Analytical problems associated with core support structure of PWR

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ANALYTICAL PROBLEMS ASSOCIA'I-EI) W I T H ( ' O R I . ; SUPPOR'I- STRUCTURI'~ O F PWR (10<>,
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1. Introduction

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011',. can appreciate tile colnplexit.,, of tile colnpoll¢llt', to be analyzed. From the analytical point of view. the problems to be studied cover a wide range of structures (plates.

shells, and columns)and a variety of conditions (static and dynamic loads, illermal stresses, etc.). The components are interconnected, making the system a comple×, indeternm~atc structure. The computation of stresses and deflections requires tile solution of problems in the field of the theory of elasticity and plasticity paired with systenl dynamics and stability problems. The most impressive developments in this field occurred during tile last decade as tile result of research and developnlent work in tile aerospace industry, which provided many analytical tools used ill tile analysis of core support structures. Their contribution has been primarily tile development el con> puler programs for solid mecilanics problems, expansion Of the theories related to tile dynamics of shells and systems, basic studies on tile solid-fluid interac-

ticlll problem, etc. Experience with nlathenlatical modeling techniques has also been acquired, but iu :l restricted way because of basic differences ill slrucrural behavior. An additional complexity is euctmnlered because analytical nlodels for reaclol colllponents are not simple to build l l

1.

No',',' techniques

have therefore been created by tile lluclear reactor analyst to handle his particular problems. ('onscquently, refined matllenlatical models, new niethods. and computer progranis have been devclot)ed b) ltle nuclear industry ill parallel with experimenlai pro.ieels on models, and tests on actual slrticlures before reactor oporatit)n. The results of these analyses have been checked against nieasurerllents obtained lroln operating reactors and in sonic cases tile COllStallD,

input, or tile nlodel itself, was improved ill tileanalysis, as information was obtained froni test resulls. r i l e problems involved ill justifying or certifying the soundness t)f tile reactor internals i'all into dil+l+er-

eni categories. These eould be: (1) static or dynanlic, or (2) related to tile type of" function that thc reactor is perforining. In tile latter category the nomenc'laiure

is established by Section I!1 of tile ASME Code [2], as normal, upset, emergency, or faulted condilions. These cases include steady-state operation, m~rmal

margin, aud 1o establish deRmnati~m Imnts which ale ct)ncellled prJlllariJy with the ttilltstit)llill~ t~l lhc vt)111 ponerits. The stress limits are established T:~,t ~,nl~ t,, assure thal peak slresses will i1oi reach un,~cceptablc values, bul :.lls~ Io limit lhe amplilude e l Ihc ~st.Jl-

latory Sllesx conlponeIlt ill COllsidera|ioll ~[ fatigue characteristics of the materials. 13oth ltm-:iHd highcycle fatigue stresses must be considered when tile allowable amplitude of oscillation i~ estabhshed. Vcrificatiotl el +the sotlndlleSS t l l the dc~,igu is t~btallied with the initial preopcralional luliclional lest. i)uring tills test, the internals are subjected i~ ~i Iolal operaling tithe at full-flow cc)udilious ~l :tl h.'asl

240 Ill, providing tile ntllnbel of cycles required it> surpass the material endurance limit, t'~fllowing this test, qualified qualit) control persollncl perf/~rnl

additional inspection of selected conlponents, t'iliCCe{~sible areas, with tile internals OLll of tile vessel receive a close visual inspection. Particular attenlion is giveu to the interface, or connection, between two or more paris which would most probably indicate evidence of the nlotion of a component or relative lnotion

between colnponenls. Tile present paper does not attempt It) review all the stress analysis problems thai the analyst must solve during reactor internals design, but only lilt' C)lieS thai have been of the greatest interesl ni recent years, and seine of tlmse which Ilse tile llIOsl adwuiccd techniques, hi this review, tile anal).lical tools

used by the analyst ',viii be described, the type oi probtenl will be classified, and the specific analytical tool for that problem will be applied.

2. Major analytical problems Among the numerous analytical studies performed to investigate reactor internals behavior, special attention has been directed toward three important areas: flow-induced vibration, blowdown, and seismic analysis. This section discusses these particular subjects and presents the methods used for their study. Analyses of other areas will be described in tile following sections.

and abnormal transients, and accident conditions.

2.1. F l o w - r e d u c e d vibration

The main objective of tile analysis is to satisfv allowable stress limits, to assure all adequate design

Tile dynamic behavior of reactor components has been studied using experimental data obtained from

G..l.BiJhm, ( b r e support stn+cn+res oJ l'|i'Rs

oper:.tting reactors, along with restllts of model tests and static :.lnd dyrlamic tests in the simp and at lilt phtnl site. Extensive instrurnenlation programs to rneasure vibration ,.fl"reactor interrials (mchiding pr,.:,t,.'.,type units of v:.lrious re;.lclors) h;.ive been C;.lrricd otll during preoper:.lti,.m;.fl 10S,ls..:uld reactor uperatit,n 13 5] , but nl
the pressure lluctuati,.)ns generated by the puinps. vortex-sltedding, c,ther fluid instabilities, tLllbtilellc,..'. cavitati'<:,n, etc.'. Other forces rnay be rr, ech.:lmcclllv induced Ivibr;.ition response of other o.mlt)oilenls). Research work <.m tile gcrlcral subject has been published [ 6 i The I~uced vibration ~1" ;i slrticltiie depellds oil the lll;.IglliitldC :llld frequent.", e l the exciting ft)l-ces :.llld cm the dyn:.ln/ic ch;.u;.lcterislics ,.fl the structcire. r h c vibr:.llicm can bectmlC large if the frequency of an import.:.mt force COlllpOllellt is ccdncident wilh :.l lll~.iin natur:.ll frequency ,.fl the struclure. Flulter ;.ind ,nther types ~.fl self-excited vibr:.ltiorl invc, lving fluid-strutlure hlteractions Call also ocCl.lr, ill these cases, lhe hydr;.lulic exciling forces are .,'ere except when the structure viblates. Fhlidel:.lslic instability c:.ill be provented by desigmng ;.i struclure such that lhe negalive lib drod>uarrlic modal danlping force resulting from an assunled alnotird of vibratioil is snlaller than lhe p~.>siti','e n'lech;.u-dc:.ll d:.unpillg force ,.fl"thc structure, This usually requires that lhe structure be made relalivel.,, stiff. ('ontr,.fl of structural response is a prin/ar\. rrieans for preventing fh.iidelastic vibration from u,.turfing. The increased flow velocities ill moderll reactors demands tile sl ud.,, alld onnirol of flow-induced vibration phcnomen:.t and nf the vibr:.ltitm response <~i h.ir'.,eect~lnplex structures l,., achieve Ic,w levels of vibratic, n ;.it nlillinltlnl coM. l)ynanfic behavior of structural parts during preoperalitmal tests is obtained using displacement gauges, acceleroineteis, and strain trallsdticer,,,. The signals arc recorded with an FM magnetic lape recordel. Oil ttlld c,tf-site spectral analysis is done using bc:,th hybrid realth'ne and digital techuiques to obtain frequcncy spectr;.i frt:,rn the data 17]. The frequency

3<17

spectra are sludicd t~ deternline lhc ( a p p l o x m l a l e ) irequenc\ and phase COIItCIII. hl :.;OIlleslftldltlfd] p~llD, the \'ibration C~HllpOIleIllS g.lfeIie;.if[\dis~_rclc-frcqtlcHcy or v e t \ narrmv-b'a~d, USlmHV due t~ cxciiati~m hv the nlah/ c~olanl pumps. Other cnmpollcnl,, relied1 th0 Iesl)(HISe OI lhc slftldILlle :II LI ll:.IltllLlJl'ict]Ile11,J~ to broad band. mech',ulicaII\ and/or I1o~-ulduced eXCitLtliOll+ l')aIllpill~I:.IClI, llS :Ife ~.l]S~, ol~l:lilleC[ [1tllll this Sttld>" I~l. Scaic nlt~de] tests have been perltunlcd tt~ ~nIiclalc stresses, displacements. 11~ distlihuli~ui, and llucluating dilIcrential pressures with the real prohd.~ pc. Prtfl~lenls ussuciatcd wilh Ihc mlcgrily <,f lcacl~l iuternals strucILires due to l]t,\~-mduccd viI)l:iiioli have heen observed in lligh ~ater reactants l. ('urlcnl designs Ila'vc' :1 t,ncpiece cbiindric;.d tllernlal sllield which i,; :lll:lched rigidly tllnmgh nlulliple bc:u Ulg bh,ck, t~, tile cow b:.u rut :.It the tt+p end. and Ilcxtired tsimply >upp,.~rted) :it the h e l i u m 110]. The analx sis ~U lhe vihr:.Hi,.m ,.fl the IhclliKll shield is C~mlplic,iled by the Ilt,'.A illg-ct~t>!:llll en\ir~ullnenl v,'hieh ;.ll'fCclsthe sl:ibi!il\ pi~fl~leln, hlcali,'cd ca~,c,~ such as the' paralIcl-plulc iu a rcstri~Icd ,:II,mtwl have beeu stw.lied I1 1 ]. h i , tile stud\ ~,l ~, shell..inch :is tile lhernl:.ll shield with cumplex bounclar\ c,.mciiti,,mn, fcqtlileS :.1 Ctllllbill:.ltion ,.)I 10st lCSIlll>, dlld ~lll:II)'sis. [:h)xv-hlduced vihr,ili{m due Io vt~ilex shedding froln l i l t lr:iiling edge at the Io\vcr end ~1 lhe lheinlal shield alid oilier l]nw-induced vibi:llitui pl/eilonlell;.i possible hi icaclt)l.~ ;.fie now ulldel sltid~, b ; the \~estinghouse Research L:.lbot;.itt)lics. It is kilo\VII I'lt)Ill tile Ihcol\ el shells th:il the iit)rlllal inodes el ~.1c,viindiicul ~hcll till/ Ilc expressed as sine and ct~sinc, conlbhlatinns wilh illdiccs #t! and H indic:.lting tile IIUll/ber t)l \',,':l\'Cs Ill axicil :.liid ,..'iICLllIlferential directions. Tile shape e l each tnodc aild tile corresponding nalUlal fr0cluencies :lie fulicli~ms of the llUillbefs I#i alld H. The gelielal ext)iessitm for the radicil displacenlent of ci siinply sui~pl~iied shell is:

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L The shell vibration at a natural frequency depends on the boundary ctmditions al the ends. The effect t)f the ends is negligible for lung shells or for higherorder m modes, and long shells will have the }owesl frequency for n = 2 {elliptical mode). For ~horl shells. the effects of the ends are more important, and the shell will tend to vibrate in modes correspot~ding to values ot'H~" 2. The thermal shield is a short shell which is m~t completely supported at the ends. It is an intermediale case between a short, simply supported shell and an infinite shell. The distribution of the fixed supports provides the boundary ctmdilitms and iudicates the likelihood lhat. for the case of eight supports, the vibration with four h)bes will have the nodes al the fixed supports. In the case tit six supports, three lobes will apply. The natural frequencies are dil"fercnt m :m and in water, duc to the effecls of the surrotmdin.tz cot)latlt in a ctmstraint v(.)hlme II 21. With these previous considerations as a basis, the folh)witlg procedures have bccn perft+rmed in Ihe stud:, of" t h e r m a l shield vibratitm: a. During a test program performed Wil]I tl ]/7the,tale model the natural t't'equencies ,4f the thermal shield in waler and the maximum vibration amplitude were measured during various operating conditkms. b. A shaker test program performed on a pr~m~type thermal shield with the actual boundary conditions, provided natural frequencies and mode shapes m air. These modes were esutblished by measuring accelerations at the center, top (supports elevation), and bottom of the shield. Ill fig. 2. the results obtained are plotted for tl = 4 and correspond to a thermal shield with eight supports which are indicated in the same figure. The amplitudes tit vibration are fitted with a curve t ' = ,4 sin 40. c. Maximum displacement are measured duriztg the preoperational reactor test and arc correlated with the is~t'ormation obtained in the 1/7-scale model and shaker IeSl.

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) nuic_::_L~=_Pr:y:~u~ ~ ~t

.~,,.qA

".

?I

MA'

M

T

W -

,I;.;A::!

~W

~ H~A'ICN

:,

c~g:IWtN"

T

{ '~!~ ~;.

•-LBI "+2 .'=~ ~,H!~I '.II ,.OR~LA' ON +A: "C'~ i for

•

AND '<'T'~

~!N

L >

l

I"J~..4. Vil.)ratlt~n d>ph.tuetn,.'nt ,~ a .,mvlc-dcprcc- ~l-1rc,.',.I,, m S~NIcFII driven by a <.lllu'~oida]or ralldo111 prc~,~,tlrcl'Icld

310

G.J.Bohm. Core support stn~ctures of Pl4'Rs

pressure fields, by obtaining the root mean-square response of each mode. The described studies on flow-induced vibration. which are the result of experience acquired wifll many reactors in various operating conditions and with various flow vibration models, provide the tools to predict the response of internals structures during the design period and ensure sate low vibration levels in service [18,19]. 2.2. B l o w d o w n analysis In recent years, a problem that has been tile subject of extensive analytical work is the so-called blowdown accident. This is a postulated accident which has been studied primarily as a result of licensing requirements. It assumes a sudden, double-ended break of a primary loop pipe. hi such a case, at the break, the pressure drops to critical discharge pressure and the decompression propagates inside the reactor causing excitation of the reactor internals components. The complex time ..... space dependence of the forcing function and the geometric complexities of the structures present a difficult dynamic problem. Several computer programs have been developed to determine the characteristics of the rarefaction waves in the system [ 2 0 - 2 3 1 . Experimental and analytical work to stud), the response of the internals during a blowdown accident have been performed under the LOFT [24--26] and CSE [27,28] programs, but publications on structural response are limited. Studies on the vertical core movement [29.30] and the stability of the upper barrel [31 ] have been published. A paper has been presented at this conference [32] with a complete study of the reactor internals response under blowdown accident. The analysis is explained for the cases of hot- and col-leg break. Vertical and horizontal dynamic responses are obtained by modal analysis and by numerical integration of the governing differential equations. Nonlinear effects due to core displacements are considered in the analysis to obtain peak impact forces. The main objective of this analysis is to prove that the internals will maintain the basic geometry requirements to assure plant shutdown and core cooling without core support structure failure. This requirement is ensured by computing maxi-

mum deflections and stresses produced b~ lhe d\.T~a,mic response of tile components, and e~,lablishh~g allowable limits with sufficient margin ol sa Iket\. From the detlection point of view lhe main objective is to maintain permanent deformations bounded by certain values in such a manner thai tile ct~olant flow is not irnpaired. To establish the allowable stress limits which ensure integ,ity of tire core support structure, il ~s recognized that some components will be subjected to stresses larger than the yield strength ol tile material. The circumstance thai stainless steel i~ a very ductile material with high strain-hardening capability. and therefore ~, very good energy absorber, is an important factor taken into consideration when establishing allowable limits. , . a . Seismic a;;alysis

Seismic analysis is another important problem that has been investigated as a result of tile construction of nuclear plants in high-risk seismic areas and tile tendency of the industry to assume higher seismic intensities for design. The vessel and its internals are part of a colnplex system (i.e., the building and the rest of the nuclear steam supply system) which will respond to a seismic excitation according to the system's dynamic properties. Knowing the seismic response of tire reactor internals is importartt because of safety and operational requirements. Usually, two seismic intensities are adopted for the analysis: I) the operating basis earthquake lOBE), for which the reactor internals response shall be of such a limited magnitude that the reactor must be able to continue or resume operation without exceeding normal operational limits; and 2) the design basis earthquake (DBE) in which tile reactor internals response shall not interfere with safe and orderly plant shutdown, both during and after the earthquake. The vertical arrd horizontal components of the earthquake are considered separately; maximuln responses are added to obtain a conservative result. The study of the reactor internals response to the horizontal component of the earthquake is much more complex than the vertical response because the latter can be easily reduced to a one-degree-of-freedom system response. In general, two basic methods are used to compute the response under seismic excitations:

(;.J.Biihm. Core .support sttTtcturuv ol PII'Rs

a. II +the response spectrum curves of the asstttllcd earthqtiake arc available (the average response spectrum [33] or the maxirnunl response spectrum 1341 ) t h e n , by super-position of mot_l:fl purticJpatJt)llS, :l valtle tOl + 111;.ixJllltltli r e s p o n s e

~I I

o5

is o b -

tained.

b+ If the t i m e - h i \ t o t \ acccic~olatll c,t the sits fur the a,,sttlned earthquuke is avail;thle, the response is ohtuined b \ integrating in time the ditTerenti:fl e(itlalJollS

().. ~.., I

OJ" t l l O t i t ) l / .

- - %

The reactor internals are mathematically modelcd by bean,s, ctmcentratcd 111;.lsses a l l d linear springs. I-:or :t t'nodel similar to the one shown in fig. 5. in which tile I)t,Jlding and the internals are included and the ground rcsp,.mse spectrtHll cttrves :.ire ~J'..'Cll. lhc an:fix sis is perl+urmcd as indic:lted in refs. [331 am.l 1351. Xatu,al frequencics :lnd nurm:fl modes arc ol-,t:finc,.I using ailalytical techniques 1361 dcvel,.q~,.:d tt, solvceJ~ctlvaluc eJgcnveclorproHents foro.mtJnut)u:-, structures. Fig. 6 shc,v..,s the first i'node obl:.tJncd for the model of fig. 5. The l+tcqucncies obtained arc the natural frequencies of the total systetn, and generally they arc also identifiablc as the natt,ral t'requet~c.,, ()I" :.l Ct)lllp(Hlgllt t)l" t h e s v s t e l l l . A l s o ,

SOllle slrl.lCltlles

are immersed in water and the l+requency in ,,\':tier is

"@B

UIt D]~'C;

[ LEG[hIBKr~' RADIAl SUPPORT SPR]NGCONSIANI ROIATIONAI (,ROIJ~ID SPRING

K,o,

"

(:OK+GIANT [~AN<,IATIONAL GROUND SPRING UO\STAi~I

Kt

I

'Jr Ssil

8lj II tq IN*;

differetlt then in air; this must I~e taken rote ct)nsidcr-

ation 137,3Sl. In a contintnt)us system, the l e s p t m s c r i ( . v . l ) of the nit)de i ;nl(l c(~xrcspouding n:llt11:tl lleqUCHC.', ~.ci u, given hv the c ( ) n v o I t l t i t ) l l illtcgr:tl: 1#i yi(x,t)=Oi(X)

cc i

sill(wit

c~i)

l

©

'+j

U ~X) ~+1 I/OH

× ,]'+7~g(r) exp{ ~ico,(l • r)}sincoi(;'

- BARRt

r)dr,

(I

© Hi

= total mass, = seismic ground acceleration time--history. ~i = r a t i o el" damping to critical, qi{x) = shape of the ith mode of vibration.

M Zg

-®

]. f - ~

"l =_,?~'ismic Participa!ion factor = i •~loidm: .(;1<:)~'dm generalized mass

rot

NOT ro SCAt+_

Fig. 5. Mathematical model.

The CttllVt)Itllion i n t e g r a l hzls t h e dilllCllSk)n.h t)l al velocity and its Fuaxinltnn value dulh|g all earthquake is tile "'spectral v e l o c i t y " St,, ihcl) B/ .)'i(x, t) = ~-i Sui ?ai(x ) "

312

(t.J.BtJhnl. (}>rc ~'ttpl)
S r depends upon natural frequency and damping. Families of spectral velocity curves are available h)r different earthquakes 133 351. SOllletillles m !he forth of !he "'spec!ral acceleration" .S'a~ = v-i.Sri. l h c Iota] rcsp,i)ll.,.e o1" the slrtlClllle is o b l a i l l c d b} a d d i n g

file tllaXillla or adop!Jllg lhe root-lIleatl ~,(.luarc :tl)proxitllalioll. Ill this manner. I/laXJllltlnl bending in(.)lllelltS, shear f(.lrCCS,defied!ions, etc.. arc available ,.t]Ollg !]le Colnponell!:,,.

If !he response spec!rum at the vessel supporl level is used. lhen the building is not included in the model and the method to apply is the modal st,perposition method mdica!ed previousl,.. Tile results obtained fiom the linear analysis indicate tha! during an earthquake, particularly !hc Design Basis Earthquake in high seismic areas, the relative displacement between the components will close the gaps and consequently !he stttlctures will impinge ,.)n each other, making tile linear analysts unrealistic and forcing the development t)l" nonlinear methods to s!udy tile problem I.+t)] I1 is clear that linear analysis ,,,,'ill not provide information about tile impact iolces generated when components impinge each !)thor. hut has the advantage of simplicity aud provides itllorllla+ titm about the natural frequency of the s\.stcm. The etTec!s t)I" the gaps that could exist between vessel and barrel, between fuel assemblies, between fuel assemblies :,nd baft]e plates, and between tile control ~od:,, and !heir guide paths are cousidercd in the anulys~s. \)',"e will explain later tile malhcmalical f)roblelns itlvolved in solving this type o1" tn,,)blem.

3..4 nall'ti
Problems (.)tiler than those .just discussed are iln!)of tan! and have also received attention from the reactor anatyst. These are difficult to solve and require the use of large computers as well as programs

capable of numerically handling problems of large magnitude. This section discusses briefly the adoption of some analytical techniques. Also, several cases are presented in which internals components are studied using different mathematical methods. At this point it is pertinent to review the computational tools available to help in solving some of the problems, i.e. analog and diDtal computers. Analog t_'ompulers have not been widely used ill the solution

~H ]utcrnals mechanic;.il prt)blerus. [he pr,,fl-)ictn t,I vibralhm ()l a beam, Ior example. ,,:Ul.iM Iw >,olved bv an allah)g ct)mputer as v,.'ell a:-, I-,y a digital ~.~mll)utcl. [( reduces tu solving a ,system c,f linear dillcl¢llt;;l! equati,,)ns ~)i' tile term D / ] .k: + ( ( l .~ + JR] x = I.(t).

Tile matrix [K] i,s usuaIl,, )lol easy to compu!e alld nltlSt be introduced intu the analog compuler term b,, term. On the other hand, by intruducing a tc~v parameters ( dimensions, sl rength properlies) as iiIpuI, the eIIgillCer iS able Io solve his whole problem ()n a digital COlnputer ;Mid t)bt;.lill altswers It)r allk single set of parameters with a wide the, ice ()f output l+orms: print+ plot. cards, lapc. tnicrofihn.,,. An(}t]lel rcstricti,.}n Oil the use t)l +tile al)ah)g con> putel is its relatively small capability. For instance. the study of a system having :.iboul 15 degrees (~1 freedom ueeds all tile resources ol +the laborutor.,, • v,,hereas the same problem uses only a small part o l the central core ()f a digilal cotnputel. One should icCOglli/.c, h,.:,wevcf. !hal we arc ct)mparillg file lilt)st advanccd digital computer with the average standard analug used b \ lhe nuclear iudu.,,try. Tills i.,, probabb. why mosl mechanical problems :ire solved \,,.lth digital computers. It is hoped that the availabilil,, t,f hybrid tempt, lets ,.viii change this situation and all,.,,a, the use of models wilh lllore degrees o} freedom in :Ill ecollOllliCai lllallllef.

Because of the c,Olllplexit) of r e a c l o r illtt.qilal

slruclures. Ihc malllenlatiC,l[ Iorw~ulalions e l the inechanlca] problems have no ciosed-Iorm -,()lulions. l.lsua]l.\ '. a ,.onvenicnt wa3 to represent these -,fractures is It) List a Ihlile-clelllenl ,~ppr,.lach. This alh)ws t)llc to c,.)ll)lecl different paris (shell. plait el beat11 elemelllS, :,pring. masses, e|t.'.) 10 sinlulale the COllliIltlUlll and nlakes it possible Io n)odel and sltJdy exIremely complex slruclures by use of standmd i11el]lc)ds of structural analysis. The Iinite-elemcnl lechlu(.it.,e is used much more l)equently than the finitedifference methods in which tile differential equalions are solved b,,. approximate nlalhematical procedUlCS.

I-or dynamic problems, the type of felting funclions that are applied !o the comp(.ments :,re usually difficult to express analytically and the best solution is to m!egra!e numerically the equations el motion. In some instances it is necessary !o invesligate a

G..LB6hm, (Tn'c support smtcturcs o f t'It'Rs

clvi~alnic claslic plastic response, hiking inh> LiCCOLII'II lhc stlain-haldci~ing clfccts, lhc loading -tmloadin 7 curv0:.,. :.il/d h\slClCSiS c.x tics. r h c ll.c:illYlClll o1 these problems reqtiir,0,; fast and lalgC coillpulcr~, r h c pro~lalliS tlscd Io sludv lhc inlori~als Call b0 cl:lssifi¢d in t\vo lll;.lill glt>lips: ~cilelal- alld sp0cialpu rp(),,0 pr ogiilills. A 7cliciaI-purpt>sc plogr:illl, s()iYlcl iilles called :i sVSlCili c1 xliticltlie,,, bt)tlild:ir} con(lilioils, exlcill:.l] loads, c l c Spccicil-t)ulposc prt>gr;.inls USll;.lll)LIIC rcshiclcd Io ihc io:icltq illlc'lll:.ils ~COlllell). t~l loads lhat arc prc~Ctil dulilL<_, nOlllial and tibilornlcl] opertilit)n. 3. I . ..tl~l~lica tD m , ~.1 .~e~wral-i~ztrposc C O m l m t c r pro£,#~t#H.s"

The ill;.lJll :iciVallhlge of those codes is that the cilgJllccr needs Io sludv and become taillJlJ:ir wilh olll) ~,~llC plt~l;.llIi it) Ollablc soltllJon of 111t)sl o1" his problclns, llowcvci, il can b0 cuinberSOlll0 and incfficJeill 1~ use o11 :ii/oltCll-uscd, simple problo111 and (it)C:,, II~>t :I]\"..:IVSprovide the oUlptll needed. The inorc powelltil and general the code, lhe more skilllul the cngiuecr lllUSl be lil analyzing and knowiilg when the COlllpulcr provides misleading answcrs. rhcsc ",Vslt.Tl'i coth2s geliClally use nit)re sophislicared techniques, bul roquir0 :i c0rlain oxp0rliso iii use It> lake lull adValllage of their capabilily. [:uriherm o l t , Ihc) arc dilfictill 1~> modil.~. The very gcncraIil) of these pltigralllS requires a largo inpul rclalcd Io lhc gcoinoliy and properties of lhe sy:~lClil Io be :inal\ Led. The i/It)S,l elal0oialc of ihcsc progr;.inls COillaill iouliiles lhai will help lilt" tlscr Io Ioiilitllalc his iilpUt, stich as mesh gclielator ioulincs. Whcil a specific prublcn/nlusl be solved malYV lilliCs with slight cllangcs, il illig]it be useful Io wrilc a pioglalll that generates all lhe iiiput for lhc general plograill frolll a ioslricled amotiiit tll inforlllalion. All exanlplc of tills silualion is the sitidy oi" the vertical 111oliOll in case t>la bh)wdt~wl~ accidenl alial,'six i.L'l. This inpul plt)glalli creates Li disc' file COlilailiiil.e, all the iiit)ul for l i l t s', Sl¢iii progralil, whh.'h is really lhc oim ihal perlorms file inte~aration of thc equaIions :.tlid provides the o l l t p u l . The t\>llo,,ving ;.li-C examples of specific problems, ill which s,,'stem codes were used in tile analysis oi" the internals

313

3.1.1. Upper intcrHals support Fig. 7 slnv,,.'s a sam.tv.'ich-t.\ i~c uppcl mlcrn,lls >,Ul',p(}ll SllUCttllC. It is lll:ldo oi Ix',.:,.}plait:-,, upp~cr stillport plate ( " t o p h:tt stluCttlrC")icmlt+tccd b\ :t gild 01" bC;.itlIS.:Illd tlppcr COle plate ,.tUltlCctcd l',\ l h~Jlov, c~flunm>, boiled h~ the plates, v, iIh lhc eLm.lc lubc-, pruned Io the core p]alc. Thi:,,>,IrtlClt.lfCcomprc~,sc>, lhc fuel asscmbIic:,, am.I the am~ulat hoM-dov, H SlUing dtttillg :.i:-,senlblv alld is stib{cclcd to ~,ct Ileal upv. ard lorccs from these springs, l)urhlg opetatioll. II,.HIlILII and abnormal, tr:msver:,e flow d i a.,..L,lorcc:, arc applied It) the columns and guide tubes alld dillctclltial l,tessure exisls acros:, tile h,.,ri.,:,.ml:H plaice,, l h c I~qcc~, on the cHJ{llllll>, ;Mid guide tubes \ a l \ wilh the ch>,lall~.c t~ the outlet ilOZlJC:-,. I:~ccau:,.c,.H the Ctqllplqxll~. ~1 Ihc tipper pilckagc ~ct,lllCllk illld JOiltJillgCiHldilh!llS. it system code ha~, I',ccN used to mt,clcl it. The tt~p hal strtlclurc, deep I',Caln. at/d upper core plate h,ivc l)ecH modeled wHh fiat sJlclI clcillClll-,;, the supporl cohmlns with "'thrcc-dimcusiomll'" beam elements and the lucl assemblic>, arid h,fld-d,,v.H springs with "'ihrec-dimeusi~mal'" ~,l-~rillgclcmcNl~.. Because il i~, approximalcl,, s,. mmelrical. ~ {me-cighlh slice oI the upper package has I,ccn modeled. Fig. ,R shows lhc ~Cc)lllCll) t)l the inodcl ~itll Ihc ~,LlilOtl:,, conlp(lllOlllS scparah_'cl. The core plait i~, pOlltuulcd and is roploscrited hv a 7eOlllOllic:illv equi~alcnl ~olid plale which lla~ uiodifiod olasli< cuulslalil', a~chlmns connc'clin 7 lhc plait,, alid Ihc ,~tl~uI coltii1111s ct)iiliOCliilg ltlc boaiil grid with Ihc upper core plalc. Under lhc loads used Ik>r design, accordill 7 hi Ihc opcralill~ condilicm tlllder slud), the COlllptllOl piogrgilll provides slrcsses aild doi'leclions :11 :ill lloda] poiuls. 3.1.2. Lower internals suppCut The studv of tile lower internals structure which supports the core is another applic~ltion of tile system code to d e t c r n u n c the behavior o l a COll/pIcx strutlure sub coted Io a given load. This is also, a sandwicJt-type structt,re and ctmsist:., csscHtialh tH the spherical pclforatcd support caslmg, support colUlllns, ;.tlld lower perforJted core plate. To obtitlll ;.i realistic represeHtath, m of the htletaction of the con> portents, the lower support structure was inudeled

314

(,'..I.B/Jhm. ('ore sulV'~,rt .~'tructurcs ~1 lqt'R.~

I

rop HA: S'RL;CIUR'~

0 SHOR~ SUPPORI COLUMN LOCATIONS

( ).. ).,=

(

LONG SUPPORI COLUMN LOCATIONS

DF~P

(

BEA~4

S'RU'A'URF

I

/~

lOP HAl S'cUCIUP~

AM STRUCiUR SHORI SUPF COLUMNS

LAb HOLO SPRING

PLENU~

LONG SUPPORI

CORE PLA:E

SSEMBLY

Fig. 7. Upper internals assembly.

G..I t¢+;hm. ('o,", +ut~t~ort stru~ m,"c', +Jr/'h'R~

"3P H~I

'13

!iw '.,t

",1 +,

S'+JC[IP!

I.lWN

,~! ~ , . , i'll

bi

/

-L ON,: SJI'P3~ " COl

+uwS

I

II-__,~HO:,

¢3tt"N

L'[t

~3!;;'~9L'~

~'31;'!L

OI

-

ipp,)~,

~

•

.

SPi':N:~S

JPP!;,'

PSCKAtif

W,I'i

~.+

Ol'S

'~'

:LLtr

^S?,flJ~IL;I', uOT,FL

( O'.'PON+ :s " 5, ~ O+'~PP," +I)

I"ig. ~. [Ipl+,Clinternal', ',Upl',~+rt,,:ru,+.'tulc

tl%illg ;.I l+iHite-clcnxctlt sttudturltl utI~ll)'sis CtHllptttc[ tuogranl. Two gecmletty piths (views front ditl+¢rent urtglc:.,) of tile :.m:.thlic;.tl model, which is buih or (inite shell :rod pipe element.,,, atc giveu m fig. 9. f h c core pJ;+tc, difft~scr p]ule, and support u;.isting, ;.is ',,,'ell :.ts the lower purl t:,l'thc core barrel, zirc represented by flat tri:mgtd,u shell d e m e n t s . Reduced plate strength, duc to the perfc, tuti<,ms, is uccotmtcd fc, r by using un equivalent clustic modultls and PoisSOll littit~ in the calculations. This structure is loaded with vuriotis vertical torces, due to iIOtlllal and abnormal ,,:,petation. ;rod the deflections mid stresses urc obtuincd

for each case. [~xperhlietlt;.ll (.Liti~ trtml ct+t,...'xupl`'orl aSSCllJl`'Jy tt2Stili+,.t,arc :tvuilublo l+lum t,._'st>,cul ricd out ,nn :+ I .7->,c:Hu model. l h c cxperhn,._'tll:t[ v;+hic,,; h,:iv¢ bu'cn LOll','OltCdaccordillg to bllsic sc,tlhlu l:+,,','s ;itld ;IppIi,.'dto the prottHypc MrtlL'turc. Fig. tO comp;trc>, experimental aIld theoretical vertical d,L'llOL'ttt)llS, shtl',.~it/~ ~t+od iigrOOllIOnt.fRo test v~ilues urc sOtllewhaI flitg,.' as expected, since they ale o b t u m e d in the absence ol +

tile ct~t-e i'd;He, diffuser plilte, ;tlld st.tpptut ct4Utlln>, strtlctt.ircs, tiiiikhlg tile +,++~.t.~tttlgillor,e flexible, tisittg the sume m o d e l , this type o f system code c;m ulst, be user] t,> o.qvdpute stregs:es and del+ortr~;Mhm duc It',

3 16

U..I. ll(~hm. ('or(' Yupl*r)t'l vl;.'uclur('~ <~I I'II'R

COREBARREL ~"'~

COREPLY',:

nOllUllilorln Ieillpeiature di~,tributiol~. ~,x.lib rcJlll~c~,~ Lure at tile colllponelll StiFfaces alld lilt Ela(.!lcHI generated by the ganlnla-heal gCllelalh,1~ ~, Jllpul t~.i tile system ct~de, the detlected shape el the ,,IttlcltllC is obtained.

],I[fUBER PLA'E /

S~PPORI I i

COLUMNS

SuPPOR"CASTING

I.ig. 9. ('ompuler geometry plot of lower internals xuppt)rl

model.

0

I

IO 20

-

I

I'ig. 10. Lower internals support structure comparison between exlYerimental and theoretical vertical deflections.

3.1.3. Lower radial suppolt key's Finite-element system codes can also be u.,,ed tt~ solve elasto plastic problems, i.e., obtaining stress..' strain distribution and deflections when rite exlermfl loads produce stresses above yield. Agaiil. the lillilc elenle~lt approach allows one to introducc plastic properties in the easiest w a \ . hut the convergence o( the solutitm while following ~, given sttcss strata curve somethnes present a problem. Sollle techlliqt,e.,, to increase the speed of convergence have been developed. one of which is to use deI'lectitms instead of loads as boundary conditiol~s. l h e bottom of the h)wcr core support structure is restrained laterally by keys which arc hi(muted ~n pads on tile lowm support plate. The keyways are also lnt)Ulll0d ()II pads ()i1 the reactor vessel. These keys illUSt b e analyzed for tlortnal operation loads and accident condititms. F ~ sleady-stalc and transient loads, tl~e btresses remain elastic, bul l(~r blowdown Io~,d:, the peak dyllallUC stresses are abe)re .,, ield and the keys are al~al,,.zcd using ~, finitc-elemm~t network as shown in fig. I 1. The analysis provides mformation abou{ dellectio~l of the key and stress: strain distributiou. The model, using triangular, plane shcss elements aJlows olle to determine stresses and deformation for different vahtes of the external force, wll~ch is mcreased lllOflOtOltical]y up to tts illaXUllUlll value. System codes are also used to solve dynamic problems. The determination of natural frequencies and normal modes of a complex structure can be obtained easily by most of the system codes m existmtce. The deternfination of dynamic response due to general forcing functions presents the well-known problems o f stability, accuracy, speed o f computalion. and convergence characteristic of all the numerical methods dealing with time integration. Limitalions due to COnlputer storage are common b e c a u s e these codes are frequently used to solve problems of complex structures with many nodes and time integration routines must be selected in such a manner as

G..I. t~;;]tm. ( 'or,' ~tqv~+)t+l s t r u < m r c ~ +~1 i ' h ' R x

7, I "?

Thi>, dectstt+n i>,usuull\ ha:.,o.l,m the iclati',,c~.aluc:,tu the ,.,.mq+,.,~cut:-,i, the I]':I~,,,u 1.11l ,,~t~+c,.,,,...\-, .~ ill!C, thc xt,.'p.I itltC~l;llltHl,d:ld tL{Ul',C(JtlClitJ\th,: .+:'.llllptttcltilllC. Ix Xtl~',ll£J) t.lcpcH'Jcnt tH~ the ~:~ti~, M u c h tnltunl:.ttiotl ha', buell I'mhl+>,ho, l ttl the ]ilCl,iturc o1+ ntHncllc,tl i l l t C ~ t t l ~ l l 14u.-¢11. ,.', ith plO',.cd lllcllhn.J:, tJ/:II ',llC illCt,tpotalcd i:1 tit,,.",,_' .,,. '-,tqlll d,, t~atm,.. <,.',de:-...\:., ,.'xplaincd l',r,.'v,+u~.i~.. I,1,+',,,,.I,.+',',t~ :.llILI]\SiS IS perlc, ln+~cd (tsillUa .,\,,tClllc<...]c [.~ +'l l,, tAbI~illl lhc Ig'~I+nAIlxCoJ thc Illtqltl~II'.

Kii..Ui.

3 . 2 . . | p p / i ¢ ~zli, ul , 4 .~pCClaI-plUT;, ,~" ~, ,IPll;H h T l, ~¢t~'~

I i,..' I I ( or,.' I'~alrcl. Im,.cr r:M~:.d ku~,.

It+ pruvMc COllSiStellt rcstl]tx with .:ircaSOllablc COlll" ptllCl tiIlIC. ;I CilCt.IIll~,l;IIICCthat SOIlICtiIlICS, iY, iIllpOXM-

bl,.:. I'hu LICCLII~IC). which ~+ dcpcI+dcut uput~ the t+~Hlllt.l-ollCrloI~,, tlLIlICdlItAn t+.'lr<.llS. ;.llld lhc pl<.ipu EtltCd el'ruts.,i~ LlllIIllp'.Ht~.tlllfaclot tIl:.ttllIlIM I+C Ct.+lls t d c r o J tu a v o M instabilit,, ~+I t h e ¢OlllplltatitHl. The speed of the ,+:t+llll>t|t;ttit;,ll depend>, c,u th,+.' stcp-s~/c tb,cd in the iutceration. |l'ms. the rneth,.+d ad,.+ptcd tlltlX|ccmsMcr the selcctitm t.fla step-size v,,hlch plt)Vldch ~1 rca~,,.ulablc LICCLIILICX,: wlthJll ;+illo p t i m u m t~tne, ht I~,,mlmu:+r p~ofllcms, wl+tere di:,,o.;ntltmitics u c c u r m the dVlWlni,.: c h a r , t c t u r i s t i c x ~I t h e phcllt)lll,,.'ll()ll. U X.'LLI~+ilI~ .~lcp iI~tegtatJon mcthud is c t + n v c t i i c n t l \ t.mcd it+ u\t)it.t Ctlors, :.itld;or illXtabi]it~ . l l ~ e m t e g r : l l i ( m s t e p is :tdju,;ted h e : u t h e di:,,ctultintUt,, lc, ,+tx.xtttt... t h a t w h e r e thu d i s c o n t i l m i t y ~ p r e s e n t t h e imlncric:tI rnethnd will ii+ctupotatc the ,,.'l'tange ,,,,ith u,,~ uud¢:+.i~aMc eftcots+ FmaII+v. it is ilnpt~rt:.ti~tt,n ;.Mopt a seII-startm~ mutht,..I.i.e., the o.m4~Uh~tit,u tlltlStsl.art w i t h no v;.due-, uther th.:m the iuitial ,,.',.mdilious. l'o s;.P,+'c O.mlputer

lilll,2, the analyst

is faced

with

the p r o b l e m o f e l e c t i n g a s i m p l e i n t e g r a t i o n s c h e t n c w i t h s m a l l i n t e g r a t i o n s t e p s , t)r m o r e c o m p l i c a t e d .,,chcmes u l l o w i n g l h c use ,.,f larger intcgr:.ltiOll ,;teps.

[I¢.,ItACIIIQ. d CtHIlpl+llCI u~'dc ',', du',cl.l+,cd :,, -.q,.c Lt pa:tiCllJat t+l ",llecili,,." l.xpC ,+t [',tt,b!c111 :m,J I'~ :c-,l:lctCt.I It+ CCIIHIll ~_IILII~icICI +sttC', ,~1 the o,H/luUb.'~lt-. ,+1 load>, um.iu~ ,_Oll.+idct~ttu,.. Ihi.. >t+ltllit,II >CItlhlICX tIIc t:,,'ed ,.q ,:lttd 3 il],.2 the ",;LIIllC htlLICILIIC III~LICI \HIIt+[i', IVpC', ol I,.+dd~. ill MltIlJ~il \'tltit.ttllC.~ t,l',.Illlct,+.'l:t t,.'a;/C'~. Utld h,+_'ip', i11 put lottlIIIl~ ]Xtl;llllCtllv ",t m.Jtc> It+ c',tah':t~h the ~Cllslli'.,it,, HI lltc , a d u l h , t l v, hc:l O.'1I;+ttll p a r a t l l c t c r ' , ate ',:Hicd. +~l~+xI ol t h c , c pltL,.2'till11~ pr,.',,.tdc th,' tcqutto.i dcl~tl+Cd ,tll,,\~.ci 11l :i It+ill1 tllal can I',,..' bc-.I u:.,cd b', Ihc cngim.'Cl.

Sp,..'Cl.fl-purp,.+:,c i',~%.,talm, Iic,.ith.'ntl,. u..,c ,.c~. cllicicllt tL'chtil'.l'LC:, a n d ,,.'ct+mm+i,.'all) l+,it+\tt.lc the IlCCdcd an:.+\vct t~+ the p1Ld+lciiP,, l',tti t h u v ,+_'.IliiltH [+~C Od',Ji\ Ll>,Cd l't++l chatlg+':, in L'c,mncl~\ ;iml ,,thcl ptOpCltlL2",. rhc\ u:.,cillcthc,+.l:,, NitlIilLIIIt+ the s',,,tom o-.lc', Ulh.l u>,ua]I',, ha\c the %dIlIC prob!cnl-, t~I xl:d;iIit\ atld a,..CI.IILId\ •

I t+ >HI\.U +q:.ItlCliIIC~Itpl~+I+~k'lll>,,l.c.. tot ",IttICltlrc~ s u h i c , : t c d t{+ ~Lx,CII ",t..ttic load:, :tiM l+,,.,tnh.lar ', ,.+tm,.litlt+Ul,., lll:tll~, pto~raltlX ;ir,,.+ av,tllal',l,.' :tl~,.l !+,tt+,,,dc ,..',..,,tltUlli,.:. ;iCCtllHIu :+,{+I(Itlt+ll,+, l+~itiJ'~lct:ix ,,I \l;tllC [tKld% uppllcd t,., plate:*,. ",hell,,. I',c.ttm, :rod I~am,..'-.. pi,lllC :',tIC~:4 ;lIId plane ',,IILIIII l+t,hlctt>,. Ihc! mt,..,l.l:,!l,.it', pr,d',l,..ms e t h e \ ,.lo ut+t pI,._'Nctll :t pal ti,.tIJ:tt ll,~v,._'II x, alld t h e tllclllt+++.]> t+l" atlal~+.q\ am.l the ,.tq111+~tit,_'t COdCS :lie rc.:tdih, a',ail:thlc.

.~.2.1. TrallS',¢rsc vibr:.liltm V,rlth hnpllCl l h e dVllillllJC LIIILI]\ M% oI" the ICLIChH lIllOllI;II> 5,IrLIdItlIC :++,tlb.iecl,.+'d to t~5:dilJilhu\ huld:., plC',clllx ;III ilItCI,._'SIJIIt~ t+lt+fl+fletn when the ciCalall,.:c bulvVCCll cOtllpt.llICllth iS ctm+,Mcred. In this ,..t>,c. mH+Jacl cc, uJd oc-

3 Ig

(;..l 11bhnt. ('otc SUpl)~Jrr ,tt'ltclttrcx o f I'h'Rs

cur and the resulting tk~rces nntst be comtmtcd. I h c determination of the reactor components re.spouse under seismic excitation is of particular interest. This problem is studied by analyzing the dytuunic behavior of a structure consisting of vessel supports, reactor vessel, core barrel, and fucl assemblies. In view of the small clearances between the ctunponenI,~. impact could occur betweeu tile reactor vessel :rod the core barrel at the lower radial supports, as well :is among the fuel assemblies. The rnathematical model and the method used to study this problem is givell ill ref. [42]. Emt)loying the finite-elenlent approach, the governing differential equations describing the hiDtion of the systenl are set up and iutegrated uunleritally ire time:

[(,1 = lWl, [Wl = [Msl 1 {[Psl

I/../]

= displacement

114' I

=

[Msl [Ps] [DsJ [Ks]

= = = =

[Os] [Wl -IK, I [UI}.

ducts the colnplllCr stor,lgC iequlrel/l¢ill', ~!ld :tllIll~Ilo l i m e considerably. The c o I n p l l l C l slol',l£C ECqLIilClIEClII redLices

lrOltl 911 2 [(.1 a b o u t 3(~1/.

This method allows deternlmatiou ~I ltw magl~rtudc of the inlpact forces when banging , ~ c c u r s amJ should include nol only tile structural dalnpiug due It) l}le coIllpOllellls vibration, but also the cuergy losses produced during impact. This i~, simulated by ,, viscous dalnpitlg mechanisnl capable t)t lepl cserltH/g the losses which normally tire characterized b~ a restitution coefficient. Fig. I 2 presents the nlodcI used to obtain the response of the major COlnponent, showitlg IIw gap', amt is taken from ref. [42], where the stud',' ix explained. Further sopllislicatitm o1 the model sttch as adding guide tubes, control rods, mechanisms, e t c . , allows refinement of particular areas, lEE particulal, scram tinlc during an earthquake can be calculated by obtaining the impact forces on the drive Imc. Fig. 13 shows a model used to perlornl this steal\.

vector,

velocity vector, mass matrix, force array, damping matrix, stiffness matrix.

These differential equations are integrated in time using the Nordseick integration scheme 142] which is capable of adjusting the integration time increment to obtain a stable and convergent solutitm with a prescribed accuracy. A distinctive feature of this analysis is the application of "'element" global stiffness nlatrices in place of tile standard structural global stiffness matrix, hi essence, this complete stiffness matrix is not really built during the computation, only the sum of all the forces acting on a particular node is computed. For a model with n nodes having three degrees of freedonl each. the standard stiffness matrix is a 3n × 3n symmetric lnatrix. After storing the stiffness matrices of each individual element, it is possible to build the internal force vector on each node by adding the contribution o f all elements. Adding the external forces, and dividing by the mass attached to the node gives the acceleration vector. The time-integration is performed on the b a s i s o f these values o f the acceleration vector. It has been shown that this feature re-

3.2.2. D vnannc stabilit> of upper barlel Another interesting problem sol','cd by using a special purpose computer program is tilt.' sludy of the reactor barrel dynamic stability during a p~,;tulated

LEGEND: •

! l i

NODES

8 --

PIN m t u s [LASTICELEMENTS

....

L

•%"I

TNDTCATE SAME NODES

:v~'l

IMPACT NODES

¢ .............. I,

oj4 / j , , .

@~ -1"

REACrO~

vEssEl T

E,M,.

s.IELo

,

--

®

........

I

,k . . . . . . T,"~

.~'o "

IQ'

, , .iO/

ted

®

Z . . . . . --/_ . . . . . - - 7. __ ~4~A '~r"'

C9

I'

O._9

I® I® _~.i 'o

91~'3_

3 t-'V~,A/~- I I-'~'X/V'v"

I-bELASSEMBLIFS. 7

..~'_~ II

Fig. 1 2. A typical reactor internal configuration used f o r n o n l i n e a r a n a l y s i s Ircf. [ 4 2 ] ).

.~ l 9

(;.J. ftiShm, ('ore s~qv~ort xtnzctur(,x o./I'II'R ~

..q

I

I

I

~1<

I

............

additiunal tlexural tnutions of the shell. 1he tnagmtudc and distribution t4 these tlexural dellectitms depends strongly on shell dimension and material propertic~,, intensity and shape uf the prcssutc pulse. and magnitude :.|Hd disliibt.ltitul of the initial mlpertectiuns. This ptobletn hus becu studied 1311 for barrel.,, of diHerent reactor ~,izcs 132[. From the 111athc11/alica[ poillt o1' view the SOIl.llit)ll C,.IIISi~,Is '.it the tlnle-itHegratitm of a system of ihmlittear dilferential equations performed by mei:tns e l a predi,-hn corleCltH algorilhllltlS. The illelllloHed reference:,. present rest,Its of the amtlvsis. ~,howillg the margin t+l satct\ for the different casesanalyzcd.

<'+

:

,-:,,q

NO +

IN

=(

4. F u t u r e d e v e l o p m e n t s

q

SCAL~

l'i.v. 13. Reactor lntcrt+u.tl~+m,adcl v,'ith dri,.'c line. bh~wdown accident. f i l e analysis considers tile dynamic elastic plastic behavior of tile barrel on tile basis uf tile tl/;.ltlUf;.|Cluring tolerances (initiul "impert'cctions'" ). In case of a sudden hot-leg break the sonic wave rapidly reduces the pressure inside tile upper barrel. l)uc h+ the pressure differences across the wall. tile shell after the bleak is subiected to an impulsive compressivc wave. For safety reasons the nlaxitlltilll del'[ectiollS and stresses are limited, particularly if perlll;.illellt delornluti,.m should occur. Consequently. tile ploblclll of core barrel bt, cklmg under dynanlic loads becomes, inlportant in establishing both tile magnitude of l/l:.lXilllUlll del',armatiol~s and stresses and the tnargm against buckling for the given pressure pulse. The response of the barrel (shell) to this type of pulse consists initially in a mliform radial inward movement of the shell elemeuts and results m compressive hoop stresses. Deviations of tile shell shape from tile perfeet cylindrical shape (initial imperfections) result iu circutnferential bending moments and consequently

[ h e experience ubtamed b~ analyzing operutiug rcaclors gives the designer of corc support 4tltlcttlres a belier understanding of the cumpouents" beha~,iu~ and reliability and enables improvcnlent~, itl perlormance. ('hunges in design are made wifll mcreasillg confidence, assuritlg that futt,re reactors ,,,,ill perform mere efficiently. Mathenlatical models adjusted according t~ rcsulb, obtained IlOti1 nlcast,remenls taken during t'ueoperatiolla[ lCSl:.;,,,,'ill predict more acctllatcl', Ill,.-"illlerll:.tls

t-e~,pOtlSe I.llldel I/Orlll;.tl oper;.lliOll

alld

II;.III:,,icIII>,.

Studie.,; related to lie\v-reduced vibrali~m will establish tile exact behavior ut +c~>mponent.,, with a higher degree uf c0ttaint.,, than hcreloforc. Some of the accidents and translenls whiuh are uctually studied will be discarded :is t,nrcalisticall 5 conservative and ethers, which will be considered more prub;lble, will be analv/ed with more s~q~histicutiotl. Matl++etmttical tt+ols and matcri:.tlx l+rt~pert let, will continue to be developed as importal+t factors it+ tttttlre iC:.lClOfilllplOVelllCllls.

5. Conclusions The analysis of nuclear reactor core support slltlctures is a new and rapidly developing branch uf tile mechanical science. The dramatic developnleut of computer technology allows the designer h~ perform increasingly complex analyses. Thus. the behavior of

32fl

f;.J t3ohm. (.'ore sl#~l~o#'! .~trlt~ttt#'¢'s ~! I'Ii'R

components is more precisely described Ihlough :~ beller understanding of past performance. Finall3. one is :isstired that a vital part of the nuclear plzini possesses the degree t)[ reliability and safety rcqttired for contmuous operation during tile pro ecl¢tl life cd Ih0 reat.'t o1. 1 o tills c o t l ¢ l u s i o n it ILIUM bc a d d e d t11;11 tile sol\ll i o n o f these a n a l y t i c a l p r o b l e m s is all i n t p o r l a n i lau'tor lOW:lrd tile o p l i n ] i z a t i t ) n t ) l COl'llpOllt211ts. a n d

c o n s e q u e n t I 3 , , to the u l t i n l a t e goal o f r e d u c i n g c o s t s without impairmg safety.

References I I I M.~V. ~ambsganss, Vibration of Reactor ('tire ('omponents, Reactor and Fuel-Processing Tecbnology. Vol. 1(I 1967) 208. [2i American Society of Mechanical Engineers, Nuclear Vessels, Section Ill ASMI:I Boiler and Pressure Vessel (?ode, AS.ME, New York 11971 ). 131 II.W. Keller and M.J. Manjomc. A Unique Application of Instrumentation for Verification of Design Load Conditions and Assessment o f Reliability oF Irradiated Reactor Internals. First Int. Conf. oi1 Structt, ral Mechanics in Reactor Technology, Berlin. September 20 24, 1971. 14] D. Knodler and R. Rut, Schwingungsuntersuchungen an den Kerneinbauten des KWO, Atmowirtschaft 13 f 1968t 535. [51 D. l lacnsel. Vibration Test Instrumentation at a l'ypical 3-Loop PWR, 261h Annual lnstruincnt Sociel$ t)l America Conference, Vibration in Nuclear Power Reactors, Chicago, O c t o b e r 4 7, 1971. [ 61 G.S. Rosenberg, M.W. Wambsganss and R.P. ('arter, editors, Proceedings of the Conference on FlowInduced Vibrations in Reactur System (?omponents. USAEC Report A N L - 7 6 8 5 ( 1970L 171 J.S. Bendat and A.(;. Piersol, Measurement and Analysb t)l Random Data. Johy Wile,.', Nov, York f 1966). [81 I I.A. ('tile. On-line Analysis of Random Vibrations, AIAAPapcr No. 68 288, A I A A - A S M E 9th Structures, Structural Dynamics and Materials Conference, t'alm Springs, California. April 1 3, 1968. 191 T. Stern, l-xpdrience acquise avec los r6acteurs de puissance mode're's "LiI'cau ldg~re, I.,nergie Nuclc'aire 12, No. 2 11970) 125, I lOt t;.A. Goldsmith, Westinghouse Nuclear Power Plants: A Decade of Reliable Operating F,xperience, Proceedings of the 1971 Electric Utility I-ngineering Conference, Colunrbia, South Carolina, .March 14 26, 1971. [ 11 I P.A. Lowe and E.A. Zanoni, A Stability Calculational Procedure for Flow-Induced Vibrations of Reactor Internals in Parallel [:low, presented at American Nuclear Society Meeting, Idaho Falls, Idaho, March. 1971

121 .I.l. Russell. ()ll lit,,'I)3 i1anli~, l~,esp,,m,,c ,,: hubl'.lei~
1201 .I.A. I~,edlield and S.(I. Mar.,.,ohs. Flash

\ Prograln lot Digital ~iniulation oI ci Loss.~ll:(.'oolant Accidenl. I.'.S. Al.('P, epori ~,VAPI) 'I'M 5 3 4 l l 9 6 6 i I211 A.II. Nahavandi, ']hc 1 tJs~,-ol-( otdant ..\ccidellt ..%nal,.sis in Prcssurizcd Veuter Re.:lct,.Ir,,. Natl. Sci. & Eng. 36. Nil. 2 11969) 159. 1221 S. I a b k . BI.OI)WN-2: IA:AI'I)(omputer Program It,r ('alctlliition o f I l u i d t'ressurc, I"Imv alld Density I raii,.icnl,, IJuriilg a [,oss-ol~-('lli)lanl .&ccidcnh .&NS lrari,,-

;tctitm', 12, N~>. 1 (19691 358.

1231 I1. K a r w a t a n d K . Wollert. BRU('II D: A lhgitalProgr:.iln for Pressurized Water Reactor 13hlwdown lnvcsligations. Nuclear t',ng, and Design 11 ( 1971)J 241. 1241 1'. l)ugonc, 1).1.i. Solbcrg and I).1t. V',alker. LOI"I Integral Proer,un. tLS. At'I(' Rep~rl. IDO 17258K April 1969. 1251 J.('. Iluire and (;.I'. Brockctt. Semiscalc 131owdowil Jild lnlcrgency ('ore Cooling ¢I.I(G) Project. U.S. A F ( Report. IN 1384. 1261 (;.11. (;ruth. 9,:IIAM Prediction of Seini.~alc I c s t RcsullsU.S. A l ' ( ' R e p o r t . lN 1431 (1971t1, 1271 ('.1'. Linderoth. Containment Systems I',xpcrimcnt Part I I)escription of Experimental Facilities, U.S. AI'I(" Report BNWI, 456 (1970). f281 f;..l. Rogers, Program for Containment Systems Experiment, U.S, Al'i('Report. llW 83607 (1964). 1291 R.I). Peak, Design of the I . O I T Reactor Internals, Trans. Am. Nucl. Soc. 9, N~. 2 (19661 549. 13OI A.S. Kadakia. Dynamic l.lvaluation of Reactor ('ore SUpl~ori Structure.'l'ranx Anl Nucl. Suc.,t tmlerencc

(;.J. l¢~)hm. ('ore SUl~l~ort strttctur,'.v o.[ I'lfl.~ ~

on I',~',*.er I,?.cactor S} s|',.'Illy. ;llld ('tllllpt)ll,,.'lllS. Nupplcmu'lll I~ V o l . 13 (Septclnbcr | 9 7 0 ) 7. 13 I I (;.J. Bi;hm and 1'. Sleek. I)} llzlllliu' Stabilit?. t~t' ( ylmdrlcal Shells Subiectcd to SC,nlU \\:avc~. duc t~ a I o~s-ot( oolallt ..\c,.'idcnl. Ntlcl. Sci. and In.er.,.:.. 44. 3111 3(b) (19711.

1321 (;..I I'~/~hm aim .l.P. I aladle, l~,e:l,,..tor Internal:,, I/esl',~:nxv t nd,.'r a Blo\t d o u n :\cu'idu'FiI. I irst It, ll. ('oIll'. o n .'¢,tttt,,.turall Mech. in I~ca,.'t,~r I t c h . . Berhn. Sel',t,:rnbe~ 21) 24. 1331 (;.\~. Ilousm.'r. I ;lrthquakcs. ('hap, 50 in Sh,ock and Vib~ali~m I l a n d b o o k , cds. ( . M . l larrin ;rod (.1.. ('redo. Mc(,rax~.-I[ill, Ne',.~. "fork (1961). 1341 I .I I. ~.;a', I,ord and ('.N. (;a?, I,.',r. cd'.;., Strtlctural I.nginecrin,_' Ilandbo,.~k. ('h,q:,. 3, I a r t h q u a k c Ilcni,;lant I/uihling I)csi,_,n. bv N.M. Ne',~. nlark. Mc(;rav-.-Ilill. Ne'.a "~ork 119fi5) 1351 R.I \t,i,+.'gcl. l'.;trthqu.lku I ngirmcrin.,_,. Prenticc-Ilall, Ne',a .Icrw_~ (197()). I 3(~1 ¢;. I';t~tHI1. N a t u r a l \ : i b r a l l t m ~+l"Rcact~,r Itltertl;tls, N:ttic;if Scicllcc dlld I'nc. 22 (19651 143.

32

[37 I J.A. Kcam.'. ()n tilt' I la:,tic Vibrala,m ,,I a ( irkul:u (antilc~.er '] ul',c in a NewH~llja]l I luM. Ph.I). 1 lit'sis, C,m'tcgic InstJttttc ~I l'cu'hnLqo~,.~. 1963. 1381 R.I. I ritz and l . Kiss. "1he Vibrati,,m l/c,,l',.n,,c ,~l a (';itltllC',cr,.+d ('?. lit',Jcr Surr-utu.lcd b,. ;m - \ n n u l , r I ILiid. L . S . . \ l ( ' R c p o r t KAPL 'q 6539tl9¢H+1. 1391 (;. I'b,~hm+ Sci',mi,.: Anal5 ,,is t,l" Rca, It11" Inlurt~als I<,r Prcs,,tlri/cd \~,:llcr [(eactors. I lr',l \alJ~:llal (',.Hl~rt.'~,", O[ Pr¢>.surc \.'eswlandt'ipictc lvclmoh:-ti,. \ S \ l l I'ancl~:l~ bt.'iSlll/t..\ll~ll?.sis atld I)csign ol Prc,,,;uru \'Cssv.l,. and Pipin~ ( Olllpt~llt-'lll?,. S;II1 I l~lllcisc~,. \1:1\ I(I 12. 19-1 1401 I ' . 1 I)a'.i,;and P. I~,abir:oult/. Numcrluallnwurati~m. ( fill'.1 ( o l l c ; c . %",althall/. \l;ix,,achLl,,ul ls ( I t l¢~,'7I 1411 L.(~II;Hx. I h c NUlllcri,.'a[ Ir,.,alnlunI ,~t I)illclu'tltlal I,.tmHitms. Sprinyvr-Verl:L,_' Bcrlil1119fiill. 1421 ( ;.J. I/,,dllll alld :\. N. N;lha\ ;llldi. I )\ I1;lllllk" \ n,ll} hi'., i,l' t~.em.'t,r llllk'l'll/ll .qlrtlC[tlrC', ",AILl1 IIIIpacl BcI\".CcH ( (llllpOIIt2t'tt~,, [O I',C publi',hed iH Nuclear Suk'n,u aiM I II.,.!t nccrin,.:. 197 I. 143l .\. N,~rdsict.'k. ()11 Nutllcrit.;tl hllc!!t~lti,,ll ,1l ()rdJn;ll~ I)illt'rct'Hi:ll ItlLLaliol~s. M;HIIcII;d!i,.S ,,I ( ,lIlll'ql:dlh'll: I~-,. 22 1 1 9 6 2 1