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MULTIPHASE MODEL

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Defnition

•In multiphase ow, a phase can be efne as anientifable class o! mate"ial that has a pa"ticulaine"tial "esponse to an inte"action with the owthe potential fel in which it is imme"se#

• $o" e%ample, i'e"ent(si)e soli pa"ticles o! the

mate"ial can be t"eate as i'e"ent phases becaeach collection o! pa"ticles with the same si)e wa simila" +namical "esponse to the ow fel#

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 Multiphase $low e-imes

•Gas-Liquid or Liquid-Liquid Flows-.ubbl+ow,D"oplet ow,Slu- ow,St"atife ow

• Gas-Solid Flows- Pa"ticle Laen ow,Pneumati T"anspo"t,$luii)e be

• Liquid-Solid Flows- Slu""+

ow,H+"ot"anspo"t,Seimentation• Three-Phase Flows

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Moelin- App"oach

Euler Euler approachDi'e"ent phase t"eate as inte"penet"atin- continua

Phasic *olume !"action that sums to one

• VOF model/0on inte"penet"atin-1

  Inte"phase between two immiscible uis a"e o! inte"est

•The Mixture Model

  P"esc"ibes "elati*e *elocities to esc"ibe the ispe"se pha

• Eulerian model

  2ouplin- is achie*e th"ou-h the p"essu"e an inte"phasecoe3cients#

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2hoosin- Moel

•

 The 4O$ moel is app"op"iate !o" st"atife o" !"su"!ace ows

• Mi%tu"e an Eule"ian moels a"e app"op"iate !o" which the phases mi% o" sepa"ate an5o" ispe"sphase *olume !"actions e%cee 678#

•$o" ows with mo"e than one "e-ime select one o! most inte"est an choose moel acco"in-l+

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2hoosin- between Mi%tu"e anEule"ian•

I! the pa"ticles *a"+ in si)e an the la"-est pa"ticnot sepa"ate !"om the p"ima"+ ow fel mi%tu"eis p"e!e""e

• I! ispe"se phases a"e concent"ate in some poo! omain use Eule"ian moel

•I! inte"phase "a- laws a"e a*ailable -o !o" Eule"

• Mi%tu"e moel less computation

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Pa"ticulate loain-

• $o" *e"+ low loain- couplin- is one wa+(Disc"ete5Mi%tu"

• $o" inte"meiate loain- couplin- is two wa+(Disc"ete5Mi%tu"e5Eule"ian

• $o" hi-h loain- aitional couplin- ue to p"essu"e ansoli phase(Eule"ian

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Sto9es numbe"

• The Sto9es numbe" can be efne as the "elation between the"esponse time an the s+stem "esponse time:

•   Pa"ticle !ollows the ow closel+(Disc"ete5Mi%tu"e

•   Pa"ticles mo*e inepenentl+(Disc"ete5Eule"ia

•   (Disc"ete5Mi%tu"e5Eule"ian

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Stabilit+ an con*e"-ence

•

Usuall+ secon o"e" implicit schemes a"e implement• It ma+ p"ouce oscillations !o" la"-e time steps

• This p"oblem is eliminate usin- boune secon o"scheme

 Time schemes

• Usuall+ secon o"e" implicit schemes a"e implemente

• It ma+ p"ouce oscillations !o" la"-e time steps

• This p"oblem is eliminate usin- boune secon o"e" sc