3D UNIFIED CFD APPROACH TO MODELING OF BUBBLE PHENOMENA

Size: px

Start display at page:

Download "3D UNIFIED CFD APPROACH TO MODELING OF BUBBLE PHENOMENA"

Aron Bell
6 years ago
Views:

1 e Ieaoa oca eeg o Nucea aco ema-hyaucs (NUREH- Pae: 47 Poes Paace Cofeece Cee Ago Face Ocobe D UNIFIED CFD APPROACH O ODELING OF BUBBLE PHENOENA am Cuao A E Akseoa ae A Pecko Nucea Safey Isue (IBRAE Russa Acaemy of Sceces 5 B yskaya oscow 59 Russa cu@baeacu aks@baeacu ae@baeacu Cubao AG Isue fo aemaca oeg Russa Acaemy of Sceces 4-A usskaya Squae oscow 547 Russa cu@mamou ABSRAC Dug of e as e yeas umeca meos a agoms fo sog of e ea a mass asfe obems comessbe/comessbe fus wee eeoe Amog ese ae agoms fo sog of comessbe fu yamcs agoms fo sog of comessbe fu yamcs a e ow ac umbes e moooe mu-mesoa scemes fo sog of a aeco equao a effece agom fo sog of eca equao fo essue coeco ese meos a agoms wee ae successfuy fo comuaoa suo of e eemes face by Nucea Eegy Agecy a Ogazao of Ecoomc Cooeao a Deeome w e ASCA ojec wee a beao of e wo o-mg qus suc as coum a see was esgae Now ese comug oos w be eee o a case of wo-ase fows as a gas-qu sysem s ae eas w acao of e eeoe aoac fo moeg of bubbe fows e eeoe ecque s gy effece a aows o a esoa comue (3GHz a Gbyes 7 RA o fuf CFD cacuaos o e g w oes Fo sge-ase fows a ossbe fas aco 6 equas 3 seco e oe a me se KEYWORDS Bubbe fows comessbe fu yamcs comessbe fu yamcs a e ow ac umbes moooc mu-mesoa scemes fo a aeco equao INRODUCION s ace eas w e ew meos a agoms fo sog of 3D ea a yoyamcs obems comessbe/comessbe fus Amog ese ae agoms fo sog of comessbe fu yamcs agoms fo sog of ow comessbe fu yamcs a e ow ac umbes e moooe mumesoa scemes of a D-ye fo sog of aeco equao e effece agom fo sog of e eca equao fo essue coeco Deeoe meos a agoms fo sog of ea a mass asfe obems ow comessbe a comessbe fus wee use successfuy ue moeg of wo o-mg fus ecey Now s ae o coec eeoe ecque ufe aoac fo smuao of bubbe eomea w e mofe ee se meo s meo s ee fo suy of eface beaou of a wo-ase sysem as qu-ao sysem Fo moeg of ao beaou se of a bubbe e moe of comessbe meums a ow ac umbes s offee (Cubao a Pao 998 Fo moeg of qu beaou ouse of a bubbe e o-saoay equaos of Nae-Sokes aua aabes fo a comessbe fu ogee w e eegy equao s ae o use (Cuao e a 999 Fo obseao be of a wo-ase sysem eface suc as qu-ao s ae o use: Coesog auo

2 e Ieaoa oca eeg o Nucea aco ema-hyaucs (NUREH- /8 Poes Paace Cofeece Cee Ago Face Ocobe -6 5 e mofe ee se meo fo ec umeca smuao of a wo-ase sysem as a qu-ao (Cuao e moooe mu-mesoa aeco sceme w sma sceme ffuso w usg of sub-g smuao Effece umeca agoms fo sog of e essue equao yoyamcs of a comessbe fu w a aabe esy e eeoe agoms meos a sofwae wee ese o a we se of e ess a some of em wee successfuy use fo umeca suo of eemes o eseac of e coum eag a e boom of e eaco esse w e RASPLA a ASCA ojecs (OECD RASPLA Fa o NUERICAL APPROACH O ODELING OF INCOPRESSIBLE CFD o smuae comessbe CFD obems e me-eee comessbe Nae-Sokes equaos e me aabes (Cuao Akseoa e a 999 coue w e eegy equao ae use: C( ga ga f ( ( ( ( k ga c( ξ ξ ( Basc feaues of eeoe umeca agom (Cuao e a 996 Cuao e a Cuao e a 998 cooae e ese aoac ae e foowg: Dscee aomaos ae cosuce usg fe-ffeece meos a e AC-ye saggee gs Fcous ego meo w a couao of coeffces a owe-oe eaes s use o ae egua come comuaoa omas (abscec 99 wc ysca sese ca be eae as cooao o e a Nae-Sokes equaos ( e moe of a oous meum: ε С ( ε ε ( ν ga ε ga cε ε fε ε (3 aous fomuae of c ε ca be emoye fo e fow essace em e aboe equaos (eg se-wse fuco fo abu `swc off' e ea Dacy ec Dougas-Racfo oeao-sg ecque s emoye o cosuc mc sceme fo meeee equaos of yoyamcs (3 Numeca memeao of s sceme s efome as e eco-coeco oceue sma o SIPLEC-agom ε ε / A ε A ε cε ε / ( f (4 / / ga ε ε ε ε ga ε c (5 ε cε Fuy mc sceme (backwa me ffeece s uze fo e useay ea equao Fo sog of coeco obem e eguaze oea moooc oeao-sg sceme s C ae eeoe (Samask&abscec 995 e seca aomao of coeco ems ( emoye oe o ee e scee coece oeao wc s skew-symmeca a oes o ge ay cobuo o e kec eegy (e eegecay eua So s sceme oes e seco oe sace a e fs oe me e agom s sabe a a age eoug egao se by me s aoac was memee COND&3D coes (Akseoa e a 998 A acaby of e COND coe was oe by aao agas e eemea a becmak ess amey: fu coeco bewee wo g was ue ffee emeaue Bea coeco eeme o meg of ue gaum eemes o aua ccuao oumec eae fu ffee geomees e esus of s aao emosae a g egee of ecos Deas ae eoe e efeeces (Cuao 998 OECD RASPLA Pojec fa eo e mos a of eemea fomao fo aao of CON3D coe was obae e fames of e RASPLA ojec (OECD RASPLA Pojec fa eo a e sa facy wc was esge fo suo of coum eemes oeoe aao ma coas ayge s eemes bo fo ecagua a semccua geomey Aso coe was aae o e coeco obem of a ea geeag fu a emseca oma wc s oumec eae u socae D eemes (Asfa & D 994 Deas ae eoe e efeeces (Akseoa OECD RASPLA Pojec fa eo

3 e Ieaoa oca eeg o Nucea aco ema-hyaucs (NUREH- 3/8 Poes Paace Cofeece Cee Ago Face Ocobe -6 5 NUERICAL APPROACH O ODELING OF COPRESSIBLE CFD UNDER LOW ACH NUBER o smuae e comessbe fows we eeo e secaze moues fo sog of e asks ue ow ac umbe wc e foowg mesoess fom equaos ae use (Cubao a Pao 998: ( ( ( ( ( ( 3 ga 3 ga ( F S & ( ( ( ( ( ga ga P s J λ ( (3 wee ( ( ( ( ( ( F o G Hs e/ F e F e Ω Hee sea of essue ( ee ae wo ukow fucos: ( a ( e fuco ( oes o ee o a saa aabe a s cosee as emoyamc essue I e moeme equao a fuco ( ays a oe of essue wc s ame by a yamc a of essue Use e equao sysem (-(3 e mesoess comees suc as umbes of aces yos Pa a Fua ae efe by eessos: P L P λ C g L F Ue cosuco of e fe ffeece scemes fo equaos (-(3 we base o e aeay eeoe meos fo moeg of comessbe fows So we use a meo of sg wc s geea cose o a kow meo SIPLER e fe-ffeece sceme ew of a eaceme of e couy equao by e equao fo e essue coeco ook ke: ( ( ( ( ( ( S ga L (4 ( ( ( ( ( ( ( s J ga G (5 I equao (4 oeao ( L aomaes o some ee coece a a of scous ems amey: ( ( ga L e em S aomaes o a o emoa aye a g a of e momeum equao ( fom wc e em ( ga s euce e oeao ( G aomaes coece a ea coucy ems of e eegy equao (3 ( ( ( 3 Hs 3 (e (6 ( ( ( ( ( ( ( Hs ga (e (7 ( ( Hs (e ( ( ( ga ( ( 3 ( ( 3 e aboe equaos ae fa o oy fo a case of ea gas bu aso ae geeaze o a case of e a e Waas EOS o eame accuacy a eauae obusess of e ew agom some es obems ae bee esgae umecay Fo eame ew agom as bee aae a e saa obem of fee coeco a cay (Das G e a 983 I sou be emasze aga a e ese meo s a a obus a eoug g ac umbes oo ( coas o e LN-aomao

4 e Ieaoa oca eeg o Nucea aco ema-hyaucs (NUREH- 4/8 Poes Paace Cofeece Cee Ago Face Ocobe EFFECIE NUERICAL ALGORIH FOR SOLING OF HE ELLIPIC EQUAION FOR PRESSURE CORRECION Fo sog of e eca equaos w aabe coeffces fo eame Posso equao fo essue coeco ga o oeao Ay f cojugae gae meo s ae wc occues 9 % fom me of e cea ocesso e oe cacuae se eefoe seacg agoms equg a smae me amou of e CPU o oe cacuae se s moa e Rcaso eae meo w Cebyse s se of aamees usg quay ecooe FF soe fo Laace s oeao w cosa faco ca see by a aeae o cojugae gae meo e acao of s aoac fo sog of e eca equaos w aabe coeffces aows eucg me amous of e CPU e oe cacuae se o % e essece of e aoac cosss a coce e oeao B (e Laace oeao suc a e ese oeao B ue sog of e equao Byk Byk k ( Ayk f s fou by ease way a e oeao A fo e u equao Ay f oeoe ao of e oeao egeaues sou be o sma (Samask a Nkoae 978 e effeceess of e Rcaso eae meo w Cebyse s se was cecke o eame of e Neuma obem fo e eca equao of e seco oe 3 u u Lu ( c( ϕ ( G c g( α α α 3 w coeffces α α α < c c( c cube w se α π a e ufom g Coeffce c ( a b was se so a e ao of magues o e eemes of a segme π a coesos o e ffee aues c c ( aπ b b As coegece ceo of e eae ocess e Eucea om of a sceacy a sace of e g fucos was use H: Ay f < ε A fgue 3 a comaso of e cojugae gae meo w Rcaso eae meo w Cebyse s 6 3 aamees s subme a ε e cues emosae cage of a eae umbe eeg o a ao wee a ae mamum a mmum egeaues of a oeao Fom ese cues w be obous a sem-eae meo w a Cebyse s se of aamees s moe effece a usuay use PCG e agom effeceess of s esecay obous o e age cacuae gs a ue age ao Numbe of eaos PCG (N 7 (N 3 ofe Pecooe Rcaso meo w FF (N 65 (N9 / Fgue 3: Amou of eaos fo e cojugae gae meo ue ffee aues N a comaso w sem-eae meo w Cebyse s aamees

5 e Ieaoa oca eeg o Nucea aco ema-hyaucs (NUREH- 5/8 Poes Paace Cofeece Cee Ago Face Ocobe ONOONE NUERICAL SCHEE FOR HE ADECION EQUAION We bu e moooe ufom o-ea ffeece scemes fo e aeco equao o e bass of e eguazao (eubao aomao sceme of e seco oe Suose a a a geeag sceme s e sceme w saa aomao of e fs eaes by e cea ffeeces of seco oe e oe-mesoa equao of aeco o-ege fom s cosee u u a( < < > (4 wc suemee by e a coo u ( g( < < (4 Le s cose e foowg sceme (Cuao e a y y a y K (43 w oea faco y a a (44 y e o-ea ffeece sceme (44 w be moooe f a ~ (45 ma a~ K (46 Fom (45-(46 foows a e oao of a moooc s obsee a egbouoo of eemums of e ffeece souo I s ecessay fom e a (geeag omoooe ffeece sceme o ocee o e ew aeay moooe sceme (43 By meas of sma faco eubao (w eseao of goo oees of e a sceme e e seco oe of aomao s ecessay o ecee e moooc sceme (43 wc w be sasfy o suffce coos of mooocy a saby (45 (46 Le's ese (44 moe coee asec as wee e faco χ equas Le's sub faco χ a ~ a χ (47 y y χ y y y χ (48 y y w aamee Pag (eguazg summas χ fom (48 ae e oe o us eguaze sceme (43 (47 (48 aomaes a a equao (4 as we as geeag sceme w e seco oe o sace Le's fomuae coos of a mooocy of e sceme (43 (47 (48 Faco a ~ (coo (45 w be o-egae a 5 Ses of a g sou sasfy o a coo (46 wc w akg o accou (47 (48 s equae o a equay ma a K (49 4 us fo eguaze sceme (43 (47 (48 ue mmum amssbe aue of aamee a ~ e mama amssbe se o me accog o (49 eceases wce comaso w e sceme w e ece ffeeces e ge esu s geeaze a e aous ecos: may-mesoa obems equao of aeco ege fom egua gs ec e efcao of eguaze ffeece scemes (Cuao e a was cae ou fo e saa es (euge a Koe 993 e aeco equao as a sef-sma souo as a a ofe oag Ω α e eocy fe s efe by e comoes aou of some as I e sme quaae ( α

6 e Ieaoa oca eeg o Nucea aco ema-hyaucs (NUREH- 6/8 Poes Paace Cofeece Cee Ago Face Ocobe -6 5 ν π ( ν π ( u ( U ( ξ η e fuco ( ξ η as ( I s case e souo of e aeco equao s eesee as U escbes oao of some g boy w eo aou of e e oao of e aaeee eses a fgue 4 5 RESULS Pemay esus of eeog ecque fo moeg of bubbe fows ae esee beow I fgue 5 e essue se a o s sow I abe 5 essue bubbe eeg o mes s sow aso I fgue 5 a foag bubbe ue σ 5 s esee I fgue 53 fagmes of bubbe fows ae sow CONCLUSIONS Fo sog comuaoa fu yamcs obems e effece fe-oume umeca agom s eeoe e eeoe agom s ae o e ea a fu fow equaos (e Nae-Sokes equaos w eegy equao e me aabes fomuao bo comessbe a comessbe a ow ac umbes aao of e eeoe aoac s cae ou o se of ess fo wc a goo ageeme s obae bewee umeca ecos a eemea aa (Akseoa 998 Pemay esus obae by ec umeca smuao w e of obseao fo a oume faco of subsace (seuococeao g ces ae aowe o seak of aequae quaae moeg of bubbe eomea REFERENCES Akseoa A e a 998 Numec oes fo RASPLA Pojec OECD RASPA Pojec o: RP-R-5 Pesee by Russa seac Cee Kucao Isue oscow Russa Akseoa A e a Deeome a acao of e CON Coes Poc of RASPLA Sema- uc Gemay 4-5 Noembe Asfa FJ D K 994 Naua coeco ea asfe oumecay eae seca oos Poc of e wokso o age moe oo ea asfe Geobe 9-5 Cuao e a 996 Oeao-sg scemes fo e comessbe Nae-Sokes equaos w cosse aomao of oeaos Book of Absacs of I Cof o Comuaoa oeg a Comug Pyscs Russa Duba Cuao e a 998 Cue Saus a aao of COND&3D coe Poc OECD/CSNI WORKSHOP ON IN ESSEL CORE DEBRIS REENION AND COOLABILIY Gemay Gacg 3-34 Cuao 999 A u-bock Oogoa G Geeao usg CAD sysem Poc 8 Ieaoa esg Rouabe Sou Lake aoe Cafoa Cuao Deeome a acao of a sofwae fo smuao of ocesses a a ae sage of seee acces o NPPs Poc of e bac cofeece Safey ssues NPP w ER S-Peesbug Russa Cuao e a No-ea eguaze ffeece scemes fo mumesoa aeco equaos Joua of comug maemacs a of maemaca yscs 4( Cubao AG a Pao AN 998 A essue-base agom o soe e fu Nae-Sokes equaos a ow ac umbe Poc Comuaoa Fu Dyamcs 98 (Es KDPaaou e a Wey Ccese ( Das G e a 983Naua coeco of a a squae cay: a becmak umeca souo I J Nume eos Fus

e Ieaoa oca eeg o Nucea aco ema-hyaucs (NUREH- 7/8 Poes Paace Cofeece Cee Ago Face Ocobe -6 5 OECD RASPA Pojec Fa o : Beaou of e coum moe oo ue eea coog Pesee by Russa seac

Fcous gos eo Pobems of aemaca Pyscs oscow Uesy Pubses oscow Russa euge C a Koe B 993 Numeca meos fo aeco-ffuso obems Bauscweg:eweg Fgue 4: 3D Dec a ese oao of aaeee: ec oao:

7 e Ieaoa oca eeg o Nucea aco ema-hyaucs (NUREH- 7/8 Poes Paace Cofeece Cee Ago Face Ocobe -6 5 OECD RASPA Pojec Fa o : Beaou of e coum moe oo ue eea coog Pesee by Russa seac Cee Kucao Isue oscow Russa Samask AA Nkoae ES 978 eos fo sog of g equaos : Nauka Samask AA a abscec PN 995 Comuaoa Hea asfe : e fe ffeece meooogy Wey Ccese abscec PN 99 e Fcous gos eo Pobems of aemaca Pyscs oscow Uesy Pubses oscow Russa euge C a Koe B 993 Numeca meos fo aeco-ffuso obems Bauscweg:eweg Fgue 4: 3D Dec a ese oao of aaeee: ec oao: u asφ acosφ φ π / ese oao: u asφ acosφ φ π / Fgue 5: essue se a o Hee R5 Sgma cuaue 8 Pessue(P P abe 5: Pessue bubbe eeg o mes

omaze by e esy g - gay acceeao - eay k - ema coucy - Pessue omaze by e esy P - essue q - ea fu -

8 e Ieaoa oca eeg o Nucea aco ema-hyaucs (NUREH- 8/8 Poes Paace Cofeece Cee Ago Face Ocobe -6 5 Fgue 5: Foag bubbe a σ 5 Fgue 53: Bubbe fows NOENCLAURE C( c [( ga ( ]- coece oeao - secfc ea f - Souce omaze by e esy g - gay acceeao - eay k - ema coucy - Pessue omaze by e esy P - essue q - ea fu - emeaue - eocy ( 3 Geek Symbos - Rao of ema caaces - ema ffusy λ - scosy - esy D - Dssae a of sess eso

. The second term denotes the transition [n 1, n 2-1] [n 1, n 2 ] and leads to an increased p ( n1,

. The second term denotes the transition [n 1, n 2-1] [n 1, n 2 ] and leads to an increased p ( n1, . THE MSTE EQUTION OCH Te mase euao oesos o e saeme a e obab of beg a gve sae ages eeg o e obabes of aso o a fom a oe sae e ssem. I oves e fu obab sbuo we a be e sove. Ufouae s s o ofe e ase so we mus