Description of the two-dimensional nodal codes "NRMS," a multigroup static code, and "NRMT," a one- and two-group transient code for solution of the neutron diffusion equation in rectangular geometry

DESCRIPTION OF THE TWO-DIMENSIONAL NODAL CODES

"NRMS", A MULTIGROUP STATICS CODE, AND "NRMT", A ONE- AND TWO-GROUP TRANSIENT CODE FOR SOLUTION OF THE NEUTRON DIFFUSION EQUATION

IN RECTANGULAR GEOMETRY

by

Randat Nee Simls

TABLE OF CONTENTS

Section 1; Intoduction and Ovextview . . . Section 2: Probiem Deciption...

Section 2.1: Geomentzy . . . . Section 2. 2: Eye/.g9y G)tup Stauctute and

MatexiaZ Pgmeteuts Section 2.3: Boundaty Conditionz . . Secticrn 2.4: Input Contwot Pattameter..

Section 2.5: Time Dependernt Speci ication4 Section 3: Implementation and Execution . .

SectLon 3. 1: Avaitability and Status . . Section 3.2: Machine De pendencies . . . Section 3.3: Pxecizion . . . . Section 3.4: Co'%e Requiement6 . . . . . SectZon-3.5: Execution TME . . . . Section 3.6: Input . . . . Section 3.7: Printed Output . . . . Appendix A: Progtam Cavd ListLng . . . . Appendix A. 1: Listing oj NRMS . . . .

Appendix A.2: LiLsting oj NRMT . . . . . .

Appendix A.3: Modi4ications to NRMT

Benchmatk SoZution 6o,% LRA Kinetics. . . . .28 Page

* 3

* 5

* 7

. . . .

13

* *

61

TABLE OF CONTENTS (Continued)

Pag e Appendix B: Pioblem Input and Output _{0 0 439}

jo'L the LRA Kineticu Benchmak *

Appendix B.1: NRMS Input . . . . . . . . . .14O

Appendix B.2: NRMS Output . . . . . . . . . - .-43 Appendix B.3: NR.MT Input . . . - - - . . . - - - . 4.59 Appendix B.4: NRMT Output . . . . .61

ABSTRACT

ComputeA code4 axe deeicLbed whic!h wee wftttten in otdeL to tet "nodaZ" method-s deveeoped

6o,%

>epteentations wh&ih axe composed oj a tegutat atay o6 >ectangutAt

homogeneous zoneu. Muwtigpoup 'static zolutionz ate handted. Onty one- oxt two-gtoup titansient Wolutions ate computed. Step and >tamp pettubation.s oS mateia diiju ion paxtamete/zs ate used to initiate tianSients. Engineexting £eedback is6 not incuded.

FOREWORD

This %epott discuwes only the detait& o6 how to 4olve problemz with the compute. codeA which ae piesented hexe. The theoty behind the methods imptemented in theze codes as wett as numexouS apptications6

a/te given in the authou's thezsi. Fu/theanote, the mateAiaZ ptesented hexe is not intended to be zu66icient 6ou% those whose putpose s to modily the computet ptogwtams. Atthough ca/td 1Listings aute prtesented, this is done .o on-y in o.tde that otheA4 can dupticate the preogitams

DESCRIPTION OF THE TWO-DIMENSIONAL NODAL CODES

"NRMS", A MULTIGROUP STATICS CODE, AND "NRMT", A ONE- AND TWO-GROUP TRANSIENT CODE FOR SOLUTION OF THE NEUTRON DIFFUSION EQUATION

IN RECTANGULAR GEOMETRY

Section 1. Introduc on and Oveview

Thi tepor.t deuseibe computeA codes which wete written in otdeA to test the methods Jotmutated in Releence 1 jot zoZution o6 neutron

di66us6ion pwobems in nucleat &eactons. The "noda2 &es ponse method" (NRM) developed in Rejeence 1 is the computationa2 technique empLoyed. The codes axe _{applicabte to two-dimensiona2 tepreentations which ate}

composed _{o6 a tegudx annay o6 tectangu&L homogeneous zonea. NRMS} (NRM static) s a multig'waup .satics code which ptoceses the xeactoL

desextiption and deteAmine6 the .6teady state sotution. NRMT (NRM ttansient) is a jewgoup time-dependent sotution. Neithe& code incorpokate6 a

genexat 6eedback modeL. Spec4L{c detaiLz oj the numeticaZ mode2s and p'ocedues employed in these codes ate given in Relexence 1.

DetaiLs concexning the use o6 these codes axe given in this eport. Section 2 discussez the capabifities and appLications o6 these codez in modeting reactoz cotes. In Section 3, the /equiements jot impLementation

and execution o6 the codes on the computex ate ptesented. A £Lsting o6 NRMS is given in Appendix A. 1 and NRMT in Appendix A. 2.

Specia2 modiications wexe made in the couxue 0a the wodk in Reektnce 1 in ordex to txeat the LRA two-dimenzionaL kinetic4 Benchmak

-2-.

which incorpoates a tempeature jeedback modeL. The detaiLs o6 these modiLications ae. given in Re6eence 1. Routines which we.e modiZied o& ctddeid Ln NPRT 'ot this spe.ria cae ate £isted in Appendix A.3.

It should be noted that these outines ate applicabte only to this patticulaw ptoblem.

Input data 6ot the LRA Benchmaz ate given in Appendix B.1. ( static - NiRMS) and 8.3 (txansient - NRIMT). Outputs o6 the p'tobtem

..

3..

Section 2. Puobtem Desciption

2.1 Geomet'u

Only two-dimensional geometxy is teated. The teacto% is& assumed to be composed oj a tegutat atvay o6 xectanguax homogeneou6 zone.6.

Zone cootdinatez axe qven on an X-Y .ystem by NDI=1,...,ND1X in the X-direction and by ND2=1,...,ND2X in the V-diWrection. Each zone cootdinate intewvae is assigned a width o HZV1 (ND1) ox HZD2 (ND2).

Zone matexia compo-sition4 axe speci4ied by a compozition index NCPI=1,...,NCPX which tegeeacez a patticulax set oj matexiaZ dijuszion paamete6 indexed by NCP. A zeo ot negative compos6ition index entexed

in the tectanguia. compo.sition a~vtay NCOMP(NV1, ND2) indicates a pos6ition which is Zocated out6ide the teactor boundaxy. These pos6tions axe not

con-sidexed to be zones and axe not inc&Lded in the catculation. Thus Lvtieguta& boundahties axe allowed.

The totat numbex oj zones Zz NZNX. This numbe Ls not necessaxly equa to the ptoduct ND1X .x ND2X because ZAtkegua& cote boundatie axe peunitted. Boundaxy conditions axe discussed in detaiZ in the 6ottowing 6 ection.

The catcuationa2 mesh "s de6Lned by division o6 the zone cooxtdinate intexvatz into tegion cootdinate intevuaLs. Fot each zone cootdinate

intetva , 'ND1 ot. ND2, the.e axe assigned NPD1(ND1) ot NPD2(ND2) >tegion cootdinate divizions. The >tegion coo'tdinate divisions axe indexed by NP1=1,..,NP1X in the X- ditection and NP2= 1,... ,NP2X in the V-diZtection. TheAe ate. a totaZ oj NPPX >tegionz. A in the. totaX numbex oj zones,

the totzt nwnbeA o6 t~egiLonz may be te/s6 .thcrn the piwdu.ct NP1X x NPZX .tthe cat6e o6 iveguwtc co'te bou~nda~'tiu

-5-0

2. 2 Enevgy Goup StxauctWae and MateiaZ Parametens

The ztatic code. NRMS txeats a muwtigoup 4txactwe Limited to downzscattening onty. Coding ZimitatioL6 a1iow a maximum o j ten enexgy g9Loup5, NG = 1, ... , NGX (NGX 10). An abit'axy numbex oj mateial

compositions ate allowed, NCP - 1, ... , NCPX (NCPX atbithavy). Fo. each

composition, N'CP, and enegy gtoup, NG, matexiaZ diLu.sion patameten -(exc&lding zcatteving) axe enteted into the arxay CMP1 (I,NCP,NG) whexe I (=1, ... , 5) is an index indicating the type o

g

bazed on the totaZ numbex o goups, NGX, and the downscatteing bandwidth IDSBW which must alzo be given. IDSBW is the maximum oveA att gkups og0

NGT - NGF, whee NGT is the "scattming to" index and NGF iz the "s cattexing

{jom" index, Jor which the mactoscopic scatteting cxos.6 section i nonze'o.

The zcattexing index, ID, Ls such that data s indexed zequentiatig jot

NGT = 2, ... , NGX with NGF = 1, ... , (NGT-1) Jot each NGT, The indexin scheme is Zwtusttate.d in the goe~owing diagram Jor a jive gtoup problem (NGX=5)

with a downzcatteing bandwidth o6 two (IDSBW=2).

ID (1X = 7) FROM GROUP (1) (2) (3) (4) (5) TO GROUP (1) - - - -(2) 1 - - - -(3) 2 3 - - -(4) - 4 5 - -(5) - - 6 7

-

-6-An wbittuuty prompt 646sson zpecttum &s allowed. Thiz a6pectum 16 enteed in the aAvag PCHI(NG), NG =1, .. , NGX.

The ttnaient code NRMT -treat:s only a one- ox two-group stuctute. The jL6,Lon apectiwum (pompt and detayed) L6 fimited to unity 4oA NG

equa2 to one. NRMT checks the output o4 NRMS to deteunine i6 the pope gtoup 6tucctue was employed.

In addition, NIRMT requires the input o4 gtoup inverse neutown 6peeds, (II(NG), NG = 1, ... , NGX and detayed neutton data 6o& NDFX detayed jamilies (NDFX = 0 to 6). Deiayed neuton 6 action/s BETA(NDF)), NDF = 1, ... , NDFX and decay constants AMDA(NDF), NDF = 1, ... , NVFX axe %equired. These parameteuts apply to att mateciaf compos6itions in which iz.Lioning occuus.

Petubations can 6e made to any oj the matetial diijusion paametens

except invextse speeds and detayed neuiton data. These pertubations may

be 6teps oir >amp. Speccilic detaiEs o the pextubation data ate given -ina. 6otowing zection.

-7

2.3 Bounda.~q Conditions

-N4o .6peciL~Lc omZen.tati'n cj the ptwbtem deacAption is 'tequiLed

6'j imptementation oj pa~ticwuwi. boumdaty condi~tions. Symmne-Vu ot'r

vacuum (zvwo entvang paxtiaZ cwnt) bouncdvy condition.a can be cpplied on each oj the 1jow% sies The pwrtZcwta&r bowundvry condi~tion ctppied is deZeAri-ned by the va&Les oj the (6Zag.6 IBC2P (Y-,.t.x), IBCZM (Y-min),

IBC1P (X-max), and IBC1M (X-min). An axia2 buckZ-ing, SSQV, is atzo '&eqwuied.

-8..

2.4 Input Cont'o Patame-tes 2.4.1 NRMS

A numbex oj conttoZ patametetz ate -input Joit s eection oj calcuvationa options, itexative 4tLategy, conveIgence, -,solution

nortmalization, and editing. Delault ate ptovided jo thee paameteu.

It Zs stongty .6uggested that the useA take advantage o6 the deautt patametez pt ovid ext s etection o j itekative st'ategie becaus e consideabte ellott has been given to optimization oj these cte'txia. The pticua ase t pa ametenz wilU not be conside/ted hexe. OtheA

paametesu oj importance to the u ex axe noted in the o-~owing discuL6,sio n.

The type oj " tansveise Zeakage" apptoximation (4.ee Re.exence 1) iz selected by the gcag ITLA. OuteA itenation convexgence is set by

CCOT. The convexgence citexia is applLed to the tegion avetage {Lux (or {jssion souxce). The itag ITPN setect6 the type o6 poweA notma2i-zation (totaL >teactoxL power ot assemnby avexage powe density). The powe noltmaLization jactot "s PNRM and the powex peAt jis-ion Z6 PFIS.

Output editing can be obtained vort zone- o't >tegion-avexage poweA denzities, gtoupwise >tegion-avexage ituxes, and gtoupw-ise tegion-avexage pattiaZ cuttvtents by 4election oj the itagz NZPESX, NPPESX, NPFESX, and'

NPCESX >tepectivety. Mo'te wiUz be given conceitnig output editing in a

Latet 6ection.

The p'toblem descxiption and .static sotution is edited to a "peinmanent" zequentiaL data et by input oj a nonzeto value of the 6S-ag NDS1R. (This6 data

can be used in a tate NRMT execution io Steady-state initia2ization.) This value gives the data.6et number oj the device a6 speciLjed in the DD catds o j he poblem Job ContuoL Language as in

//FTnnFOOl DD ...

wheve NDSR = nn. A space altocation 6o,% this dataset equal to that o the core size &equir)ed 6o,% data in the static zoiution is mote than

adequate. Speci6-ic 4 pace tequittements wiZe be given in a 6ottowing .6ecton.

2.4.2 NRMT

Othet than ptinted edit contot, onty three contot paametets ate aequited jor NRMT. Thez e paametets ate the datas et &ejeence numbe, NDSR, 6o& the dataset on which the static 4o1.ution

'redes s e Section 2.4. 1)., IPSA, a Zcag toL 4election o gthe

"pecus o4 shape" apptoximation (,see Re.exence 1 }, and CONV, the zpatiat iteAation conve'gence cirtexia (See Rejexence 1 jor guideLines on choice

a thi pa-ameteA).

-10-2.5 Time-dependent SpeciLications (NRMT onLy)

The probtem time Z6 divided into a numbex o6 discete,

nonovext-Zapping time domains, NTT MD = 1, ... , NTIMDX. The extent og each time domain Ls given by TFINAL (NTIMD), the Lina2 time o S the domain in s econds.

The time/step size in each time domain is detexmined 6ltom the numbex o6 timesteps pex time domain, NTS PT D (NTIMD). Printed editing is contiled

by .6pecil ying the numbex og timestep6 pex edit, IEDFRQ (NTIMD) , and the edit Levet, IEDLVL (NTIMD), Jot each time domain.

Step o tamp (tLineax ) pertubations oJ all mateiat paametex6 except neution veocitie and detayed pxecwrtst data can be made. Pettubation.s arte appLied ove. pettubation "intexvaL6", NIPRT = 0,

NIPRTX. The maxmnum number o6 peitubation intexuats is tbmited to ten (NIPRTX <10) . Th es e inteiuat ate nonov etapping and the extent o each .4s given by the initiaZ time., TIPRTX (1,NIPRT) and {ina2 time, TIPRTX (2,NIPRT). In each pektubation intexvat, NCPRTX (NIPRT) composi-tions ate modi ied. NCPRTX is 12mited to ten ot Zes -in any pe/tu-bation inteuvat (NCPRTX(NIPRT) < 10 ot NIPRT = 1, ... , NIPRTX). (Step-wize pextubations can be 4speciLied by zetting TIPRTX(1,NIPRT) equa

to TIPRTX(2,NIPRT).)

The indices o6 the NCPRTX(NIPRT) pextuxbed compositions axe entexed in the avcay ICPRTX(NCPRT,NIPRT), NCPRT = 1, ... , NCPRTX(NIPRT) 6oi the pertubation inteva NIPRT. Changes in the mateiaL diZuszion paametens

ae enteted into the axvays PRT1 (I,NCPRT,NG,NIPRT) (excLuding s6catteting) and PRT2(1,NCPRT,NG,NIPRT) (4cattexing) just as the pa'ametes themsetves in the compo6tion a-vay CMP1 and CMP2 o6g NRMS.

Section 3. Implementation and Execution 3.1 AvatabLity and Status

Souce Zistings oj NRMS and NRMT ae in the posess6ion o6 the MIT Cornpute Code Lib'atian. lnquie4 concening these code4 6hould

be addrtessed to that .o6lice. Cad image Listing o6 the codes axe given in th~lis

epoxt.-Debugging o6 the codes was not complete at the tetmination o6 the wok in Releence 1. SpecZLcaLly, onty the two enegy gtoup option

oj each code was tested. ALso, those options which have been used have

n ot been exetcised extens vety oveA a bioad tange o6 test cases.

-12-3.2 Machine Dependencies

The codea wete wtitten Jot execution on IBM 360/370 syztems. Both codes axe written in the IBM Fouttan IV tanguage except Jot a zingie asembtex &outine (subxoutine ZIGET) in each purogam. The

Fotxan *outines shoud be compited undex the IBM H-ZeveL compitex

with

gu2Z

6o'L communication betwee.n the pxogtams. Only unomatted input/output i&s used with this device.

-13-3. 3 Preciaion

Both codes ate wxitten in 4ingte pteci.zion except 6o. 6ome pant6 o6 the coeiLicient genexatio n toutines (in which matAix. inve.sions ate done). Some care has been taken in the NRMS ptogwram to pevjonm openations in which ptecision ptoblems could possibZy occu in doubte pteccziion. Such measwueS have not been extenivety u6 ed in thL NRMT program.

HoweveA, obvious precision probZems wexe not encountexed in the couse o devetopment and teuting oj eithex code.

The codez can be eaily changed to use doubte precision 6o4 the calcutationa2 atxays. This is accomptJished by changing the value og the va-'iabte KDORG in the main pwgtam {.om KDORG = 1 to KDORG = 2 and

modi-6ication o6 the teaL zpecijication .tatements associated with the van able DDAT in aLU Fotttan suboutines 6/tom

CoL. #1 CoL. #7 REAL * 4 C --- REAL 8 X DDAT(l) -to C --- REAL* 4 REAL * 8 X DDAT (1)

It 6houPld also be noted that at integex anuays axe teated in a haJ4-woxd jomat in the pzesent vesions 06 the codes. These anVays can be changed to a 6u&otd o'nat in a mannet simita to that use d 6or

the teat precis6ion conversion. The integeA conve6ion is acrcompished by changing the vaLtue oj the vaiable KTIORG in the main ptogtam Qrm KIORG = 2 to KIORG = 1 and modi4ication oj the integex s peciLication statements associated with the Vaxiabte IDAT in- atf FoAttan subtoutines

Qwom ot. #1 Cot. # 7 INTEGER * 2 C INTEGER* 4 x IDAT(1) to C --- INTEGER* 2 INTEGER * 4 x IDAT(1)

-

Coxe stokage in the cumrent vexZions oj the cods is dynamicaLLy allocated. The total avaiabLe ztorage space as detenmined by the .size o the useA'4 REGION patametex Ls acceusabte by the p'og'tams.

The progtam use p'obtem-dependent-4ize a'tay and att data is contained within the cote. The use. ne-ed not spectjy a REGION size giteater than that xequited £oxt each patticuLat ptobtem. This p'oblem size (in K-bytes6) can be _{deteAmined dixecty >tm the jo22owing exptesszons (assumming 4-byte}

waod& ).

P~tog'tam NRMS:

'Deine REGION = cote (in K-bytes) Lequitted ct: NRMS with the constant ttanvve&s e Zeakage apptoximation and jszsion zouxce extxapol-ation option.

REGION

REGION 2

additiona co'te (in K-bytez) tequited 6o,% the quadtatic tasvveitse Zeakage option (equas zeo ij constant ttans vee Zeakage app'toximation is us ed.

additionaZ coxe (in K-bytes) >equit.ed jot the ittx exttapotation- option (equaLs zeto ij ji~sson zoutce

extta~potation is used).

Then the >tequited REGION pataumete iz given by:

REGION ₌ REGION ₊ REGIONI + REGION₂

10

-1 6-0

*[5

1 6uuood integeAt auatj

KIORG

2 hallwo,%d integeVt ataj6

J

-17-Totat numbeV oj compositions zones ( ND1X * ND2X) Totat numbeA o6 mesh &egons.. (; NP1X * NP2X) Total numbeV oj compositions

Tota2 numbex o6 ene'gy gtoup6

REGION _0, coe' (in K-bytes) >equied Jot NRMT with the the constant ttansvete teakage appt ximatlion and the itat ptecutot shape apptoximation option.

REGION1 additiona2 co'le (in K-byte.s) >tequited sot the

quadtatic ttans6verze 2eakage appiwoximation option fequats zeto i4 constant ttansvekse Zeakage

apptoximation is us ed)

REGION_{2 =} additiona2 coute (in K-bytes) >tequited 6ot the impLicit precursot shape appwoximation option

(equaLs zeo ij itat p-tecuso&t shape apptoximation is used).

Then the >tequitted REGION paametex is given by:

REGION = REGION₀ .+ REGION₁ + REGION₂

0l

0

(

and pa ametems appeating in thens exptesions which have not been pteviousty

deined in this 4ection ate:

NIPRTX = Totat numbet o6 peAtubation intetvat

NCPRTX(N) = Totai numbe o6 pettubed .compo6itions in pUtttbation intetta N

-19.

3.5 Execution Time

Execution times vaity wideiy 6ot both codeu depending on the pa'ttLculat p'tbtem being 6oLved. Howevet, quantitiez telated to the oveta computation time which may be uz elut can be 6ound jot each code.

The times given betow axe 6o& an IBM 370/168 computet with Foxttan G1(OPT= 2) compilations.

In NRMS, the CPU times pet node pe innex itetation ate apputximatety .0002 .6ec. Jot the constant Leakage app'oximation and .0003 zec.

60>t

(azzembly-size nodee,) in thexmaZ >teactots (two-gktoup sotutions ), typicatly 10 (contant Leakage) o't 15 (quadtatic Leakage) innet ite.tations ate

>tequited pet oute' iteation. The numbe. o6 outeA itexat.ion jo>t teactou os6 the size o ju2L scate LWR's is typically 30 to 50.

In NRMT , the CPU time pe' node pe itetation ( to-gutoup szoLutions) .s 0004 zec.. The number o6 itetations .ztequited

6o>

di66icuLt to obtain. The inteested >teadex is >te6meved to Re6e'ence 1 iort dwutheA dis cazsion o6 this topic

-20-3.6 Input

3.6.1 NRMS Input

The input to NRMS is deseibed in thi zection. Catcds ate gouped by junction and indexed in each

gunctiona.

FORTRAN tead Lszt, the tead jotmat, and a desctiption o caxd entxies ate given jor each caxd type. The lunctionat gtoupings axe

A. heading B. geometAy C. neutonicu D. boundaxy conditionz E. conitot patametens F. powe. notmatization G. editing

H. zotution dump (Jot tans.ient initiatization)

A desexiption o4 each caxd type jotIows. A Listing o6 input jot the s6tatic 4oution (with the quadtatic txansvese Zeakage apptoximation and jission souxce ex&apoLation) o4 the LRA kinetics Benchmatk Zs given in Appendix B. 1. A detaited descniption o6 the physicat probtem can be

sound in Regetence 1 ot Regenence 2. CatcuationaZ details axe. given in Re.etence 1.

0

Description

0

NOTE: Two cads .ate >equited.

B

-21-Program: NRMS

Card(s) Type: A. 1, heading

Required, if: atway6

Read List: (TTL(I),1 = 1,40)

Format: (20A4)

Variable

-22-0

Variable Description

X-directed zone cooLdinate timit.

y-directed zone cootdinate limit. Program: NRMS

Card(s) Type: _{B.1, zone cootdinate Limit6} Required-, --if: -a&laga

Read List: (ND1X,ND2X) Format: (2112)

NDlx

Descri ption

intedvat width (cm.) 6o& x-diected zone coordinate ND1.

numbeA o6 'tegion inteAvaZ divizion6

6o , x-directed zone coordinate NV1.

Note: A can'td L.u -equited Jot each zone cootdinate ND1.

-23-Program: NRMS

Card(s). Type: B.2, x-directed zone. and mesh inteAvat de cAiptionz Required, if: atwdyg

Read List: (HZD1(ND1),NPD1(ND1)) Jot ND1 = 1 to ND1X

Format: (E12.1,112)

Var iab 1 HZD1 (ND1)

Descri ption

intevaL width (cm.) jot y-dirLected zone cooxdinate ND2

number oj tegion intekvat. diviion.6 jor y-diUected zone cootdinate ND2

Note: A cad s .&equited jot each zone coordinate ND2. -214.

Program: NRMS

Card(s) Type: 8.3, y-directed zone and mesh intevual dec'iptions Required, if: atwdyZ

Read List: (HZD2P(ND2) ,NPD2(ND2)) 4ot ND2 1 to ND2X Format: (E12. 1,112)

Variable

H Z2 (ND2)

-25-Program: NRMS

Card(s) Ty; e: B.4, matutiaL composLtion index b y zone cootdinate

- - Required, if: _aday6

Read List: (NCOMP(NV1,ND2), ND1 1,ND1X) joL ND2 ND2X to 1 Format: (2413)

0

Description

matetiaL composition index jot zone delined by zone coordinates (ND1,ND2)

0

Note: At Zeazt 1 cad is requ~red jot each zone coordinate ND2.

0 Variable

-26..

Description

Tota2 number o6 matetia2 composLitions.

Tota2 numbeA o6 enegy gtoupS.

Down catte ing -babiwdth.

Program: NRMS Card(s) Type: C.I Required, if: afwags

Read List: (NCPX,NGX,IDSBW) Format: (3112)

Variable

NCPX

NGX *

-27-Variable CMP1 (1,NCP,NG) CMP1 (2,NCPNG) CMP1( 3,NCP,NG) CMP1(4,NCP,NG) CMP1 (5,NCPNG)

0

Jot compozition NCP, enegy gtoup NG x-diected dijnusion coejLicient (cm.) y-ditected dijlusion coe66icient (cm.)

Mactoscopic totii temovat ciozs 6ection (cm.

-(incude4 captuwe, 6isiLon, and cscatteving). Macvoscopic poduction .cvos section (cm.-1)

(neutxons pe("Lsion time 6ission cxozz section).

Macho.copic ission c'o.6s6 section (cm.~1).

0

Note: One caxd iz Aequied peA composition NCP 4o& each enegy gtoup NG. CWds 6o% _{at2 compositions NCPX ate enteAed togethet 6o& each gioup,} in o,%deA NCP = 1 to NCPX. Biock6 o6 aZL compositions ate enteced

by guoup in odex NG =1 to NGX.

0 Program: NRMS

Card(s) Type: C.2, group djjgusion paramete/s (excuding 6 catteving) Required, if: aCwayA

Read List: (CMP1(I,NCPNG),I = 1,5) 6o% NCP = I to NCPX

-28-Program: NRMS

Card(s) Typc: C.3, 'catte2ing coaa sectLons. Required, if: NGX > I

Read List: (CMP2(NCP,ID),NCP = 1,NCPX) Format: (GE12.1)

Variable

dot ID 1 to IDX

Description

Mac Ao.6copic ateting cw o ection {Jot tan 6leA Jtom NG1 to NG2 (cm.-I).

CMP2(NCP, ID)

where

ID = NG'2*(NG2-1)/2 - IG*(IG-1)/2

-lDX = NGX*(NGX-1)/2 - IGX*(IGX-1)/2

and

I= maximum (ONG2 - IDSBW)

(NG2-NG1-1)

IGX = NGX - IDSBW

.29.

BLANK PAGE

-30-Descripti on

Pxompt 6iszion .pecinm 6ot energy group NG (appiled to alC compositions ).

Program: NRMS

Card(s) Type: C.4, prompt 6ssion spectum -Required-, -if: NGX >1

Read List: (PCHI(NG),NG = 1,NGX) Format: (GE12. 1)

Variable

-31-Variable Description

IBC2P ' ntegveA PZag Jot boundaxy conditLon at maximum y bounday.

IBC1P Integev itag 6oft, bounday condition at maximum x boundauj.

IBC2M Integex 6tag 6or bounday condition at minimum y bounday

IBC1M Integer. ag 6o& boundaty condition at minimum x boundaty

BSQD Axiat buckling (cm.-2).

whexe jo'i the bounduj condition 6ag.

1

Program: .NRMS

Card(s) Type: D.2, boundaxy conditLon4

Required, if: alawdy

Read List: (IBC2P,IBC1P,IBC2M,IBCM,BSQD) Format: (4112,E12.1)

-32-Descripti on

Intege itag 6ot zetection oj ttanzvete Leakage apptoximation

<1 = constant apptoximation

7 = qtad/atic apptoximation Program: NRMS

Card(s) Type: E.1, titansve&6e Leakage contawct Required, if: atwags (deautt6 ptovided)

Read List: (ITLA) Format: (112).

Variable

-33-Program: NRMS

Card(s) Type: E. 2, outet iteation cont'ot Required, if: atug

Read List: (CCOT,WOTXITCA) Format: _{(E12.1, 2712)}

Variable Description

CCOT OuteA £teAation conveAgenc. ctitia (appLied to tegion aveuage tLux o,% Aegion avetage 6ission 6ouce depending on acceZLetation a6cheme zZected)

<0.0 dejauLts to 10-5

NOTX Maximum numb ie. o outeA iteAations _allowed

<0 dejaults to 100

-ITCA _Intege 4tag _{Jot zelecti-on o6 Chebyshev}

accetexation on the

64s.ion

1 = i oux

Program: NRMS

Card(s) Type: _{E.3, Chebyohev accetevation contoZ} Required, if: abtwag (deLauwt6 ptovided)

Read List: (IPSC,RNSC,RESC,ICLN,PRFN, POMX)

Format:

Variable Description

IPSC Numbet oj unacceteated intetations belote accetexation can be apptied

<0 de6auLts to 3

RNSC Avetage vot teduction uequited bejo/%e acceteataion can be atpptie.d

<0 dejauts to 0.025

RESC Poi.nvise etwo, >teduction Lequited bejofte acceLtvation can be apptie.d

-35-Program: NRMS

Card(s) Type: E.3, continued Required, if:

Read List: Format:

Variable Description

ICLN Minimum numbeA o outens done bejoe

convergence tate 1s examined and accetexaton patameters can be modi4ied

<0 deSauLts to 3

PRFN Miniwmum Aatio o6 actual _{conveAgence &ate} to theotetica2 conveigence Aate a2Zowed

<0 deauLts to 0.9

DOMX Maximum dominance Aatio atowed

<0 delawts to 0.999

-36-*

Variable Description

NION Minimum number og inne allowed peA oute itexation _{in each eneAgy goup}

<0 delaults to 5

ERIN Avexage exWo. teduction tequwxed jot the innenA ite ations in each eneAgy gtoup

<0 dejauttct to 0.01

CCIN Convexgence exitenia on the oveelaxation

jactot AoC detexntnation og optimum innex ite'tation patametex

<0 dejauLts to 0.1

NINX Maximum numbe o g i4eations allowed in deteAmination oj optimum inne iteation paAameteA6

<0 deSaults to 20 Program: _NRMS

Card(s) Type: E.4, innev iteAation contAot Required, if: atuwaz (delauto prwvided)

Read List: NION,ERIN,CCINNINX) Format: (112,2E12.1,112)

-37-Variable Description

ITPN Integev 6ag .t seiection oj powev

notmaLization

ptoceduxe-<1.= totai %eactot powe 2 = poweA dens6ity

PNRM _{Factor to which powex (ITPN) is nonazed}

5:0 deauLtes to 1.O

PFIS PoweA peM gis-ion

-<0 delauLts to 1.0

Program: NRMS

Card(s) Type: F. 1, pow&% nomaaization

Required, if: atwc% (detaultz puovided) Read List: IITPN,PNRM,PF1S)

-38-Description

TotaX numbeA o4 zone powet p~tint edit s ets <0 delauLts to 1

TotaX numbe.t o4 >tegion poweu print edit zets <0 delautts to 0

Tota numbet o >tegion 4tux p'tint edit set. <0 deaults ,.to 1

To.ta2 numbet oj >tegion pauttiat cuttent edit et6 <O dejauts to 0

Program: NRMS

Card(s) Type: G.1, edit cont/to

Required, if: attacryA

Read List: (NZPESX,NPPESXNPFESX,NPCESX) Format: (4112) Variable NZPESX NPPESX NPFESX NPCESX

-39-Variable

IZPES( 1,NZPES)

Description

Fot zone powve pAint edit zet NZPES

Minimum vatue oj the x-directed zone coo-dinate, ND1 de6Lautt6 to 1

I Z PES (2,NZ PES)

IZPES( 3,NZPES)

IZPES (4, N ZPES)

Maximum value oj the x-directed zone coodina.te, ND1 delaufts to ND1X

Minimum vatue o6 the y-directed zone coo'rdinate, ND2 delaults to 1

Maximum value o6 y-i&ected zone cootdinate, ND2 deautt6 to ND2X

Note: One cwLd is -equied _{6o,% each edit zet NZPES.}

0

Card(s) Type: G.2, zone powe pAint edit set deweniption Required, if: NZPESX> 0 (dejautt6 povided)

Read List: (TZPES(I,NZPES),I 1,4) 6o& NZPES = I to NZPESX)

Format: (4112)

0

Fo, egion powe& pkint edit z et NPPES

--MZnimum vaLue o the x-di&ected tegion cootdinate, NP1

Maximum value oj the x-directed Pzegion cooItdinate, NP1

Minimum value o the g-directed tegion coortdinate, NP2

Maximum value o6 the g-ditected tegion coordinate NP2

Note: One cutd is uequired jox each edit 6et NPPES. Program: NRMS

Card(s) Type: G. 3, tegion powe. pint edit set des c/tiption Required, if: NPPESX

>

Read List: (IPPES(INPPES),I = 1,4) Jot NPPES = 1,NPPESX Format: (4112)

-141-Variable

IPFES(Z, NPFES)

Description

.FoI Aegion avexage 6tux ptint edit set NPFES

--Minimum value o6 the x-di&ected tegion coodinate, NP1

dejautt6 to 1

IPFES (2,NPFES) Maximum value o6 the x-diected %egion cooLdinate, NP1

delaults to NP1X

IPFES(3,NPFES) Minimum vaZue o6 the y-diected tegion cootdinate, NP2

de auLts to 1

IPFES(4,NPFES) _{Maximum vatue} o6 the y-diected &egion coordiZnate, NP2

dejaalt6 to NP2X Program: N RMS

Card(s) Type: G.4, tegion ave'age Jtux pAint edit 6et deciption Required, if: WPFESX> 0 (dejaut6 povided)

Read List: IIPFES(,NPFESI = 1,6) Jot NPFES = 1 to NPFESX Format:

₄₁₁₁₂₎

Description

IPFES (5,NPFES) Minimum valtue index, NG

o4 the eneAgy group

deauLtts to 1

IPFES ( 6, NPFES) Ma.ximum vatue o6 the enexg y gioup inde x, NG

dejautt6 to NGX

Note: One cand as %equited Jox each edit zet NPFE. Program: NRMS

Card(s) Type: G.4, continued Required, if:

Read List * Format:

-043M

FoIL tegion paxtiat cuwLent edit set NPC ES

--Minimum value o the x- directed tegion cootdinate, NP 1

Maximum value oi the x-directed 'egion coordinate, NP1

Minimum value o j the y- dL'ected 'egion cootdinote, _NP2

Maximum value o6 the y-ditected Itegion

cooIdinate, NP2

Minimum vaf-ue oj theeneAgy goup index, NG

Maximum vatue o the enexgy gAoup index, NG

Note: One caxd is %equired

Lot

Card(s) Type: G.5, edit 6et descxnption Jot intetiace ave'age .eakage Required, if; NPCESX> 0 paJtiaX cwtents by %egion Read List: (IPCES(I,NPCES},I 1,6) 6o& NPCES = 1 to NPCESX

Format: (6712)

Variable Description

NDSR IntegeA itag Jot edit o4 Aolution to a zequentiat datcaset 4o ZateA u-6e by NRMT

<0 = no edit

"n" = edit to dataset uJedence numbet "n"

Program: NRMS

Card(s) Type: H.1, selection oj 6otution edit 6o twan&lent Required, if: a&ways (dejault ptovided)

Read List: (NDSR) Format: (112)

-45-3.6.2 NRMT Input

The input to NRMT Zs deuc'tibed in this section. Cakds axe gtouped by 6anction and indexed in each 6unctionaZ gtouping by sequentiaZ o'Ldeting. Requirement6 6ot inctusion c6 a catd, the Foxtttan tead izst, the &ead loxmat, and a descxiption oj caxd entties axe given 6o& each ca'd type. The 6unctionat goupingz ae

A. Heading

S. Static 'n&tia.ization ({xom NRMS dump) C. Neuton 4peeds

V. Detayed ptecu'sou E. Ti me dorrains

F. Pextubations

G. Ite-ation convexgence

A dezaciption each caxd type JoR-ows. A Lsting o6 input jot

the tttani.ent soution (with the quadatc tPansveuee teakage appoxi-mation and imipZicht ptecu so 6hape appioximation) oj the LRA Kineticz Bench-madk is given in Appendix B.3. A detaiLed deictiption o6 the phy.6icaL probelem can be Jound n Re.exence 1 ot Relexence 2.

-466-Variable Description

TTL De.ceiptive heading

Note: Two card6 ate equited.

Program: NRMT

Card(s) Type: A.1, heading Required, if: a&oay

Read List: (TTL(I),1 = 1,40) Format: (20A4)

-047-0

Program: NRMT

Card(s) Type: . 1, static sotution dataet

Required, if: atways6 Read List (NVSR)

Format: (112)

Variable _Description

NDSR _{Rejvtence numbe 6o% .6 equentia dataset}

containing static soZution

Description

Invetse o6j neuxton 6peed 6ot

enetgy gtoup NG (zec/cm.) Program: NRMT

Card(s) Type: C. 1, neut'on zpeed6 Required, if: afw&xy

Read List: (VI(NG), NG = 1,NGX Format: (2E12.1)

Variable

V I (NG)

-49-W

Description

Tota numbe,% o de(ayed ptecwu oL jamitez (NDFX 6)

Integex gtag ot tselection o6 ptecu o spatiaZ shape appuoximation

1 = "impicit" precutot sha.pe appo ximatXion

2 = 6tat" ptecuot shape appuLorximation Program: NRMT

Card(s) Type: D.1, detayed ptecutsot .contot and data

Required, if: atagjz Read List:. NDFX, JPSA Format: (2112)

Variable

NDFX

I PSA

-50-0

Variable

AMDA(NDF)

Description

Decay con.6tant 6o& precuuor 6amily NDF (.6ec.) Program: NRMT

Card(s) Type: D.3, deLayed pecuusot data Required, if: NDFX > 0

Read List: (AMDA(NDF),NDF = 1,NDFX) Format: (6E12.1)

Description

De2ayed 6>taction 6o,% p'tec6so[ 6amily. NDF Program: NRMT

Card(s) Type: D.2, _{detayed pxecuwsot data} Required, if: NDPX>0

Read List: (BETA(NDF),NDF = 1,NDFX) Format: (6E12. 1)

Variable

BETA(NDF)

0

Description

Tota2 numbVt oj time domainS (NTIMDX _<10)

-52-Program: NRMT

Card(s) Type: E.1, time domain contwt Required, if: atwcy4

Read List: '(NTIMDX) Format: (112)

Variable

Description

For time domain NTITMD

--TFINAL(NTXMD)

NTSPTD (NTlMD)

IEDFRQ(NTIMD)

TEDLVL (NTIMD)

FinaZ time (6ec.)

To-tal number o6 timestep6

Pkint Edit Frequency (number P6 timeutepz)

Print edit ZeveZ indicatot

whee-Continued on next page. Program: NRMT

Card(s) Type: E.2, time domain cont&oZ Required, if: allags

Read List: (TFINAL(NTIMD )NTSPTD{ NTIMD EDFRQ(NTT MD )I EDLVL (NTIMD) Format: (E12.1, 3112) o NTI TMD = 1 to NTIMPX

Variable

01

u--51.-Program: NRMT

Card(s) Type: E.2, time domain Required, if: Read List: Format: Variable controt, continued Description

IEDLVL = LKI a 6ow digit integen -and

I -- 1.eection jtag Jot zone aveage powev density edit

0 = no edit 1 = edit J -- .etection 6tag .6Lux edit. 0 = no edit 1 = edit K -- 6etection itag ptecuuso& edit '0 = no edit 1 = edit

Jot tegion avetage

Jot xegion avevage

L -- zetection 6Lag jot tegion. aveAage

"6&equency" edit 0 = no edct

1 = edit

-55-Variable _Description

NTPRTX _{NumbeA oi time intexuaLs ( nonovejtapping) 6jo&} which matetiat composition pejttuhaton- ate deined

NI PRTX 10)

0#

Card(s) Type: F. 1, pertubation conttoZ and data

Required, if: ab&afg

Read List: NiPRT)( Format: ₍₁₂₎

Variable

NCPRTX(NIPRT)

Description

Fot peAtubation intewat NIPRT

--Tota numbe o6 compositionz pertubed in thi6 intevat

(NCPRTX< 10)

TIPRTX ( 1,NIPRT)

TIPRTX(2,NIPRT)

Time (6 ec. ) at which LineaA &a=p petubation begin6

Time (4ec.) at'which 'eineaA Aamp pe4tubation ends

Note: One caxd is 4equied 4ot each pentabation intevat NIPRT. Catd(s) type F.3, F.4, and F.5 must 4olow each associated caxd type F.2. Program: NRMT

Card(s) Type: F.2, pentabation controi and data Required, if: NIPRTX> 0

Read List: '(NCPRTX(NIPRT),(TIPRTX(I,NIRPT),I = 1,2)

)

-57-Variable

ICPRTX(NCPRT ,NI PRT)

Description

The composition index o the NCPRTth compO4i-tion which is pettutbed in the petubation intetvat NIPRT

0

Note: This catd type Jo22ow4 ea.ch associakted ca.td type F. 2 in the input stteam. At teast one catd izs >eqttdted Jot each

peAitubation intexuaL.

0

Card(s) Type: F.3, pertubation conttot and data

Required, if: NIPRTX.> 0

Read List: (ICPRTX(NCPRT,NIPRT) ,bNCPRT = 1,NCPRTX(NIPRT)) FOR NIPRT = 1 to NIPRTX

Format: (6112)

Fo the. NCPRTth composition wi&ch is petubed in gtoup NG in the pettubation inteivaZ NIPRT

--Change in x-ditected diZ sion coejicient (cm.)

Change in y-ditected di6usion coeLicient (cm.)

Change in the macveocopic tota2 emovat cxozz z ection ( cm.-1 )

Change in the macos copic ptoduction cios section

Change in the .mac owcopic {jZsion cto.s ection

Note: AUZ compositions NCPRTX(NIPRT) ae btocked by gtoup and otdeed

NCPRT = 1 to NCPRTX(NIPRTX). _{Biocks oj al compozitions ate}

oLdeted by gioup as NG = 1 to NGX. These cad6 joLfow each. asociated cad(6) _{type F. 3 in the input steam. At Zeast one cad is %equiAed}

Jot each pettukbed composition, each goup, and each petubation

.nteAvai. Program: NRMT

Card(s) Type: F.4, pe.tubation data Required, if: NIPRTX> 0

Read List: '(PRT1(1,NCPRT,NGNIPRT),I= 5)

6o&

-59-0

Variable

PRT2 (NCPRT,NIPRT)

Description

Change in the macros opic downs catteting

cross section in the NCPRTth petutubed composition

6o&

Note: This caid type Zs &equired t two -gtoupp'boblems onky. At teast

one cad is %equited jo% ea.ch pektubation intevua2. ThLis cwd(6)

type jotlowz cand(z) type F.4 in the input stAeam.

0

Program: NRMT

Card(s) Type: F.5, pevttubation data Required, if: NIPRTX> 0, NGX = 2

Read List: (PRT2.(NCPRTNIPRT) ,NCPRT=1, NCPRTX(NIPRT))

Description

Convegene citexia jot the zpatia2 itetation4 petdotmed at each timeztep

10- 3 _recommended) Program: NRMT

Card(s) Type: G.1, itetation controZ Required, if: atayz

Read List: (CONV) Format: _{(E12. 1)}

Variable

-61-3.7 ?Pinted Ouput 3.7.1 NRMS Output

The printed output orm the input proces.sing og NRMT is e en-tia2Zy ze2i-expianatoty and only a Jew btie comments wilU be made hexe. This output is divided into essentialZy the. same patitions a the input catd gtoups: geomet y, neutxonics , boundaxy condZtions., and centuot paxametenu. The notation used jot code vatiabes in editing is the .6ame aus tha.t appeaxing in this teport. These edits axe pteceded by a Listing o6 the input c=rd "images." and

60oZowed

uzext. The patametex which L6 useu2 is the tota. unused cote. which the use& may employ to teduce the s6toft-age costs in simiLax subsequent executions.

The input processing editing Z6

60oLowd

paametes Jot the inne. iteAationz (the s patiaZ itexations within each guoup

duting a powet ok outer ite'ation) appeas. The Labets appeating in this P-dit are,.

NG - ene'gy goup index

SR -- estimated 6quate oJ the spectxaL adius o the associated

Jacobi -tea-tion matxix

PNT-MIN - minimum vaZue estimated 6tom the pointwise.

s-olution

NORM - "aveAage" vaLue estimated 'om zotution no9rm

PNT-MAX - maximum vatue etimated J,'om the pointwis e

-"62-0MG - eutimatd optmum ove.a.a&on' rxt~tcmetVL SoL scce-6,sive ovevela&tion

PNT-MIN- minimunm vatuee. ,ystimatd Jkcm the poinwi&se

NORM -"ctve/~tge vcdue .timctted Qtcm .6o!twton no/-tLm.s

PNT-MAX - rax-&rim vatue es-timacte~d om the poittZs e

IT-TOT - nwrmbeA oj .itemt~onz~ used -to: e..6Iinpcte pJ.rnete/ CONV - covetgence teveE ahi.-eve~d in -Ltma.tionz

10-MIN- rri-ni&nwn nwibvr. o4 innf. A ite'titons allowed pex

oLutL .{teLtionf

10-USE -ac-tuaZ nwribeA o iytybcet, pe!L owteL necust 5 (-to

achee cdcqwLzte conve.'tgence

T-E-R - thcoteticati mt Aeducon jctoIL SoiL 10-USE

.Lnne/m PeAk oute/t

A eswnrnay o6 owteAt -te~tttion %euts 6jo-towi,. The !tbet&z cppetz~ing in the edt t ze.:

IT # -owtex Ztetaiuon nwnbet.

PUT-MWL, -tmn-nwn %at~o vj zce6s-Lve uzegion--aee/,r.ge 4s-ion

NORM -- "cve/age" x'a.tic (in .the no'wi) o6 6uce66ve

IAeg90n avexa~ge. 64-)6tn .0wtce . (OA~ 6-tx) e,6tCmates

PUT-MAX - maximum &atio o6 scce/s61ve t-'LCUopt LZvVLge j-,sion- . outcc (oIl iLac) mtimatez

AVG-ERR - taat~tve evto't. (in -the no-un) oj5 Legion ave/Lige 6i.6.6ion .6oWce (ott.PL*Six

PUT-'ERR- maximum tetti'e poin-tw-Ze eAVr~ok o6 -the %~egion avv~age 6-L.6ion souLIce. (o.,Ltitx1

CP # -otdet o6 Chebqzhcv potjncr~a?2 used 601L oute}

DR-U - dominance >tatio cuvtentty u- sed

DR-P - revised estimate oj the dominance natio

ERR' RED- emxot >teduction jactot (in .the norm) 'achieved by acceteaton PERF - 'tio oj actuac to theoteticat etco& keduction, the

acceteetation pe otmajice iratio.

Fina2Zy, 6otution edit6 ade pe.nsented. A.s pteviousty noted, the zone avewage powe density, tegion avetage powex density, tegion avetage i&ux, and >tegion intetjace-avetage pantial cutiVents ate edited depending on ze2ection o6 edit options by the u.sex.

The owtput o6j the steady state soution o4 the LRA Kinetics

Benchma'k piobtem is shown in Appendix B.2. The input 6oT this ptobtem i6 given in Appendix B.1. The pobtem i.6 a quattelt cote tep'Lezentation

oj a BWR with 49 matxria zones, .six compositions and two enex.gy g-toups. DetaiLsZ o6 the probtem de.sciption ate ptesented in Relexence. 1 and 2.

3.7.2 NRMT Output

Although 6uLLZ poblem intialization is done jtom a NRMS 6olution dump, this injowation is not edited by NRMT. Only intomation ide;t6yin₉ the NMS exectution s given. This inSomation conzists

oj the date and time o6 day (obtained by MIT installation dependent outines) a.d the NRMS p'oblem tite. This initiazization in4otmation. appeaus at the beginning o6 the ottput.

Following is output 0A'rnm the input proces 'ing ol time-dependent data. The _{ZabeL~ng use/s vaiiables deined in the tepott and should} be essentia2y 6e6-expLanatoty. A 6ummary oj unused cote stomage is also given.

The output o the cacitation itsete is not paticulauiy sttaightsotaad because e sentia!2y no &abeting is ptesent. At the statt oj each time domain the joelowing ingotmation Zs given in the o/tdet Listed hee:

1) time domain index-2 ) ztanuting time .s ec.)

3) ending time (4ec.)

4) tota2 numbeA o4 timestepz

5 ) time-tep size (,sec..) 6) edit tequency

7) edit Zeve2

8) squatte o the >teat uccmponent o . the specttat tadiu's oj _the asociat.ed Jacobi itexation mattix.

9) zquate o the imaginaty component og the specttat >tadius