laserbyAnkitSharmaFromAnkitSharma(MTechThesis)

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16%InternetSources: 5%Publications: 14%StudentPapers: 0%

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TurnitinOriginalityReport

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3%match(publications)Bansal,Ankit,AndrewFeldick,andMichaelModest."SimulationofHypersonicFlowandRadiationoveraMarsReentryVehicleUsingOpenFOAM",50thAIAAAerospaceSciences

MeetingincludingtheNewHorizonsForumandAerospaceExposition,2012.

2%match(publications)MMODEST."RadiativePropertiesofMolecularGases",RadiativeHeatTransfer,2003

1%match(publications)Joarder,R.,G.C.Gebel,andT.Mosbach."Twodimensionalnumericalsimulationofadecayinglasersparkinairwithradiationloss",InternationalJournalofHeatandMass

Transfer,2013.

1%match(publications)Goebel,Florian,andChristianMundt."ImplementationoftheP1RadiationModelintheCFDsolverNSMBandInvestigationofRadiativeHeatTransferintheSSMEMainCombustion

Chamber",17thAIAAInternationalSpacePlanesandHypersonicSystemsandTechnologiesConference,2011.

1%match(Internetfrom07May2014)http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710021465.pdf

1%match(publications)Sohn,Ilyoup,AnkitBansal,MichaelModest,andDeborahLevin."AdvancedRadiationCalculationsofHypersonicReentryFlowsUsingEfficientDatabasingSchemes",40th

ThermophysicsConference,2008.

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Shuen,J.S.."Inviscidfluxsplittingalgorithmsforrealgaseswithnonequilibriumchemistry",JournalofComputationalPhysics,199010

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J.J.Camacho."LaserinducedbreakdownspectroscopyoftrisilaneusinginfraredCO[sub2]laserpulses",JournalofAppliedPhysics,2007

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whenlaserpulseisfocused.Also,theprobabilitythatafreeelectronwillbepresentnaturallyinthefocalregionisnegligible.So,thesecond3processdependsonthefirstprocess[8].1.2.1MultiphotonionizationPhotoelectriceffect[9]isdefinedastheprocessofemissionofelectronsfromasurfacewhenlight(electromagneticradiation)fallsonit.ItwasdiscoveredbyHeinrichHertzin1887butitHertzfailedtoexplainitonthebasisofclassicalelectromagnetics.Itwasin1905whenEinsteinexplaineditin1905onthebasisofquantumtheory.[10]Whenlightstrikesthesurfaceofthemetalwithafrequencywhichislesserthanaspecifiedamount,therewouldbenoelectronemittedfromthesurfaceofthemetaltocauseemission.Classicalwavemodelfailedtoexplainthis.Einsteinpublishedhisworkontheoryofphotoelectriceffect[11]in19thcenturyexplainingitintermsofthequantummodeloflightwhichstatesthat

13Electromagneticradiationisastreamofparticles(photons)thattravelasawave.Supposethereisa

lightwavewithfrequencyhavingnumberofphotons.

13Eachphotoncarriesadefinedamountofenergy.E

?hv(1.1)Where

36hisPlancksconstanth=6.63x1034Jsandthetotalenergy

ofthewavelightisETotal=nh.E.g.

13Violetlight400nm,eachphotoncarriesE?hv?hc/fE?(6.

63x10?34Js)(3x108m/s)(400x10?9m)E=51019JHigherintensityoflightmeansthatthenumberofthephotonsislargeri.e.

13moreparticles4arebeingtransmittedinatimeperiod.Now,whenthephotonscarryingenergy

hvstrikesthesurfaceofamaterial,the

58energyofthephotonisabsorbedbythe

electron.ThisphotoncanfreeelectronsfromthesurfaceonlyifthephotonenergyisgreaterthanorequaltotheminimumthresholdfrequencyVo.WhichisdifferentfordifferentmaterialsElectronsabsorbthepartofthephotonenergyknownasWorkfunctionWtogetreleasedandtheremainderenergyofthe

photongoestothekinetic

21energyoftheelectronemittedwhichisequaltotheenergyofthephotonminustheworkfunctionofthe

metal.Ek(max)?hf?W(1.2)WhereEk=MaximumkineticenergyofejectedelectronForthresholdfrequency(f0),putE=00=hfWf0=W/h5Figure0.1MPIandcascadeionizationIn1929,MariaGoppertMayer[12]predictedtheoreticallythatlargenumbersofphotonscanbeabsorbedbyanatomwhichmakeselectrontotransittostateswhicharenotreachablebytheabsorptionofasinglephoton.Atomabsorbingmultiplephotonssimultaneouslymightbeionizedbyphotonshavingfrequencieslessthanthethresholdfrequency.Thiseffectwasinvestigatedfirstwithconstructionofthefirstlaserin1960.Duetothesmallenergyofthelaserphotons,theusualphotoelectriceffectisnotpossible(i.e.oneatomabsorbingonephotonandreleasingoneelectron).[13]Asenergyabsorbedwhenasinglephotonofrubylaserradiationcollidesisapproximately1eVbutthe

8ionizationpotentialofmanygasesisgreaterthan1020eV.So,asinglephoton

isnotsufficienttocauseionizationHence,multiplephotoncollisionsareneededtoreleaseanatomicelectron.6Whenwefocus

8apulsedlaserbeamonasmallfocalvolume,thenthe

moleculespresentinthegasabsorbsthepartofenergyresultingintoairbreakdownandplasmaformationtakesplace.Thiswholeprocessoccursinfollowingsteps:multiplephotoswhichareincidentonanatominitiatethereleaseoflargenumberofelectronsareduetomultiphotonionization(MPI).[14]

8M+mhvM++eWheremhvrepresentsthetotalenergyofmphotonseachhavingenergyhv.

Ifnphotonsareabsorbed,transitionsthatrequireenergylessthanorequaltonhvareenergeticallyallowed.DuetothisMPIreaction,

8electronnumberdensityincreaseslinearlywithtime.1.3CascadeIonization

DuetotheMPIprocessasdescribedabove,freeelectronsareavailableinthefocalvolume.Thesefreeelectronsthenabsorbmoreandmorephotonsandgetsexcited.Assoonastheionizationreachesacertainlevel,attemperaturesoftheorderofseveralthousanddegrees,thelightgetsabsorbeddueto

37freefreetransitionsoftheelectronsinthefieldoftheions.

ThisprocessisknownasInverseBremsstrahlungprocess[15].Whenthesesfreeelectronshaveabsorbedenergywhichishigher

28thantheionizationenergyofthegas,thentheystartimpactionizationofatoms/gasthroughthisreactionM+eM++2e

Ascanbeseenthatthisreactionresultsinreleaseoftwomoreelectronswhichcanstarttheprocessagainandtheprocessrepeatsagain.Thechainofthesereactionscausesa

59cascadereleaseofelectronsandhencetheconcentrationofthe

electronsincreasesexponentiallywith7time.Subsequentlyduetocascadeionizationprocess,plasmaisformed.1.4ExpansionofPlasmaItisobservedexperimentallytheplasmaformationtakesplaceoppositetothedirectionoftheincidentlighti.e.Plasmaexpandsoppositetothedirectionofthelightflux.Thisbackwardexpansionofplasmaisexplainedbythreedifferentandindependentmechanisms[16,17]RadiationsupportedshockwaveJustafterthebreakdownhasoccurred,intenseheatingofthegastakesplaceduetotheabsorptionofenergyinthegasatthefocusofthelaserbeamandhightemperatureandpressureregionisobtainedatthefocus.Duetothesepressureandtemperaturegradients,

23ashockwaveisproducedwhichtravelsinalldirections

(againstthelaserbeamalso)whichheatsthegasfurther.Gasintheshockwavethatistravellingagainstthelaserbeamgetsheatedtoahightemperatureandgetsionizedandhenceabsorbsmoreandmorelaserlight.Henceasshockwavemovestowardsthesource,zoneofabsorptionalsogetstransportedwithitagainstthebeam.Thisisknownashydrodynamicmechanism,firstproposedbyRamsdenAndSavic[18],andismuchsimilartowhatoccursindetonatingwavesinreactinggasesandiscalled"radiationsupportedshockwavemechanism.ProgressivebreakdownmechanismWithtime,powerofthelaserbeamincreases.Whenthetimeintegratedeffectofthelaserbeamissufficientfortheelectronstoacquiretheenergyneededforionizationoftheatoms,8regioninwhichthresholdconditionsareattainedalsostartsincreasingandpropagateswithtimetowardsthesourcei.e.ionizedvolumeincreasesandbreakdownregionstartspropagatingtowardsthelensandisknownasProgressivebreakdownmechanismandwasproposedfirstbyRaizer.[16]Afanasetal(1969)[17]studiedtheoreticallytheinteractionofpowerfulultrashortlaserpulseswithagasusingpicoseconddurationpulses.Theyfoundthatduetothecascadeionizationmechanism,theconcentrationofelectronsingasesatnormalpressureislesserascomparedwiththeconcentrationofneutralatomsbyseveralordersofmagnitude.Duetothislowelectrondensitytheplasmaproducedisalmosttransparenttotheincidentradiation,andhencetheonlypossiblemechanismwhichremainsforsparkexpansionisthebreakdownwave.RadiationtransportwaveThefocalregionwhichgetsionizedandbreakdownthenstartsemittingthermalradiation.This

8thermalradiationfromthestronglyheatedregionsisthenabsorbedbythegasinfrontofthe

absorbinglayerswhichalsogetsheatedandstartsabsorbingthelaserradiationwhich

25leadstotheheatingofthisregionbytheenergyofthelaserbeamandasaresulttheregionofhightemperatureand

increasedionizationmovesalongtheluminouschannel.ThisiscalledRadiationtransportmechanism[16]ThemeanfreepathofPhotonswithenergyhv=KT,attemperaturesoftheorderof105Kormore,radiatedbytheheatedgasisapproximatelyL=10cmwhichismuchlargerthanL=1/Kandeverycharacteristicdimensionoftheheatedregion[19].Hencetheheatedgasistransparenttoitsownradiationandstartsemittingfromitsownvolumewhichisabsorbedby9theadjacentcoolerlayerswheretheionizationiseithersmallornotyetstarted.Duetotheabsorbedradiation,thisregionsalsostartsionizingandwhentheionizationhasbecomesufficient,thenthenewionizationregionalsobeginstoabsorbthelaserlight.TheintensityofthefocusedlaserradiationishighascomparedwiththatofthermalradiationwhichisbeingemittedfromthehotterregionstowardsthecoolerlayersDuetowhichthenewlayerwhichhasjustabsorbedthelaserlightbecomesrapidlyheatedandstartsexpanding.1.5DecayandRecombination[19]Whenlaserpulsehasbeenstoppedthenattheendastronglyheatedvolumeisobtainedwhichhasateardropshape

8alongtheaxisofthelaserbeam.Thelengthof

thisteardropshapeisonlyfewmillimetersasitisequaltothedistancetravelledbytheabsorptionwavei.e.v.t.Thetransversedimensionsoftheconverginglightisalsoequaltothedimensionsofthefocusinglaserlightandisapproximatelyequaltofewmillimeters.Thiswholeprocesscanbecomparedtotheprocessofstrongexplosioninagas.Assoonastheenergyisreleased,

23ashockwaveisproducedwhichtravelsinalldirections

anditsintensitydecreaseswithtime.Initiallyitsshapeisteardropandastimepassesitthesurfaceoftheshockwavebecomesspherical.Breakdownofairandconsequentsparkformationoccurswhentheheatfluxatthefocalpointexceedsthebreakdownthresholdlimitofthegas.Atthispoint,atomsinthefocalregiongetsionizedandexcitedtohigherenergylevels.Assoonasthebreakdownhasbeenachieved,thegaswhichwasearliertransparenttothelaserradiationbecomesopaqueandhencethisgasnowstartsabsorbingthelaserradiationandplasmaisobtained.Theplasmasoobtainedalsoabsorbsmoreenergyandalsostartsreflectingthesame.Thereflectedradiationiseventuallyabsorbedinthenearbyadjacentmolecules.Inthebeginning,10thecascadeionizationwasoccurringthefocalregioni.e.atthepointwherethelaserintensitywasmaximum.Afterafewnanosecondswhenthisfocalregionhasbecomefullyionized,thencascadeionizationshiftstotheadjacentregionandverysoonitalsogetsfullyionizedandemitradiationtothecoolerregions.Thisprocesskeepsonrepeatingwhichcausestheabsorptionregionstoshifttowardsleftandfinallytheplasmaevolvesintoteardropshape[20].Figure1.0.2SchematicdescriptionofPlasmaFormation1.6ApplicationsofLaserIgnitionLaserbeamcanbeusedasapotentialsourceforignition[2,3,21].IthasvariousadvantagesoverconventionalmethodofignitionasunderAslasercanbefocusedpreciselyoverafixedpoint,sotheignitionlocationcanbe

controlledeasily.

52IgnitiontimingIgnitionenergy11DepositionrateHeatlosscanbe

controlledFlamestabilizationTheblastwavewhichisproducedfromthelaserinducedbreakdowncanbeusedtoprovidepropulsivepowertosmallvehicles.Reductionofdragonthebluntbodiesisalsooneoftheimportantapplicationsofthe

65energydepositedbythelaser.In

figure,energyhasbeendeposited

42inasupersonicflowpastahemisphere.Duetothedepositionofenergytheflowafterthe

bluntbodyshockgetsdisturbedcausingthevariationinpressuredistributionthroughtime.Thisvariationinpressurecausesthedragcoefficienttochange.[22].[22]1.7LiteratureReview12Afterthedepositionofthelaserenergy,varioustypesofchangesareobservedinthefocalvolumeaschemicalreactions,fluiddynamicphenomenonandradiationemission.Focalregionshasabsorbedhugeamountofinternalenergyascomparedtothesurroundingregionduetowhichthetemperatureofthatregionincreasesandcorrespondinglypressureincreasesanddensitydecreases.Duetothis,pressuregradientsarecreatedbetweenthebreakdownregionandambientwhichleadstotheoccurrenceoffluiddynamicphenomenonsuchasformationofblastwavewhichthentravelsinalldirections.ChemicalchangesoccurringinthefocalregioninvolvesionizationofthegasespresentinairasN2,O2intovariousspecies(N,O,NO)andtheirrecombinationdependinguponthetemperatureandpressure.Studyingofthelaserbreakdownprocessandtheconsequentfluiddynamicandchemicalchangesinthewholeprocesshasbeenverywellstudiedbyanumberofresearchersandtheiruseshasalsobeenexplored.ShankarGoshandKrishnanMahesh[20]havenumericallysimulatedthe

16fluiddynamiceffectsoflaserenergydepositioninair.

Theyclassified

26theflowfieldintothreephasesnamely:shockformation,shockpropagationandsubsequentcollapseoftheplasmacore.

Vorticitygenerationintheflowfieldhasalsobeenstudied.

16Threedifferentmodelswereusedbasedondifferentlevelofcomplexity.Inallthesemodels,

radiationlosseswereassumedtobenegligible.Phuoc[2]hasexplainedthe

45laserinducedsparkignitionfundamentalsincludingthelaserinducedgasbreakdownprocessand

thesparkevolutionandignitionmechanism.Hehasalsohighlightedpotentialbenefitsandapplications.13Bradleyetal.[21]havepresentedthe

49fundamentalsofhighenergysparkignitionwithlasers.

33Experimentalstudyoflaserinducedsparkignitionofflammablegaseousmixturesisreported.

61Probabilitiesofbreakdownwerefoundforair

overrangesofpressureandtemperatures.

29RamnathKandalaandGrahamV.Candler[8]hasdonenumericalstudiesoflaserinducedenergydepositionforsupersonicflowcontrol.

48Fluiddynamiceffectsoftheenergydepositionprocess

havebeenpredicted.Theyhavesuccessfullycapturedthemain

24physicalprocessesasinversebremsstrahlungabsorption,evolutionoftheplasmashapeandstructure,airbreakdownchemistryandthesubsequentfluiddynamics.

IvanG.Dors[23,24]etalhavestudied

16computationalfluiddynamicmodeloflaserinducedbreakdowninair.

Theyhavecomputedtemperatureandpressureprofilesfor

1710nsopticalbreakdownlaserpulses.

Fluiddynamicphenomenon

17followinglaserinducedbreakdownarerecordedwithhighspeedshadowgraphstechniques.The

characteristics

17lasersparkdecayflowpatternswere

found

17causedbylaserinducedopticalbreakdown.

Joarderetal[25]havedone

3twodimensionalnumericalsimulationofadecayinglasersparkinairwithradiationloss.

3Distributionofthetotalabsorbedenergyintoitsconstituentpartsblastwaveenergy,radiationenergyandleftoverenergy

hasbeencalculated.Theyhavemadeanattempttoincludetheradiationlossesofadecayinglaserspark.Spectralradiativepropertieswerefoundusingmultigroupmethod[26]soastoeasetheprocessofsolvingRTE.141.8ObjectiveofthecurrentthesisOwingtothehightemperatureofthegasesinthebreakdownregion,radiationlossesmaycontributeasignificantpart.Butinalltheabovereferences,radiationlosseshavebeenneglectedorhasnotbeenstudiedeffectivelytilldate.Jordaretalhastriedtoevaluatetheradiationlossesbuttheyhavealsofoundradiationlossestobenegligible[25].Theyhaveusemeanabsorptioncoefficientsmethodforthecalculationsoftheabsorptioncoefficients.Sinceradiationishighlyspectral,soinordertodotheradiationcalculationscorrectlyitisnecessarytocalculatetheradiativepropertiesofgasesateachandeverywavelengthpointforalargerange.Predictingtheradiativepropertiesoftheseradiativelyparticipatinggasesisadifficulttaskrequiringhighcomputationalpower.Thisisthemainthemeofthethesistofindoutthoseradiationlossesmoreaccuratelyinabetterwaywithdetailedlinebylinespectralmodelling.1.9LayoutofthethesisChapter1:IntroductionThischaptercoversthebasicsofairbreakdownduetolaserenergydepositionandprovidesabriefideaabouttheirapplications.Chapter2:FlowModellingModelingtheplasmaandcarryoutfurthersimulationstofindoutthevariousfluiddynamicandradiativeeffectsisdonebyusingopensourceCFDpackageknownasOpenFOAM.Thischapterdescribesallthegoverningequations,meshinformation,initialandboundary

conditionsofthedomain.hypersonicfoamsolverdevelopedforstudyingthefluiddynamiceffectshasbeendescribed.Chemicalkineticsgoverningtheprocesshasbeenincluded.AbriefintroductionabouttheCFDsolveOpenFOAMhasbeendone15Chapter3:RadiationModellingInthischapter,radiationmodellinghasbeendescribed.Radiationinparticipatingmediahasbeenexplained.Spectrallinesandtheirbroadeningduetovariouseffectshasbeenhighlighted.Varioustypesofatomicradiationhasbeendescribed.RadiativeandspectralpropertiesmodelshavebeendiscussedCalculationofthespectralradiativepropertieshavebeenshownusingLBLmethodandthensolvingtheRTEusingP1approximation

43method.Chapter4:ResultsandDiscussionsChapter5:Conclusions

andFutureWorkChapter6:References16EquationChapter(Next)Section12CHAPTERFLOWMODELLINGModelingtheplasmaandcarryoutfurthersimulationstofindoutthevariousfluiddynamicandradiativeeffectsisdonebyusingopensourceCFDpackageknownasOpenFOAM.Thischapterdescribesallthegoverningequations,meshinformation,initialandboundaryconditionsofthedomain.hypersonicfoamsolverdevelopedforstudyingthefluiddynamiceffectshasbeendescribed.Chemicalkineticsgoverningtheprocesshasbeenincluded.AbriefintroductionabouttheCFDsolverOpenFOAMhasbeenhighlighted.172.1OpenFOAMCFDSoftware

57OpensourceFieldOperationandManipulationcommonlyknownasOpenFOAM[27,28]is

anopensourceCFDsoftwarepackagewhichisusedfordevelopingnewnumericalsolversandvariouspre/postprocessingutilitiesforsolvingvariousproblemsofcontinuummechanicsasComputationalFluidDynamicsproblems(CFD).Itisavailableforfree

50undertheGNUGeneralPublicLicense.Itcanbe

usedtosolvecompressible/incompressibleNavierStokesequationforvarioustypesofmeshesstructuredorunstructured.Ithasalreadyinbuiltsolvers,variousapplications,numerousutilitiesandtoolstosolvevarioustypesoffluidflowproblem.IthasbeenwritteninC++.AtypicalsolverinOpenFOAMincludessetofequationswhichhasvariousmathematicaloperators(suchas,,etc.).ManytypesofsolversarealreadyavailableinOpenFOAMandhavebeenusedandtestedbyvarioususersforsolvingvarioustypesofCFDproblems.Inaddition,newsolverscanalsobeadded.Forthisnewcustomobjectssuchasboundaryconditionscanbecreatedwhicharemergedwiththeexistingsolverstosolveparticularproblems.ThisisoneofthemajoradvantageofOpenFOAMthatnewfeaturesandfunctionscanbeaddedoroldfeaturescanbemodifiedwithrelativeease.Varioustypesofpreandpostprocessingutilitiesareusedtomakegeometry,meshitproperly,setupthecase,runthesimulationandtheninterprettheresults.HypersonicFoamForsolvingthefluidflow,anewsolverhypersonicFoamhasbeendevelopedforthiscase.Itbasicallyincludesfeatureoftwoexistingsolverswhichhavebeencombinedalongwithnew18features

1todevelopanewsolvercapableofmodellinghightemperatureflows.

OneofthetwosolversalreadypresentinOpenFOAMwhichhasbeenusedtoconstructthenewsolverisrhoCentralFoam.Itis

1adensitybasedcompressibleNavierStokesflowsolverbasedoncentralschemeofKurganovetal.

[29]Butthissolverlacksfew

1featuressuchaschemistrymodelling,transportofspecies,andmodels

tofindvariousthermodynamicpropertiesathightemperature.reactingFoam[30]isthesecondsolverwhosefewfeatureshavebeenaddedinthenewhypersonicFoamsolver.ThisreactingFoamsolverisbasically

1apressurebasedsolverforsolvingchemicallyreactingcombustionproblems.

ItincludesvariousfeatureswhichwerenotavailableinrhoCentralFoamsuchashightemperature

1chemicalkineticsandthermodynamicpropertiesbasedonChemkinformatdata.Also,thethermodynamicdata

19whichisalready

1availableinOpenFOAMisvalidonlyupto6,000K

forfindingoutthermosphysicalproperties(thosematerialpropertiesthatvarywithtemperaturewithoutalteringthematerialidentity)asthermalconductivity,diffusivity,heatcapacity,viscosity,rho,enthalpy,entropy,cp,cv,internalenergy.Asthetemperatureinourcaseexceeds6,000K,soitisnotsuitableformodellinggaspropertiesathightemperatures.Toovercomethis,thethermodynamic

1datafromGordanandMcBride[31]wasaddedwhichprovidespolynomialfitsfor

1alargenumberofspeciesandalsovaliduptoalargetemperaturerange20,

000K.Likewisesomechangeswerealsodone

1intheOpenFOAMsolversoastoreadthenewdata.

cpisevaluatedbyafunctionwithcoefficientsfromnasathermodynamictables,fromwhichh,sareevaluated.Byincludingabovechangesandcombiningthefeaturesofthetwoexistingsolvers,thisnewhypersonicFoamsolveriscreated.[28]2.2GoverningEquationsGoverningequationsarethemathematicalexpressionwhichgovernordefinethephysicalprinciplesof

23conservationofmass,momentumandenergywhicharedescribedas

followsContinuityequation[32]Itrepresentstheconservationofglobalmassinthesystem.Indifferentialform,itcanbeexpressedas???t??.?U???0(2.1)WherethedensityandUistheaveragevelocity.Speciecontinuityequation:20The

1massconservationequationforspeciessisgivenas

[33,34]???tYS??.?U?YS???.??DS?YS??wS?0(2.2)Wherethefourtermsrespectively

1aretherateofchangeofmassofspeciesperunitvolume,themassfluxconvectedacrosscellfaces,themassdiffusionduetogradientsinconcentration,andthemassproductionrateduetochemicalreactions.Ysrepresentsthe

massfractionandDsrepresentstheeffectivediffusioncoefficient.MomentumEquationThemomentumequation

46canbewritteninvectorformas:[32,34]????tU???.??U??U?????p??.T

?0(2.3)Wherethe

27firsttermrepresentstherateofchangeofmomentumperunitvolume,thesecondtermrepresentsthefluxof

1momentumacrosscellfaces,thirdtermrepresentthepressureforcesactingoncellwalls,and

thelasttermrepresents

1viscousforcesactingoncellfaces.TheshearstresstensorTiswrittenasT?????U???U?T?23?.U

????(2.4)EnergyequationThetotalenergyconservationequationisasunder[32]21????tE???.??U??H?????.?T.U??k?2T??.????hSDS?Ys????.qrad?0(2.5)

1Wherethetermsintheequationintheorderoftheirappearancerepresentrespectivelythe

1rateofchangeoftotalenergyperunitvolume,thefluxoftotalenthalpyacrosscellfaces,theworkdonebyshearforces,theconductionofenergyduetotemperaturegradients,thediffusionofenthalpyduetoconcentrationgradients,andtherateofenergylossduetoradiation.Thetotalenthalpyofthegasiswrittenas

?H??E?????e?0.5

1?U2?p(2.6)Whereeistheinternalenergyofthegas.Pressureandtemperaturearenotsolvedexplicitlyasvariables,andareevaluatedfromthesolutionvariablesasfollows.p?

??(2.7)Whereisthe

1compressibilityofthefluidgivenby=(2.8)AndthetemperatureiscalculatediterativelyfromthetotalenergyasT?Cv?T

??E?T??0.5U2?1(2.9)The

31unsteadycompressibleNavierStokesequationsareamixedsetofhyperbolicparabolicequationsintimeandthe

steadystateNavierStokesequationhavemixed(parabolicelliptic)natureandhencearemoredifficulttosolveascomparetounsteadyequation.So,22steadystate

1equationsarealsosolvedasunsteadyevenifdesiredsolution

issteady.Inthesecases,unsteadyequationsaresolved

1fromaninitialdatapointuntilasteadystatesolutionisreached.

Shockisalsosimultaneouslycaptured

1asthesolutionevolvesintime.Inhighspeedflows,discontinuitiesasshocksandcontactssurfacescan

affectthenumericalsolutionbycausingoscillations.Drugetetal.havedoneacomparisonofvariousschemesforsolutionofconservationlaws.[35]Amongallthoseschemes,upwindschemesaremorecommonlyusedduetothefactthattheyhaveaccurateshockcapturingcapability.HowevertheyaredifficulttoimplementastheyrequireRiemannsolvers.Anotherschemeis

1centralupwindschemeofKurganovetal[36]which

hasupwindnatureandiscomparativelysimplerandcanbeappliedeasilytogeneralconservationlaws.ThesecentralandcentralupwindschemeshavetheadvantagethattheyhavenonoscillatorycharacteristicandavoidcomplexityinvolvedwithRiemannsolvers.[37]OpenFOAMsolverworksbysolvingthevariousequationsas

1continuity,momentumandenergyequationina

sequentialmanneroneaftertheother.Afterthisexplicitschemeisthenappliedi.e.

1usingdatafromtheprevioustimestepfortheneighboringpoints

1tointegrateintimeforaparticularcell.

Theexplicitschemesaresolvedforverysmallstepsduetothestabilityconditions.Howeverimplicitschemesarerelativelystableformuchlargertimestepsbuttheyarenotusedduetotheirhighcomplexitylevel.Finally,iftimeaccuratesolutionsaredesiredthen

1higherorderschemesas4thorderRungeKuttamethod

[38]isusedwhereEulerexplicitschemecanbeusediftimeaccuratesolutionsarenotrequired.23TransportPropertiesEffectoftemperatureonthe

47viscosityofthegasiscalculatedbySutherland'sLaw

[39]??1A?s?TTs(2.10)TWheretheconstantsAsandTs

1arehardcodedinthesolver.As=1.67212

x106kg/(msK0.5)andTs=170.672K.2.3ChemicalKineticsAslaserenergyisdeposited,temperatureofthefocalregionstartsrisingandreachestoaveryhighvalueofalmost17800K.Atsuchahightemperature,dissociationofairintovariousspeciesstartsoccurring.Finiteratechemistrymodelhasbeenusedwhichincludes

3fivespecies(O2,N2,O,N,andNO)andelevenelementaryreactionstepsforthedissociationandrecombinationofair

.However

9completemodelwithionizationreactionsinvolves11speciesand26elementaryreaction

step.Butherethe

9effectofionizationisneglectedonlyforthesakeofsimplicity.[

40]

22ForasetofNRelementaryreactionsinvolvingNspeciestherateequationscanbewrittenintheformNN?vi'jnj

?

66?vi''jnj(2.11)j?1

j?1Wherei=

31,2,NRisthenumberofreactions,v'ij

9andvijarethestoichiometriccoefficientsforspeciesjappearingasareactantintheithforwardandbackwardreactionsrespectively24andnj=Cj/Wjisthemolarconcentrationforspeciesj.

3ThereactionrateconstantsaregivenbytheArrheniusexpression

?Eiki?AiTmieRuT(2.12)

41WhereEirepresentstheactivationenergyofreactioniandAi,miareconstants.

Total

9changeofmolarconcentrationofspeciesjis

3obtainedbysummingupthechangesinmassconcentrationofspeciesjduetoallreactionsi.e.

Sj?Wj?NR???v?ij?vi?j???kfi?nlv?ilNN?????l?1?kbi?nlv''il(2.13)i?1?l?1??Wherekfi,

3kbiaretheforwardandbackwardreactionrateconstantsrespectively.

25Table1:Listofreactionsconsideredforthesimulationsare[40]Reaction3.6x1018T1.0exp(5.95x104/T)ForwardRateCoefficient,KF(cm3/molesec)(3c.0mx31/m01o5Tle0s.5ec)BackwardRateCoefficient,KBThirdBody,O2+M2O+M1.9x1017T0.5exp(1.33x105/T)1.1x1020T0.5NM,NON2+M2N+M3.9x1020T1.5exp(7.55x104/T)1.0x1020T1.5O,NO,O2NO+MN+O+M3.2x1019T1exp(1.97x104/T)1.3x1010T1.0exp(3.58x103/O2,N2O+NON+O27.0x1013exp(3.8x104/T)T)1.56x1013O+N2N+NO4.08x1022T1.5exp(1.13x105/T)2.27x1021T1.5N+N2N+N+N9.0x1019T1.0exp(5.95x104/T)7.5x1016T0.5O2+O2O+O3.24x1019T1.0exp(5.95x104/T)2.7x1016T0.5O2+O22O+O27.2x1018T1.0exp(5.95x104/T)6.0x1015T0.5O2+N22O+N24.7x1017T0.5exp(1.13x105/T)2.72x1016T0.5N2+N22N+N27.8x1020T1.5exp(7.55x104/T)2.0x1020T1.5NO+

51MN+O+O,N,NMO

Asexplainedpreviouslyduetothemovementoftheabsorptionregion,theplasmafinallyevolvesintoteardropshape.Thedomainchosenforthenumericalsimulationisofsize2620x20mm2whichisthendiscretizedinto500x500controlvolumes.Thedimensionsofthefocalvolumeareasshowninfig.Ithasbeenassumedthat93mJoftheenergyhasbeenfocusedandabsorbedbythe3mm3ofthefocalvolume[25].Thisspecificvalueofenergyhasbeentakenfromthepastexperimentsthathasbeencarriedouttostudythefluiddynamiceffectsoccurringduetolaserenergydeposition.Table1:ValuesofvariousvariablesatInitialandequilibriumconditions(att=0.02s)VariableInitialConditions(entiredomain)EquilibriumConditions(atplasmaregion)T300K17800KP101325Pa5071070PaN20.7550.325064O20.23220.000989AR0.01280.0128N00.423377O00.223719NO00.01405327Figure2.0.1MeshforaxisymmetricsimulationFigure2.0.2BlastWaveformationThisblastwaveformationwasobservedusinghypersonicfoam.ThecodewastakinglargetimetoconvergeandsincemuchworkhasalreadybeendonetostudythefluiddynamiceffectssothefluiddynamicresultsweretakenfromearlierpublisheddatabyJordaretal[25].Fromflowmodellingresultswegetmassfractions(Y)ofvariousspecies.Thismass28fractionisthenusedtofindoutnumberdensitywhichisthenfurtherusedtofindforradiationmodellingasexplainedinnextchapter.Ni?(NA)(Yi)(?)(2.14)WiWhereNi=Numberdensityofthespeciei(m3)NA=Avogadroconstant=6.022141291023(mol1)Yi=Massfractionofspeciei(ObtainedfromflowmodellingresultsfromOpenFOAM)Wi=Molecularweight(kg.mol1)=density(kg.m3)29EquationChapter3Section13CHAPTERRadiationModellingInthischapter,radiationmodellinghasbeendescribedusingtheresultsfrompreviouschapter.Radiationinparticipatingmediahasbeenexplained.Spectrallinesandtheirbroadeningduetovariouseffectshasbeenhighlighted.Varioustypesofatomicradiationhasbeendescribed.RadiativeandspectralpropertiesmodelshavebeendiscussedCalculationofthespectralradiativepropertieshavebeenshownusingLBLmethodandthensolvingtheRTEusingP1approximationmethod.303.1IntroductionWhenradiativeenergyisemitted,ittravelsinalldirections.Duetothis,

34mostoftheradiativeenergyemittedintheshocklayergetsescapedfromtheregionandhencetheshocklayerto

getcooled.Thiscoolingeffectcanaffecttheflowfieldparametersandhencecorrespondingheatloads.IfthiscoolingeffectisalsoconsideredsimultaneouslywhilesolvingforflowconditionsthenitisknownasRadiationFlowfieldcouplingifthiseffectisnotconsideredthenitisknownasuncoupledapproach.Incoupledapproach,RTEequationissolvedalongwithflowequations.Hence,coupledapproachiscomparativelydifficultandcomputationallyexpensiveascomparedtouncoupledapproach.Inuncoupledapproach,radiationeffectsarenotconsideredandadiabaticconditionsareassumedintheflowfield.Butactually,radiationistakingplace.So,neglectingtheradiationseffectsmayresultinoverestimationoftheheatloads.Buteventodaymostoftheresearchersuseuncoupledapproachduetoitssimplicity.Nowadays,thefullycoupledmethodhasbeenreplacedbylooselycoupledapproach.Inthismethod,RTEandflowequationsarenotsolvedateveryiterations.Flowequationsaresolvedateachiterationandradiativepropertiesareupdatedafterfewflowiterations.Betweenanytwoflowiterations,radiationfieldisassumedtobeconstant.[41]3.2RadiativeTransferthroughparticipatingmedia:Radiativetransferbetweensurfacesthatareseparatedbyparticipatingmediaisdifficulttoevaluateascomparedtothosesurfaceshavingvacuumormediumwhichisradiativelynonparticipatingmedium.Butinmostoftheengineeringapplicationsasburningofanyfuel,

5nuclearexplosions,hypersonicshocklayers,rocketpropulsion,andplasmageneratorsfornuclearfusion,andablatingsystems,etc.theinteractionof

thermalradiationwiththe31mediumcannotbeneglectedandmustbeconsidered.RadiativeTransferEquation(RTE)isusedtodescribethe

12Radiativeintensityfieldwithintheenclosureasafunctionoflocation(fixedbylocationvectorr),direction(fixedbyunitdirectionvectors)andspectralvariable(wavenumber)[

42].DerivingRTEforabsorbing,emittingandscatteringmediaisnotaneasytaskasitinvolvesseveralcomplications.Sinceabsorption,emissionandscatteringareoccurringateverypointwithinthemediumsowemustknowthevariousphysicalpropertiesastemperatureetc.ofthemediumatallpointsinthesystem.Also,radiationprocessishighlyspectralandthesespectraleffectsbecomemoreeminentingasesascomparedtosolidsurfaces.So,adetailedspectrallymodelingisneeded.Thetotal

55radiativeheatfluxcrossingasurfaceelementisobtainedbyintegratingthe

radiativeenergywhichisincidentonthesurfacefromalldirectionsoveralargerangeofwavelength.Themathematicsdescribingsuchasituationisinherentlycomplex.Also,largenumberofatomicandmolecularradiatingspeciesandnonBoltzmanndistributionsofpopulationsofvariousenergymodesmakeitverydifficulttorepresentthegaspropertiescorrectly.Duetoextremetemperatures,thediatomicairspeciesget

18highlydissociatedandemissionfromtheresultingtwoatomicspeciesNandO

isthemajorsourceofradiation.Emissionorabsorptionofphotonandhencecorrespondingchangeintheenergyoftheparticleismainlyduetothreetypesoftransitions

10boundbound,boundfreeandfreefreetransitions.

3.3

10RadiativeTransferEquationTheradiativeheattransferinamediawhichis

participatingi.e.in

12anabsorbing,emitting,and/orscatteringmediumisaffectedbya

numberofphenomena.Intensityoftheradiation32travellingthroughaparticipatingmediummaygetattenuatedbyabsorptionandscattering.Figure:attenuationofradiativeintensityConsideringtheabsorption,theamountofradiationabsorbed

11canbewrittenas?dI??abs??k?I?ds

(3.1)Whereisthelinearabsorptioncoefficientofthemedium,Iistheintensityofincidentradiationanddsisthedistancetravelledinspace.Intensityoftheradiationcandecreasebyscatteringalsoanditisgivenby?dI??sca???s?I?ds(3.2)Similarly,radiationintensitycangetaugmentedbyemission.Forthermodynamicequilibriumtheemissioniswrittenas33?dI??emis?k?Ib?ds(3.3)WhereIbisthePlanckfunction.Neglectingscatteringandcombiningequations(3.1)and(3.3)wegetthecompleteradiativetransferequationforaparticipatingmedium.Theradiativetransferequation[43]describesradiationintensityfieldinspaceasafunctionoflocation,directionoftransferandspectralvariabledI??k??Ib??I??(3.4)dsTheaboveRTEhasbeenderivedneglectingtheeffectofscattering.Thisassumptionmaynotbevalidformanyflowconditions.Butscatteringphenomenonisnotwellunderstood,soinmostofthecasesitisneglected.3.4RadiationfromAtomicSpeciesTheabsorptionandemissionofthethermalradiationmainlyoccursduetotransitionsbetweenenergylevelsofthegaswhicharecommonly:boundbound,

19boundfreeandfreefree.BoundBoundRadiation:Itoccurswhenaphotonis

absorbedoremittedbyagasmoleculesuchthatresultingchangeofenergylevelofthemoleculeisassociatedwithelectronic,orvibrationalorrotationalstates[44].Incaseofmonoatomicgases,thetransitionsinvolveonlyelectronicstatesandincaseofmoleculesallthreestatesmaybeinvolved.

5Energytransitionfromhigherboundstatetolowerboundstate

occursbyemissionof

40photonhavingenergyequaltothedifferenceoftheenergyofthetwolevelsandcorrespondinglya

fixedtransitionisoccurswiththetransitionof34electronfromaparticularenergyleveltootherandhencecausingtheradiationemittedintheformofaspectralline[45].Similarly,whenparticleabsorbsenergythenitcangotoanyofthediscretehigherenergylevelduetoquantumnatureoftheprocess.Thisprocessinwhichanatomormoleculeemitsorabsorbsphotonand

5noionizationorrecombinationofionsandelectronsoccursisknownasboundboundabsorptionandemission.

Quantizedboundenergystatesbetweenwhichelectronictransitionsoccurs

5canberotational,vibrational,orelectronicinmoleculesandforatoms

onlyonestatei.e.electronic.Tochangetheorbitofelectron,relativelylargeamountofenergyisneededwhichresultsinabsorptionemissionlinesbeingemittedatlargefrequencies(orsmall

2wavelengths)betweentheultravioletandthenearinfrared(between102mand1.5m)[42].Electronicenergylevelchanges

occuratshortwavelengthsinthevisibleregionand

5atportionsoftheultravioletandinfrarednearthevisibleregion.

Vibrationaltransitionsneedsomewhatlesserenergyincomparisontotheelectronorbittransitionsandhencespectrallinesemittedduetovibrationalenergylevelchangesarefoundintheinfraredregion

10(between1.5mand10m)Rotationaltransitions

donotrequiremuchenergyandhencerotationalspectrallinescanbeseeninthefarinfraredregion(beyond10m).Vibrationalenergylevelchangesaremostlyaccompaniedwithrotationaltransitionsanditgivesrisetovibrationrotationbandsintheinfrared.Asexplainedearlierthattheenergychangesinboundboundtransitionsoccurbetweenspecificenergylevels,sothespectralvariationofabsorptionandemissioncoefficientscanbeseen

5intheformofaseriesofspectrallines[

45].Probabilityofallelectronictransitionsare35different.Somearemoreprobablethanothersand,therefore,thoselineshavinghighelectronictransitionprobabilityarestrongerthanothers.Anexcitedatominahigherenergystatemayspontaneouslyemitphotonofappropriatewavelengthandmovestoalowerenergystate.

6Thespontaneousspectralemissioncoefficientisdefinedas

[46,47]??????gUnU???AULhc??T,Te,ne??4?11(3.5)Fig:SymbolicDiagramshowingenergy

statesandtransitionsforatom

38(a)Boundboundtransition(b)BoundFreetransition(c)Freefreetransition

36WheregUisthedegeneracy,

62istheEinsteincoefficientforspontaneousemission,

=(,,)

39isthegasstatevector,and(,,)isthelineshapefunction.

Spontaneousemissionoccursbyitself.Noexternalphotonsarerequiredforit.However,thisisnotincaseofstimulatedemissionandabsorption.Forstimulatedemissionandabsorptiontooccur

6presenceofphotonsinthevicinityofemittingorabsorbingspecies

isrequired.Combining

19stimulatedemissionandabsorptioncoefficients,theeffectivevolumetricabsorptioncoefficientisgivenas

???????gUnL???BLU?gUnU???BUL???T,Te,ne?h?(3.6)WhereBisthe

6Einsteincoefficientforstimulatedemissionandabsorption.

Usingthelawofdetailedbalance=,the

6absorptioncoefficientexpressioncanbereducedto

???????nL????nU????gUBUL??T,Te,ne??h(3.7)Simplifyingequations(3.5)and(3.7),theabsorptionandemissioncoefficientsfromasingleatomiclinecanbewrittenas[41]???????cnU????T,Te,ne?(3.8)????????c?nL????nU?????T,Te,ne?(3.9)Whereandareconstantsindependentofgasconditions.TheEinsteincoefficientsAULandBLUarerelatedtooneanotherthroughthefollowingrelation37BUL?8?hcAUL?5(3.10)Thus,theemissioncoefficientcanalsoberewrittenas???????????2hc2nU?5nL?nU??????nbe????(3.11)Where()isthenonequilibriumPlanckfunctionforanisolatedatomiclinegivenasbne?????2hc2nU?5nL?nU(3.12)Underthermodynamicequilibrium,thepopulationratioisgovernedbytheBoltzmannDistributionas[46]nL?

exp(C2)(3.13)nU?WhichleadstothefollowingwellknownrelationforthePlanckfunctionIb?????2hc2?5??eC?2(3.14)?1????WhereC2isthesecondradiationconstant.Mostofthe

15atomiclinesareopticallyverythick.Thesethicklineshavestrongselfabsorptioncharacteristics.Almostmorethan90%oftheemissionfromtheselinesgetsabsorbedbythelineitselfoverdistancesasshortas0.1mm.

Itmaybeupto99%forfewlines.[41]Thus,insteadofthelinecenters,widthofatomiclinesismore

18importantfromaheattransferpointofview.

Sample

6emissionandabsorptionspectrumforatomicspecieO38andN

atrespectivenumberdensityobtainedattime0.58softhenumericalsimulationareshowninfiguresasbelow.Weknowthatvariouselectronicenergylevelsarepresentinanatom,andwhenelectronsjumpfromoneleveltoother,itisaccompaniedbyemissionorabsorptionofphotons.Theprobabilityofthesetransitionsdependsontheelectroniclevelsbetweenwhichthistransitionistakingplace.Forstrongtransitionstooccurtherearesomesetofselectionruleswhichshouldbesatisfied.Forexample,dipoletransitionscantakeplaceonlybetweenthoseenergylevelswhoseangularmomentumparameterdiffersbyone.Hence,forenergylevelswithsameangularmomentumdipoletransitioncannottakeplacei.e.theyareforbidden[48]andhencegapinthespectrumisobservedinthatrange.39Figure:SampleEmissionSpectrumforatomicspecieNatT=8100K,numberdensity=3.75x1019cm3Figure:SampleAbsorptionSpectrumforatomicspecieNatT=17800K,numberdensity=3.75x1019cm340Figure:SampleEmissionSpectrumforatomicspecieOatT=8100K,numberdensity=1.75e19cm3Figure:SampleAbsorptionSpectrumforatomicspecieOatT=8100K,numberdensity=1.75e19cm341SpectralLineBroadening:Inanatomvariouselectronsarespinningatdifferentdistancesaroundthenucleus.Mainly,theenergyoftheseelectronsdecidetheinternalenergyoftheatom.Internalenergyoftheatomalsodependsontheatomsspinningaroundeachotherinamolecule,andonthoseatomswhichare

2vibratingagainsteachother[49].AccordingtoQuantummechanics

itisknown

20thattheenergylevelsforatomicormolecularelectronorbitaswellastheenergylevelsformolecularrotationandvibrationarequantized

whichmeansthatthechangein

2electronorbitsandrotationalandvibrationalfrequenciescanoccurbycertaindiscreteamounts

only.Also

63byPlanckslawweknowthattheenergyofa

2photonorelectromagneticwaveisdirectlyproportionaltofrequency,soquantizationmeansthat,boundboundtransitions

canoccuronlyifthephotonshaveaspecificfrequencysothattheycangetabsorbedorreleased.Inthisprocessdiscretespectrallinesareemittedbythephotons

2forabsorptionandemission[42].AccordingtoHeisenberg'suncertaintyprinciple,

itisknownthatthe

2energylevelofanatomormoleculecannotbedefinedpreciselyand

thereisalwayssomeamountofuncertainty,sothisphenomenon(alongwithsomeothers)resultsinaslightspectralbroadeningoftheselinesandtheyappeartohavesomewidth.Duetosomeeffectstheseslinesgetsbroadenedandhencehaveafinitespanorwidtharoundthetransitionwavenumber.Linewidthisthatparameterwhichrepresentshowfartheeffectofaparticularlineisfelti.e.itrepresentshowfarfromthecenter,thestrengthofalineispresentandafterthis,itscontributiondecreasestoacomparativelylowinsignificantvalue.Thisvariationoftheabsorptioncoefficientwith42wavenumberwithinabroadenedlineisLineshape.ShapeofatypicalspectrallineisasshowninFig.Thelineintensityistheintegralunderthecurve[43],?Sij????,ijd?(3.15)0Theisverysmall

5exceptforclosetoij.Theregionsawayfromijwhereisverysmallarethewingsoftheline.Othercharacteristicofthe

lineshapeislinehalfwidthwhichisonehalfofthelinewidthathalfofthemaximumlineheight.Fig:Atypicalbroadenedspectrallinea.NaturalBroadening:Ineveryexcitedmolecule,energylevelsdecayspontaneouslybyemittingaphotontoalowerstate,evenifthemoleculeiscompletelyundisturbed.Theuncertaintyprinciplegives43therelationshipbetweentheuncertaintyofitsenergyandthelifetimeofanexcitedstate.Ashortlifetimeofanexcitedstateimplieslargeenergyuncertaintyandahencebroademission.AccordingtoHeisenberg'suncertaintyprincipleanytransitionofelectronfromoneleveltoother

cannotoccurwithexactlythesameamountofenergy,thusresultinginlittlevariationintheenergyofemittedphotonswhichcausesbroadeningofthespectrallines[49].

2However,theaveragetimebetweenmolecularcollisionsismuchlesserthantheaveragetimeforspontaneousdecay.Therefore,naturallinebroadeningeffectsarenotsoimportant

andcanbeneglected.b.CollisionalbroadeningorImpactpressurebroadening:Theemittingparticlescollidewitheachotherandinthisprocesstheydisturbstheemissionprocessofotherparticlesbydecreasing

7thecharacteristictimefortheprocess,andhencecausingtheuncertaintyintheenergyemitted.

Thetimeperiodofthesecollisionsisquitesmaller

7thanthelifetimeoftheemissionprocess.Thiseffectvarywiththechangesinthedensityandtemperatureofthegasandalsowiththe

2frequencyofcollisionsbetweengasmoleculescausingthe

linetogetbroadened.The

2shapeofsuchlinescanbedeterminedfromtheelectrontheoryofLorentzorfromquantummechanics

[49]k???????b0c?2?bc2,S????k?d?,S(3.16)

2WhereSisthelineintegratedabsorptioncoefficientorlinestrength,bcisthesocalledlinehalfwidthinunitsofwavenumber(halfthelinewidthathalfthemaximumabsorptioncoefficient),and0isthewavenumberatthelinecenter.Theshapeofacollisionbroadened44lineisidenticaltothatofnaturallinebroadening,andthecombinedeffectisgenerallytermedLorentzbroadeningwithalinehalfwidth

bL.Withincreaseinpressure,theeffectofcollisionbroadeningalsoincreasesduetoincreaseincollisionrate.As

2molecularcollisionsareproportionaltothenumberdensityofmolecules

andtotheaveragemolecularspeed(vavT),so

2halfwidthcanbecalculatedfromkinetictheory[43]asbc?2D2p

?c0mkT(3.17)

2WhereDistheeffectivediameterofthemolecule,misitsmass,pistotalgaspressure,Tisabsolutetemperature,andthesubscript"0"denotesareferencestate.Collisonbroadeningisthe

mainbroadeningmechanismforinfraredconditions.ThespectraldistributionofaLorentzlineandDopplerlineisshowninfigure.Itcanbeobservedfromthefigurethatatthelinecenter,LorentzprofileislowerthantheDopplerprofileandatpointsfarfromthecenter,Lorentzprofileismorepredominant.So,collisionbroadeningeffectsareimportantfarfromthecenterwhiletheDopplerbroadeningisdominatingatpointsnearthelinecenter[45].45Figure:

2SpectralLineshapeforLorentz(collision)andDopplerbroadening[

43]c.DopplerbroadeningInanabsorbingoremittinggas,theatomsormoleculesarenotstationary.Dependingupontheirthermalenergythey

7haveadistributionofvelocities.Eachphotonemittedmayeitherbe"red"or"blue"shiftedbytheDopplerEffect.Thisshiftdependsonthevelocityoftheatomrelativetotheobserver.

Velocitydistributiondependsonthetemperature.Withincreasein

7temperatureofthegas,thevelocitydistributiongetswider.So,asthetemperatureof

thegasincreases,thespectrallinebecomesbroadened.ThisbroadeningeffectcanbeshownbyaGaussianprofile.

2Dopplerlinehalfwidthisgivenby

[43]46bD??02kTmln2(3.18)c0

2Wheremisthemassoftheradiatingmolecule.

Collisionandnaturallinebroadeningdoesnotdependonthespectralpositionwhilethe

2Dopplerlinewidthisdependentonitsspectralposition

and

2ismuchmoreconcentratedneartheline

centre.Forlinebylinespectralmodelling,thespectroscopicdatarequiredforthecalculationofemissionandabsorptioncoefficientswillbetakenfromNIST[50].Thisdataconsistsof914boundboundlinesforNand682forOforwavelengthsbelow20,000.TheNISTdatabasecontainsinformationforlinepositions(),Einsteincoefficients,energyofupperandlowertransitionstates(EU,EL),andthedegeneracyoftheenergystates(,).Weknowanyquantummechanicalsystemorparticlewhichisboundorconfinedspatiallycanhaveonlyfixeddiscretevaluesofenergyincomparisonwiththeclassicalparticleswhichcanhaveanyenergy.Inanatom,electricalfieldofnucleusboundstheenergylevelsofelectrons.Henceatomshavevariousdistinctenergylevelswhichareknownaselectronicstates.Iftheelectronsinanatomareatthelowestpossibleenergylevelthentheyaresaidtobeinthegroundstateandiftheyhaveenergyhigherthanthegroundstatethentheyaresaidtobeexcited.Asatomsmove

15fromoneelectronicstatetoother,theyemitorabsorbaphotonofspecificwavelength.

Fortransitionofelectronfromalowerenergystatetohigher,theyabsorbaphotonandtransitionfromhighertolowerenergystateisdone

35byemittingaphotonhavingenergyequaltothedifferenceintheenergy

levelofthosetworespectivestates.Thesetransitionsarepredictedbyquantummechanics.Inthebeginningofthischapter,variousexpressionsforemissionandabsorptioncoefficientswerepresentedintermsofspectroscopic47constants??cand??c.AtransitionfromoneenergyleveltootheratanywavelengthisgovernedbyanupperandalowerelectronicenergyleveldenotedbyEUandEL,respectively.Therearemorethan200suchenergylevels.Johnsonetal.havecombinedalltheseenergylevelsintogroupedenergylevels,UandL.Itwasdonesoastosimplifytheexcitationmodelforthecalculationofpopulationsoftheseenergylevels.Thereare35suchgroupedenergylevelsforNandOintheJohnstonsmodel.[47]DetailsoflinesofNandOareprovidediBoundFreeContinuumRadiationWhentheabsorptionofaphotonproducesanelectronandiontheprocessiscalledboundfreeabsorption.Initiallytheelectronisinaboundstateandafterionizationitisfreetotake48onanyvalueof

thekineticenergy,sotheboundfreeabsorptionisacontinuousfunctionofthefrequency.Thereverseisfreeboundemissioninwhichanionandfreeelectroncombineandaphotonofenergyisreleased.Duetothis,theenergyoftheresultingatomdrops.Italsoproducesacontinuousspectrumastheparticleswhicharecombiningcanhaveanyinitialkineticenergy.Now,theboundfreetransitionsoccuronlywhenthegasisionized,sothisprocessistakenintoconsiderationforhightemperatureapplicationsonly.Intheboundfree

6case,thewavelengthoftransitioniscalculatedbythekineticenergyofthefreeelectron.[41]??11?E

E??Ei?Ee?(3.19)WhereEistheenergyofanimaginarystate,whichliesaboveandclosetoionizedstateandEi

6istheenergyoftheithboundlevel.SincetheelectronenergyiscontinuouslydistributedaccordingtoaMaxwelldistribution,theradiation

isessentiallycontinuous,unlikelinesintheboundboundcase.FreeFreeContinuumRadiationItoccurs

5whenaphotonisabsorbedoremittedby

afreeelectron.Theemissionproducedbyelectronatomcollisionsisofimportanceinplasmasoperatingathighpressure,wheretheelectrondensityquitehighinspiteplasmabeingonlypartiallyionized.Ifthephotonisemitted,itisalsocalledbremsstrahlungemission(whichinGermanmeansbrakeradiation)asthe

2releaseofaphotondecreasesthekineticenergyoftheelectronandhencedeceleratingit.Ifthephotonisabsorbeditisknownasinversebremsstrahlung

asthecapture

2ofaphotonincreasesthekineticenergy

andhenceacceleratingit.Herealso,theinitialandfinalfree49energiesoftheelectroncanhaveanyvalues,soacontinuousabsorptionoremissionspectrumisobtained.Freefreeradiationisgenerallyweak,andtheonlysignificantcontributioncomesfromthelargewavelengthregionofthespectrum.

2Boundfreeandfreefreetransitionsgenerallyrequirehigh

energyandhencetheymostly

2occuratveryhightemperaturesi.e.whenionizationsand

dissociationisofnoticeablevalue.Theradiationemittedwiththesetypesoftransitionsaremostlyfoundatshortwavelengthsorlargefrequencies(ultraviolettovisible).Therefore,thesetransitionsareverylessimportantascomparedtoboundboundandboundfreetransitions.WehaveconsideredboundboundtransitionsonlyFigure:Spectrallinesduetovarioustypesoftransitions[43]3.5RadiativePropertyModels:Theprocessofevaluatingtheradiativepropertiesofhightemperatureplasmaisdifficultdue50to

18thepresenceoflargenumberofradiativespecies.Furthertheeffectsof

thermodynamicnonequilibriummaketheaboveprocessmorecomplicated.OneoftheearliestandwidelyusedradiationcodeisRAD/EQUILwhichwasdevelopedbyNicolet[51].Inthiscode,calculationofallpropertiesisdonebyassumingthermodynamicequilibrium.Fornonequilibriumcases,NEQAIRwasdeveloped.ItusesatomiclinedatacompiledbyWieseetal.[52]tocalculatelinestrengthofeachatomicline.Butitwascomputationallyexpensivebeingalinebylinecode.VariousnewmodelshavebeenintroducedwhicharecomputationallylessexpensivethanNEQAIRsuchasLORAN(LargelyOptimizedRadiativeNonequilibrium),[53]etc.Inourcase,Localthermodynamicequilibrium(LTE)andchemicalequilibriumconditions[24,54]havebeenassumedontheterminationofthelaserpulse,sowewillbefindingequilibriumelectronicstatepopulationsofvariousenergystatesofatomsbyBoltzmanndistribution.3.6SpectralModelsforRadiativePropertiesInearliertimes,radiationsimulationswerecarriedoutbyassumingtransparentandgraygasassumptions[55].Accordingtothis,itwasassumedthatthe

54radiativepropertiesofthemediumarenotdependentonthe

wavelength.i.e.graygasassumptionandalsoalltheenergywhichisemittedisnotabsorbedandleavesthesystemwithoutanyattenuationorlossinitsintensity.HoweandViegas[56]werethefirsttostudytheeffectofradiationabsorptionandmodelledtheabsorptioncoefficientasgray.Hoshikawaetal.[57]foundthatthegraygasapproximationissameasneglectingtheabsorptionandtheresultsobtaineddidnotvary51muchinbothofthesecases.Heprovedthatnongrayselfabsorptionisimportanttoconsider.NongrayselfabsorptionwasfirstindicatedbyOlstad[58]whofoundthatnongrayselfabsorptionmayreducetheradiativeheattransferandhencecancauseasubstantialeffect.ThesignificanceofconsideringtheatomiclineswasnoticedfirstlybyBibermanetal.[59]beforethis,mostofthespectralmodelsforatomswerebasedonstepmodels[60]whicharenotasaccurateaslinebylinemodels.Butlinebylinecalculationswereavoidedduetothefactthattheyrequirehighcomputationalpowerwhichwasnotavailableinthosetimes.Butfrompastfewyears,LinebyLinecalculationshavebecomepossible.Allthankstothegrowingmoderntechnologywhichmadepossibletofabricatepowerfulcomputerscapableofperforminghighendcalculationsinvolvinghugelevelofcomplexity.The

64linebylinecalculationsareveryexpensivecomputationallyas

theyrequireveryaccuratedataforabsorptioncoefficientsatverylargenumbersofwavelengthsmaybehundredsofthousandsofwavelengths.Also,thespectralatomiclineshaveastrongopacitynature,so

30inordertofindtheabsorptionandemissioncoefficients

accurately,veryhighspectralresolutionisneeded.Higherthespectralresolution,higheristheaccuracywithwhichtheabsorptionandemissioncoefficientarecalculated.Afterfindingthespectralradiativeproperties,RTEissolvedateachofthewavelengthpointandthetotalintensityisthesummedbyusinganyintegrationscheme.3.7CalculationofAtomicElectronicExcitedStatePopulationusingBoltzmanndistributionOntheterminationofthelaserpulse,LTEandchemicalequilibriumconditionshavebeenassumedintheregionofplasmaformation.Bychemicalequilibrium,itismeantthatifleft52alonethennochemicalreactionwilloccuri.e.theconcentrationofthereactantsandproductswillnotchangeovertime.Itcanalsobestatedasthattherateoftheforwardreactionissameasthatofthebackwardreaction,bothproceedingatthesamerate.Similarly,bythermalequilibriumitisreachedwhenanidealgasdistributionfunctionhasreachedtoacertainMaxwellBoltzmanndistributionandgetsstabilized.Thisprocessmayoccurslowlyorfast.Forslowprocesses,itcanbeapproximatedbyasequenceofequilibriumstates.Weknowthattheenergiesofmolecules,atoms,orelectronsarequantized.Inordertoexplainanychemicalsystemsweshouldfirstknowtheenergiesofthequantumstatesandalsothedistributionofparticlesamongthevariousquantumstates.Energiesofthequantumstates

56canbeobtainedfromtheSchrodingerequationandtheBoltzmanndistributionlaw

instatisticalmechanicsenablesustodeterminehowvariouslargenumberofparticlesdistributethemselvesthroughoutasetofallowedenergylevels.Forequilibriumcases[41],allthedegreesofthefreedomi.e.translational,vibrational,rotationalandelectronic,degreesoffreedomareall

60populatedaccordingtotheBoltzmanndistribution.Itischaracterizedbyonecommontemperature.

[61]TheBoltzmanndistribution[62]isgivenas?C2Ejnj?eTnQ(3.20)Wheren

21isthetotalpopulationofthespecies,Qisthepartitionfunction

andEj[cm1]istheenergyofthejthstate.Thepartitionfunctionisgivenby53Q??gjeTL?C2Ej(3.21)j?1WhereListhetotalnumberofenergylevels,gjisthedegeneracy.SpectralModelsSpectralradiationmodelsmaybecategorizedintothefollowingmethods:1)GreyGasModel2)linebylinecalculations(LBL)3)Bandmodels4)Globalmodelsand5)kdistributionmethods(whichcanbeformulatedasnarrowbandandglobalmodels)GreyGasModelGraygasmodelassumesthatthelinestrengthisevenacrossthespectrumofinterest.Tocarryoutagraycalculation,

11aconstant(gray)absorptioncoefficientcanbedefinedforeachcellandtheRTEcanberewrittenas[41]=(())WherekP()

11isthePlanckmeanabsorptioncoefficient,givenas54()=0

0()()()Wherek

11()isthespectralabsorptioncoefficientforthegasmixture

LBLAccuratesimulationofradiationheattransferrequiresthelinebylineradiationmodelwhichisnearlyimpossibleforengineeringpracticebecauseofthehighcomputationalcost.But

2withthehelpofpowerfulcomputers,linebylinecalculationshave

becomepossible,thoughveryexpensive.Theselinebylinecalculationsalsorequireveryaccurateabsorptioncoefficientdataathundredsofthousandsofwavelengths.TheRTEmustbesolvedateachwavelength,andthetotalintensityiscalculatedbyapplyingasuitableintegrationschemeinwavelengthspace.Thespectrumissampledalongaseriesofchosenfrequencies3.8RTEsolutionMethodsThetwobasicstepsinvolvedinsolvinganyradiationproblemare:?Findingthegaspropertiesintheflowfieldforallgasconditions?SolvingtheRTEusinganymethodCompletethreedimensionalsolutionoftheRTEwithextensivespectralmodellingisveryexpensivecomputationally.RTEequationasobtainedfromequation(3.4)dI??k??Ib??I??(3.22)ds55TheaboveRTEdescribesthechangeintheintensityoflightasitpassesthrougharadiativelyparticipatingmedium.SpectralintensityIisobtainedfromthe

10solutionoftheRTE,thedivergenceofthespectralradiativefluxcanbecalculated

as[45]?qrad,??k?(4?I?b?G?)(3.23)WhereGisthespectralincidentradiationandisdefinedasG???I?d?(3.24)4?AndtheIbisthespectralblackbodyintensityand

4isgivenbyPlanckslaw[42]I?

b??b?E2hc2?h0c0(3.25)n2?5(en??T?1)The

12divergenceofthetotalradiativeheatfluxisthenobtainedbyintegrationovertheentirespectrum

??.qrad???qrad,?d?(3.26)0RTEis

10anintegrodifferentialequationanditdependsonthethreespatial,twodirectionalandonespectralvariable.

Duetothis,the

4analyticalsolutionisalmostimpossibleformostofthe

problems.ThiscreatestheneedtosolveRTE

4numericallyusingvariousradiationmodelsforspatialanddirectionaldependenciesandspectralmodelsforthespectraldependency.OnesuchradiationmodelistheP1radiationmodel[

63].56P1ApproximationModelItisoneofthevariousmethodswhichareusedtosolveRTEnumerically.Itisalsocalledasmethodofspecialharmonics.AsexplainedabovethatintegrodifferentialnatureofRTEmakesitadifficulttasktosolveitanalytically.Themethodofspecialharmonicsprovidesamethodtogettheapproximatesolutionbytransformingtheequationoftransfer

53intoasetofsimultaneouspartialdifferentialequations.

ItwasfirstproposedbyJeans.P1radiationmodelavailableinOpenFOAM,the

1lowestorderimplementationofthesphericalharmonicsmethod

isusedtosolveRTEequation

1byexpandingtheradiativeintensityintoaseriesofsphericalharmonics.

Oneofthe

14mainassumptionofthismodelisthatthedirectionaldependenceintheradiativetransferequationisintegratedoutresultinginadiffusionequationfortheincidentradiation[

64].Thismethodisquiteuseful

1becauseofitscomparativelyhighaccuracyandlowcomputationalcost.Advantagesofthe

P1model:?RTEisquiteeasytosolvewithlesscomputationaldemand?

14Itworkswellforcaseswheretheopticalthicknessislarge,=a*L>3,whereL=distancebetweentheobjects.?Conversionofthe

governingRTEintorelativelysimplerpartialdifferentialequations

4Inthismethod,theradiativeintensityisapproximatedbyatwodimensionalFourierseries,splittingtheintensitysspatialanddirectionaldependency.[45]IftheFourierseriesistruncatedafteroneelement,thenP1radiationmodelis

obtained.

4P1radiationmodelgives57twospatialdifferentialequations,oneforthegradientofthedirectionallyaveragedintensityG

4andanotherforthegradientoftheradiativeheatflux

whichareasunder[64]:qrad,????G?13k?(3.27)And?.qrad,??k?(4?I?b?G?)(3.28)Thesetwoequations

4canbecombinedtoasecondorderpartialdifferentialequationofelliptictype

[42]?.(?G?)?k?(G??4?I?b)1(3.29)3k?It

1isaHelmholtzequationwhichcanbediscretizedinthefinitevolumeframeworkofOpenFOAM.

The

1boundaryconditionsfortheP1equationareofmixedtype(thirdkind)andgivenby

G??32k???2????w?w??G?..nw?4?I?bw??(3.30)?Wherethespectralwallemittance,Ibwisthespectralblackbodyintensityofthewallbasedonthewalltemperatureandnwisthenormalvectortothewall.TheP1equationisthensolvedforcompleterangeofwavelengthfrom800A0to20,000A0takingspectralresolution=0.02584CHAPTERResultsandDiscussionsInthischapter,variousresultsandimportantfindingshavebeendiscussedwiththehelpoffigureswhichwereobtainedduringsimulationAlso,workingofthecodehasbeendiscussed.594.1WorkingMethodologyHypersoniccodethatwasdevelopedtocalculatetheflowconditionswastakinglargetimetoconverge.So,theinitialflowfileddataattime0.02swastakenfrompastliterature[25].Theflowfielddataforvariousspeciesobtainedwasintermsofconcentration.ItwasfirstconvertedintomassfractionsastheinitialconditionsinOpenFOAMaredefinedusingmassconcentrations.TheinitialflowfielddatainOpenFOAMisasshowninthefollowingfigures:Teardropplasma60Figure:ContourPlotofdensity(rho)att=0.02sFigure:ContourPlotofpressure(p)att=0.02s61Figure:ContourPlotoftemperature(T)att=0.02sFigure:ContourPlotofconcentrationofOatt=0.02s62Figure:ContourPlotofconcentrationofNatt=0.02sFigure:LineplotforatomicspecieNalong

3alinepassingthroughthemiddleofthedomain

alongXaxisattime=0.02s63Figure:LineplotforatomicspecieOalong

3alinepassingthroughthemiddleofthedomain

alongXaxisattime=0.02sFigure:Lineplotforpressurealong

3alinepassingthroughthemiddleofthedomain

alongXaxisattime=0.02s64Figure:Lineplotfortemperaturealong

3alinepassingthroughthemiddleofthedomain

alongXaxisattime=0.02sFigure:Lineplotfordensityalong

3alinepassingthroughthemiddleofthedomain

alongXaxisattime=0.02s65Calculationofnumberdensityfrommassfractions12FindingBoltzmannequilibriumpopulationdistributionusingnumberdensity3UsingthepopulationdistributionandspectroscopicdatafromNISTdatabase,spectralcoefficientsaredeterminedusingLBLmethod[10]SolvingRTEusingP1solverandintegratingoverwavelength.[12]4Tocarryoutthesimulationsandsolvealltheequations,aC++coderadLBLhasbeendeveloped.AftermodellingtheentiredomainincludingtheplasmainOpenFOAM,numberdensityofNandOiscalculatedatT=17800K(EquilibriumPlasmatemperature).NumberdensityofNcomesouttobe2.53x1018cm3andforOitsvalueis1.43x1019cm3atatimestep=0.02s.Thisnumberdensityisusedtofindouttheatomicelectronicstate

equilibriumpopulationusingBoltzmanndistribution.Usingpopulationdistributionandspectroscopicdata,

30absorptionandemissioncoefficientsarecalculatedusingtheequationsdescribedinthe

previoussection.Spectroscopicdatarequiredforthecalculationof

19emissionandabsorptioncoefficientswastakenfromNISTdatabase.Absorptionandemissioncoefficientsare

66determinedfortherangeofwavelengthfrom800A0to20,000A0takingspectralresolutiontobe=0.02.Asexplainedinthepreviouschapteralso,thevalueofthespectralresolutionshouldbeverysmalltogetaccurateresults.Thisvaluewastakenafteritwasfoundthattherewasnotmuchnoticeablechangeinthetotalemission.Foreachspecie,fourhundredwavelengthspointsweretakenatatimeduetomemorylimitationi.e.withspectralresolutionof0.02,thewholewavelengthsintervalfrom80020000A0wasdividedinto2250blockseachhaving400wavelengthspoints.Eachblockwassolvedseparatelyforfindingtheabsorptionandemissioncoefficients.Fig4and5showsvariationofabsorptionSpectrumofNandabsorptionSpectrumofOwithwavelengthatT=17800K.67Figure:EmissionSpectrumofOatT=17800K,numberdensity=1.43e19cm3Figure:EmissionSpectrumofNatT=17800K,numberdensity=1.43e19cm3Figure:AbsorptionSpectrumofOatT=17800K,numberdensity=1.43e19cm368Figure:AbsorptionSpectrumofNatT=17800K,numberdensity=1.43e19cm3Usingabsorptionandemissioncoefficients,RTEissolvedforeachwavelengthpointandintegrationisdoneoverallthewavelengthrangetofindoutthetotalradiationlossoverallthewavelengthrangeintheentiredomain.Specie.q(mJ/s)O145.33N52Total197.35Table:Showingthevalueof.qoverentiredomainforOandNatatimestep(0.02s)Theradiationlossoverthewholesimulationtimeupto60sfrom0.02swasroughlyestimatedas69=197.35mJ/sx30s=5.92JThisisthemaximumapproximatelosswhichcanoccur.Previouslyreportedradiationlosswas0.33J.Sowehaveestimated20timeshigherlossesthanthepreviouslyreporteddata.[25]70

445ChapterConclusionsandFutureWork5.1Conclusions

Whenalaserpulsedisfocussedonadomainthenitundergoesmainlythreetypesofchangesfluiddynamic,chemicalandradiativechanges.Fromthepastliterature,itwasfoundthatfluiddynamicandchemicalchangeshavebeenstudiedwellinthepastbuttheradiativechangesweremostlyneglectedinmostofthecases.Jordaretaltriedforthefirsttimetocalculatetheradiativelossesbuttheyalsoconcludedradiativelossestobenegligible.TheycalculatedtheradiativepropertiesusingmultigroupmethodinwhichameanvalueofabsorptioncoefficientisassignedtofrequencygroupssoastoeasetheprocessthesolvingtheRTE.WehavetriedtousethemostaccuratemethodforcalculatingtheradiativelosseswhichisLinebyline.Inthismethod,thewholerangeofwavelengthisfinelydiscretizedintolargenumberofwavelengthpoints.RadiativepropertieswerecalculatedateachofthewavelengthpointsandthenRTEwassolvedatallthosepointsseparately.Itwasfoundthatthetotalradiativelossis5.92J.TheearliervaluefortheradiativelossesbyJordaretal.was0.33J.Hence,ourvaluewascomingouttobeatleasttwentytimesmorethanthepreviouslyreporteddata.Butthetotalenergywhichwasdepositedwas

93mJ.Hencetheradiativelosswhichisoccurringduetoradiativecoolingisverylessascomparedtotheenergydeposited.71So,theseimportantconclusionscanbederived:?Emissionspectrumandabsorptionspectrumhavethickopticallines.?Ascanbeseenfromthefigures4.9to4.11thattheemissioncoefficientishighforNandObutstilltheradiationlossesarecomingoutverylessbecausetheabsorptioncoefficientisalsohighforboththesespecies,sotheenergywhichisemittedduetoradiationgetsabsorbedagainduetohighabsorptioncoefficientoftheatomicspecieNandOandhencethenetlosscomesouttobenegligible.?SincethemostaccuratemethodLBLalsoshowedthatradiationlossesarenegligiblesoourstudyvalidatestheassumptionofneglectingtheradiationlosseswhichwasassumedinallpreviousstudieswithoutanyproof.Inallthepreviousstudiesofthelaserenergydeposition,itwasassumedthattheradiationlossesarenegligibleduetodifficultyinfindingthem.Ourstudyhasvalidatedthatassumptionwithproperjustification.5.2FutureWork?Theworkdescribedinthisthesiswasdoneatatmosphericconditions.Laserenergydepositionalsohasapplicationsatlowpressureconditions.So,thereisaneedtostudylowpressureeffectively.?Hypersonicsolverwastakinglargetimetoconverge.Itsefficiencycanbeimproved.726ChapterReferences1.Radziemski,L.J.,etal.,Timeresolvedlaserinducedbreakdownspectrometryofaerosols.Analyticalchemistry,1983.55(8):p.12461252.2.Phuoc,T.X.,Laserinducedsparkignitionfundamentalandapplications.OpticsandLasersinEngineering,2006.44(5):p.351397.3.Radziemski,L.J.andD.A.Cremers,Laserinducedplasmasandapplications.1989.4.Cheroff,G.,F.Stern,andS.Triebwasser,QuantumEfficiencyofGaAsInjectionLasers.AppliedPhysicsLetters,1963.2(9):p.173174.5.Shen,Y.R.,Principlesofnonlinearoptics.1984.6.Cremers,D.A.,etal.,LaserInducedBreakdownSpectroscopy,ElementalAnalysis.2006:WileyOnlineLibrary.7.Miziolek,A.W.,V.Palleschi,andI.Schechter,Laserinducedbreakdownspectroscopy.2006:CambridgeUniversityPress.8.Kandala,R.andG.V.Candler,Numericalstudiesoflaserinducedenergydepositionforsupersonicflowcontrol.AIAAjournal,2004.42(11):p.22662275.9.Goodman,J.W.,Statisticaloptics.NewYork,WileyInterscience,1985,567p.,1985.1.10.Justin,J.Z.,Quantumfieldtheoryandcriticalphenomena.Clarendon,Oxford,1989.11.Einstein,A.,Thephotoelectriceffect.Ann.Phys,1905.17:p.132.12.Hirschfelder,J.O.,etal.,Moleculartheoryofgasesandliquids.Vol.26.1954:WileyNewYork.13.Eisberg,R.M.,Fundamentalsofmodernphysics.1967:Wiley.14.Chin,S.L.,MultiphotonlonizationofAtoms.2012:Elsevier.15.Delone,N.B.,Basicsofinteractionoflaserradiationwithmatter.1993:AtlanticaSguierFrontires.16.Mandel'Shtam,S.,etal.,Investigationofthesparkdischargeproducedinairbyfocusinglaserradiation,II.SovietPhysicsJETP,1966.22(1).17.Orr,D.,Magneticpulsationswithinthemagnetosphere:Areview.JournalofAtmosphericandTerrestrialPhysics,1973.35(1):p.150.18.Ramsden,S.andP.Savic,Aradiativedetonationmodelforthedevelopmentofalaserinducedsparkinair.1964,DTICDocument.19.DeMichelis,C.,Laserinducedgasbreakdown.IEEEJournalofQuantumElectronics,1969.5(4):p.188202.20.Ghosh,S.andK.Mahesh,Numericalsimulationofthefluiddynamiceffectsoflaserenergydepositioninair.JournalofFluidMechanics,2008.605:p.329354.21.Bradley,D.,etal.,Fundamentalsofhighenergysparkignitionwithlasers.CombustionandFlame,2004.138(1):p.5577.22.Mortazavi,M.,etal.,NumericalSimulationofEnergyDepositioninaSupersonicFlowPastaHemisphere.AIAAPaper2014,2014.944:p.118.7323.Dors,I.,C.Parigger,andJ.Lewis,Fluiddynamiceffectsfollowinglaserinducedopticalbreakdown.AIAApaper,2000.717:p.2000.24.Dors,I.G.andC.G.Parigger,Computationalfluiddynamicmodeloflaserinducedbreakdowninair.Appliedoptics,2003.42(30):p.59785985.25.Joarder,R.,G.Gebel,andT.Mosbach,Twodimensionalnumericalsimulationofadecayinglasersparkinairwithradiationloss.InternationalJournalofHeatandMassTransfer,2013.63:p.284300.26.Bogatyreva,N.,M.Bartlova,andV.Aubrecht.Meanabsorptioncoefficientsofairplasmas.inJournalofPhysics:ConferenceSeries.2011.IOPPublishing.27.Jasak,H.,A.Jemcov,andZ.Tukovic.OpenFOAM:AC++libraryforcomplexphysicssimulations.inInternationalworkshoponcoupledmethodsinnumericaldynamics.2007.28.Bansal,A.,A.Feldick,andM.Modest.SimulationofHypersonicFlowandRadiationoveraMarsReentryVehicleUsingOpenFOAM.in50th

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