enclosure-fire-dynamics-c05

5©2000byCRCPressLLCPressureProfilesandVentFlowsforWell-VentilatedEnclosuresTheclassicalrepresentationofafireinaroomorbuildingrepresentsthestructurewithanopening,suchasadoororawindow,totheambientsurroundingsortoanadjacentcompartment.Weshallcallsuchanopeningavent.Theflowofgasesinandoutthroughaventiscontrolledbythepressuredifferenceacrossthevent.Inordertoestimateanyoftheenvironmentalconsequencesofafireinanenclosure,itisnecessarytoquantifythemassofhotgasesexitingandthemassofcoldergases(air)enteringtheenclosure.Thisgivesinformationonthemassandenergybalanceandthereforeallowscalculationofsuchenvironmentalconsequencesashotgastemperatureandsmokelayerheight.Thischapterderivesengineeringequationsusedtocalculatepressuredifferencesacrossvents,aswellasequationsforcalculatingthemassflowofgasesinandoutthroughvents,forseveralcommonenclosurefirescenarios.Ventflowsfornearlyclosedcompartmentsorthosewithverysmallventsandleakages,wherethepressurebuild-upismainlyduetodynamicpressures,willbedealtwithinChapter8.CONTENTS5.1Terminology5.2Introduction5.2.1SomeCharacteristicsofPressure5.2.2ApplicationtoaSimpleExample5.2.3MassFlowRatethroughVents5.2.4Summary5.3ExamplesofPressureProfilesinaFireRoomwithaVent5.4TheWell-MixedCase5.4.1MassFlowRatesandtheHeightoftheNeutralPlane5.4.2ASimplifiedExpressionfortheMassFlowRateinthroughanOpening5.4.3TakingintoAccounttheMassProducedintheRoom(theBurningRate)5.4.4Summary5.5TheStratifiedCase5.5.1MassFlowRatesintoandoutoftheVent5.5.2SpecialCase:MassFlowoutthroughaCeilingVentReferencesProblemsandSuggestedAnswers5.1TERMINOLOGYFlowcoefficient—Whenapressuredifferenceexistsacrossanopening,fluidwillbepushedthrough.Inpracticalapplicationsthefluidisnotideal(itisnotfriction-free,incompress-ible,andisothermal)andtherewillbesomeresistancetotheflow.Thisresistanceistakenintoaccountbyaflowcoefficient,whichbasicallystatesthatonlyapartoftheopeningwillallowthefluidtofloweffectivelythroughit.TheflowcoefficientisdenotedCdandtakesthevalue0.7formostoftheapplicationsinthistext.©2000byCRCPressLLCHydrodynamicpressuredifference—Thepressuredifferencecausedbyastaticpressureheadacrossanopeningatagivenheight,whereavolumeoffluidgoesfrombeingatresttohavingavelocityv.Hydrostaticpressuredifference—Thepressuredifferenceacrossanopening,atagivenheight,duetotheweightofacolumnofgasorliquid.Neutralplane—Whenhotandcoldgasesareateithersideofanopening,thehotgaseswillflowoutthroughtheupperpartoftheopeningandthecoldgaseswillflowinthroughitslowerpart.Theflowiscausedbythepressuredifferenceacrosstheopening,whichinturniscausedbytemperaturedifferenceofthegases.Atsomeheightaboveagivenreferenceheight,thepressuredifferencewillbezero,andthisheightiscalledtheheightoftheneutralplane.Hotgaseswillflowoutabovetheneutralplaneandcoldgasesflowinbelowit.Stratifiedcase—Whenafirecompartmentisassumedtobedividedintotwozones,anupperhotzoneandalowercoldzone(assumedtohavethesamepropertiesastheoutsideambientair),apressureprofilewillbeestablishedacrosstheopeningtotheoutside.Thepressureprofilewillbeidentifiedwiththe“stratified”case.Well-mixedcase—Anenclosurehasanopeningtotheoutside,ambientair.Whenthegasintheenclosureisassumedtohaveauniformtemperatureoveritsentirevolume(tobewellmixed),thepressureprofileacrosstheopeningisidentifiedwith“thewell-mixed”case.5.2INTRODUCTIONTheflowoffluidsalwaysoccursfromaplaceofhighpressuretoaplaceoflowerpressure.Theflowofgasesfromanenclosurecontainingfiredependsonthepressuredifferencesbetweentheenclosureandthesurroundings.Aquantificationofthepressuredifferencesisthereforeoffundamentalimportance.Itisconvenienttosplitthedrivingpressuredifferencesintotwocategories.Inthefirstcategorythepressuredifferencesarecausedbythefire.Inthesecondcategorythepressuredifferencesarecausedbynormalconditionsthatareeitheralwayspresentinabuildingorarecreatedbydifferencesinconditionsinsideandoutsideofthebuilding.Pressuredifferencescausedbythefirearemainlyoftwotypes:1.Pressuredifferencescausedbythermalexpansionoftheenclosuregases.Whenthegasesheatuptheyexpand.Inaverytightlyclosedroomthiswillcauseariseinpressure.However,innearlyallbuildingstherearesmallleakageareasthatcausesuchpressurebuild-uptobenegligible,andthisphenomenonisusuallyignoredinengineeringcalcu-lations.Incertaintypesoftightlyclosedrooms,suchasanengineroominaship,thispressurebuild-upmaybeverysubstantialandmustbeaccountedfor.InChapter8,whendiscussingsmokefillingahermeticallyclosedroom,weshallgiveexpressionsforcalculatingpressuresduetopreventedthermalexpansion.2.Pressuredifferencesduetobuoyancyofthehotgases,orrather,duetodensitydifferencesbetweenthehotandthecoldgases.Thisisthemostcommoncauseofsmokeflowinabuildingcontainingfire.Inthischapterweshalluseclassicallawsofhydraulicstoderiveequationsforcalculatingthepressuredifferencesandthemassflowcausedbythese.Normalpressuredifferencesinabuildingaremainlyofthreetypes:1.Pressuredifferencesduetodensitydifferencesinsideandoutsideofthebuilding,orduetothedifferenceininsideandoutsidetemperatures.Thepressuredifferencescreatedaregovernedbythesamelawsofhydraulicsasthosementionedintype2above.Theequationsthatweshallderiveandu