Multiphase Flow Simulation Based on Unstructured Grid

Transcription

1 200 Tuoral School o Flud Dyamcs: Topcs Turbulece Uversy of Marylad, May 24-28, 200 Oule Bacgroud Mulphase Flow Smulao Based o Usrucured Grd Bubble Pacg Mehod mehod Based o he Usrucured Grd Remar B CHEN, May 2, 200 Bacgroud The dffculy o smulae mulphase flows s he presece of deformg erfaces Meshless mehod SPH, MPS Grd based mehod Ierface racg mehod Ierface capurg mehod (, Levelse) Bacgroud Ierface-racg mehods Overdd ad Tryggvaso, 992 explcly rea he erface as a dscouy. Usually, s specfed by a ordered se of marer pos, coeced by a erpolao curve. The marers are advaced he Lagraga maer ad he redsrbued o oba he bes resoluo of he erface. Dffcul o deal wh opology chage Orgac lquds polluo subsurface evrome, Lda & Sco 998 Hele Sog e al. Mcrocrculao

2 Bacgroud Ierface capurg mehod Level se Osher & Seha,988 The dea s ha sead of movg he red fro, oe mgh ry ad sead move he surface. φ + u φ = 0 φ κ = φ Seha The curvaure ca be compued accuraely ad he smoohess of dscouous physcal quaes ear erfaces s very good However, he LS mehod produces more umercal error, especally whe he erfaces experece severe srechg or earg. The coservao of mass s o guaraeed Bacgroud I he mehod, a volume fraco fuco f, whose value les bewee 0 ad, s defed o deoe wheher a space s occuped by he dspersed phase or couous phase. f = : dspersed phase f = 0 : couous phase 0 < f < : coas boh he dspersed ad couous phases f dsrbuo For a gve flow feld, he sadard adveco equao govers he evoluo of f: f + ( u ) f = 0 Accurae algorhms ca be used o advec he volume fraco fuco so ha he mass s coserved whle sll maag a sharp represeao of he erfaces Because he volume fraco fuco f s a sep fuco, s dffcul o oba he accurae curvaure ad Flud dsrbuo deoed by F smooh he dscouous physcal quaes ear he erfaces Bacgroud Ierface recosruco Objecve To develop hgh qualy usrucured grd geerao mehod To develop mehod based o usrucured grd To aalyze he fluece of cell regulary o resuls SLIC Mehod (Noh & Woodward,976) PLIC Mehod (Yougs, 982) FLAIR Mehod (Ashgrz & Poo, 99) 2

3 Oule Bacgroud Bubble Pacg Mehod mehod Based o he Usrucured Grd Remar Bubble Pacg Mehod K.Shmada, 995 Add bubbles wh vrual mass o doma Defe a force for each bubble o adjus he bubble s poso,.e., opmal ode s dsrbuo Bubble populao corol To delee he overlappg bubbles To add bubbles o fll he gaps Coec hese odes by Delauay ragulao o geerae he mesh Bubble Pacg Mehod Bubble Pacg Mehod l > l 0 : aracve force l < l 0 : repulsve force f(λ) Leard-Joes K. Shmada F. Bosse l λ λ + λ f ( λ) = , λ < 0, λ >.5 0( ), λ=l/l 0 2 d x() dx() f 2 ( ) m + c = () =,2,, d d Forh-order Ruge-Kua mehod s ulzed o solve he bubble moo equaos so as o oba he opmal posos of bubbles 60 The codos for furher subdvso: ( ) ( ) d r + r r + r 2 2 2

4 Bubble Pacg Mehod Bubble Pacg Mehod r + r r = N 2 2 r 2 r r/r Bubble Pacg Mehod 0~ 0. 0.~ ~ 0. 0.~ ~ ~ ~ ~ 0.48 m g = m = R Delauay & smoohg 0.48~ Toal umber Geomerc rregulary D_S BPM η r (0.5 ) r N d = m ω r r = m ω = d d 2 2 = r N r, d = 0 d 0 Bubble Pacg Mehod Bubble Pacg Mehod f s Δs x = ϕ() ( a b) y = φ() '2 '2 () = ϕ () + φ ()d a s 4

5 Bubble Pacg Mehod Bubble Pacg Mehod 60º Oule Bacgroud Bubble Pacg Mehod mehod Based o he Usrucured Grd Remar f = ( u ) f 0 f d S + ( u f ) d l = 0, =, 2, ΔS = l f ds f ds + f u d dl = 0 + ( ) ΔS ΔS = l F F f u l + = = ΔS = l = ( d ) d F Δ F, F = f( x, y, )ds Δ S Δ S Problem : oreao ad locao of he erface? 5

6 SLIC : A lear segme s se hrough each cell as he erface parallel wh oe sde of he cell To judge he erface ormal: K=(F-F2)-(F2-F) (F>F2>F) K>0, (F >> F2, F) K<0, (F, F2 >> F) PLIC : A pecewse lear segme defed by a slope ad ercep s se hrough each cell as he erface The slope of he le s gve by he erface ormal he ercep follows from vog volume coservao U d f = f C ( xj x0) ( Fj F0) 2 2 j= ( x j x0) ( yj y0) ( yj y0) ( Fj F0) 2 2 j= ( x j x0) + ( yj y0) 2 x = + 2 y = F E D B PB A B E H A U d G F C U d Pc U d B specfc phase B specfc phase U d u = 0.4 v = 0.4 u = π( y 0.5) v= π ( x 0.5) u = π cos π( x 0.5)s π( y 0.5) v= π s π( x 0.5)cos π( y 0.5) Srucured grd (, 6400cells) Bubble Pacg (BPM, 7600) Delauay Tragulao (DTM, 7600). Adveco model (A hollowed square adveco) 2. Zalesa model (Roao of a sloed crcle). Shearg Flow (A crcle shearg flow) Relave dsoro e f ( T) f Ed = 0 f Geomercal error e Eg = ( ΔS f ( T) f ) Relave mass coservao error e f ( T) f Em = 0 f 6

7 Grd Type E d 2.5e- 2.2e e- BPM 9.2e e e- DTM 9.6e e- -.07e-2 Grd Type E d 5.7e-2 2.e e-2 BPM 5.48e e e-2 DTM.07e- 4.77e e- Grd Type E d 6.52e-2 8.6e e-2 BPM.64e- 2.04e e- DTM 2.67e-.5e e- Grd Type E d 5.89E E-0.64E-07 BPM 5.42E-02 5.E-0-4.0E-0 DTM 6.26E E E-0 7

8 Grd Type E d.86e E-0.65E-06 BPM 2.5E-02.2E E-02 DTM.6E-02.40E E-02 Grd Type E d 2.9E-02.67E-0.4E-05 BPM 6.6E E E-02 DTM.6E-0.45E-02 -.E-0 Oule Bacgroud Bubble Pacg Mehod mehod Based o he Usrucured Grd Remar Tha you for your aeo 8