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火羽流理论火羽流第讲理想羽流第二讲理想羽流陆守香：sxlu@ustceducn陆守香：sxlu@ustc.edu.cn办公地点：力学一楼214室0551-3603141，13956966718点源考察火z点源：考察火源上部的羽流特征可把火源看征，可把火源看成点火源，并且，随着高度上升，随着高度升，羽流区与环境密度差下降，羽流愈来愈弱愈来愈弱。z点源羽流往往z点源羽流往往被看作弱羽流TheIdealPlume-point-sourceplumedaupooupu2.1Assumptions22InitialConsiderations2.2InitialConsiderations2.3TheContinuityEquationforMass24TheMomentumandBuoyancyEquation2.4TheMomentumandBuoyancyEquation2.5SolutionoftheTwoDifferentialEquations2.1基本假设基本假设1.Weassumethatalltheenergyisinjectedatthepointsourceofoiginandthatenegemainsintheplmeiethattheeaeoriginandthatenergyremainsintheplume,i.e.,thattherearenoheatlossesinthesystemduetoradiativelosses.Inrealfireplumestheradiativepartistypically20to40%ofthetotalenergyreleasedfrommanycommonfuelsourcesthetotalenergyreleasedfrommanycommonfuelsources.点羽流理论2.1基本假设基本假设2.Weassumethatthedensityvariationsthroughouttheplumeheightaresmallandonlyneedtobetepueegtaesaadoyeedtobeconsideredwhenthedifference(ρ∞–ρ)appearsdirectly.2.1基本假设基本假设ThereforetheidealplumetheoryissometimesreferredTherefore,theidealplumetheoryissometimesreferredtoastheweakplumetheory,where,duetomixing(entrainment)ofair,theplumetemperatureisonlyslightlyhigherthantheambientslightlyhigherthantheambient.Atcertainpointsinthederivationweshallthereforeassumethatρ∞≈ρ.However,whenexpressingthebfhihidbthditbuoyancyforce,whichiscausedbythedensitydifference,(ρ∞–ρ),thisassumptiondoesnotapply.ThisapproximationissometimesreferredtoastheThisapproximationissometimesreferredtoastheBoussinesqapproximation.Inpracticaltermsthismeansthattheequationscannotbeusedatheightsclosetothefiresourcebutwillgivebeusedatheightsclosetothefiresourcebutwillgivereasonableanswersatheightsfurtherabovethesource(farflowfield).2.1基本假设基本假设3.Weassumethatthevelocity,temperature,andforceprofilesareofsimilarformindependentoftheheight,z.fhhhfllldhWefurtherassumethattheseprofilesareso-calledtophatprofiles,sothatthevelocityandtemperatureareconstantoverthehorizontalsectionatheightzalongtheradiusb,andthatu=0,andT=ToutsidetheplumeradiusandT=T∞outsidetheplumeradius.2.1基本假设基本假设4.Weassumethattheairentrainmentattheedgeoftheplumeisgpproportionaltothelocalgasvelocityintheplume,sothattheentrainmentvelocitycanbewrittenasv=α·u,whereαisaconstantandistakentobe≈0.15(appliestotophatprofile).Inotherwords,thehorizontalentrainmentvelocityisassumedentrainmentvelocityisassumedtobe15%oftheupwardplumevelocity.Thisvalueisdifficulttomeasurebuthasbeenfoundtocorrespondreasonablywithcorrespondreasonablywithexperimentallymeasuredvalues.假设假设Assumethesimplecaseofapointsourceofheatatheightz=0ofheatatheightz=0.Theenergyisconsideredtobetotallytransportedintheplume,andnoradiativeheatisemittedfromthepointsource.TheforcedrivingthesystemcanthereforeTheforcedrivingthesystemcanthereforebeassumedtoariseduetothedensitydifferenceofthehotairabovethepointandthecoldsurroundingair.FurtherassumethattheflowprofileacrossFurtherassumethattheflowprofileacrossthesectionoftheplume,atanyheight,isaso-calledtophatprofile.Therefore,theupwardvelocityisassumedtobeconstantacrossthewidthoftheplumeandzeropoutsideit.Theplumetemperatureissimilarlyassumedtobeconstantacrossanysectionoftheplume.Assumethatthereisarelationshipbetweentheupwardvelocityintheplumeandthehorizontalentrainmentvelocityintotheplume,v,suchthatv=α·u,whereαiscalledtheentrainmentwhereαiscalledtheentrainmentcoefficient.2.2基本方程基本方程massflowratemassflowratebuoyancyforceMomentumEEnergy2.2基本方程基本方程2.3质量方程质量方程Axisymmetricplume?2.3质量方程d&质量方程ppdmmdz+&pedmdm=&&fltdzdz=edmdz&massflowratepm&空气卷吸速率空气卷吸速率2edmbdzvπρ=⋅⋅⋅&2edmb&2ebudzρπαρ=⋅2ebudzπαρ=2.3质量方程质量方程dmdm&&pedmdmdzdz=2edmbudπαρ=&dzρ2.4动量方程和浮力方程动量方程和浮力方程浮力方程浮力方程2.4动量方程和浮力方程动量方程和浮力方程由动量方程由动量方程由浮力方程2.4动量方程和浮力方程动量方程和浮力方程wweakplumme2.5质量与动量方程的解质量与动量方程的解Weakplume2.5质量与动量方程的解质量与动量方程的解2.5质量与动量方程的解质量与动量方程的解2.5质量与动量方程的解质量与动量方程的解2.5质量与动量方程的解质量与动量方程的解2.6小结小结0150.15α=2.6小结小结WeakplumeWeakplume2.6小结小结WeakplumeWeakplume问题思考问题思考1点源羽流的含义是什么?1.点源羽流的含义是什么?2.为什么说理想羽流是弱羽流?3.推导点源羽流模型有哪些假设?4.弱羽流模型有哪些主要结果?4.弱羽流模型有哪些主要结果?5.如果羽流参数分布不是帽型分布,而是正态分布或者其他分布形式能够推出羽流公式吗?或者其他分布形式,能够推出羽流公式吗?6.羽流半宽,请加以评论。
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本文标题：火羽流第2讲-[兼容模式]
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