火羽流第2讲-[兼容模式]

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„Thereforetheidealplumetheoryissometimesreferred„Therefore,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.„Theforcedrivingthesystemcantherefore„Theforcedrivingthesystemcanthereforebeassumedtoariseduetothedensitydifferenceofthehotairabovethepointandthecoldsurroundingair.„Furtherassumethattheflowprofileacross„Furtherassumethattheflowprofileacrossthesectionoftheplume,atanyheight,isaso-calledtophatprofile.Therefore,theupwardvelocityisassumedtobeconstantacrossthewidthoftheplumeandzeropoutsideit.„Theplumetemperatureissimilarlyassumedtobeconstantacrossanysectionoftheplume.„Assumethatthereisarelationshipbetweentheupwardvelocityintheplumeandthehorizontalentrainmentvelocityintotheplume,v,suchthatv=α·u,whereαiscalledtheentrainmentwhereαiscalledtheentrainmentcoefficient.2.2基本方程基本方程massflowrate„massflowrate„buoyancyforce„MomentumE„Energy2.2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。