book-chapt5——Dispersed Phase Closure Models.pdf

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1、Chapter5DispersedPhaseClosureModels5.1PrimaryatomizationmodelsTheatomization/breakupmodelmustbeapplicabletoeithertheintactliquidcoreorthedispersedliquidcluster.Tocompletethemathematicaldescriptionofthebreakupsourceterm,itisconvenienttodecomposethissourcetermintoF_=+;(5

2、.1)buwhere+representstheproductionterm,andaccountsforthedestructionterm.Aglobuleisbrokenupabruptlywhenthedistortionparameteryexceedsunity.ThenumberofparentdropletsundergoingbreakupmustbeoftheformdS~dt=F(~x;~v;r;T;1;y_;;t)d~xd~vdrdTdy_dy_dt(5.2)ddTheaboveexpressionst

3、atesthatthenumberofglobuleinagivenparameterrangeundergoingbreakupinacertaintimeintervalisequaltothenumberofdropletswiththesurfacedistortionyexceedingunitymultipliedbythelocaluxofthedropletsthroughthesurfacey=1.TheexpressionforthetotalnumberofdropletsaddedtotherangeisdS~

4、dt=B(S~0;t)dS~F(~x;~v;r;T;1;y_;;t)d~xd~vdrdTdy_dy_dt;(5.3)ddwhereB(S~0;t)standsforthedropletnumberdistributionproducedduringbreakupwiththeattributesS~0.ThedistributionfunctionBisassumedtobeinthefollowingformZdG(r)010B=(TdTd)(y)(y_)()[~v(~v+V?
~n)]d~n;(5.4)dr2whe

5、retheintegralistakenovernormaldirectionstotherelativevelocityvectorbetweenthegasandthedroplet.ThevaluesofTd0,and~v0arethoseoftheparentdropletbeforebreakup.Aproductdropletisgiventhesametemperatureastheparentglobuleanditsdeformationandoscillationparametersaresettozero.Afterb

6、reakup,aglobuleinitiallybelongingtotheliquidcoregeneratesproductdropletscomprisingthedispersedliquidcluster.Thus,usingEqs(5.3),thebreakupsourcetermfortheliquidcoremaybewrittenasg_bu;l=gl(~xl;)(5.5)Thefollowingrelationisimpliedintheaboveexpressiong(=0)f(=0)(5.6)25Similar

7、expressionsmaybewrittenforthedispersedliquidclusterassumingthatdropletsmakingupthedispersedclusterbreakupintosmallerdropletsbelongingtothedispersedclus-ter.Forthespraydistributionfunctionofinstantaneousdiameterf(d)istypicallyusedtochar-acterizethespray.thefunctiondenesanu

8、mberofdropletshavingacertaindiameter.Often,theaverageddropletdiameterdmnisselectedtorepre