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9.9斗.Lm range，ourIRcamerashou1dbeab1etodetect thesurfacetemperaturetowithina1esthan1% eror.
B. InfraredAbsorptionwithFuelVapor
Asthe1iquidfue1formsthevaporconcentrationdis-
tributionoveritssurface，theIRcameracandetect
thesurfacetemperaturethroughthe釦 e1vapor1ayer.
Ifthespectra1radiationofintensityemitedfromthe
liquid.surfacerepresents10λ"thereductionofinten司
sitybecomesdI astheradiationpasesthroughfue1 A
vaporthicknesdS. Thisre1ationcanbeexpresed as
dIλ=一α'l¥mp1 dS， (3) λ0
whereα入m istheabsorptionmasscoeficientwith unitsofareaperunitmass，andpisthe1oca1density ofthe五1e1vapor.10 IntegratingEq.(3)overafinite path1engthhggives
五 ( 目 ( 吋 -[hhgM
wherezisthenorma1distancefromthe1iquidsur回 face，andp(z)indicatesthatthedensityisafunction ofz. Inourpreviouspaper10wesugestedthatthe 1oca1densityprofi1escanbegivenby
p(z)=αz+Po， (5)
whereαisthegradientofvaporconcentration，andPo isthedensityofthe1iquidsurface，whichequa1sthe equilibriumvaporpresureofaspecifictemperature. SubstitutingEq.(5)intoEq.(4)andintegratingEq. (4)a10ngpath1engthhgyie1d
(a) 1油 aredray L
h(h上 1
'1\(O)
exp
la ¥I l-αλm\~h/ +的)1.
(6)
whereg(z)isthere企 activefunctionofthetrayedge. Therefore，thefue1vapor1ayerovertheliquidfue1is containedinthefueltrayandisilustratedinFig. 5(c). CombiningEq.(7)withEq.(8)，yie1ds
人(z)=10~(z)exp卜 αλmp(z)L]. (9) WhenTfand，Tαareconstant，thedensityofthefue1
vaporcanbecalculatedas
whereλαm istheaverageabsorptionmasscoeficient overthespectralrangeoftheIRcamera. Byusing theStefan-Bo1tzmann1aw，weobtainedthespectral intensityofthegraybody:
The absorption coef五cient shows iregu1ar wave- 1engthdependencies. Absorptionbyagaseousspe- ciesissigni五canton1yforcertainwave1engthregions. Toourknow1edge，absorptioncoef五cientsareavai1- ab1eon1yforafewgasessuchasCO2，H20，CH4，and CO，whichiswhywedecidedtoobtainexperimen- talytheabsorptioncoeficientof1-propano1vaporby usinganIRcameraandab1ackbodyradiationsource andsuperimposingcontributionsoftheentire1ine andcontinuumwave1engths. AsshowninFig.5(a)， thefue1vapordifuses企oma1iquidsurfaceintoam- bientairandconsequent1yformsthestratifiedmix- tureoffue1vaporandairoveritssurface.
Theblack-paintedcoperblock(greaterthan0.9 emisivity)canbetreatedasab1ackbody. Toensure thatourdiscusionincludesthegraybodyradiation source，anisotherma1graybodywasassumed. As theradiationemited企omtheisotherma1graybody pasesthroughdistanceL，thespectra1intensityre- ducestoIf入， whichgives
1fλ(z)=10λexp[-αλmp(z)L].. (7)
ん
1 σεTω，
'1T
I臥(z)
FUElvapor
L--'1-
Fig.5. SchematicilustrationoftheatenuationoftheIRray: 司( absorptionoffuelvapor，(b)re企actionattheedgeoffuel廿ay， (c)formationoffuelvaporoverthefueltray.
AsshowninFig.5(b)，ifradiationisatenuatedbythe edgeofafueltraybecauseofrefraction，weobtaIn
)~ノ向、:
~~~
1eλ (z)=10~(z)，
(8)
whereσistheStefan-Boltzmannconstant，εisthe emisivity，andTw isthewaltemperatureofthe graybodyasmeasuredbytheIRcamera. AsinFig. 5(b)，thesurfacetemperaturemeasuredbytheIR cameraisrepresentedbyTe(z). Assumingthatthe surfacetemperatureofthegraybodyequalsTe(z)，the spectra1intensitybecomes
Ie(z)=~σεT汽z)， (12) '1T
20August2000/Vo.l39，No.24/APPLlEDOPTICS 4281
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