Journal of Scincs, Islamic Rpublic of Iran 19(3): 73-81 (008) Univrsiy of Thran, ISSN 1016-1104 hp://jscincs.u.ac.ir CFD-Calculaion of Fluid Flow in a Prssurizd War Racor H. Farajollahi, * A. Ghasmizad, and B. Khanbabai Dparmn of Physics, Faculy of Scinc, Univrsiy of Guilan, Rash, Islamic Rpublic of Iran Absrac An accura dscripion of h fluid flow and ha ransfr wihin a Prssurizd War Racor (PWR), for h safy analysis and racor prformanc is always dsirabl. In his papr a mahmaical modl of h fundamnal physical phnomna which ar associad o a ypical PWR is prsnd. Th mahmaical modl govrns h fluid dynamics in h racor. Using commrcial sofwar CFX, a compuaional fluid dynamics (CFD) cod, a hr-dimnsional flow disribuion in h downcomr and h lowr plnum of h racor was also calculad and a valuabl analysis of h racor prformanc is givn. Du o compuaional limis, simplificaions of h cor, downcomr and h lowr plnum of h racor ar inroducd. Nvrhlss, i has bn shown ha compuaional fluid dynamics and in paricular appropria usag of CFX sofwar improvs our undrsanding of fluid flow disribuion, vlociy disribuion and ha ransfr in diffrn pars of h racor prssur vssl, in paricular, in h downcomr and h lowr plnum. Kywords: Coolan mixing; Downcomr; Prssurizd war racor; CFD; CFX Inroducion Prssurizd war racors (PWRs) ar h mos common yp of powr producing nuclar racor ha ar widly usd all ovr h world o gnra lcric powr. In h PWR, war undr prssur as coolan is usd in closd sysm of racor vssl. A lo of assmbls of h ful rods is housd in a largr vssl, h shll. Th ha crad by h nuclar fission racion ha as plac in h ful rods is hn xracd by bul war on h shll sid. Gnrally h limiaion of h ha ransfr is found on h ful rod sid of h procss and spcially in h rgion clos o h ful rod wall [1]. In PWR racors faciliaing fasr ha ransfr in hs xrmly xohrmic procsss is usually achivd by dsigning h racor as a vssl wih narrow ful rod assmblis. For propr dsign and opraion, an accura nowldg of h ha ransfr propris is rquird bcaus of high snsiiviy of racor bhaviour o som opraing paramrs, such as coolan mixing mpraur []. Th fac ha indusrial powr racor opraion has bn drivn as clos as possibl o runaway condiions for maximum capaciy w nd a compl undrsanding of h ha ransfr in hs racors. In paricular, for rasons of mor safy imporanc in nuclar racors, spcificaion of h fluid disribuion hlps us o prvn and prdic h possibl * Corrsponding auhor, Tl.: +98(131)3313, Fax: +98(131)3313, E-mail: hossinf@guilan.ac.ir 73
Vol. 19 No. 3 Summr 008 Farajollahi al. J. Sci. I. R. Iran bra loss of coolan accidn [3,4]. Accura modling of hs PWRs is complicad, spcially in high ful rod o shll diamr raios, and for h larg numbr of ful rods. Th simpls mhod, which is probably mos commonly usd, is modlling ha ransfr by using som mpirical corrlaions. Du o h mpirical naur, his approach migh bcom highly inaccura. This is bcaus hos corrlaions canno accoun for h complx naur of h fluid dynamics and h gomry for spcific siuaion. Consqunly, whil i is prfrabl for iniial sima in dsign, his mpirical approach migh no b sufficin for acquiring an accura nowldg of h ha ransfr. Th mos xpnsiv and im-consuming mhod is obviously xprimnal sudy. Howvr, hr ar major difficulis inhrn in his approach including obaining mpraur profils (spcially for h insid ful rods). Forunaly, wih nw mhods such as "Compuaional Fluid Dynamics", (CFD) i is possibl o g a daild viw of h fluid flow and ha ransfr phnomna in h vssl sid of h racors which rcnly is bcoming of incrasing inrs. This migh b bcaus h hr-dimnsional cs in h flows disribuion canno b prdicd wll by on dimnsional sysm cods [5]. Alhough CFD is a rlaivly young ool in h fild of nuclar nginring; i is applid mos commonly in mixing chnology. Th rcn dvlopmns of h incorporaion of chmical and nuclar racion in h major CFD pacags opnd up a larg ara of applicaion of CFD in racor nginring [6]. In gnral, CFD involvs numrically solving consrvaion quaions for mass, momnum and nrgy in flow gomry of inrs, oghr wih addiional ss of quaions rflcing h problm a hand. This papr a firs prsns h dscripion of a mahmaical modl for h shll sid of h racor (whr h coolan mixing xis), which is solvd numrically by ANSYS CFX 5.7.1, spcific o ypical VVER-1000 racors. Nx, h approach o urbulnc modlling and h numrical mhod implmnd in CFX 5.7.1 will b dscribd. Thn, spcificaion of h numrical simulaion in CFX will b givn and h rsuls will hn b prsnd and discussd. For his modl, w us an Inl cor dual procssor of 4.8 GHz and GB RAM. Tss wih CFX 5.7.1 hav shown ha his is sufficin for h ramn of singl phas flows wih sandard -ε urbulnc modl using a 3 grid of 53 10 unsrucurd clls. For grid gnraion h ool ICEM CFD is usd ha allows h ramn of 6 1. 10 clls. Nvrhlss, h rspons im for a singl grid manipulaion acion for such a cas ofn rachs 7 hours. CFX-5.7.1 allows h ramn of compuaional domains whos boundary nods do no nd o mach xacly. For sing and handling such an approach is advisabl and in h prsn cas vn ncssary bcaus h compl grid canno b handld as on par du o limiaions of h grid gnraion procssing. Som ohr compuaional limis ar givn by h pr-procssing of CFX 5, whr h compuaional domains and h flow physics ar dfind [7]. 1. Mahmaical Modl Marials and Mhods Th saring poin for modlling h fluid flow in h vssl sid of h racor is h s of h fundamnal quaions ha can b found in many wll nown xboos: [8] Coninuiy quaion: 1 D r +Ñ. v = 0. (1) r D Momnum quaion: Dv r =-Ñ. ω+ r g. () D Enrgy quaion: DE r =Ñ. ( ωä v) +Ñ. ( lñ T ) + r vg. + r q, (3) D whr and ω =- pi+ lñ. v+ mτ, (4) τ =Ñ v+ ( Ñv ) T, (5) 1 E = + vv.. (6) Th scond rm in E is h inic nrgy pr uni mass of a marial paricl. Inspcion of hs quaions rvals h bacground for a fw of h common racor modl assumpions. Firs, hs sysms ar low vlociy flows and h fluid mass dnsiy, r can b rad as (incomprssibl flow) uniform in h flow fild so ha h rms conaining h im or spaial drivaiv of r can b nglcd. Th mass dnsiy is no dpndn on h prssur changs du o h flow, and h viscous dissipaion and prssur 74
CFD-Calculaion of Fluid Flow in a Prssurizd War Racor rms in h nrgy quaion can b nglcd. Scond, h dnsiy and hrmodynamic coicins ar no gnrally consans and may b funcions of mpraur. Th govrning quaions for low Mach numbr flow drivd basd on h dimnsional analysis can hn b xprssd as: ( r ) Ñ. v = 0, (7) ( r v) ( r ) +Ñ. vä v = Ñ. ω+ rg, (8) ( re ) +Ñ. ( re v ) ( l T ) =Ñ. Ñ + r q. (9) Modlling urbuln flows rang from "Dirc Numrical Simulaion", (DNS) o h "Rynolds Avragd Navir-Sos", (RANS) approach. Whn RANS approach is applid o h sandard quaions, h rsul is: ( r ) Ñ. v = 0, (10) ( r v) ' '.( r r ) +Ñ vä v+ v Äv =Ñ. ω+ S M, (11) ' ' ( re ) +Ñ.( re + r E o ) whr and v v ( l T ). SE =Ñ Ñ +, (1) 1 E = + v +, (13) 1 ' = ( v ), (14) T ω =- p I+ m( Ñ v+ ( Ñv ) ). (15) Th nonlinar rms involvd h urbuln flucuaions ar calld h Rynolds srss r v ' Ä v ' and h Rynolds flux r v ' E. Ths rms hav o b modlld o nabl soluion of h Navir-Sos quaions. Thr ar many urbulnc modls for his purpos including zro quaion modl, - modl, RNG - modl and diffrnial Rynolds Srss modl [9-11]. Only sandard - modl, which is of ddy viscosiy modl yp, was usd for h CFD simulaion. As a rsul of urbulnc, in summary, h mahmaical modl o b solvd for h shll sid of h racor consiss of h following quaions: Coninuiy quaion: ( r ) Ñ. v = 0. (16) Momnum consrvaion: whr ( rv) ( rv v) +Ñ. Ä ( ) T =-Ñ p +Ñ. æ m é v v ùö ç Ñ + Ñ + SM, è êë úûø (17) ' é æ ö ù p = êp + r + ç m -z Ñ. 3 3 ú ë è ø u û, (18) and m = m+ m. (19) Enrgy consrvaion: ( ρ E ) +Ñ. ( r E ) v ( l T ) =Ñ Ñ +. (0). S E Turbulnc inic nrgy consrvaion: ( r ) +Ñ. ( rv ).( ) =Ñ G Ñ + q, (1) whr q = P - r, () Turbulnc inic nrgy dissipaion consrvaion: whr ( r) +Ñ. ( rv ) ( ) =Ñ. G Ñ + q, (3) q = ( C1P - Cr ), (4) and T u ( u ( u ö ) ) ø ( )( mdiv( u) r ) P = m æ Ñç Ä Ñ + Ñ è - div u + 3. (5) In our modl so far hr ar nin unnown including fluid mass dnsiy r, vlociy v (including hr coordinas), oal prssur P, oal nrgy E, mpraur T, urbulnc inic nrgy and urbulnc dissipaion ra. Howvr, hr ar only svn quaions (16), (17), (0), (1), (3) and hrfor 75
Vol. 19 No. 3 Summr 008 Farajollahi al. J. Sci. I. R. Iran o spcify h modl complly, wo mor quaions ar rquird. Th firs quaion (16), involvs h fluid dnsiy r. For war coolan, h dnsiy was spcifid as a consan and hnc indpndn of im, prssur and mpraur: r = r 0, (6) Th scond quaion, (17), including hr quaions usually calld consiuiv quaion rlas h nhalpy chang o h mpraur and prssur. For consan r and c p, i follows d = c dt. (7) p For war coolan h hrmal and physical propris (a prssur 155 bar) ar in Tabl 1. Analyical soluions o h Navir-Sos quaions ar impossibl o obain for any sysms bu h simpls flows undr idal condiions. For ral flows, a numrical approach mus b adopd whrby a discrizaion mhod involvs rplacing h Navir- Sos quaions by hir algbraic approximaions, which can hn b solvd using a numrical mhod. Th CFD approach uss Navir-Sos quaions and nrgy balancs ovr conrol volums, small volums wihin h gomry a a dfind locaion rprsning h racor inrnals. Th siz and numbr of conrol volums (msh dnsiy) is usr drmind and will influnc h accuracy of h soluions o a dgr. Afr boundary condiions hav bn inroducd in h sysm h flow and nrgy balancs ar solvd numrically. An iraion procss dcrass h rror in h soluion unil a saisfacory rsul has bn rachd. By using CFD in h simulaion of coolan of h nuclar racors a daild dscripion of h flow bhavior wihin h barrl can b sablishd, which can hn b usd in mor accura modling. Th CFX 5.7.1 sofwar is basd on a "Fini Volum", (FV) approach, whr h soluion domain i.. h fluid domain is subdividd ino a fini numbr of small "Conrol Volums", (CVs) by mshing. All of h soluion variabls and fluid propris ar sord a h compuaional nods which ar assignd a h cnr of h CVs or arrangd so ha CV facs li midway bwn nods. To compl h approximaion, i is now ncssary o sima h informaion for ach nod in rms of nown variabls. Svral schms for inrpolaion pracics hav bn usd including "Upwind Inrpolaion", (UDS) which CFX 5.7.1 implmns a modifid vrsion of i, whr an addiional rm namd "Numrical Advcion Corrcion", (NAC) is includd in h inrpolaion. This mas h approximaions scond-ordr accura bu a h sam im lss robus [1].. Gomry and Tchnical Daa of VVER-1000 Th VVER-1000 is a four loop prssurizd war racor wih hxagonal ful assmbly dsign and horizonal sam gnraors. Th ANSYS ICEM was usd o gnra h gomrical dails; mos of hs ar modlld accuraly, li: inl nozzls, oul nozzls, downcomr, prforad llipical siv pla. Th gnral characrisic of h racor is givn in Tabl. In hs nuclar racors h coolan nrs h vssl by h inls, flows downwards hrough h downcomr and nrs h lowr plnum by passing a prforad llipical boom pla. Thn h flow crossing h cor boom pla and nrs h cor. Th flow is had up by h cor xis from ouls. In his papr w assum ha h PWR consiss of vssl and 64 ful rod assmblis. Th basic gomry of considrd racor is givn in Figur 1. In his papr w only modl h shll sid of h racor. From plan daa h mpraur profil along h ful rod has bn obaind and usd in his modl. 3. Calculaions 3.1. Th CFX-5.7.1 CODE As nod, CFX-5.7.1 is a CFD-cod using an Tabl 1. Physical propris of war ρ (g.m -3 ) 70 μ (g.m -1.s -1 ) 5.56 10 6 c p (J.g -1.K -1 ) 9.0678 λ (W.m -1.K -1 ) 0.004 Tabl. Th gnral daa of VVER-1000 Thrmal powr (MW) 3000 Prssur (MPa) 15.7 Inl mpraur ( K) 560.15 RPV high (m) 10.8 Innr diamr of RPV (m) 4.1 Inl & Oul diamr (m) 0.85 No. ful assmblis 163 Racor Coolan flow (Kg/s) 17611 76
CFD-Calculaion of Fluid Flow in a Prssurizd War Racor lmn-basd fini-volum numrical mhod wih scond-ordr discrisaion schms in spac and im. I wors wih unsrucurd hybrid grids consising of rahdral, hxahdral, prism and pyramid lmns. Th ohr CFX-5 opions ar: 1) Soluion of h Navir- Sos-Equaions for sady and ransin flows for comprssibl and incomprssibl fluids, ) Modlling of ha ransfrs and 3) Us of diffrn coordina sysms. 3.. Inpu Dc 3..1. Gnral Assumpion Th following assumpions for h modlling of h coolan flow in prssurizd war racor ar mad: 1) incomprssibl fluid ) us of h Sandard -ε urbulnc modl and 3) prssur boundary condiion a h oul. 3... Gomrical Simplificaions, Local Dails Th gomric dails of h consrucion inrnals hav a srong influnc on h flow fild and on h mixing. Thrfor, an xac rprsnaion of h inl rgion, h downcomr blow h inl rgion, h igh spacr lmns in h downcomr and h lowr plnum srucurs ar ncssary [13]. 3.3.3. Grid Modl In ordr o rciv an opimal n griding for h lar flow simulaion on mus considr h following ims: Chcing grid numbr in spcial rgions o minimiz numrical diffusion, rfinmn of h griding in filds wih srong changs of h dpndn variabls, adapaion of h griding o simad flow lins, gnraion of ns as orhogonal as possibl. In his 6 wor, h msh conaind 1.115 10 rahdral 6 lmns and 1.118 10 nods. 3.3.4. Boundary Condiions A VVER-1000 nuclar racor yp h inl boundary condiions (mass flow ra and mpraur) wr s a h inl nozzls. No spcific vlociy profil was givn. Th wall was modlld using adiabaic condiions [14]. Thr wr hr boundary condiions imposd on h modl including inl, oul and a h ful rod wall. Iniial condiions for ³ 0 : A inls: T = T z = z 0 (8) 0 r = r 0 for all z (9) A ouls: p = p z = z o for all z (30) 0 A ful rods: TFR = T. (31) 0 By spcifying h ful rod s ha ransfr coicin obaind from xprimn, h ful rod s mpraur can b calculad in CFX-5.7.1 using h o = q FR ( T -T ) FR, (3) whr q FR is h ha ransfr obaind from solving h ha balanc, T is h fluid mpraur nar h ub rods and T is h ful rod s mpraur. In his papr, FR w assumd ha h ha flux disribuion along h ful rod is consan. Rsuls Prior o h ransin calculaions, h sady-sa was simulad. Th paralll ransin calculaion wih 10 iraion pr im sp oo 7 hours of compuaion im using wo procssor (dual CPU compur nods, conaining GB RAM). Th convrgnc criria wr s o 1.0E-04 for RMS rsiduals (mass, momnum and mpraur). In h calculad cass h im sp of 1s was an ino accoun. Figur 1. Thr-dimnsional imag of h racor prssur vssl from modl in ANSYS ICEM-CFD cod. 77
Vol. 19 No. 3 Summr 008 Farajollahi al. J. Sci. I. R. Iran 1. Sady Sa Simulaion 1.1. Vlociy Disribuion A snapsho of h vlociy disribuion from loop 3 in h vssl is shown in Figur. I is clarly sn ha h flow from h corrsponding loop covrs a sharp scor of h vssl. Th sramlins originaing in his loop subsania his finding. Mixing wih h flow from h ohr loops as plac a h our boundaris of h scor. Thr is a small layr only, whr h vlociy is lss han 1 m/s. 1.. Oul Tmpraur Disribuion A comparison of h prdicd mpraur a h Ho-lgs (oul nozzls) wih h plan daa is showd in Tabl 3. Th mpraur diffrncs in h oul nozzls ar only in h rang up o.70 K which is no vry significan. On h ohr hand, h mpraur ris a h oul nozzls is ovr-prdicd by CFX-5. This discrpancy could b du o svral rasons including simplificaion of h gomry, h grid usd for h numrical simulaions and/or inaccuracy in h compuaional modl du o fluid laag flows no bing an ino accoun. In paricular, h gomric dails of h consrucion inrnals hav a srong influnc on h flow fild and on h mixing. Hrin, h flow fild was compud on a hr-dimnsional srucurd grid; howvr, h lowr plnum srucurs and also spacrs wr no includd in h modl, hrfor, hir cs on h fluid flow wr no obsrvd. 1.3. Flow Fild a h Downcomr W calculad h vlociy disribuion a h downcomr by CFX and his rsul can b sn a h Figur 3. I can b sn ha h flow filds in h downcomr is no vry homognous and also no rcirculaion vorics ar found. Howvr, a maximum vlociy xiss on azimuhal posiions approximaly blow h inl nozzls. In Figur 4, h vlociy a azimuhal posiion a h nd of h downcomr is shown. As can b sn maximum vlociis xis a h posiions blow h inl nozzls a h nd of h downcomr. Thr ar posiions bwn h inl nozzls a h nd of h downcomr ha h fluid flow has minimum vlociy.. Transin Simulaion Examining h sramlins prsnd in Figurs 5 o 8 dpic sramlins of war flowing in h downcomr and lowr plnum of h PWR. Thr ar four plos in Figur. Snapsho of h vlociy disribuion in loop 3 and h sramlins a h sady sa. Figur 3. Flow fild in h downcomr a nominal condiions (sady sa). Vlociy (m/s) 9.00 8.00 7.00 6.00 5.00 4.00 3.00.00 1.00 0.00 0 50 100 150 00 50 300 350 azimuhal posiion Figur 4. Vlociy disribuion a h nd of downcomr of VVER-1000. 78
CFD-Calculaion of Fluid Flow in a Prssurizd War Racor Tabl 3. Comparison of h mpraur a h ho-lgs in CFX and xprimn CFX-rsul ( K) Masurmn ( K) [1] Ho-lg 1 600.5 59.15 Ho-lg 600.15 59.15 Ho-lg 3 598.85 59.15 Ho-lg 4 600.44 59.15 Figur 4 dscribing h flow sa a 1, 10, 40 and 80 s. A 1 s, h flow is vnly disribud around h downcomr. Howvr, whil h pump is opraional and h flow ra is a 100%, h sramlins flow around h circumfrnc of h racor o rcombin opposi h inl posiion a a similar high bfor moving down hrough h diffusr and ino h downcomr. No ha sramlins ha mov dircly Figur 5. Snapshos of h vlociy sramlins in h downcomr simad by ANSYS-CFX cod, 1s afr sar-up. Figur 6. Snapshos of h vlociy sramlins in h downcomr simad by ANSYS-CFX cod, 10s afr sar-up. Figur 7. Snapshos of h vlociy sramlins in h downcomr simad by ANSYS-CFX cod, 40s afr sar-up. Figur 8. Snapshos of h vlociy sramlins in h downcomr simad by ANSYS-CFX cod, 80s afr sar-up. 79
Vol. 19 No. 3 Summr 008 Farajollahi al. J. Sci. I. R. Iran ino h downcomr afr nring hrough h inl loop also mov around h circumfrnc of h racor and ha hr is virually no flow down h downcomr in h rgion blow inl. Figurs 5 o 8 dpics h sramlins in h rgion of h lowr plnum, whr h flow is passing hrough and around h prforad drum in ordr o rduc h c of scor formaion on h racor cor. Discussion In his papr a daild CFD modl for a whol racor prssur vssl of a PWR-racor of VVER- 1000 yp for h simulaion of a coolan mixing is prsnd. Th hug compur mmory rquirmns of such a daild modl forcd us o find a compromis bwn h dgr of spaial rsoluion of som dsign dails of h racor componns and our compuaional limiaion. Thrfor som lmns in h racor such as ful rod assmblis ar modld in a simplifid way. Nvrhlss h final compl modular RPV-modl consiss of approximaly million clls. Th modl has bn validad by h oul mpraur obaind from xprimn. Th mahmaical bacground of fluid dynamics and also h CFX simulaion rsul wr discussd. Fuur wor is dircd o h dvlopmn of a modl for VVER-1000 yp racors o improv h gomry and o sudy in mor dails h ransin mixing bhavior. Acnowldgmn Th auhors li o han Guilan s Fanavary Par and also rsarch dpuy of h faculy of scinc of h Univrsiy of Guilan for h suppor wih compur faciliis. Nomnclaur C p Spcific ha (J.g -1.K -1 ) C 1 = 1.44 Modl consan C = 1.9 Modl consan C m = 0.09 -ε urbuln modl consan D/D =d/d + v.d/dx Toal drivaiv E Toal nrgy pr uni mass (J/g) Inrnal nrgy pr uni mass of a marial paricl (m.s ) g Graviaional acclraion (m.s ) I Uni nsor Turbuln inic nrgy (m.s Kg 1 ) P Shar producion du o urbulnc (incomprssibl flows) (Kg.m -1.s -3 ) P Saic prssur (Kg.m -1.s - ) ' p Modifid prssur (Kg.m -1.s - ) q Ha addd o ach marial paricl is a a ra pr uni of Mass q Sourcs for q Sourcs for S Enrgy sourcs or sins (Kg.m -1.s -3 ) E S Momnum sourcs or sins (Kg.m -.s - ) M T Tmpraur ( ºK ) Tim (s) v Vlociy (m.s 1 ) z Axial (m) Gr Symbols r Fluid mass dnsiy (g.m -3 ) Ra of dissipaion (m.s -3 ) m Dynamic molcular viscosiy (g.m -1.s -1 ) m = C m r Turbuln viscosiy (Kg.m -1.s -1 ) m = m+ m Effciv viscosiy (Kg.m -1.s -1 ) Pr Turbuln Prandl numbr (Dimnsionlss) G Diffusiviy (Kg.m -1.s -1 ) m G = Turbuln diffusiviy (Kg.m -1.s -1 ) Pr G= G+G Effciv diffusiviy (Kg.m -1.s -1 ) m G = Effciv diffusiviy for (Kg.m -1.s -1 ) s m G = Effciv diffusiviy for (Kg.m -1.s -1 ) s s = 1 Modl consan s = 1.3 Modl consan l Thrmal conduciviy (W.m -1.K -1 ) l Effciv hrmal conduciviy (W.m -1 K -1 ) l m = l+ c p Effciv hrmal conduciviy Pr (Kg.m.s -3.K -1 ) z = m Bul viscosiy (Kg.m -1.s -1 ) 3 Rfrncs 1. Espinoza S., Hugo V., and Bochr M. Invsigaions of h VVER-1000 Coolan Transin Bnchmar Phas 1 80
CFD-Calculaion of Fluid Flow in a Prssurizd War Racor wih h Coupld Sysm Cod RELAP5/PARCS. Progrss in Nuclar Enrgy, 48: 865-879 (006).. Rohd U., Hohn T., Klim S., Hmsromb B., Schurr M., and Toppila T. Fluid Mixing and Flow Disribuion in a Primary Circui of a Nuclar Prssurizd War Racor-Validaion of CFD Cods. Nuclar Enginring and Dsign, March (007). 3. Carland Glovr G.M., Hohn T., Klim S., Rohd U., Wiss F.P., and Prassr H.M. Hydrodynamic Phnomna in h Downcomr during Flow Ra Transins in h Primary Circui of a PWR. Nuclar Enginring and Dsign, 37: 73-748 (007). 4. Bidr U., Gauhir F., Sylvi B., Niola K., and Dimiar P. Simulaion of Mixing Effcs in a VVER-1000 Racor. Nuclar Enginring and Dsign, Fb (007). 5. Schurra M., Hischa M., Mnrb F., Egorovb Y., Tohc I., Bsiond D., and Pignyd S. Evaluaion of Compuaional Fluid Dynamic Mhods for Racor Safy Analysis (ECORA). Nuclar Enginring and Dsign, 35: 359-368 (005). 6. Bidr U., and Graffard E. Qualificaion of h CFD Cod TORIO-U for Full Scal Nuclar Racor Applicaions. Nuclar Enginring and Dsign, In prss, 007. 7. Bochr M. Daild CFX-5 Sudy of h Coolan Mixing Wihin h Racor Prssur Vssl of a VVER-1000 Racor During a non Symmrical Ha-up Ts, Bnchmaring of CFD Cods for Applicaion o Nuclar Racor Safy (CFD4NRS), Worshop Procdings Garching (Munich), Grmany 5-7 Spmbr (006). 8. Fox R.W., and McDonald A.T. Inroducion o Fluid Mchanics. John Wily & Sons Inc. (1978). 9. Muralidhar K., Sundararajan T. Compuaional Fluid Flow and Ha Transfr, IIT Kanpur Sris of Advancd Txs. Nw Dlhi, Narosa Publishing Hous (1995). 10. Frzigr J.H., and Pric M. Compuaional Mhods for Fluid Dynamics. Springr- Vrlag (1996). 11. Wilcox D.C. Turbulnc Modlling for CFD. Wilcox Publicaions, La Canada, California, DCW Indusris (1993). 1. ANSYS CFX, Rlas 10.0, Rfrnc Guid (005). 13. Klim S., Kozmnov Y, Hohn T., and Rohd U. Analyss of h V1000CT-1 Bnchmar wih h DYN3D/ATHLET and DYN3D/RELAP Coupld Cod Sysms Including a Coolan Mixing Modl Validad Agains CFD Calculaions. Progrss in Nuclar Enrgy, 48: 830-848 (006). 14. Hohn T., and Klim S. Coolan Mixing Sudis of Naural Circulaions Flows a h ROCOM Ts Faciliy Using ANSYS CFX, Bnchmaring of CFD Cods for Applicaion o Nuclar Racor Safy (CFD4NRS), Worshop Procdings Garching (Munich), Grmany 5-7 Spmbr (006). 81