火羽流第7讲-[兼容模式]

火羽流理论火羽流理论第七讲线型火源羽流模型第七讲线型火源羽流模型陆守香：sxlu@ustceducn陆守香：[e-mail]办公地点：力学一楼214室0551-3603141，13956966718LineSourcePlumemodel7.1线型火源特征参数线型火源弱羽流模型7.2线型火源弱羽流模型7.3线型火源火焰区羽流模型LineSourcePlumemodel7.1线型火源特征参数LineSourcePlumemodel7.1线型火源特征参数在第三讲中，对于点源，给出了特征长度zc，它是一个非常重要2/5Q⎛⎞&在第三讲中，对于点源，给出了特征长度c，它是个非常重要的参数，与火源直径一样，决定了大涡旋结构的尺寸和火焰的高度。cpQzcTgρ∞∞⎛⎞=⎜⎟⎜⎟⎝⎠对于一定厚度的线火源，引入线火源单位长度热释放速率'/QQL=&&无厚度的线火源特征长度2/5//cQLzT⎛⎞=⎜⎟⎜⎟&？2/3'Qz⎛⎞=⎜⎟⎜⎟&无厚度的线火源特征长度/pccTgzρ∞∞⎜⎟⎝⎠？,clinepzcTgρ∞∞=⎜⎟⎜⎟⎝⎠2/3⎛⎞&',clineQzcTgρ⎛⎞=⎜⎟⎜⎟⎝⎠&pcTgρ∞∞⎜⎟⎝⎠对于宽度为D的线火源，无量纲火焰高度表示为fclinezzf⎛⎞⎜⎟,fclinefDD⎛⎞=⎜⎟⎝⎠LineSourcePlumemodel7.2线型火源弱羽流模型„Rouse，Yih&Humphries,Gravitationalconvectionfromaboundarysource,Tellus,1952,4:202~2102exp()urubz⎡⎤⎛⎞=−⎢⎥⎜⎟⎢⎥⎝⎠⎣⎦2()expmubzTTrβ∞⎢⎥⎝⎠⎣⎦⎡⎤⎛⎞−=−⎢⎥⎜⎟exp()mTTbzβ∞⎢⎥⎜⎟−⎢⎥⎝⎠⎣⎦,1()rbzηβ=„具有相似解回顾-弱羽流假设回顾弱羽流假设„Assumethesimplecaseofapointsourceofheatatheightz=0ofheatatheightz=0.„Theenergyisconsideredtobetotallytransportedintheplume,andnoradiativeheatisemittedfromthepointsource.„Theforcedrivingthesystemcantherefore„Theforcedrivingthesystemcanthereforebeassumedtoariseduetothedensitydifferenceofthehotairabovethepointandthecoldsurroundingair.„Furtherassumethattheflowprofileacross„Furtherassumethattheflowprofileacrossthesectionoftheplume,atanyheight,isaso-calledtophatprofile.Therefore,theupwardvelocityisassumedtobeconstantacrossthewidthoftheplumeandzeropoutsideit.„Theplumetemperatureissimilarlyassumedtobeconstantacrossanysectionoftheplume.„Assumethatthereisarelationshipbetweentheupwardvelocityintheplumeandthehorizontalentrainmentvelocityintotheplume,v,suchthatv=α·u,whereαiscalledtheentrainmentwhereαiscalledtheentrainmentcoefficient.3.2SolutionforGaussianprofilep()/TTTΦ=,()//mmclineTTTUuu∞∞Φ=−=,,/clineBbz=,/clinezzς=7.2SolutionforGaussianprofilep0.091α=()/TTTΦ=−2/30.8453.30(1)TrCβχ==−,()//mmclineTTTUuu∞∞Φ==1/32.25(1)0.103urlCCχ=−=,//clineclineBbzzzζ==1TCζ−Φ=21.54Uς=Φ,clineζ0TuUCBCζζζ=1/32/32/35/61/6(1)(1)2TrCβαχβ−−⎡⎤+=−⎢⎥⎣⎦22lBCUζ==β⎣⎦1/61/31/31(1)Cβαχ−⎡⎤⎛⎞+=−⎢⎥⎜⎟2lCα=ζβΦ(1)2urCαχβ=−⎢⎥⎜⎟⎝⎠⎢⎥⎣⎦lπ7.2SolutionforGaussianprofilep10TCζ−Φ=5/31/3TCζ−Φ=线点0ulUCBCζζ==1/3ulUCBCζζ−==线火源点火源22Uζβ=Φ232Uβζ=Φ0.0910.845αβ==0.0980.913αβ==2/31/33.30(1)225(1)TrCCβχχ=−2/31/310.58(1)417(1)TrCCχχ=−=1/32.25(1)0.103urlCCχ=−=4.17(1)0.118urlCCχ=−=21.54Uζ=Φ21.64Uζ=Φ7.2SolutionforGaussianprofile10TCUCζζ−Φ=5/31/3TCUCζζ−−Φ=p02ulUCBCζζ==1/323ulUCBCζζ==22Uζβ=Φ232Uβζ=Φ7.2SolutionforGaussianprofile10TCUCζζ−Φ=5/31/3TCζ−Φ=p02ulUCBCζζ==1/3ulUCBCζζ−==22Uζβ=Φ232Uβζ=ΦLineSourcePlumemodel线型火源火焰区羽流模型7.3线型火源火焰区羽流模型7.3SolutionforGaussianprofilep()/TTTΦ()//mmcTTTUuu∞∞Φ=−=/mccBbz=/czzς=7.3SolutionforGaussianprofilepψ0.30χ=0TCζΦ=2TCnCψψ=0.300.5901rχαβ==1/2TuUCBCζζζ=4uCnCψα==9.63.10.450TnCorβψ==22lBCUζ=3lCπ=2.30.8770.272ulCorCψ==ζβ=Φ21.42lUζ=Φ2,(1)rcOhYχψ∞−Δ=pcTrψ∞=7.3SolutionforGaussianprofilep0TCζΦ=线点01/2TCUCζζΦ=1/2ulUCBCζζ==线火源点火源1/2ulUCBCζζ==232Uβζ=Φ22Uζβ=Φ2TCnψ=2TCnψ=43uCnψ=uCnψ=345lnCα=43lCαπ=52,(1)rcOphYcTrχψ∞∞−Δ=7.3SolutionforGaussianprofilep线点0.20rχ=线火源点火源0.30rχ=0.221αβ==0.5901αβ==9.62.730.347TnCorψ==9.63.10.450TnCorψ==2.020.7200.176ulCorCψ==2.30.8770.272ulCorCψ==21.49Uζ=Φ21.42lUζ=Φζ