2017 Water Reactor Fuel Performance Meeting September 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jeju Jeju Island, Korea

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1 2017 Watr Ractor Ful Prformanc Mting Sptmbr 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jju Jju Island, Kora Study of Ful Rod Bhavior with Missing Pllt Surfac Dfct Zhnhai Liu 1, Yi Zhou 1, Ping Chn 1, Yuanming Li 1, Kun Zhang 1, Changbing Tang 1, Shuo Xing 1, Liangliang Lv 1 1 Scinc and Tchnology on Ractor Systm Dsign Tchnology Laboratory, No. 328 Sction 1, Changshun Road, Shuangliu Country, Chngdu, China, , 1989lzhh@sina.com ABSTRACT: During th powr ramp transint, th cladding may b subjctd to high strss and strain du to diffrntial thrmal xpansion of ful and cladding, which may lad to cladding failur. This is so calld pllt cladding intraction (PCI) phnomnon. Th missing pllt surfac (MPS) dfcts that rsult from pllt mishandling or manufacturing play an important rol in th PCI causd cladding failurs. Th MPS dfcts can caus svr bnding and high strss and strain in th cladding nar MPS dfct during powr ramp transint, which may lad to critical situation for cladding to fail. Accurat modling MPS dfct involvd in PCI phnomnon can hlp to undrstand its bhavior and tak masurs to prvnt ths typs of failurs. Th traditional ful rod cods ar unabl to trat this local asymmtric problm du to 1.5D numrical framwork, hnc a combination of traditional ful cod and modrn 3D finit lmnt mthod (FEM) cod is usd to study this typ of problm. Th traditional 1.5D ful cod is usd to modl global rspons of ful rod. Th 3D FEM cod is usd to modl local 3D rspons of pllt and cladding with MPS dfct. Th ful rod global paramtrs usd by local 3D modl lik intrnal prssur is calculatd by traditional 1.5D ful cod. This coupling stratgy can provid accptabl rsults and rduc massivly th computing ffort of modling full lngth ful rod in 3D. To dmonstrat this coupling procdur, th ABAQUS softwar nhancd by adding a st of modls rprsnting ful and cladding bhavior is usd to calculat local 3D modl, and th 1.5D ful cod COPERNIC is usd to simulat th full-lngth ful rod rspons. Th ful rod bhavior nar of MPS dfct during typical condition II transint is studid. Paramtric studis ar also carrid out to dmonstrat th ffct of diffrnt MPS dpth siz on th rspons of th cladding nar MPS dfct. KEYWORDS: Missing Pllt Surfac Dfct, Pllt Cladding Intraction, Finit Elmnt Mthod, Ful Rod Bhavior, Ful Rod Modl 1. INTRODUCTION Th ful rod cladding is th first barrir which contains th radioactiv fission products. Th intgrity of cladding is vry important to th safty of th ractor. Undr crtain oprating history such as powr ramp, th cladding may b subjctd to high strss and strain du to diffrntial thrmal xpansion of pllt and cladding, which may lad to cladding failur and rlas of radioactiv fission products into th coolant. This strong intraction du to pllt and cladding contact is calld pllt cladding intraction (PCI) phnomnon. Th PCI may b dividd into two groups, on is classical PCI, th othr on is non-classical PCI (Rf. 1). Classical PCI is associatd with strss-corrosion cracking mchanism (SCC) and mainly drivn by th high strss of cladding and th prsnc of chmical spcis, such as iodin (Rf. 2). Non-Classical PCI is associatd with th prsnc of missing pllt surfac (MPS) dfcts which is formd by pllt mishandling or manufacturing. This dfct typ has bn provn to nhanc th PCI failur by incrasing local strss concntration in th cladding (Rf. 3). Th MPS dfct plays an important rol in th pllt cladding intraction procss, which is th focus in th papr. Th MPS dfcts can caus svr bnding in th cladding nar MPS dfct during powr ramp transint, compard to th complt pllt, which may lad to critical situation for cladding to fail. Accurat modling MPS dfct involvd in PCI phnomnon can hlp to undrstand its bhavior and tak masurs to prvnt ths typs of failurs. Howvr, th traditional ful rod cods ar not suitabl to trat this local asymmtric problm du to 1.5D numrical framwork. Th 1

2 2017 Watr Ractor Ful Prformanc Mting Sptmbr 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jju Jju Island, Kora bhavior of th MPS dfcts is ssntially a 3D problm, hnc highr dimnsional cods or 3D cods ar ndd to accuratly study this kind of problm. Although it is possibl to modl ntir ful rod in 3D with MPS dfcts, but it would b vry computationally xpnsiv and tim consuming which is not frindly for rsarch or paramtr study (Rf. 4). Sinc th bhavior nar th MPS dfct is of primary intrst, so only modlling a local sction of ful rod with MPS dfct in 3D is suitabl. Th ful rod global bhaviors lik intrnal prssur or fission gas concntration ar ndd in local 3D modl as boundary condition or gap conductanc calculation input, which ar not possibl to obtain by only using a local sction. Hnc a combination of traditional ful cod and modrn 3D finit lmnt mthod (FEM) cod is usd (Rf. 4). Th traditional 1.5D ful cod is usd to modl global rspons of ful rod. Th 3D FEM cod is usd to modl local 3D rspons of pllt and cladding with MPS dfct. Th ful rod global paramtrs usd by local 3D modl lik intrnal prssur is calculatd by traditional 1.5D ful cod. This coupling stratgy can provid accptabl rsults by providing rasonabl boundary condition or input for local 3D modl and avoid modling full-lngth ful rod in 3D. In this papr, th combination of ABAQUS softwar and 1.5D ful cod COPERNIC ar usd to dmonstrat this coupling procdur. Th ABAQUS softwar is nhancd by adding a st of modls rprsnting ful and cladding bhavior through various usr subroutins to calculat local 3D modl, and th COPERNIC is usd to simulat th full-lngth ful rod rspons to provid ncssary data usd by local 3D modl. Th ful rod bhavior nar MPS dfct during typical condition II transint is studid. Paramtric studis ar also carrid out to dmonstrat th ffct of diffrnt MPS dpth siz on th rspons of th cladding nar MPS dfct. 2. ABAQUS BASED 3D FUEL PERFORMANCE CODE To analysis th ful rod bhavior with MPS dfct, th commrcial ABAQUS softwar is usd as a gnral platform to modl 3D ful prformanc. Th ABAQUS us finit lmnt mthods to solv nonlinar thrmo-mchanical quations in a fully coupld way. Th cod has built-in contact algorithms considring friction which is ncssary for accurat modling pllt-cladding intraction. Th ABAQUS provids a gnral and flxibl framwork to implmnt usr dfind thrmal and mchanical bhavior for ful prformanc modling by diffrnt usr subroutins and utility routins (via FORTRAN cod), such as UMATH (subroutin for usr dfind thrmal bhavior) and UMAT (subroutin for usr dfind mchanical bhavior), dtaild subroutin list can b found in rfrnc manual. It is sufficint to modl main ful rod bhavior by adding a st of modls using ths usr intrfac. Th primary rquirmnt for ful modling is to dtrmin th tmpratur and strss of ful and cladding. Th hat transport in this study is modld by hat conduction quation: Whr, T c p ( k T ) S (1) t c and k ar th matrial proprtis of dnsity, spcific hat capacity and thrmal conductivity, rspctivly. p T is th tmpratur, and S is th volumtric nrgy sourc trm. Th matrial proprtis ar dpndnt on many factors such as tmpratur, burnup and so on. Th pllt and cladding s thrmal bhavior is implmntd in UMATH usr subroutin. Th volumtric nrgy sourc trm in cladding is assuming zro, th volumtric nrgy sourc trm in pllt is dscribd in DFLUX usr subroutin and is prscribd by tim-varying axial and radial distribution to considr th powr variation during tim. Th hat transport btwn pllt and cladding gap is modld assuming on-dimnsional stady-stat hat transfr as: q h T T ) (2) Whr q is th radial hat flux of pllt out surfac, divid into thr parts, h gap r hgap gap ( po ci h h h (3) g s is th total hat conductanc across th gap, which can b hr is th radiant conductanc controlld by surfac tmpratur or missivity, hg is th gas conductanc rlatd to gas thrmal conductivity and gas concntration, and hs is th solid-solid contact conductanc only activatd whn pllt and cladding contactd. Th hat transport btwn pllt and cladding gap is implmnt using th GAPCON usr subroutin in ABAQUS. 2

3 2017 Watr Ractor Ful Prformanc Mting Sptmbr 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jju Jju Island, Kora Th Momntum consrvation is prscribd assuming static quilibrium at ach tim incrmnt using Cauchy s quation and nglcting inrtial ffcts: f 0 (4) Whr is th Cauchy strss tnsor and f is th body forc pr unit mass. Th strss is calculatd according to isotropic linar lastic modl 2G Tr( )I (5) is lastic strain tnsor,g and ar lam constants, I is scond-ordr idntity tnsor. To considr th Whr inlastic strains lik plastic strain, crp strain, dnsification strain and so on, th lastic strain tnsor is calculatd as th total strain tnsor minus th inlastic strain tnsor. in (6) in Whr is th total strain tnsor, is th inlastic strain tnsor. Th strss updat rspct to givn strain incrmnt in ach tim incrmnt is implmnt in UMAT usr subroutin. Sinc th strss updat in ABAQUS is incrmntal, at ach tim incrmnt, th inlastic strains incrmnt othr than plastic and crp strain ar calculatd xplicitly. Th instantanous plastic and crp strain incrmnt ar calculatd using th implicit schm, known as th radial rturn mthod (Rf. 5). Th classical Prandtl-Russ flow rul is usd to dtrmin individual plastic and crp strain componnts as follow: Whr p i 3 p 2 p i is th individual plastic or crp strain componnt incrmnt, is th dviatoric strss, is th ffctiv p is th ffctiv plastic or crp strain. Th mchanical contact btwn pllt and cladding is modld using Hard contact rlation in ABAQUS, and th or quivalnt strss, pnalty mthod is usd to incras th convrgnc stability. Th tangncy friction btwn pllt and cladding is considrd by using classical Coulomb friction modl with constant friction cofficint. Sinc th ABAQUS softwar is nhancd by using various usr subroutins to simulat th complx thrmo-mchanical bhavior of ful rod, it is ncssary to vrify th corrctnss of simulation with various usr subroutins. So suitabl thrmal and mchanical cass for ABAQUS built-in modul ar constructd. Th corrctnss of usr subroutins is vrifid by comparing th rsults basd on usr subroutin and th rsults basd on ABAQUS built-in modul for ths problms. 3. POWER RAMP SIMULATION WITH MPS DEFECT Typical condition II transint basd on Qinshan phas II nuclar powr plant is usd to study th bhavior of ful rod with MPS dfct. Th powr ramp occurs at th nd of on cycl opration. For consrvativ considration, assum th maximum powr axial sgmnt has MPS dfct. Th powr history of maximum powr axial sgmnt is prsnt at fig1. Th full-lngth ful rod bhavior without MPS dfct during stady opration and powr ramp is simulatd using th 1.5D cod COPERNIC to gt th global paramtrs lik intrnal prssur, fission gas concntration and cladding tmpratur tc. Ths tim-varying paramtrs is usd as input for local 3D modling. Th MPS dfct is much smallr compar to ntir ful rod and its impact on th global paramtrs is limitd. It is rasonabl to apply th global paramtrs basd on fulllngth ful rod simulation to local modl with MPS dfct. (7) 3

4 2017 Watr Ractor Ful Prformanc Mting Sptmbr 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jju Jju Island, Kora Fig. 1. Th powr history of maximum powr axial sgmnt for stady opration and powr ramp Fig. 2. 3D gomtry of dfctiv pllt and cladding. In gnral, th MPS dfct can xist on th pllt nd, cylindr sid or both. Th typical MPS dfct obsrvd for cladding failur is missing pllt surfac on pllt nd and cylindr sid. So, this typ of MPS dfct is of intrst. Th 3D modl usd in this study rprsnts all gomtric aspcts of pllts, including dishs, chamfrs and dfcts. A slic is rmovd from on sid of th pllt. Fig. 2 shows th 3D gomtry of dfctiv pllt and cladding sction usd in analyss. Thr diffrnt sizs of dfct dpth, D/8(1.024mm), D/16(0.512mm) and D/32(0.256mm) ar modld to study th ffct of dfct dpth siz on cladding bhavior as shown in Fig. 3. To rduc computation ffort, th 1/4 symmtry modl of on pllt and cladding is usd. Dfct dpth of D/8 Dfct dpth of D/16 Dfct dpth of D/32 Fig. 3. Gomtry of diffrnt dfct dpth Th outr and top surfac of pllt and innr surfac of cladding ar applid with tim-varying prssur condition. Surfac contact intraction is applid on pllt outr surfac and cladding innr surfac. Th outr surfac is applid with tim-varying tmpratur and systm prssur. Th top surfac of cladding is applid with prssur which is calculatd basd on intrnal prssur and systm prssur. 4

5 2017 Watr Ractor Ful Prformanc Mting Sptmbr 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jju Jju Island, Kora Fig. 4. Tmpratur distribution at maximum powr momnt during transint Th rsults of D/16 dfct dpth ar slctd as a typical MPS dfct to show th ful rod bhavior. Th tmpratur distribution at maximum powr momnt during transint is shown in Fig. 4. Th rsult shows that th maximum tmpratur of pllt is slightly drift from cntr to MPS dfct sid du to th lowr thrmal conductanc of gap at MPS dfct sid, which is diffrnt from typical symmtrical situation. Sinc th gap btwn th pllt and cladding at th MPS dfct is significantly largr than th othr position, th largr claranc mans lowr hat transfr capacity, which will lad to an incras in th cntr tmpratur of th pllt, th hat flux around th MPS dfct is lowr than th adjacnt ara, which caus lowr tmpratur at th cladding innr surfac. Th tmpratur at th dg of th dfct is significantly highr than th surrounding, which is du to th strong intraction btwn th pllt and cladding at th dg of th dfct, and gratr contact prssur rsults highr thrmal conductanc. Th hoop strss of cladding at maximum powr momnt during transint is shown in Fig. 5. Th cladding hoop strss distribution nar th MPS dfct prsnts a typical "plat bnding" condition. At th cntr of th dfct, th innr surfac of th cladding is subjctd to tnsil strss, and th innr surfac nar th dfct dg is subjctd to comprssiv strss. Th strss distribution at cladding outr surfac is opposit to th innr surfac. Fig. 5. Hoop strss distribution at maximum powr momnt during transint Th hoop strss distribution along th cladding bottom innr and outr dgs is givn in Fig. 6. Th strss distributions of thr diffrnt dfct dpth sizs ar includd. All ths strss distributions xhibit fluctuation nar th dfct ara and tnd to b gntl away from th dfct ara. Th maximum hoop strss of th cladding bottom innr dg lis at th position corrsponding to th dfct cntr. For th cladding bottom outr dg, th maximum hoop strss position is corrsponding to th dfct dg. Among thr diffrnt dfct dpth sizs, th dpth siz D/16 has th maximum hoop strss. 5

6 2017 Watr Ractor Ful Prformanc Mting Sptmbr 10 (Sun) ~ 14 (Thu), 2017 Ramada Plaza Jju Jju Island, Kora Fig. 6. Hoop strss distribution along cladding bottom dgs (Th hoop position 0 locats at th cladding bottom corrsponding to th cntr of th dfct) 4. CONCLUSIONS Th ful rod thrmal and mchanical bhavior with MPS dfct hav bn studid by modling local 3D pllt and cladding sction using th 3D ful prformanc cod basd on ABAQUS, and th ncssary global paramtrs for local 3D modl ar obtaind from 1.5D ful prformanc cod. Thr diffrnt dfct dpth sizs ar modld. Th study of tmpratur and strss distribution with MPS dfct is carrid out. Th currnt work is a prliminary study. Thr ar many ara ndd to b improvd, lik modlling mor pllts to avoid th nd ffct instad of on pllt, studying th ffct of diffrnt dfct shap instad of diffrnt dfct dpth siz, including pllt cracking and attmpting to prdict th cladding failur tc. Mor work is ndd to b don in th futur. REFERENCES 1. N. Capps, R. Montgomry, D. Sundrland, M. Pytl, and B.D. Wirth, Evaluation of Missing Pllt Surfac Gomtry on Cladding Strss Distribution and Magnitud, Nuclar Enginring and Dsign, 305, 51-63(2016). 2. B. COX, Pllt-Clad Intraction(PCI) Failurs of Zirconium Alloy Ful Cladding a Rviw, Journal of Nuclar Matrials, 172, (1990). 3. G. Knvostov, W.Lyon, M.A. Zimmrmann, Application of th FALCON cod to PCI inducd cladding failur and th ffcts of missing pllt surfac, Annals of Nuclar Enrgy, 62, (2013). 4. B.W. Spnc, R.L. Williamson, D.S. Stafford tc. 3D modlling of missing pllt surfac dfcts in BWR ful, Nuclar Enginring and Dsign, 307, (2016). 5. Fionn Dunn, Nik Ptrinic, Introduction to Computational Plasticity, pp , OXFORD Univrsity Prss (2004). 6