

turbine,andalsohowarealgasturbineengineworks.

IdealisedCycle(AirStandardCycles)Asforthediscussionofinternalcombustionenginecycles,weuseairstandardcycleswhenwefirstconsidergasturbineengines.Thatis,weassumethatthe

workingfluidisair,whichcirculateswithintheengineasinatrueclosedsystem.

ThisgivesagoodapproximationbecausetheprincipalconstituentofairisN2.

JouleCycleTheJoulecycleisanairstandardcycleapproximatingthegasturbineengine.

Therearefourprocessesasillustratedinthefigurebelow.


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Thecompressionandexpansionprocesses,1→2and3→4,arebothreversibleandadiabatic,soif

theairbehavesasanidealgas,theycanberepresentedusingthepolytropiclawby

Joulecycleefficiencyvspressureratio


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ThusthethermalefficiencyoftheairstandardJoulecycleisdeterminedsolelybythepressureratio.

Increasingthepressureratiorpincreasesthethermalefficiency.

Thisisillustratedforγ=1.4infigurethefigureabove.Notethattheefficiencyfallstozeroatrp=1.Theworkratiorwisdefinedastheratioofthenetworkouttotheturbinework

Schematicdiagramofagasturbineengine


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Additionalnoteson• Behaviourofsteam-watermixtures• PolytropicProcesses

*Engineering Tables and Data, known affectionately as HLT after the initials of its authors, has been the primary reference for generations of Oxford University engineering students.

Behaviourofsteam-watermixturesSaturatedTableinHLTWhenwaterandsteamareinequilibriumwitheachother,wesaythatthesteamissaturated.Tofindthepropertiesofsuchsteam–watermixturesweusethesaturatedtableinHLTonpages54–65.Pages54–55aretabulatedasafunctionoftemperatureandpages56–65asafunctionofpressure.


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Drynessfraction


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SuperheatedsteamSuperheatedsteaminHLT

PolytropicprocessesPolytropicequations

Polytropicprocessesonp-vdiagram

whereniscalledthepolytropicindex.Figure6.14showstheformofthis


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relationshiponap–Vdiagram.Manyprocessesapproximatetoareversiblelawofthissortin

practice.Usuallyn≥1.

Effectofpolytropicindex

- n = 1.0 is called an isothermal process because DT = 0 - n = 1.4 is called an adiabatic process because Q = 0.

engineering science the life behind an internal combustion

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