enclosure-fire-dynamics-c04

4©2000byCRCPressLLCFirePlumesandFlameHeightsWhenamassofhotgasesissurroundedbycoldergases,thehotterandlessdensemasswillriseupwardduetothedensitydifference,orrather,duetobuoyancy.Thisiswhathappensaboveaburningfuelsource,andthebuoyantflow,includinganyflames,isreferredtoasafireplume.Asthehotgasesrise,coldairwillbeentrainedintotheplume,causingalayerofhotgasestobeformed.Manyapplicationsinfiresafetyengineeringhavetodowithestimatingthepropertiesofthehotlayerandtherateofitsdescent.Thisdependsdirectlyonhowmuchmassandenergyistransportedbytheplumetotheupperlayer.Thischapterwillexplainsomeofthemostfundamentalpropertiesoffireplumesandprovideanalyticalexpressionsfortheirproperties.Further,thesizeandgeometryoftheflamesduetoaburningobjectareofgreatinteresttothefiresafetyengineer.Anestimationoftheflameheightcanfacilitatecalculationsonheattransfertodistantobjects,secondaryfuelandfiredetection,andsuppressionequipment.Thischapterdiscussesflameheightsingeneralandgivesexpressionsforcalculationoftheflameheightsforcertaingivenscenarios.CONTENTS4.1Terminology4.2Introduction4.2.1FlameCharacteristics4.2.2TurbulentFirePlumeCharacteristics4.3TheIdealPlume4.3.1Assumptions4.3.2InitialConsiderations4.3.3TheContinuityEquationforMass4.3.4TheMomentumandBuoyancyEquation4.3.5SolutionoftheTwoDifferentialEquations4.3.7InsertingtheConstantsandConcluding4.4PlumeEquationsBasedonExperiments4.4.1TheZukoskiPlume4.4.2TheHeskestadPlume4.4.3TheMcCaffreyPlume4.4.4TheThomasPlume4.5LinePlumesandBoundedPlumes4.5.1WallandCornerInteractionswithPlumes4.5.2LineSourcePlumes4.6CeilingJets4.6.1CeilingJetTemperaturesandVelocities4.6.2FlameExtensionsunderCeilingsReferencesProblemsandSuggestedAnswers©2000byCRCPressLLC4.1TERMINOLOGYAxisymmetricplume—Thebuoyantaxisymmetricplume,causedbyadiffusionflameformedabovetheburningfuel,isthemostcommonlyusedplumeinfiresafetyengineering.Anaxisofsymmetryisassumedtoexistalongtheverticalcenterlineoftheplume,andairisentrainedhorizontallyfromalldirections.Otherfireplumecategoriesinclude,forexample,lineplumes,whichmaybeformedabovealongandnarrowburner,allowingairtobeentrainedfromtwosidesonly.Plume—Whenamassofhotgasesissurroundedbycoldergases,thehotterandlessdensemasswillriseupwardduetothedensitydifference,orrather,duetobuoyancy.Thisiswhathappensaboveaburningfuelsource,andthebuoyantflow,includinganyflames,isreferredtoasafireplume.Plumemassflowrate—Thetotalmassflowingupward,atacertainheightabovethefuelsource,withintheplumeboundaries.Theplumemassflowrateismostoftengiveninkg/sandisdenotedp.Plumeradius—Theaxisymmetricplumeradiusatasomeheightabovethefuelsource.Theplumeradiusisgiveninmandisdenotedb.Plumetemperature—Thetemperatureofthegaseswithintheplumeboundaries,atacertainheightabovethefuelsource.Atanygivenheightthehighesttemperatureisattheplumecenterline(foraxisymmetricplumes),decreasingtowardtheedgeoftheplume.Thecenterlinetemperaturechangeswithheightisgivenin°CorKanddenotedT0,wherethesubscript“0”referstothecenterline.Plumevelocity—Thevelocityatwhichthegaseswithintheplumeboundariesmoveupward,atacertainheightabovethefuelsource.Inanaxisymmetricplume,thehighestvelocity(atagivenheight)isattheplumecenterline.Thiscenterlinevelocityisgiveninm/sandisdenotedu0,wherethesubscript“0”referstothecenterline.4.2INTRODUCTIONThisintroductiondiscussessomeofthegeneralcharacteristicsoffireplumesandflamesmostcommonlyoccurringinbuildingfires.Definitionsaregivenofanumberofconceptsthatwillbeusedinlatersections.Thediscussionisdividedintotwoparts,oneonflamesandtheotheronfireplumes.4.2.1FLAMECHARACTERISTICSInmostfiresafetyengineeringapplicationsweareconcernedwiththeso-calledbuoyant,turbulentdiffusionflame.Herewediscusssomeoftheprocessesthatcharacterizesuchflames,showresultsfromflameheightmeasurements,andgivecorrelationequationsthatcanbeusedforestimatingflameheights.Diffusion:Diffusionflamesrefertothecasewherefuelandoxygenareinitiallyseparated,andmixthroughtheprocessofdiffusion.Burningandflamingoccurwheretheconcentrationofthemixtureisfavorabletocombustion.Althoughthefuelandtheoxidantmaycometogetherthroughturbulentmixing,theunderlyingmechanismismoleculardiffusion.Thisistheprocessinwhichmoleculesaretransportedfromahightolowconcentration.Oppositetothisisthepremixedflame,asisthecasewithawelder’storch,wherethefuelandtheoxidantaremixedbeforeignited.Flamesinaccidentalfiresarenearlyalwayscharacterizedasdiffusionflames.Buoyancy:Whenamassofhotgasesissurroundedbycoldergases,thehotterandlessdensemasswillriseupwardduetothedensitydifference,orrather,duetobuoyancy.Theupwardvelocityoftheflowwithinaflamewillbedominatedbythebuoyancyforceifthevelocityatwhichthefuelisinjectedisnotexceptionallyhigh.Oppositetothebuoyancy-dominatedflamesaretheflows˙m©2000byCRCPressLLCformedaboveahigh-pressuregaseousfuelsource(forexample,arupturedpipelineunderhigh-pressure)wheretheflowisnotbuoyancydominated,butmomentumdominated;thesearetermedjetflames.Turbulence:Verysmalldiffusionflamescanbelaminar,suchastheflameonacandle.Largerdiffusionflamesareturbulentandwillfluctuatewithperiodicoscillationswithlargeeddiessheddingattheflameedge(seeFigure4.1).Theeddies,whic