Interferometer Flame

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    LabReport1:TemperatureMeasurementsbyLaserInterferometry AnandDhariya

    AERO521:ExperimentalMethodsinFluidDynamics14

    th

    February2008

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 1Abstract:Thisreportdescribestheuseoflaserinterferometrytomeasurethetemperatureofacandle

    flamebasedontheexperimentperformedinlabbyGroup6ofAERO521course.Thesetup

    is firstexplainedalongwithdetailedproceduretoobtainthe imagesofthefringesformed

    duetointerference.Alsothereportexplainstheanalysisofthesefringeimagestoobtainthe

    temperature of the candle flame at different locations. Based on this analysis, plots are

    generated for the temperature field and the results are discussed along with the final

    conclusions.

    1.ExperimentalSetup:Theexperimentalsetupisasshowninthepicturebelow.Theexperimentwasperformedon

    a special optical bench which has threaded holes on it for attachment of the various

    components.Themajorapparatususedinthisexperimentaredescribedasfollows.

    Fig.1:Experimentalsetupforflametemperaturemeasurementusinginterferometry

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 2HeNeLaser:A5mWattHeliumNeonlaserwasusedforthisexperiment.Theoutputofthe

    laserislinearlypolarizedlightofwavelength632.8nm(red).

    SpatialFilter:Wehaveuseda40xmicroscopeobjectivewitha10microndiameteraperture

    and160mm focal length lens to formourspatial filter thatensures removalofdiffractedlight.

    Collimating Lens:A collimating lensof focal length 371.6mm isused which is required to

    makethelightraysparallel.

    BeamSplitter:A50:50beamsplitterwasusedforthisexperiment.Thismeans ittransmits

    50%oftheincidentlightandreflectstheremaining50%.Thebeamsplitterissoalignedthat

    itbisectstheanglebetweenthe2mirrors.Sincethemirrorsaremutuallyperpendicularthe

    beamsplitterisalignedat45o

    .

    Mirrors: Highly polished glass mirrors were used in this setup. The mirrors have 2

    diametricallyoppositescrewsforadjustingtheirinclination

    Screen:Aflatpieceofpaperismountedonthestandtoformthescreenonwhichthefringe

    patternisobserved.

    Camera:AblackandwhitePolaroidcamerawasusedtotakepicturesofthefringepattern.

    To take the pictures the paper screen was removed so that the fringe pattern is directly

    incidentonthecamera.Thisisaveryoldsystemhowever,thebiggestadvantageisthatthe

    picturesproduced are1:1 and thiseliminates theneedof additionalopticsand it greatlysimplifiesthemeasurementsandcalculations.

    Alltheapparatuswereproperlyaligned.Thealignmentofthe2mirrorswascritical.Forthis

    thelaserwasturnedONanditwasseenthat2redspotswereformedonthelaserface.The

    brighter spot corresponded to the light reflected from themirrordirectlyopposite to the

    laser.Thismirrorwasalignedsuchthatthereflectedspotisdirectlyabovethelaseroutput

    spot.Once thiswasdonea faint red spotwasobservedat2oclockpositionon the laser

    face.Thisisduetothelightreflectedbythebeamsplitterandthisspotwasusedtocorrect

    thealignmentofthebeamsplitter.

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 32.ExperimentalProcedure:

    Once the experimental setup was complete we could begin the experiment which was

    carriedoutinthefollowing3stages.

    Measurementofcoherence length:FortheHeNe laserusedofwavelength632.8nm,the

    theoreticallycalculatedvalueofspatialcoherence length is20cm.Wecanexperimentally

    measurethecoherencelengthbydisplacingoneofthemirrorsandadjustingittoseeifwe

    get interferencepattern.Whenthetwomirrorsareequidistant fromthebeamsplitterwe

    get thebestpossible interferencepattern.Now theholeson theopticalbenchare1 inch

    aparti.e.about2.54cm.Theobjectmirrorisbroughtclosertothebeamsplitterinintervals

    of 1 inch and the mirror is adjusted till we get interference patterns on the screen. The

    coherence lengthof the laser is twice themirrordisplacement.Weobserved interference

    patterns formirrordisplacementsof1 inch,2 inchand3 inch.Howeverondisplacing the

    objectmirrorby4inchesitwasnotpossibletoobservetheinterferencefringes.Thismeans

    thattheactualcoherencelengthofthelaserinlabconditionsissomewherebetween6to8

    inchesorabout15to20cmasexpected.

    Effectofvaryingtheangleofthemirrorbyasmallvalue :Itispossibletomeasurethelaser

    wavelengthbytiltingoneofthemirrorsbyasmallvalue .

    Fig2:Effectoftiltingthemirrorby

    SupposeoneofthemirrorsM2isdeflectedbyasmallangle asshownintheabovediagram.

    ThewavefrontreflectedbymirrorM2willbeatanangle2 relativetothewavefrontreflected

    bymirrorM1.Thusforsmallvaluesof,thefringespacingwillbe /2.Nowiffringespacingis

    Beamsplitter

    2

    M1

    M2

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 4,wehave = /2.Thusifwemeasurethefringespacing thenwecanfind bytiltingthe

    mirrorbyasmallknownangle .

    Measurementofflametemperatureofcandle:

    To aid in the measurements of fringe spacing and other parameters for analysis of

    photographsweneedtohavesomereference.Forthisa12mmdiametersteelrodisplacedin

    thepathoftheobjectbeamandaphotographistaken.Nowallthelengthsonthepicturescan

    bescaledtothisreferencelengthtoensurethedataiscorrect.

    Fig3:Photographof12mmdiameterrodforscaling

    Next thecandle isplaced in thepathof theobjectbeamand is lighted.Themirror is

    adjustedtogetstablefringesonthescreen.ThepaperscreenisremovedandaPolaroidpicture

    istakenoftheinterferencepattern.Thefilmsaredevelopedandtreatedwithastabilizingfluid.

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 53.DataCollection:

    The photograph of the interference pattern of flame was analyzed in Photoshop. I have

    selected3stationsonthepictureasshownbelowandfringespacingwasmeasuredatthese

    3locationstofinddensityandtemperature.

    Fig4:Photographofinterferencepatternduetocandleflame

    I tabulated the fringe spacing at the 3 stations in MS Excel and then interpolated the

    intermediatevaluesusing r=0.78.Theplottedcurvesforthesevaluesareasshownbelow.The

    exceltableisshowninAppendix(B).

    Fig5:InterpolatedfringespacingatStation1

    Aquadraticcurvefitwasobtained inMSExcelforthesepointsshownbytheblacksolid line.

    Theequationsforthiscurvefitarealsoshownintherespectiveplots.

    N1=0.123y2 +0.003y 8.455

    10

    8

    6

    4

    2

    0

    10 5 0 5 10

    Nv/syatStation1

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 6

    Fig6:InterpolatedfringespacingatStation2

    Fig7:InterpolatedfringespacingatStation3

    The rest of the analysis was done in MATLAB and the code for it is attached at the end in

    Appendix(A).

    N2=0.111y2 +0.014y 6.870

    8

    7

    6

    5

    4

    3

    2

    1

    0

    10 5 0 5 10

    Nv/syatStation2

    N3=0.099y2 +0.001y 5.778

    7

    6

    5

    4

    3

    2

    1

    0

    10 5 0 5 10

    Nv/syatStation3

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 74.DataAnalysis:

    Theanalyticalequationsforfindingthedensityandhencethetemperatureoftheflameare

    asbelow.

    where,

    isthewavelengthoflight=632.8nm,

    Nisthefringenumber

    n=indexofrefraction

    Sincethetemperaturedistributionisaxisymmetricwecanwrite

    wheref(r)=n(r)nrefandhence

    ,

    thisequationgivesusarelationbetweenthefringenumber,NandthedifferenceinR.I.f(r).

    ThesolutiontothisisgivenbytheAbelTransformasfollows

    ,

    Sincewehavevaluesatdiscretepointswecannotuse theseanalyticalequationsdirectly

    andhencehavetousethediscretizedversionoftheequationsasfollows.

    Therefore

    ,

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 8with

    , , , ,

    AndM=2forMichelsonInterferometer.

    IhavefoundtheR.I.differencefvectorby invertingtheAmatrix.Density canbefound

    using

    whereKistheGladstoneDaleconstantfoundbyinterpolatingthevaluesgivenintablefor

    airfor =632.8nmand ref=1.225kg/m3forairatstandardtemperaturepressure.

    TofindtheTemperatureT,theequationofstate

    where

    P=101325N/m2and

    R=287J/kgK

    Once thevaluesofdensity, andTemperature,Twere foundthesewereplottedagainst

    theradialdistanceshown.

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 95.Results:

    ThesegraphswereplottedinMATLABandtheyshowhowthedensityandtemperaturevary

    withintheflameasafunctionofradialdistancer.

    Fig8:Densityvariationasafunctionofradialdistancewithintheflame

    Fig9:Temperaturevariationasafunctionofradialdistancewithintheflame

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 106.Conclusion:

    Wecansummarizetheconclusionsdrawnsofarfromtheanalysisasfollows:

    (i) Thecoherentlengthofthelaserisabout20cm.Fromourexperimentwecansaythatitisbetween1520cm.

    (ii) The wavelength of light can be found by tilting the mirror by a small value (measuredinradians)andusingtheequation

    2where isthefringedisplacement.

    (iii) Theflamedensitydecreasesaswemoveradiallyoutwardsfromtheflamecentreandislowestatstation1andhighestatstation3foragivenradiallocation.

    Also, the flame temperature decreases radially outwards and the highest at

    station1andlowestatstation3foragivenradiallocation.

    Thuswehave successfullydetermined the temperatureanddensitywithin the flame

    andplottedtheresults.

    7.References:(i) HolographicinterferometrybyCharlesV.WestWileyPublishing(ii) Fluid Mechanics Measurements edited by Richard J. Goldstein Taylor and

    Francis

    (iii) LabnotesbyProf.LuisBernal

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 11APPENDIX(A):MATLABcodeforfindingandplottingdensityandtemperature:% I nter f eromet r y measur ement s do f i nd t emperature of f l ame %cl ear ;dr=0. 70;

    M=2;l ambda=632. 8*10 - 6;r ho_r ef =1. 225;K=0. 2256*10 - 3;P=101325;R=287;f or i =1: 11

    f or k=1: 11i f k>=i

    A( i , k) =sqr t ( ( k) 2- ( i - 1) 2) - sqr t ( ( k- 1) 2- ( i - 1) 2) ;el se

    A( i , k)=0;

    endend

    endy=( 0: 10) *dr ;N1=0. 123*y. 2+0. 003. *y- 8. 455;N2=0. 111*y. 2+0. 014*y- 6. 870;N3=0. 099*y. 2+0. 001*y- 5. 778;

    f 1=l ambda/ ( 2*M*dr ) *( A - 1*N1' ) ;f 2=l ambda/ ( 2*M*dr ) *( A - 1*N2' ) ;f 3=l ambda/ ( 2*M*dr ) *( A - 1*N3' ) ;

    r ho1=r ho_r ef +f 1/ K;r ho2=r ho_r ef +f 2/ K;r ho3=r ho_r ef +f 3/ K;

    T1=P. / ( r ho1*R) ;T2=P. / ( r ho2*R) ;T3=P. / ( r ho3*R) ;f i gur e( 1) ;pl ot ( y, r ho1, ' k V' , y, r ho2, ' k * ' , y, r ho3, ' k o' , ' Marker FaceCol or ' , ' k' ) ;l egend( ' St at i on1' , ' St at i on 2' , ' St ant i on 3' , ' Locat i on' , ' Best ' ) ;xl abel ( ' r adi al l ocat i on, r ( mm) ' ) ; yl abel ( ' Densi t y, \ r ho( kg/ m 3) ' )t i t l e( ' Densi t y v/ s r adi al l ocat i on' ) ;xl i m( [ 0 7. 5] )f i gur e( 2) ;pl ot ( y, T1, ' k V' , y, T2, ' k * ' , y, T3, ' k o' , ' Mar ker FaceCol or ' , ' k' ) ;l egend( ' St at i on1' , ' St at i on 2' , ' St ant i on 3' , ' Locat i on' , ' Best ' ) ;xl abel ( ' r adi al l ocat i on, r ( mm) ' ) ; yl abel ( ' Temper at ur e, T( K) ' )t i t l e( ' Temper at ur e v/ s r adi al l ocat i on' ) ;xl i m( [ 0 7. 5] )% End of code %

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    Lab1:TemperatureMeasurementsbyLaserInterferometry 12APPENDIX(B):FringespacingatStations1,2and3:ThefringenumberN=0correspondstothefringeattheborderoftheflameandaswemove

    radiallyinwardsthefringenumberdecreases(becomesnegative).

    Station1 Station2 Station3N y(mm) N y(mm) N y(mm)0 8.22222

    1 7.74074 0 7.96296

    2 7.2963 1 7.33333 0 7.7037

    3 6.7037 2 6.66667 1 6.96296

    4 6.07407 3 5.96296 2 6.11111

    5 5.37037 4 5.11111 3 5.2963

    6 4.48148 5 4.14815 4 4.07407

    7 3.33333 6 2.66667 5 2.70378 0 7 0 6 0

    7 3.518519 6 2.777778 5 2.851852

    6 4.592593 5 4.074074 4 4.148148

    5 5.407407 4 5.037037 3 5.259259

    4 6.074074 3 5.777778 2 6.111111

    3 6.703704 2 6.518519 1 6.962963

    2 7.185185 1 7.185185 0 7.62963

    1 7.703704 0 7.814815

    0 8.111111

    Table1FringespacingatStations1,2and3