Interferometer Flame
-
Upload
matheus-loss-lize -
Category
Documents
-
view
237 -
download
0
Transcript of Interferometer Flame
-
7/30/2019 Interferometer Flame
1/13
LabReport1:TemperatureMeasurementsbyLaserInterferometry AnandDhariya
AERO521:ExperimentalMethodsinFluidDynamics14
th
February2008
-
7/30/2019 Interferometer Flame
2/13
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
-
7/30/2019 Interferometer Flame
3/13
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.
-
7/30/2019 Interferometer Flame
4/13
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
-
7/30/2019 Interferometer Flame
5/13
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.
-
7/30/2019 Interferometer Flame
6/13
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
-
7/30/2019 Interferometer Flame
7/13
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
-
7/30/2019 Interferometer Flame
8/13
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
,
-
7/30/2019 Interferometer Flame
9/13
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.
-
7/30/2019 Interferometer Flame
10/13
Lab1:TemperatureMeasurementsbyLaserInterferometry 95.Results:
ThesegraphswereplottedinMATLABandtheyshowhowthedensityandtemperaturevary
withintheflameasafunctionofradialdistancer.
Fig8:Densityvariationasafunctionofradialdistancewithintheflame
Fig9:Temperaturevariationasafunctionofradialdistancewithintheflame
-
7/30/2019 Interferometer Flame
11/13
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
-
7/30/2019 Interferometer Flame
12/13
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 %
-
7/30/2019 Interferometer Flame
13/13
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