Eulerian multiphase flow model

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1 1 Lere CF-4 Elerian mliphase flow moel Simon Lo C-aapo 00 Shephers Bsh Roa Lonon W6 7NL Conens Elerian mliphase flow eqaions Fores on a parile Boiling flows Bbble size isribion Conjgae hea ransfer + boiling Copling wih neronis 1

2 3 Boiling flow in PSBT 5x5 bnle 4 Boiling flow in PSBT 5x5 bnle

5 Boiling flow in PSBT 5x5 bnle 6 Boiling wo-phase flows Phenomena in boiling wo-phase flows in a verial pipe are very omplex. Flow regimes inle: bbbly, slg, hrn, annal, mis flows.

3 5 Boiling flow in PSBT 5x5 bnle 6 Boiling wo-phase flows Phenomena in boiling wo-phase flows in a verial pipe are very omplex. Flow regimes inle: bbbly, slg, hrn, annal, mis flows. Nee o onsier he omplee range of flow regimes: from sb-oole boiling bbbly flow, hrogh annal film boiling o pos ry-o mis flow. Moelling inles: iner-phase fores, boiling hea an mass ransfer, wall hea pariioning an iner-phase srfae opology hanges. 3

4 7 Elerian-Elerian moel We onsier he phases are mixe on lengh sales smaller han we wish o resolve an an be reae as oninos flis. Boh phases oexis everywhere in he flow omain. The porion of volme opie by a phase is given by he volme fraion. This onep is alle Inerpeneraing onina. Conservaion eqaions for mass, momenm an energy are solve for eah phase, hene his is ofen alle he Elerian-Elerian moel. 8 Conservaion of mass Conservaion of mass for phase is: N. m j m j j1 =volme fraion, =ensiy, =veloiy, N=oal nmber of phases, =mass ransfer rae. Sm of volme fraion is niy, 1 m 4

5 9 Conservaion of momenm Conservaion of momenm for phase is:. =pressre, =sm of inerfaial fores (rag, rblene rag, lif, viral mass) an momenm ransfer assoiae wih mass ransfer. p g. ( ) M p M M F F T F L F VM N m j j m j j1 10 Conservaion of energy Conservaion of energy for phase is: h T Q h. h. T h Q =enhalpy, =hermal oniviy, =emperare, =inerfaial hea ransfer. h 5

6 11 Fores on a parile Fores aing on a pariles: Boyany, B. rag,. Lif, L. Viral mass, V. Basse fore. An ohers. Boyany an rag are he ominan ones. B L g V Basse fore is ompliae an almos always ignore. Lif, viral mass an oher fores will be onsiere laer. B g 1 rag fore on a parile rag fore on a parile,, is sally allae from: 1 C Ar r rag oeffiien, C, is a fnion of he parile Reynols nmber. Re r Sbsrip =oninos phase, =isperse phase. r A 4 (Relaive veloiy) (Projee area) 6

7 13 rag oeffiien of a parile C 0.44 Re 14 rag oeffiien for spherial pariles Soes s regime C 4 0 Re 0. Re Transiion regime (Shiller-Namann) C Re 0 Re 1000 Re Newon s regime C 0.44 Re

8 15 rag fore of mliple pariles Nmber of pariles per ni volme is n 3 V / 6 Toal rag fore per ni volme : F A 3 C n 4 3 C r 4 r r A r rag fore oeffiien, A, is se in rblene moels. 16 Boyany fore on a parile Boy fore F B g There are nmerial avanages o absorb hyrosai pressre ino pressre an wor wih ree pressre. * p p 0gh Boy fore now expresse in erms of boyany fore: p g p g * 0 8

9 9 17 Mliphase rblene Mliphase rblene moelling is learly a iffil sbje an rrenly no very well evelope. Mos freqenly se moel is he ey visosiy moel. -epsilon moel (wih or wiho moifiaions) is applie o he oninos phase an some algebrai formlae for he isperse phase. 18 Moifie - eqaions - eqaions solve for he oninos phase are: Where he aiional sore erms e o rag beween he phases are: S C C G S G 1 1. C A S C A A S

10 19 Trblene sress in oninos phase Similar o single phase flow moel we efine he rblene sress in he oninos phase as: T An he rblen visosiy as:. I I Trblene sress in isperse phase We efine rblene sress in isperse phase relaive o oninos phase: C The oeffiien C is he raio of isperse phase veloiy flaion o ha of oninos phase: ' C ' C =1: rblene haraerisis of isperse phase ienial o oninos phase. 10

11 1 Trblene rag fore Inerphase rag fore inles a mean an a flaing omponen. Flaing omponen aons for aiional rag e o ineraion beween pariles an rblen eies. F A r A Trblen Pranl nmber sally se o The rblene rag fore has he effe of ispersing he pariles as fnion of parile onenraion graien. Lif fore Lif fore: F L L C r Lif fore oeffiien, C L, ol be beween 0.8 an 0.8 epening on parile size. 11

12 3 Viral mass fore Viral mass fore: F VM C VM Viral mass fore oeffiien: C VM Wall boiling hea ransfer Toal wall hea flx is herefore mae p by hree omponens: q T q q q q e Conveive heaing Qenhing Evaporaion q q q q e 1

13 5 Koamsafaogllari (1983) Correlaion base on waer experimenal aa a pressres from o bar w x g g is ona angle in egree. 0.5 Bbble eparre iameer Bbble size moel : IAT an S Yao & Morel (004) erive he inerfaial area ranspor (IAT) eqaion wih boiling erms as: a i. i i g, i n n 3 g 3 a i ai g 36 CO BK NUC av n n Bl boiling Coalesene Breap Wall boiling S-gamma in STAR-CCM+ /3 S.( /3 S ) s blboil s l s br s wallboil 13

14 7 = 0.01 m L = m P = 147 bar T sa = 613 K Q = MW/m G = g/m s T sb = K Barolomei (198) 147 bar experimens g Wall hea flx Waer + seam L Sb-oole waer 8 Bar -6 : 147 bar, esing effe of Q Cases P (bar) G (g/m s) Q (MW/m ) Tsa- Tin (K) Δ

15 9 Bar -6 : Comparison of axial voi profiles 30 Bar : Resls Voi Bbble iameer Conensaion rae 15

16 31 Conjgae hea ransfer boiling Soil emperare (K) Liqi emperare (K) Voi fraion Fel Gap Claing Fli 3 CHT boiling + neroni opling A sanar NNR moel for ople allaions Five UO pins Three MOX pins Cenral gie be Symmery bonaries (infinie array) Cople allaions wih boiling wo-phase flow an neroni moels. MOX MOX MOX 16

17 33 Voi Fraion 34 Coolan Temperares 17

18 35 Fel Temperares 36 Power ensiy W/ 18

19 Smmary Elerian mliphase flow eqaions: Conservaion of mass, momenm an energy Fores on a pariles: rag, boyany, lif, viral mass, rblen ispersion Boiling flows: Bbble size isribion Conjgae hea ransfer Copling wih neronis 19

CFD modelling of mixing and separation in multiphase flows

CFD modelling of mixing and separation in multiphase flows ACHEMA 006, 15-19 May 006, Franfur am Main CF moelling of mixing an separaion in muliphase flows Simon Lo C-aapo, UK ABSTRACT Mixing an separaion of maerials in muliphase flows are exremely ommon an frequen