The interaction of thermal radiation and water

FireSafetyJournal39(2004)41–66TheinteractionofthermalradiationandwatermistinfiresuppressionWenhuaYanga,TerryParkera,H.D.Ladouceurb,RobertJ.Keea,*aDivisionofEngineering,ColoradoSchoolofMines,Golden,CO80401-1887,USAbCode6111,NavalResearchLaboratory,Washington,DC20375,USAReceived26August2002;receivedinrevisedform22May2003;accepted23July2003AbstractWatermistisahighlyeffectivefire-protectionagent.Inadditiontothedirectinteractionofevaporatingdropletswithaflametocauseweakeningorextinction,themistservestoscatterandabsorbthermalradiation.Thecentralobjectiveofthispaperistocharacterizetheinteractionofthewatermistwiththermalradiation.Thedropletcloudcanabsorbthermalradiation,especiallyinthewavelengthsassociatedwithwaterbands.Theradiationservestopreheatandpre-evaporatethedropletsupstreamoftheflameitself,alteringthestructureandextinctionoftheflame.Themistalsoactsasaradiationshieldthatattenuatesradiation.Theradiativecharacteristicsofthemistdependstronglyondropletsizeandnumberdensity.Spectrallydependentgas-phaseemissionandabsorptionismodeledusinganexponentialwide-bandmodelandradiation-dropletinteractionismodeledusingMie-scatteringtheory.Radiativetransferinthemistisdescribedwithatwo-fluxmodel.r2003ElsevierLtd.Allrightsreserved.1.IntroductionFinewatermistsarefoundtobeaneffectiveandenvironmentallyfriendlyalternativetofluorocarbon-basedfire-suppressionagents[1].Inthedevelopmentanddeploymentofpracticalsystems,itisimportanttounderstandhowtheflame-extinctioncharacteristicsdependondropletdiameter,numberdensity,andoverallwaterloading.Thecentralobjectiveofthispaperistoquantifytheinteractionofthermalradiationwiththewatermist.Atwo-fluxmodelisusedtodescribetheARTICLEINPRESS*Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](R.J.Kee).0379-7112/$-seefrontmatterr2003ElsevierLtd.Allrightsreserved.doi:10.1016/j.firesaf.2003.07.001radiativescatteringandabsorptionbythemist.Thismodel,whichconsidersspectrallydependentscatteringandin-scattering,isanimprovementoverpreviouslyusedLambert–Beermodelsbecauseitmoreproperlyaccountsformultiplescattering.Inafireenvironmentthereareamplesourcesofthermalradiation.Theremaybeburningsolidobjectsthatcanradiatewithnear-black-bodyefficiencyathightemperatures.Thehot-gascombustionproductsalsoradiate,especiallyinthewaterandcarbon-dioxidespectralbands,withthestrengthdependingongas-phasecompositionandeffectivepathlength.Therecanbeconsiderableinteractionbetweenamistcloudandthermalradiation,especiallyinthewaterbandsaround2.7and6:3mm:Themistscattersandabsorbsradiation,thebehaviordependinggreatlyonthedropletsize,numberdensityandcloudgeometry.Hereweareconcernedprimarilywiththeextenttowhichradiationcanpenetrateintothemist.Thispaperfocusesonaplanarslabgeometry.Thesameradiationmodelsarealsoincorporatedintotwo-phasechemicallyreactingflamemodels,althoughthoseresultsarenotreportedhere.Asadropletabsorbsradiation,theheatloadtendstopromoteevaporationandthusreducethedropletdiameter.Inpreviouswork[2,3],wehavepredictedhowdropletsizeandnumberdensityaffectsthestructureandextinctionofpremixed,freelypropagating,stoichiometric,methane-airflames.Oneinterestingresultoftheearliereffortwasthepredictionofturning-pointextinction,withtheextinctionbehaviordependingstronglyonthedropletsizeandnumberdensity.Anotherinterestingaspectisthemodelingandexperimentalcharacterizationofasmall-dropletlimitingbehavior,whichshowsthatfordropletsbelowabout10mm(formethane-airpremixedflames)theburningvelocitydependsonthewaterloadingbutnotthedropletdiameter[3].Theradiationmodeldescribedinthepresentpaperhasnowbeenincorporatedintothetwo-phaseflamemodel,whichenablesstudyingtheeffectsofradiationonthedropletsandthusthesuppressioncharacteristicsofthemist.2.RadiationmodelsThethermalradiationabsorbedbyanindividualdropletdependsonthespectralcontentandintensityoftheincidentradiationandthedroplet-absorptioncharacteristics.Thespectralradiationmustbemodeledasitisscatteredandabsorbedalongtheentirepathfromthesourcetoadroplet.Fordropletsintherangeoftenstohundredsofmicrons,scatteringcanbesignificantandisnotisotropic.Whenscatteringisassumedonlytoremoveradiationfromitspath(forsystemswithhighnumberdensitiesandlongpathlengths),theLambert–Beerlawtendstoover-estimatethetotalattenuationbywatermist.Infact,resultsofthemodelingshowthatforwardscatteringisquiteimportantinwatermistsystems.Asradiationtravelsalongaparticularrayinthemist,itmaybepartiallyabsorbedoritmaybepartiallyscatteredintoanotherdirection.Ofcourse,thereareotherraysthatarebeingscatteredandabsorbed.RadiationthatisscatteredoutofoneARTICLEINPRESSW.Yangetal./FireSafetyJournal39(2004)41–6642directionmaycontributetoradiationinanotherdirection.Itisthisin-scatteringprocessthatcausesthemajordifficultyinsolvingtheradiation-transportproblem.Ascanbefoundintextsonthermalradiation[4–6],thereareseveralapproximatemethodsthatmaybeusedtoreducethecomputationalburdenofrepresentingthein-scattering.Themethodusedhereisthetwo-fluxmodel,whichassumestheradiationintensitiesatanypointareuniformoveraforwardandbackwardhemisphere.Asimplementedi