COBRA-WC: A Version of COBRA for Single-Phase … · Multiassem bly Thermal Hydraulic Transient...

COBRA-WC: A Version of COBRA for Single-Phase Multiassem bly Thermal Hydraulic Transient Analysis

July 1980

Prepared for the U.S. Department of Energy under Contract DE-AC06-76RLO 1830

Pacific Northwest Laboratory Operated for the U.S. Depilrtment of Energy ,

by Battelle Memorial lnsZDtute

Tkir r q m ~ was prapar J a s n amaunt at w ~ r b ap U & & ~ ? ~ l r ~ & v ~ c A ~ e ~ , kcsieher the U H & ~ noa tlm Clepartment of Fnclr&y, mar any of &air nar MY bl fh i r €4~18- dbmntmm+ ,h@lgeea rnalk% any wdr~anQ, e r p m , ~ S@M, w wum arly $gat Yiattilky oa rwlponribiifty for Ihe aew~ggy* - amml- sfusaW#~~s 9t any infmm~ion, apparaqs. pduet a pmrers d k h d . ~~~r'npreanatrhot its y v hmt InWm @iir~te.--d right?++ 4 L I

>

- R.. uiwr, epinkl* ~d an(limxi jn t ~ m ripen w thou t b A- m I

q e e m thiW CPf O@ %tes Geverma~lt of f b United States 43qwunemt of ber&y, r4Y

PACIEK NORTHWEST LABORATORY aperatled hy

BATTEUE for the

UNrTED STATES DEPARTMENT Of ENERGY Under Conr.r4ct DE-AC0676RlO 7830

COBRA-WC: A VERSION OF COBRA FOR SINGLE-PHASE MULTIASSEMBLY THERMAL HYDRAULIC TRANSIENT ANALYSIS

T. L. George K. L. Basehore C. L. Wheeler W. A. P ra ther R. E. Masterson

J u l y 1980

Prepared f o r the U.S. Department of Energy under Cont rac t DE-AC06-76RLO 1830

P a c i f i c Northwest Laboratory Rich1 and, Washington 99352

DOE R~ch land . W A

CONTENTS

SYMBOLS AND NOTATIONS

1.0 INTRODUCTION . 2.0 SUMMARY . 3.0 CONSERVATION EQUATIONS .

3.1 FLUID CONTROL VOLUMES . 3.2 CONTINUITY EQUATION . . 3.3 FLUIDENERGYEQUATION . 3.4 AXIAL MOMENTUM EQUATION . 3.5 TRANSVERSE MOMENTUM CONTROL VOLUME . 3.6 TRANSVERSE MOMENTUM EQUATION . 3.7 ROD ENERGY EQUATION . 3.8 CLADDING ENERGY EQUATION . 3.9 WALL ENERGY EQUATION

3.10 HEAT GENERATION AND TRANSFER TERMS

4.0 SOLUTION TECHNIQUE . 4.1 ENERGY SOLUTION

4.2 MOMENTUM AND CONTINUITY SOLUTION . 4.2.1 PSOLVE Scheme

4.2.2 RECIRC Scheme

4.3 BOUNDARY'CONDITIONS AND OTHER EQUATIONS . 4.3.1 Network Model

4.3.2 R a d i a l Thermal Boundary C o n d i t i o n

4.3.3 F r i c t i o n F a c t o r s and F i l m C o e f f i c i e n t s

4.3.4 M i x i n g C o r r e l a t i o n s . 4.3.5 E q u a t i o n o f S t a t e .

5.0 OVERALL CODE DESCRIPTION . 5.1 INPUT SUBROUTINES . 5.2 SOLUTION OF THE CONSERVATION EQUATIONS . 5.3 DATA STORAGE .

5.3.1 DUMP and RESTART .

6.0 NODING, INPUT PARAMETERS AND NODING CONVENTIONS . 6.1 NODING LMFBR ASSEMBLIES . 6.2 NODING OTHER FLOW PATHS . 6.3 A X I A L NODES AND TIME STEPS . 6.4 CONVERGENCE CRITERIA

6.5 DAMPERS AND ACCELERATORS . 7.0 COBRA-WC INPUT .

7.1 GENERAL DESCRIPTION . 7.2 CARD GROUP SUMMARY . 7.3 COBRA-WC INPUT INSTRUCTIONS .

8.0 PROGRAM SPECSET

8.1 SPECSET INPUT . 9.0 PROGRAM GEOM .

9.1 GEOM INPUT

REFERENCES . APPENDIX A: SUBROUTINE DESCRIPTIONS . APPENDIX B: VARIABLE L I S T . APPENDIX C: COMDECKS . APPENDIX D: CONTROL STATEMENTS FOR REDIMENSION . . APPENDIX E: SAMPLE PROBLEMS .

FIGURES

1 Poss ib le Cont ro l Volume Shapes Using t h e Genealized Subchannel Noding Approach .

2 Transverse Momentum Cont ro l Volume f o r Standard Subchannel Nodi ng .

3 Cross Sect ion o f COBRA-WC Model f o r a Nuclear Fuel Rod .

4 Cross Sect ion o f COBRA-WC Model f o r a Heat-Conducti ng Wall

5 Schematic Desc r i p t i on o f t h e Network Model f o r Pressure Drop Through Reactor Vessel

6 Flow Chart f o r COBRA

7 Flow Chart Subrout ine SCHEME . 8 Flow Chart f o r Subrout ine R E C I R C . 9 Ar ray Equivalency t o F a c i l i t a t e Data

Management f o r t h e R o l l Opt ion

10 Standard Subchannel Noding f o r a 19-Pin Bundle . 11 Lumped Subchannel Noding f o r a 61-Pin

Blanket Assembly . 12 Ax ia l Fuel P i n Model Showing t h e M a t e r i a l

Typed Assuded fo r Each Computational C e l l . 13 Samples o f GEOM Rod and Channel Numbering System . 14 Optimal GEOM Numbering Scheme f o r Standard Subchannel

Noding o f a 37-Pin Bundle

15 D e f i n i t i o n o f Wrap S t a r t i n g Angle and Ro ta t i on D i r e c t i o n .

SYMBOLS AND NOTATION

* @: r e f e r s t o donor c e l l quan t i t y , e.g., Q j = J + v j < O

Qi - set o f gap numbers f o r gap which connect channel i t o adjacent channels

X i - se t o f r od numbers f o r rods which connect t o channel i

T - se t o f wa l l numbers f o r w a l l s which connect t o channel i i

'n - set o f channel numbers f o r channels w i t h a thermal connect ion t o rod n

5, - se t o f channel numbers f o r channels adjacent t o wa l l m

ek - m u l t i p l i e r ( f l ) which g ives the c o r r e c t s i gn t o the t ransverse

connect ion terms

- se t o f m a t e r i a l s which make up w a l l w

SUPERSCRIPT

n - t ime s tep l e v e l

SUBSCRIPTS

c - r e f e r s t o c l add ing

f - r e f e r s t o f u e l o r m a t e r i a l r e p l a c i n g f u e l i n the p i n model

g - f u e l - c ladd ing gap

i - subchannel number or genera l ized subsc r i p t f o r m a t r i x n o t a t i o n

j - a x i a l l e v e l o r genera l i zed subsc ip t f o r m a t r i x n o t a t i o n

'I)- r e f e r t o channel numbers on e i t h e r s ide o f a t ransverse gap

J J

k - t ransverse gap number

m - wa l l number

n - rod number

w - r e f e r s t o heat coi tduct i ng wa l l

VARIABLES

2 A - subchannel area ( f t )

*H TR 2 - e f f e c t i v e area fo r heat t r a n s f e r f rom a rod ( f t )

A~~~ 2 - area fo r heat t r a n s f e r f rom a w a l l ( f t )

2 A,- - area for t ransverse f low between channels ( S x) ( f t )

c - f l u i d s p e c i f i c heat ( ~ t u / l bm-OF)

C - a x i a l l oss c o e f f i c i e n t

Cc - c ladd ing spec if i c heat ( ~ t u / l bm-OF)

f - f u e l s p e c i f i c heat (~ tu / l bm-OF)

Cw - e f f e c t i v e wa l l heat capac i t y ( B t u / l bm-OF)

C T - t ransverse loss c o e f f i c i e n t

DH - channel hydrau li c diameter = 4* AREA/WETTED PERIMETER

Dw - w a l l w id th ( f t )

f - f r i c t i o n f a c t o r

h - f l u i d enthalpy (Btu/lbm)

H - channel f i l m c o e f f i c i e n t ( ~ t u / s e c - f t ~ - ~ F )

Hg - fue l - c l add ing gap conductance ( ~ t u / s e c - f t 2 - O F )

2 0 HR - r o d f i l m c o e f f i c i e n t (B tu /sec- f t - F )

HW - w a l l f i l m c o e f f i c i e n t ( ~ t u / s e c - f t ' - ' ~ )

K - f l u i d c o n d u c t i v i t y (Btu/ f t -OF)

Kf - f u e l c o n d u c t i v i t y ( ~ t u / s e c - f t - O F )

Kw - w a l l c o n d u c t i v i t y ( ~ t u / s e c - O ~ - f t )

R - leng th o f t ransverse momentum c o n t r o l volume ( f t )

rn - a x i a l f l o w r a t e (lbm/sec) 2 P - f l u i d s t a t i c pressure ( l b f / f t )

q - heat depos i t i ed i n f l u i d (Btu/sec)

qf - heat generat ion i n the f u e l (Btu/sec)

qw - heat generat ion i n t he w a l l (Btu/sec) 3

q " ' - volumentr ic heat generat ion i n f u e l (B tu / sec - f t ) 3 " ' - vo lume t r i c heat generat ion i n w a l l (B tu / sec - f t ) qw

r - r a d i a l l o c a t i o n i n t h e r o d ( f t )

Rc - ou te r r a d i u s o f t he c ladd ing ( f t )

Rf - ou te r r a d i u s o f the f u e l m a t e r i a l ( f t )

S - t ransverse gap w id th ( f t )

A t - t i m e step (sec)

T - f l u i d temperature (OF) h

T - average f l u i d temperature around a rod (OF)

tw - e f f e c t i v e wa l l th ickness f o r heat storage ( f t )

- e f f e c t i v e wa l l th ickness f o r heat generat ion ( f t )

Tc - c ladd ing temperature (OF)

Tf - f u e l temperature (OF)

Tf s - temperature o f t he f u e l sur face (OF)

Tw - w a l l temperature (OF)

u - t ransverse v e l o c i t y ( f t / s e c )

U - e f f e c t i v e wa l l conductance ( ~ t u / s e c - f t ~ - ' ~ )

v - a x i a l v e l o c i t y ( f t / s e c )

W~ - c ross f low due t o t u r b u l e n t exchange (lbm/sec)

A X - a x i a l s tep ( f t )

Yc - c ladd ing th ickness ( f t )

Z - f a c t o r f o r e f f e c t i v e f l u i d r a d i a l conduct ion l eng th

B - c o e f f i c i e n t f o r t u r b u l e n t m ix ing

"a - a x i a l power f a c t o r

"r - r a d i a l power f a c t o r

" t - t r a n s i e n t power f a c t o r

0 - problem o r i e n t a t i o n , angle f rom v e r t i c l e (degrees) 3 p - f l u i d dens i t y ( l b rn / f t )

3 Pc - c ladd ing dens i t y ( I b m / f t )

3 Pf - f u e l d e n s i t y ( l b m / f t )

3 w - e f f e c t i v e wa l l d e n s i t y ( I b m / f t )

@ - rod-to-channel heat f r a c t i o n

1.0 INTRODUCTION

The o b j e c t i v e of t h i s r e p o r t i s t o p rov i de t he user of t he COBRA-WC (Whole

Core) code a b a s i c unders tanding o f t h e code o p e r a t i o n and c a p a b i l i t i e s .

Inc luded i n t h i s manual a re t h e equa t ions so lved and t he assumptions made i n

t h e i r d e r i v a t i o n s , a genera l d e s c r i p t i o n o f t h e code c a p a b i l i t i e s , an explana-

t i o n o f t he numer ica l a lgo r i thms used t o s o l v e t h e equat ions, and i n p u t

i n s t r u c t i o n s f o r u s i n g t h e code. Also, t h e a u x i l i a r y programs GEOM and SPEC-

SET are descr ibed and i n p u t i n s t r u c t i o n s f o r each are given. I n p u t f o r

COBRA-WC sample problems and t h e cor responding ou tpu t a re g i ven i n t h e

append i ces .

The COBRA-WC code has been developed f r om t h e COBRA-IV-I(') code t o

analyze L i q u i d Meta l Fast Breeder Reactor (LMFBR) assembly t r a n s i e n t s . I t was

s p e c i f i c a l l y developed t o analyze a co re f l o w coastdown t o n a t u r a l c i r c u l a t i o n

coo l i ng . I n t h i s t r a n s i e n t , s ing le-assembly a n a l y s i s i s no t s u f f i c i e n t s i n c e

heat t r a n s f e r between ad jacen t assembl ies and in te rassembly f l o w r e d i s t r i b u t i o n

can be s i g n i f i c a n t , p a r t i c u l a r l y i n heterogeneous cores. The COBRA-WC core was

designed t o model many assemblies s imu l taneous ly and can account f o r these

in te rassembly e f f e c t s .

The bas i c subchannel na tu re o f t he COBRA-11-1 code has been r e t a i n e d i n

t h e COBRA-WC code and t h e equa t ions so lved a re e s s e n t i a l l y t h e same, a l though

t h e new code i s l i m i t e d t o s ing le-phase problems. The COBRA-WC code c a l c u l a t e s

a s o l u t i o n t o t h e incompress ib le subchannel conse rva t i on equat ions f o r mass and

momentum and so lves energy equa t ions f o r t h e coo lan t , c ladd ing , f u e l and o t h e r

heat -conduct ing media i n t h e core. The equat ions a re a l l so lved f u l l y i m p l i c -

i t l y t o a l l o w t he use of l a r g e t ime s teps i n l ong LMFBR t r a n s i e n t s as w e l l as

p r o v i d e f o r s teady s t a t e s o l u t i o n s . Whi le t h e code was developed t o o b t a i n

r e s u l t s f o r t he n a t u r a l c i r c u l a t i o n t r a n s i e n t , i t s use i s no t l i m i t e d t o t h i s

problem. COBRA-WC has a1 1 t h e s i ngle-phase capabi 1 i t i e s o f t h e COBRA-IV-I code

and can be app l i ed t o many o f t he problems t h e COBRA-IV-I code has been used

f o r . The subchannel model ing approach used i n COBRA-WC makes t h e code s u i t a b l e

f o r o b t a i n i n g d e t a i l e d f l o w and temperature d i s t r i b u t i o n s f o r one o r severa l

assembl ies and l e s s d e t a i l e d r e s u l t s on a core-wide bas i s .

Since COBRA-WC was w r i t t e n t o so l ve l ong t r a n s i e n t problems, c o n s i d e r a b l e

a t t e n t i o n was p a i d t o r educ ing the computat ion t ime whenever p o s s i b l e . Some

success has been ob ta i ned i n t h i s area w i t h t h e COBRA-WC code s o l v i n g s tandard

COBRA-IV-I problems i n as l i t t l e as one-quar ter o f t h e t ime r e q u i r e d by t h e

COBRA-IV-I code w i t h o u t s a c r i f i c i n g any o f t h e p h y s i c a l model ing o r any d e t a i l

i n t i m e and space. Also, t he COBRA-WC code i s capable o f r unn ing some t r a n -

s i e n t s which c o u l d n o t be r u n u s i n g t h e COBRA-IV-I code due t o numer ica l

i n s t a b i l i t i e s r e s u l t i n g f r om the e x p l i c i t ( i t e r a t i v e l y ) c o u p l i n g between t h e

r o d and c o o l a n t energy equa t ions .

As t h e code i s re leased and begins t o ge t wider usage, e r r o r s i n t h e code

w i l l undoubted ly be d iscovered. Users a re encouraged t o p r o v i d e t h e developers

w i t h a d e s c r i p t i o n o f t h e d i f f i c u l t i e s encountered w i t h COBRA-WC so t h a t these

problems may be remedied i n f u t u r e e d i t i o n s o f t h e code. It i s hoped t h a t t h i s

manual w i l l p r o v i d e enough i n f o r m a t i o n f o r a person knowledgable i n the rma l -

h y d r a u l i c s t o app l y t h e code e f f e c t i v e l y .

2.0 SUMMARY

The COBRA-WC code r e t a i n s many o f t he u s e f u l f ea tu res o f t he COBRA-IV-I

code. The most s i g n i f i c a n t f e a t u r e s are l i s t e d below.

1. The subchannel model ing approach has been re ta i ned .

2. The card group i n p u t format , though modi f ied t o a l l o w f o r t h e a d d i t i o n a l

i npu t , i s b a s i c a l l y t he same.

3. The equat ions so lved a re t h e same as those i n COBRA-IV-I, and f i n i t e d i f -

fe rence form s i m i l a r .

4. The c a p a b i l i t y t o so l ve large-bundle o r many-channel problems us ing

p e r i p h e r a l s to rage devices has been re ta i ned .

5. W i re-wrapped and g r idded assemblies are so lved i n e s s e n t i a l l y t he same

manner as i n COBRA-IV-I.

6. The or thogonal c o l l o c a t i o n method i s used t o model t h e f u e l p i ns .

7. "Dump" and "Res ta r t " c a p a b i l i t i e s have no t been changed.

8. The a u x i l i a r y program GEOM can be used t o generate i n p u t da ta f o r LMFBR

assemblies.

9. The a u x i l i a r y program SPECSET i s used t o red imension t h e COBRA-WC common

b lock v a r i a b l e s t o a l l o w f l e x i b i l i t y i n problem s i ze .

There are a few c a p a b i l i t i e s t h a t were removed f r om COBRA-WC i n t he

i n t e r e s t s o f c r e a t i n g a code t h a t cou ld per fo rm LMFBR ana l ys i s w i t h t h e smal-

l e s t p o s s i b l e computat ion t ime.

1. The two phase c a p a b i l i t y has been removed, r e s t r i c t i n g the use o f the code

t o f l u i d c o n d i t i o n s p r i o r t o b o i l i n g .

2. The f u l l y temperature dependent f u e l p r o p e r t y c a p a b i l i t y was removed and

rep laced w i t h a s imple b u t much f a s t e r approx imat ion t h a t accounts f o r t h e

temperature dependence o f the f u e l p r o p e r t i e s on a more average bas is .

3. A x i a l conduc t ion i n t h e f u e l o r coo lan t i s no t considered.

4. The l i n e p l o t t i n g c a p a b i l i t y i n COBRA-11-1 has been removed.

Some f e a t u r e s o f the COBRA-WC code s u b s t a n t i a l l y i nc rease the c a p a b i l i t i e s

over those o f COBRA-I V - I . 1. The energy equa t ions f o r t he r od and coo lan t are so lved s imu l taneous ly

r a t h e r than i t e r a t i v e l y , e l i m i n a t i n g a severe r e s t r i c t i o n on t i m e s tep

s i z e f o r c e r t a i n LMFBR t r a n s i e n t s .

2. The sub rou t i ne XSCHEM i n COBRA-IV-I was rep laced by a much f a s t e r scheme,

RECIRC, which can be used t o so l ve problems w i t h f l o w r e c i r c u l a t i o n .

3. The i n p u t has been mod i f i ed t o make i t eas ie r f o r t h e user t o app l y t h e

code t o mu l t iassembly problems.

4. In te rassembly heat t r a n s f e r nodes are a u t o m a t i c a l l y generated a t t he

u s e r ' s reques t .

5. Sodium p r o p e r t i e s c o r r e l a t i o n s are a v a i l a b l e i n t e r n a l l y t o t he code as a

d e f a u l t op t i on . Other c o o l a n t p r o p e r t i e s may s t i l l be i n p u t i n t a b u l a r

form.

6. A v a r i e t y o f use r -de f i nab le f o r c i n g f u n c t i o n s has been added t o make t h e

code more f l e x i b l e .

7. A f l o w r e d i s t r i b u t i o n o r network model was added t o COBRA-WC t o account

f o r i n te rassembly f l o w r e d i s t r i b u t i o n t h a t may occur d u r i n g low f l o w o r

n a t u r a l c i r c u l a t i o n t r a n s i e n t s . I n con junc t i on w i t h t h i s network model,

t h e code was g i ven t h e c a p a b i l i t y o f c a l c u l a t i n g an i m p l i c i t t r a n s i e n t

s o l u t i o n when a t ime-dependent pressure drop i s s p e c i f i e d .

8. V a r i a b l e a x i a l s tep s i z e has been i nc l uded t o a l l o w users more model ing

f l e x i b i l i t y and t o save computer t ime and storage.

9. For many problems a d i r e c t s o l u t i o n o f t h e momentum equat ions a t each

a x i a l l e v e l i s much f a s t e r than us ing t he i t e r a t i v e procedure o f

COBRA-IV-I. An o p t i o n e x i s t s i n COBRA-WC t o use t h e d i r e c t - i n v e r s i o n

technique.

10. The conduc t ing w a l l model was modi f ied t o o p t i o n a l l y couple t o a s i n g l e

coo lan t node r a t h e r than t o c o o l a n t nodes on bo th s i des t o model addi -

t i o n a l t r a n s i e n t heat c a p a c i t y e f f e c t s . Heat genera t ion w i t h i n a w a l l may

a l s o be modeled.

11. A v a r i e t y o f o the r minor m o d i f i c a t i o n s were made t o reduce s to rage and

computer r unn ing t imes.

I n the sec t i ons which f o l l o w , t he COBRA-WC equat ions and t he methods o f

s o l u t i o n are discussed, t h e code o r g a n i z a t i o n descr ibed, i n p u t i n s t r u c t i o n

given, and sample problems presented.

3.0 CONSERVATION EQUATIONS

The COBRA-WC code was developed t o s o l v e equat ions f o r t h e conserva t ion

o f mass, momentum, and energy i n a r o d bundle o r p o r t i o n o f an LMFBR core. The

equat ions are e s s e n t i a l l y t he same as those found i n t h e COBRA-IV-I code w i t h

a few f u r t h e r s i m p l i f y i n g assumptions which w i l l be d iscussed l a t e r .

The equat ions have been de r i ved by per fo rming s u i t a b l e balances on f i n i t e

c o n t r o l volumes. The f i n i t e - d i f f e r e n c e equat ions found i n t h e code come

d i r e c t l y f r om these balances so no a t tempt w i l l be made t o o b t a i n t h e p a r t i a l

d i f f e r e n t i a l equat ions f rom t h e f i n i t e - d i f f e r e n c e equat ions a l though a term-

by- term correspondence w i l l be po in ted ou t .

The presence o f t h e rods i n an assembly and t h e coarse noding make i t

necessary t o make some approx imat ions and assumptions f o r some o f t h e terms i n

t h e conse rva t i on equat ions and these assumptions a re noted a f t e r each equa t ion .

3.1 FLUID CONTROL VOLUMES

The f l u i d c o n t r o l volume f o r c o n t i n u i t y , energy, and a x i a l momentum i s

cha rac te r i zed by i t s c r o s s - s e c t i o n a l area a v a i l a b l e f o r f l ow , t h e h e i g h t Ax and

t he w i d t h S o f t he connect ion between i t s e l f and an ad jacen t c o n t r o l volume.

F i g u r e 1 shows t h r e e conce ivab le shapes f o r t h e c o n t r o l volume w i t h l a be ing

t he s tandard subchannel c o n t r o l volumes. Any s e r i e s o f c o n t r o l volumes con-

nected a x i a l l y i s cons idered a subchannel. I n t h e equat ions presented i n t h e

n e x t sec t ion , t he f i n i t e - d i f f e r e n c e terms are w r i t t e n w i t h t h e cor responding

d e s c r i p t i o n and p a r t i a l d i f f e r e n t i a l fo rm g i ven i n b racke t s immediate ly below.

The l i s t o f symbols and n o t a t i o n a t t he beg inn ing o f t h i s document should be

r e f e r r e d t o f o r exp lana t i on o f t h e n o t a t i o n used.

A C

FIGURE 1. Poss ib le Contro l Volume Shapes Using the General ized Subchannel Noding Approach a) Standard Subchannel Noding b ) Lumped Subchannel Nod i ng c ) Noding f o r F l u i d Not i n a Rod Ar ray

3.2 CONTINUITY EQUATION

mass rmass t ranspor ted l a t e r a l l y

Here and i n t h e f o l l o w i n g equat ions the subchannel s u b s c r i p t i has been

omi t ted where the re fe rence i s c l e a r . The assumptions made i n t he d e r i v a t i o n

o f t h e c o n t i n u i t y equat ion are t h a t t he channel area changes l i n e a r l y w i t h

d is tance over t he l eng th o f the c o n t r o l volume, the f l u i d d e n s i t y i s un i f o rm

throughout t h e c o n t r o l volume, t h e a x i a l and l a t e r a l v e l o c i t i e s g i v e t h e b u l k

f l o w r a t e through the respec t i ve areas, and the l a t e r a l connect ion w id th i s

constant over the l eng th o f the c o n t r o l volume. Donor c e l l d i f f e r e n c i n g i s

used f o r t h e convected q u a n t i t i e s as i n d i c a t e d by t h e a s t e r i s k .

3.3 FLUID ENERGY EQUATIONS

energy s torage

energy t ranspor ted a x i a l l y 1 energy t ranspor ted

1 a t e r a l l y

+ [ rod heat f l u x I + [wall heat f l u x I

conduct ive heat I + [ t u r b u l e n t energy t rans fe r l a t e r a l l y exchange I

I n a d d i t i o n t o t h e assumptions made f o r t h e c o n t i n u i t y equat ion, i t i s

assumed i n t he energy equat ion t h a t t he f l u i d en tha lpy i s un i f o rm throughout

t h e c o n t r o l volume and t h a t t he re i s no a x i a l heat conduct ion i n the f l u i d .

The use o f en tha lpy r a t h e r than i n t e r n a l energy i n the energy s torage term

requ i res t h a t a term of the form ( P - P n ) / ~ t be subtracted f rom the l e f t s ide o f

Equat ion 2. For t h e problems o f i n t e r e s t t h i s term i s i n s i g n i f i c a n t and has

been n e g l e c t e d . A l l o t h e r fo rms o f ene rgy wh ich a r e n o t e x p l i c i t y r e p r e s e n t e d

i n Equa t ion 2 (e.g., p o t e n t i a l and k i n e t i c ene rgy ) have been n e g l e c t e d .

3.4 AXIAL MOMENTUM EQUATIONS

v* p* *j-lVj-I J-1 J -1 A .v .v+p+ A pv - ( P V ) ~ j =

A t Ax . + e k ( ~ k s k ~ c $ ) j Ax

J

I : a x i a l monien tum s t o r a g e

~ P V A - a t

a x i a l momentum t r a n s p o r t e d

[ a x i a l l y 1

g r a d i e n t

r - a x i a l momentum t r a n s p o r t e d 1 a t e r a l l y

apuvAT

L aY -

momentum I

i r r e v e r s i b l e l o s s e s g r a v i t a t i o n a l head f r i c t i o n and f o r m 1 - [ 1

I n t h e d e r i v a t i o n o f t h e a x i a l momentum equa t ion , i t i s assumed t h a t a l l

i r r e v e r s i b l e l o s s e s can be o b t a i n e d by use o f s u i t a b l e f r i c t i o n f a c t o r s and

l o s s c o e f f i c i e n t s a p p l i e d t o t h e b u l k v e l o c i t y . A lso , i t i s assumed t h a t

p r e s s u r e changes l i n e a r l y a long t h e c o n t r o l volume and t h e shear s t r e s s terms

due t o f l o w i n t h e a d j a c e n t subchannels can be neg lec ted .

3.5 TRANSVERSE MOMENTUM CONTROL VOLUME

The subchannel approach t o model ing rod bundles r e q u i r e s t h a t t he t r ans -

verse momentum c o n t r o l volume be somewhat a r b i t r a r i l y determined. F igu re 2

shows the t ransverse momentum c o n t r o l volume as i t would appear f o r standard

subchannel noding.

1 a 000~~

FIGURE 2. Transverse Momentum Cont ro l Volume f o r Standard Subchannel Noding

The l e n g t h S i s r e q u i r e d code i n p u t and should be r e p r e s e n t a t i v e o f t h e ac tua l

f l u i d gap w i d t h between adjacent subchannels. The c o n t r o l volume leng th , R,

i s determined e i t h e r by a s p e c i f i e d w id th - t o - l eng th r a t i o o r by code i n p u t f o r

each t ransverse connect ion. Due t o t h e predominate ly a x i a l na tu re o f t h e f l o w

i n r od bundles, the f l u i d - t h e r m a l solutSon i s r e l a t i v e l y i n s e n s i t i v e t o

p h y s i c a l l y reasonable dimensions o f t h e t ransverse momentum c o n t r o l volume.

I t i s assumed t h a t i n s i d e t he c o n t r o l volume the t ransverse v e l o c i t y i s normal

t o t h e t ransverse gap (g-g i n F i g u r e 2 ) . Outs ide o f t h e c o n t r o l volume t h e

f l o w i s taken t o have no t ransverse component. The l e n g t h R should be chosen

w i t h these assumptions i n mind.

3.6 TRANSVERSE MOMENTUM EQUATION

- - 1 a t e r a l momentum s to rage

- -

- t ransverse momentum1 t r anspo r ted a x i a l l y

apuvA - - - ax -

pressure g r a d i e n t

F u r t h e r assumptions i n t h e t r ansve rse momentum equat ion a re t h a t 1 ) a l l

t he i r r e v e r s i b l e pressure l o s s can be accounted f o r by t he fo rm l o s s

c o e f f i c i e n t , C 2 ) t h e r e i s no momentum c o n t r i b u t i o n f rom ad jacen t gaps ( i .e . , T ' t h e aPuu/ay and aPuw/az terms have been neg lec ted) , and 3 ) t h e r e a re no a p p l i e d

body f o r c e s i n t he t r ansve rse d i r e c t i o n . It may a l so be noted f rom Equat ion 4

t h a t t h e leng th , 2 , c o n t r o l s t h e magnitude o f t h e f l u i d i n e r t i a ( t i m e and

space) r e l a t i v e t o t he r e s t o f t he terms i n t he t r ansve rse momentum equat ion.

As t he l eng th i s increased, t h e i n e r t i a l terms become more impor tan t i n d e t e r -

m in ing the t r ansve rse f l ow .

3.7 Rod Energy Equat ions

A one-dimensional hea t conduct ion equat ion i s so lved f o r t h e f u e l temper-

a t u r e d i s t r i b u t i o n . Since or thogonal c o l l o c a t i o n techniques a re used t o s o l v e

t he d i f f u s i o n equation, t he p a r t i a l d i f f e r e n t i a l equat ion r a t h e r than t h e

f i n i t e - d i f f e r e n c e equat ion i s descr ibed here.

For t h e f u e l i t i s assumed t h a t 1) the re i s no heat t r a n s f e r a x i a l l y , 2 )

the heat i s generated u n i f o r m l y throughout the f u e l a t a given a x i a l he igh t ,

and 3 ) t h e f u e l p r o p e r t i e s do no t vary w i t h t h e r a d i a l v a r i a t i o n i n tempera-

t u re . An o p t i o n i n the code t h a t al lows the users t o make the f u e l p r o p e r t i e s

vary w i t h t h e a x i a l temperature changes i s descr ibed l a t e r i n t h i s sec t ion .

The a x i a l node lengths correspond t o the f l u i d c e l l l eng th Ax The rod J

m a t e r i a l s and dimensions w i t h i n each a x i a l l eng th are assumed cons tan t bu t may

vary f rom one a x i a l s tep t o the next. F igure 3 shows a cross sec t i on o f a

t y p i c a l rod. The reg ion marked as f u e l may a c t u a l l y be any m a t e r i a l . Also,

the gap may be e l im ina ted s imp ly by making the gap conductance very large. I n

t h i s manner t h e rod model may be used t o s imu la te s o l i d p ins such as those i n

a r e f 1 ec t o r r e g ion.

The code i s a lso capable o f model ing an annular f u e l sec t ion which cou ld

be u s e f u l i n c a l c u l a t i n g temperature d i s t r i b u t i o n s i n a bundle w i t h s i n t e r e d

f u e l o r e l e c t r i c a l l y heated rods. The method of s o l u t i o n and the assumptions

are t h e same as f o r t h e s o l i d c y l i n d r i c a l f u e l except t h a t t h e user may s p e c i f y

t h a t the heat generat ion be un i fo rm throughout the f u e l o r converted t o a heat

f l u x imposed on t h e inner surface.

The nature o f the or thogonal c o l l o c a t i o n technique fo r s o l v i n g the con-

duct i o n equat ion makes i t d i f f i c u l t t o handle problems w i t h temperature-

dependent p rope r t i es . I n t he COBRA-WC code the temperature-dependent f u e l

p r o p e r t i e s are modeled i n an approximate manner. The f u e l p r o p e r t i e s a re

area-weighted averaged a t each a x i a l l e v e l as

where Kf i s computed f r om the f u e l temperature a t the r a d i a l l o c a t i o n i

( r i + ri-1)/2. A s i m i l a r c a l c u l a t i o n i s c a r r i e d o u t f o r t h e average

s p e c i f i c heat . Th is method g i ves reasonable r e s u l t s f o r most LMFBR t r a n s i e n t s

w i t h o u t i n c r e a s i n g t h e computat ion t i m e s i g n i f i c a n t l y .

FIGURE 3. Cross Sec t ion o f COBRA-WC Model f o r a Nuclear Fuel Rod

3.8 CLADDING ENERGY EQUATION

The c l a d d i n g energy equa t ion i s ob ta ined by per fo rming a lumped energy

ba lance on t h e c l add ing m a t e r i a l a t each a x i a l s tep.

- convec t i ve hea t hea t t r a n s f e r ( 7 ) [ ~ ~ ~ ~ ~ ~ e 2 T c 1 - - l r a n s f e r t o t h e f l u i d ] + [.cross t h e g a j

YcPccc at

Here i t i s assumed t h a t t h e r e i s no a x i a l heat t r a n s f e r and t h e tempera-

t u r e i s un i f o rm around t h e c i rcumference o f t h e c l add ing . The gap conductance,

H i s assumed cons tan t and the f i l m c o e f f i c i e n t i s g i ven by u s e r - s p e c i f i e d g '

c o r r e l a t i o n s .

3.9 WALL ENERGY EQUATION

F igu re 4 shows a cross s e c t i o n o f a t y p i c a l w a l l node, which cou ld be used

t o r ep resen t t h e duct w a l l and t h e i n t e r d u c t s o d i u m - f i l l e d gap i n an LMFBR.

The w a l l energy equa t ion i s s i m i l a r i n fo rm t o t he c l add ing energy equa t ion

s i nce a lumped f o r m u l a t i o n i s again used.

[ a t t r a n s f e r hea t [ iF : :eaTj = f r om subchannel [genera t ion ] hea t (8)

PwCwtw at

I n t h e w a l l energy equa t ion i t i s assumed t h a t t h e r e i s no heat t r a n s f e r

a x i a l l y . The conductances are ob ta ined as

where Hi i s t h e f i l m c o e f f i c i e n t and K, i s t h e e f f e c t i v e w a l l conductance

de f i ned i n equa t i on (11). The user must supply t h e e f f e c t i v e heat capac i tance,

PwCwtw, and t h e e f f e c t i v e w a l l conductance. When a s i n g l e w a l l node i s

made up o f two o r more d i f f e r e n t m a t e r i a l s (e.g., i n t h e s i t u a t i o n shown i n

F i gu re 4), t h e e f f e c t i v e heat capac i tance i s c a l c u l a t e d as t he sum o f t h e

e f f e c t i v e heat capac i tance o f t h e va r i ous m a t e r i a l s .

INTER ASSEMBLY G A P

FIGURE 4. Cross Sect ion o f COBRA-WC Model f o r a Heat-Conducting Wall

where ow i s the set of wa l l components ( 2 ducts and the sodium f o r t h e case

i n F igu re 4 ) . S i m i l a r l y , t h e e f f e c t i v e w a l l conductance i s c a l c u l a t e d as

3.10 Heat Generat ion and Trans fer Terms

3 The heat generat ion i s s p e c i f i e d i n i n p u t as a heat dens i t y (MBtu/hr- f t ) .

The ac tua l heat generated i n any a x i a l step i n a rod i s determined by t h e r o d

dimensions and th ree m u l t i p l i e r s . The m u l t i p l i e r s are the r a d i a l power f a c t o r ,

t h e a x i a l power f a c t o r and the t r a n s i e n t power f a c t o r . The t o t a l heat produced

i n an a x i a l s tep i n a rod i s g iven by

If t h e orthogonal c o l l o c a t i o n model i s not used, t h e dimension used f o r c a l -

c u l a t i n g the m a t e r i a l volume f o r heat generat ion i s t he rod rad ius r a t h e r than

t h e f u e l rad ius .

The heat de l i ve red t o the f l u i d i n channel i from rod n i s g iven by:

q = H q" HTR i ,n n

where $in i s the f r a c t i o n o f heat produced by rod n de l i ve red t o channel i,

and i s spec i f i e d by the user. This $in may be se t t o values l a r g e r than 1.0

t o model many rods w i t h a s i n g l e p i n .

For the w a l l s t he t o t a l heat generated i n an a x i a l s tep i s g iven by

where t; i s an e f f e c t i v e th ickness f o r heat generat ion which need not be

cons i s ten t w i t h t h e phys i ca l th ickness o f t h e w a l l .

The f i l m c o e f f i c i e n t , HR, used i n Equations 2 and 6 i s de f ined as a

weighted average o f channel f i l m c o e f f i c i e n t s . A channel f i l m c o e f f i c i e n t ,

Hi, i s ca l cu la ted f o r each channel based on the l o c a l Reynolds and P rand t l

numbers and t h e use r - spec i f i ed c o r r e l a t i o n . The rod f i l m c o e f f i c i e n t i s then

ca l cu la ted as:

The average temperature o f t h e f l u i d around a rod, ?, i s de f i ned analo-

gous ly as

If t h e rod i s connected t h e r m a l l y t o o n l y one channel, then ? i s s imp l y t h e

f l u i d temperature, T.

4.0 SOLUTION TECHNIQUES

The d i scuss ion o f s o l u t i o n techniques can be conven ien t l y separated i n t o

two p a r t s : 1) t h e s o l u t i o n o f a l l t h e energy equat ions, and 2 ) t h e s o l u t i o n

o f the momentum and c o n t i n u i t y equat ions.

4.1 ENERGY SOLUTION

I n t he COBRA-11-1 code, t he rod and f l u i d energy equat ions are so lved

separa te ly , pass ing a boundary c o n d i t i o n back and f o r t h u n t i l bo th se t s o f

equat ions converged. The rod temperatures are c a l c u l a t e d us ing t he f l u i d

terr~peratures as a boundary c o n d i t i o n . A r od heat f l u x i s then c a l c u l a t e d and

used i n the s o l u t i o n f o r t he f l u i d entha lpy. The h igh rod power d e n s i t y and

low e f f e c t i v e heat capaci tance o f t h e sodium make t h i s procedure uns tab le f o r

LMFBR t r a n s i e n t s unless v e r y smal l t ime s teps are used. To overcome t h i s

problem i n t he COBRA-WC code a l l t h e energy equat ions ( f u e l , c lad, w a l l and

f l u i d ) are solved s imu l taneous ly a t each l e v e l , e l i m i n a t i n g the e x p l i c i t c a l -

c u l a t i o n o f a r od heat f l u x . ( 2 )

Orthogonal c o l l ~ c a t i o n ( ~ ) i s app l i ed t o the s p a t i a l term i n t he f u e l

conduct ion equat ion w h i l e t h e t r a n s i e n t term i s c a l c u l a t e d by f i n i t e d i f f e r -

ence. By l e t t i n g r ' = r / R t he f u e l conduct ion equat ion can be r e w r i t t e n as:

Tf - T; - Kf a ( r , ~ ) + q l l t

PfCf A t - - -

2 a r ' Rf 'I art

Since a u n i f o r m p e r i p h e r a l boundary c o n d i t i o n and un i f o rm heat genera t ion i s

assumed f o r each rod, the temperature p r o f i l e must be symmetric. It i s assumed

t h a t

where N i s t he c o l l o c a t i o n order p l u s one. With t he unknowns (di) the f u e l

temperature can be matched a t N r a d i a l p o s i t i o n s ( i .e. t h e conduct ion equat ion

i s s a t i s f i e d a t these N p o i n t s ) . The r a d i a l p o s i t i o n s or c o l l o c a t i o n p o i n t s

are chosen as t h e r o o t s o f a se t o f orthogonal polynomials. Using t h i s tech-

nique, the problem can be reduced t o s o l v i n g f o r t he temperatures a t t he c o l -

l o c a t i o n s p o i n t s d i r e c t l y r a t h e r than the expansion c o e f f i c i e n t s , di.

Given the c o l l o c a t i o n p o i n t s r ' (j = 1,2, .... N - 1 the i n t e r i o r co l l oca - j

t i o n po in t s , p l u s j=N, t h e f u e l sur face) t he temperature a t each p o i n t can be

w r i t t e n as

o r

{Tf )= [ Q ] { d l

where Qji = r , 2 i -2 j

t a k i n g the f i r s t and second d e r i v a t i v e s o f Tf f rom Equation 19 we have

and

o r a{Tf I - -

a r ' - CCI [QI-' { T ~ 1

and 1 a

where

and [PI-' { T f } was s u b s t i t u t e d f o r { d l .

S u b s t i t u t i o n o f Equation 24 i n t o Equat ion 17 and forward d i f f e r e n c i n g the

temporal d e r i v a t i v e g ives

{ T ~ I - ~ T ~ I ~ Kf

P f C f - -

A t - [B] I T f } + q " '

R:

where CBI = CDI CQI-'

It i s assumed here t h a t the inverse o f [Q] ex i s t s , as i t does f o r the

second- and t h i r d - o r d e r c o l l o c a t i o n schemes used i n t he COBRA-WC code. The

boundary c o n d i t i o n necessary f o r the c a l c u l a t i o n o f the f u e l temperature i s

g iven by

where T N + ~ i s t he lumped c ladd ing temperature, Tc.

Using Equat ion 23 i n Equat ion 26,

where

[ A ] = [ c l [QI -l

The c l add ing temperature i s g iven by Equat ion 7 which, w r i t t e n i n terms

o f t h e c o l 1 ocat i o n temperatures, i s

where 7 i s an average temperature o f t h e f l u i d surrounding t h e rod.

Equat ions 25, 27, and 28 are combined t o y i e l d a m a t r i x equa t ion o f t he

fo rm

which g i ves t he f u e l and c l add ing temperatures as a l i n e a r f u n c t i o n o f t he

averaged f l u i d temperature, ?, t h e o n l y o the r unknown a t t h i s p o i n t . Equa-

t i o n 29 i s then reduced by Gauss e l i m i n a t i o n t o g i v e

It may be noted t h a t i f t h e geometry and f u e l and gap p r o p e r t i e s f o r a

g iven rod remain constant , then t he m a t r i x [M] i s cons tan t except f o r t h e f i l m

c o e f f i c i e n t , H. Consequently, most o f t h e c a l c u l a t i o n s r e q u i r e d f o r M ' need

be done o n l y once. The source term S' (TF) i nvo l ves the power d e n s i t i e s q ' ' ' and t he o l d t ime temperatures, ' and so must be updated as these q u a n t i -

J t i e s change. It i s impor tan t t o r e a l i z e t h a t s ' ( ? ) i s s t i l l l i n e a r w i t h

r e s p ~ t t o ? and t h a t 7 i s a l i n e a r combinat ion o f the f l u i d temperatures T by

Equation 16. Equat ion 30 can t h e r e f o r e be e a s i l y combined w i t h t he f l u i d

energy equat ion t o so lve f o r t he f l u i d temperatures. S u b s t i t u t i o n o f Equa-

t i o n 16 i n t o Equat ion 30 g ives

which i s l i n e a r i n Ti.

Equat ion 31 i s used t o e l i m i n a t e t he c l add ing temperature i n the f l u i d

energy equat ion.

The w a l l temperature f o r w a l l m a t some a x i a l l e v e l can a l so be expressed

as a l i n e a r combinat ion o f t h e ad jacent subchannel f l u i d temperatures.

Rearrangement o f Equat ion 8, t he w a l l energy equat ion, g ives

S u b s t i t u t i n g Equat ions 31 and 33 i n t o t h e f l u i d energy Equat ion 2 f o r channel i

a t a x i a l l e v e l j g i ves

To so l ve f o r t h e f l u i d en tha lp i es , i t i s necessary t o conve r t t h e f l u i d

temperatures t o e n t h a l p i e s by t he f o l l o w i n g approx imat ion

where t h e re fe rence temperature and en tha lpy a re chosen a r b i t r a r i l y as t h e

p rev ious i t e r a t i o n va lues f o r T and h, and c i s t h e f l u i d s p e c i f i c heat . Sub-

s t i t u t i n g Equat ion 35 i n t o Equat ion 34 and assuming t h a t a l l v a r i a b l e s o the r

than t h e f l u i d e n t h a l p i e s a t t h e j l e v e l a re t h e l a s t i t e r a t e va lues g i v e s an

equat ion which i s l i n e a r i n t h e e n t h a l p i e s a t l e v e l j. The equat ions o f t h i s

fo rm f o r each subchannel a t l e v e l j are combined t o form t h e m a t r i x equa t i on

For l a r g e problems the m a t r i x [L] i s sparse ( i .e., few nonzero elements), and

t h e r e f o r e o n l y t h e nonzero elements a re s to red . The m a t r i x equa t ion i s so l ved

by success ive over r e l a x a t i o n (SOR) ( r e l a x a t i o n f a c t o r = 1.2). The number o f

i t e r a t i o n s i s genera l l y independent of t he number o f subchannels, and conver-

gence i s u s u a l l y achieved i n fewer than 10 i t e r a t i o n s s ince the m a t r i x i s

s t r o n g l y d iagona l l y dominant . When Equation 36 i s converged a t one l eve l , the en tha lp ies are used i n the

equat ion o f s t a t e t o ob ta in f l u i d dens i t ies , and the s o l u t i o n proceeds a t t he

nex t a x i a l l eve l .

Once values f o r the f l u i d en tha lp ies have been obtained, the wa l l , c lad-

d ing and f u e l temperatures can be backed out . The equ iva len t f l u i d tempera-

t u res are found us ing the equat ion o f s t a t e and these are s u b s t i t u t e d i n t o

Equation 32 t o ob ta in the wa l l temperatures. S i m i l a r l y , t he c ladd ing tempera-

t u res are ca l cu la ted us ing Equation 31 and the fue l temperatures are ca lcu la ted

us ing the upper t r i a n g u l a r ma t r i x equat ion corresponding t o Equation 29. It

may be noted t h a t it i s not necessary t o back ou t the n o n f l u i d temperatures

u n t i l a converged s o l u t i o n t o a l l equations has been obta ined and we are ready

t o proceed t o the nex t t ime step.

4.2 MOMENTUM AND CONTINUITY SOLUTION

Two techniques are a v a i l a b l e i n t he COBRA-WC code t o so lve the momentum

and c o n t i n u i t y equations. The f i r s t i s very s i m i l a r t o t he scheme found i n

COBRA-IV-I except t h a t pressure r a t h e r than c ross f low has been chosen as the

v a r i a b l e t o be solved f o r . Also, a d i r e c t i nve rs ion scheme has been added t o

the momentum s o l u t i o n t o decrease running time. The second method i s somewhat

l i k e t h e e x p l i c i t scheme i n COBRA-IV-I i n t h a t a Poisson equat ion i n pressure

i s solved, b u t several mod i f i ca t i ons have been made which g r e a t l y reduce the

running t ime and a l l ow f o r s o l u t i o n s which are i m p l i c i t i n t ime. This i m p l i c i t

s o l u t i o n s t ra tegy i s s i m i l a r t o t h a t i n the SIMPLE'^) and SABRE'^) codes.

The f i r s t method works w e l l f o r most LMFBR opera t ing cond i t i ons b u t r e s u l t s i n

numerical i n s t a b i l i t i e s when the re are l a rge a x i a l v e l o c i t y g rad ien ts i n the

t ranverse d i r e c t i o n tending toward a l o c a l i z e d f l o w reve rsa l w i t h i n an assem-

b ly . This s i t u a t i o n a r i s e s when the f l ow r a t e i n an LMFBR bundle decreases t o

a small percentage of nominal and a r a d i a l temperature skew e x i s t s i n t he

assembly (e. g., n a t u r a l c i r c u l a t i o n t rans ien ts ) . The second s o l u t i o n method

was developed t o solve the conservat ion equat ions i n these s i t u a t i o n s . The

two methods solve nea r l y i d e n t i c a l equations, so s h i f t i n g from one s o l u t i o n

scheme t o the other i n the course o f a t r a n s i e n t causes no d i f f i c u l t i e s . The

f i r s t scheme w i l l be r e f e r r e d t o as t h e PSOLVE scheme and the second as t h e

REC I R C scheme.

4.2.1 PSOLVE Scheme

I n the PSOLVE scheme the a x i a l and t ransverse momentum equations are com-

bined w i t h t h e c o n t i n u i t y equat ion i n much the same way as i n COBRA-IV-I.

Since t h i s scheme i s used o n l y f o r problems when the f l o w d i r e c t i o n i s p o s i t i v e

throughout t h e subchannels, t h i s assumption i s made i n the f o l l o w i n g der iva-

ti on. Under t h i s assumption the a x i a l momentum equation (Equation ( 3 ) )

becomes :

m - rn. n j J - - - j -1 - Pj - - A~ ' j -1

A t A x ; A x ;

where the AVP* have been combined i n t o a s i n g l e var iab le , M, f o r t he mass f l o w

ra te .

A rearrangement o f terms y i e l d s :

The c o n t i n u i t y r e l a t i o n s h i p (Equa t ion 1) i s used t o e l i m i n a t e t h e f i r s t f a c t o r

on t h e r i g h t s ide, g i v i n g an express ion f o r t h e a x i a l p ressure g r a d i e n t i n

terms o f t h e t r a n s v e r s e v e l o c i t i e s .

The t r a n s v e r s e momentum equa t ion (Equa t ion 4 ) can be r e w r i t t e n as

where

For each o f t h e t r ansve rse connect ions t o a subchannel an equa t i on o f t h e

f o rm o f Equat ion 40 i s s u b s t i t u t e d i n t o Equat ion 39 f o r t h e P * ~ U ~ t e rm on

t h e r i g h t s ide . The r e s u l t i n g s e t o f equat ions f o r one a x i a l l e v e l i s t hen

assembled i n t o a m a t r i x equat ion.

AS i n t he energy equat ion, Equat ion 42 i s sparse s i nce MAi j 0 o n l y i f

i = j o r subchannel i i s connected t o subchannel j. Furthermore, a t any a x i a l

l e v e l , t h e equa t ions which generated Equat ion 42 are o n l y coupled on a assembly

b a s i s . That i s , i f t h e problem i n v o l v e s more than one assembly, an equa t i on

o f t h e fo rm o f Equat ion 42 w i l l be cons t ruc ted and so lved f o r each i n d i v i d u a l

assembly. Two methods a re a v a i l a b l e i n t h e COBRA-WC code f o r s o l v i n g Equa-

t i o n 42. The f i r s t method i s t h e same as t h a t found i n t h e COBRA-IV-I code

which uses SOR on t h e nonzero terms o f t h e AAA m a t r i x . The zero terms a re n o t

s to red . The second method so l ves Equat ion 39 by Gaussion e l i m i n a t i o n . Th i s

method uses more s to rage s i nce many o f t h e ze ro terms must be s to red . However,

by j u d i c i o u s l y choos ing t he numbering scheme f o r t h e subchannels, t h e nonzero

terms can be con ta ined w i t h i n a smal l band sur round ing t he d iagona l . Only

elements w i t h i n t h i s band need be s t o r e d and operated on t o o b t a i n t h e so lu -

t i o n vec to r . When core s t o rage requi rements a l l o w t he use o f t h i s d i r e c t

s o l u t i o n scheme, CPU t i m e sav ings o f 2 t o 3 t imes (depending on t h e problem)

can be r e a l i z e d . The f i r s t method i s r e t a i n e d s i n c e f o r some very l a r g e

problems t h e subchannels cannot be numbered i n a manner t o make t he band-width

(and t h e r e f o r e t h e co re s t o rage ) smal l enough f o r t h e use o f t he d i r e c t so l u -

t i o n . The numbering o f subchannels and t h e r e s u l t i n g bandwidth w i l l be

d iscussed i n t h e s e c t i o n on noding.

Once Equat ion 42 has been so lved f o r t h e subchannel p ressure g rad ien t s a t

a p a r t i c u l a r l e v e l t h e y can be s u b s t i t u t e d i n t o Equa t ion 40 t o o b t a i n t h e

t r ansve rse mass f l u x e s . The o the r terms r e q u i r e d i n Equat ion 40 are taken t o

be t h e p rev i ous i t e r a t i o n va lue. These t r a n v e r s e f l u x e s a re then s u b s t i t u t e d

i n t o t he c o n t i n u i t y equa t ion (Equa t ion 1) and t h e a x i a l f l o w r a t e , m i s j '

obta ined. The t r ansve rse p ressure g r a d i e n t i s then updated u s i n g t h e f o l l o w i n g

express ion.

which w i l l be used i n Equat ion 40 on t h e n e x t sweep through t h e a x i a l l e v e l s .

For problems where t h e r e i s a p o s s i b i l i t y o f a r e c i r c u l a t i o n zone f o rm ing

w i t h i n a bundle or f l o w reg ion , t h e RECIRC s o l u t i o n scheme, descr ibed i n t h e

f o l l o w i n g sec t ion , may be app l i ed .

4.2.2 RECIRC Scheme

The numer ica l model f o r s o l v i n g r e c i r c u l a t i n g f l o w s i n t h e COBRA-WC code

uses t h e same b a s i c techn ique as t h e e x p l i c i t scheme i n COBRA-IV-I, which was

based on t h e ICE'^) methodology, i.e., t h e s o l u t i o n o f a Poisson equa t ion i n

p ressure w i t h subsequent s o l u t i o n o f a l i n e a r i z e d momentum equa t ion f o r ve l oc -

i t i e s . The fundamental f i n i t e - d i f f e r e n c e equa t ions are e s s e n t i a l l y t he same

as those descr ibed i n t h e l a s t s e c t i o n f o r t h e PSOLVE scheme except f o r

t h e use o f an average, r a t h e r than dono r - ce l l , dens i t y . The major d i f f e r e n c e s

between t h i s scheme and t h e e x p l i c i t scheme i n COBRA-IV-I a re i n t h e develop-

ment o f t h e Poisson equat ion based on c o n t i n u i t y r a t h e r than t h e energy equa-

t i o n , the techniques used t o o b t a i n a s o l u t i o n t o t he Poisson equat ion i n a

smal l amount o f computer t i m e and t h e i m p l i c i t / e x p l i c i t ope ra t i on t o m in im ize

o v e r a l l problem run t ime.

The momentum and c o n t i n u i t y equat ions are so lved by l i n e a r i z i n g t he

momentum equat ions t o ge t v e l o c i t y as a l i n e a r f u n c t i o n o f pressure.

and

where Fu, Fv, Cu, and C v are evaluated us ing t he l a t e s t va lues f o r each

o f t h e v a r i a b l e s and are then h e l d cons tan t f o r t h e s o l u t i o n o f t h e pressure.

The r e s i d u a l e r r o r i n t he c o n t i n u i t y equa t ion f o r each c e l l i s then computed

as

and t he d e r i v a t i v e s o f Ec w i t h r espec t t o the c e l l pressure and t he sur-

round ing c e l l pressures are then formed i n terms o f Fu and Fv and t he

v e l o c i t y c o e f f i c i e n t s i n Equat ion 46. For each c e l l 6P1s a re needed such t h a t

aEc - -Ec where t h e sum i s over a l l c e l l s . C ~ P -

The e n t i r e m a t r i x equat ion t o be so lved f o r n c e l l s i s then

As before, most o f the terms i n t he above m a t r i x w i l l be zero s ince aEi/3P. C 0 J

o n l y i f i = j o r c e l l j i s connected t o c e l l i w i t h a f l o w path.

The s o l u t i o n o f the above m a t r i x equat ion t akes up a l a r g e p o r t i o n o f t he

o v e r a l l computat ion t i m e f o r t h e s o l u t i o n o f a l l t h e conserva t ion equat ions.

Therefore, t he p a r t i c u l a r s o l u t i o n method chosen i s ve ry impor tant . U s u a l l y

t h e problems so lved us ing t h e COBRA codes r e q u i r e many c e l l s and s i nce t h e c e l l

arrangement does no t lead t o a s imple m a t r i x form, t h e m a t r i x equat ion i s

so lved i t e r a t i v e l y . I n t h e expl i c i t v e r s i o n o f COBRA-IV-I, t h e e n t i r e m a t r i x

i s solved by Gauss S iede l i t e r a t i o n . Convergence us ing t h i s method can be

ext remely slow, e s p e c i a l l y f o r a c e l l c o n f i g u r a t i o n w i t h a l a r g e aspect r a t i o .

The convergence r a t e f o r Equat ion 47 can be g r e a t l y increased by s o l v i n g

p o r t i o n s o f t h e m a t r i x equat ion by d i r e c t i nve rs i on . I n t h e COBRA-WC method,

a banded m a t r i x i s formed f o r t he s o l u t i o n o f a l l 6P1s on one a x i a l p lane. The

6P1s on t h e l e v e l s above o r below the l e v e l o f c u r r e n t s o l u t i o n a re taken t o

be f i x e d a t t h e i r p rev ious i t e r a t i o n value. Th is m a t r i x i s so lved by d i r e c t

i n v e r s i o n t o o b t a i n t h e new 6P1s f o r t h a t l e v e l , and t h e process con t inues a t

the nex t a x i a l l e v e l . The computat ional mesh i s r epea ted l y swept through,

l e v e l by l e v e l , s o l v i n g f o r t h e BP's u n t i l no s i g n i f i c a n t change i n any o f t h e

6P1s takes p lace . A l l problems f o r which t h e R E C I R C scheme i s t o be used

should be noding i n such a way as t o m in im ize t h e bandwidth as descr ibed i n

Sec t ion 6.

Th is process i s s i m i l a r t o s o l v i n g a one-dimensional problem by Gauss

S iede l i t e r a t i o n . But t h e s o l u t i o n o f a one-dimensional problem by Gauss

S iede l can be ve ry t ime consuming, e s p e c i a l l y when i t i s cons idered t h a t a

one-dimensional problem can be so lved v e r y q u i c k l y by i n v e r t i n g t h e t r i d i a g o n a l

m a t r i x . To t a k e advantage o f t h i s , a one-dimensional approx imat ion o f t h e

problem i s so lved between t h e l e v e l - b y - l e v e l sweeps. Th is i s done w i t h o u t

d i s t u r b i n g the shape o f pressure p r o f i l e s a t each l e v e l . To fo rm t h e one-

d imensional tr i d i agonal m a t r i x equa t ion t h e ne t c o n t i n u i t y e r r o r i s c a l c u l a t e d

as

A t r i d i a g o n a l m a t r i x i s then formed:

t o so lve f o r an average 6 7 a t each l e v e l , which can be used t o a d j u s t t h e

magnitude o f each pressure on t h a t l e v e l . The v e l o c i t i e s are then updated

us ing t h e new pressures and Equat ions 44 and 45 and new c o n t i n u i t y e r r o r s a r e

c a l c u l a t e d by Equat ion 46.

When the c o n t i n u i t y e r r o r f o r each c e l l becomes s u f f i c i e n t l y small, the

i t e r a t i o n procedure i s stopped. A t t h i s p o i n t t h e c o n t i n u i t y and l i n e a r i z e d

momentum equat ions have been solved. The energy equat ions fo r a l l c e l l s are

solved s imul taneously us ing t h e method p r e v i o u s l y descr ibed. The new f l u i d

d e n s i t i e s are obta ined from the equat ion o f s ta te .

If t h e scheme i s runn ing i n t h e e x p l i c i t mode, t h i s i s t h e end o f t h e

c a l c u l a t i o n s f o r a given t ime step. I n the i m p l i c i t mode the f u n c t i o n a l r e l a -

t i o n s h i p between pressure and v e l o c i t y (Equat ions 44 and 45) are recomputed,

and the c o n t i n u i t y and energy equat ions are solved as before. Convergence i s

assumed when t h e change i n v e l o c i t y as computed from Equat ions 44 and 45 i s

i n s i g n i f i c a n t .

BOUNDARY CONDITIONS AND OTHER EQUATIONS

To c l o s e t h e system o f equat ions descr ibed i n t he two prev ious sect ions,

some system boundary cond i t i ons and c o n s t i t u t i v e r e l a t i o n s h i p s are requ i red .

The f l u i d enthalpy o r temperature i s requ i red a t t he subchannel i n l e t . The

user may s p e c i f y an i n l e t temperature d i s t r i b u t i o n by i n p u t t i n g the i n l e t

temperature f o r each subchannel. For f l o w reve rsa l s t h e code c a l c u l a t e s t h e

f l u i d temperature a t the t o p o f t he subchannels based on the mixed mean o u t l e t

temperature i f t h e ne t bundle f l o w r a t e i s p o s i t i v e . I f t h e ne t bundle f l o w

r a t e becomes negat ive the user must supply a temperature f o r the incoming f l u i d

a t t h e t o p o f t h e assembly.

The code a lso r e q u i r e s an i n l e t f l o w r a t e o r a pressure drop. When us ing

t h e i n l e t f l o w r a t e opt ion, t h e user may request un i f o rm i n l e t mass f l u x f o r

a l l subchannels o r he may s p e c i f y f l o w r a t e s f o r each assembly. Fur ther , he

may s p e c i f y an i n l e t f low d i s t r i b u t i o n f o r any o r a l l assemblies. The user

a lso may choose t o a l l ow the code t o c a l c u l a t e an i n l e t f low d i s t r i b u t i o n g iven

a t o t a l assembly f l o w r a t e . Under t h i s o p t i o n t h e code i t e r a t e s on t h e i n d i -

v i dua l subchannel f l o w r a t e s w i t h i n an assembly u n t i l t h e pressure drop across

the f i r s t computat ional c e l l i s t h e same f o r a l l t he subchannels. I n ca lcu-

l a t i n g t h i s pressure drop, which inc ludes o n l y f r i c t i o n , form loss, and g r a v i -

t a t i o n a l head, i t i s assumed t h a t t h e r e i s no t ransverse f l o w a t t h e f i r s t

l e v e l o f computat ional c e l l s . When runn ing a t r a n s i e n t under t h i s op t ion , o n l y

t h e s teady-s ta te i n i t i a l i z a t i o n s o l u t i o n w i l l use t he equal-pressure drop

op t i on . I n l e t f l ows du r i ng t h e t r a n s i e n t are determined by m u l t i p l y i n g t h e

c a l c u l a t e d s teady-s ta te i n l e t f l ows by the app rop r i a te t ime-dependent f o r c i n g

f u n c t i o n .

The t ime-dependent pressure drop boundary c o n d i t i o n may be used w i t h o r

w i t h o u t t h e network model descr ibed below. When used w i t h o u t t h e network

model, a d i f f e r e n t time-dependent pressure drop may be s p e c i f i e d f o r each

assembly. The i n l e t f l o w i n each subchannel i s ad justed so t h a t t h e c a l c u l a t e d

pressure drop matches t he s p e c i f i e d boundary cond i t i on .

4.3.1 Network Model

For many model ing s i t u a t i o n s i t may be d e s i r a b l e t o a l l o w the code t o

c a l c u l a t e t h e f l o w d i s t r i b u t i o n between assemblies based on t h e o r i f i c i n g and

assembly arrangement. The network model has been developed f o r t he COBRA-WC

code t o model t h e pressure losses above and below t h e core reg ion . When t h e

network model i s used, a s i n g l e pressure drop i s s p e c i f i e d as a f u n c t i o n o f

t ime, and t h e subchannel f l o w r a t e s a re ad jus ted so t h a t t he p ressure dr0.p

through each p o s s i b l e f l o w pa th matches t he s p e c i f i e d pressure drop. F i g u r e 5

i s a schematic d e s c r i p t i o n o f t h e network model f o r a three-assembly problem

w i t h a bypass channel. I n t h i s p a r t i c u l a r example, assemblies 1 and 2 may be

inner -core assembl ies connected t o a common h igh-pressure plenum. Assembly 3

may be an ou te r core assembly connected t o a low-pressure plenum. The bypass

channel may represen t t h e thermal l i n e r reg ion . The conserva t ion equat ions

descr ibed i n t h e p rev ious s e c t i o n are so lved o n l y f o r t h e noded l e n g t h as noted

i n F i g u r e 5. Th i s noded l eng th no rma l l y represen ts t h e rod bundle where f l o w

r e s i s t a n c e i s g iven by f r i c t i o n f a c t o r s and l o s s c o e f f i c i e n t s . The g r a v i t a -

t i o n a l head i s a l s o accounted f o r i n t h i s reg ion . Along t he r e s t o f t h e f l o w

pa ths a reduced momentum equat ion i s solved, which takes i n t o account o n l y t h e

f low r e s i s t a n c e due t o f r i c t i o n and form and t h e s t a t i c loss . No i n e r t i a terms

are inc luded. The energy equat ion i s no t so lved ou t s i de t h e noded reg ion, and

i t i s assumed t h a t t h e t r a n s p o r t t ime through t h e network model i s zero.

I

R + H R + H R + H Gout Gout Gout Gout Gout Gout

+ H R + HA R ~ O u t Aout Aout out

1

FIGURE 5. Schematic Descr ip t ion o f the Network Model f o r Pressure Drop Through Reactor Vessel

I n the example described by Figure 5, the res is tances marked RAin and

R ~ o u t would be the f l o w res is tances associated w i t h the assembly i n l e t o r i -

f ices and the o u t l e t hardware (hand1 ing socket, etc.) , r espec t i ve l y . These

loss c o e f f i c i e n t s can be made dependent on Reynolds number. A g r a v i t a t i o n a l

pressure drop can a l so be modeled by supplying head lengths a t the i n l e t and

o u t l e t noted as HA i n F igure 5. The assen~bly i n l e t g r a v i t a t i o n a l head loss

i s ca l cu la ted us ing the i n l e t temperature f o r dens i t y ca l cu la t i ons . The o u t l e t

g r a v i t a t i o n a l head loss i s a r r i ved a t us in~g the mixed mean assembly o u t l e t

temperature.

The group dynamic loss c o e f f i c i e n t s , RGin and RGout, may represent the

f l o w res is tance from a common plenum t o the h igh- and low-pressure plenums o r

t o the bypass entrance reg ion. The group dynamic loss c o e f f i c i e n t s are assumed

t o be independent o f Reynolds number. Here too, g r a v i t a t i o n a l losses may be

m d e l e d by supply ing the head lengths. F i n a l l y , RT may represent the dynamic

loss c o e f f i c i e n t f o r f l o w from the i n l e t nozzle t o t h e common plenum.

For most problems the ac tua l l oss coe f f i c i en ts fo r each o f these r e s i s t -

ances w i l l no t be known, bu t t he f l o w and corresponding pressure drop across

each res i s tance should be ava i lab le . The e f f e c t i v e loss c o e f f i c i e n t s are then

def ined as:

where A P has u n i t s 1 b f / f t 2 , and F i s i n lbm/secy g i v i n g R t he u n i t s o f

l i f t - l b m . For R A Y which may be dependent on Reynolds number, it i s necessary

t o supply a wetted per imeter so the Reynolds number may be ca l cu la ted from t h e

f l o w r a t e . The wetted per imeter need not have any phys ica l s i g n i f i c a n c e b u t

should be chosen so t h a t t he c o r r e c t loss i s obtained f o r a g iven f l o w r a t e

when us ing the s p e c i f i e d res i s tance versus Reynolds number curve.

4.3.2 Radia l Thermal Boundary Cond i t ion

The thermal boundary c o n d i t i o n i n the r a d i a l d i r e c t i o n i s zero heat f l u x

a t t h e outermost faces o f an assembly o r group o f assemblies. Constant tem-

perature boundary cond i t i ons can be simulated f a i r l y e a s i l y by surrounding the

reg ion o f i n t e r e s t by one o r more subchannels having a l a rge f l o w r a t e a t a

spec if ied i n l e t temperature and modeling connect ing wa l l s f o r heat t r a n s f e r

between these ou ts ide channels and the adjacent inner channels.

4.3.3 F r i c t i o n Factors and F i l m C o e f f i c i e n t s

A t l e a s t one f r i c t i o n f a c t o r o f t he form

i s requ i red as code i npu t . Add i t i ona l f r i c t i o n f a c t o r c o r r e l a t i o n s may be

i n p u t w i t h s p e c i f i e d subchannel type numbers determining the subchannels where

each c o r r e l a t i o n i s t o be used. Two f r i c t i o n fac to r c o r r e l a t i o n s may be read

i n f o r each subchannel type; one t o model t he t u r b u l e n t f r i c t i o n f a c t o r and t h e

o ther f o r the laminar region. The l a r g e s t o f the two f r i c t i o n f a c t o r s a t a

g iven Reynolds number i s used i n t h e a x i a l momentum equat ion.

A heated-wal l c o r r e c t i o n f a c t o r t o the v i s c o s i t y i s ava i lab le . ( 7 ) This

f a c t o r accounts f o r t h e smal le r drag fo rces along a heated w a l l due t o t h e w a l l

v i s c o s i t y being smal ler than the bu l k subchannel v i s c o s i t y . The c o r r e c t i o n

f a c t o r i s app l ied as a m u l t i p l i e r on the f r i c t i o n f a c t o r , which i s c a l c u l a t e d

us ing the v i s c o s i t y a t the bu l k temperature. The m u l t i p l i e r i s computed as

where P w a l l i s evaluated a t the wa l l tempeieature ca l cu la ted f rom

This c o r r e c t i o n i s based on the assumption t h a t the t o t a l per imeter cons i s t s

of two reg ions - one u n i f o r m l y heated (Ph) a t q ' and the o ther unheated

(Pw-Ph) The H i s the channel heat t r a n s f e r coe f f i c i en t .

Two f i l m c o e f f i c i e n t c o r r e l a t i o n s may be i n p u t f o r each channel t ype where

the l a r g e s t o f the two based on l o c a l Reynolds and P rand t l numbers i s used f o r

computing t h e heat f l u x . I f no f i l m c o e f f i c i e n t c o r r e l a t i o n s are inpu t , t h e

code uses the d e f a u l t c o r r e l a t i o n o f Lyon and M a r t i n e l l i (8) f o r tube bundles

i n l i q u i d meta l . F i l m c o e f f i c i e n t c o r r e l a t i o n s are o f t h e form

where t he user supp l i es t h e cons tan ts A, a, B y and b f o r c a l c u l a t i n g t h e

Nu sse l t number.

Loss c o e f f i c i e n t s t o represen t g r i d spacers o r f l o w b lockages may be

i nc l uded as p a r t of t h e i n p u t . The f u n c t i o n a l form o f l oss c o e f f i c i e n t s i s :

These l oss c o e f f i c i e n t s are assumed t o be independent o f Reynolds number.

4.3.4 M i x i n g C o r r e l a t i o n s

The t u r b u l e n t m i x i ng c o r r e l a t i o n s , which a re t h e same as those found i n

COBRA-IVY g i v e t h e user a cho ice o f f o u r d i f f e r e n t forms: ( 9 Y ~ 0 , ~ ~ )

where I I

G D Re = - 1-I

D ' = 4 ( ~ 1 1 + Ajj)/(PwII + P w j j )

G I = (mII + mj j ) / (AI I + A j j )

The user may s p e c i f y d i f f e r e n t c o r r e l a t i o n s o r d i f f e r e n t c o e f f i c i e n t s f o r each

assembly type.

The wi re-wrap model i n t h e COBRA-WC code i s e s s e n t i a l l y t h e same as t h a t

used i n COBRA-IIIC. ( I 2 ) I n t h i s model t h e wi re-wrap i n v e n t o r y i n each chan-

n e l i s determined, and t h e a x i a l p o s i t i o n where each wrap passes th rough a

t r a n s v e r s e gap i s c a l c u l a t e d based on t h e wi re-wrap p i t c h and s t a r t i n g l o c a -

t i o n . When i t has been determined t h a t a wrap passes th rough a gap a t some

a x i a l l o c a t i o n , t h e t r a n s v e r s e f l o w i n t h a t gap i s s e t t o a f r a c t i o n o f t h e

a x i a l f l o w and i s n o t a d j u s t e d f u r t h e r i n t h a t i t e r a t i v e sweep. The t r a n s v e r s e

f l o w d i v e r t e d th rough t h e gap i s g i v e n as

where 6 i s t h e angle t h e w i r e wrap makes w i t h t h e r o d and 6 i s a u s e r s p e c i f i e d

wi re-wrap parameter. When 6 i s s e t t o 1.0 i t f o l l o w s f r o m Equat ion 60 t h a t t h e

d i r e c t i o n o f f l o w i n t h e gap i s p a r a l l e l t o t h e w i r e wrap. As w i r e wraps move

i n and o u t o f channels, t h e subchannel areas, wet ted per imete rs , and h y d r a u l i c

d iamete rs a re a d j u s t e d a c c o r d i n g l y .

When u s i n g lumped-channel nod ing schelmes i t may n o t be f e a s i b l e t o use t h e

s tandard wi re-wrap model. For these cases a p e r i p h e r a l s w i r l model i s s i m i l a r

t o t h a t used i n t h e ENERGY ( I 3 ) s e r i e s o f codes a v a i l a b l e . For t h e s w i r l

model t h e user must s p e c i f y o n l y a d i r e c t i o n and a parameter which g i v e s t h e

p e r i p h e r a l t r a n s v e r s e v e l o c i t y as a f r a c t i o n o f t h e assembly average a x i a l

v e l o c i t y .

4.3.5 Eaua t ion o f S t a t e

A l though t h e code was w r i t t e n f o r LMFBR a p p l i c a t i o n s , equa t ion o f s t a t e

i n f o r m a t i o n may be i n p u t f o r any s ingle-ph(ase f l u i d . I f no e q u a t i o n o f s t a t e

i n f o r m a t i o n i s i n p u t , t h e f l u i d i s assumed t o be sodium, and t h e f l u i d p roper -

t i e s are o b t a i n e d f r o m t h e ANL-7323 sodium p r o p e r t y c u r v e f i t s . ( 1 4 ) For

problems u s i n g a c o o l a n t o t h e r than sodium i t i s necessary t o i n p u t a s e r i e s

o f cards, each o f which s p e c i f i e s a p ressure and a co r respond ing temperature,

entha lpy , the rma l c o n d u c t i v i t y , s p e c i f i c heat, s p e c i f i c volume, and v i s c o s i t y .

L i n e a r i n t e r p o l a t i o n i s used t o o b t a i n p r o p e r t i e s a t f l u i d temperatures between

those i n p u t va lues. The f l u i d i s assumed t o be incompress ib le b u t i s a l l owed

t o expand thermal 1 y.

OVERALL CODE DESCRIPTION

Th is s e c t i o n shows how a l l t h e p a r t s descr ibed i n t h e p rev ious s e c t i o n a re

combined t o o b t a i n a s o l u t i o n f rom a se t o f i n p u t cards. The ac tua l i n p u t w i l l

be descr ibed card by card i n Sec t ion 7.

The main program and execu t i ve r o u t i n e i n t h e COBRA-WC code i s c a l l e d

COBRA. COBRA t r a n s f e r s c o n t r o l t o var ious subrou t ines t o read i n p u t , so l ve t h e

conservat ion equat ion and p r i n t o u t result!; . COBRA a l s o handles most o f the

boundary c o n d i t i o n s p e c i f i c a t i o n . A f l o w c h a r t i n d i c a t i n g t h e f u n c t i o n o f

program COBRA i s g iven i n F igu re 6. COBRA reads t h e f i r s t i n p u t card t o

determine i f t h e r u n i s t o be a r e s t a r t ( i .e. , p i c k up t h e r e s u l t s f r om an o l d

s o l u t i o n and con t inue c a l c u l a t i o n s p o s s i b l y w i t h m i nor i n p u t changes), o r a new

case i n which a l l t h e c a l c u l a t i o n a l v a r i a b l e s a re i n i t i a l l y zeroed. An i n p u t

card image l i s t i n g i s then generated f o r user debug. I f new i n p u t i s t o be

read, COBRA c a l l s t h e i n p u t r o u t i n e s , whicl i a re descr ibed i n Sec t ion 5.1. Once

t he i n p u t has been read and the problem geometry and ope ra t i ng c o n d i t i o n s

es tab l i shed , COBRA begins t h e t r a n s i e n t t ime loop w i t h one pass through t h e

loop f o r each t ime step. The f i r s t pass t~hrough t h i s loop i s used f o r ob ta i n -

i n g a s teady-s ta te s o l u t i o n f o r t h e problem, which then serves as an i n i t i a l

c o n d i t i o n f o r the t r a n s i e n t . Th is s teady-s ta te s o l u t i o n i s accomplished s imp ly 6 by s e t t i n g the t ime s tep t o a l a r g e number (A t = 10 ) and c o n t i n u i n g on as

though i t were any o the r t i m e step. S e t t i n g t h e t i m e s tep t o a l a r g e number

e f f e c t i v e l y e l i m i n a t e s any c o n t r i b u t i o n o f the s to rage terms i n t he conserva-

t i o n equat ions.

W i t h i n the t r a n s i e n t t ime loop i n COBRA t h e boundary c o n d i t i o n s co r re -

sponding t o t h e t r a n s i e n t t ime elapsed a re then se t . Th is inc ludes s e t t i n g t h e

i n l e t temperature and the pressure drop o r i n l e t f l o w f o r each subchannel. The

app rop r i a te r o u t i n e s f o r s o l v i n g t h e conserva t ion equat ions are then c a l l e d .

These r o u t i n e s were descr ibed t o some ex ten t i n Sec t ion 4.2, b u t Sect ion 5.2

f u r t h e r descr ibes them i n terms o f t h e i r i n t e r a c t i o n w i t h o the r p a r t s o f t h e

code. When c o n t r o l i s r e tu rned back t o program COBRA a s o l u t i o n t o t he con-

s e r v a t i o n equat ions has been ob ta ined f o r t h a t t ime step. A r o u t i n e i s then

c a l l e d t o p r i n t t he des i red r e s u l t s and t h e c a l c u l a t i o n s con t inue w i t h t h e n e x t

t-ime step.

I STARTCOBRA I

T I M E L I M I T

RESTART -

t \ ~ ~ ~ RESTART ROUT l NES

NO YES

I CALL INPUT

CALL ROUT l NES TO SOLVE CONSERVATION

I LOOP

PR INT RESULTS w

I

FIGURE 6. FLOW Chart f o r COBRA

FIRST T I M E STEP STEADY STATE CALCULATION

(At = 106 s,) SET BOUNDARY

CONDITIONS ( INLET FLOW OR A P, INLET TEMPERATURE

I

5.1 INPUT SUBROUTINES

The i n p u t r o u t i n e s have been s p l i t i n t o th ree par ts ; SETUP, SETIN and

SETOUT. Subrout ine SETUP, which i s t he r o u t i n e c a l l e d by program COBRA, does

not read any i n p u t b u t acts as the i n p u t execut ive rou t i ne . SETUP f i r s t c a l l s

subrout ine SETIN, which a c t u a l l y reads a l l o f t he data cards. The card-group

i n p u t format i s i s s imi 1 a r t o t h a t o f COBRA- I V - I . Each group i s headed by a

group card t h a t prov ides in format ion t o subrout ine SETIN f o r t r a n s f e r r i n g con-

t r o l t o a p a r t of the subrout ine which processes the r e s t o f the in fo rmat ion

i n t h a t group. When a l l groups have been processed c o n t r o l i s re tu rned t o

SETUP where some f u r t h e r c a l c u l a t i o n s are done t o e s t a b l i s h a l l the parameters

necessary t o s t a r t t he run. Subrout ine SETOUT i s then c a l l e d t o p r i n t ou t a l l

the in fo rmat ion generated by SETIN and SETUP. This p r i n t o u t prov ides the user

an easy means f o r checking t o see t h a t t he code i s running the problem t h a t he

intended t o run. Fo l lowing t h i s , c o n t r o l i s re tu rned t o SETUP and then back

t o COBRA t o begin the t ime loop.

5.2 SOLUTION OF THE CONSERVATION EQUATIONS -

At each t ime step, c o n t r o l i s passed t o subrout ine SCHEME o r t o RECIRC

depending on the user -cont ro l led opt ion. Subrout ine SCHEME i s c a l l e d i f the

PSOLVE s o l u t i o n technique i s requested, and RECIRC executes the R E C I R C s o l u t i o n

scheme described i n Sect ion 4.2. As before, these two paths are discussed

separately.

F igure 7 l i s t s the program f l o w when subrout ine SCHEME i s ca l l ed . A c a l l

t o subrout ine PREFIX i s necessary t o c a l c u l a t e the constant m a t r i x elements

used i n the energy equat ion s o l u t i o n scheme and t o e s t a b l i s h the indexing

arrays f o r t h e rod and subchannel connections. The f i r s t pass through a l l o f

the a x i a l l e v e l s i s then s t a r t e d w i t h c a l l s t o REHEAT and ENERGY, which calcu-

l a t e t h e v a r i a b l e m a t r i x elements f o r t he energy s o l u t i o n and so lve the energy

equat ions f o r the f i r s t l e v e l o f computat ional c e l l s . A c a l l t o PROP g ives the

f l u i d dens i t ies , subchannel f i l m c o e f f i c i e n t s , and f r i c t i o n fac to rs , and a c a l l

t o FORCE gives the w i re wrap or g r i d spacer fo rced d i ve rs ion t ransverse f low.

Since a t any l e v e l t he momentum equations as solved i n subrout ine PSOLVE are

coupled o n l y w i t h i n an assembly, there i s one c a l l t o the

START SCHEME

I CALL PREFIX TO CALCULATE COEFFICIENTS FOR ENERGY SOLUTION

START ITERATION LOOP I

START A X I A L LEVEL LOOP 1 I I

CALL REHEAT AND ENERGY TO SOLVE ENERGY EQUATIONS

I 1 CALL PROP FOR DENSITIES, F I L M C&FFCIENTS AND FRICTION FACTORS I I I

1 CALL FORCED FOR FORCED DIVERS ION CROSSFLOW

START ASSEMBLY LOOP I I

CALL PSOLVE TO SOLVE MOMENTUM EQUATIONS I

1 SOLVE CONTINU ITY EQUATIONS

AND TRANSVERSE A P

CALL HOTROD TO BACK OUT ROD TEMPERATURES I

YES

1 RETURN TO COBRA I

CALL PBOUND AND NETWORK TO ADJUST INLET FLOWS

FIGURE 7. F low Chart Subrout ine SCHEME

s o l u t i o n r o u t i n e f o r each assembly. A t t he end o f the assembly loop t h e newly

c a l c u l a t e d t r ansve rse f l ows and d e n s i t i e s are used t o c a l c u l a t e t h e a x i a l f l ow .

The t ransverse pressure g rad ien ts are then updated, and t he c a l c u l a t i o n con-

t i n u e s a t t h e nex t a x i a l l e v e l . When c a l c u l a t i o n s f o r a l l a x i a l l e v e l s have

been completed, t he re are c a l l s t o subrou t ines PBOUND and NETWORK i f a pressure

boundary c o n d i t i o n i s used. I n these subrloutines, t h e i n l e t a x i a l f l o w s a re

adjusted, based on t he c a l c u l a t e d subchannlel pressure drop t o s a t i s f y t he

boundary cond i t i on .

Whether o r no t a pressure boundary c o n d i t i o n i s used, the convergence o f

t h e a x i a l f l o w r a t e i s checked a t t h i s p o i n t . I f t h e percen t change i n any o f

t h e a x i a l f l ows i s g rea te r than a use r - spec i f i ed convergence c r i t e r i a , then a l l

t h e l e v e l s a re swept through again. When convergence has been obtained, t h e

rod temperatures are backed o u t f r om the f l u i d temperatures w i t h a c a l l t o

HOTROD. Cont ro l i s then r e t u r n e d t o program COBRA f o r t h e nex t t i m e s tep.

The s o l u t i o n o rder i n R E C I R C i s s i m i l a r t o t h a t o f SCHEME b u t d i f f e r e n t

enough t o warrant a separate d e s c r i p t i o n here. F i gu re 8 g i ves a f l o w c h a r t f o r

subrou t ine RECIRC. The f i r s t p a r t o f t he subrou t ine i s ve ry s i m i l a r t o t he

SCHEME technique except t h a t R E C I R C c a l c u l a t e s temporary va lues o f t h e f l o w

r a t e s us ing the c u r r e n t pressure d i s t r i b u t , i o n i ns tead o f s o l v i n g t he momentum

equat ions f o r pressure. An i nne r i t e r a t i o n assembly-by-assembly loop i s then

s t a r t e d t o so l ve the momentum and c o n t i n u i t y equa t ion s imul taneously . Th i s

p a r t o f t h e sub rou t i ne was descr ibed e a r l i e r i n Sec t ion 4.2.2. When conver-

gence has been achieved i n t he inner loop, a check i s made t o determine i f t he

code i s runn ing i n t h e t i m e i m p l i c i t o r e x p l i c i t mode. If i t i s i n t h e

e x p l i c i t mode, the c o n t r o l i s r e tu rned t o program COBRA f o r t he nex t t ime s tep

c a l c u l a t i o n s . I n t h e i m p l i c i t mode, a f u r t h e r check on convergence i n t h e

ou te r loop i s made. I f convergence has no t been a t t a i ned , then t h e r e i s

another sweep through t h e o u t e r loop as p r e v i o u s l y descr ibed. A check i s made

a t the end o f t he ou te r loop t o determine whether t h e s o l u t i o n scheme would be

more e f f i c i e n t i n t h e i m p l i c i t o r e x p l i c i t mode. Th i s i s determined by t h e

number o f ou te r i t e r a t i o n s t he problem has been t a k i n g i n t h e i m p l i c i t mode,

t h e u s e r - s p e c i f i e d i m p l i c i t t ime step, and t h e maximum a l l owab le e x p l i c i t t i m e

START OUTER ITERATION LOOP I I

I

CALL REHEAT AND ENERGY TO SOLVE ENERGY EQUATIONS I 1

CALL PROP FOR DENSITIES, F I L M COEFFICIENTS AND FRICTION FACTERS I I

CALL FORCE FOR FORCED DIVERS ION CROSS FLOW I

I I

CALCULATE d F l d P AND I N I T I A L FLOW VALUES

I START ASSEMBLY LOOP I

I .I START l NNER ITERATION LOOP

I

SOLUT l ON FOR I - D SOLUT I ON

START A X I A L LEVEL LOOP I

I CALCULATE CONTINUITY ERRORS I

I

I I UPDATE R O W S A N

YES YES I

I RETURN TO COBRA I

FIGURE 8. Flow Chart f o r Subroutine RECIRC

step. Since one sweep through the ou ter loop takes somewhat less t ime than one

e x p l i c i t t ime step, t h e mode i s switched from i m p l i c i t t o e x p l i c i t i f

A t exp

> 1.5At imp/number o f ou ter i t e r a t i o n s

The e x p l i c i t t ime step i s determined by the Courant l i m i t

A t = 0.9* M I N (Ax./v .) exp a l l c e l l s J J

A s teady-state s o l u t i o n i s obta ined i n t h i s scheme by s e t t i n g the t ime s tep t o

a l a r g e value and runn ing i n t h e i m p l i c i t mode.

5.3 DATA STORAGE

The p o t e n t i a l l y l a r g e problems t o be r u n on t h e COBRA-WC code r e q u i r e

c a p a b i l i t y t o s t o r e much o f t h e data ou ts ide o f t h e core memory. The maximum

problem s ize, as determined by the number o f coo lan t c e l l s and rod nodes, t h a t

may be r u n w i t h o u t use o f p e r i p h e r a l s torage i s governed by t h e co re s i z e o f

t he p a r t i c u 1 a r computer i n s t a l 1 a t ion. However, a 217-pin wire-wrapped f u e l

assembly us ing standard subchannel noding w i l l most l i k e l y r e q u i r e p e r i p h e r a l

s torage on any n o n - v i r t u a l memory machine c u r r e n t l y i n use.

The a l l o c a t i o n and use o f t h e pe r i phe ra l storage i n COBRA-WC i s ve ry much

l i k e t h a t i n COBRA-IV-I. Since t h e c a l c u l a t i o n s necessary t o so lve the con-

se rva t i on equat ions a t any a x i a l l e v e l r e q u i r e i n fo rma t i on f o r t h a t l e v e l and

the l e v e l s above and below it, o n l y s u f f i c i e n t room f o r t h a t i n fo rma t i on i s

made a v a i l a b l e i n core i f t h e p e r i p h e r a l s torage o p t i o n i s requested. As t h e

s o l u t i o n a l g o r i t h m moves f rom one l e v e l t o t h e next, i n fo rma t i on f rom the J-1

l e v e l i s w r i t t e n onto d i s k f i l e space and data f rom t h e J + l l e v e l i s read i n t o

core. These data t r a n s f e r s are taken care o f by t he subrout ines ROLLIT, IMAGE

and COPY. To f a c i l i t a t e t h e t rans fe r o f t h e data t o and f rom t h e d isk, a sys-

tem o f v a r i a b l e equiva lencing i s used, s i m i l a r t o t he system used i n

COBRA- I V- I.

A l l of t h e v a r i a b l e s t h a t need t o be t r a n s f e r r e d t o and from a p e r i p h e r a l

s to rage dev ice are equiva lenced t o one l a r g e a r r a y named SAVEAL. Three addi -

t i o n a l ar rays, SAVEA1, SAVEA2 and SAVEA3 are a l s o equivalenced t o SAVEAL i n

such a way t h a t SAVEAl con ta ins a l l t h e J-1 l e v e l i n f o rma t i on , SAVEA2 con ta ins

t h e J l e v e l i n f o rma t i on , and t h e J+1 l e v e l i n f o r m a t i o n i s equiva lenced t o

SAVEA3. F igu re 9 shows how the a r rays would be equivalenced i f t h e r e were o n l y

t h r e e va r i ab les , F, H and P, which were s to red e x t e r n a l l y . I n t h i s example,

t h e a r rays F, H and P are a l l two-dimensional a r rays (number o f channels x 3 ) .

For any channel i, o n l y t h r e e a x i a l l e v e l s are s to red i n core; e.g., Fils

Fi2, and Fi3 are t he a x i a l f low r a t e s a t J-1, J, and J+1, r e s p e c t i v e l y .

The p a r t i c u l a r arrangement o f hav ing t h e t h r e e va r i ab les , F, H, and P, t oge the r

-in t h e s i n g l e a r r a y i s accomplished by dimensioning each o f t he t h r e e v a r i a b l e s

as 3N x 3 and then o v e r l a y i n g t h e 3 a r rays by equ iva lenc ing t h e f i r s t e lement

t o the proper p o s i t i o n i n SAVEAL. For t h i s example t h e f o l l o w i n g statements

would produce t h e v a r i a b l e arrangement i n F i g u r e 9.

Dimension F(3N,3), H(3N,3), P(3N,3), SAVEAL(9N), SAVEA1(3N), SAVEA2(3N),

SAVEA3 ( 3N ) ,

Equivalence (SAVEA1(1), SAVEAL(l)), (SAVEA2(1), SAVEAL(3N+l)),

(SAVEA3(1), SAVEAL(6N+l)), (F(1,1), SAVEAL(l)),

(H(1,1), SAVEAL(N+l)), (P(1,1), SAVEAL(ZN+l))

Use o f t h i s s to rage scheme a l l ows a l l t h e v a r i a b l e s a t one a x i a l l e v e l t o

be t r a n s f e r r e d f rom or t o e x t e r n a l s to rage by a s i n g l e read o r w r i t e w i t h

SAVEAl, SAVEA2 o r SAVEA3 as t h e v a r i a b l e l i s t f o r t r a n s f e r . The user does n o t

have t o be d i r e c t l y concerned about the ac tua l d imension ing and equ i va lenc ing

s i nce t h e aux i 1 i a r y program SPECSET (descr ibed i n Sec t ion 8) handles t h i s f un -

c t i o n . The general d e s c r i p t i o n o f t he da ta s to rage technique has been

presented here t o g i v e t h e i n t e r e s t e d user a more complete understanding o f how

t h e code works.

FIGURE 9. Array Equivalency to Facilitate Data Management for the Roll Option

DUMP and RESTART

The same data storage scheme described above i s a lso very use fu l f o r

s t o r i n g o r "dumping" a l l t he in fo rmat ion a t t he end o f a computation f o r use

a t a l a t e r t ime as a " r e s t a r t ." The dump and r e s t a r t c a p a b i l i t y can be used

i n two ways. I n running the code f o r a s teady-state so lu t i on , t he c a l c u l a t i o n

may terminate before convergence i f more than a user-spec i f i ed maximum compu-

t a t i o n t ime has been used o r i f convergence has not been achieved i n a speci -

f i e d number o f i t e r a t i o n s . I f the user takes the necessary steps t o perma-

n e n t l y s t o r e the "dumped" in format ion, he may r e s t a r t t he s o l u t i o n and cont inue

i t e r a t i n g toward a converged s o l u t i o n a t a l a t e r time. At the t ime o f r e s t a r t

t he user may a l so change some o f t he problem input , i n which case the dumped

s o l u t i o n may be used as a f i r s t guess f o r the s o l u t i o n t o the new problem.

Secondly, t he dump and r e s t a r t system i s use fu l i n making long ( i n terms o f

computer t ime) t r a n s i e n t runs. I n t h i s case, the user s p e c i f i e s a number o f

t ime steps o r t r a n s i e n t seconds t o be run be fore dumping the so lu t i on . The

user may then cont inue the t r a n s i e n t run w i t h or w i thou t making changes t o the

i n p u t by us ing the r e s t a r t opt ion.

At the t ime a run i s completed, a c a l l t o subrout ine DUMPIT w r i t e s o u t a l l

o f t h e necessary i n fo rma t ion stored i n core and on ex te rna l devices t o a new

f i l e i d e n t i f i e d as TAPE 8. When a r e s t a r t r u n i s made a t a l a t e r t ime sub-

r o u t i n e RESTART i s c a l l e d t o read the dump f i l e , se t the value o f a l l v a r i a b l e s

s to red i n core, and p u t the necessary in fo rmat ion on the ex te rna l devices.

6.0 NODING, INPUT PARAMETERS, AND NODING CONVENTIONS

The subchannel noding approach makes t h e COBRA-WC code very f l e x i b l e i n

terms o f the geometries which can be modeled. I n general, as t he f l e x i b i l i t y

and g e n e r a l i t y o f a code increases, t h e amount o f i n p u t requ i red a l so

increases. There are many parameters and dimensions t h a t the user must supply

t o use t h e COBRA-WC code, and i t i s important t h a t t h e user understand how each

o f these i n p u t values i s t o be used t o o b t a i n r e s u l t s . The purpose o f t h i s

sec t i on i s t o p rov ide some d i r e c t i o n f o r t h e user i n p repar ing the i n p u t f o r a

problem and t o descr ibe some o f the model ing convent ions used i n the code.

6.1 NODING LMFBR FUEL AND BLANKET ASSEMBLIES

There has been considerable experience gained i n us ing the COBRA-IV-I code

f o r model ing LMFBR assemblies. Since t h e bas is of t h e COBRA-WC code i s t h e

same, i t i s des i rab le t o t ake advantage o f t h i s experience whenever poss ib le .

The COBRA-WC code may be used i n t h e same manner as t h e COBRA-IV-I code f o r

standard subchannel (F igure 10) ana lys is ; the same se t o f i n p u t parameters

which have produced r e l i a b l e r e s u l t s us ing COBRA-IV-I should be adequate f o r

t h e COBRA-WC code. However, i t i s a n t i c i p a t e d t h a t much o f the use o f the

COBRA-WC code w i l l be d i r e c t e d toward mul t iassembly t r a n s i e n t ana l ys i s r e q u i r -

i n g t h a t coarser noding schemes be used f o r many of the assemblies. Without

p r o v i d i n g t h e r e s u l t s o f a complete noding study here, some suggest ions can be

made concerning the node arrangement and the requ i red i n p u t parameters. It i s

suggested t h a t any coarse noding be done i n such a way as t o preserve t h e

o r i g i n a l subchannel boundaries ( i .e., the coarse node boundaries should be

co inc iden t w i t h and no t cross t h e standard subchannel boundaries). F igu re 11

shows a 37-channel model o f a 217-pin bundle. I f t h i s t ype o f coarse noding

i s used, t h e assumptions made f o r t h e t ransverse connect ions i n standard sub-

channel ana lys is are s t i 11 app l i cab le . I n prev ious sec t ions i t was mentioned

t h a t care should be taken when us ing t h e d i r e c t i n v e r s i o n m a t r i x so l ve r w i t h

PSOLVE or when us ing the R E C I R C scheme. The amount o f core s torage requ i red

t o s e t up and so lve t h e m a t r i x equat ion depends on t h e maximum bandwidth f o r

any assembly. The bandwidth f o r an assembly i s one p lus tw i ce the maximum

F I G U R E 10. Standard Subchannel Noding f o r a 19-Pin Bundle

d i f f e r e n c e o f channel numbers connected by a t ransverse gap. An i l l u s t r a t i o n

o f t h i s numbering technique i s g iven i n Sec t ion 9.

For coarse noding i t i s suggested t h a t t h e t ransverse momentum c o n t r o l

volume l e n g t h be N * P 1 where 2' i s the l e n g t h which would be used f o r s tandard

subchannel ana l ys i s and N i s t h e number o f rows o f rods between channel cen-

t r o i d s . Th is w i l l g i v e approx imate ly t he c o r r e c t area f o r momentum t r a n s p o r t .

The t r ansve rse gap w i d t h should be t h e sum o f t h e i n d i v i d u a l rod- to - rod gaps

t h a t make up a connect ion between lumped subchannels.

The l e n g t h f o r c a l c u l a t i n g conduc t i ve heat t r a n s f e r between ad jacen t

channels i s g iven by

where t he i n p u t GK i s an assembly-dependent conduct ion f a c t o r . Doubl ing t h e

va lue o f GK e f f e c t i v e l y doubles t h e r a d i a l heat t r a n s f e r due t o conduct ion.

Note t h a t 1 / G K = ZK used i n Equat ion 2.

The op t ima l va lue o f GK i s ve ry problem dependent, and much more work i s

r e q u i r e d t o be ab le t o predetermine t h e conduc t ion f a c t o r . For problems where

t he re i s no i n f o r m a t i o n on t h e conduct ion f a c t o r , GK should be chosen t o make

gc approx imate ly equal t o t h e subchannel c e n t r o i d - t o - c e n t r o i d d is tance .

Turbulence model ing i n LMFBR bundles has n o t y e t been w e l l def ined.

Usua l l y , when us ing the COBRA w i r e wrap model i n standard subchannel ana lys is ,

has s imple m i x i n g c o r r e l a t i o n o f t h e fo rm g i ven i n equa t ion (56) i s used. B i s g iven a va lue o f 0.01 t o 0.02. When us ing lumped noding schemes w i t h o u t t he

wire-wrap model i t i s d e s i r a b l e t o enhance t h e t u r b u l e n t m i x i n g by us ing a

va lue o f B o f up t o 0.1. The t u r b u l e n t momentum f a c t o r g e n e r a l l y has a ve ry

smal l e f f e c t on v e l o c i t y and temperature d i s t r i b u t i o n , b u t a va lue o f 1.0 may

be used i f des i red. The t u r b u l e n t momentum f a c t o r i s used as a m u l t i p l i e r on

t h e t u r b u l e n t momentum exchange term i n t h e a x i a l momentum equat ion

(Equat ion 3).

When us ing lumped noding schemes f o r the f l o w channels, it i s a lso d e s i r -

ab le t o reduce t h e d e t a i l i n t h e model ing o f t h e p i ns . It i s suggested t h a t

one p i n be modeled f o r each f l o w channel. The r a d i a l power f a c t o r o f the s i n -

g l e p i n can be determined by t a k i n g a weighted average o f t h e r a d i a l power

f a c t o r s o f t he assoc ia ted p ins . The we igh t i ng f a c t o r should be t he f r a c t i o n

o f each r o d sur face exposed t o t h e lumped channel. The p roper amount o f heat

i s d e l i v e r e d t o the channel by making the channel power f a c t o r equal t o t he

number o f p i n s t h e lumped p i n represents . Study o f t h e i n p u t i n s t r u c t i o n s and

sample problems should c l a r i f y t h i s procedure. F i gu re 11 shows one p o s s i b l e

lunped noding scheme f o r a 61-p in bundle.

Some o f the COBRA-WC i n p u t i s i n t he form o f t a b l e s f o r va r i ous p r o f i l e s

( a x i a l power genera t ion p r o f i l e , t r a n s i e n t f l o w f a c t o r s , e t c . ) . I n s e t t i n g up

a problem it i s impor tan t t h a t t he user knows how each o f these p r o f i l e s i s t o

be appl ied. Genera l ly , s imple l i n e a r i n t e r p o l a t i o n i s used t o determine t h e

appropr ia te f a c t o r f rom a p r o f i l e t a b l e . For t he t r a n s i e n t p r o f i l e s t h e t o t a l

e lapsed t i m e i s c a l c u l a t e d as t h e sum o f a l l p rev ious t i m e s teps p l u s t h e

cu r ren t t ime step. This elapsed t ime i s then used t o determine f a c t o r s f o r t h e

i n l e t f l o w and temperature, power, and pressure drop by i n t e r p o l a t i o n between

t h e nearest two tabu la r values t o the elapsed t ime. For t he a x i a l power p ro -

f i l e the a x i a l d is tance used f o r i n t e r p o l a t i o n i s the d is tance t o the center

of t h e c e l l f rom the i n l e t ( t he bottom o f t he f i r s t computat ional c e l l ) . The

Reynolds-number-dependent l oss c o e f f i c i e n t s are ca l cu la ted by i n t e r p o l a t i n g

from the Reynolds-number-versus-loss-coeff ic ient-factor t a b l e a t the l o c a l

Reyno 1 d s number.

A t a b l e may a lso be i n p u t t o change the ma te r ia l o r dimensions o f a rod

a x i a l l y . I n t h i s t a b l e the endpoint o f each ma te r ia l i s s p e c i f i e d i n terms o f

t he d is tance from the i n l e t . The a x i a l c e l l s i n the rods correspond t o the

a x i a l c e l l s f o r t he coolant . Each a x i a l rod c e l l i s assumed t o be e n t i r e l y

w i t h i n one ma te r ia l zone. A c e l l i s assumed t o be i n a p a r t i c u l a r zone i f the

t o p o f t he c e l l f a l l s w i t h i n the zone o r i s co inc iden t w i t h upper boundary o f

the zone. F igure 12 shows a rod d i v ided i n t o 7 a x i a l c e l l s and th ree m a t e r i a l

zones. The m a t e r i a l assumed f o r each c e l l i s noted.

FIGURE 11. Lumped Subchannel Noding f o r a 61-Pin Blanket Assembly

A X I A L REFLECT0 R

(STAINLESS STEEL)

FUELED REG ION

A X I A L REFLECTOR

(STAINLESS STEEL)

STA INLESS STEEL

STAINLESS STEEL

FUEL

FUEL

FUEL

FUEL

STA INLESS STEEL

FIGURE 12. A x i a l Fuel P in Model Showing the Ma te r ia l Typed Assumed f o r Each Computational C e l l

6.2 MODELING OTHER FLOW PATHS

I n modeling mult iassembly problems i t i s an t i c i pa ted t h a t the user w i l l

want t o model some f l o w paths which are not p i n bundles (e.g., r e f l e c t o r s o r

bypass f l o w paths) . Experience on the use of the code i n t h i s area i s l i m i t e d

bu t as long as the bas ic assumptions used i n t h e code are not v i o l a t e d and care

i s taken t o ensure t h a t the i n p u t i s reasonable, then usefu l r e s u l t s can

be obta ined. Since the v a r i e t y of a p p l i c a t i o n s i n t h i s area i s so la rge , no

at tempt w i l l be made t o i n d i c a t e how t h e i n p u t should be chosen f o r p a r t i c u l a r

problems. I t should be noted t h a t t he code i s no t g e n e r a l l y a p p l i c a b l e t o f r e e

f i e l d c a l c u l a t i o n s s i nce t h e f l u i d shear terms a re n o t i nc l uded i n t h e momentum

equat ions.

6.3 AXIAL NODES AND TIME STEP

The v a r i a b l e a x i a l node l e n g t h o p t i o n a l lows t he user some f l e x i b i l i t y i n

s e l e c t i n g a noding scheme f o r a p a r t i c u l a r problem. There i s no s t a b i l i t y

l i m i t on the number o r l e n g t h of each node, b u t t h e a x i a l node arrangement

should be chosen t o p rov ide t h e bes t r e s u l t s f o r t h e lowes t computat ion cos ts .

For t h i s i t i s impor tan t t o remember t h a t us i ng t he p e r i p h e r a l s to rage o p t i o n

p laces a r a t h e r severe j o b cos t p e n a l t y (depending on t h e computer f a c i 1 i t y

cos t a l go r i t hm) on l a r g e jobs and can be worse f o r smal l jobs. The o p t i o n

should be avoided i f a t a l l p o s s i b l e by keeping t h e number o f nodes t o a

minimum.

There should always be enough a x i a l nodes t o adequately r e s o l v e t he a x i a l

power p r o f i l e . The o n l y o t h e r l i m i t on t h e number o f nodes i s imposed when t h e

wire-wrap model i s used. Wi th t h i s o p t i o n t he re must be a t l e a s t s i x nodes per

a x i a l wire-wrap l e a d l e n g t h s i nce a w i r e i s n o t a l lowed t o pass through more

than one t r ansve rse gap a t each a x i a l l e v e l .

Time s teps should be chosen i n much t h e same way as t h e a x i a l steps, i.e.,

t h e y must be s u f f i c i e n t l y smal l t o r e s o l v e changes i n the boundary c o n d i t i o n s

and t o f o l l o w t h e changes i n t h e t r a n s i e n t s o l u t i o n . Each problem must be

looked a t c a r e f u l l y t o determine what t r a n s i e n t e f f e c t s are impor tan t and how

smal l t h e t ime s teps must be so as n o t t o miss them. It i s o f t en adv i sab le t o

r u n a. s imple s ing le-channel problem w i t h a l l t h e e s s e n t i a l f e a t u r e s severa l

t imes w i t h var ious t ime s teps t o determine t h e l a r g e s t a l lowab le t i m e s t e p i n

each r e g i o n o f the t r a n s i e n t .

6.4 CONVERGENCE CRITERIA

As p rev ious l y described, convergence i s checked i n the code i n several

ways. The e r r o r i n t he energy equat ion i s computed as (h-k) /h where h i s t he

prev ious outer i t e r a t i o n enthalpy. The i n p u t v a r i a b l e HERROR c o n t r o l s t h i s

convergence and has a d e f a u l t va lue 0.001, which i s adequate f o r most appl i ca -

t i ons . There i s another check on the convergence o f the energy s o l u t i o n i n t he

Gauss-Siedel i t e r a t i v e scheme. The e r r o r i s computed s i m i l a r t o t h a t f o r t he

ou ter loop, bu t the convergence c r i t e r i a has been i n t e r n a l l y se t i n the code

t o 1.0 x

Convergence f o r momentum and c o n t i n u i t y i s checked i n d i f f e r e n t ways

depending on whether t h e PSOLVE scheme o r the R E C I R C scheme i s used. I n PSOLVE

the r a t e o f change o f both and c ross f low and a x i a l f l o w are checked as:

where W and F are the l a s t i t e r a t e values f o r t he c ross f low and a x i a l f l o w

ra te . Defau l t values o f 0.1 and 0.01 are a v a i l a b l e f o r the t ransverse (WERRY)

and a x i a l f l o w (FERROR) convergence c r i t e r i a , respec t i ve l y . General l y , i t i s

not necessary to converge on the t ransverse f lows as t i g h t l y as on the a x i a l

f lows s ince the magnitude o f t he t ransverse f l o w i s smal l and changes i n t h e

crossf low have a small e f f e c t on the a x i a l f l o w and temperature d i s t r i b u t i o n .

When us ing the Gauss-Siedel s o l u t i o n scheme f o r t h e momentum equations, t he

i n t e r n a l convergence c r i t e r i a , WERRY, may be se t or allowed t o d e f a u l t t o a

value o f 0.001 which i s genera l l y s u f f i c i e n t .

I n the R E C I R C scheme convergence i s checked as the r a t i o o f the e r r o r i n

t h e c o n t i n u i t y equat ion t o the maximum o f the f lows a t t he c e l l boundaries.

FERROR i s used as the c r i t e r i a f o r convergence i n the outer loop, and WERRY i s

used as t h e c r i t e r i a i n t he inner pressure loop.

F. - F 1 ,j i , j

Fi,j and Max

i ,j Max k , j

- 'k,j - k , j

k, j

6.5 DAMPERS AND ACCELERATORS

A damper or acce lera tor i s appl ied a t several p o i n t s i n the code t o main-

t a i n s t a b i 1 i t y and t o increase convergence ra tes . General ly, the damper ( o r

acce le ra to r ) i s app l ied as

where $ i s t h e q u a n t i t y being damped, a i s t he damper and 6 i s the l a s t i t e r a t e

value. The th ree dampers used i n the COBRA-WC code are DAMPING, ACCELY and

ACCELF. DAMPING i s used t o damp the t ransverse pressure g rad ien t term used i n

the t ransverse momentum equation. A d e f a u l t value o f 0.8 i s suppl ied and i s

u s u a l l y s u f f i c i e n t . ACCELY i s the acce lera tor f o r the SOR s o l u t i o n scheme f o r

the momentum equations i n PSOLVE. It d e f a u l t s t o 1.6 which, from experience,

has g iven good r e s u l t s f o r a wide v a r i e t y o f problems. The a x i a l f l o w damper,

ACCELF, d e f a u l t s t o 0.7 and cannot be increased too much except f o r problems

which r e q u i r e very l i t t l e i t e r a t i o n f o r convergence.

There are th ree ramps a v a i l a b l e i n t he code t o help convergence a t the

s t a r t o f a new problem. These ramps a l l ow some o f the boundary c o n d i t i 6 n t o

be brought i n t o f u l l e f f e c t over a number o f i t e r a t i o n s . The th ree ramps are

i d e n t i f i e d as: NARAMP, the number o f i t e r a t i o n s over which channel area

changes are introduced; NRAMP, the number o f i t e r a t i o n s over which the w i re -

wrap and l oss c o e f f i c i e n t e f f e c t s are in t roduced i n the noded r e g i o n (network

losses are not ramped i n ) and NRAMPH, the number o f i t e r a t i o n s over which the

power i s in t roduced. Each o f t he ramps i s operable o n l y f o r s teady-state s o l -

u t i o n s and must be r e s e t by card i n p u t i f they are desi red f o r a r e s t a r t case.

COBRA-WC INPUT

7.1 GENERAL DESCRIPTION

COBRA-WC was developed by mod i f y i n g and extending COBRA- I V - I t o mode 1

mult iassembly LMFBR t r a n s i e n t problems. The geometry modeling f l e x i b i l i t y has

been increased w h i l e l i m i t i n g the code's c a p a b i l i t y t o so lve single-phase

problems.

I n designing the i n p u t fo r COBRA-WC, two ob jec t i ves were i d e n t i f i e d :

1 ) ma in ta in t h e modeling f l e x i b i l i t y o f prev ious vers ions o f COBRA, and 2 ) keep

the requ i red i n p u t t o a minimum. To meet t he f i r s t ob jec t ive , the general form

o f t he COBRA i n p u t was reta ined, i.e., descr ib ing the geometry by subchannels.

This means tha t , i n a d d i t i o n t o the mult iassembly c a p a b i l i t i e s , COBRA-WC has

a l l t h e single-assembly LMFBR modeling c a p a b i l i t i e s o f COBRA-IV-I, except f o r

a x i a l conduction. To meet the second o b j e c t i v e i t was decided t o a l l ow the

user t o spec i f y types o f assemblies w i t h associated rod c o n f i g u r a t i o n types.

A p a r t i c u l a r assembly type i s described by i n p u t i n much the same manner as a

s i n g l e assembly would be described us ing COBRA-IV-I; i.e., by spec i f y i ng sub-

channel dimensions and t ransverse connections. Once a p a r t i c u l a r assembly type

has been described, t he user can i d e n t i f y o ther assemblies o f t he same type.

The code w i l l then generate the geometry in format ion fo r other assemblies o f

t he same type. A s i m i l a r procedure i s used f o r descr ib ing rod con f i gu ra t i ons .

An opt ion a l lows the user t o change the rod r a d i a l power f a c t o r s f o r a given

rod c o n f i g u r a t i o n type so t h a t assemblies o f one type may have va r ied power

p r o f i 1 es. The rod con f i gu ra t i on types must correspond t o the assembly types;

i.e., a type one assembly must have a type one r o d con f i gu ra t i on , e t c .

To s i m p l i f y the input , the code has been se t up t o use two sets o f sub-

channel i d e n t i f i e r s , the l o c a l and g loba l i d e n t i f i e r s . The l o c a l subchannel

i d e n t i f i e r s r e f e r t o a subchannel by i t s assembly number and subchannel number

w i t h i n t h a t assembly. A l l code i n p u t and output r e f e r t o these numbers.

I n t e r n a l l y the code uses a g lobal subchannel i d e n t i f i e r which i s a s i n g l e sub-

channel number. This was done t o a l l ow use o f a l a rge p a r t o f the C O B R A - I V - I

coding as i t appl ied t o s i n g l e assembly analys is .

The procedure f o r s e t t i n g up a mul t iassembly problem should become c l e a r e r

a f t e r s t udy ing t h e i n p u t i n s t r u c t i o n s a long w i t h t he sample problem i n p u t .

As i n p rev ious vers ions o f COBRA, t he i n p u t i s arranged i n card groups

w i t h group header cards i n d i c a t i n g t h e problem s i z e and t h e requested op t i ons .

As much as poss ib le , the i n p u t was separated i n t o the va r i ous groups based on

some common purpose; e.g., t h e f l u i d computat ional g r i d i s s e t up u s i n g Card

Group 4 i n p u t and the rod data i s supp l ied i n Card Group 8. A b r i e f sumnary

o f i n p u t i n each card group i s g iven below t o he lp t h e user l o c a t e those groups

f o r which i n p u t i s r e q u i r e d f o r a s p e c i f i c problem.

7.2 CARD GROUP SUMMARY

Card Group I n p u t

P r e l i m i n a r y Card(s) - maximum computat ion t ime l i m i t

- r e s t a r t o p t i o n

- r e s t a r t parameters

- case number and t i t l e

Group 1 - f l u i d p r o p e r t y t a b l e

F l u i d P r o p e r t i e s (no t r e q u i r e d i f the f l u i d i s sodium)

G r o w 2 - c o r r e l a t i o n s f o r f i l m c o e f f i c i e n t s and

F r i c t i o n Fac to rs f r i c t i o n f a c t o r s f o r t u r b u l e n t and

and F i l m laminar f l o w

C o e f f i c i e n t s

Group 3 - any number o f t a b l e s o f hea t genera t ion

A x i a l Heat m u l t i p l i e r versus normal ized a x i a l d i s t a n c e

F lux P r o f i l e


Group 4 - in te rassembly heat t r a n s f e r parameters

Subchannel and connect ions

and Assembly - f o r c i n g f u n c t i o n i d e n t i f i e r f o r each assembly

I n fo rma t i on - network model i n f o rma t i o n (assembly)

- subchannel dimensions and connect ions

- thermal connect ion da ta

Group 5

Area V a r i a t i o n - t a b l e s g i v i n g normal ized area versus normal ized

a x i a l d i s t ance

Group 6

Gap V a r i a t i o n - t a b l e s g i v i n g normal ized gap w id th versus

normal i z e d a x i a l d i s t ance

Group 7

Wire Wraps and - w i r e wrap parameters

Loss C o e f f i c i e n t s - spacer g r i d parameters

- network model i n f o r m a t i o n (assembly groups)

- l o s s c o e f f i c i e n t versus Reynold's number t a b l e s

- b locked channel i n f o r m a t i o n

Group 8

Rod I n fo rma t i on - r o d dimensions

- r a d i a l power f a c t o r s

- r o d m a t e r i a l p r o p e r t i e s

- temperature dependent m a t e r i a l p r o p e r t i e s

- r o d m a t e r i a l d i s t r i b u t i o n ( a x i a l l y )


Group 9

C a l c u l a t i o n - r o l l o p t i o n

Parameters - momentum equat ion s o l u t i o n o p t i o n

- subchannel l e n g t h

- t r a n s i e n t t i m e

- convergence c r i t e r i a

- c r o s s f l o w r e s i s t a n c e

- number o f a x i a l nodes

- number o f t i m e s teps

- t i m e s tep versus t r a n s i e n t t ime t a b l e

- v a r i a b l e a x i a l node leng ths

Group 10

M ix i ng Parameters - t u r b u l e n t m i x i n g c o r r e l a t i o n

- conduc t ion geometry f a c t o r

- s w i r l model parameters

Group 11

Boundary

Cond i t ions

- i n l e t temperature d i s t r i b u t i o n

- i n l e t f l o w d i s t r i b u t i o n

- pressure drop

- assembly power l e v e l s

- t r a n s i e n t f o r c i n g f u n c t i o n s

Group 12

Output Parameters - o p t i o n s t o p r i n t a l l o r any p a r t o f t h e c a l -

c u l a t e d r e s u l t s .

The f o l l o w i n g s e c t i o n descr ibes t h e i n p u t op t i ons f o r us ing t h e COBRA-WC

code. I n s e t t i n g up an i n p u t deck, t h e user should i n i t i a l l y decide f r om which

o r i e n t a t i o n ( l o o k i n g upstream or l o o k i n g downstream) t he problem i s t o be

viewed and m a i n t a i n a l l i n p u t c o n s i s t e n t w i t h t h a t v iewpo in t . Th is i s p a r t i c -

u l a r l y impor tan t i n d e s c r i b i n g the r a d i a l power p r o f i l e i n Card Group 8 and t h e

w i r e wrap model i n Card Group 7.

62

7.3 INPUT INSTRUCTIONS FOR COBRA-WC

The i n p u t i n s t r u c t i o n s are d i v ided i n t o two sect ions. The f i r s t sec t ion

describes t h e p r e l i m i n a r y cards requ i red f o r every run. The second l i s t s a l l

o f the group i n p u t cards, some or a l l o f which may not be requ i red f o r r e s t a r t

runs. The f i r s t card f o r each group c o n t r o l s t he user op t ions f o r t h a t group.

PRELIMINARY CARDS

Card Label Var iables Format and Expl anat i o n

COBRA. 1 MAXT,IECHO Format (215)

Must be the f i r s t da ta card o f t h e i n p u t deck.

MAXT = t h e computer t ime l i m i t (seclO) allowed f o r

problem ca l cu la t i ons . Computer CP t ime l i m i t

must be greater than MAXT t o a l l ow f o r p r i n t i n g

o f r e s u l t s i f MAXT i s exceeded. Negative MAXT

ind i ca tes a "Restar t " problem from a p rev ious l y

s to red so lu t i on .

I ECHO = o p t i o n t o have i n p u t card images p r i n ted .

IECHO = 0: images w i l l be p r i n ted , IECHO = 1:

no p r i n t o u t . IECHO = 0: d e f a u l t .

R E S T R T . ~ (a ) NJUMP, NA, Format (415, F5.0) IT, NTT, ITT Opt ional i npu t : MAXT negat ive

Restar t opt ions, where:

(a) For f u r t h e r in fo rmat ion on the r e s t a r t opt ions, see the d e s c r i p t i o n o f subrout ine RESTRT i n Appendix A.

Card Label Var iab les

RESTRT.l NJUMP

(con td )

TTT

Format and Expl anat i o n

= r e s t a r t f l a g . NJUMP = 0: con t i nue c a l c u l a

t i o n s on a p rev ious s teady-s ta te o r t r a n s i e n t

s o l u t i o n ; do no t read i n any a d d i t i o n a l data.

NJUMP = 1: new problem c a l c u l a t i o n w i t h a

p rev ious s o l u t i o n as t h e f i r s t computat ional

guess o r con t i nue c a l c u l a t i o n s on a p rev ious

s o l u t i o n read ing a d d i t i o n a l da ta f rom sub-

r o u t i n e setup. The code expects r e s t a r t

i n f o r m a t i o n t o be on a f i l e w i t h l o g i c a l l i f e

name, TAPE8. Res ta r t i n f o r m a t i o n i s dumped t o

TAPE8 a f t e r a r u n i s completed.

NJUMP = 2: read dump tape, p r i n t i n p u t and

r e s u l t s then STOP. NJUMP = 3: same as NJUMP

= 0, b u t a l l t h e i n p u t da ta i s p r i n t e d .

= number o f a d d i t i o n a l i t e r a t i o n s . The o l d

va lue o f NTRIES (SETUP 9.3) i s increased by NA

i n a s teady-s ta te problem o r i s s e t t o NA i n a

t r a n s i e n t . NTRIES may be r e s e t d i r e c t l y i n

Card Group 9 i f NJUMP = 1.

= 1: f l a g t o begin a t r a n s i e n t s o l u t i o n a t t i m e

zero f rom a p rev ious s teady-s ta te s o l u t i o n .

T rans ien t da ta must be read i n (NJUMP=~) f rom

setup. For o the r r e s t a r t cases, t h e va lue o f

I T i s ignored.

= number o f a d d i t i o n a l t r a n s i e n t t ime s teps

al lowed. NTT i s used t o increase t h e va lue o f

NDT (SETUP.9.3) i n order t o con t inue o r s t a r t

a t r a n s i e n t .

= t o t a l a d d i t i o n a l t r a n s i e n t t ime (sec) . The

t i m e s tep s i z e i s TTTINTT un less a t i m e s tep

s i z e f o r c i n g f u n c t i o n has been o r w i l l be

(NJUMP=l) supp l ied i n Card Group 9.

Card Label Variables Format and Explanation

SETUP.0 KASE, J1, TEXT Format (215,17A4)

Case control card, where:

KASE = problem case number. K > 0: begin case with core i n i t i a l i z ed t o zero. K < 0: use previous case solution as f i r s t guess. K = 0: STOP.

TEXT

= print option fo r input data. J1 = 0: p r in t only new input data. J1 = 1: p r in t a l l input

data. J1 = 2: pr in t only operating condi- t ions . J1 = 10: p r in t a l l input data, then

stop.

= output t ex t for problem iden t i f i ca t ion ; maximum: 68 characters.

GROUP INPUT CARDS

Group 1 - Fluid Property Table

If t h i s group data i s not input, the f l u id propert ies will be taken from

ANL-7327 sodium property curve f i t s . The system pressure, PLIQ i s used only

for calculat ing a sa turat ion temperature. Calculations will be terminated if

any temperature r i s e s above the sa turat ion temperature.

Card Label Variables Format and Explanation

SETUP. 1 1,Nl Format (15 15)

N 1 = NPROP, number of property cards to be read

Format (8E10.5), ( I = l , N 1 )

Read in N1 f l u id property cards, where

Card Label Va r i ab les

SETUP.l.l PLIQ

( con td ) TEMLIQ

HLIQ

CONLIQ

CPLIQ

VLI Q

VISLIQ

Format and Exp lana t ion

= pressure ( p s i a )

= temperature ( O F )

= en tha lpy ( B t u / l bm)

= thermal c o n d u c t i v i t y ( ~ t u / h r - f t - O F )

= spec i f i c heat ( ~ t u / l bm-OF)

3 = s p e c i f i c volume ( f t /Ibm)

= v i s c o s i t y ( l b rn / f t - h r )

G r o w 2 - F r i c t i o n Fac tors and Heat Trans fer C o e f f i c i e n t s

Any number of f r i c t i o n f a c t o r and f i l m c o e f f i c i e n t c o r r e l a t i o n s may be

i npu t . I n p u t i n Card Group 4 determines which c o r r e l a t i o n w i l l be app l ied t o

each channel.

Card Label Var iab les Format and Explanat ion

SETUP.2 2,N19N2,N3 Format (1515)

= NFRICT, number o f f r i c t i o n f a c t o r c o r r e l a t i o n

se ts t o be read i n . De fau l t s t o 1.

N 2 = NMEAT, number o f heat t r a n s f e r c o e f f i c i e n t

c o r r e l a t i o n se ts t o be read i n . If NHEAT < 1,

d e f a u l t s t o t he Lyon -Mar t i ne l l i c o r r e l a t i o n .

N3 = NVISCW, wa l l v i s c o s i t y c o r r e l a t i o n op t ion . N3

= 0: no heated w a l l c o r r e c t i o n t o t he f r i c t i o n

f a c t o r . N4 = 1: inc lude heated w a l l c o r r e c t i o n

t o t he f r i c t i o n f a c t o r .

SETUP.2.1 AA(I ) , BB(I ) , Format (8F5.3) ( I = 1, N1) CC(I) , DD(I ) , EE( I ) , AAL(I ) , BBL(I), CCL(I),

AA, BB, CC, DD, EE = constants i n t he c o r r e l a t i o n o f t he form:

f T = AA ( R , ) ~ ~ + CC ( R , ) ~ ~ + EE

AAL, BBL, CCL = o p t i o n a l constants f o r laminar f r i c t i o n f a c t o r

c o r r e l a t i o n o f the form:

fL = AAL ( R ~ ) ~ ~ ~ + CCL

When the laminar f r i c t i o n f a c t o r c o r r e l a t i o n i s

s p e c i f i e d t h e code takes the f r i c t i o n f a c t o r t o

be the maximum o f fT and fL.

Card Label Var i abl es Format and Expl anat i o n

SETUP.2.2 Format (8F5.3), ( I = 1, N2)

AHL3(I ) , AHL4(I ),

Opt ional input : N2 > 0.

AH1, AH2, AH3, AH4 = constants fo r the single-phase heat t r a n s f e r

c o r r e l a t i o n o f the form:

= constants f o r the op t i ona l laminar single-phase heat t r a n s f e r c o r r e l a t i o n o f

the form:

When the laminar heat t r a n s f e r c o r r e l a t i o n

i s used, t he code takes H t o be the maximum

o f HT and HL.

When N2 = 0, code de fau l t s the t u r b u l e n t

f i l m c o e f f i c i e n t : AH1 = 0.025; AH2 = 0.8;

AH3 = 0.8; AH4 = 7.0.

Group 3 - Axi a1 Power P r o f i l e s

Any number o f p r o f i l e s may be read i n . The p a r t i c u l a r p r o f i l e t o be used

f o r each assembly i s determined f rom Card Group 4 i npu t .

Card Label Var iab les Format and Exp 1 anat i o n

SETUP. 3 3,Nl,N2 Format (15 15)

N 1 = NHFT, number o f power p r o f i l e s t o be read i n

N 2 = NAX, number o f e n t r i e s i n each power p r o f i l e

tab1 e

SETUP.3.1 Y(I) Format (12F5.3), ( I = 1, N2)

Y = r e l a t i v e p o s i t i o n (X/L) a t which power f a c t o r

i s given, where L i s t h e t o t a l bundle length.

must inc lude 0.0 and 1.0 as end po in ts .

SETUP.3.2 AXIAL( 1,L) Format (12F5.3), ( I = 1, N2)

AX I AL = r e l a t i v e power dens i t y a t (X/L). Repeat f o r

t h e N 1 p r o f i l e s ; i.e., L = 1, N1.

G r o u ~ 4 - Channel Lavout and Dimensions

I n the Card Group 4 i n p u t i n s t r u c t i o n s are several references regard ing

t h e order i n which c e r t a i n parameters must be i npu t . The code se ts up a r e f -

erence frame based on the f i r s t assembly i npu t . The s ide i d e n t i f i e d as s ide 1

on t h e f i r s t assembly must be s ide 1 on a l l assemblies. The o ther s ides must

be a l l numbered i n a c lockwise o r a l l i n a counter-clockwise fashion. This

r e s t r i c t i o n i s necessary t o s e t up t h e in terassembly heat t r a n s f e r nodes.

Also, t h e manner i n which the face channel numbers are i n p u t must be done con-

s i s t e n t l y , e i t h e r a l l c lockwise or a l l counter-clockwise. Since i t does no t

mat te r whether the i n p u t i s counter-clockwise or clockwise, i t makes no d i f -

fe rence whether t h e u s e r ' s core p i c t u r e i s l ook ing from t h e top or bottom, as

l ong as h i s numbering i s cons is ten t .

When two assemblies w i t h s i m i l a r noding are adjacent t he re w i l l be one

heat t r a n s f e r (IAHT) node generated f o r each f l u i d c e l l a1 ong t h e assembly

face. When adjacent assemblies have d i f f e ren t nodi ng schemes, t he number o f

IAHT nodes generated i s determined by t h e assembly w i t h t h e greater number o f

f l u i d c e l l s on a face. To ob ta in s a t i s f a c t o r y r e s u l t s i n t h i s s i t u a t i o n , t he

number o f f l u i d c e l l s along a face i n t h e more f i n e l y noded assembly should be

an i n tege r m u l t i p l e o f the number o f f l u i d c e l l s on a face i n the coarse ly

noded assembly.

I n a l l cases, i t i s assumed t h a t the IAHT nodes between two assemblies are

a l l o f equal length. Examination o f t h e sample problem i n p u t should help t o

c lea r up the Card Group 4 i n p u t i n s t r u c t i o n s .


SETUP .4 4,NlYN2,N3,N4

N 1

N 2

SETUP.4.1 RHODF , W IDTDF RWALLDF . WTHDF

RHODF

WIDTDF

RWALLDF

WTHDF


Format ( I 5 1 5)

= NASSEM, number o f assemblies. D e f a u l t i s 1.

= IAHT; s e t t o 1 i f code-generated i n t e r -

assembly heat t r a n s f e r nodes between ne igh-

b o r i n g assemblies are des i red. IAHT = 2:

same as 1, b u t i n a d d i t i o n w a l l nodes on t h e

uncoupled s i des o f a l l t he assemblies are

generated t o model t h e i r heat c a p a c i t y

e f f e c t s . Th is same a d d i t i o n a l noding can be

performed f o r s p e c i f i c assembl ies by u s i n g

IAHT = 1 and u s i n g SETUP.4.5.

= NWK, number o f a d d i t i o n a l w a l l thermal con-

nec t ions no t generated by IAHT = 1 o r IAHT =

2 op t i on .

= NETWK; s e t t o 1 i f the pressure drop network

model i s t o be used.

Format (4E10.5)

Opt iona l i n p u t : IAHT = 1

= d e f a u l t w a l l hea t c a p a c i t y parameter

( B ~ u / F ~ ' - o F ) f o r 1 /2 o f IAHT connec t ion

= s i d e l eng th o f duc t ( i n . )

= d e f a u l t conduc t i ve r e s i s t a n c e f o r t he IAHT

connect ion; i nc l udes 1/2 t h e gap and one duc t 2 w a l l ( f t -sec-OF/B~U)

= d e f a u l t va lue f o r t h e w a l l decay heat para-

meter ( i n . )

Card Label Var iab les Format and Exp lana t ion

NASS

I TY PA

NC HANA

I NTAPE

IEDGE

Format (515,4E5.0)

= assembly number

= assembly t ype number

= number o f channels i n an assembly o f t ype

ITYPA

= t a p e number f rom which t h e i n p u t f o r assembly

NASS should be read. Cards w i l l be read i f

INTAPE = 0. Use INTAPE = 10 i f i n p u t i s

generated by program GEOM.

= 1 i n d i c a t e s t h a t t he s i d e channel numbers are

t o be i n p u t i n Setup.4.2 (necessary i f s w i r l

model i s t o be used f o r assemblies o f t y p e

ITYPA). Otherwise, IEDGE=O.

WALLC (1, NASS) = va lue f o r t he w a l l hea t c a p a c i t y parameter

f o r assembly NASS; 1/2 t h e IAHT connec t ion

o n l y ( ~ t u / f t ' - ' ~ ) . De fau l t s t o RHODF.

WALLC ( 2 ,NASS) = va lue o f t he conduc t i ve r e s i s t a n c e ( i n c l u d e s

1/2 o f t h e gap and t h e assembly NASS duc t 2 w a l l ) ( f t -sec-OF/B~U). De fau l t s t o

RWALLDF . WALLS = w a l l hea t generat ion parameter f o r t h e

assembly NASS duc t w a l l and t h e in te rassembly

1 /2 gap ( inches) . De fau l t s t o WTHDF.

Card Label Var i ab 1 es Format and Exp lana t i on

SETUP.4.2 TMNCVL(NASS) = Nomi na l t r ansve rse momentum c o n t r o l volume

( con td ) 1 ength ( i n ) used f o r c a l c u l a t i n g c ross f l ow

r e s i s t e n c e f o r lumped subchannel ana lys is .

Should be s e t t o t h e t r ansve rse momentum

c o n t r o l volume l e n g t h which would be used f o r

s tandard subchannel ana lys is .

Format (515)

m y m y MDFLT NPFVT NASS

NAFL X = i d e n t i f i c a t i o n number o f ax i a1 heat f l u x

p r o f i l e (Card Group 3 ) t o be used i n assembly

NASS. D e f a u l t s t o 1.

NFLMC

NHFVT

NPFVT

MDFLT

= i d e n t i f i c a t i o n number o f heat t r a n s f e r coef -

f i c i e n t c o r r e l a t i o n (Card Group 2 ) used i n

assembly NASS. Def au l t s t o 1.

= i dent i f i c a t i on number o f heat f 1 ux versus

t ime p r o f i l e (Card Group 11) f o r use i n

assembly NASS. D e f a u l t s t o 0, i .e., uses

s teady-s ta te va l ue th roughou t t h e t r a n s i e n t . = i d e n t i f i c a t i o n number o f pressure drop o r

f l o w versus t ime p r o f i l e (Card Group 11) f o r

use i n assembly NASS. D e f a u l t s t o 0; i.e.,

uses s teady-s ta te va lue f o r a l l t ime.

= d e f a u l t va lue f o r t he subchannel f r i c t i o n

f a c t o r c o r r e l a t i o n s p e c i f i e d as N i n

SETUP.4.7. D e f a u l t s t o 1.

SETUP.4.4 Format ( 3 I5,6F10.0)

NOUTFF NASS RAIN NASS ,

Card Label Va r i ab les Format and Expl anat i on

SETUP.4.4

( con td )

HAOUT NASS 99 Opt iona l i n p u t : NETWK = 1

NETGRP = assembly grouping number t o be used w i t h

NASS. Loss c o e f f i c i e n t s f o r group NETGRP

must be s p e c i f i e d i n Card Group 7. D e f a u l t s

t o NETGRP = 1.

NINFF

NOUTFF

RAIN

PWIN

HA IN

RAOUT

= i d e n t i f i c a t i o n number f o r l o s s c o e f f i c i e n t

f o r c i n g f u n c t i o n (Card Group 7) versus Rey-

no lds number t o be used w i t h assembly i n l e t

loss, RAIN. De fau l t s t o 0; no f o r c i n g func-

t i o n .

= i d e n t i f i c a t i o n number f o r l o s s c o e f f i c i e n t

f o r c i n g f u n c t i o n (Card Group 7 ) versus Rey-

no lds number t o be used w i t h assembly o u t l e t

l o s s RAOUT. D e f a u l t s t o 0, no f o r c i n g f unc -

t i o n .

= i n l e t l o s s parameter ( l / f t - l b m ) t o be a p p l i e d

a t NASS i n l e t . PLOSS 2 = RAIN*m /gc.

= wet ted per imete r ( i nches ) assoc ia ted w i t h

i n l e t l o s s RAIN; used o n l y i n Reynolds number

c a l c u l a t i o n when NINFF > 0. D e f a u l t s t o 1.0.

= g r a v i t a t i o n a l head l e n g t h ( i nches ) assoc ia ted

w i t h t h e assembly i n l e t l oss .

= o u t l e t l o s s parameter ( l i f t - l b m ) t o be

app 1 i ed a t NASS o u t 1 e t . PLOSS - - 2 RAOUT*m /gc.

Card Labe l V a r i a b l e s

SETUP.4.4 PWOUT

( c o n t d )

Format and E x p l a n a t i o n

= we t ted p e r i m e t e r ( i n c h e s ) a s s o c i a t e d w i t h

o u t l e t l o s s RAOUT; used o n l y i n Reynolds

number c a l c u l a t i o n when NOUTFF > 0. D e f a u l t s

t o 1.0

HAOUT = g r a v i t a t i o n a l head l e n g t h ( i n c h e s ) a s s o c i a t e d

w i t h t h e assembly o u t l e t l o s s .

SETUP.4.5 ISIDE(NASS,I) Format (1615), ( I = 1, 6 )

ISIDE

O p t i o n a l i n p u t : IAHT > 0

= a d j a c e n t assembly number f o r asserr~bly NASS

on s i d e I. Sides must be c o n s i s t e n t l y

o rde red f o r a1 1 assembl i e s and p r o g r e s s

around t h e assembly. I f ISIDE(NASS,I) = 0

t h e n t h e r e w i l l be no i n t e r a s s e m b l y h e a t

t r a n s f e r on t h a t s i d e . I f ISIDE (NASS,I) =

NASS, w a l l nodes on s i d e I w i l l be s e t up

which connect o n l y t o assembly NASS.

SETUP.4.6" IFACE(ITYPA, 1,J) Format (1315/) , ( ( J = 1, 13) , I = 1, 6 )

O p t i o n a l i n p u t IAHT > 0 o r IEDGE = 1

IFACE(ITYPA, 1,J) number o f channels on s i d e I f o r an assembly

o f t y p e ITYPA (when J = 1 ) .

Number o f channels on f a c e I f o r assembl ies

o f t y p e ITYPA (when J 1 2) . Numbers must

p rog ress around t h e assembly, and t h e p a t t e r n

must be c o n s i s t e n t f o r a l l assembl ies.

SETUP.4.7* Format (11,14,3E5.2, 4(15,2E5.2)),

( ( L = 1, 4 ) I = 1, NCHANA)

Read NCHANA c a r d s of Channel Geometry, where:

* i n d i c a t e s t h a t those ca rds must be r e a d i n o n l y t h e f i r s t t i m e a new assembly t y p e number, ITYPA, appears on SETUP.4.2.

7 5


SETUP .4.7 N

(contd)

GAPS

DIST

Format and Explanat ion

= f r i c t i o n f a c t o r c o r r e l a t i o n type. I f b lank

o r zero, type MDFLT (SETUP.4.3) i s assigned.

I f N > 0, t ype N i s assigned. The subchannel

type i n d i c a t e s t h e appropr ia te f r i c t i o n f a c -

t o r c o r r e l a t i o n t o be used (Card Group 2) .

= subchannel i d e n t i f i c a t i o n number.

2 = nominal subchannel area ( i n . ) .

= nominal subchannel wetted per imeter ( i n . ) .

= nominal subchannel heated per imeter ( i n . ) . = adjacent subchannel i d e n t i f i c a t i o n number,

f o r up t o 4 subchannels adjacent t o sub-

channel I. Each connect ion should be

i d e n t i f i e d o n l y once.

= nominal GAP w id th ( i n . ) between subchannel I

and t h e adjacent subchannel s p e c i f i e d by LC.

= t ransverse momentum c o n t r o l volume l e n g t h

( i n . ) between the adjacent subchannels

s p e c i f i e d by LC. Opt ional inpu t , DIST w i l l

be c a l c u l a t e d from GAPS and SL (group 9)

parameter i f se t t o 0.

**Repeat SETUP.4.2-4.7 u n t i l a l l assemblies have been read in.***

SETUP .4.8 Format (2(12,13,E5.2),3E5.2), (KW = 1, N3)

Opt ional i npu t : N3 > 0 can be used i n con-

j u n c t i o n w i t h IAHT > 0.

Card Labe l V a r i a b l e s

SETUP .4.8

( c o n t d )

J1, 52

IKW, JKW

Format and E x ~ l a n a t i o n

Thermal connec t ion d a t a f o r subchannels w i t h

the rma l w a l l connec t ions n o t generated u s i n g

t h e IAHT o p t i o n s .

= assembly numbers assoc ia ted w i t h l o c a l sub-

channel IKW and JKW

= l o c a l subchannel numbers a d j a c e n t t o w a l l .

JKW and J2 may be s e t t o ze ro t o s i g n i f y a

w a l l w i t h o n l y one connec t ion f o r mode l ing

w a l l t r a n s i e n t h e a t c a p a c i t y e f f e c t s .

RWALL(l,KW), RWALL (2,KW) = e f f e c t i v e r e s i s t a n c e o f t h e w a l l a s s o c i a t e d

w i t h t h e IKW and JKW subchannels, respec- 2 t i v e l y ( f t - sec -OF/B~U) . I f JKW = 0,

RWALL(2,KW) need n o t be s p e c i f i e d .

RHOLCP = w a l l hea t c a p a c i t y parameter ( 6 t u / f t 2 - O F )

WIDTH = w i d t h o f w a l l ( i n . ) . Heat conduc t ion area =

WIDTH x A X .

WLTHCK = w a l l decay hea t parameter ( i n . )

G r o u ~ 5 - Area V a r i a t i o n

Card Group 5 represents i n p u t a x i a l p r o f i l e s f o r subchannel area v a r i a t i o n

f a c t o r s . This i s an op t i ona l group.

Card Label Var iab les Format and Expl anat i o n

SETUP. 5 5,Nl,N2,N3 Format (1515)

= NAFACT, number o f subchannels f o r which area

v a r i a t i o n tab les are t o be read

= NAXL, number o f a x i a l l oca t i ons f o r subchannel

area v a r i a t i o n

= NARAMP, the number o f i t e r a t i o n s f o r gradual

i n s e r t i o n o f area va r ia t i ons . I f blank o r zero,

NARAMP = 1. For a " r e s t a r t " case, NARAMP must

be reread i f requi red.

SETUP. 5.1 AXL(I), Format (12F5.3), (I = 1, N2)

Table o f a x i a l loca t ions , where:

AXL = a x i a l l o c a t i o n (X/L) where subchannel area var-

i a t i o n s w i l l be spec i f i ed . Read i n N2 values

which apply t o a l l subchannels s p e c i f i e d i n

SETUP.5.2.

SETUP.5.2 NASS, I, Format (215/(12F5.3), ( ( L = 1, NZ), J = 1, N1) (AFACT(L,J)

For N1 subchannels read area v a r i a t i o n f a c t o r s

a t N2 ax i a1 l oca t i ons corresponding t o (AXL),

where:

NASS

I

= assembly number

= i d e n t i f i c a t i o n number o f a subchannel f o r which

area v a r i a t i o n s are being spec i f i ed . Read NASS

and I, then s k i p t o the next card and read a

complete se t o f f a c t o r s (AFACT) corresponding

t o the AXL loca t ions . Repeat u n t i 1 f a c t o r s f o r

N 1 subchannels are read.


AFACT


= r e 1 a t i v e subchannel area (Ai/AnOmi rial 1 a t

each a x i a l l e v e l (AXL)

Group 6 - Gap Size V a r i a t i o n s

Card Group 6 represen ts i n p u t a x i a l p r o f i l e s f o r gap s i z e v a r i a t i o n . Card

Group 6 i s an o p t i o n a l group.

Card Label Va r i ab les Format and Expl anat i on

SETUP. 6 6,Nl,N2 Format (1515)

= NGAPS, number o f gaps f o r which gap v a r i a t i o n

t a b l e s are t o be read

N 2 = NGXL, number o f a x i a l l o c a t i o n s f o r gap v a r i a -

t i o n

SETUP.6.1 GAPXL (L ) Format (12F5.3), (L = 1, N2)

Table o f a x i a l l oca t i ons , where:

GAPXL = a x i a l l o c a t i o n s (X/L) where gap v a r i a t i o n s w i l l

be s p e c i f i e d . Read N2 va lues which app ly t o a l l

gaps (K) s p e c i f i e d i n SETUP.6.2.

SETlJP.6.2 NASS, K, GFACT(L,LL ) Format ( 215 / (12~5 .3 ) ) , (L = 1, N2), LL = 1, N1)

For N1 gaps, read gap v a r i a t i o n s a t N2 a x i a l

1 ocat i on s (GAPXL )

N ASS

K

G FAC T

= assembly number

= gap i d e n t i f i c a t i o n number o f gap t o be var ied .

Read NASS and K, then s k i p t o t h e nex t ca rd and

read N2 gap v a r i a t i o n f a c t o r s . Repeat u n t i l

f a c t o r s f o r N 1 gaps are read.

= gap v a r i a t i o n f a c t o r s f o r gap K. Read N2 va lues

f o r each K corresponding t o each

GAPXL l o c a t i o n . GFACT = (GAPi/GAPnomi rial ) .

Group 7 - Wire Wraps and Loss C o e f f i c i e n t s

C u r r e n t l y t h e w i r e wrap model can o n l y be used f o r assembly # l . Loss

c o e f f i c i e n t s and w i r e wraps may be used i n the same assembly

Card Label Var iab les Format and Expl anat i o n

SETUP. 7 7,Nl,N2,N3, Format (1515) N4,N5,N6,N7, N8.N9

N 1 = J6. N 1 = 1 s p e c i f i e s w i r e wrap i n p u t on ly . N 1

= 2 s p e c i f i e s g r i d spacer i n p u t on ly . N 1 = 3

s p e c i f i e s bo th w i r e wrap i n p u t and g r i d spacer

l o s s c o e f f i c i e n t i n p u t .

= number o f gaps f o r which w i re wrap c ross ing da ta

i s supp l i ed

= NOLC, number o f l o s s c o e f f i c i e n t s t o be i n p u t

i n SETUP.7.4

= NRAMP, number o f i t e r a t i o n s over which t h e l o s s

terms and/or w i r e wrap e f f e c t s are t o be ramped

i n t o the s o l u t i o n . For a " r e s t a r t " , NRAMP must

be re read i f requ i red .

= l o g i c a l u n i t f rom which card se ts SETUP.7.2 and

SETUP.7.3 are t o be read. N5 = 0: read f rom

i n p u t deck. N5 > 0: read f rom l o g i c a l u n i t N5.

N5 = 9 i f us ing GEOM. output .

= NLCFF, number o f l oss c o e f f i c i e n t f o r c i n g func-

t i o n s versus Re p r o f i l e s t o be i n p u t i n (SETUP

7.7) f o r use w i t h t h e network model o r t h e l o s s

c o e f f i c i e n t s (SETUP.7.4). De fau l t s t o 0.

= NLCFP, number o f p o i n t s i n l o s s c o e f f i c i e n t

f o r c i n g f u n c t i o n versus Re p r o f i l e s (SETUP.7.6

- 7.7). When N6 > 0 , N7 i s s e t t o aminimum

va lue o f 2.


SETUP. 7 N 8

(contd)

= NOGRP, number o f assembly groups f o r t h e

network model. NOGRP must be > 0 when

NETWK = 1 (Card Group 4 ) .

= NBLOCK, number o f a x i a l l o c a t i o n s where a x i a l

f l o w blockages occur; can be used o n l y w i t h

scheme R E C I R C .

SETUP.7.1 PITCH, DIA, THICK Format (3E10.5)

o p t i o n a l i npu t : J6 = 1 or 3

Wire wrap spec i f i c a t ions, where :

PITCH = w i r e wrap p i t c h ( i n . )

D I A = r o d or c ladd ing ou ter diameter ( i n . )

THICK = w i r e wrap diameter ( i n . )

SETUP. 7.2 Mw), Format (15, 2E5.2), (L = 1, 2)

Opt iona l i npu t : J6 = 1 or 3

Wrap c ross ing data, where:

K = gap number

DUR = parameter determin ing the amount o f f o r ced

c ross f l ow due t o w i r e wrap. Recommended

value DUR = 1.0.

XCROSS = w i r e wrap c ross ing angle. XCROSS i s ca lcu-

l a t e d by d i v i d i n g t h e angle between t h e gap

and w i re ( a t the bundle i n l e t ) by 360. The

value i s p o s i t i v e i f t h e wrap i s moving f rom

a smal le r t o a h igher number subchannel and

negat ive i f otherwise. If the w i r e wrap i s

on.. a gap boundary a t t h e bundle i n l e t ,

XCROSS = 51.0, not zero.


SETUP. 7.3 NWRAPS ( I )

NWRAPS ( I )

Format and E x ~ l anat i on

Format (1015) ( I = 1, Number o f channels i n

Assembly #1)

Opt ional i npu t : 56 = 1 o r 3

Wrap i nven to ry where:

= number o f w i res i n i t i a l l y i n subchannel I.

Read an i n t e g e r va lue o f t h e number o f w i res

present a t t he bundle i n l e t . For w i res

l oca ted on t h e gap boundary, t h e wrap i s

assumed t o be i n t he subchannel i n t o which

i t i s proceeding. Read 10 values per da ta

card u n t i l the i nven to ry f o r a l l subchannels

i s read.

SETUP. 7.4 Format (315, 2E10.4, 15, E10.4), ( I=l ,N3)

CD I , KLC I . , FXFLOW I

Opt ional i npu t : 56 = 2 o r 3 AND N3 > 0

ILC

LCFF

FACTOR

C D

= assembly number i n which loss c o e f f i c i e n t i s

t o be appl i e d

= l o c a l channel number i n which l oss coef-

f i c i e n t i s t o be appl ied; changed t o g loba l

channel number i n SETIN

= the loss c o e f f i c i e n t f o r c i n g f u n c t i o n p r o f i l e

which i s t o be app l i ed t o t h i s l o s s coef-

f i c i e n t ; r e f e r s t o SETUP.7.5 i npu t . D e f a u l t

= 0; no f o r c i n g f u n c t i o n .

= the r e l a t i v e he igh t i n channel ILC a t which

t h e l oss c o e f f i c i e n t i s t o be app l i ed (X/L)

= loss c o e f f i c i e n t

Card Label V a r i a b l e s Format and E x p l a n a t i o n

SETUP. 7.4 KLC = l o c a l gap number a t which f o r c e d d i v e r s i o n

( c o n t d ) c r o s s f l o w f r a c t i o n FXFLOW i s t o be s p e c i f i e d .

B l ank i n d i c a t e s no f o r c e d c r o s s f 1 ow.

FXFLOW = f r a c t i o n o f a x i a l f l o w i n n e i g h b o r i n g

channel t o be d i v e r t e d across gap KLC a t t h e

a x i a1 node co r respond ing t o FACTOR. P o s i t i v e

f l o w across t h e gap i s d e f i n e d i n t h e d i r e c -

t i o n of i n c r e a s i n g ad jacen t channel number.

O p t i o n a l i n p u t , KLC > 0.

SETUP.7.5 RTIN, RGIN(L), Format (F10.5/(4F10.5)), (L = 1, N8)

O p t i o n a l i n p u t : NETWK = 1

RTIN

RGIN

HG I N

RGOUT

HGOUT

SETUP. 7.6 RECL(1)

RECL

= l o s s parameter ( l / f t - l b m ) t o be a p p l i e d t o

t h e t o t a l f l o w r a t e (sum o f a l l assembly f l o w

r a t e s ) ; Reynolds number independent

= l o s s parameter ( l / f t - l b m ) t o be a p p l i e d a t

assembly g r o u p i n g L i n l e t ; Reynolds number

independent

= g r a v i t a t i o n a l head l e n g t h ( i n . ) a s s o c i a t e d

w i t h t h e group i n l e t p ressure l o s s

= l o s s parameter ( l l f t - l b m ) t o be a p p l i e d a t

assembly g roup ing L o u t l e t ; Reynolds number

independent

= g r a v i t a t i o n a l head l e n g t h ( i n . ) assoc ia ted

w i t h t h e group o u t l e t p ressure l o s s

Format (12E5.0), ( I = 1, N7)

O p t i o n a l i n p u t : (NETWK = 1 o r J6 > 1 ) AND

N6 > 0

= Reynolds number a t which p o i n t s i n t h e N6

l o s s c o e f f i c i e n t f o r c i n g f u n c t i o n s a re g i v e n

84

Card Label Var i abl es

SETUP.7.7 FFLC ( I ,L)

FFLC

SETUP.7.8 NBLOKA , NBLOKC ,

NBLOKA

NBLOKC

I BLOKA

I BLOKC


Format (12E5.0), ( I = 1, N7)

Opt ional i npu t : N6 >O

= l oss c o e f f i c i e n t f o r c i n g f u n c t i o n p r o f i l e

corresponding t o RECL. Read i n N6 p r o f i l e s .

Format (215/(16(12,13))), I=l,NBLOKC) Repeat NBLOCK t imes

= a x i a l l e v e l where the blockage i s loca ted

= number o f channels blocked a t a x i a l l e v e l

NBLOKA

= assembly number w i t h blocked channel

= blocked channel number

Group 8 - Rod Layout and Fuel P rope r t i es

Card Group 8 de f i nes r a d i a l r od power fac to r , rod-channel connect ions, and

m a t e r i a l p rope r t i es . Sample problems should be h e l p f u l i n s e t t i n g up t h e Card

Group 8 i n p u t data.


SETUP. 8 8,Nl,N2, Format (1515) N3,N4,N5

= number o f assemblies f o r which r o d da ta i s t o

be read

= NC, order o f approximation used i n f u e l model.

N2 = 0: no f u e l model. N2 = 2: 2nd order

c o l l o c a t i o n so lu t i on . N2 = 3: 3 rd order c o l -

l o c a t i o n . N2 > 3 o r N2 = 1 i s no t acceptable.

= NFUELT, t h e number o f f u e l m a t e r i a l s f o r

which thermal p r o p e r t i e s are t o be spec i f i ed ;

no t app l i cab le i f N2 = 0. I f blank, NFUELT = 1

i s assigned.

= NQAX, a d d i t i o n a l f u e l model op t ions :

NQAX = 0: no a d d i t i o n a l opt ions. NQAX = 1:

f u e l p r o p e r t i e s are temperature dependent

a x i a1 ly.

Operat ional o n l y f o r NC = 2.

= NRODTP, op t i on f o r a x i a l l y va ry ing f u e l mater-

i a l . N5 = 0: each f u e l r o d i s cons t ruc ted o f

a s i n g l e m a t e r i a l and no a x i a l l y va ry ing da ta

are read. N5 > 0: must read f u e l zone i n f o r -

mation (SETUP.8.6) f o r each rod t ype N.

SETUP.8.1 NOA, ITYPA, Format (515) NORODS. INTAPE.

NOA = assembly number

Card Label Var iab les Format and Expl anat ion

SETUP. 8.1 ITYPA = r o d c o n f i g u r a t i o n t ype number (con td)

NORODS = number o f rods i n c o n f i g u r a t i o n t ype ITYPA

INTAPE = tape number which f rom i n p u t should be read,

INTAPE = 0: i n p u t w i l l be on cards. Use

INTAPE = 11 i f us ing i n p u t generated by pro-

gram GEOM.

I PFR = o p t i o n t o change r a d i a l power f a c t o r s f o r a

r o d c o n f i g u r a t i o n type. I f IPFR = 0, no

changes w i l l be made. IPFR > 0 i n d i c a t e s the

number o f cards t o be read SETUP.8.3

SETUP.8.2* Format (12,13,2E5.2,6(15, E5.2)), ( L = 1, 6 )

Read i n NORODS cards o f r o d i n p u t data,

where:

= t he f u e l shape and f u e l m a t e r i a l opt ions.

The value o f N determines t h e m a t e r i a l prop-

e r t y c o n f i g u r a t i o n o f Rod I. D e f a u l t N = 1.

For N5 = 0 ( a x i a l l y un i fo rm f u e l ) N co r re -

sponds t o one o f N3 m a t e r i a l s (SETUP.8.2) o f

which Rod I i s made.

For N5 > 0 ( a x i a l l y vary ing f u e l zones) N

corresponds t o one o f N5 m a t e r i a l

con f i gu ra t i ons s p e c i f y i n g the f u e l ma te r i a l

versus a x i a1 h e i g h t (SETUP.8.6).

I f any r o d i s s p e c i f i e d t o have a x i a l l y

vary ing f u e l zones (N5 > 0) , a1 1 rods

( i n c l u d i n g a x i a l l y un i fo rm rods) must have

an a x i a l c o n f i g u r a t i o n s p e c i f i e d (SETUP.8.6).

* Ind ica tes ca rd (s ) must be read i n o n l y t he f i r s t t ime a new r o d c o n f i g u r a t i o n number, ITYPA, appears on SETUP.8.1.

Card Label Va r i ab l es Format and Exp lana t i on

SETUP. 8.2 I (con td )

= r o d i d e n t i f i c a t i o n number f o r assembly t y p e

ITY PA

= o u t e r r o d diameter ( i n . ) . I f t h e r e i s c l ad -

d i n g around rod , DR i s t h e c l add ing o u t e r

d iameter .

RADIAL = r a d i a l power f a c t o r f o r r o d I as a f r a c t i o n

o f t h e average r o d power (Group 11)

PHI

= i d e n t i f i c a t i o n numbers o f subchannels su r -

r ound ing r o d I. Read i n up t o 6 subchannels.

= f r a c t i o n o f t he t o t a l r o d power i n p u t t o

ad jacen t subchannel

SETUP.8.3 IRN(L), IDF(L) , RPF(L) Format (215, F5.0) (L=1, IPFR)

IRN

Op t i ona l i npu t : IPFR > 0 f o r assembly number

NOA.

= r o d I D number (must be read i n o r d e r )

I DF = same d e f i n i t i o n as N i n SETUP.8.2

RPF = r a d i a l power f a c t o r f o r r o d I R N

***Repeat SETUP.8.1 - 8.3 f o r up t o NASSWR timesk**

SETUP.8.4 Format (lOE5.2,15,E5.2)), ( I = 1, N3)

.E& TCLADO,

Card Label Var iables Format and Explanat ion

SETUP. 8.4 (contd)

KFUEL

CFUEL

RFUEL

DFUEL

KCLAD

CCLAD

RCLAD

TCLAD

HGAP

DROD

GEOMF

Optional Input : N3 > 0 and NC > 0

Mater i a1 p rope r t i es . Read N3 cards

corresponding t o N3 m a t e r i a l s f o r which

thermal p rope r t i es are spec i f ied . Each f u e l

r o d cons is ts o f one o r more o f these ma te r i -

a ls . For N5 = 0, the f u e l type N (SETUP.8.2)

corresponds t o t h e ma te r ia l t ype I.

= thermal c o n d u c t i v i t y o f the f u e l

( B t u / h r - f t O ~ )

= s p e c i f i c heat o f f u e l (Btu/lb-OF)

3 = f u e l dens i t y ( l b / f t )

= f u e l diameter ( i n . )

= thermal c o n d u c t i v i t y o f c ladd ing

(Btu/hr- f t -OF)

= s p e c i f i c heat o f c ladd ing ( ~ t u / l b - O F )

3 = dens i t y o f c ladd ing (1 b / f t )

= c ladd ing th ickness ( i n . )

= Fuel-Clad Gap conductance c o e f f i c i e n t

( ~ t u / h r - f t 2 - O ~ )

= ou ter diameter o f the f u e l rod, i n c l u d i n g the

c ladding ( i n . )

= f u e l rod geometry i n d i c a t o r

= 0: s o l i d c y l i n d r i c a l f u e l rod w i t h i n t e r n a l

heat generat ion

= 1: annular c y l i n d r i c a l f u e l rod w i t h i n t e r -

na l heat generat ion

Card Label Va r i ab les Format and Exp lana t i on

SETUP.8.4 GEOMF = 2: annular c y l i n d r i c a l f ue l r o d w i t h a heat

( con td ) ( con td ) f l u x boundary c o n d i t i o n on t h e i n n e r f u e l

s u r f ace

DFUEL I = i n n e r diameter of t he f u e l f o r an annular

f u e l r o d ( i n . ) . (Read i n o n l y i f GEOMF> 0 ) .

SETUP. 8.5 NTNODE, NFNODE, Format (215/(12E5.3)), ( I = 1, NTNODE)

Opt iona l i n p u t : NC = 2 and NQAX = 1

Temperature dependent f u e l p r o p e r t y t ab le ;

f o r m a t e r i a l t ype 1 on ly .

NTNODE

NFNODE

TV ARY

VARYK

VARY CP

NZONE

= number o f e n t r i e s i n t h e p r o p e r t y t a b l e

= number of p o i n t s used f o r i n t e g r a t i n g r a d i a l

temperature p r o f i l e t o o b t a i n f u e l p r o p e r t i e s

= temper a t u re (OF )

= thermal c o n d u c t i v i t y ( ~ t u / h r - f t - O F )

= s p e c i f i c heat ( ~ t u / l b-OF)

Format (15/(6(E5.2,15))), ( (K = 1, NZONE(I)),I = 1, N5)

Opt iona l i n p u t : N5 > 0

Opt ion t o s p e c i f y a x i a l l y v a r y i n g f u e l

m a t e r i a l s . Must read i n a f u e l zone con f i g -

u r a t i o n t a b l e f o r each r o d t y p e (SETUP.8.2).

= number o f a x i a l zones t o be read f o r a t a b l e

o f f u e l m a t e r i a l versus a x i a l d i s t a n c e f o r

f u e l t y p e I


SETUP. 8.5 ZEND

IZTYPE


= r e l a t i v e a x i a l l o c a t i o n (X/L) o f t he end o f

a f u e l zone. I f f u e l t ype I i s a x i a l l y u n i -

form, ZEND(1,l) = 1.0.

= Type o f m a t e r i a l i n f u e l zone ending a t

ZEND. Each IZTYP corresponds t o a m a t e r i a l

s p e c i f i e d i n SETUP.8.4. O n l y m a t e r i a l t ype

1 can have temperature-dependent thermal

p rope r t i es .

Group 9 - C a l c u l a t i o n a l Va r i ab les


SETUP .9


Format (151 5 )

= NSKIPX, ou tpu t p r i n t op t i on . N 1 = 0 o r 1:

p r i n t a l l a x i a l l e v e l s . N 1 > 1: p r i n t every

N1 a x i a l l e v e l s .

= NSKIPT, ou tpu t p r i n t op t i on . N2 = 0 o r 1:

p r i n t a l l t i m e steps. N2 > 1: p r i n t every

N2 t ime s teps. N 2 < 0: p r i n t every TRANT

(SETUP.9.6) t r a n s i e n t seconds.

= ISCHEME

= 1: i t e r a t i v e s o l u t i o n scheme f o r momentum

equat ions (SCHEME)

= 2: d i r e c t s o l u t i o n scheme f o r momentum

equat ions (SCHEME)

= 3: r e c i r c u l a t i o n s o l u t i o n scheme f o r momen-

tum equat ions (RECIRC)

= IROLL, problem r o l l op t i on . N4 = 0: no r o l l

op t ion ; a l l v a r i a b l e s r e s i d e i n c o r e a t a l l

t imes. N4 = 1: o n l y 3 a x i a l l e v e l s o f

i n f o r m a t i o n ( J - 1, J, and J + 1 ) a r e s t o r e d

i n core a t one t ime. Use o n l y when problem

s i z e demands ex te rna l s torage.


SETUP .9 N 5

( con td )


= ITSTEP, maximum t ime s tep t ab le . N5 = 0: a

cons tan t t i m e s tep o f TTIME/NDT (SETUP.9.1,

9.3) w i l l be used. For N5 > 0, read i n N5

p a i r s o f ( t i m e versus maximum t i m e s tep )

i n f o r m a t i o n f o r v a r i a b l e maximum t ime s teps

(SETUP.9.4).

= NAZONE, number o f a x i a l zones f o r v a r i a b l e

a x i a l s tep s ize . A d i f f e r e n t a x i a l s tep s i z e

may be s p e c i f i e d f o r each zone (SETqP.9.5).

If NAZONE = 0 t h e a x i a l s tep s i z e w i l l

d e f a u l t t o Z/NDX (SETUP.9.1, 9.3).

SETUP.9.1 Z, TTIME, WERRX, Format (16E5.0) WERRY , FERROR , HERROR, DAMPNG , ACCELY, ACCELF

Z = t o t a l a x i a l l e n g t h ( i n . )

TTIME = t o t a l t r a n s i e n t t ime (sec)

W ERRX = e x t e r n a l c ross f l ow convergence l i m i t . Th i s

i s de f ined f o r i m p l i c i t pressure s o l u t i o n as

t he maximum a l l owab le 'e r ro r i n i t e r a t i v e

c ross f l ows a t any a x i a l l e v e l . If any e r r o r

i s g rea te r than WERRX, the s o l u t i o n proceeds

through another i t e r a t i v e sweep over t h e

e n t i r e bundle. D e f a u l t i s l.E-2.

W ERRY = i n t e r n a l pressure convergence l i m i t . N3 = 1

convergence l i m i t f o r t he i t e r a t i v e Gauss

Se ide l s o l u t i o n scheme a t a x i a l l e v e l J.

N3 = 3: i n n e r loop l i m i t f o r r e c i r c u l a t i o n

s o l u t i o n scheme. D e f a u l t i s l.E-3.

Card Label Var i ables

SETUP.9.1 FERROR

(contd)


= the ex te rna l a x i a l f l o w convergence l i m i t ,

def ined f o r t he i m p l i c i t a x i a l momentum

equat ion as the maximum a l lowab le e r r o r f o r

i t e r a t i v e a x i a l f lows. I f e r r o r i s g rea te r

than FERROR, another i t e r a t i v e sweep o f the

e n t i r e bundle i s made. De fau l t i s l.E-3.

H ERROR = convergence l i m i t f o r f l u i d enthalpy.

De fau l t i s 0.001.

DAMPNG = damping f a c t o r f o r i t e r a t i v e t ransverse

pressure drop term i n the c ross f l ow momentum

equation. De fau l t i s 1.0.

ACC ELY = acce lera tor f o r the i t e r a t i v e Gauss Siedel

s o l u t i o n f o r t h e momentum equations.

De fau l t i s 1.6.

ACCELF = damping f a c t o r f o r i t e r a t i v e a x i a l f low.

De fau l t i s 0.7.

Note: A l l dampers and acce lera tors are

app l ied as xn = xn + (1-cx)xn-' where

X i s t he v a r i a b l e damped (acce lera ted) , a i s

the damping f a c t o r , and n i s t he i t e r a t i o n

l e v e l .

SETUP. 9.2 KIJ, SL, t lM, THtTA

FTM

Format (16E5.0)

= gap f l o w res i s tance between adjacent chan-

nels . De fau l t = 0.5

= t ransverse momentum geometry f a c t o r . Width-

t o - l eng th r a t i o o f t he t ransverse momentum

c o n t r o l volume. Used o n l y i f DIST i s no t

s p e c i f i e d i n card group 4 (SETUP 4.7).

De fau l t = 0.5.

= t u r b u l e n t momentum parameter. De fau l t i s 0.

Card Label Va r i ab l es Format and Expl anat i o n

SETUP.9.2 THETA = bundle o r i e n t a t i o n i n degrees away f rom the

( con td ) v e r t i c a l . D e f a u l t = 0.0.

SETUP.9.3 NDX, NDT, Format (515) NTRIES, ITRY

NDX = number o f a x i a l nodes

NDT

NTRI ES

I TRY

= t o t a l number o f t ime s teps al lowed. For

i m p l i c i t t r a n s i e n t s , t h e t i m e s tep s i z e i s

(TTIMEINDT) un less a t i m e l s t e p t a b l e (N5 > 0 )

i s read i n .

= maximum number o f e x t e r n a l i t e r a t i o n s a l lowed

rega rd less o f WERRX and FERROR. D e f a u l t i s

20.

= maximum number o f i n t e r n a l i t e r a t i o n s a l lowed

rega rd less o f MERRY. D e f a u l t i s 20 o r 2

t imes t h e number o f gaps, whichever i s

1 arger .

SETUP. 9.4 Format (12E5.0), ( I = 1, N5)

Op t i ona l i n p u t : N5 > 1

Read i n N5 p a i r s o f va lues f o r a t a b l e o f

t i m e s teps s i z e versus t ime, where:

= t i m e (sec) f o r maximum t ime step. Table must

i n c l u d e t i m e = 0.

FT = maximum t ime s t e p (sec) a l lowed a t t h i s t ime.

SETUP.9.5 NSTEPS(I), VDX(1) Format (8(15,E5.0)), ( I = 1, N6)


Va r i ab le a x i a l s tep s i z e i n f o r m a t i o n

NSTEPS ( I )

VDX(1)

= number o f computat ional c e l l s i n Zone I

= a x i a l s tep s i z e ( i nches ) i n Zone I

Card Label Variables

SETUP.9.6 TRANT

TR ANT


Format (F5.3)

Opt ional input : N2 < 0

= op t ion t o p r i n t t r a n s i e n t r e s u l t s based on a

TRANT t ime i n t e r v a l (sec)

Group 10 - Turbu len t M i x i n g C o r r e l a t i o n and F l u i d Conduct ion

Card Label Var iab les Format and Expl anat i on

SETUP.10 10,Nl,N2,N3 Format (151 5)

N 1 = NSCBC, s ing le-phase t u r b u l e n t m i x i n g op t i on .

Several forms o f t he equat ion f o r t u r b u l e n t

c ross f l ow W ' a re poss ib l e :

1 ) W t K = ABETA * (SKG)

2 ) W t K = ABETA * Re ** BBETA * (SKG)

3 ) W t K = ABETA * Re ** BBETA * (DG)

4 ) W I K = ABETA * Re ** BBETA * (s,/e,) (DG)

where t he constants ABETA and BBETA

(SETUP.10.1) are app l i ed t o t h e equat ion

se lec ted by N1. R e i s t he l o c a l Reynolds

number based on a x i a l v e l o c i t y ; G i s t h e

a x i a l mass f l u x ; SK i s t he gap width; D

i s t h e average (across t h e gap) h y d r a u l i c

diameter; and !Lk i s t he t ransverse momen-

tum c o n t r o l volume leng th .

N 1 = 1: use equat ion 1.

N1 = 2: use equat ion 2.



= Number o f assembly types i n which a s w i r l

f l o w m ix i ng model w i l l be used

= 1 i f f l u i d conduct ion i n t he r a d i a l d i r e c -

t i o n i s t o be cons idered

Card Label Var iables Format and Explanat ion

SETUP.lO.l Format (15,3E5.0), ( I = 1, MAXTYP)

Opt ional input : N 1 > 0 or N3 = 1

Read one card f o r each assembly type

(MAXTYP = t o t a l number o f assembly types)

NATY PE = assembly type number

ABETA, BBETA = constant c o e f f i c i e n t s f o r t he t u r b u l e n t mix-

i n g c o r r e l a t i o n selected (see N l ) . BBETA =

0, i f N 1 = 1.

SETUP.10.2 NATYPE, I D I R , CONSTI

NATY PE

I D I R

CON ST I

= Geometry f a c t o r f o r r a d i a l conduction. I f

N3 = 0 o r GK = 0.0, conduct ion i n the f l u i d

w i l l no t be included i n the ca l cu la t i on .

Format (215,E5.0)

Optional input : N2 > 0

Read N2 cards.

= assembly type number

= s w i r l d i r e c t i o n i nd i ca to r . Zero i n d i c a t e s

counterclockwise ( f rom top o f bundle l ook ing

upstream); 1 ind ica tes clockwise.

= s w i r l v e l o c i t y as a f r a c t i o n o f the average

bundle v e l o c i t y

Group - 11 Operat ing Cond i t ions and Trans ien t Fo rc ing Funct ions


S E T U P . l l l l ,Nl,N2,N3,N4, Format ( 1 5 1 5 ) Ns,N6,N7,N8,N9, N lO,Nl l ,N12,N13

= I H , op t i on f o r s p e c i f i e d i n l e t enthalpy o r

temperature. N 1 = 0: H I N (SETUP.11.1) i s

the i n l e t enthalpy. N 1 = 1: H I N i s the

i n l e t temperature. N 1 = 2: read i n an i n l e t

en tha lpy f o r each subchannel. N 1 = 3: read

i n an i n l e t temperature f o r each subchannel

S SETUP.^^.^).

= IG, op t i on t o s p e c i f y i n l e t mass f l u x . N 2 =

0: G I N (SETUP.11.1) i s t h e i n l e t mass f l u x

f o r each subchannel. N 2 = 1: G I N i s t h e

average core mass f l u x , bu t t h e subchannel

f l o w i s s p l i t t o g i ve equal DP/DX across the

f i r s t a x i a l node w i t h i n each assembly. N 2 =

2: G I N i s t h e average core mass f l u x , bu t

assembly f l o w i s s p l i t by f l o w f r a c t i o n s

supp l ied i n SETUP.11.3 and uses un i f o rm mass

f l u x w i t h i n each assembly. N 2 = 3: sub-

channel f l o w i s s p l i t w i t h i n each assembly

by f l o w f r a c t i o n s supp l ied i n SETUP.11.4.

N2 = 4: both op t ions N2 = 2 and N2 = 3 are

taken. A l l f l o w f r a c t i o n s are on GIN .

= t r a n s i e n t f o r c i n g f u n c t i o n f o r system pres-

sure. Read i n NP p a i r s o f values f o r a t a b l e

o f system pressure f a c t o r s versus t ime.

Card Label Var iables

S E T U P . l l N 4

(contd)


= t r a n s i e n t f o r c i n g func t i on f o r i n l e t

enthalpy or temperature. Read i n NH p a i r s

of values fo r a t a b l e o f i n l e t enthalpy or

temperature f a c t o r s versus t ime.

= NG, t r a n s i e n t f o r c i n g f u n c t i o n f o r i n l e t

mass f l u x o r pressure drop. N 5 = number o f

e n t r i e s i n each tab le .

= NGPRFL, number o f t r a n s i e n t f o r c i n g func t i ons

f o r i n l e t mass f l u x o r pressure drop p r o f i l e s

t o be read i n .

= K10 , an op t i on f o r pressure drop boundary

c o n d i t i o n t rans ien ts . If K10 = 1, the tab-

u l a r values f o r the i n l e t mass f l u x ( N 5 ) are

a f r a c t i o n o f the steady-state pressure drop.

I f K 1 0 = 2, the tabu la r values are the

desi red pressure drop (ps ia ) . = NHX, t r a n s i e n t f o r c i n g f u n c t i o n f o r e x i t

enthalpy. Read i n NHX p a i r s o f values f o r a

t a b l e o f e x i t enthalpy f a c t o r versus time.

= t r a n s i e n t f o r c i n g f u n c t i o n f o r average power

densi ty . N 9 = number o f e n t r i e s i n each

tab le .

= NQPRFL, number o f power dens i t y t r a n s i e n t

f o r c i n g f u n c t i o n p r o f i l e s t o be read i n .

= NRPF, op t i on t o s p e c i f y i n d i v i d u a l subchannel

o r assembly power dens i t ies . N 1 1 = 0: PDN

(SETUP.11.1) i s the power dens i ty f o r each

assembly. N 1 1 = 1: read i n r e l a t i v e power

f a c t o r s f o r each assembly (SETUP.11.12).

N 1 1 = 2: read i n power dens i ty f o r each

assembly (SETUP.11.12).

Card Label Va r i ab les Format and Expl anat i o n

SETUP. 11 N12 = NDPA, o p t i o n t o spec i f y d i f f e r e n t pressure

(con td ) drop boundary c o n d i t i o n s f o r each assembly

( i f s e t t o 1 ) . Th is o p t i o n a v a i l a b l e o n l y

when NETWK = 0 (Group 7 ) . D e f a u l t s t o 0.

= NRAMPH, t he number o f i t e r a t i o n s over which

t h e power i s t o be ramped i n . D e f a u l t s t o 1.

SETUP.ll.l PEXIT, H IN , GIN, Format (6F10.0) PDN. HOUT. DPS

Opera t ing cond i t i ons , where:

PEXIT = system pressure ( p s i a )

HIN = i n l e t en tha lpy (Btu/ lbm) o r temperature

(OF) depending on N 1

G I N 2 = i n l e t mass f l u x (Mlbm/hr- f t ) t o be d i s -

t r i b u t e d by t h e N2 o p t i o n

PDN 3 = nominal power d e n s i t y (Mb tu /h r - f t ) (based

on f u e l diameter when f u e l model i s used)

HOUT

DPS

= e x i t en tha lpy (Btu/ lbm). I f HOUT i s spec i -

f i e d , and t h e f l o w reverses, t h e "new" e x i t

en tha lpy w i l l be HOUT. Otherwise, f o r HOUT

b lank, t h e "new" e x i t en tha lpy w i l l be t h e

c a l c u l a t e d core average e x i t entha lpy.

= an o p t i o n t o s p e c i f y a pressure drop r a t h e r

than a f l o w boundary c o n d i t i o n i n t h e

s teady-s ta te i m p l i c i t s o l u t i o n scheme. The

code i t e r a t e s on t h e t o t a l i n l e t f l o w r a t e

u n t i l the c a l c u l a t e d pressure drop i s c l ose

t o DPS ( p s i a ) . When NETWK = 1, DPS i s t h e

pressure drop across t he whole problem and

i n d i v i d u a l assembly boundary c o n d i t i o n s a re


SETUP.ll.l DPS

(contd)

SETUP.11.2 HINLET(1)

HINLET

G INLET

SETUP.11.4 NASSIN, IA, -j

Format and Expl anat i on

found based on user i n p u t l oss c o e f f i c i e n t s

(Card Groups 4 and 7 ) . When NETWK = 0, DPS

i s t he pressure drop f o r each subchannel,

unless N12 = 1 and SETUP.11.13 i s read in .

Format ( 1 2 ~ 5 . 0 ) ~ ( I = 1, NCHANL)

Opt iona l input : N 1 = 2 or 3

I n l e t enthalpy or temperature, where:

= i n l e t enthalpy (N1 = 2) or i n l e t temperature

(N1 = 3 ) o f each i n d i v i d u a l subchannel ; read

one value f o r each subchannel.

Format (12E5.0), ( I = 1, NASSEM)

Opt iona l i npu t : N2 = 2 o r 4

Assembly i n l e t f l o w r a t e m u l t i p l i e r , where:

= assembly i n l e t f l o w f a c t o r (GIN(I) /GIN) f o r

each i n d i v i d u a l assembly.

Format (15/(15/(12E5.0))), ((IC = 1, NCHANA(IA)), I = 1, NASSIN)

Opt ional i npu t : N2 = 3

Subchannel i n l e t f l o w r a t e f r a c t i o n , where:

NASS I N = number o f assemblies f o r which i n d i v i d u a l

subchannel f l o w f r a c t i o n s are suppl i e d

I A = assembly number

GINC(IA,IC) = f r a c t i o n o f core mass f l u x f o r subchannel I C

SETUP.11.5 YP(I ) , FT(1) Format (12E5.0), ( I = 1, N3)

Opt iona l i npu t : N3 > 1

Pressure t r a n s i e n t table, where:

YP = t r a n s i e n t t ime (sec) when f a c t o r i s app l ied

= f r a c t i o n o f steady-state system pressure a t

t r a n s i e n t t ime (YP)

102

Card Label Var iables Format and Expl anat i on

SETUP.11.6 YH(I) , FH(1) Format (12E5.0), ( I = 1, N4)

Opt ional i npu t : N4 > 1

Enthalpy or temperature t r a n s i e n t t ab le .

= t he t r a n s i e n t t ime (sec) when f a c t o r i s

appl i e d

= the f r a c t i o n o f i n l e t enthalpy (N1 = 0 or 2 )

o r the f r a c t i o n o f i n l e t temperature (N1 = 1

o r 3) a t the t r a n s i e n t t ime (YH)

Format (12E5.0), ( I = 1, N5)


I n l e t f l o w or pressure drop boundary condi-

t i o n t r a n s i e n t t ab le .

= t h e t r a n s i e n t t ime (sec) when f a c t o r i s

appl i e d

Format (12E5.0), ( ( I = 1, N5), J = 1, N6 )


= t h e f r a c t i o n o f steady-state i n l e t f l o w a t

t he t r a n s i e n t t ime (YG) i f i n l e t f l o w bound-

a ry c o n d i t i o n i s spec i f i e d K10 = 0 (Group

11). For pressure drop boundary cond i t i ons

(K10 = 1 or 2), FG i s e i t h e r the f r a c t i o n o f

t he steady-state pressure drop (K10 = 1 ) o r

FG i s the pressure drop i n p s i (K10 = 2) a t

t he t r a n s i e n t t ime (YG). I npu t N6 p r o f i l e s .

Format (12E5.0), ( I = 1, N9)


Power dens i t y t r a n s i e n t tab le .

= t h e t r a n s i e n t t ime (sec) when f a c t o r i s

appl i e d

Card Label Va r i ab les Format and Expl anat i o n

SETUP.ll.10 FQ(1,J) Format (12E5.0), ( ( I = 1, N9), J = 1, N10))


= t h e f r a c t i o n o f s teady-s ta te heat f l u x a t t h e

t r a n s i e n t t ime (YQ). I n p u t N10 p r o f i l e s .

SETUP.l l . l l YHX(I), FHX(1) Format (12E5.0), ( I = 1, NHX)


E x i t en tha lpy t r a n s i e n t t ab le .

FHX

= t he t r a n s i e n t t ime (sec) when f a c t o r i s

appl i ed . = t h e f r a c t i o n o f steady s t a t e e x i t en tha lpy

(HOUT) a t t h e t r a n s i e n t t i m e (YHX) t o be used

i f t h e f l o w reverses.

SETUP .11.12 PDNA(NASS) Format (16E5.0), (NASS = 1, NASSEM)

Op t i ona l i npu t : N 1 1 > 0

Assembly power d e n s i t i e s .

PDNA = t h e r e l a t i v e assembly power (N11 = 1 ) o r t h e

abso lu te assembly power d e n s i t y (N11 = 2 )

( ~ b t u / h r - f t 3 )

Format (12E5.0), ( I = 1, NASSEM)

Op t i ona l i npu t : NDPA = 1

= pressure drop boundary c o n d i t i o n s p e c i f i e d

f o r each assembly, r e p l a c i n g DPS i n

SETUP.ll.l. Used o n l y when NETWK = 0.

Group 12 - Output Opt ions f o r C a l c u l a t i o n s

Card Label Var iab les Format and Expl a n a t i on

SETUP .12 12,Nl,N2,N3,N4, Format (1515) hb,N6,N/

= NOUT, p r i n t op t i on . Each o f the f i v e d i g i t

l o c a t i o n s s p e c i f y a separate p r i n t o p t i o n

where a one means p r i n t a l l t he da ta f rom

t h a t o p t i o n and a zero i n d i c a t e s no p r i n t o u t

i s desired. The op t i ons c o n t r o l l e d by the

d i g i t s i n t he f i r s t f o u r l o c a t i o n s a re sub-

channels, rods, crossf lows, and w a l l data,

r e s p e c t i v e l y . A one i n the f i f t h d i g i t i s

t he same as N 1 = 11110. These p r i n t op t i ons

may be ove r r i den by op t ions N2 through N7.

= NPCHAN, an o p t i o n f o r s p e c i f i c subchannel

da ta p r i n t o u t . N2 = 0: da ta f o r a l l sub-

channels p r i n t e d i f c a l l e d f o r by N1. N2 >

0: read N2 subchannel i d e n t i f i c a t i o n numbers

o f subchannels t o be p r i n t e d .

= NPROD, an o p t i o n f o r s p e c i f i c f u e l r o d heat

f l u x and/or temperature p r i n t o u t . N3 = 0:

da ta f o r a l l r ods are p r i n t e d i f c a l l e d f o r

by N1. N3 > 0: read i n N3 r o d i d e n t i f i c a -

t i o n numbers o f rods t o be p r i n t e d .

= NPNODE, an o p t i o n f o r i n t e r i o r f u e l node

temperature p r i n t o u t f o r a l l rods s p e c i f i e d

by N3. Opt ion o n l y a p p l i e s i f i n t e r i o r r od

temperatures a re c a l c u l a t e d us ing t h e f u e l

model (GROUP 8). N4 = 0: p r i n t r od cen te r -

l i n e , r od sur face and c l add ing su r f ace tem-

pera tu re . N4 = 3 t o 7: N4 e q u a l l y spaced

i n t e r i o r r o d temperatures a re p r i n t e d a long

w i t h t h e c l add ing sur face temperature.


SETUP.12 N 5 = NPGAP, an op t i on f o r s p e c i f i c gap c ross f low

(contd) p r i n t o u t . N 5 = 0: data f o r a l l gaps p r i n t e d

i f c a l l e d f o r by N1. N5 > 0: read gap num-

bers o f gaps t o be p r i n t e d .

PRINTA,

PRINTC

PRINTA,

PRINTR

= an o p t i o n t o have the assembly average and/or

channel e x i t values p r i n t e d . N 6 = 0:

no a d d i t i o n a l p r i n t o u t . N 6 = 1: subchannel

e x i t values p r i n t e d . N6 = 2 : assembly

averaged values p r i n t e d . N 6 = 3: i nc lude

both N 6 = 1 and N 6 = 2 opt ions.

= NPWALL, an o p t i o n f o r s p e c i f i c w a l l tempera-

t u r e p r i n t o u t . N 7 = 0: p r i n t a l l w a l l tem-

pera tu res i f c a l l e d f o r by N1. N 7 > 0: read

N 7 thermal connect ion numbers t o be p r i n t e d .

Format ( 1 6 ( 1 2 , 1 3 ) ) , ( I = 1, N 2 )


= read assembly and subchannel i d e n t i f i c a t i o n

numbers o f N2 subchannels f o r which da ta i s

t o be p r i n t e d

Format ( 1 6 ( 1 2 , 1 3 ) ) , (I = 1, N 3 )


= read assembly and rod numbers o f N3 rods f o r

which heat f l u x and temperatures are t o be

p r i n t e d

Card Label Var i abl es Format and Expl anat i o n .-

Format (16(12,13)), ( I = 1, N5)

PRINTA,

PRINTG

PR I NTW


= read assembly and GAP numbers o f N5 gaps f o r

which c ross f lows are t o be p r i n t e d

Format (1215), ( I = l , N7)


= read N7 thermal connect ion numbers f o r which

wa l l temperatures are t o be p r i n t e d

8.0 PROGRAM SPECSET

A u x i l i a r y program SPECSET i s used t o redimension COBRA i n order t o m i n i -

mize the computer core storage requirements. I n t h i s way, COBRA u t i l i z e s on l y

t h a t p o r t i o n o f core storage necessary t o solve a p a r t i c u l a r problem. The

SPECSET r o u t i n e has th ree main func t ions :

1. t o au tomat i ca l l y se t up a cons is ten t se t o f dimensions f o r COBRA

compatible w i t h t h e use r -spec i f i ed problem s i z e

2. t o ca l cu la te the r e l a t i v e storage l o c a t i o n o f the va r iab les equiva-

lenced t o t h e vec tor SAVEAL

3. t o a l l o c a t e storage i n l a r g e core memory (LCM) on CDC-7600 machines,

i f desired.

The f i r s t f u n c t i o n i s accomplished by per forming a character-by-character

search through a complete se t o f COBRA s p e c i f i c a t i o n statements f o r dcmmy

dimension parameters. Each statement i s w r i t t e n t o an ou tput f i l e w i t h the

dummy parameters replaced by i n tege r values ca l cu la ted o r s p e c i f i e d f rom t h e

user-suppl ied i n p u t d e f i n i n g the problem s ize.

The second f u n c t i o n i s requ i red because the storage scheme i n COBRA uses

equivalencing t o over lap ar ray storage as described i n Sect ion 5. Program

SPECSET c a l c u l a t e s the appropr iate equivalencing s t a r t i n g l oca t i ons based on

the problem s i z e i n fo rma t ion suppl ied by the user .

The t h i r d f u n c t i o n i s accomplished by s imply removing a C f rom column 1 on a l l l e v e l 2 statements i f storage i n LCM i s desired. I f not, the l e v e l 2

statements are considered t o be comnents.

8.1 SPECSET INPUT

The i n p u t t o SPECSET i s i n two sect ions. The f i r s t sec t ion conta ins dumny

card images o f a1 1 COBRA COMDECKS (as shown i n Appendix D, Table D - 1 ) . This

data se t must be a v a i l a b l e f o r i n p u t f rom l o g i c a l u n i t 2 (TAPE 2).

The da ta i n the second sec t i on cons i s t s o f a se t o f parameters which

d e f i n e t h e problem s i z e and code op t ions requi red. With t h e except ion o f t h e

f i r s t da ta card, t he order i n which the da ta are s p e c i f i e d i s immater ia l .

The f i r s t card must con ta in the characters LCM i n the f i r s t t h ree columns

i f l a r g e core memory on a CDC-7600 i s t o be u t i l i z e d f o r v a r i a b l e storage. I f

1 arge core memory i s no t des i red or the code i s t o be run on some o the r system,

t h e f i r s t card should be blank. The remaining cards s p e c i f y t h e va lue o f t h e

dimensioning parameters us ing the form

Columns 1 and 2 3 4 through 6

" parameter " - - I1xxx"

where "parameter" cons i s t s o f a t w o - l e t t e r code and "xxx" i s i t s requ i red

numerical value, which must be r i g h t j u s t i f i e d t o column 6. D e f a u l t values

w i l l be suppl ied f o r any parameter no t spec i f i ed . The parameters may be i n p u t

i n any order. The a v a i l a b l e parameters, w i t h t h e i r d e f a u l t values i n paren-

theses, are l i s t e d below.

I E - Width o f energy and momentum c o e f f i c i e n t m a t r i x (21)

IH - Maximum number o f second-order connect ions t o any channel ( through

t h e r o d ) ( 6 )

I R - Maximum number o f rods i n t e r a c t i n g w i t h a channel (6 )

I T - Maximum number o f assembly types (7 )

I U - Maximum number o f assemblies ( 7 )

I V - Maximum number o f channels on an assembly face p lus one ( 4 )

I W - Maximum number o f loss c o e f f i c i e n t f o r c i n g f u n c t i o n p r o f i l e s ( 3 )

I X - Maximum number o f f l o w separated reg ions w i t h i n a s i n g l e assembly

(1) ; t h i s must be s p e c i f i e d when us ing t h e R E C I R C scheme.

MA - Maximum number o f subchannels t h a t can have area v a r i a t i o n s ( 1 )

MC - Maximum number o f subchannels (95)

ME - MX i f no s to rage on p e r i p h e r a l s (34)

ME - 3 f o r s to rage on p e r i p h e r a l s ( t h i s i m p l i e s t h a t a x i a l values w i l l be

r o l l e d i n COBRA)

MG - Maximum number o f subchannel gap connect ions (160)

M I - Maximum number o f connect ions t o a channel ( therma l + f l o w ) ( 7 )

MJ - Maximum number of assembly groupings i n network model (1)

MK - Maximum number o f l oss c o e f f i c i e n t s ( 1 )

ML - Maximum number o f a x i a l l o c a t i o n s f o r gap and area v a r i a t i o n ( 1 )

MM - Maximum number o f p o i n t s i n any one o f the f o l l o w i n g p r o f i l e s : Loss

c o e f f i c i e n t versus Reynolds number, f l o w o r p ressure drop versus

t ime, heat f l u x versus t ime, system pressure versus t ime, i n l e t and

e x i t en tha lp i es versus t i m e (29)

MN - Number o f f u e l c o l l o c a t i o n p o i n t s p l u s t h r e e ( 5 )

MO - Maximum number o f gaps coupled t o any one gap ( v i a a channel) p l u s

one ( 7 f o r square ar rays, 5 f o r t r i a n g u l a r ) (11)

MP - Maximum number o f cards i n p r o p e r t y t a b l e , a x i a l heat f l u x t a b l e o r

f o r c i n g f u n c t i o n versus t ime t a b l e s (31)

MR - Maximum number o f f u e l rods (80)

MS - Maximum number o f gaps t h a t can have gap spac ing v a r i a t i o n s ( 1 )

MT - Maximum number o f f u e l types (10)

MV - Maximum number o f a x i a l heat f l u x p r o f i 1 es ( 2 )

MW - Maximum number o f wa l l connect ions (60)

MX - Maximum number o f a x i a l nodes p l u s one (34)

MY - Maximum number o f a x i a l f u e l t ype d i v i s i o n s ( 4 )

MZ - Maximum number o f a x i a l l o c a t i o n s f o r g r i d spacers ( 1 )

Appendix D g ives a l i s t and explanat ion of the c o n t r o l cards which cou ld be

used t o change the dimensions (SPEC) i n a COBRA f i l e . If t h e user in tends t o

r u n a se r ies o f problems o f s i m i l a r s i z e the COBRA f i l e need o n l y be redimen-

sioned once and permanently f i l e d . Any problem o f smal ler dimensions w i l l

a lso r u n on the f i l e though it may not be economical i f the problem i s long

runn ing and considerably smal ler than the problem the code was o r i g i n a l l y

redimensioned f o r .

9.0 PROGRAM GEOM

Program GEOM au tomat i ca l l y ca l cu la tes and makes card images o f COBRA i n p u t

data f o r i n p u t Card Groups 4, 7, and 8 f o r hexagonal rod bundles. It can be

used t o generate:

subchannel areas, wetted perimeters, heated per imeters and the subchannel

connect ion l o g i c requ i red i n Group 4

the r e l a t i v e wirewrap c ross ing in fo rmat ion f o r the w i re wrap model i n

Group 7

the i n i t i a l w i re wrap i nven to ry f o r Group 7

the f u e l rod diameter, r a d i a l power f a c t o r and rod-to-channel connect ion

data f o r Group 8

an op t i on t o c a l c u l a t e geometries t h a t e i t h e r inc lude or omit the corner

subchannel s.

There i s op t i ona l i n p u t t h a t a l lows the user t o change the standard GEOM

numbering scheme f o r t he subchannels o r t o conso l ida te subchannels and rods f o r

coarser noding schemes. The opt ion t o change the standard numbering scheme can

be use fu l when i t i s desi red t o run the problem w i t h t h e d i r e c t s o l u t i o n o f

momentum equations s ince the w id th o f the c o e f f i c i e n t m a t r i x i s determined by

the l a r g e s t d i f f e r e n c e i n channel i d e n t i f i c a t i o n numbers f o r any two adjacent

channels. The standard subchannel and rod numbering scheme i s demonstrated i n

F igure 13. F igure 14 g ives the opt imal subchannel numbering scheme f o r t h e

standard subchannel noding o f a 37-pin bundle when us ing the d i r e c t i nve rs ion

r o u t i n e f o r t he momentum so lu t i on .

Two general i n p u t forms are a v a i l a b l e t o the user. Under the f i r s t

opt ion, t he user s p e c i f i e s t h e subchannel area, wetted perimeter, and heated

perimeter f o r t y p i c a l i n t e r n a l , s ide and corner subchannels. Under the second

opt ion, t he code ca l cu la tes t h e areas and per imeters from the o v e r a l l bundle

geometry descr ip to rs . A d e s c r i p t i o n o f the GEOM i n p u t fo l lows.

FIGURE 13. Samples o f GEOM Rod and Channel Numbering Scheme

FIGURE 14. Optimal GEOM Numbering Scheme f o r Standard Subchannel Noding o f a 37-Pin Bundle

9.1 GEOM INPUT

Card Label Vari ables

GEOM .1 JCONTU , HEADER

JCONTU

HEADER

GEOM .2 %¶

ICHANS

IOLD

INEW

GEOM .3 I FORM

IFORM

HPI

GEOM. 5 AS, WPS, HPS

Format and Expl anat i on

Format (15,18A4)

= 1: standard GEOM r u n

= -1: read i n op t iona l i npu t t o renumber

subchannel s (GEOM.2)

= 2: read i n opt iona l i npu t t o lump sub-

channels and rods (GEOM.13)

= j o b or problem t i t l e up t o 72 characters.

Format (I5/1615), ( I = l , ICHANS)

Opt ional input : JCONTU = -1

= number o f channels f o r which GEOM i s t o

generate data

= standard channel number

= new channel number

Format (11)

= 1: use op t ion 1 f o r GEOM inpu t cards

(GEOM.4, 5, 6, 7)

= 2: use op t ion 2 f o r GEOM inpu t cards

(GEOM.8)

Format (3F5.3)

Opt ional input : IFORM = 1 2

= area ( i n . ) o f an i n t e r i o r channel

= wetted per imeter ( i n . ) o f an i n t e r i o r chan-

ne 1

= heated perimeter ( in . ) o f an i n t e r i o r chan-

ne 1

Format (3F5.3)

Opt ional i npu t : IFORM = 1


AS,WPS ,HPS

GEOM. 6

GEOM. 7

AC ,WPC ,HPC

AC, WPC ,HPC

G I I , C I I , GIs, C I S . GSS. CSS.

G I I , C I I

GIs, CIS

GSS, CSS

GCS, CCS

PITCH, RDIAM, PDR, FFD, RPF

PITCH

R D I A M

PDR

FFD

R PF

WDIAM


= same as GEOM.4 b u t the i n fo rma t i on i s f o r a

s i de channel

Format (3F5.3)

Opt iona l i npu t : IFORM = 1

= same as GEOM.4 b u t f o r a corner channel

Format (8F5.3)

Opt iona l i npu t : IFORM = 1

= gap w id th ( i n . ) and t ransverse momentum

c o n t r o l volume leng th ( i n . ) f o r i n t e r i o r -

t o - i n t e r i o r connect ions

= same f o r i n t e r i o r - t o - s i d e connect ions

= same f o r s ide- to -s ide connect ions

= same f o r corner- to-s ide connect ions

Format (5F5.3)

Opt ional i npu t : IFORM = 2

Only two o f f i r s t th ree parameters a re

requ i red .

= r o d p i t c h ( i n . )

= rod diameter ( i n . )

= r a t i o o f rod p i t c h t o rod diameter

= f l a t - t o - f l a t I.D. duct dimension ( i n . )

= r o d packing f a c t o r . RPF = 1: assembly

to le rances u n i f o r m l y d i s t r i b u t e d ( i n t e r i o r

and s ide gaps have same wid th ) . RPF = 0:

assembly to le rances are app l ied o n l y t o t h e

s ide channels and gaps. RPF can be anyth ing

between 0.0 and 1.0.

= w i r e wrap diameter ( i n . )

Card Label Var i abl es Format and Expl anat i on

GEOM. 9 IOUT(1) , IOUT(2), Format (611) OUT(3), NPUN,

IRODP, NZONE

IOUT(1) = 1: area and gap connection da ta f o r COBRA

group 4 w i l l be generated. Set t o zero i f

t h i s data i s not desired.

IOUT(2) = 1: COBRA group 7 wire wrap data generated

IOUT(3) = 1: rod t o channel connect ion data f o r

group 8 generated

NPU N

IRODP

NZONE

= 1: output i s punched

0: i n d i v i d u a l rod powers f o r group 8 a re

t o be read from l o g i c a l u n i t IRODP us ing

format spec i f i ed by NZONE. Card reader i s

l o g i c a l u n i t 5.

= 1: i n p u t r a d i a l power f a c t o r s by zones

r a t h e r than rod by rod. NZONE equals t h e

number o f zones. A l l rods w i t h i n one zone

w i l l be assigned the same r a d i a l power fac -

t o r . NZONE = 0: i n p u t r a d i a l power f a c t o r s

rod by rod.

GEOM.10 NRODS, RD, Format (15,2F5.3,315,F5.3,15) RP, IFF, IDIR, WWSA, DUR, I C O R

NRODS

RD

RP

= nurr~ber o f rods i n the bundle

= nominal rod diameter

= nominal rod power f a c t o r


GEOM. 10 IFF

(contd)

I D I R

WWSA

DUR

I COR

Format and Exp lanat ion

= subchannel f r i c t i o n t y p i n g parameter.'

IFF = 0: a l l subchannels are type 1.

IFF = 1: i n t e r i o r subchannels are t ype 1,

s ide are type 2, and corner are type 3.

IFF = 2: t h e subchannels are typed v i a

op t i ona l i n p u t card GEOM 12.

= w i re wrap d i r e c t i o n i n d i c a t o r . I D I R = 0

i n d i c a t e s counterc lockwise wrapping

(F igure 15) and I D I R = 1 f o r clockwise..

Note t h a t I D I R = 0 l ook ing f rom t h e down-

stream end o f the bundle wraps the w i re i n

t h e same d i r e c t i o n as I D I R = 1 from t h e

upstream end. User view o r i e n t a t i o n i s

unimportant as long as a l l i n p u t i s consis-

t a n t w i t h t h a t view.

= w i re wrap s t a r t i n g angle t o t he nearest

degree ( i n t e g e r va lue) . Measure counter

c lockwise as shown i n F igure 15.

= w i re wrap crossf lows f o r c i n g parameter f ~ r

Card Group 7.

= corner subchannel switch. I C O R = 0: , cor -

ner subchannels omi t ted. I C O R = 1: corner

subchannels w i l l be inc luded i n the Group 4

output .

Format (1215), ( I = 1, NTYPS)

Opt ional inpu t : IFF = 3 Format (GEOM.lO)

NTY PS = number o f subchannel types

a) Wire wrap s t a r t i n g angle = 00 b ) Wire wrap s t a r t i n g angle = 900 counterc lockwise r o t a t i o n counterclockwise r o t a t i o n *

c ) Wire wrap s t a r t i n g angle = 900 d) Wire wrap s t a r t i n g angle c lockwise r o t a t i o n * convent ion

*NOTE: When a wrap i s i n i t i a l l y on a gap the i n i t i a l wrap i nven to ry i s determined by moving t h e wrap complete ly i n t o t h e channel toward which i t i s moving. Compare b and c above.

FIGURE 15. D e f i n i t i o n o f Wrap S t a r t i n g Angle and Ro ta t i on D i r e c t i o n


GEOM. 11 I M I N , IMAX = niinimum and maximum subchannel numbers f o r

(contd) each type; assumes the subchannels are num-

bered i n t h e standard p a t t e r n

GEOM.12 RPFF (N ) Format (12F5.3), (N = 1, NRODS)

Opt ional i npu t : IRODP > 0 and NZONE = 0

(GEOM.9)

RPFF = i n d i v i d u a l r o d power f a c t o r

GEOM.13 Format (15,~5.3/(1415)), ( ( ~ = l , I S I Z E ( I ) ) ,

IZONE(1 ,L,) I = 1, NZONE)

Opt ional i npu t : IRODP > 0 and NZONE > 0

(GEOM.9)

IZSIZE(1) = number o f rods i n Zone I

ZFACTR ( I ) = r a d i a l power f a c t o r f o r rods i n Zone I

IZONE(1 ,L) = r o d numbers i n Zone I (any o rde r )

GEOM.14 ICH1, ICH2, NEWC Format (315)

Opt ional i npu t : JCONTU = 2 Format (GEOM.l)

ICHl,ICH2,NEWC = channels ICHl through ICH2 i n c l u s i v e l y w i l l

be lumped i n t o channel NEWC. Read as many

cards as necessary. A p a r t i c u l a r va lue f o r

NEWC may be read more than once. A b lank

card i n d i c a t e s the end o f i n p u t f o r GEOM.14.

Mult iasserr~bly problems may be se t up us ing GEOM by simply reading another

header card (GEOM.l) and proceeding as f o r the i n i t i a l bundle. A b lank card

terminates the GEOM run.

REFERENCES

Wheeler, C. L., e t a l . March 1976. COBRA-IV-I: An I n t e r i m Version o f COBRA f o r Thermal Hyd rau l i c Ana lys is of Rod Bundles, Nuclear Fuel Elements and Cores. BNWL-1962, P a c i f i c Northwest Laboratory, Richland, Washington.

Masterson, R. E., and C. L. Wheeler. November 1978. "A New Scheme f o r So lv ing t h e COBRA Energy Equations Dur ing Natura l C i r c u l a t i o n Condit ions." ANS Transact ions.

Finlayson, B. A. 1972. The Method of Weighted Residuals. Academic Press, New York.

Caret to , L. S., A. D. Gosman, S. V. Patankar and D. B. Spalding. 1972. "Two C a l c u l a t i o n Procedures f o r Steady Three Dimensional Flows With Rec i r cu la t i on . " I n Proceedings o f t h e T h i r d I n t e r n a t i o n a l Conference on Numerical Methods i n F l u i d Mechanics, Springer.

Gosman, A. D., R. Herbert , S. V. Patankor, R. P o t t e r and D. B. Spalding. October 1973. "The SABRE Code f o r P r e d i c t i o n o f Coolant Flows and Tem- peratures i n P i n Bundles con ta in ing Blockages." Imper ia l Col lege o f Science and Technology, Report HTS/73/47, September, 1973. (Presented a t I n t e r n a t i o n a l Meet ing on Reactor Heat Transfer , K a r l sruhe. )

Harlow, F. H., and A. A. Arnsden. 1971. "A Numerical F l u i d Dynamics Method f o r A l l Flow Speeds." Journal o f Computational Physics 8:197-213.

Tong, L. S. 1968. "Pressure Drop Performance o f a Rod Bundle." I n - Heat Transfer i n Rod Bundles. ASME, pp. 57-69.

Lyon, R. N. (ed.). June 1952. L i q u i d Meta ls Handbook. Sponsored by Committee on the Basic P rope r t i es o f L i q u i d Metals, O f f i c e o f Naval Research, Dept. o f Navy, i n c o l l a b o r a t i o n w i t h U.S: Atomic Energy Commis- s ion and Bureau o f Ships, Dept. o f Navy.

El-Waki l , M. M. 1971. Nuclear Heat Transport . I n t e r n a t i o n a l Textbook Company. Scranton, Pennsylvania.

Rogers, J. T., and N. E. Todreas. 1968. "Coolant M ix ing i n Reactor Fuel ~ o d Bundl es--Si ng l e-Phase Cool ants .I1 Heat Trans fer i n ~ o c k Bundles. ASME pp. 1-56.

Ingesson, L. and S. Hedberg. 1970. "Heat Transfer Between Subchannels i n a Rod Bundle." Paper No. FC7.11, 4 th I n t e r n a t i o n a l Heat Trans fer Con- ference, V e r s a i l l es, FRANCE.

REFERENCES (contd)

11. Rogers, J. T., and R. G. Rosehart. 1972. "Mix ing by Turbu len t I n t e r - change i n Fuel Bundles, Co r re la t i ons and Inferences." ASME Paper No. 72-Ht-53.

12. Rowe, D. S. March 1973. COBRA-I11 C: A D i g i t a l Computer Program f o r Steady S ta te and Trans ien t Thermal Hyd rau l i c Ana lys is o f Rod Bundle Nuclear Fuel Elements. BNWL-1695. P a c i f i c Northwest Laboratorv. Rich1 and, Washington.

13. Khan, E. U., e t a l . March 1975. "A Porous Body Model f o r P r e d i c t i n g Temperature D i s t r i b u t i o n s i n Wire-Wrapped Fuel and Blanket Assemblies o f an LMFBR." COO-2245-16TR, MIT.

14. Golden, G. H. and J. V. Tokar. August 1967. Thermophysical P rope r t i es o f Sodium. ANL-7323. Argonne Nat iona l Laboratory, Argonne, I l l i n o i s .

APPENDIX A

SUBROUTINE DESCRIPTION

APPENDIX A

SUBROUTINE DESCRIPTION

Subrout ine AREA (J, JX)

This subrout ine c a l c u l a t e s subchannel area, gap and h y d r a u l i c diameter

v a r i a t i o n s by us ing a t a b u l a r l i s t o f area and gap v a r i a t i o n s as a f u n c t i o n o f

a x i a l d is tance as inpu t . L inear i n t e r p o l a t i o n i s used t o s e l e c t values from

these tab les . When w i r e wrap m ix ing i s included, AREA c o r r e c t s t h e subchannel

f l o w area and h y d r a u l i c diameter according t o the w i re wrap inventory . J and

JX are t h e c a l c u l a t i o n a l l e v e l and t h e a x i a l node, r e s p e c t i v e l y . For n o n r o l l e d

problems, J = JX. For r o l l e d problems J = 2. Subrout ine AREA i s c a l l e d by

subrout ines R E C I R C and SCHEME.

Subrout ine CLEAR

Subrout ine CLEAR i s used t o s e l e c t i v e l y zero COMMON p r i o r t o execut ion.

The s i z e o f any COMMON area t o be zeroed i s computed us ing t h e CDC system rou-

t i n e LOCF. I f the code i s t o be used on a system o ther than CDC t h i s r o u t i n e

may have t o be changed t o remove t h e c a l l s t o t h e LOCF r o u t i n e . Subrout ine

CLEAR i s c a l l e d by the main program, COBRA.

Program COBRA

The main program performs v a r i a b l e i n i t i a l i z a t i o n e i t h e r by s e t t i n g the

v a r i a b l e t o zero o r by c a l l i n g t h e RESTRT r o u t i n e which i n i t i a l i z e s v a r i a b l e s

t o the values saved f rom a prev ious run. I t a lso c o n t r o l s i n p u t and ou tpu t v i a

t h e subrout ines SETUP and RESULT. The user s p e c i f i e d s o l u t i o n o p t i o n f o r t h e

conservat ion equat ions i s i n i t i a t e d e i t h e r w i t h a c a l l t o SCHEME ( f o r the PSOLV

E steady s t a t e and i m p l i c i t t r a n s i e n t method descr ibed i n Sect ion 4.2.1) o r a

c a l l t o R E C I R C ( f o r the R E C I R C steady s t a t e and i m p l i c i t / e x p l i c i t t r a n s i e n t

method descr ibed i n Sect ion 4.2.2). The t r a n s i e n t boundary cond i t i ons and

f o rc ing func t i ons are s e t i n COBRA a t t h e beginning o f each t imestep. A more

d e t a i l e d d e s c r i p t i o n of COBRA I s prov ided i n Sect ion 5 of t h i s document.

Subrout ine COLOC ( IA, ISYM, KK, RMIN, RMAX)

Subroutine COLOC sets up the fue l model orthogonal c o l l o c a t i o n c o e f f i c i e n t

m a t r i c i e s A , B , and Q as defined i n Sect ion 4.1. Although the r o u t i n e

was se t up f o r both c y l i n d r i c a l (IA=2) f u e l geometries w i t h an annular o r s o l i d

(ISYM = 1 or I S Y M = 2 ) con f i gu ra t i on and p lanar f u e l geometry ( I A = l ) , o n l y the

c y l i n d r i c a l f u e l op t ions are c u r r e n t l y a v a i l a b l e i n COBRA-WC. Subrout ine COLOC

i s c a l l e d by subrout ine SETIN.

E n t r y COPY (KEYS, LU, RECORD)

COPY i s used t o w r i t e data from v a r i a b l e a r ray RECORD i n computer memory

t o record KEYS o f p e r i p h e r i a l s torage f i l e LU. RECORD can correspond, through

equivalencing, t o the set o f f i e l d va r i ab les a t one o f the th ree c a l c u l a t i o n a l

l e v e l s i n core, J-1,J, o r J+1. Thus COPY, i n con junc t ion w i t h subrout ine IMAGE

can swap a r e c e n t l y ca l cu la ted se t of va r i ab les a t c a l c u l a t i o n a l l e v e l J -1 t h a t

are i n core w i t h a se t o f previous i t e r a t e values a t l e v e l J+2 from p e r i p h e r i a l

s torage as the c a l c u l a t i o n l e v e l proceeds up the a x i a l mesh.

En t r y COPY i s an e n t r y p o i n t i n subrout ine IMAGE and i s c a l l e d by most o f

the major subrout ines.

Subrout ine CURVE (FX, X, F, Y, N, J, ISAVE)

This subrout ine performs l i n e a r i n t e r p o l a t i o n o f tabu la ted data. The

va r iab les i n the argument l i s t are de f ined as:

FX = q u a n t i t y t o be found

X = independent v a r i a b l e

F = i n p u t a r ray o f values o f t he dependent v a r i a b l e

Y = i n p u t a r ray o f values o f the independent v a r i a b l e

N = number o f F values i n t a b l e

J = e r r o r s igna l

ISAVE = Table search sw i tch . For ISAVE = 1, a complete t a b l e search on

t h e independent v a r i a b l e i s done. For ISAVE = 2, t h e l o c a t i o n i n

t h e t a b l e which b racke ts t h e indepdent v a r i a b l e i s known f rom a

p rev ious c a l l t o curve, and t h e t a b l e search i s n o t performed.

Subrout ine CURVE i s c a l l e d by a l l t h e major subrou t ines i n COBRA-WC.

Subrou t ine DIFFER (IPART, J, JX)

Subrout ine DIFFER i s d i v i d e d i n t o 4 p a r t s as i n d i c a t e d by t h e v a r i a b l e

IPART.

Pa r t 1 i s c a l l e d by subrou t ines SCHEME and RECIRC f o r each a x i a l l e v e l a t

t h e beg inn ing o f t h e o u t e r i t e r a t i o n loop. The f l u i d l a t e r a l conduc t ion terms

f o r t he energy equa t ion are determined based on p rev ious i t e r a t e en tha lp i es .

I f t h e w a l l hea t t r a n s p o r t model i s used, t h e o v e r a l l w a l l - t o - c o o l a n t hea t

t r a n s f e r c o e f f i c i e n t UWALL i s determined.

P a r t 2 c a l c u l a t e s t h e d i v e r s i o n c ross f l ow res i s t ance , C i j , and i s c a l l e d

by s u b r o u t i ne PSOLVE . Par t 3 c a l c u l a t e s t h e i r r e v e r s a b l e pressure l o s s c o e f f i c i e n t , DPK(I), due

t o f r i c t i o n and drag f o r t h e a x i a l momentum equat ion. The o t h e r components o f

t h e pressure g rad ien t are computed, w i t h t h e excep t ion o f t h e d i v e r s i o n c ross -

f l o w terms, and a re des ignated as DPDX(1). P a r t 3 i s c a l l e d by sub rou t i ne

SCHEME.

Pa r t 4 c a l c u l a t e s t h e i r r e v e r s i b l e p ressure l o s s c o e f f i c i e n t , DPK(I), due

t o f r i c t i o n and drag f o r t h e RECIRC f o r m u l a t i o n o f t h e a x i a l niomentum equa t ion .

P a r t 4 i s c a l l e d by MOMENT.

Subrou t ine DUMPIT

Th is sub rou t i ne i s used t o s t o r e a l l l abe led and b lank COMMON on l o g i c a l

u n i t 8. Th i s r o u t i n e a l l ows t h e user t o save t h e c u r r e n t computed values, l ook

a t t he r e s u l t s and, then, i f des i red, con t inue t h e s o l u t i o n .

Subrout ine DUMPIT i s c a l l e d by t h e main program, COBRA.

Subrout ine ECHO (IPR, I C R , IFL)

Subrout ine ECHO reads the COBRA-WC i n p u t f rom l o g i c a l u n i t I C R and p r i n t s

alphanumeric card images t o l o g i c a l u n i t IFL and t h e p r i n t e r IPR. These

p r i n t e d card images can be used by the user t o debug t h e i n p u t da ta deck. A t

t h e end o f ECHO, l o g i c a l u n i t IFL i s rewound and i s used as t h e i n p u t f i l e f o r

subrout ine SETIN. Subrout ine ECHO i s c a l l e d as an op t i on by subrou t ine COBRA.

Subrout ine ELAP (MTIME)

ELAP determines the CPU t ime used thus f a r i n the c a l c u l a t i o n . Th is i s

compared w i t h t h e maximum t ime allowed, MAXT, t o determine i f t h e c a l c u l a t i o n

should be terminated.

Subrout ine ELAP i s c a l l e d by subrout ines COBRA, R E C I R C and SCHEME.

Subrout ine ENERGY (J, JP1, JM1, JX)

Subrout ine ENERGY sets up and solves the combined rod, wa l l , and coo lan t

energy equat ions (see Sec t ion 4.1) a t a x i a l l e v e l J and a x i a l node JX, us ing

the method of successive ove r re laxa t i on t o determine the coo lan t en tha lpy d i s -

t r i b u t i o n . The energy equat ion c o e f f i c i e n t m a t r i x i s designated HAH and t h e

source vec tor as DHDX. A f t e r the coo lan t temperatures are found, t h e w a l l

temperatures, i f any, are backed ou t us ing Equat ion 30. Subrout ine ENERGY i s

c a l l ed by sub rou t i nes RECIRC and SCHEME.

Subrout ine EXPROP ( J )

Subrout ine EXPROP determines the average enthalpy, d e n s i t y and v i s c o s i t y

a t t h e bundle e x i t . These p r o p e r t i e s are used f o r i n l e t cond i t i ons i n t h e

event o f f l o w reve rsa l . Subrout ine EXPROP i s c a l l e d by subrou t ine ENERGY.

Subrout ine FORCE (J, JX)

Subrout ine FORCE i s prov ided t o s p e c i f y f o rced d i v e r s i o n c ross f l ow a t

se lec ted gaps and a t se lec ted a x i a l p o s i t i o n s . I f a fo rced c ross f l ow i s spec-

i f i e d , t he v a r i a b l e FDIV = 1.0; otherwise, FDIV = 0. Subrout ine FORCE

inc ludes two opt ions f o r f o rced c ross f low mixing. One op t i on i s t he w i re wrap

mix ing model f o r which FORCE computes a fo rced c ross f low when a w i r e crosses a

gap. The o ther op t ion i s f o r a s p e c i f i e d f l o w f r a c t i o n d i ve r ted from one sub-

channel t o an adjacent subchannel by g r i d spacers.

Subroutine FORCE i s c a l l e d by subrout ines SCHEME and RECIRC.

Subrout ine HOTROD ( J )

HOTROD ca lcu la tes the f i n a l f u e l rod temperature f i e l d a f t e r the energy

and f l u i d so lu t i ons have converged f o r a given t imestep. This i s accomplished

f i r s t by f i n d i n g the c l a d temperature us ing Equation 24 and the surrounding

f 1 u i d temperatures, and then back -subs t i t u t i ng i n t o t h e reduced temperature

Equations 22 and 23. Subrout ine HOTROD i s c a l l e d by subrout ines RECIRC and

SCHEME.

Subrout ine IMAGE (KEYS, LU, RECORD)

IMAGE i s used t o w r i t e data f rom record KEYS o f p e r i p h e r i a l storage f i l e

LU t o va r iab le a r ray RECORD i n computer memory. RECORD can correspond, through

equivalencing, t o the se t o f f i e l d va r i ab les a t one o f the th ree c a l c u l a t i o n a l

l e v e l s i n core; J-1, J, o r J+1. Thus IMAGE, when used i n con junc t ion w i t h

E n t r y COPY, can swap a r e c e n t l y ca l cu la ted se t o f va r i ab les a t c a l c u l a t i o n a l

l e v e l J -1 t h a t are i n core w i t h a s e t o f prev ious i t e r a t e values a t l e v e l J+2

from p e r i p h e r i a l storage as the c a l c u l a t i o n l e v e l proceeds up the a x i a l mesh.

Subrout ine IMAGE i s c a l l e d by most t h e major subrout ines.

Subrout ine INVR (A, N)

INVR f i n d s the inverse o f N x N m a t r i x [A]. Subrout ine INVR i s c a l l e d by

subrout ine COLOC t o f i n d t h e inverse o f t he c o l l o c a t i o n c o e f f i c i e n t [Q] defined

i n Equation 18.

Subrout ine LIMITS (NUM, MIN, MAX, GROUP, CARD, ERROR)

This r o u t i n e i s designed f o r use w i t h i n subrout ine SETIN t o enhance t h e

e d i t i n g o f i n p u t data. I t s f u n c t i o n i s t o guarantee t h a t the number o f values

read i n t o an a r ray are w i t h i n the dimensioned l i m i t s o f the code. I f not, t he

parameter, NUM, i s changed o n l y f o r t he convenience o f ed i t i ng ; however, t h e

case w i l l be terminated a f t e r the i n p u t i s edi ted. I n add i t ion , a l i m i t o f

twen ty - f i ve accumulated e r r o r s are allowed, a f t e r which t h e e d i t i n g w i l l cease.

NUM = i n p u t parameter t o be checked

MIN = minimum al lowable value f o r NUM

MAX = maximum a1 1 owable value f o r NUM

GROUP = card group i d e n t i f i e r f o r e d i t i n g d iagnost ics

CARD = i n p u t card counter; fo r l a b e l i n g which card may be i n e r r o r

ERROR = alphanumeric f l a g f o r e d i t i n g . I f ERROR = "yes", t h e code w i l l

te rminate f o l l o w i n g the e d i t i n g o f i npu t data.

Subrout ine LOAD (X, Y, Z, M I N , MAX, LIMIT, STEP, IMAGE, CARD, LU)

LOAD i s used t o rep lace redundant l o g i c w i t h i n subrout ine SETIN. It i s

designed t o a l l ow t h e load ing o f i n p u t data o n l y a f t e r t h e group card para-

meters have been v e r i f i e d .

X = f i r s t v a r i a b l e t o be loaded (Step = 1 ) .

Y = second v a r i a b l e t o be loaded (Step = 2 ) .

Z = t h i r d v a r i a b l e t o be loaded (Step = 3 ) .

STEP = t h e number o f var iab les t o be loaded sequen t ia l l y . ( 1 STEP 3)

MIN = the maximum al lowable sets o f (X,Y ,Z) which can be loaded.

MAX = t h e number o f sets o f (X,Y,Z) t h e user attempts t o load.

I f (MAX MIN), then a dummy read i s used t o account f o r remaining cards.

This a l lows subsequent i n p u t t o be ed i ted .

LIMIT = the maximum number o f da ta values per card which can be loaded

v i a t h e format ted IMAGE

IMAGE = the v a r i a b l e FORMAT t o be used f o r load ing i npu t data

CARD = i n p u t card counter f o r l a b e l i n g which card may be i n e r r o r

LU = i n p u t device used f o r read ing i n p u t data.

Subrout ine LOADL (X, Y, Z, MIN, MAX, LIMIT, STEP, IMAGE, CARD, LU)

LOADL I s i d e n t i c a l i n f u n c t i o n t o subrout ine LOAD, except t h a t (X,Y,Z) a re

va r iab les which may be a1 1 ocated t o Level 2 (1 arge core memory) on a CDC-7600

system. This r o u t i n e i s used regardless o f t h e system on which COBRA i s being

r u n and the necessary storage a l l o c a t i o n s are provided by Program SPECSET.

Subrout ine LOADL i s c a l l e d by Subrout ine SETIN.

Subrout ine M I X ( J l

M I X ca l cu la tes the t u r b u l e n t mix ing parameters WT, which i s designated

by WP(K). The var ious forms o f user i n p u t c o r r e l a t i o n s t h a t are ava i l ab le are

described i n Sect ion 4.3 and the i n p u t i ns t ruc t i ons . Subroutine M I X i s c a l l e d

by subrout ines RECIRC and SCHEME.

Subrout ine MOMENT (JX, J, JMI , JPI, IPART)

MOMENT ca l cu la tes t h e a x i a l and l a t e r a l subchannel f l owra tes f o r a g iven

pressure f i e l d a t computational Level J f rom the l i n e a r i z e d momentum Equa-

t i o n s 37 and 38. The p a r t i a l d e r i v a t i v e s W/ P and F/ P are a lso ca l cu la ted

f o r use by RECIRC i n the s o l u t i o n o f the c o n t i n u i t y and l i n e a r i z e d momentum

equations. Subrout ine MOMENT i s c a l l e d b y subrout ine RECIRC.

Subrout ine NETWORK (ITER)

When the pressure boundary cond i t i on network model i s spec i f ied , subrou-

t i n e NETWORK ca lcu la tes t h e c o n t r i b u t i o n b y network o r i f i c e and head losses t o

the t o t a l spec i f i ed problem pressure boundary cond i t ion . These losses are

based on t h e l a t e s t assembly f l owra tes .

Subroutine NETWORK i s c a l l e d by subrout ines PBOUND and RESULT.

Subrout ine ONED (IPARTL

ONED forms a one dimensional approximation t o the mul t i -d imensional con-

t i n u i t y and momentum s o l u t i o n (see Sect ion 4.2.2) a t a given l e v e l and solves

i t us ing d i r e c t invers ion. Subrout ine ONED I s c a l l e d by RECIRC.

Subrout ine PBOUND (JUMPS, NT, ACCF)

PBOUND i s c a l l e d by subrout ine SCHEME when a pressure boundary c o n d i t i o n

i s spec i f i ed . PBOUND I s used t o mod i fy t h e i n l e t f l o w r a t e u n t i l a l l subchannel

pressure drops are equal t o t h e i r i n d i v i d u a l l y s p e c i f i e d pressure drops. This

pressure drop i s t h e user i n p u t pressure boundary c o n d i t i o n minus t h e network

o r i f i c e and head losses, determined i n NETWORK, if any. Each new f l o w guess

i s determined by an extrapolation/interpolation procedure based on damped, o l d

i t e r a t e value f l o w r a t e s and pressure drops. The parameter JUMPS i s a conver-

gence f l a g which when s e t t o 2 by PBOUND, i nd i ca tes t h a t t h e code has converged

upon a s p e c i f i e d pressure drop. NT i s the i t e r a t i o n count and ACCF i s the f l o w

acce le ra t i on f a c t o r .

Subrout ine PREFIX

PREFIX i s used t o compute the constant f u e l rod c o l l o c a t i o n c o e f f i c i e n t s

f o r t h e m a t r i x [M] shown i n Equation 27. These c o e f f i c i e n t s are used t o

i m p l i c i t l y l i n k the f u e l and coolant energy equations. The subrout ine i s

d i v i d e d i n t o sec t ions f o r t h e d i f f e r e n t combinations o f c o l l o c a t i o n order and

f u e l rod type. PREFIX i s c a l l e d by RECIRC and SCHEME.

Subrout ine PROP (IPART, J, JX, JMI, JPIL

PROP cons i s t s o f two par ts . The f i r s t p a r t uses the code sodium p rope r t y

c o r r e l a t i o n s o r op t i ona l Group 1 p roper t y t a b l e t o b u i l d t h e phys ica l p r o p e r t y

a r rays stored i n v a r i a b l e DATA. Pa r t 2 ca l cu la tes f l u i d p roper t ies , t he f r i c -

t i o n f a c t o r , and t h e f i l m c o e f f i c i e n t f o r a given s e t o f f l u i d cond i t ions .

Subrout ine PROP i s c a l l e d by subrout ines COBRA, RECIRC, SCHEME, SETIN and

SPLIT.

Subrout ine PSOLVE (J, JX)

PSOLVE sets up and solves the combined momentum and c o n t i n u i t y Equa-

t i ons 37 described i n Sect ion 4.2. l by successive-over-re1 axat ion a t t he c a l -

c u l a t i o n a l Level J. I f the d i r e c t Gaussian e l i m i n a t i o n s o l u t i o n i s desired,

subrout ine SOLVER i s ca l l ed . Subrout ine PSOLVE I s c a l l e d by subrout ine SCHEME.

Subrou t ine RECIRC (JUMP, ISTART, JUMPS)

R E C I R C i s the managing subrou t ine f o r t h e RECIRC s o l u t i o n scheme f o r

r e c i r c u l a t i n g f l ows . It c a l l s t h e subrou t ines which so l ve t h e energy momentum

and s t a t e equat ions w h i l e s o l v i n g t h e c o n t i n u i t y equa t ion i n t e r n a l l y . JUMP i s

t h e f l o w convergence f l a g ; ISTART i s t h e s t a r t i n g i t e r a t i o n number; and JUMPS

i s t h e i n d i c a t o r f o r convergence on pressure drop boundary c o n d i t i o n problems.

Subrou t ine REHEAT (J, JX)

REHEAT computes t he heat f l u x dependent terms i n t he r o d energy equat ion

m a t r i x [M] shown i n Equat ion 27. These terms a re used t o imp1 i c t l y l i n k t h e

f u e l and coo lan t energy equat ions. The subrou t ine i s d i v i d e d i n t o sec t i ons f o r

t h e d i f f e r e n t combinat ions o f c o l l o c a t i o n o rder and f u e l type. Subrout ine

REHEAT i s c a l l e d by subrou t ines RECIRC and SCHEME.

Subrou t ine REHEATV (N, NT, L, KL, J, JX, IPART, LN, LQ)

REHEATV m o d i f i e s some o f the terms computed i n REHEAT when t h e v a r i a b l e

f u e l r o d p r o p e r t y o p t i o n i s s p e c i f i e d . Th is o p t i o n i s c u r r e n t l y a v a i l a b l e o n l y

f o r second o rder c o l l o c a t i o n f o r a s o l i d f u e l type. REHEATV i s c a l l e d by sub-

r o u t i n e REHEAT.

Subrou t ine RESTRT (NTSTRT, ISTART)

Th i s r o u t i n e i n i t i a l i z e s v a r i a b l e s t o t h e values t h a t were saved by sub-

r o u t i n e DUMPIT f rom a p rev ious s o l u t i o n . The f i r s t f u n c t i o n o f RESTRT i s t o

r e t r i e v e the p r e v i o u s l y saved s o l u t i o n and i n i t i a l i z e COMMON t o t he s to red

values. Next, a RESTRT da ta card i s read d e f i n i n g t h e t ype o f r e s t a r t des i red .

I n a d d i t i o n t o t he r e s t a r t da ta read, c e r t a i n values f rom t h e p rev ious s o l u t i o n

d i c t a t e how t h e s o l u t i o n may be r e s t a r t e d . The f l o w c h a r t i n F i g u r e A . l

i l l u s t r a t e s the RESTRT op t i ons a v a i l a b l e i n t he code. RESTART i s c a l l e d by

sub rou t i ne COBRA.

INITIALIZE COMMON TO SAVED VALUES

NJUMP = 1 FROM SUBROUTINE SETUP

DO NOT READ ANY FOLLOWING RETURN ADDITIONAL INPUT FROM RESTART

BEGIN A TRANSIENT FROM TIME ZERO 1

NDT :O FROM A PREVIOUS STEADY-STATE SOLUTION

AND RESULTS

CALCULATE A NEW

USING PREVIOUS SOLUTION AS FIRST GUESS

CONTINUE ITERATIONS ON

PREVIOUS STEADY - STATE SOLUT l ON

NTT = 0 NTl ' 0 YES

NO TRANSIENT SOWTION

CONTINUE TIME STEPS

ON PREVIOUS TRANSIENT SOLUTION

CONTINUE TIME STEPS . FOLLOWING ON A PREVIOUSTRANSIENT STEADY -STATE SOLUTION I SOLUTION. WITH ADDITIONAL 1 ( CALCULATE 1 DATA READ TRANSIENT SOLUTION

FIGURE A.1. Subrout ine RESTRT Ava i l ab le Code Options

Subrout i ne RESULT (NT)

A l l p r i n t i n g o f t he r e s u l t s i s done by t h i s subrout ine. NT i s t he c u r r e n t

t ime increment number.

Subrout ine RESULT i s c a l l e d by subrou t ine COBRA.

Subrout ine ROLLIT (J , JX, SAVEA1, SAVEA2, SAVEA3, NWR, NDXP1, LUO, LUI)

Th is subrou t ine i s used i n con junc t i on w i t h t he r o l l o p t i o n t o i n p u t and

ou tpu t temporary s to rage values o f t h e a x i a l dependent va r i ab les . J i s t h e

c u r r e n t c a l c u l a t i o n l e v e l , and JX i s t he phys i ca l a x i a l l e v e l . The v a r i a b l e s

SAVEA1, SAVEA2, and SAVEA3 are vec to rs o f l e n g t h NWR, which a re equiva lenced

t o the a x i a l dependent v a r i a b l e s a t t he a x i a l l e v e l s J-1, J, and J+1, respec-

t i v e l y . NDXPl and LUI are t h e number o f a x i a l nodes p l u s one, and t h e l o g i c a l

u n i t , r e s p e c t i v e l y . ROLLIT c a l l s subrou t ines IMAGE and COPY t o accomplish t h e

ac tua l da ta t r a n s f e r . ROLLIT i s c a l l e d by subrou t ines SCHEME and RECIRC.

Subrout ine SCHEME (NTRIES, JUMP, ISTART,MAXT,NJUMP , JUMPS)

SCHEME i s s i m i l a r t o R E C I R C i n t h a t i t i s t h e managing sub rou t i ne f o r t h e

PSOLVE s o l u t i o n scheme. SCHEME c a l l s subrou t ines t o so l ve t he energy, momentum

and s t a t e equat ions and so lves t h e c o n t i n u i t y equat ion. NTRIES i s t h e maximum

number o f sweeps through the a x i a l l e v e l s a1 lowed; JUMP i s the f l o w convergence

f l a g ; ISTART i s t h e f i r s t i t e r a t i o n number; MAXT i s t h e maximum a l lowab le com-

p u t a t i o n t ime; NJUMP i s the r e s t a r t f l a g ; and JUMPS i s the convergence i n d i c a -

t o r f o r pressure drop boundary c o n d i t i o n problems.

Subrout ine SETIN (IGPERR, ERROR)

SETIN i s used t o i n p u t t he COBRA-WC data, per form e r r o r checks and i n i -

t i a l i z e va r i ab les . Subrout ine SETINs6 i s c a l l e d by subrou t ine SETUP.

Subrout ine SETOUT

SETOUT p r i n t s ou t the i n p u t read i n SETIN. Subrout ine SETOUT i s c a l l e d

by subrout ine SETUP.

Subrout ine SETUP

SETUP i s the d r i v e r r o u t i n e fo r the da ta i n p u t phase. It a lso performs

some v a r i a b l e man ipu la t ion and i n i t i a l i z a t i o n . Subrout ine SETUP i s c a l l e d by

the main program, COBRA.

Subrout ine SOLVER

SOLVER performs a d i r e c t Gaussian e l i m i n a t i o n s o l u t i o n f o r banded m a t r i -

c i e s and i s used i n t he WC s o l u t i o n o f t he momentum and c o n t i n u i t y equations.

Subrout ine SOLVER i s c a l l e d by subrout ines PSOLVE and RECIRC.

Subrout ine SPLIT (GIN)

SPLIT co r rec ts the i n p u t f 1 ow by an ex t rapo l a t i o n l i n t e r p o l a t i o n i t e r a t i o n

procedure u n t i 1 an equal pressure drop across t h e f i r s t node i s found. The

procedure assumes t h a t no d i ve rs ion c ross f low occurs w i t h i n the f i r s t node.

To ta l bundle i n l e t f l o w i s conserved. Subrout ine SPLIT i s c a l l e d by subrout ine

SETIN.

Subrout ine SWIRL (J)

SWIRL imposes a c i r cumfe ren t i a1 s w i r l f l o w on the p e r i p h e r i a l subchannels

i n an assembly type, i f t h e s w i r l o p t i o n i s spec i f ied . Subrout ine SWIRL I s

c a l l ed by subrout ines RECIRC and SCHEME.

Subrout ine VPROP ( J i

VPROP c a l c u l a t e s the volume average thermal c o n d u c t i v i t y and heat capac i t y

f o r a f u e l r o d when us ing t h e v a r i a b l e f u e l p rope r t y opt ion. Subrout ine VPROP

i s c a l l e d by subrout ine HOTROD.

APPENDIX B

VARIABLES USED I N CODE

APPENDIX B

A l i s t o f t h e v a r i a b l e s used i n t h e code and a b r i e f d e s c r i p t i o n i s g i ven

t o h e l p the i n t e r e s t e d user i n understanding t h e code. The subrou t ine o r co rd

group where t h e v a r i a b l e i s p r i n c i p l y used i s i d e n t i f i e d and t h e COMDECK where

t h e v a r i a b l e i s s t o red i s l i s t e d . The subsc r i p t s on t he v a r i a b l e s correspond

t o t h e dimension g iven by program SPECSET. Many o f t h e v a r i a b l e s a re equiva-

lenced t o each o the r so care must be taken no t t o i n d i s c r i m i n a t e l y r e s e t t h e

v a r i a b l e s i n t h e code.

Var iab les

A(MI,ME)

AA( IN)

AAD(IE,MC)

AAL(1W)

AASAV(16,MT)

ABAR (MC )

AC (MC )

ACCELF

ACCELH

ACCELY

AFACT(ML ,MA)

AHL1 (1W)-AHL4(IW)

AHl(1W)-AH4(IW)

ALLF

AMIX(1T) . . a3

r\) AN (MC )

APP (MI ,ME)

ATOTAL

AVGCP(M1 ,ME)

AVGK(M1,ME)

AXIAL(MP,MV)

AXL (ML)

B(MG) BB(1W)

BBL(IW)

BBSAV (16 ,MT)

BMIX(1T)

CARD

CC(1W)

CCL(1W)

CCLAD(MT)

CD(MK)

2 Subchannel f l o w area ( f t )

C o e f f i c i e n t f o r t u r b u l e n t f r i c t i o n f a c t o r c o r r e l a t i o n

C o e f f i c i e n t m a t r i x f o r t h e s o l u t i o n o f banded m a t r i c e s

C o e f f i c i e n t f o r laminar f r i c t i o n f a c t o r c o r r e l a t i o n

Orthogonal c o l l o c a t i o n m a t r i x W4 3

Subchannel e x i t d e n s i t y ( 1 bm/f t ) 2 Subchannel nominal f l o w area ( i n . )

Ex te rna l a c c e l e r a t i o n f a c t o r f o r a x i a l f l o w

I n t e r n a l a c c e l e r a t i o n f a c t o r f o r combined energy equa t ion

I n t e r n a l a c c e l e r a t i o n f a c t o r f o r pressure s o l u t i o n

R e l a t i v e subchannel area v a r i a t i o n

C o e f f i c i e n t s f o r laminar heat t r a n s f e r c o e f f i c i e n t equa t ion

C o e f f i c i e n t s f o r t u r b u l e n t heat t r a n s f e r c o e f f i c i e n t equa t ion

To ta l problem f lowra te ( lbm/s )

C o e f f i c i e n t f o r t u r b u l e n t m i x i n g c o r r e l a t i o n 2 Subchannel nominal f l o w area ( f t )

Average o f t h area a t t h e c u r r e n t node, J, and a t t h e p r e v i o u s 5 node, J -1 ( f t ) 2 Sumnation o f subchannel f l o w areas ( f t )

Fuel average spec i f i c heat (Btu/lbm-OF)

Fuel average c o n d u c t i v i t y (B tu /sec - f t -OF)

R e l a t i v e a x i a l power d i s t r i b u t i o n s

R e l a t i v e a x i a l l o c a t i o n o f channel area v a r i a t i o n s

C o e f f i c i e n t f o r c a l c u l a t i n g c r o s s f l o w



Othogonal c o l l o c a t i o n m a t r i x @3 C o e f f i c i e n t f o r t u r b u l e n t m i x i n g c o r r e l a t i o n

I n p u t data card counter



Spec i f i c heat o f the c l a d d i n g m a t e r i a l ( B t u / l bm-OF)

Channel l o s s c o e f f i c i e n t

P r i n c i p l e D e f i n i t i o n

AREA

Group 2

SOLVER

Group 2

COLOC

EXPROP

Group 4

Group 9

SET I N

Group 9

Group 5

Group 2

Group 2

NETWORK

Group 2

SETIN

AREA

SETIN

VPROP

VPROP

Group 3

Group 5

PSOLVE

Group 2

Group 2

COLOC

Group 10

SETIN

Group 2

Group 2

Group 8

Group 7

Comdeck

SPEC 3

SPEC 9

SPEC 2

SPEC 9

SPEC 12

SPEC 19

SPEC 1

SPEC 2

SPEC 2

SPEC 2

SPEC 7

SPEC 10

SPEC 10

SPEC 6

SPEC 32

SPEC 2

SPEC 14

SPEC 2

SPEC 5

SPEC 5

SPEC 2

SPEC 7

SPEC 14

SPEC 9

SPEC 19

SPEC 32

SPEC 9

SPEC 9

SPEC 12

SPEC 6

Var iab les

CINlV(MT)-CIN6V(MT)

CIP(MC)

CON (MC )

CONK(MG)

CONLIQ(MP)

CONS(MX)

CONST(IB)

CP(MC)

CPLIQ(MP)

CR(MT)

C1 (MT) -C13 (MT)

DAMPNG

DATE

DATIN(NZ)

DC(MC)

DFUEL

DFUEL I

DHYDN(MC)

DIA

S p e c i f i c heat o f f u e l m a t e r i a l (Btu/lbm-OF)

Crossf low r e s i s t a n c e

Terms i n t h e f u e l rod energy equa t ion c o e f f i c i e n t m a t r i x

Var iab le p r o p e r t y m o d i f i c a t i o n o f CIN1-CIN6

Inverse f l u i d s p e c i f i c heat, l / c ( l bm-OF/B~U) P

F l u i d thermal c o n d u c t i v i t y ( B t u / h r - f t - O F )

F l u i d l a t e r a l conduc t ion term

Proper ty t a b l e f l u i d thermal c o n d u c t i v i t y e n t r y ( ~ t u / h r - f t - O F )

Source vec to r f o r c a l c u l a t i n g average 6 P ' s

Source vec to r f o r c a l c u l a t i n g a x i a l f l o w s

F l u i d s p e c i f i c heat (Btu/lbm-OF)

Proper ty t a b l e f l u i d s p e c i f i c hea t e n t r y ( ~ t u / l b m - O F )

DFU EL/DROD

Terms i n t h e f u e l r o d energy equa t ion c o e f f i c i e n t m a t r i x

Rod diameter, DR/12 ( f t )

Damping f a c t o r on the t r a n s v e r s e pressure drop, SP

Today's da te

Per iphera l s to rage v e c t o r f o r i n p u t da ta

Subchannel hydrau l i c d iameter , 4AC/PW ( i n . )


Array which g i v e s t h e f l o w separated r e g i o n s w i t h i n one assembly

aF/3P, d e r i v a t i v e o f a x i a l f l o w w i t h r e s p e c t t o pressure

Diagonal terms i n t r i d i g o n a l m a t r i x f o r s o l u t i o n o f 6P

Of f -d iagonal terms i n t r i d i g o n a l m a t r i x f o r s o l u t i o n o f 6P

Same as DFDP, used w i t h t h e r o l l o p t i o n

dF/dX, d e r i v a t i v e o f a x i a l f l o w w i t h r e s p e c t t o d i s t a n c e

Diameter o f t h e f u e l p e l l e t , ( f t )

Inner diameter o f the f u e l f o r an annual f u e l rod, ( f t )

dH/dX, d e r i v a t i v e o f f l u i d e n t h a l p y w i t h r e s p e c t t o d i s t a n c e

Local subchannel h y d r a u l i c d iameter ( f t )

Nominal hydrau l i c d iameter ( f t )

Diameter o f r o d i n c l u d i n g c lad, w i r e wrap model ( f t )


Group 8

DIFFER

PREFIX, REHEAT

REHEATV

DIFFER

PROP

DIFFER

Group 1

ON ED

MOMENT

PROP

Group 1

PREFIX

PREFIX, REHEAT

SETIN

Group 9

DOY

SET I N

SETIN

Group 2

SETIN

MOMENT

ON ED

ONED

RECIRC

SCHEME

Group 8

Group 8

ENERGY

SETIN

SETIN

Comdeck

SPEC 12

SPEC 14

SPEC 33

SPEC 34

SPEC 2

SPEC 1

SPEC 8

SPEC 9

SPEC 2

SPEC 2

SPEC 2

SPEC 9

SPEC 34

SPEC 33

SPEC 12

SPEC 2

SPEC 19

SPEC 1

SPEC 1

SPEC 9

SPEC 2

SPEC 14

SPEC 2

SPEC 2

SPEC 2

SPEC 8

SPEC 12

SPEC 32

SPEC 8

SPEC 3

SPEC 2

SPEC 6

Var iab les

DPK(MC)

DPOLD(MC,2 )

DPPRI ( I U )

D PS

DPT(1U)

DPWP (MC)

DR(MR) m DROD (MT) P

DS1-DS21

D T

DTGC

DTI I (MG)

DTIMP

DTJJ(MG)

DTMAXE

DUR(MG)

DWDP(MI,ME)

DWDPR(IN,IM)

DX (MX )

EE(1W)

ELEV

END1-END19

~*DROD/DFUEL

Transverse momentum c o n t r o l volume leng th , 2, ( i n . )

Terms i n the f u e l r o d energy equa t ion c o e f f i c i e n t m a t r i x

2 S t a t i c pressure drop ( l b f / f t ) o r assembly pressure drop

2 Bundle average t o t a l pressure drop ( l b f / f t ) 3 A x i a l pressure g r a d i e n t ( l b f / f t )

Losses due t o f r i c t i o n a l and l o s s c o e f f i c i e n t 2 Old i t e r a t e va lue f o r subchannel t o t a l p ressure drop ( l b f / f t )

2 Old i t e r a t e va lue f o r bundle pressure drop ( l b f / i n . ) 2 Desi red t o t a l pressure drop ( l b f / i n . )

2 Desi red bundle t o t a l pressure drop ( l b f / f t )

Turbulent momentum exchange

Rod diameter i n c l u d i n g c ladding, ( i n . )

Rod diameter i n c l u d i n g c l a d d i n g f o r a p a r t i c u l a r m a t e r i a l type, ( i n .

Terms i n the f u e l r o d energy equa t ion c o e f f i c i e n t m a t r i x

Nominal t i m e step ( s e c )

DT*GC

Temporary s torage o f channel IK (K) c r o s s f low c o e f f i c i e n t s i n momentum equat ion s o l u t i o n

I m p l i c i t t ime step

Same as D T I I f o r JK(K)

Maximum a l lowab le e x p l i c t t ime s tep

M u l t i p l i e r on e f f e c t i v e f r a c t i o n o f w i r e wrap p i t c h f o r f o r c i n g c r o s s f low

Change i n c ross f low w i t h respec t t o pressure change

Same as DWDP, used w i t h t h e r o l l o p t i o n

A x i a l node l e n g t h f o r node J ( f t )


G r a v i t y , COS(THETA)

Common b lock end p o i n t s f o r de te rmin ing common l e n g t h


PREFIX

Group 4

PREFIX, REHEAT

NETWORK

PBOUND

PSOLVE , SCHEME

DIFFER

PBOUND

NETWORK

Group 11

PBOUND , NETWORK

DIFFER

Group 4

Group 8

REHEAT, PREFIX

Group 9

COBRA

PSOLVE

COBRA

PSOLVE

RECIRC

Group 7

MOMENT

RECIRC

Group 9

Group 2

SET I N

Comdeck

SPEC 34

SPEC 1

SPEC 33

SPEC 6

SPEC 2

SPEC 8

SPEC 1

SPEC 2

SPEC 6

SPEC 2

SPEC 6

SPEC 14

SPEC 1

SPEC 34

SPEC 33

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 6

SPEC 14

SPEC 2

SPEC 2

SPEC 9

SPEC 2

SPEC 2

V a r i a b l e s

ERROR

ETIME

F(M1,ME)

FACTOR(MK)

FDIV(MG)

FERROR

FFLC(MM,IW)

FFOLD(MC ,2)

FG(MM,IW)

FINLET

w FLO(IU) vl FLOG(MJ )

FLOW(MC)

FOLD(M1,ME)

FP(MM)

FPRI ( I U )

FQ(MM, IN) FR(IL,IM)

FSP(MC)

FT(MP)

FTEMP (MC)

FTM

FXFLOW(MK)

GAP(M1,ME)

GAPN (MG)

GAPS(MC,4)

GAPXL (ML )

I n p u t data e r r o r f l a g

Elasped t r a n s i e n t t i m e ( s e c )

Subchannel l o c a l mass f l o w ( I bm/sec)

R e l a t i v e h e i g h t a t which l o s s c o e f f i c i e n t i s t o be a p p l i e d

F lag f o r f o r c e d c ross f low; FDIV=l.O, c ross f low i s f o r c e d

Flow convergence c r i t e r i a

Loss c o e f f i c i e n t f o r c i n g f u n c t i o n p r o f i l e

Old i t e r a t e va lue f o r subchannel i n l e t f l o w r a t e ( lbm/sec)

Forc ing f u n c t i o n f o r s teady s t a t e f l o w o r p ressure drop a t t r a n s i e n t t ime, YG

F o r c i n g f u n c t i o n f o r i n l e t e n t h a l p y o r temperature a t t r a n s i e n t time, YH

Forc ing f u n c t i o n f o r s teady s t a t e e x i t e n t h a l p y a t t r a n s i e n t t ime, YHX

Subchannel i n l e t f l o w ( 1 bm/sec)

T o t a l assembly f l o w ( lbm/sec)

T o t a l group f l o w ( lbm/sec)

Sum o f J and J-1 a x i a l l e v e l f l o w ( lbm/sec)

Mass f l o w f rom t h e p rev ious t i m e s t e p ( lbm/sec)

Forc ing f u n c t i o n f o r s teady s t a t e system pressure a t t r a n s i e n t t ime, YP

2 Old i t e r a t e assembly pressure drop ( l b f / f t ) F o r c i n g f u n c t i o n f o r s teady s t a t e hea t f l u x a t t r a n s i e n t t ime , Y Q

Same as F, used w i t h t h e r o l l o p t i o n

F r i c t i o n f a c t o r

Maximum t ime s t e p s i z e a t t r a n s i e n t t ime, YT

Old i t e r a t e va lue o f a x i a l f l o w ( lbm/sec)

Turbulent momentum parameter

User s p e c i f i e d f o r c e d c r o s s f l o w f r a c t i o n

Local gap spacing between ad jacen t channels ( f t )

Nominal gap spacing, GAPS/12 ( f t )

Nominal gap spacing between ad jacen t channels ( i n . )

R e l a t i v e a x i a l l o c a t i o n s o f gap w i d t h v a r i a t i o n


SETIN

COBRA

SCHEME, REC IRC

Group 7

FORCE

Group 9

Group 7

PBOUND

Group 11

Group 11

Group 11

SETIN

NETWORK

NETWORK

DIFFER

COBRA

Group 11

NETWORK

Group 11

REC IRC

PROP

Group 9

MOMENT

Group 9

Group 7

SETIN

SETIN

Group 4

Group 6

Comdeck

SPEC 19

SPEC 3

SPEC 6

SPEC 6

SPEC 2

SPEC 6

SPEC 2

SPEC 19

SPEC 19

SPEC 19

SPEC 2

SPEC 6

SPEC 6

SPEC 2

SPEC 2

SPEC 19

SPEC 6

SPEC 19

SPEC 2

SPEC 2

SPEC 19

SPEC 14

SPEC 11

SPEC 6

SPEC 4

SPEC 7

SPEC 2

SPEC 1

V a r i a b l e s

GASSEM(1T)

GC

GEOMF (MT)

GFACT(ML ,MS)

GIN

GK(1T)

H(M1,ME)

HAH(IE,MC)

HAIN(1U)

HAOUT(1U)

HEATER (MR)

HERROR

HEXIT(MC)

HFILM(MC)

HGAP(MT)

HGHP1 (MT)

HGCRT(MT)

HGIN(MJ)

HGaJT(MJ)

HGRK(MT)

HIN

HINLET (MC)

HLIQ(MP)

HOLD(MI,ME)

HOUT

HPERIM(MC)

HSCM(IB)

HSURF (M1 ,ME)

IAHT

I BWL

I BWR

IDAREA(MC)

S w i r l v e l o c i t y as a f r a c t i o n o f average bundle v e l o c i t y

32.2 l b m - f t l l b f - s e c 2

Fuel r o d geometry i n d i c a t o r

R e l a t i v e gap w i d t h v a r i a t i o n 2 Bundle i n l e t mass f l u x ( l b m l h r - f t )

Geometry f a c t o r f o r conduc t ion

Loca l subchannel en tha lpy ( B t u l l b m )

Combined energy equat ion c o e f f i c i e n t m a t r i x

S t a t i c head l e n g t h associated w i t h assembly i n l e t l o s s ( i n . )

S t a t i c head l e n g t h assoc ia ted w i t h assembly o u t l e t l o s s ( i n . )

C o e f f i c i e n t f o r r o d temperature c a l c u l a t i o n s

Energy equat ion a l lowab le e x t e r n a l convergence e r r o r

Enthalpy a t t h e bundle e x i t (Btu/ lbrn)

Heat t r a n s f e r c o e f f i c i e n t ( ~ t u / h r - f t2-OF)

Gap conductance c o e f f i c i e n t between f u e l and c l a d d i n g ( ~ t u / h r - f t 2 - ' ~ )

HGAP/ (l+HGAP*TCLAD/KCLAD)

HGAPl*CR/TCLAD

S t a t i c head l e n g t h assoc ia ted w i t h group i n l e t l o s s ( i n . )

S t a t i c head l e n g t h associated w i t h group o u t l e t l o s s ( i n . )

HGAPl*DFUEL/(Z*KFUEL)

I n l e t en tha lpy (Btu/ lbm) o r temperature (OF)

Subchannel i n l e t en tha lpy (Btu/ lbm) o r temperature (OF)

Proper ty t a b l e f l u i d e n t h a l p y e n t r y (Btu/ lbrn)

Loca l en tha lpy a t p rev ious t imes tep (Btu/ lbrn)

Problem e x i t enthalpy (Btu/ lbm)

Heated per imeter , P H / 1 2 ( f t )

Vector used f o r s o l u t i o n o f t h e energy equa t ion

Average r o d surface heat t r a n s f e r c o e f f i c i e n t ( ~ t u l h r - f t 2 - O F )

F l a g f o r in terassembly heat t r a n s f e r o p t i o n

= 0, no in terassembly heat t r a n s f e r

= 1, in terassembly heat t r a n s f e r

L e f t m a t r i x band w id th

R i g h t m a t r i x band w i d t h

I d e n t i f i c a t i o n number f o r a subchannel t h a t has area v a r i a t i o n s


Group 10

COBRA

Group 8

Group 6

Group 11

Group 10

ENERGY

ENERGY

Group 4

Group 4

REHEAT

Group 9

COBRA

PROP

Group 8

PREFIX

PREFIX

Group 7

Group 7

PREFIX

Group 11

Group 11

Group 1

COBRA

Group 11

SETIN

ENERGY

PROP

Group 4

SOLVER

SOLVER

SETIN

Comdeck

SPEC 32

SPEC 2

SPEC 32

SPEC 7

SPEC 19

SPEC 11

SPEC 2

SPEC 2

SPEC 6

SPEC 6

SPEC 34

SPEC 2

SPEC 19

SPEC 2

SPEC 12

SPEC 34

SPEC 34

SPEC 6

SPEC 6

SPEC 34

SPEC 19

SPEC 2

SPEC 9

SPEC 2

SPEC 19

SPEC 2

SPEC 2

SPEC 5

SPEC 2

SPEC 2

SPEC 7

V a r i a b l e s

IDFUEL (MR)

IDGAP (MG)

IDIRECT

IDTGC

IDTY P(MT)

I E

IERROR

I EXP

IFTYP(M1,ME)

I G

I H

IHALT

IHIGH

IK(MG)

IKW(MW)

ILC(MK)

ILOC(N8)

ILOCS(N~,MC)

ILOW

ILOWPl

IM(MS)

IPRNTA

IPRNTE

I R

Rod type f o r p r o p e r t y d e s i g n a t i o n

I d e n t i f i c a t i o n number f o r a gap t h a t has gap v a r i a t i o n

F lag f o r d i r e c t Gaussian e l i m i n a t i o n o f momentum equa t ions

1/ (DT*GC )

F lag f o r f u e l shape and c o l l o c a t i o n order

SPECSET parameter - w i d t h o f HAH m a t r i x

E r r o r f l a g , i f > 1 p r i n t e r r o r messages

F l a g t o s e t i m p l i c i t o r e x p l i c i t mode i n RECIRC

The channel numbers on each f a c e o f each ad jacen t assembly

Temporary s to rage f o r p r i n t i n g w i r e wrap f o r c e d c r o s s f l o w da ta

Fuel t ype i d e n t i f i e r

Opt ion f o r s p e c i f y i n g i n l e t mass f l u x (see input-N2)

Opt ion f o r s p e c i f y i n g i n l e t e n t h a l p y (see input-N1)

Maximum number o f i n n e r energy equa t ion i t e r a t i o n s a t each l e v e l

= I E

I d e n t i f i e s subchannels ad jacent t o a gap when p a i r e d w i t h JK

I d e n t i f i e s subchannels ad jacen t t o a w a l l when p a i r e d w i t h JKW

Subchannel number i n which l o s s c o e f f i c i e n t , FACTOR, i s a p p l i e d

S i n g l y dimensioned ILOCS

Array t o i d e n t i f y gaps and w a l l s connected t o subchannel I

= MI+1

= ILOW+l

I d e n t i f i e s subchannels on o p p o s i t e s i d e s o f a gap w i t h gap

v a r i a t i o n s

Dumy v a r i a b l e used i n p r i n t o u t o f c r o s s f l o w i n f o r m a t i o n

For each assembly, i d e n t i f i e s assembly type, f i r s t and l a s t channel number, f i r s t and l a s t gap number and t h e f i r s t and l a s t rod number

F lag s p e c i f y i n g t h e assembly average e x i t v a l u e p r i n t o u t o p t i o n

F lag s p e c i f y i n g the subchannel e x i t va lue p r i n t o u t o p t i o n

SPECSET parameter - maximum number o f rods i n t e r a c t i n g w i t h a channel

Data s torage o p t i o n ; i f 1, t h e ROLL o p t i o n i s used (N4)


Group 8

SETIN

SET I N

COBRA

SETIN

COBRA

COBRA, REC IRC

Group 4

SCHEME, REC IRC

SETIN

Group 11

Group 11

SETIN

PREF I X

SETIN

SETIN

Group 7

SETIN

SET I N

PREFIX

PREFIX

SETIN

RESULT

SETIN

SETIN

SET I N

Group 9

Comdeck

SPEC 12

SPEC 7

SPEC 2

SPEC 2

SPEC 12

SPEC 1 9

SPEC 2

SPEC 2

SPEC 2

SPEC 6

SPEC 5

SPEC 19

SPEC 1 9

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 6

SPEC 14

SPEC 2

SPEC 2

SPEC 2

SPEC 19

SPEC 19

SPEC 2

SPEC 2

SPEC 2

SPEC 19

Var iab les

ISAVIT(MC)

I SCHEME

ISIDE(IU,6)

I STAR(MG)

ISWIRL(IT)

I T

I TERAT

I TRY

ITRYM

I TSAVE

ITSTEP

ITYPIN(IT,3)

I W IDE

I X

Stores t h e number o f i t e r a t i o n s f o r which a va lue has been used i n the pressure boundary c o n d i t i o n scheme

S o l u t i o n o p t i o n t o be used. (see i n p u t manual) (N3)

S p e c i f i e s t h e assembly number ad jacen t t o each f a c e

Number o f t h e donor channel f o r c r o s s f l o w th rough gap K .

M i x i n g model o p t i o n 0 = pure m i x i n g model, 1 = s w i r l f l o w model, 2 = w i r e wrap model

SPECSET parameter - maximum number o f assembly t ypes

Loop counter f o r t h e e x t e r n a l i t e r a t i o n loop

Maximum number o f e x t e r n a l i t e r a t i o n s

Minimum number o f i n t e r n a l i t e r a t i o n s f o r PSOLVE

Number o f i t e r a t i o n s p e r i m p l i c i t t i m e s tep t h e code i s t a k i n g

Number o f elements i n v a r i a b l e maximum t i m e s t e p t a b l e (N5)

For each assembly type, i d e n t i f i e s f i r s t assembly number o f t h a t type, number o f channels, and number o f gaps

SPECSET parameter - maximum number o f assemblies

SPECSET parameter - maximum number of channels on an assembly f a c e + 4

SPECSET parameter - maximum number of l o s s c o e f f i c i e n t f o r c i n g f u n c t i o n p r o f i l e s

M a t r i x band w i d t h . SPECSET parameter - maximum number o f f l o w separated r e g i o n s

w i t h i n a s i n g l e assembly

I d e n t i f i c a t i o n number o f the f u e l t y p e i n each f u e l zone

L o g i c a l u n i t f o r input , d e f a u l t e d t o 5

L o g i c a l u n i t f o r p r i n t o u t , d e f a u l t e d t o 6

L o g i c a l u n i t f o r r e s t a r t dump i n p u t and ou tpu t , d e f a u l t e d t o 8

See IK

See IKW

A x i a l node number a t which l o s s c o e f f i c i e n t , FACTOR, i s a p p l i e d

see I M


PBOUND

Group 9

Group 4

DIFFER

SETIN

SCHEME, RECIRC

Group 9

SCHEME

RECIRC

Group 9

SETIN

SOLVER

Group 8

COBRA

COBRA

COBRA

SETIN

SETIN

SETUP

Comdeck

SPEC 6

SPEC 2

SPEC 2

SPEC 6

SPEC 32

SPEC 19

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 19

SPEC 2

SPEC 19

SPEC 19

SPEC 19

SPEC 2

SPEC 19

SPEC 12

SPEC 2

SPEC 2

SPEC 19

SPEC 2

SPEC 2

SPEC 6

SPEC 19

V a r i a b l e s

JMP(10)

J 1

55

J 6

KCLAD(MT)

KFUEL (MT)

K I J

KLC(MK)

K 10

LPMNF (IW)

LAMNH(1W)

LC(MC ,4)

LCASS ( I U )

W LCFF (MK)

cO LENGTH (MG)

LR(MR,6)

LRI (IR,MC)

LU I

MA

M AXT

MAXTY P

MC

ME

MFLAG ( K )

See IMP

D i r e c t s p r i n t o u t o f i n p u t data

F lags r a d i a l thermal conduc t ion o p t i o n ( N 3 )

Flags w i r e wrap and l o s s c o e f f i c i e n t o p t i o n s ( N l )

Thermal c o n d u c t i v i t y o f c l a d d i n g m a t e r i a l ( ~ t u / h r - f t - O F )

Thermal c o n d u c t i v i t y o f f u e l m a t e r i a l ( ~ t u / h r - f t - O F )

Crossf low r e s i s t a n c e c o e f f i c i e n t

Gap number a t which s p e c i f i e d d i v e r s i o n c r o s s f l ow, FXFLOW, i s app l ied

Opt ion f o r pressure drop boundary c o n d i t i o n t r a n s i e n t s (N7)

F lags when laminar f r i c t i o n f a c t o r s a re i n p u t

F lags when laminar heat t r a n s f e r c o e f f i c i e n t s are i n p u t

Adjacent subchannel, LC(1 , J ) , i s t h e J t h subchannel ad jacen t t o subchannel I

I n d i c a t e s i f l o s s c o e f f i c i e n t s are a p p l i e d t o a p a r t i c u l a r assembly

Loss c o e f f i c i e n t f o r c i n g f u n c t i o n number a p p l i e d t o a g i v e n l o s s c o e f f i c i e n t

Transverse momentum c o n t r o l volume leng th , !L, ( f t )

I d e n t i f i c a t i o n number o f subchannel f a c i n g r o d N

I d e n t i f i c a t i o n number o f rod f a c i n g Channel I

READ/WRITE dev ice f o r ROLL o p t i o n

SPECSET parameter - maximum number o f subchannels w i t h area v a r i a t i o n

Maximum computer execu t ion t i m e a l l o w a b l e b e f o r e dump

To ta l number o f assembly types

SPECSET parameter - maximum number o f subchannels

SPECSET parameter - MX i f no p e r i p h e r a l s torage, 3 i f r o l l o p t i o n i s used

Interpolation/extrapolation scheme i n d i c a t o r f o r equal f l o w s p l i t o p t i o n

SPECSET parameter - maximum number o f subchannel gap connect ions

SPECSET parameter - maximum number o f thermal and f l o w connec t ions t o a channel

SPECSET parameter - maximum number o f assembly groupings

P r i n c i p l e D e f i n i t i o n Comdeck

RESULT

Case C o n t r o l Card

Group 10

Group 7

Group 8

Group 8

Group 9

Group 7

Group 11

SETIN

SET I N

Group 4

FORCE

Group 7

SETIN

Group 8

PREFIX

COBRA

SETIN

SPLIT

SPEC 19

SPEC 2

SPEC 11

SPEC 6

SPEC 12

SPEC 12

SPEC 2

SPEC 6

SPEC 19

SPEC 9

SPEC 10

SPEC 1

SPEC 6

SPEC 6

SPEC 2

SPEC 12

SPEC 34

SPEC 2

SPEC 19

SPEC 19

SPEC 2

SPEC 19

SPEC 19

SPEC 2

SPEC 19

SPEC 19

SPEC 19

SPEC 19 SPECSET parameter - maximum number o f l o s s c o e f f i c i e n t s

Var iab les

ML

MLEN

MM

NAAA

NAAAPl

NAAH

NAAHPl

NACH(MC)

NAFACT

NAF L X

NARPMP

NASSEM

N AX

NAX L

NAZONE

NC

SPECSET parameter - maximum number o f a x i a l l o c a t i o n s f o r gap and area v a r i a t i o n s

Length o f 110 records when us ing the r o l l o p t i o n w i t h RECIRC

SPECSET parameter - maximum number o f p o i n t s i n t h e temporal p r o f i l e s

SPECSET parameter - number o f f u e l c o l l o c a t i o n p o i n t s p l u s t h r e e

SPECSET parameter - maximum number o f gaps coupled t o any one gap ( v i a a channel)

SPECSET parameter - maximum number o f e n t r i e s i n p r o p e r t y t a b l e , and f o r c i n g f u n c t i o n vs. t ime t a b l e

SPECSET parameter - maximum number o f f u e l r o d s

SPECSET parameter - maximum number o f gaps w i t h gap v a r i a t i o n s

SPECSET parameter - maximum number o f f u e l types

SPECSET parameter - maximum number o f hea t f l u x p r o f i l e s

SPECSET parameter - maximum number o f w a l l connect ions

SPECSET parameter - maximum number o f a x i a l nodes p l u s 1

SPECSET parameter - maximum number o f f u e l t y p e d i v i s i o n s

SPECSET parameter - maximum number o f a x i a l l o c a t i o n s f o r g r i d spacers

SPECSET parameter - computed w i d t h o f SAVEA1, SAVEA2 and SAVEA3 a r rays

Maximum w id th o f AAA m a t r i x

NAAA + 1

Maximum number o f connect ions t o a channel p l u s one

NAAH + 1

Assembly number t h a t channel I i s a p a r t o f

To ta l number o f subchannel area v a r i a t i o n s ( N l )

A x i a l heat f l u x p r o f i l e associated w i t h assembly NASS

Number o f i t e r a t i o n s f o r i n s e r t i n g area v a r i a t i o n s (N3)

T o t a l number o f assemblies

Number o f e n t r i e s i n each a x i a l heat f l u x t a b l e (N2)

Number o f a x i a l p o s i t i o n s f o r subchannel area v a r i a t i o n s (N2)

Number o f a x i a l zones f o r v a r i a b l e a x i a l s tep s i z e (N6)

Order o f the f u e l c o l l o c a t i o n model ( N l )

P r i n c i p l e D e f i n i t i o n Comdeck

SPEC 19

COBRA

COBRA

COBRA

COBRA

COBRA

SETIN

Group 5

Group 4

Group 5

Group 3

Group 5

Group 9

Group 8

SPEC 2

SPEC 19

SPEC 19

SPEC 19

SPEC 19

SPEC 19

SPEC 19

SPEC 19

SPEC 19

SPEC i 9

SPEC 19

SPEC 19

SPEC 19

SPEC 19

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 7

SPEC 2

SPEC 7

SPEC 2

SPEC 2

SPEC 7

SPEC 12

V a r i a b l e s

NCH(MA)

NCHANA

NC HAN

NCHANl

NC HAN 2

NCOUNT(MR)

NCTYPE (MC)

NDT

NDTPl

NDX

NDXPl

NETGRP(IU)

NETWK

NFLAG(MC) w F w

NFLGC

NFLGR

NFLGS

NFLGW

NFLMC(IU)

NFNODE

NFRICT

NFUELT

NG

NGAP(MS)

NGAPS

NGAPl

NGAP2

NG PR FL

NGXL

N H

G loba l channe l number f o r wh i ch a r e a v a r i a t i o n i s s p e c i f i e d

Number o f channe l s i n assembly t y p e ITYPA

T o t a l number o f c h a n n e l s

F i r s t channe l number i n assembly NASS

L a s t channe l number i n assembly NASS

Number o f channe l s connec ted t o r o d N

Channel t y p e d e s i g n a t o r ; 1 = i n t e r i o r channe l , 2 = edge channe l

Number o f t i m e s t e p s f o r t r a n s i e n t

NDT + 1

Number o f a x i a l nodes

NDX + 1

Assembly g r o u p i n g number t o b e used w i t h assembly NASS d u r i n g network o p t i o n

P ressu re bounda ry c o n d i t i o n ne twork model o p t i o n (N4)

Interpolation/extrapolation scheme i n d i c a t o r f o r ne twork i n l e t f l o w guess

P r i n t f l a g f o r c r o s s f l o w r e s u l t s

P r i n t f l a g f o r r o d t e m p e r a t u r e r e s u l t s

P r i n t f l a g f o r subchanne l r e s u l t s

P r i n t f l a g f o r w a l l t e m p e r a t u r e r e s u l t s

Heat t r a n s f e r c o e f f i c i e n t c o r r e l a t i o n number t o be used w i t h NASS

Number o f p o i n t s f o r a v e r a g i n g t e m p e r a t u r e dependent f u e l p r o p e r t i e s

T o t a l number o f f r i c t i o n f a c t o r c o r r e l a t i o n s e t s ( N l )

Number o f i n t e g r a t i n g p o i n t s used i n v a r i a b l e f u e l p r o p e r t y o p t i o n

Number o f e n t r i e s i n i n l e t mass f l u x o r p r e s s u r e d r o p t r a n s i e n t

f o r c i n g f u n c t i o n t a b l e (N5)

Gap number f o r wh i ch gap w i d t h v a r i a t i o n o c c u r s

T o t a l number o f gaps f o r wh i ch gap v a r i a t i o n s o c c u r ( N l )

F i r s t gap number i n assembly NASS

L a s t gap number i n assembly NASS

T o t a l number o f t r a n s i e n t f o r c i n g f u n c t i o n p r o f i l e s f o r i n l e t mass f l u x o r p r e s s u r e d r o p (N6)

Maximum number o f p o s i t i o n s f o r gap v a r i a t i o n s (N2 )

Number o f e n t r i e s i n t h e i n l e t e n t h a l p y vs . t i m e f o r c i n g f u n c t i o n t a b l e (N4)


SETIN

Group 4

SETIN

SETIN

SETIN

PREFIX

SETIN

Group 9

SETIN

Group 9

Group 4

Group 4

PBOUND

Group 12

Group 12

Group 12

Group 12

Group 4

SETIN

Group 2

Group 8

Group 11

Group 6

Group 6

SETIN

SETIN

Group 11

Group 6

Group 11

Comdeck

SPEC 7

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 3 1

SPEC 32

SPEC 1 9

SPEC 19

SPEC 2

SPEC 2

SPEC 6

SPEC 6

SPEC 2

SPEC 19

SPEC 1 9

SPEC 19

SPEC 1 9

SPEC 10

SPEC 9

SPEC 9

SPEC 12

SPEC 19

SPEC 7

SPEC 7

SPEC 2

SPEC 2

SPEC 19

SPEC 7

SPEC 19

Var iab les

NH EAT

NHFT

NHFVT(1U)

NH IGH (MC )

NHX

NINFF(IU)

N JUMP

NK

NLCFF

NLCFP

NLOW(MC)

NOGRP

NO LC

NOU T

N P

NPCHAN

NPFVT(1U)

NPGAP

NPNODE

NPOINT

NPROD

NPROP

N PWALL

NQ

NQAX

NQPRFL

T o t a l number o f hea t t r a n s f e r c o r r e l a t i o n s e t s (N2)

T o t a l number o f a x i a l heat f l u x f o r c i n g f u n c t i o n t a b l e s ( N l )

Heat f l u x vs. t ime p r o f i l e assoc ia ted w i t h assembly NASS

Number o f h igher order thermal connec t ions t o subchannel I

Number o f elements i n e x i t e n t h a l p y t r a n s i e n t t a b l e (N8)

Loss c o e f f i c i e n t f o r c i n g f u n c t i o n number assoc ia ted w i t h assembly i n l e t loss, RAIN

R e s t a r t o p t i o n f l a g ; = 1 problem i s r e s t a r t e d

To ta l number o f gap connect ions

T o t a l number o f l o s s c o e f f i c i e n t f o r c i n g f u n c t i o n p r o f i l e s (N6)

Number o f e n t r i e s i n l o s s c o e f f i c i e n t f o r c i n g f u n c t i o n p r o f i l e s (N7)

Number o f lower order thermal connec t ions t o Channel I

Number o f assembly groupings f o r network model (N8)

Number o f subchannel l o s s c o e f f i c i e n t s , CD (N3)

Output op t ions f o r subchannel, rod, c r o s s f l o w , and w a l l r e s u l t s o r any combinat ion ( N l )

Loss c o e f f i c i e n t f o r c i n g f u n c t i o n number assoc ia ted w i t h assembly o u t l e t loss, RAOUT

Number o f elements i n pressure t r a n s i e n t t a b l e s (N3)

Output op t ion , number o f channels t o be p r i n t e d (N2)

Pressure drop o r f l o w vs. t ime p r o f i l e number assoc ia ted w i t h assembly NASS

Output op t ion , number o f gaps t o be p r i n t e d (N5)

Output op t ion , r a d i a l nodes f o r which f u e l temperatures w i l l be p r i n t e d (N4)

= I E

Output op t ion , number o f rods t o be p r i n t e d (N3)

Number o f e n t r i e s i n p r o p e r t y t a b l e ( N l )

Output op t ion , number o f w a l l s t o be p r i n t e d (N7)

Number o f e n t r i e s i n t h e average hea t f l u x t r a n s i e n t t a b l e (N9)

A x i a l l y temperature dependent f u e l p r o p e r t y o p t i o n (N4)

T o t a l number o f hea t f l u x t r a n s i e n t f o r c i n g f u n c t i o n p r o f i l e s (N10)

Number of i t e r a t i o n s t o i n s e r t t h e e f f e c t o f w i r e s o r l o s s c o e f f i c i e n t s (N4)


Group 2

Group 3

Group 4

PREFIX

Group 11

Group 4

RESTRT

SETIN

Group 7 , Group 7

PREFIX

Group 7

Group 7

Group 12

Group 4

Group 11

Group 12

Group 4

Group 12

Group 12

PREFIX

Group 12

Group 1

Group 12

Group 11

Group 8

Group 11

Group 7

Comdeck

SPEC 10

SPEC 2

SPEC 12

SPEC 3 1

SPEC 19

SPEC 6

SPEC 19

SPEC 2

SPEC 6

SPEC 6

SPEC 31

SPEC 6

SPEC 6

SPEC 19

SPEC 6

SPEC 19

SPEC 19

SPEC 19

SPEC 19

SPEC 1 9

SPEC 2

SPEC 19

SPEC 9

SPEC 19

SPEC 19

SPEC 12

SPEC 19

SPEC 6

V a r i a b l e s

NR C

NROD

NRODTP

NROW

NR PF

N SC BC

NSK I PT

NSKIPX

NSW IRL

NTNODE

NTRI ES

NTY PE (MC )

NVI SCW

NWK

NWR

NWRAP(MC )

WRAPS (MC )

NZONE(MT)

OUTPUT(12)

P(MI,ME)

PDN

PDNA( I U )

PDROP

PERIM(MC)

PEXIT

PH (MC )

PH EAD

PHI(MR,6)

PHITOT(MR)

PHTOT

P I

PITCH

= NR

T o t a l number o f r o d s

O ? t i o n f o r a x i a l l y v a r y i n g f u e l m a t e r i a l (N5 )

Number o f rows i n m a t r i x t o be s o l v e d

O p t i o n t o s p e c i f y i n d i v i d u a l assembly power d e n s i t i e s

Subcooled m i x i n g o p t i o n ( N l )

O u t p u t o p t i o n , p r i n t e v e r y NSKIPT t i m e s t e p s (N2 )

Ou tpu t o p t i o n , p r i n t e v e r y NSKIPX a x i a l nodes ( N l )

Number o f assembly t y p e s i n wh i ch s w i r l f l o w m i x i n g model i s used (N2)

Number o f e n t r i e s i n t h e t e m p e r a t u r e dependent f u e l p r o p e r t y t a b l e

Maximum number o f e x t e r n a l i t e r a t i o n s

F r i c t i o n f a c t o r c o r r e l a t i o n number a s s o c i a t e d w i t h Channel I

O p t i o n f o r w a l l v i s c o s i t y c o r r e c t i o n t o t h e f r i c t i o n f a c t o r (N3)

Number o f w a l l c o n n e c t i o n s

Maximum number o f c o n n e c t i o n s t o a channe l ( t h e r m a l + f l o w )

Number o f w i r e wraps i n each channe l

I n i t i a l w i r e wrap i n v e n t o r y f o r each channe l

Number o f f u e l zones

A r r a y used t o p r i n t o u t p u t 2 R e l a t i v e p r e s s u r e a t a x i a l l o c a t i o n J i n subchanne l I ( l b f / f t )

3 Nominal power d e n s i t y ( M B t u / h r - f t )

R e l a t i v e assembly power o r a b s o l u t e assembly power d e n s i t y ( ~ B t u / h r - f t 3 ) 2 O l d t i m e t o t a l p r e s s u r e d r o p ( l b f / f t )

Wet ted p e r i m e t e r , P W / 1 2 ( f t )

System o p e r a t i n g p r e s s u r e , ( p s i a )

Subchannel hea ted p e r i m e t e r , ( i n . )

T o t a l s t a t i c p r e s s u r e d r o p ac ross ne twork model ( l b f / f t Z )

F r a c t i o n o f t h e hea ted p e r i m e t e r o f r o d N f a c i n g subchanne l I

l/PHTOT ( l / f t )

T o t a l heated p e r i m e t e r ( f t )

Cons tan t = 3.14159

Wi re wrap l e a d l e n g t h ( f t )


PREFIX

SETIN

Group 8

SOLVER

Group 11

Group 1 0

Group 9

Group 9

Group 10

Group 8

Group 9

SET I N

Group 2

SETIN

COBRA

AREA

Group 7

Group 8

RESULT

SCHEME, RECIRC

Group 11

Group 11

COBRA

SETIN

Group 11

Group 4

NETWORK

Group 8

PREFIX

SETIN

COBRA

Group 7

Comdeck

SPEC 2

SPEC 2

SPEC 1 2

SPEC 2

SPEC 2

SPEC 11

SPEC 1 9

SPEC 1 9

SPEC 2

SPEC 9

SPEC 1 9

SPEC 9

SPEC 9

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 1 2

SPEC 1 9

SPEC 3

SPEC 2

SPEC 2

SPEC 6

SPEC 2

SPEC 2

SPEC 1

SPEC 6

SPEC 1 2

SPEC 34

SPEC 1 9

SPEC 2

SPEC 6

V a r i a b l e s

PLIQ(MP)

POWR(1J)

PR(IL,IM)

PREF

PREFOL'

PRINT(12)

PRINIC(MC)

PRINTG(MG)

PRINTN ( 1 0 )

PRINTR(MR)

PRINTW(MW)

PW(MC)

PWIN(1U)

QQSAV(16,MT)

Ql(MR)-Q4(MR)

RADIAL(MR)

RAIN(1U)

RAOUT(IU)

RCCLAD(MT)

RCFUEL (MT)

RCLAD(MT)

RECALL

RFUEL (MT)

Pressure e n t r i e s i n t h e f l u i d p r o p e r t y t a b l e ( p s i a )

Assembly t r a n s i e n t power f a c t o r

Same as P used w i t h r o l l o p t i o n i n RECIRC 2 System p r e s s u r e ( l b f / i n )

2 O l d t i m e sys tem p r e s s u r e ( l b / i n )

L o g i c a l v a r i a b l e ; d i r e c t s o u t p u t o f s e l e c t e d i n p u t d a t a g roups

Channel numbers f o r wh ich i n f o r m a t i o n w i l l be p r i n t e d

Gap numbers f o r wh ich i n f o r m a t i o n w i l l be p r i n t e d

A r r a y f o r r a d i a l f u e l node p r i n t i n g

Rod numbers f o r wh ich i n f o r m a t i o n w i l l be p r i n t e d

Wal l node numbers f o r wh ich i n f o r m a t i o n w i l l be p r i n t e d

Subchannel w e t t e d p e r i m e t e r ( i n . )

Wetted p e r i m e t e r a s s o c i a t e d w i t h t h e ne twork model assembly i n l e t l o s s c o e f f i c i e n t ( i n . )

Wetted p e r i m e t e r a s s o c i a t e d w i t h t h e ne twork model assembly o u t l e t l o s s c o e f f i c i e n t ( i n . )

I n t e r p o l a t e d l o c a l power f a c t o r o b t a i n e d f r o m a x i a l h e a t f l u x t a b l e

Maximum e r r o r i n energy s o l u t i o n

Source te rm i n energy e q u a t i o n

Or thogona l c o l l o c a t i o n m a t r i x ( Q )

Fue l r o d c o l l o c a t i o n sou rce terms

R a d i a l power f a c t o r o f r o d N

Network model assembly i n l e t l o s s parameter ( l / f t - l b m )

Network model assembly o u t l e t l o s s pa rame te r ( l / f t - l b m ) 3 o P roduc t o f c l a d d i n g d e n s i t y and s p e c i f i c h e a t ( B t u / f t - F )

P roduc t o f f u e l d e n s i t y and spec i f i c h e a t ( B t u / f t 3 - O ~ ) 3 D e n s i t y o f c l a d d i n g m a t e r i a l ( l b m / f t )

F l a g t o compute r o d t e m p e r a t u r e s . RECALL = 1 .0 i f r o d t e m p e r a t u r e s a r e t o be c a l c u l a t e d

Reyno lds number e n t r i e s i n l o s s c o e f f i c i e n t f o r c i n g f u n c t i o n t a b l e s

Terms i n reduced f u e l r o d ene rgy e q u a t i o n

3 D e n s i t y o f f u e l m a t e r i a l ( l b m / f t )


Group 1

COBRA

REC IRC

Group 11

COBRA

SETIN

Group 12

Group 12

SETIN

Group 12

Group 12

Group 4

Group 4

Group 4

REHEAT

ENERGY

DIFFER, ENERGY

COLOC

REHEAT

Group 8

Group 4

Group 4

PREFIX

Group 8

SCHEME, REC IRC

Group 7

PREFIX

Group 8

Comdeck

SPEC 9

SPEC 12

SPEC 2

SPEC 10

SPEC 9

SPEC 19

SPEC 19

SPEC 1 9

SPEC 19

SPEC 1 9

SPEC 19

SPEC 1

SPEC 6

SPEC 6

SPEC 2

SPEC 2

SPEC 2

SPEC 12

SPEC 34

SPEC 12

SPEC 6

SPEC 6

SPEC 34

SPEC 34

SPEC 12

SPEC 12

SPEC 6

SPEC 32

SPEC 12

V a r i a b l e s

RGIN(MJ)

RGOUT(MJ)

RHO(M1,ME)

RHOBAR (MI ,ME)

RHOLCP(MW)

RHOOLD(M1,ME)

RMU INLT

ROTATE(1T)

RTIN

RWALL(Z,MW)

R ZKF ( MT)

SAVEAL (M2)

S A V E A ~ ( M ~ )

SAVEA2 (MI )

SAVEA3(Ml)

SAVRES(M5)

SAVRI (10)

SFOLD(MC,2)

SIGNAL (18)

Network model group i n l e t l o s s parameter ( l / f t - l b m )

Network model group o u t l e t l o s s parameter ( l / f t - l b m ) 3 Local d e n s i t y ( l b m / f t )

Average dens i t y , .5*(p j + ~ . + 1 ) J

Wall heat c a p a c i t y parameter ( B t u / f t2-OF) 3 Dens i t y a t the p rev ious t i m e s t e p ( l b m / f t )

I n l e t v i s c o s i t y used i n network model c a l c u l a t i o n ( l b m / f t - s e c )

I n d i c a t e s d i r e c t i o n o f s w i r l f l o w

Network model t o t a l f l o w l o s s parameter ( l / f t - l b m ) 2 Wall thermal r e s i s t a n c e ( f t - ~ e c - ~ F / ~ t u )

DFUEL'/(~*KFUEL)

Equivalenced a r r a y f o r p e r i p h e r a l s to rage o f a x i a l l y dimensioned

v a r i a b l e s

Dumny a r r a y t h a t s to res v a r i a b l e s f o r t h e J-1 l e v e l d u r i n g ROLL o p t i o n

Dummy ar ray t h a t s to res v a r i a b l e s f o r t h e J l e v e l d u r i n g ROLL o p t i o n

Dumny a r r a y t h a t s to res v a r i a b l e s f o r t h e J + l l e v e l d u r i n g ROLL o p t i o n

Dummy a r r a y used f o r o u t p u t

Dumny a r r a y used f o r r o l l 1/0 i n RECIRC

Old i t e r a t e va lue o f f l o w i n equal p ressure drop f l o w s p l i t c a l c u l a t i o n ( lbm/s)

Alphanumeric v a r i a b l e t h a t names s u b r o u t i n e i n which e r r o r has occurred

Transverse momentum parameter, S/L 2 In terchannel pressure d i f f e r e n c e , ( l b f / f t )

Old i t e r a t i o n va lue o f node p ressure d rop i n equal p ressure d r o p f low s p l i t c a l c u l a t i o n

Subchannel c o o l a n t temperature (OF)

Cladding th ickness, ( f t )

Temperature e n t r y i n f l u i d p r o p e r t y t a b l e (OF)

U t i l i t y a r r a y

Ut i 1 i t y a r r a y

Alphanumeric problem i d e n t i f i e r


Group 7

Group 7

SCHEME, RECIRC

PROP

Group 4

COBRA

COBRA

Group 10

Group 7

Group 4

PREFIX

COBRA

COBRA

COBRA

COBRA

RESULT

REC I R C

SPLIT

SETUP

Group 9

SCHEME, REC IRC

SPLIT

PROP

Group 8

Group 1

Comdeck

SPEC 6

SPEC 6

SPEC 3

SPEC 3

SPEC 2

SPEC 3

SPEC 6

SPEC 32

SPEC 6

SPEC 2

SPEC 34

SPEC 2

SPEC 15

SPEC 15

SPEC 15

SPEC 15

SPEC 2

SPEC 2

SPEC 2

SPEC 4

SPEC 2

SPEC 2

SPEC 12

SPEC 9

SPEC 1 4

SPEC 2

SPEC 1 9

V a r i a b l e s

M ETA

THICK

TICLAD(MT)

TIME(2)

TIN

TINLET(MC)

TMH (MC )

TPRINT

TR AN T

TR EF

TROD(MN,N4,ME)

TSAVE ( 4 ,MR)

TTIME

w TVARY (MP)

w TWALL (M1,ME) m US(MG)

UWALL(E,MW)

UWCP(2,MW)

V ( K ) VARYCP (MP)

VARYK (MP)

VASSEM(1U)

vr SC(MC)

VIscW(MC)

VISLIQ(MP)

VLIQ(MP)

VP (MC )

VPA(MC)

W(M1,ME)

Subchannel o r i e n t a t i o n f rom v e r t i c a l (degrees)

Diameter o f w i r e wrap ( f t )

l/TCLAD

Clock t ime

Nominal i n l e t coo lan t temperature (OF)

Subchannel i n l e t coo lan t temperature (OF)

C o r r e c t i o n t o coo lan t temperature f o r f l u i d conduc t ion hea t t r a n s f e r (OF)

T o t a l t ime t o nex t p r i n t o u t o f t r a n s i e n t r e s u l t s

T rans ien t t i m e p r i n t o u t i n t e r v a l , ( s e c )

Reference temperature f o r t a b l e lookup

Rod temperatures a t c o l l o c a t i o n p o i n t s

Temporary va lue o f rod temperatures

To ta l t r a n s i e n t t ime ( s e c )

Temperature e n t r y i n temperature dependent f u e l p r o p e r t y t a b l e (OF)

Temperature o f the w a l l (OF)

Average a x i a l v e l o c i t y a t a gap ( f t / s e c )

To ta l w a l l - t o - c o o l a n t r e s i s t a n c e ( ~ t u / s - f t ~ - O F )

UWALL/cool ant heat c a p a c i t y 3 S p e c i f i c volume ( f t / lbm)

S p e c i f i c heat e n t r y i n temperature dependent f u e l p r o p e r t y t a b l e ( B t u / l bm-OF)

Thermal c o n d u c t i v a t y e n t r y i n temperature dependent f u e l p r o p e r t y t a b l e ( B t u / h r - f t - F )

Average assembly v e l o c i t y

Coolant v i s c o s i t y ( l b m / s e c - f t )

Wall v i s c o s i t y c o r r e c t i o n t o f r i c t i o n f a c t o r ( l b m / f t - s e c )

V i s c o s i t y e n t r y i n p r o p e r t y t a b l e ( l b m / f t - s e c ) 3 S p e c i f i c volume e n t r y i n p r o p e r t y t a b l e ( f t / lbm)

3 Same as V ( f t / lbm)

V/A ( f t / l b m )

Crossf low ( 1 bm/f t -sec )


Group 9

Group 7

PREFIX

TODS

SETIN

SETIN

DIFFER

RESULT

Group 9 I

PROP

HOTROD

HOTROD

Group 9

Group 8

ENERGY

PSOLVE

Group 4

DIFFER

PROP

Group 8

Group 8

SCHEME

PROP

PROP

Group 1

Group 1

PROP

SCHEME

SCHEME, RECIRC

Comdeck

SPEC 2

SPEC 6

SPEC 34

SPEC 19

SPEC 19

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 12

SPEC 2

SPEC 34

SPEC 19

SPEC 9

SPEC 4

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 9

SPEC 9

SPEC 32

SPEC 2

SPEC 2

SPEC 9

SPEC 9

SPEC 2

SPEC 2

SPEC 4

Var iab les

WALLC (2, IU)

WALLS(IU)

WBAR (MX)

WERRX

WERRY

WR(IN,IM)

WSAVE (MG)

WSIGN

WTEMP (MG)

(33 X(MX) + XCROSS (MG, 2 ) V

Y(MP)

YG(MM)

YH (MM)

YHX(MM)

YP (MM)

YQ (MM)

YT(MP)

z ZEND(MT,MY)

U t i 1 i t y Array

U t i l i t y Array

Average c r o s s f 1 ow magnitude

Convergence c r i t e r i a

Convergence c r i t e r i a

Width o f w a l l connec t ion ( i n . )

Wall decay heat parameter ( i n . )

Crossf low f rom prev ious t i m e s t e p ( l b m / f t - s e c )

Turbu len t c r o s s f low ( l b m / f t - s e c )

To ta l o f t u r b u l e n t and c o n d u c t i o n energy t r a n s f e r

Same as W, used w i t h r o l l o p t i o n i n RECIRC

Old i t e r a t e va lue o f c r o s s f l o w ( l b m / f t - s e c )

Gives s i g n o f c r o s s f l o w f o r s w i r l

Old i t e r a t e v a l u e o f c r o s s f l o w

A x i a l d i s tance f rom bundle ent rance ( i n . )

R e l a t i v e angle/3600 o f w i r e wrap gap c r o s s i n g

R e l a t i v e a x i a l l o c a t i o n f o r a x i a l heat f l u x t a b l e

Time ax is f o r i n l e t f l o w o r pressure d rop f o r c i n g f u n c t i o n ( s e c )

Time a x i s f o r i n l e t e n t h a l p y f o r c i n g f u n c t i o n ( s e c )

Time a x i s f o r e x i t en tha lpy f o r c i n g f u n c t i o n ( s e c )

Time a x i s f o r system pressure f o r c i n g f u n c t i o n ( s e c )

Time a x i s f o r heat f l u x f o r c i n g f u n c t i o n ( s e c )

Time a x i s f o r maximum t i m e s tep f o r c i n g f u n c t i o n ( s e c )

T o t a l a x i a l l e n g t h ( f t )

R e l a t i v e a x i a l l o c a t i o n o f t h e end o f a f u e l zone

To ta l a x i a l l e n g t h ( i n . )


PSOLVE

Group 9

Group 9

Group 4

Group 4

COBRA

DIFFER

DIFFER

REC IRC

PSOLVE

SET I N

MOMENT

SETUP

Group 7

Group 3

Group 11

Group 11

Group 11

Group 11

Group 11

Group 9

SETIN

Group 8

Group 9

Comdeck

SPEC 2

SPEC 2

SPEC 6

SPEC 2

SPEC 2

SPEC 2

SPEC 2

SPEC 4

SPEC 2

SPEC 14

SPEC 2

SPEC 2

SPEC 32

SPEC 14

SPEC 2

SPEC 6

SPEC 2

SPEC 19

SPEC 1 9

SPEC i 9

SPEC 1 9

SPEC 19

SPEC 1 9

SPEC 2

SPEC 12

SPEC 19

APPENDIX C

COMDECKS

U N L b R F L t D O L D P L M A S T E R 11101T, I D E N T CAQO T O T A L

S P E f S ~ P E ~ S S P E r S S P E r s OPEC S

S P E F S S P E ~ S S P E r s SPECS S P E ~ S S P E C S S P E r d S P E r S S p E r 9 S P E f 3 SPECS S P E f S 9 ~ E r 9 S p E r 3 S P E ~ ~ S P E ~ S SPEC S ~ P E ~ S SPEC 3 s P E r s S P E ~ S SPEC 3 S P E f 9 S P E f S S P e r s s w r s S P E r d

S P E f 1 S P E ~ I s P E r 1 SPEC 1 s P E r I S p E r l SPEC 1 S p E r 1 SPEC I S P E f 1 S P E r I

SPEC? 3 P E r 2

L I S T OF COYTROI-I ACTTVF, A N n / O P I N A C T I V E C b R D 3 I N 9 P F C q

r C O r n E c U S P E C S MA. MC. t3F. MS. MI. HJ. MU 1

ML 8

I4 M 8

* IN8

MO. MP8 M u 8 MS. HT. MV8 M W. M I S

HY. MI!. M I hi I . MI. 11. I € . TR. I T . 1 I J . T V * IW. I Y JH.

L I S T OF CONTROL, A C T I V F . A N n / O Q T N A C T I V E C A R D 3 I N S ~ F C ;

U N L b B E L r D O L D P L HIRT~R r t 1 0 I T . I u E N T CIQD T O T A L

S P E r b 8 P E r Z S P E r P SPEC P S P E ~ B S P E r 2 SPEC Z $ P E r ? S P E r ? SPEC 2 S P E r ? SPEC P S P E ~ ? S P E r 2 SPEC 2 S P E r d SPEC 2 SPEC? SPEC P s P E r ? S P E r 3 S P E ~ P SPEC? S P E r E S P E ~ B SPEC? SPEC 2 S P E C 2 S P E r P s P E r P SPEC? S P E r Z S p F r ? S P F r Z 3 p E r ?, SPEC P SPE r 7 S P E ~ Z S P E t P S P E ~ S P E ~ Z S P E r W SPEC a S P E C 2 SPEC 2 S p E r 2 S P E r P S P E T Z S P E ~ 2 S P E f 2 9 P E r E S P E r ?

2 W J ~ ~ H ( M W ) , I ~ W I M U ) ~ J U ~ ~ ~ N ) ~ ~ O H ~ ~ I W ~ P ~ ~ ~ ~ ~ ~ ) ~ I ~ ~ A L ~ ( ~ , H Y ) , 2 R ~ A L ~ ( P , M ~ ~ ) , R ~ ~ ~ C P ~ M ~ ) , K I J P ~ ~ T ~ E T A P P ~ ~ ~ ~ ~ , ~ ~ P T ~ ~ ~ ~ ~ Q ~ Q P 3 J ~ p ~ T ~ T ~ L p Q ~ ~ p ~ ~ E V p ~ E R ~ ~ ~ ~ I T E R 1 T p D ~ d C ~ G C ~ R ~ ~ P n U T ~ ~ U ~ ~ I ~ D L L ~ 4 D T , P E ~ ~ ~ , N ~ P ~ N ~ R R X , W E Q ~ ~ V ~ I T Q Y # I T R ~ ~ ~ ~ ~ C C E L Y ~ A C ~ E L ~ ,NAAIP 5 N A I P ~ , A C C F ~ F ~ ~ I ~ P N R , N A ~ ~ ~ N ~ A H P ~ , I T D ~ P ~ P S , ~ Y ~ ~ Y ) , I ~ T ~ C , 7 E x T P A ( ~ o o ) ~ ~ ~ I ~ ~ C C E ~ Y P I ~ I G ~ ~ I L O W ~ ~ L O ~ P ~ , N D ~ ~ ~ N T P 6 NRC,I .~~ILVE, ~ H ~ ~ T P H F R R O P , T P R I Y T ~ T R I N T ~ ~ ~ O M T ) M ~ ~ ~ H F T ~ N I F ~ X ( I I ~ I ~ 9 I ~ S S ~ N S U I I ~ L , I T S A V E , F T ~ ~ J ? , N $ C S C P G ~ ( I T ] P ~ J ~ A M P M t ~ ~ S C H E M ~ ~ ~ O ~ ~ E C T ~ I ~ Y ~ ~ I F ~ ~ . ~ I R H ~ ~ ~ ~ P I ~ I ~ E ~ ~ ~ ~ O U *;END!

~ O M M n N / L n O P / k l C H A N L , N K , t f D X o 1 0 ~ * O D ~ N T R Y X ~ N ~ ~ P ~ ~ ~ U I , K E Y ( ~ V ~ Y ) ~ M L F N *;END? c ~ ~ ~ D ~ / ~ & ~ ~ ~ l / ~ ~ ~ ~ b L [ ~ ~ ~ p l ~ ~ H 2 ~ ~ ~ ) , ~ ~ ~ f ~ ~ ~ p ~ ~ ~ ~ ' ~ ~ t ~ l , ~ ~ ~ 1 ~ ~ ~ ~ ~ ~

1 V ~ H ~ ) ~ V P A ~ ~ C ) P V I ~ C ( ~ ~ C ) P V I ~ C ~ ~ ~ ~ ~ ) P V ~ J ~ M ~ ~ C ~ ~ 2 ~ ~ ~ N ( H ~ ) , ~ P ( ~ ' c ) P F ~ P ( ~ ~ ) , c I P ( H ~ ) P V P ( ~ ~ ) P ~ ( ~ C ) , 3 T M ~ ~ M C ) , N ~ R ~ P ( M C ~ , P E W I M ~ H ~ ~ ~ H P E ~ ~ ~ ~ ( ~ ~ ~ ~ T I ~ I L E T ~ ~ ~ C ~ ~ 4 C J N ~ E T ( N C ) , H I N L F T ( H ~ ) , ~ P ( H G ) PDTII(HG) P D T J J O ~ G ~ , I JS (HG) , 3 N S A v E r H t ) , V A L ( R ( I ~ I ) ~ ~ A L ~ C ( Z ~ I U I ~ W L T H C ~ ~ ~ ~ ~ , P D u A ( I I I ) , I E X P P 6 D T H ~ X E , O T I M P , P O N , N P P ~ ~ I P ~ N T E ~ I P R N ~ D ~ U C ~ ~ I U ~ T X ) *;END*

C O H M D N / ~ F I E D / ~ F ~ P ~ ( ~ I ) , ~ F O P ~ I ~ ~ Y ) ~ C O N S ( L ( X I c 0 M M n N / L h P t F 3 / I ~ ~ ( ~ C ) , F ~ Y ~ N ( M C ) , Y W P ~ P ~ [ M ~ ) , D P O ~ ~ ~ M C , ? ) ,

1 C F O l O ( M c ~ ? ) , N ~ L I G ( * C ) . ENOU R E A L I D T ~ C I L E N G T H O I I J L n G I r r L N F L I G

CLCM L E V F ~ 2 0 S A v F A L

U N L n R E L C D O L O P L n A 8 T E Q I I f O I T , I D t N T C A R 0 T O T A L LIPDATE 1.3 .4 j7 :

L I S T OF CONTROLV ACTIVFI AtJO/fJR T t J A C T I V E C A A D S I N 3 P E C q

L I S T OF CONTROL, A C T T v F , AND/OR INACTIVE CAQOS I N S P E C *

S P E r s *COf lFEcY SPEC^ S P E r S ~ I M E N S ~ ~ N X F T V P ( M ~ , ~ E ) , F L ~ ~ ( M ~ , M E ) , T Q ~ ~ ~ ( M N V Q ~ , ~ E ~ , 9 ~ ~ 5 1 H P U k r f ~ l v ~ E l , A V ~ C P f ~ l ~ ~ ~ ) , A V G I ( f M ~ , ~ E ) S P E r 5 FDUIVALLIICE ( I F T V P ( ~ , I ) ~ S ~ V ~ ~ L ( M ~ ~ I ~ ( ~ L U ~ ( ~ ~ ~ I ~ S ~ ~ F A L ( ~ B ) ) ~ S p ~ r 5 1 ( H ~ ~ ! D F ( ! ~ ~ ) ~ S ~ V E ~ L ( H D ) ) ~ ( T P O O ( ~ ~ ~ ~ ~ ~ I S A V F A L ( ~ F ) ) ~ S P E r 5 z ( ~ V G ~ ~ ~ , ~ ) , ~ ~ ~ C ~ L ( N ~ ) ) ~ ( ~ V G C P ( ~ ~ ~ ) V S ~ ~ ~ A L ~ ~ J ~ ) ~ S P e r T C L C * LEVEL 2 , F L U U , T R @ ~ ~ H S U P F , I F T Y P ~ A V C C P , ~ V G K

s w r b S e E r * S p E r h S P E r b S P E r b S P E r h S P E r b S P E C 6 S P F r b S P E C 6 S P E t b S P E r h S P E r b R P E r b S P E C 6 S P C C h

S P E r i n SPEC l o SPEC 10 S P E r 10 S P E t l O

SPEC I 2 S p E r 1 ? S P E r I g SPEC 12 S P E r 12 B P E C I k B P E C I ? SPEC 1 2 S P E ~ i 2 SPEC I ? S P E r I e

L I S l OF C O H 1 R o l . p A C T l V F , ANn/OR T N A C T I V E c A 7 n 6 I t ! s D F C m

U N L b R E L E O OLDPL M A S T E R AL IOIT , I D C N T C A Q D T O T A L

L I S T OF CONTROL, ~ c T I V F , ANn/OR INACTIVF C A ~ D S I N aPCc;u

S P E r l u s C 0 Y F E c Y S P t c l o S p E r I u ~IMEUSION T F R ~ ~ ( M C ) , R ( M G ) . C I J ( ~ G ) , O P P I P ( ~ C ) ~ I C ~ C ( L I R ) ~ SPEC 1 r ~ w P P ~ M G ) , w T F M P ( ~ C ~ , F T E ~ P ~ ~ C ~ ~ O W D P ( ~ ~ , H E ) S P E r 1 0 ~ ~ U I V A L E ~ I C E ( ~ ~ R ~ ~ ( ~ ) , v I s c ~ ( ~ ) ) ~ ( R ( ~ ) ~ w P ( ~ ) ~ c I J [ ~ ~ , u P P ( ~ ) ) , S P E ~ 1 u 2 ( T L D C ( ~ ) , ~ L O C ~ ( I , I ) ) , ( D P ~ ~ P ( I ) ~ F S P ( ~ ) ~ , S P E ~ 1 r 3 ( D ~ D P ( ~ , ~ ) , ~ T E ~ ~ P ( ~ ) , ~ P ( ~ , ~ ~ I , ( C T E Y P ~ ~ ~ ~ T E ~ M ~ ~ ~ ~ ~ S P E C I O CLC'I L E V E ~ e , l j s , TERt41 ,5 ,C IJ ,OPJP, d p p , * I T E H P ~ F T E ~ P , ~ w ~ P

S P E r t 9 r C O Y l S P E r 1 9 s p c r t 9 s P E r i o SPEC 1 9 S P E ~ i 9 9 P E r 1 4 S P E C 1 9 S P E r 1 9 S P E ~ 1 P s e f r 1 o s P ~ r 1 9 S P € r ! 9 S P E r 19 S P F r l o S P E ~ 1 9 S P E ~ I ~ C L C M

L I S T OF CO'JTPOLc A C T I V F , )blr)/OR ~ " I A C T I V E C4RD.9 I N aDFC>c I

L I S T OF CONTROL, A r T r V F , AMn/UQ l M b C T I V E C4RDS I N 9 P F C j 3

U N L E R E L F D OLDPL * ~ A A T F R A I I O I T , I Q E N T CIRD T O T A L

~ C O M D E C K S P E C 2 6 C L C H L C V E ~ 2 , 1 S T ~ ~ F , S T n P C , O T U R E S o L O G I C L

9 P E f S? S P E C > ? SPEC T ? s r E r S P E r J ? s P E r ~ z 9 P E y 3 ? spcr S ? 3 P E r l ?

U N L c B F L F O O L D P L w 4 9 T e R 4 1 l O I T ; I D E N T C A R D T D T A L

APPENDIX D

CONTROL STATEMENTS FOR REDIMENSIONING A COBRA-WC F I L E

APPENDIX D

CONTROL STATEMENTS FOR REDIMENSIONING A COBRA-WC FILE

I n s t r u c t i o n s f o r red imensi on i ng a COBRA-WC f i l e on a CDC 7600 computer

under t h e SCOPE o p e r a t i n g system are g iven i n t h i s appendix. I t i s assumed i n

t h e c o n t r o l statements l i s t e d below t h a t t h e user has cata logued under ID=COBRA

permanent f i l e s f o r updatab le ve r s i ons o f COBRA-WC, COMDECKWC, and SPECSETWC.

The c o n t r o l statements below w i l l p r obab l y r e q u i r e some niodi f i c a t i o n f o r each

computer i n s t a l l a t i o n , b u t a l l t h e general sequence o f s teps descr ibed by t h e

comments should be f o l l owed . The ope ra t i on o f program SPECSET i s desc r ibed i n

Sec t ion 8 o f t h e main r e p o r t .

Comments

ATTACH,NEWS,UCOMDECKWC,ID=COBRA Updatable v e r s i o n o f COMDECKWC

UPDATE (P=NEWS, S=TAPEZ,F, N. L=12347) Creates t he source f i l e on l o g i c a l u n i t 2 o f t h e specdecks w i t h v a r i a b l e s u b s c r i p t s

RETURN,NEWS.

REWIND (TAPE2)

COPYSBF (TAPE2,OUTPUT)

REWIND (TAPE2)

L i s t comdec ks

Updatable ve r s i on o f SPECSETWC

Creates comp i lab le v e r s i o n of SPECSETWC. Changes t o program SPECSETWC can be made a t t h i s p o i n t .

Creates b i n a r y ve r s i on o f SPECSETWC

RETURN, COMP ILE

SPEC.

REW IND(NEWPU)

COPYSBF(NEWPU ,OUTPUT)

REWIND (NEWPU)

ATTACH (DUM1,UCOBRAWC , ID=COBRA)

UPDATE(P=DUMl,N=NUMl ,C=O,L=l,F, E)

RETURN(NUM1 ,DUMl)

REQUEST(NEWPL,*PF)

UPDATE (P=NUM2,F,E,N,L=l)

Runs program SPECSETWC - r e q u i r e s i n p u t f rom u n i t 2 and spec parameters as shown below - w r i t e s specdecks t o f i l e NEWPU

L i s t s specdecks w i t h cons tan t s u b s c r i p t s

Updatabl e ve r s i on o f COBRAWC

F i r s t COBRA update - removes o l d specdecks f rom f i l e

Second COBRA update - removes o l d specdeck i d e n t s f r om f i l e - changes t o COBRAWC can be made a t t h i s p o i n t

T h i r d COBRA update - i n s e r t s new specdecks (on f i l e NEWPU) - c rea tes new upda tab le v e r s i o n o f COBRAWC

Permanent ly s t o r e s upda tab le ve r - s i o n of COBRAWC under f i l e name FNU

Permanent 1 y s t o r e s b i n a r y v e r s i o n o f COBRAWC under f i l e name FNB

REDUCE.

*/COMDECK UPDATES

*/SPECSET UPDATES

LCM MJ= 1 MA= 1 MS= 1 MK= 1 ML= 1 MP= 31 MZ= 1 M I = 7 MM= 2 9 MR= 80 MW= 6 0 I E = 2 1 I V = 4 MC= 9 5 MN= 5 MX= 3 4 ME= 3 4 I R = 6 I W = 3 MO= 11 MT= 10 MY= 7 I T = 7 MG=160 MV= 2 I A = 75 I X = 2 0

*PD SPECS, SPEC34

*/COBRA UPDATES

Updates t o COMDECKWC, i f any

Updates t o SPECSETWC, i f any

SPECSET parameter i n p u t

LCM on f i r s t ca rd i n d i c a t e s t h a t LEVEL 2 s to rage i s t o be used.

Updates command t o remove o l d specdec ks

Updates t o COBRAWC, i f any

*AF NEWPU ,YANK$$$

***EOF ***

Updates comnand t o add new specdecks

APPENDIX E

SAMPLE PROBLEMS

APPENDIX E - SAMPLE PROBLEMS

XX08 SAMPLE PROBLEM

Several n a t u r a l c i r c u l a t i o n exper iments have been conducted i n t h e Exper-

imenta l Breeder Reac to r - I I (EBR-I I ) as p a r t o f t h e XX08 inst rumented assembly

e f f o r t . XX08 t e s t 7A was one o f these exper iments and w i l l be used t o i l l u s -

t r a t e t h e use o f t h e COBRA-WC code. I n t h i s t e s t , t h e r e a c t o r was operated a t

a reduced power (28.19 percen t o f nominal) and f low r a t e (33.0 percen t o f nom-

i n a l ) u n t i l t h e f i s s i o n p roduc t i n v e n t o r y a t t a i n e d a near e q u i l i b r i u m s ta te .

The p r ima ry and a u x i l i a r y pumps were then manual ly t r i p p e d and s h o r t l y there -

a f t e r (3.4 seconds) t h e r e a c t o r a u t o m a t i c a l l y scrammed because o f a low f l o w

t r i p . The secondary system pumps were then manual ly shut down t o s imu la te

t o t a l l o s s o f o n - s i t e and o f f - s i t e p l a n t power. E v e n t u a l l y t h e f l o w coasted

down t o the p o i n t where t h e r e was o n l y n a t u r a l c i r c u l a t i o n through t h e l oop

d r i v e n by t he decay heat i n t h e core and t h e c o o l i n g f rom t h e secondary system.

The XX08 assembly was inst rumented w i t h f l o w meters a t t he assembly i n l e t

and o u t l e t , e ighteen coo lan t thermocouples i n and above t h e f u e l reg ion , and

s i x f u e l c e n t e r l i n e thermocouples 0.322 m above t h e core bottom ( t o t a l co re

l e n g t h was 0.343 m) . Temperatures and f l o w on t h e XX08 assembly were recorded

du r i ng the 5-minute t r a n s i e n t , a f t e r which t h e p r ima ry pumps were tu rned on t o

p rov ide 100 percen t o f normal ope ra t i ng f l ow .

The COBRA-WC code was used t o s imu la te t he exper iment d u r i n g t he n a t u r a l

c i r c u l a t i o n t r a n s i e n t i n o rder t o i n c l u d e t h e in te rassembly heat t r a n s f e r among

the XX08 and surrounding assemblies. S i g n i f i c a n t l y lower power - to - f l ow r a t i o s

i n t h r e e ad jacent assemblies made in terassembly heat t r a n s f e r a p o t e n t i a l l y

impor tant cons idera t ion . The s teady-s ta te thermal and h y d r a u l i c c h a r a c t e r i s -

t i c s o f t h e seven assemblies and o t h e r i n i t i a l c o n d i t i o n s a re l i s t e d i n

Tables E . l and E.2.

TABLE E.1. EBR-I1 Assembly Steady-State P re tes t Power and Flow C h a r a c t e r i s t i c s

Assembly Model

Subassembly Number XX08 1

Power F 1 ow

TABLE E.2. Operat ing Cond i t ions Used i n S imu la t i n o f EBR-11 Natura l C i r c u l a t i o n Experiment?a)

I n l e t Temperature (OF)

Pressure ( p s i a) 2 ( a ) I n l e t mass f l u x ( 1 0 ~ 1 bm/hr- f t )

6 3 ( b ) Power d e n s i t y (10 B t u / h r - f t )

Turbulent m ix ing f a c t o r ,

Rad i a1 Conduction Geometry f a c t o r , GK (XX08)

Radi a1 Conduction Geometry f a c t o r , GK(adj .ass. )

Traverse Moment um Geometry f a c t o r , (S/L)

( a ) Based on XX08. (b ) Actual power d e n s i t i e s are prov ided f o r i n d i v i d u a l assemblies;

t h i s i s a dummy number.

The XX08 assembly shown i n F igu re E . l i s a double-ducted, 61-pin assembly.

It was modeled by 55 channels: 37 channels i n the rod bundle and 18 channels

i n t h e f l o w annulus between ducts. The power generated by t h e 61-rods was

modeled by 37 p ins, one f o r each channel. The r a d i a1 power used f o r each model

p i n represents an average o f t h e r a d i a l power o f each o f t he f u e l rods f a l l i n g

w i t h i n a model channel weighted by i t s f r a c t i o n a l con t r i bu t i on . F igure E.2

shows t h e model channels w i t h respect t o t h e 61-pin rod bundle. The t o t a l

power generated a t any t ime ( i n c l u d i n g t ime zero) w i l l be the product o f the

steady-state nominal power, r a d i a1 power f a c t o r (F igure E. l ) ax i a1 power f a c t o r

(Table E.3) and the t r a n s i e n t power (Table E.4). The th ree t r a n s i e n t power

f a c t o r s f o r each t ime are f o r d i f f e r e n t assemblies i n t h e seven-assembly c lus -

t e r model. The p r o f i l e number used f o r each assembly i s i d e n t i f i e d i n the

i npu t . Table E.5 gives t h e f l o w m u l t i p l i e r s f o r t h e t rans ien t . Other XX08

asserr~bly c h a r a c t e r i s t i c s are g iven i n Table E.6.

The surrounding assemblies comprise two d r i v e r f u e l assemblies (MK-I I ) and

four experimental assemblies, one o f which i s s t r u c t u r a l (X263) and the o ther

t h ree fue led (X280A, X321, X316). The l o c a t i o n o f each adjacent assembly w i t h

respect t o the XX08 assembly i s shown-in F igure E.3 w i t h d e t a i l s o f each

i n d i v i d u a l assembly model g iven as Figures E.4 through E.8. The s t r u c t u r a l

assembly (F igure E.4) was modeled w i t h o n l y s i x channels and p i n s because i t

had a r e l a t i v e l y f l a t r a d i a l p r o f i l e . The f u e l experiments (F igures E.5 and

E.8) and the d r i v e r f u e l assembly (F igure E.6) were modeled by t h i r t e e n chan-

ne l s and pins. The X321 f u e l experiment (F igure E.7) has h a l f tubes on each

duct face which have coolant f l o w i n g i ns ide .

The XX08 t e s t 7A na tu ra l c i r c u l a t i o n t r a n s i e n t has been analyzed w i t h t h e

COBRA-WC code us ing the model described above. The p r i n t o u t inc ludes the i n p u t

l i s t i n g , s teady-state r e s u l t s , and t r a n s i e n t r e s u l t s through ten seconds. The

actual ana lys is covered 120 seconds b u t i t i s hoped t h i s w i l l be s u f f i c i e n t t o

meet t h e ob jec t i ves o f t h i s sample problem.

TO CORE CENTER

FIGURE E.1. XX08 Assembly and Rad ia l Power Profile

FIGURE E.2. COBRA-WC Model o f XX08 Assembly (Channel s are numbered t o m i n imi ze bandwidth f o r d i r e c t s o l u t i o n scheme. )

TABLE E.3. A x i a l Power D i s t r i b u t i o n

X ( i n . )

0

0.5

A x i a l Power Fac tor

0.017

0.020

1.641

1.650

1.706

1.784

1.853

1.909

1.931

1.939

1.920

1.877

1.810

1.713

1.610

1.508

1.414

0.020

0.010

0.006

0.004

0.001

TABLE E.4. T rans ien t Power Fac to r s

Time (set>

0.00

TABLE E.5. T rans ien t Flow Fac to rs

TABLE E.6. XX08 Subassembly C h a r a c t e r i s t i c s

Subassembly Parameters Dimens i o n Hex can, f l a t - t o - f l a t I . D . 1.83 i n .

Hex can w a l l

Thimble gap (between hex w a l l s )

Element diameter, O.D.

Wire wrap d i ameter

Wire wrap p i t c h

Sodium bond th ickness

Clad t h i ckness

Number o f elements

0.04 i n .

0.15 i n .

0.174 i n .

0.049 i n .

6.0 i n .

0.010 i n .

0.012 i n .

61

Wire wrap zero re fe rence angle

( s t a r t o f f u e l , Z = 0.5 i n . ) 105'

Steady S ta te P r e t e s t ~ o n d i ti on^(^) Value

T o t a l bundle f low, l b / h r 5.804 x l o 3 T o t a l t h i m b l e f low, l b / h r 0.6052 x l o3 Average element heat f l u x (over

24 i n . o f l e n g t h ) ~ t u / h r - f t 2

I n l e t temperature, OF 664

I nne r Hex can average heat f l u x

(over 24 i n . o f l eng th ) , B t u l h r - f t 2 ( b ) 1.69 x l o 3 To ta l subassembly power, kW 110.1

To ta l S/A pressure drop ( i n l e t and

o u t l e t o r i f i c e s inc luded) , p s i 3.7

( a ) A u x i l i a r y pump has been t u rned o f f . ( b ) It was assumed t h a t t h i s heat f l u x was e q u a l l y d i v i d e d over

bo th i nne r (bundle s i d e ) and ou te r ( t h i m b l e s i d e ) hex can faces.

XX08 MULTl ASSEMBLY MODEL

FIGURE E.3. Model o f XX08 and Adjacent Assemblies

FIGURE E.4. X263 S t r u c t u r a l Test Assembly and Model Noding

E. 10

FIGURE E.5. X280B Experimental Fuel Assembly and Model Noding

FIGURE E.6. MK-I1 D r i v e r Fuel Assembly and Model Noding

FIGURE E.7. X321 Fuel Assembly and Model Noding

FIGURE E.8. X316 Experimental Fuel Assembly and Model Noding

E.12

0 0

C

'C

C

C

u rr . . a G

0

u

J 0

00

-

0 0

= C

CN

m

m*

... oaa

a

Q

0 0

m

a

a a

Om

0

0 0 0

oo

uo

P

u J

0

0

0

C 0

.... ....

. . 0.20

CO

CO

CC

CC

CC

CF

CC

CC

C~

~~

YC

CC

C~

~C

~C

CL

CC

-

-- N

NN

n

SN

."R

(.

. '. '. C

- -

(L

O

ON

.0

--0

0

a

6-n

cu

0

N

0G

5O

W

....

a

-0

-0

P

O

cC

n-

=l

-u

C

r e

mn

-o

m-

N

mu

OQ

-

*

....... C

OC

JC

CJ

UJ

3

05

65

10

00

V

LY

Iw

=lm

ma

*J

0

00

00

C0

C0

- -

--

--

-

a

m

=a

00

0

0

0

CO

OC

c

...... m

oc

co

c-

~O

OC

CB

- .

-.

~.

.

r

-0

-0

~

00

0r

n=

lJ

OO

NC

=l

C

e .

n.a

an

.oo

an.

T

J

-~

CC

JU

w

4

........

m

-0

-r

n

a

OO

OO

CO

OO

OO

OC

OC

OO

OO

OC

Oo

CO

CO

CO

c

3n.0SbUl .hU01 eb'I0 3l.n292;81~9.~l~Q 3?.n2?3.b1bn.1lR9 31.0223qblb0~~1~9 SU.0387~993ft.5~hb 3T.n?23.bibn.2In9 36.n?22;bibn.3la9 37.n38?.q93u14Ubb 3Rm~521 ,bqUh SQm0¶21.b9"h 'Jn.0~2106QUb U l .nbT2,P96n U?.nb7?,PQb0 o3on521.b94h Uo.ob72.89bn u5.0521.b9ab 1600q21,b945 ut.n072,~9bn ob.052lmb9Uh U'o0521,6945 5n.nSZl .bq~r 51 e 0 5 2 1 qb9Uh S?m052!.69"6 53aOb7?.Plb0 S~.ob7Z,0900 55.n521.69Uh ? ? h O ? l P l o n 1 1 I " f 3

P I 1 I b I S 1.112 U.226P.Q ?.I12 amt?h?.' -.112 fl.2262.9 hell2 U.22h2.q 5.112 e.??hk?.q Poll? U.22h2.9 1 5 I? I 1 1 1 n o o u ! P 1 0 1 10 9 1 1 1 12 1 13 1.'[email protected]?> 2*1513?.h951 .'I61 1.15t51.e9~1.~hI Um151~7,bq~l.U61

1 Sf ' 1 6! 1 L? 16' 1 b U

16'; 1 h#. 1 AT I SP t b0 1 7 0 171 1 T? 1 7 - 1 T 11 1 7 2 116 177 1 TC 170 1'0 1qq 1 n? 1 9 1 1 all

1 n= 1 8 ~ 187 1np 1 na 190 19 1 1 Q? 10- ) 011 10- 106 191 t 9 P 1 9 0 ?on ?01 PO? - 2 3 - ?no PO'; en* 207 2 0 P 230

?1P ? I 1 ? I ? ? I .

-

rn m

e-

-

J

Cr

OC

O

w.

IC

CC

N

m

-.. -

.w

.m

m

C

Y

v

VI

C

~~

~C

CJ

~C

~-

~~

J~

~~

P.

CC

CI

CO

C~

~

cn

rn

C

-I

CC

~=

-.

C-

JP

~C

~O

VL

~

Y

J

-~

aa

am

mr

nn

~~

~~

mm

--

--

--

n,

o-

--

N

QI

II

DJ

--

-

~C

C(

OC

-~

U~

LL

-~

-.

(U

~~

C-

J

F. r-O

GC

GO

OG

CC

CC

OO

OC

CO

CG

CC

GC

C

um

eo

o=

C

CO

DO

OC

CO

OO

CC

-

=O

OU

C

c

N ..

..

..

..

..

..

..

..

-a

.m

..

m

..

.

.me...

......-...... ..... h

abn 2 5 0 2 7 n 271 ? 7 ? ? 7 1 ?TO ? l F 27 6

2 7 7 2 7 s ? ? a

281 2 9 7 20 - 2 9 0 2 8 = a r c ~ 9 7 e q n 1 4 0 7 9 0 2 9 1 79? ?qx ?QO ?q= 7 9 6 297 2 9 6 2 9 0 30CI 3131 3 0 ? l n x 3111 30G 3 0 6 3 0 7 SOP 3 n n 3 1 0 3 1 ! S t ? 3 1 7 J l l ' 3 ! * 31 C ? ! I S I R 7 1 0 3 2 0 3?1

$IJI?E'ACY OF INPUT OPTIflh9 GPO(IP E l l N? ~ 3 ' J ~ I N 5 ti6 k ? J R VP ~ l ' l N 1 f P ' I ? ~ 1 3 h,ILI Ellq

? i n 0 1 0 o o o n n o n o n n t 0 a n n O o O O n 0 n n n 7 1 8 n O n O O n O O n ~ O n ~ 7 ? 9 n 5 f l @ O O n @ n O n n 0 0 - t n h a d 3 o n O O n o

l o l n l ~ O O 0 0 0 0 b n O O n I * 1 a O @ ? u 1 0 0 1 1 3 2 n O b n 1 1 1 1 0 f 0 I n o 0 1 0 0 n n 0 n 0 0 n

F R I r T l 0 h ~ FACTOR C O Q O E L I T I O ~ ~ T V P F 1 C ~ M A U OF ( . f f h * n ~ r * ( -.?Tn) + - O , O O ~ * R E * * ( - ~ . O ~ P I + - .onnO) na r a : n n ~ * ~ ~ r * r , i , n n p ) + POD)

HEAT FLtlX O 1 3 T R ~ R l l f ~ 0 ~ 1 Y / I - R E L A T I V E F L U X P R ~ F T L F ~

-PC-*-

COGlLOC

CC

CO

CC

OCOnOO

...... 1

18

8

1

...... OCOb03

CCO=JCC

000000

...... 1

81

1

8

-----.

0C0C00

N

-.-- aoc

nc

C

JCO

... 8

1

.... OClO

0 C C

000

... 8

1

,.

--

- 0

0

n

r--.-.-r

OCOOCC

CC

C<

CC

OOCOCC

...... 8

11

11

8

,.-.---

0303C13

CCCCCC

000005

...... 1

81

11

1

--

--

-a

OOCCOO CCCCCrr

Ccco000

CC

CC

CC

C

OOCOOCO

....... 1

88

11

#1

-..-

.-.

~~

CC

CC

CC

~C

C~CoQOCOOOO

CC

CC

CC

CC

CC

OCOOCOCOCf

.......... 8

81

81

11

18

1

ocococ

CC

CC

CC

CcoOCO

...... 8

11

88

8

...... OC005~

CCCCCC

000000

...... 1

88

88

1

-----.

COOOCO

~.

-

-.-

---.-

.. 0000000000

CCCOCCCCCC

00C000 0000

.......... 8

88

18

11

18

8

-..-

-.-

---

0"-00000C)00

--

--

--

--

--

--

-

=JCCOCCCuuCCCCOOOCCCCuuuCCCCCC~ccccccccCCcCc~cCccccCcc~C

~0

0~

OO

CJ

J~

CC

0~

~~

3G

O0

JJ

OJ

CC

OC

C*

O0

OO

OO

OO

CC

G~

GO

~O

CC

OC

o~

O~

~

< C

C

C

C

C

C C C

C

.C

C

C C

.C

C

'C

C

,C.C

C

'C

C

C

.C C

C

C

c

C*

C C

C

.C,C

.C

C.

C4

C C

,C.C

C

.CC

C

C.C

#C

.C.C

.C,C

.C.C

C

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

--------.-------

0e

u0

uF

uO

uu

uu

uu

uo

JJO*eaJPJJJJa=OJ

CCCOOCOCCCOCCCCO

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

a

a W

tL

2

8-

l-

C

I

CU

1

Yn.

-1

0

8 U 1L'

1- s

8

C

a

BX

C

LL 8

; =

#A

.

Il

Ym

3

8 >

1

8C

8

(Z

L

>

8 Lu;

A*

XA

2

ff

i8

Y

*

I8

J

IJ

O

L

L-

Z

-n

r.

au

rr

-c

o c

-n

r=

r~

r-

ao

c-

a~

au

~~

rr

a

c-

nv

a

ud

r-

ac

r-

ar

cu

rr

-a

o c

.-

hr

,c

r

ma

-a

a

0

--

--

--

--

--

na

hm

n~

~f

i&

ma

nn

nm

nn

w~

rn

ni

l

JPJO=I aao~mms~anwu~

ff, 30x

e

8a

T

BA

U

r-rCCCCrC-CrCCrCrrr--PPr-rPc-PrrePe*C

OO

OC

OG

OO

CO

OO

OO

OC

CG

OC

OC

OC

OO

OO

OO

CC

OG

CO

O

CC

CC

CC

CO

CC

CC

0

00

00

00

00

C3

0

CC

CC

CC

CO

tC

CC

CG

CC

CC

CC

CC

CC

0

3C

00

00

03

00

C

CC

CC

OC

c~

CG

CC

C

CO

OO

OC

OO

OG

OC

o

oo

oo

oo

oo

oo

o

............ 0

0C

C0

0O

00

CO

C

#8

11

1*

11

81

#8

00000000000C0000000000000000000000000

CCCCCCCOCCOCCGCCCCCCCCCCCCCCCCCCCCC C

C

OOCCCOOOGOOOOCCOOOCOCCCCOOCCCOCOOGCCC

CCCCCCCCCCCCCCCcCctcCCCCcCcCCtcCcCCCC

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

CO

CG

~C

CC

CO

CD

CC

CC

CC

C

OO

OO

CC

OO

Co

oO

cO

CO

GC

C

CC

CC

CC

CC

CC

CC

CO

GC

t

OO

CC

CO

Oc

CO

OO

CO

OC

CO

~

CC

CC

CC

CC

CC

CC

CC

CC

CC

C

CC

CO

CO

Cc

CO

CC

OC

CC

C

.... ...

C..C

C

C*

..

CC

..

CC

I.

..

I

OO

OC

OC

CO

OO

OO

OO

OO

OC

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

CC

CC

CC

OC

CC

CC

CC

CC

CC

CC

CC

CC

CC

CC

CC

CC

CC

C C

C

11

b1

88

88

11

88

18

8#

11

11

81

11

11

11

88

11

88

~8

1

Sm

1

C c n

2e

I-

GU

M

ua-

Q

CCOCCGOCOCCGCOCCCGCCCCCCCCCCCOCCCCCCC

y OCOOCCOOOCCCCCcCCCCCGCCCCcCCCCCCCCCCC

CCCCCCCCCCCcCCCCCCCCCCCCcCCCCCCCCcCCC

O

00

QC

00

00

00

0~

OC

CO

CC

CC

OO

OG

OO

OO

OG

OC

;O

CC

iC

C

a

..................................... COOCOCCCCCCCCCCOCCCCCCCCCCCCCCCCCCCCC

IL

81

88

18

18

18

18

11

18

88

11

~8

1~

88

1I

11

88

81

11

8

0

-

-. L

G

~~

z-

~~

~~

Q~

~D

G-

~~

J~

~Z

CC

~~

~~

~~

~~

QC

~O

O-

~~

CJ

YY

.O

C

- .-

--

.-

.-

.-

.-

--

.-

.-

.n

nn

nm

~~

an

nr

r.w

.r.r

.r.r

.v.

OU

O

OO

G

cr -1a

Fe

e-

-*

CC

OO

OC

C

CC

CC

C

CC

OO

OC

......

88

88

88

Cr

rr

rC

eC

Cr

Cr

r

CC

CC

C0

00

CO

CO

C

CC

CC

CC

CC

CC

CC

C

CC

OO

CO

CC

CC

cO

C

............. 8

88

88

88

88

88

88

-..-

-..-

--.-

. 0

00

0C

00

00

33

0C

C

CC

CC

Ct

Ct

CC

CC

O

OO

OO

OO

OO

GO

OO

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

r

88

88

88

II

81

88

I

x

-----.---.--.

8-

Cc

0C

GC

CC

C"

CC

C

w

2

d

--u

u-u

uu

-u

uu

u

CG

CC

CC

0

00

00

0

CC

CC

CC

O

OO

EC

O

...... C

OO

OC

C

18

88

88

OO

CO

OC

C

CC

CC

C

0c

00

00

......

88

81

88

-

-*

.-

-

CC

OC

CC

-1

en

----

CO

OO

GG

.

OO

OO

OC

>

C

CC

CC

C

----n

-.-.----n

n

OC

OC

oo

CO

Co

CO

C

OO

OO

OO

OO

CO

OO

C

CO

CO

OC

CO

OG

CC

C

00

00

00

C

CC

CC

C

OC

OC

OC

C

CC

CC

C

...... IC

C

.ClC

'C.C

8

88

88

8

............. 8

11

88

81

18

81

18

.---.-.------

CC

CC

CC

CC

CC

CC

C

OC

CG

CO

CO

CC

OO

C

C C

'C

~C

.C

~C

~C

~C

~L

.C

.C

C

.C

............. 8

88

81

8I

18

88

~8

---.---------

CC

CC

CC

CC

CC

CC

C

-

CC

CC

CC

.

00

00

00

x

'C

.C

~C

'C

.C

~C

=,

...... I

88

8I

88

------

- C

CC

CC

C

C' -

-----.-. C

CC

CC

C

- L

UL

IL

.U

C

L,

Pe

e.- *

-

CC

CC

CC

a

CC

CC

CC

(r.

UC

CC

CC

I*.,..,,.

. . 8

88

88

9

.

...I(

.?

..... D

Y

CO

CC

O

2

CC

CC

CC

G

CC

CC

C

.*..*.,*.

CC

CC

CC

C

CC

C.

CC

.C

C

.C.C

.C

C

cc

oc

cc

I

E

----L

C

c--c--

b- C

CC

CC

C

z C

CC

CC

C

Lli

WW

6U

OO

v

...... C

8

7

------ c

Y.K

.U

.T

.V

C

00

00

CC

-

00

C0

0C

...... I -.-

-.-

m

w*

= K

.I C

GO

CC

CC

C

CC

CC

C

CC

CC

CC

C

CC

OC

C

...... C

Ct

CC

C

88

88

88

rC

CC

CC

hC

rC

TC

-

CC

CC

CC

CC

CC

CC

C

c-

--

--

-a

ua

a

au

c

CC

Cd

C.

LR

wn

w-

w,

A

Z e

c, k

cl C

j I-Q

4

n

-1

Iu IL

C

I

a - G C

C

CC

OC

CC

C

CC

Cl

OC

.

CC

CC

CC

c

oo

oc

c

U

00

00

00

ca

?$

, c

cc

cc

c

-I

-

CJ

d.

LC

J

~W

-0

00

cc

0

z-----.-,

OU

.4

...... -

--

--

-

...... C

CC

CC

C

88

88

88

c0

00

00

0

0 0

0 0

C

0.

0

0C

00

0

Y=

C

CO

CC

C

'--.^

00

00

00

CO

OC

OO

OC

OO

CO

C

CC

0~

C0

0C

C0

00

0

0.

C

OC

CO

OO

OC

CO

OC

wx

,b

------m

w,n

cm

7w

,

t-

-N

mm

Cf

Q~

Nm

NN

NN

co

oc

oc

C

CC

CC

C

.s

4.4

.L

.s

9

------ ...... ------

CC

CC

CC

O

0C

OO

O

OC

CO

Oc

- u- 1 O

OO

OC

O

Oa

m4

NO

.N

C

rLaL;n

.u 0 l

a-

C

UU

UC

CC

A

".

..

..

.

u -

--- u C

Y

WO

a u

&u

- IL

C

CO

CC

CO

CC

CC

CC

n

- c

cc

cc

co

co

cc

cc

0

2

Cu

'~

.v

wu

FL

Cu

E4

~

a i

xc

&

8=

U

.8

2.

I

8L

W,

>

2

88

-

8-

X

> IIu

J

28

T-

l

=I

i~

X

8A

Y

. I c+

m

8-

-

u, I

XW

8

4I

Cr

rr

Cr

rC

CC

CC

C

0O

CC

CC

CO

00

0G

C

CC

CC

CC

CC

CC

CC

C

CO

CC

CC

CC

OC

OO

t

............. *

11

8#

1I

B1

11

8I

C

CC

CC

CC

CC

CC

CC

0

53

03

30

~5

00

51

C

CC

CC

CC

CC

CC

CC

0

C0

00

00

C0

00

G0

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

CC

OC

CC

CO

GC

CO

O

11

88

11

8I

81

88

1

............. 0

00

00

00

09

36

04

C

CC

CC

CC

CC

CC

CC

0

00

O0

00

00

0O

0C

............. 1

11

11

.I

II

I.

11

- z ,"

uu

uu

uu

uu

uv

uu

-

--

--

-C

--

--

CC

C

-1 ----------C

--

OC

CC

Ct

CC

CO

OO

C

OO

CG

OO

CC

OO

OC

C

cC

oC

00

~O

U0

0c

0

CY

Iu

VI

YI

-I

IV

I

>

Ot

CC

OC

CC

OO

CC

C

............. I

I8

81

11

81

T1

II

0

C0

00

00

0C

00

00

u

CC

CC

CC

CG

CC

CC

C

............. C

3C

cC

GO

oc

Oc

SC

C

CC

CC

CC

CC

CC

CC

C

CC

CC

CC

CC

CC

C C

O

OC

OO

OC

CO

OO

CC

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

3

IC

CIC

.CIC

.C.C

.C

C CqC

C

C

-r

C C

CtC

C C

C'C

< C

C

C

C

- .............

- 8

11

18

88

11

88

18

J.

II

II

II

I8

8I

II

I

C

------..-----

Z

- C

CC

CC

CC

CC

CC

CC

L'

C-

C.

-C

C-

CC

_C

CC

-

CC

CC

CC

CC

CC

LC

C

- L &

w

u

ub

-V

ue

cu

u-

-u

Z

00

00

00

00

c0

00

0

CC

CC

CC

CC

CC

CC

c

CC

cO

cC

C0

o0

CO

O

CC

CC

CC

CC

CC

CC

C

............. .r

C C

C C

+C

*C

IC~

C.C

.C~

CL

CIC

.

tl

8~

68

1I

I~

~I

I

- L 2 -.-

--_-c-----c

J

CC

CO

GC

OC

CC

UC

C

I, - ; c

L-

rr

rr

v-

cb

c-

Q

U

r

--

-r

rr

rC

rr

rr

2

---c

c---e

cc

LL

-

CC

CC

CC

CC

CC

OC

C

a

a

CO

OO

OO

OC

P~

~~

~

I

CC

CC

CC

CC

CC

CC

C

u

OC

CP

CC

CG

CC

CC

C

U

CC

CC

CC

CC

CC

CC

C

.Y

"I

II

CC

uC

.r

.I

.

'. u

CC

CC

CC

C.

C.

CC

CC

C

------ ..

Co

cc

cC

cc

cc

cc

c

.... ..

!..* .... ..-.*

r..:

4

.

- .

".

.C

..

..

..

.-

C.

.C

I.

..

C

@C

CO

OC

GY

~K

mu

C c

CO

CC

CC

CC

CC

CC

C

2

CU

UU

YY

~U

N~

~O

~O

r

I I I I I I

1 I

8 8

I

8 I

00

CO

OO

OO

CC

CG

0

r

...... _

..

l*

".

.*

C

P.

."

.

U. r

-e

.-

.-

r-

rr

~m

r-

-

CC

CL

CC

CC

CC

CC

C

'5 2

ru

~u

uu

uu

-u

uu

-

e

IL

8

Y

--

--

--

~r

-~

~-

~

Z

tr

?4

-s

-I

.L

.t

e.

L.

!e

.C

I)

.

- C

.C

CC

C C

CC

CC

CC

C

O

~~

~Z

CN

O

O-

NC

C

w

I

CC

CO

CC

CC

CC

CC

C

C

CC

CC

CL

CC

CC

CC

C

CC

CC

CC

Cc

CC

CC

O

r

CC

Ct

CC

CC

CO

OO

C

Z

............. IL

C

CC

CC

CC

CC

CC

CC

U

II

II

II

8I

II

II

I

- ----I--------

x

CC

CC

CC

CC

CC

CC

C

P

C

CC

CC

CC

CC

CC

CC

C

c

CC

CC

CC

CC

CC

CC

C

* z

CC

CC

CC

CO

OC

UU

O

OC

CC

~C

CC

CC

CO

C

PC

w

CC

CC

LC

C~

&&

&&

~ t

~C

CC

CC

CC

CC

CC

C

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

x 0

2

LZ,

Q

1

U

CC

CC

CC

CC

Cf

CC

C

............. 52

3

.--.--.------

U

d

c

CC

CC

C.

LC

~C

CC

CC

C -

ZP

- 0

mu

.u

-m

mr

mu

D~

vv

- J

-

CO

CG

CC

CO

CC

CC

C

C

--r----------

............. Z

C

I 0

CO

CG

CC

CC

CC

.C

O

G

Lk I

D

CC

CC

Ca

OO

cO

cC

O

Y

CC

CC

CC

CC

CG

OG

C

2

LC

CC

CC

CC

CC

CC

C

o

CO

CC

CO

CO

OO

OO

~

CC

CG

CC

OC

CC

CC

C

CC

CC

CC

CC

CC

CC

C

CC

CC

CC

CC

CC

CC

C

CO

Cc

OC

CC

GO

CC

O

............. C

CC

CC

CC

CC

CC

CC

1

1*

*D

I1

11

*1

11

----m

t,,

4.Z

C.K

O u

C

CC

CP

O

GC

CC

CC

C

CO

ON

N

--

-I

-.

--

...... NN

NN

O

OO

D

OO

OU

C

CC

t

NI

UN

N

---- ....

a

............. C

C0

CC

CC

CC

CC

CC

U

8

II

II

I.

81

I8

II

I

ci

C

- C

O

OO

OC

OO

OO

UO

CC

4

OO

OO

OC

CC

OO

CO

O

u

CC

CC

OC

CC

CO

CC

C

CW

0

.

OO

OO

OO

OO

OO

OO

C

Y

GC

OO

CD

G?

-C

CC

CC

u

-1

WI

CC

CO

CC

CC

~C

CC

u

wz

C

.-

-d

OJ

JI

Je

m€

nm

mm

m

CG

GC

CC

O4

&C

4.

44

x-

uQ

zm

CC

LC

CL

J=

sl

aa

0

mm

mm

mm

c.n

o.r

.n

.c

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

Q

W

cc

cc

cc

cc

co

cc

c

CG

OO

OO

CO

OO

OC

O

DG.

00

00

3U

OC

OO

OC

C

SW

L

h4

..I..I.&

..C

b1

00

J=

AI

-C

--

C

VV

U,

WV

YO

JJ

JJ

-

zta

za

nn

nn

nn

------

WW

-.

-.

..

..

..

..

..

t

la

-t

LC

CC

CC

rm

CC

~r

rr

-I

a

r

U

3

0G

0O

00

00

0G

SC

0

aa C

NO

~C

&L

J

CG

CV

JO

9

PC

Ce

.L

IC

--

=C

CY

&v

.

tC

CQ

UO

CC

CU

QU

CC

LO.............

4 a 6..

- c -

d d

0 hi.

U'C

a I

x 0

- -

W

0C

00

CC

C0

CC

CC

C

n -

cc

~o

oo

oo

oc

~o

o

m ;

~n

n~

mm

r-

--

--

-

c -

-C

uL

rF

mr

rF

mm

uu

-

u -

EC

LI

U~

OO

QC

OV

E

WD

N

--

--

-c

00

0G

OC

t. P

(r:

..........'..... L

a-

-.

-.

.-

r#

-C

rr

F*

r

OC

QC

OC

GC

OC

CC

O

CC

CC

CC

CC

CC

Cc

C

CC

OC

CC

CC

CC

CO

G

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

81

11

11

11

11

1

..-..-

-..-

.-

r- C

03

00

30

05

35

P

OC

OC

CC

CC

CC

C

00

00

C~

00

C0

00

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

11

81

81

11

11

8

............ E

CC

CC

CC

CC

CC

O

GC

CC

CC

CC

CC

CG

C

CO

13

03

CO

c3

11

90

C

CC

C C

CC

CC

CC

CC

3

00

GC

0C

C0

00

0G

Ca

00

00

O0

00

03

0

CC

CC

CC

CC

CC

CC

C

00

00

00

0C

C0

00

C

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

CC

CC

CG

CO

CG

CC

O

11

11

11

11

11

11

1

1B

11

11

S1

11

11

1

............. O

CO

CC

OC

CC

CO

CO

-- -..----------- C

Oc

Co

O=

Oo

CO

CC

.

00

00

C0

CC

0C

C0

0

5

OC

CC

CC

CC

CC

OC

C

---- O

CC

C

CC

CO

C

CC

C

.... 1

11

1

OC

OC

oc

0c

C5

o0

0

Cc

CC

cC

Cc

cL

CC

C

CC

OC

CO

OO

CC

CO

C

CC

CC

CC

CC

CC

CC

C

----.-

-..-

-.-

C

CC

CC

CC

CC

CC

CC

0

00

00

CC

00

C0

0C

C

.C*C

C

IC

C C

IC'C

C

.C

.C

C

..-

-

-.

-----.---..-

CC

PC

CC

CC

CC

CC

.------------

Z

- C

CC

CC

CG

CC

CC

CC

C

L-

CC

-C

CC

C*

hC

L' J

CC

CC

CC

CC

CC

CC

C

I. -

-------L

-r---

2

C-

CC

CC

CC

Ch

CC

C

CC

CC

CC

CC

CC

CC

C

CC

CC

cC

OC

.l

u~

.l

.x

C

CC

CC

* C

GC

CC

CC

,.U*".,*

..,. "..*. C

CC

CC

CC

CC

C C

CC

O

Cl

CC

CC

Ct

CC

CC

C

C

LC

C C

lC

C C

CfC

,C

C

CO

CC

CC

CO

CC

CO

C

.w

e.

C

Cl

.r

C*

CY

.

OC

CC

CC

CC

CO

CO

O

11

11

11

11

18

11

1

CC

C C

C

hC C

r C

C

.C

r

CC

CC

CC

CC

CC

CC

C

Lb

L-

bL

%b

LL

-L

.-,-.*-------*-

OJ

=J

JJ

IP

:C

CC

C

OC

OC

bD

OJ

tr

CC

a

CG

OC

C;

CC

C

LC

............ 1

CC

CC

C

CC

C

CC

CC

C

CC

C

.... O

CC

C

11

11

CC

C C

OO

C

CC

CC

C

CC

CC

CC

C

CC

GC

C

...... C

CC

CC

C

11

11

11

CC

O

CC

C

CC

C

CC

C

m.

..

CC

t

11

8

00

cC

CC

CC

Cc

C0

c

CC

CC

GC

C O

CC

CC

C

CC

CC

CC

CC

CC

CC

C

OO

cO

OO

CC

cO

oO

o

............. C

CC

CC

CC

C~

CC

CO

1

11

11

81

81

88

81

u-U

Y v

IF

m

r.r n

wv

r

CCCCCC

------ <*.a.ss4.

--

-e

m-

...... N

WN

N

00

00

'

UO

U0

c

cc

-C

N

NN

N

---- =

tC

C

CC

C*

CC

UU

-

C

CC

C~

tO

CC

CC

4 W

-C

3C

C

CC

ON

N

a z

z-------~-

I'

VI

P

Z c

UJ

u L

a-

CC

CC

CC

CC

CC

CC

C

CC

oc

CC

CG

Cc

C

Ci .

CC

OO

CO

CC

OC

uC

&"I

CC

C.

CC

cu

.Y

Yu

Yv

~

c~

-C

~~

WF

DD

ID

U~

ID

~P

~U

~

QW z

~~

1i

n~

.m

~n

mu

r

ua

ia

00

0C

00

0C

00

0C

0

CO

CC

CO

CC

CC

CO

C

0.

CO

CC

CO

GO

CI

OO

CC

LI

CC

CC

OC

Ck

CL

C4

0

r-

e&

ao

aa

a~

mm

tn

~n

m

-Q

ZP

CC

CC

CC

OJ

JP

JJ

m

~.

bc.. ...........

I&

-S

cn

mt

"m

mF

.-.-

C-

--

0

n

~~

CC

CP

CC

PC

CC

C I

8 LU

0

00

G0

OC

OO

OC

CO

7.

OO

OO

GC

GO

OO

OO

O

I

(rc.

C~

OC

CC

OO

OO

OO

C

oa

o~

ca

ma

r~

nr

nm

r-

a

1

&&

A

CI

CJ

d.

4C

JQ

aJ

OO

Y

PL

L~

OL

CG

-P

UL

YC

~

I1

-

CC

-C

UC

YU

WW

OO

JJ

OJ

t

CC

QO

OC

CC

OU

DC

C

............... tj

1.-

z#

-a

z~

r~

mm

rn

rn

--

--

--

-

UI

WT

I.

~~

~~

~~

~~

~~

~~

c

= n

1b

3 r -

cc

cc

cc

oc

co

co

o 7

rc

cc

co

co

oc

co

o

w

8~

2

e

z

rn

n~

rw

r-

--

--

-

SC

PJ

J=

=J

JZ

=J

- a=*

G

1s

*

rr

-u

.lr

ww

IF

vL

rIP

LP

uY

Y(r

Z

IZ

CC

CC

CC

LC

CC

CC

L

-*

.-

Pr

CC

rP

e.

-*

CC

OO

CC

OO

OO

OC

.

-*

.-

-*

P.

-r

rr

*F

*

CO

Cc

CO

CO

Oc

CO

C

CC

CC

CC

CC

CC

CC

C

OC

CC

CC

CC

CC

CC

C

............. 8

88

88

18

88

8

88

8

-.-..-.-----.

30

C0

00

00

00

00

0

CC

OO

OO

CC

CC

OC

C

OO

oO

GO

oC

Oo

CO

O

............. -

88

88

81

88

18

8a

8

I

-----.----.--

C

00

00

C3

0C

CO

OC

C

0

2

w

vlu

uu

uu

--u

uu

-

A

---------n

-m

.. c

OO

Cc

OC

OO

OC

CO

.

CO

Co

CO

oC

CO

CO

O

>

OC

Cc

Cc

CO

CC

CC

c

............. 8

88

81

88

k8

88

&&

v

.

.-

--

.-

--

--

r-

C

CC

CC

CC

CC

CC

CC

0

4C

O~

Oc

oC

OC

OC

a

.C C

.C

C.C

.C.C

.C~

C.C

'C~

C~

C

............. %

88

88

88

18

88

18

8

..-.-

.---..-

-

- C

CC

CC

CC

C=

Cc

CC

:

CC

CC

CC

CC

CC

CC

0

33

c0

~0

00

00

3

CC

CC

CC

C O

OC

CC

~

OC

O~

CO

OO

oa

C

------------ C

OC

CO

GO

OC

OC

C

YU

YI

YI

I-----

CO

O0

C

CC

F

CC

CC

C

CC

C 0

00

0~

00

0

CC

CG

CC

CC

O

CO

OO

OO

C

CC

CC

CC

CC

I ........ .C

IC

C

.C

C C

IC C

00

00

00

00

00

00

0

CC

CC

CC

CC

CC

tO

C

Oo

oC

CC

CO

cC

OC

O

CC

CC

CC

CC

CC

CC

C

............. 'C

'C C

<C

.C.C

C'C

.C C

.C.C

.C

88

88

88

88

88

18

8

ii

ii

ii

il

li

il

--.-.e.-m

.-.--P--

CC

CC

CC

CC

C C

CC

C

C----C

-O

-C

--

CC

CO

CC

CC

CC

CC

C

I

CC

CC

CC

CC

CC

CC

c

CC

CC

CC

CC

CC

CC

C

C C

C C

C.C

C

C.C

,CIC

..

CC

CC

CC

CC

OC

CO

-, ................

CC

CC

CC

CC

CC

CC

C

CC

CO

CC

CC

C0

CC

C

C.C

.C C

C c

C C

lClC

C C

c

CC

CC

CC

OO

CC

CC

C

'C

OC

CU

OC

U8

C*

~.

G

O

CC

OC

OC

OO

OC

C

- 8

I8

~~

18

18

88

8

- x L

GC

LC

VC

CC

C~

CC

C

Cm

-C

-n

--

--

--

-

C

CC

CC

CC

CC

CC

CC

C

7

CO

UO

UO

W4

**

~4

*

W

CC

CC

CC

C,-

uN

nIr

bN

N

............. 0

<

8

CC

CC

CC

CC

OC

CC

C

CC

CC

CC

CC

CC

C

CC

CC

C0

C0

CC

CC

C

CC

OC

GC

CC

CC

C

cc

cc

cc

cc

cc

co

c

CC

CC

CC

CC

CC

CC

C

CC

CC

CC

CC

CC

CO

C

CC

OC

CC

CC

CC

OC

C

-n

--n

--.-b

n-m

e.-b

O

OO

OO

OO

CO

CC

OO

C~

CC

CC

GO

CC

00

c

oo

Cc

cC

3c

cC

c

n

CC

CC

CC

CC

CC

CC

C

CC

~O

OC

Cb

CC

CO

O

P

............ C

GC

CC

CC

CC

CO

C

&L

88

88

88

8S

88

88

9

OC

CC

OO

CG

CC

CC

C

CC

CC

CC

CC

CC

CC

C

CC

CC

CC

CC

CC

C~

CC

O

CC

C 0

C0

0C

C0

C0

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

CC

CC

CC

CC

CC

C C

C

&8

88

88

18

8L

88

8

CC

OC

---- K

CF

(P

C

CC

C

ObFm

CO

oO

CO

Oc

OO

OC

C

OC

OC

OC

CC

CC

OC

C

0.

0

0C

00

00

C0

00

CO

W

I

CJ

PJ

IJ

J-

--

--

-

- a

CC

CC

CC

CC

CO

OC

L

O

CC

CC

OC

CC

CC

C

CC

CC

CC

*Q

~C

3Q

0

00

0 0

0-e

----

............ P

C

OO

GO

OO

CC

GC

CC

IA

. O

CC

CC

CC

OO

CC

CC

C

C.

K.

DC

44

CO

CC

SC

o

~-

~-

-~

Oc

OO

CC

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

n.n

nln

#tu

nc

n.------

- - LC

%

G

CO

OO

OO

OC

OO

O

am

Cw

o-

--

3C

ue

~-

C

DC

LO

UC

G-

JU

CC

Ck

C

CO

DO

CC

t0

0U

C.

C

2 O

............ C

CC

C

OO

OC

3

CC

C

CG

CC

C

. C.

P-

C.

m U

l ul u

.

CC

CC

CC

3

CC

Ce

)C

I

OP

U6

~U

...... .

mn

.n

n;

~n

CO

CC

OC

o

c=

cc

o

-=3ae7*

NU

DO

00

C

CC

CC

C

*---c-

' .- . .' .' C . C

CC

O

C C

ilc

r

00

0

C Y

u.

--- ,

C.

4

OC

CC

O

OC

C

P3

lr.C

C

I

rm

uo

b

-U

KV

....

I.

C

..

- z

OC

OC

OC

CO

CC

QO

C

I~

r.

CC

CC

CC

CO

CC

C

C

~.

LO

oO

DI

rO

OO

wa

Du

u

~-

rn

an

.a

n.n

.n

nt

~n

hf

ia

m

e-

..

..

..

..

..

..

.

-

Lr

.*

20

aa

zu

~~

ao

C

-&

C.J

W&

C

b-k

6

66

00

00

00

00

00

4

00

-e-d----

C 20

csu

0, L

C;

->

Z-

N*

,J

W$

QL

Co

0

-k

-

-. -..- a

t2

0

OG

C

QAQ

T Y P E LAYPUT F l IF l ZOIIE ~ F ~ c R T D T I P u

FUEL ~ V P F - ( Y / L RANG:) 1 o . I P - I .?t - ,601 1 - r .be - 1.50) ? to.00 - 1 .on, u ( o n .a21 5 - [ .?? - .kc) 4 - ( .6n - 1.00) - o n - . 7 - ( . - 0 b - ( .0* - 1.00) a , (a.no , .nZ1 q - ( .n2 - .bo) 8 - f ,be - 1.sO)

IF FIISL MLTFYI~L FIJcL Pr :nPFQTrES

SP . YFLT D F " S 1 T V ( q / \ 9-F ) f L " / F T -

. luO0 a-1.n

.C)~IUT 97Z.s

.l unn u a l .n .I no u q 1 . 0

.naus 972.n .I U O ~ uq1 .o ,0qf15 972.0 . I n 0 0 UA1.n ,0140$ 972.0

r? I i O F R OF C n L L f l r b T l n u CLAD P~nPFOTTFq

1014 . C ~ ~ I O . q V . UFAT r)FNcrTV Tu I rK ; ' J I ~ R / H P - F T - F ) ( ? / I 4 - F ) ( L a I F T J I ( I t

. \ ? u ? 13.na 1 ~nnn u n l .n ,n tac l l f ) ? 13.00 .I rlhn u n l , n . 0 r ? n .qn53 LS.?O .I J ~ I -0 ,n1an , 8 1 0 ~ f3.00 . l o 0 0 un1.n ? n q ? n .?ho@ 13.00 . l r O O ( 1 n l . n .n>on . 5 i ~ b n i s .no . I aon u a 1 . n ;oqr?n . ~ 7 3 ? t ~ . n o . l o o 0 PAl.0 t n 1 9 ~ .?qO9 I3 .00 1 1 1 0 0 ,o ,012n .?h03 13.00 ,1000 Un1.n . @ ( ? n

CALCULATION P A R A ~ E T F R ~ 1 ATEPAL REblqTANrF FhCToa 9 / L PARAMETEQ TIIP~(ILENT MOMCNTIIM FACTOR ~HANVEL OQ~E!ITATTFM (nFGQEcS) CHANblEL LENGTH [INCHES) ~~UHSFR OF & # I L L NOoEq T O T A L T R ~ N ~ I F N T TIHE I ~ F c O U O I ) NUI~OFR OF TIME OTEPS NOMlklAL TIME STEP ( 9 ~ C f l N Q l ) POLL OPTION (0 - 40 ROLL)

NU9F INTEGQAL NnOAL UnDF 1~'TFGPAl NODAL N O . HEIGHT (IN.) LFMGTH ilkl.) ttn: H ~ I $ H T ffrl.7 ~ ~ r l G 1 n ( T I ' . )

2 2.0- a.0 2.000 3 a.n- 6 . 6 2.00'3 S 0.0- 1n.c 2.000 h 1n.o- 12.0 e.000 9 14.0- lb,@ 2.000 9 1h.n- 1 n . 0 2.000

11 20.0- 22.0 2.000 t a ??.no r r . 0 2.0nn

AYIbL NFDING

Nn o f I N ~ C G R A L M ~ I D A L NO. HEIGHT f I t i m ) LENGTH (IN;)

1 0.0. 2.0 ?,no0 u 6.0- - 8 . 0 ?.non 7 12.0- 14.0 2,000

10 1u.o- 2n.n ?.no0 TTMF ~ T E P VbRIATInN TIRLE

T I W E STFP SIZF [ S E C ) ( ~ E c )

o:ooo~o . I nnoo I P;PPOPO .l no00 15,00000 .sonon ?P,Q93PG .5nno0 25,0000fl ~ . o n o n 0

i ?o .noo~o C.OFOOO

MIYYNG PIR4qETERS A S F E P ~ L V r I x I n G H I Y I N G COEFFICIFYTS TYPE NP. CnRQELbTIPY rBFTb 0 4 ~ T b

I 1 .n?n -o.nno z 1 .n7n -0.nno I I .n?n -n.ona o I .nao - 0 . n ~ n 9 I .02n -0 .0 '~) 6 1 ,ntn -o.nnn

C ~ R C F D HIITYE rn r1011Ci rnN ~ ~ r r r r r : HnnEL nIQECTtON PAPAMFTcQ ~ ~ n ? r F i s v FbrTnR NnuF n. noo ;?no MnvF n. nOn ,?no NnwF n. n0n ,?no Nn*'E n.non , en@ N ~ N F n.nOn ,2 no NFVF n.nnn .?nq

19SrM.LY H l 3 S FLUY ~ R ~ c t I n u q ( A S S E V R L V F L U X F Q A C T I O ~ ) r 1 - l.OeoC+001 ( 2 - b.lq?F-nl) ( 3 - 1.00iE+n0) ( u - I . ~ U ¶ F + O O ) ( e - 1:cnqr+nni I 7 - b.O?5~-011

F O P C I N p F U N C T I O N S FnQ ~ E 1 7 FLUY TIP5 R E L L T I V E H E 4 7 FL IJY r+UI T I P L T F R S

(SEt)

E R L I I ~ . O ~ A L I T V

O.0On n . 0 0 n 0.non u e n n n o.ono 0 . 0 0 0 0.00n 0 .003 O.OOn O.Ofl0 o.fIOn 9 . Con 0 , non

FLOW rib-9 F ~ I I ~ ( L n / S F r ) MI R?HF-FT>I

. P ~ Q u ,5350 ,nun1 ,54U9 .nenq ,4909 .nboq , 5 5 3 q ,nuns ' 5 5 5 2 ,nuno , 5 5 5 ~ .nono 5 5 5 1 .nune :553m .ou07 . S T > * , 0 0 0 ~ ;5%h .01J07 ,55?4 .nun? ,552a . o u ( 1 9 - 5 5 3 u

OO

OO

Cc

0C

OO

aJ00JOa00a

.~.c

s.L

c

.c

~.0

0J

:

Ln

ln

om

mm

mm

IC

In

C

GC

C O

CC

LC

C

..........

.-. CC

CC

CC

CC

CC

CC

CC

-

=,L

--

-d

--

--

-&

--

-

- 7

-.

I-

CC

CC

CC

OC

C

CC

OC

-

-C

OC

GC

3G

c0

0c

?c

C

~J

00

0G

00

00

00

C0

0

............... W

30

0C

30

00

00

03

00

0

ai

a -

ace

o

oa

o P

-W

.~I-

, D

CE

CU

C-

FC

C-

OC

C-

L

&b

QO

.6

CL

C~

~C

CC

UC

n

o

.-. - 2

3 n

2C

=

I-

-J

aC

Cu

C~

Ce

uC

CC

I4

-

A&

c I C

W~

-~

PI

O nb

or z

cc

as

n,

tm

-z

~e

bu

eu

ew

L

8r

u.

3C

cu

CO

OC

Er

aL

cL

-F

~O

Yu

uY

vu

u.

rv

.u

Q

-V

J

UY

FY

YV

UV

K~

C

CI

)4

6@

44

CC

&6

Cg

C

uI

4~

CQ

Ca

CO

4C

Q0

0

.................. ,

..

I*

C0

0.

.0

*.

.C

..

0.

.I a

*

I

C

=

2 -

w

i -

w

r

r

w

- u

-

a

a

=

P- 4

z

=> z

0)

t

.: E

j

0)

-0

00

CO

OO

OO

OO

OC

e

m0

G0

00

0C

C0

00

00

W

CC

OC

CO

CC

GC

CC

CC

C

u

CC

cC

CC

CC

oC

CC

OO

C

u

-u

CO

OC

oO

OO

CO

OC

O

u

~U

CC

CO

OO

O~

OC

OO

C

............... 0

c*.............

E

.= >a C

~E

CC

CO

OC

CC

GO

O

>P

CO

CC

CC

OC

CO

Cc

C

. * .I.

. >

JC

CC

CC

CC

CC

~C

CC

C

-m

Ct

C0

30

CC

dO

OO

C

i-

10

00

00

00

00

00

00

m

e.

..

..

..

..

..

..

W

30

00

0e

00

0C

00

G0

c¶

- >

WP

JJ

rm

-r

uD

mU

'P

Fm

+

L-

OO

C1

NC

Om

mE

Q*

m

,.

..

..

..

..

..

..

n

3O

an

mm

mm

NN

NN

NN

z

om

mm

nm

nm

mm

mn

nr

k

J\

0 u?

-I -

CIL~ULA~ED F L i l l n C Q N O I T I O ~ ~ A T CHANNEL 8 ASSFWRLV 6

DISTANCE DELTA-P ENTHLLPY ( ~ t ! . ) [ P S ~ ) ( B r U I L n l

0 <o .~TIJ 3su.no .'I073 35n.nl

to ,641 6 3ba.U'

640 .-7*3 qT8,q?

n t o .qt 10 lbR.h5 10.0 m14h9 39R.22 12;o . 'n?T oOT.lZ 1 4,0 * ? i n 9 ~ 1 5 . 1 1 16.0 .?551 ~ 1 4 . 1 9 1 8;0 .191P (116.35 2010 - 1 FT6 ulh.01 P2,O ,0bl8 ulT.0b ~ 4 . 0 0.00n0 a1T.qT

TErPrRbTU*f D E N S I T Y EOLIIL. (DFo-F) (LB/CU-FT) O U A L ~ T V

hh(1.09 50.18 0.000 67K.13 5U.@A 0.000 b02.59 53.94 0.000 ?ICI.U? 53.79 0,Oon 1?8,7U 53.6(1 0.00(, l 'JT.12 93.49 0.000 lhU.75 Sj.34 0.006 191 .2b 53.21 0.00n 78U.Rq 53.18 0.000 7 8 ~ . 5 7 53.15 0.00n 7 0 ~ ~ 3 7 53.12 0.000 706.18 53.00 0.000 190.97 0 0.006

( 1- u i l ( 7- l n )

r?3.*h h89.*¶ TOT. *9 72b.70 ?47.*1 ?bT.*U 756. t R 791.47 no1 .nT nOb.65 n i t .en R15.eO

C A L ~ U L ~ T E O ROF TCMPFRATIIRFB AT T t u E 1 0.0000 OEtDYDS ROD Ntl. I S ASSTWI;LV 1 (FUEL TYPE 1 - CVLI~DER)

RnD 0.0: - ,174 ( ~ u . 1 Z ~ U E - ( F ~ F L D I ~ . ( 1 1 4 , ) ) - I - ( .17d) 2 * ( .I>@) 3 - ( . { 7 n l

ZONE HEAT FLIIY TYPE I .) r n n r u / n R - f 12 )

2.0 . n 0 7 ~ 4, n -1257 B 6.0 . ? l U b i' 8.0 e l 367 ?

10.0 e t Y 2 3 ? 12.0 .I F O ~ B 14.0 .1004 2 16.0 .PO19 1 1e.o .(I010 1 e0.o .no06 I 22.0 .nonu I c4.0 .no02 I

DATE FRPn I T E R 4 t I V C 8 0 L l 1 f l O N (1SlbJG T*F RCCIRCULATION MODULE T I M F 1 .!no0 0 1 I . I 0 0 0 I " !PLICTT OT 1 . I 0 0 0 FYPL~CIT OT • ,0931 ~ 0 - F I n

ITEPATIPN P W E $ R U ~ C cLnw F N E ~ R V ~ I O , P W f E P 9 E R R O R F R R O R E u 4 l I F H P X J

1 1 0 .nnnli ,0001 u 4 1 3

O A T b F R P H I T E P P T ~ V E B o L I I T I O N I I S T Y R T u F R C C I H C U L A T I O N M O D U L E T I H F I , 7 3 2 4 D T . n b j ? I M P L I C I T 0 1 I , 1 0 0 0 F X F L T C I T D T I . n H 3 3 h 4 O n t 1

D L T C F R n n I T E R A T I V E SClLI lTTCIIJ I J S T Y G T H F R E c I R c u L ~ T ~ ~ ) Y M O D U L E T 1 H C I . 9 l S Q D T I . n R s S I * P L I C l T D T I . i 0 0 0 F Y P L l t l T D T I .n83Y r O n E I i

DATA FRPM ~ T E R A T I V E S O L ~ I T I O N :J9TN[; T r F R E c I R C ~ J L A T I O Y rtODULE T I M F . l.bQ93 OT . .qbJu I M P L I C I T DT I . l o o 0 FVPLTCIT OT 8 . n 8 T r n o n f i

I T E P A T I ~ N PRE9BIJQF F L P ~ F Y t R G v PO. IUECPB FRW@Q FRQOP C r 4 X I E M A U J

1 I Z .b05? . n o 0 1 7 1 2

I T E D A T I ~ N no.

1 2 3 u

O A T ) FRpM I T E R A T I V E SOLl lTtnN U S I N G TuF RECIRCULATION MODULE T1MF 8 1 . 2 8 3 0 OT I . O u r 1 I M F L I C I T 0 1 .I000 F Y P L T C I T Or . . a a a u r f lnC j

I T E P A ~ I ~ N P D E ~ S U R F FLOW FNFRGV N f l . ~ U E F P B FRRUD FRPOD EMAYl CMAXJ

I 12 .no67 ,on03 1 P I 1 3

I T E P ~ T I ~ N P O E q S U R F c L n r F N C R G V F I ~ , $U!EPR F Q R ~ U F Q R J R E w 4 U I E M b X J

I ? .Otlh? ,000U 1 2 1 13

0 1 t h FRPM I T C P I T I V E J L l L ~ l f l n V t191NC THF P C r I Q C u L A t l O N M O D U L E T I n F 8 l . t Q U 7 D T 8 . o a h O I r P L I C r T 01 . .lo00 5 r P L ~ c y T D T 8 . n R b l w n n ~ * 9

C O O P A wrOLE C O R E CODE R E S ~ I L T S C A S F 1 F D R - T I Y x O A 4 3 s E M R L V Ct18R4,r lC S A Y P L C P R O B L E M

EQLJIL . Q U I L I T V

0.000 @.Onn 0.000 O.Onn @.OOn 0.00n o.cno o.Oon 0.ClOn 0.onn 0 * 0 0 n 0. OOn 0.000

C A L ~ U L A T E D F ~ l i I 0 C O N D I T ~ O N S A T T I R E rn 1 *Qh77 SECONDS P R F S 9 l I Q E a ?o..o P q I h CHANNEL 1 5 b S 9 F M R L v 1

A R F A (PO-IN1 .n56u0 .n5640 .n§hPO ,05640 .n5huO , n ~ b u o .nfhoO ,nShoO .n5bUO *IrSbOO .OSbUO .OShUO .P54UO

EIJU J L . OUALITY 0.00~ o.mn O.OOn 0.000 o.oan 0.000 0.OOn O.OOn 0.001) o,onn 0. OOn 0.060 o.ooo

~ C L n c I r v AREA ( F T I J E t ) ( $ 0 - l Y ) 1,qqTh ,11200 1 '5sEn .I 1200 1 : *a87 . I I P O O 1 ,5Q9.-3 .I 1200 I .'rnl? .I 1200

1 I .hnun .h0?n . I .r 1200 ieoa l.hl07 .tl200 1.hluP .I1200 1;~19a .lleoO 1 ,4?42 . I iron 1.6297 .llZOO I .oruu .i 1200

T E I ' P F Q D T ~ I ~ C D E N S I T Y ( D E G - F ) t L ~ / c u - F T )

bhu.nn 5U.lR b79.51 5U,04 ?Of .4h 53.87 7 2 l l . S ~ 53.68 7'17a79 53.00 ~ t o . s t 53.30 701 .Oh 53.13 eno.7n 52.97 ~ 1 1 .UU 52.96 Al1.50 52.98 4 l q r ( l l 7 2 - 9 2 F ~ P . ~ ! I 52.00 R10e9! 52.011

T E M P F R A T U ~ E D E N S I T Y ( D E G - F ) ( L B / C U - F T ) G

DbO.On S'J.18 bR0.10 54.01 71?.9g 53.77 t u u . i a 93.52 776eZb 93.25 klO7.8l 52.99 837.06 5 e . r s Ah?,33 52.53 OhP.5? 92 .52 8bCeOq 52.50 867.79 52.49 Abo.U¶ 52.48 871.09 52.46

vn l r ) r R ~ c T I n h l

n.on0 0.0qn n.ono o,ono n.ono o.nno n. on0 0.000 0.000 0.bbO 0.000 0,000 o. nnn

D E N S I T Y . P / C U - F T )

SU.lU 51J.00 53.03 5 3 - 7 0 53.63 53.48 53..33 53.19 53.17 5 1 - 1 0 ss;11 53.01 53.09

AREA ( 9 ' 2 - I N ) ,19300 , 1 ~ 3 @ b . I 9 3 0 0 .19soo ,19300 ,19300 .19100 . t ~ r n n . I 9 3 0 0 .! 9300 .79JOO . I 9 3 0 0 . I 9 3 0 0

ROO 0.0.' - . !TO ( IN. ) ~ ~ ~ F I E - ( F I J E c o I ~ , ( I N . ) ) - 1 1 7 2 - t . 1 3 0 ) 3 - ( . 1 7 0 )

F U E L T E M P F P ( T U O F ~ ( F . ~ * ( u E L A T I V F U A ~ T ( ~ ~ ( ~ I P O ) I

A Y I A L 20" H t A T F L l l x TYPE 4s lJQF r r L l l 1 D 5 L 4 n T ( 1 ) T ( 2i (111.) ( H F I T U / ~ I R ~ F T ~ ~ ( ~ I M - ~ - F T ~ ) ( i . o n n ) ( o . n o n )

0;o - 2.n .nnbS P 2 7 7 7 9 . b 696.1 h ~ s . 2 7 l o . n ?al l ;? t,n - 0.0 1 3 P 2 7 2 6 9 . 5 7 . 2 7 4 6 ' 7 7 . n l t . 3 u,0 - 6.0 m t l l b P Z 6 1 7 9 . 3 791.3 7 9 b ' 3 R27.R R65,l 6,O P.0 , 4 3 3 0 ? 2 b 9 0 4 . 7 8 4 0 . 9 f l ~ ~ b ' 0 R77.9 9 t 5 . 7 n , n - 10.0 * ! ? A 2 s z s * 1 9 . 9 s a ~ . 3 n 9 3 ' 3 o 2 u . i 9*n;6

10;O - 12.0 . l l h J ? 25U13.8 93O.R 9 3 5 ' 4 9b3.U 996.7 12,o * 14.0 .! 0 2 0 2 PSIOO.S 7 9 7 1 ' ~ 9 9 h . n ! n > ~ ; 2 ju,n - 1b.0 -.no27 1 ? 5 r r q , 9 963.9 9 6 3 ' 0 965.1 Q*?,P I ~ , O - 18.0 -.no111 I 2 5 1 7 1 . 2 959.8 959 '7 9 5 0 . 5 059.3 I n t o - 20.0 - 1 0 0 1 0 1 2 5 2 1 2 . 6 Q5h.2 9 5 6 ' 1 9 5 b . 0 9.5;9 9o.n - 22.0 - .no05 i 25905.9 952.6 9 q ~ ' b 992.5 0 ~ 9 ; s 7 2 . 0 2"D - 1 0 0 0 3 1 257S9.b 9 ~ 9 . 0 ~ n 9 : n 9 4 9 . 0 ~ ~ 8 . 9

OAT) F ~ P H I T E R A T ~ v F O F L I I T T ~ U 119JN1: TWF R F C I P C : I L I T I ~ Y n O D l l ~ € T I M F 8 2 .4 *3h DT . .nR9o ~ " P L I C l ~ UT . . 1 0 0 0 F X P L ~ C I T D T . ,069, w n n ~ . 1

D b T s FRPM I T C P L T ~ V E SOLI ITTON I I S ~ N G T U F R E c I U C U L I T T O N MODULF TIPF . 2.6~33 D T . .on97 I M F L I C X T DT rn .I000 FYPLICTT D T s . n o n u rnnr rn i

O A T ) FRPM ITEPATIVE S U L I . T I ~ N I ISJNG T U F RECI@CULLTIOY MODULE TIMF . 2 . w a i D T . . n q t l I M P L I C T T O T . l o o 0 F Y P L T C I T O T . n o l a v n ~ F . j

D r T b FRClM 1 ~ E Q l l l v E S O L l l T t f l N U S l N n T H F RECIRCULATION MODULE T I n r w 3 . 2 7 6 ~ D T I .0qu0 I M P L I C T ~ D T I .!on0 F ~ P L T C I T O T I .nqr7 MOPF . ;

I T C W A I ~ ~ N P R E ~ S U R F r L n w F N F R G V b f 0 . bJEEP8 r R P Q R FRROR C q L U I E M h X J

1 1 3 . O f 1 1 , onu1 1 a 1 1 3

I T E P I T I P N P R C ~ S U R ~ FLnw F N E R G V NO. PWfEPb ~RRfll? FRROR E u ~ X I E M 4 X J

1 13 ;O!F0 ,0047 1 Z 1 1 3

0111 f R p H ITEPITIVE B U L I ~ T I ~ M 1 l s I N 6 T Y E R E c I @ c u L ~ l l o N MODULE TIMF w 3 . 6 0 9 h D T I .oQ?O I r P L I C I T 01 I , 1 0 0 0 FYPLTCIT D T 1 . 0 9 7 n v O n E I (

rn ITEPATI ( !N PPEJSURF r ~ n u FNERBV Ft@. SWEEPS E R R O R FQROR CMAYX E M 4 X J

P 1 1 3 ;O,QU ,0056 f ? l 1 3

D ~ f s FROM I T E P A T T v E 3 O L l l T l n P l ( I S ~ N C T H F R C C I ~ C U L ~ T I O Y MODULE T l n F s 3 . 9 0 5 5 O T I , 0 9 9 5 IMPLICIT O T I .IOOD EYPLTCIT D T I ,Inns r o n F I i

I T L P I T I P ~ U PPE351JRF FLnW f N E S G V 110. RUEFPS ~ R p t l R FUROR C M A Y I E M I Y J

1 i 3 .n?oo . o n g o 42 R

D A T d F Q P M I T E O ~ T I V E S n L ~ l T 1 0 t 4 u S l W T H F R E C I Q C u L A T I O N MODULE TIPF I a,oos5 D T I . in00 I M P L I C K T O T 1 . l o r 1 0 C U P L ~ C ~ T D T 1 , 1 0 1 ~ r nn r m i

EPuII.. nuALIrv

0.nOn O.OOn 0.0On n.onn 0 . 0 0 ~ 0 . OOn o.ono 0.000 0 .000 0.000 Q.oOn 0.00n o.onn

tn l lxc . v n r n F L ~ W rarqs F ~ I J Y v € ~ n c I ~ Y A R E A Q U A L I T Y c W ~ C T I O N I L R / S F C ) I M ! R ~ H P - c T ~ ) ( F T I 9 E : I I S Q - I N )

0.000 a.or>o .a943 2569 i : 7 i 3 s .i l e o o 0.000 o,nno .OSSU : ? 4 5 ~ 1 3 ,11200 0.Or)n 0.600 .05Su ,2961 1.11'46 .11?00 0.000 0.000 . ' )55a ,29150 r .1190 .! l e o o O.OOn 0 . 0 ~ 0 ,055 4 ,295'1 1.3177 . !1200 0.000 rl.000 .OSSs , 2 5 6 ~ 1.520? .11200 0.000 0.000 .05'1h ,?ST1 1,3235 . I 1 2 0 0 0 . 0 0 ~ 0 . 0 ~ 0 . n 5 9 ~ ,9376 1 .T?TII .11200 0.00n 0,onO . O 5 3 q %8'191 1.331n . i l 2 0 0 O.OOn 9,nnO , 0 5 9 ~ ,2'1@7 1 .1357 .11200 0 . 0 0 ~ 0.000 .05bc ,2590 1.7n ln . i l ~ 0 0 0.000 n,ono . n 5 6 r ,2609 ! f a ? ! . t l 2 0 0 0.000 0 . 0 ~ 0 . O S ~ U . t h t n 1 o . I i e o o

D I S T ~ N C F D E L T A - P F U l H d L P V t r y . ) ( P S T ) I S T U I L R )

0 .Pb00 15U.PO ? t o , 1 8 6 ~ - ~ n . a 3

2; a7139 367.50 .hUl 6 159.4R

8 :n .5605 376.15 10,0 .U977 382.90 I ? , " .42SI tR9.cl3 iu,n ,1549 199.60 16,o .?R18 197.93 1 R,O . ? I 2 6 7QQ.71 P0,O a1019 ~ 0 1 . 0 6 ?P,O e0709 uO?.r)R $4.0 o.o000 002. Rq

C I L ~ L I L A ~ E O F L I I I D C O b f b ~ T r f l b J q A T TI"€ m 4 . 0 0 S 5 ~FcONDS PRFSJL IRE 20:0 PqIr CHANNEL 10 A S S F M R L V 7

A R E A 190-IN) . 1 9 s o n e l 9 3 0 0 .I 9 3 0 0 . I 9 3 0 0 . 1 9 3 0 0 . I 9 3 0 0 . I 9 3 0 0 . I 9 3 0 0 . 9 9 3 0 0 . 1 9 1 0 0 0 1 9 3 0 0 . 1 9 3 0 0 . 1 9 3 0 0

C A L ~ U L A T E D R O F TCMPFDATIJRFS 4 1 TTt4E m ~ . O 0 5 5 9ECDN0S R O O NO. 13 A ~ S F M A L ~ 1 (FUEL T Y P E I - CYLINDER)

I N P U T T R A N ~ I E N T T I M E C ~ M P L E T E D

NRU SAMPLE PROBLEM

One o f the p r ima ry concerns i n commercial l i g h t water r e a c t o r s a f e t y i s

t h e h y d r a u l i c and m a t e r i a l behavior d u r i n g t h e heatup, re load , and quench

sequence o f a l oss -o f - coo lan t acc iden t (LOCA). An exper iment has been designed

a t PNL which w i l l be used i n t h e Canadian Na t i ona l Research Un i ve rsa l (NRU)

r e a c t o r i n an at tempt t o p rov ide da ta on the LOCA. The COBRA-WC code was used

t o model t h e p r e - t r a n s i e n t phase o f t h i s exper iment. Dur ing t h i s phase, t h e

assembly i s operated i n a steady, low-power c o n d i t i o n us ing steam as t h e coo l -

ant . I t i s r e f e r r e d t o as t h e p r e t r a n s i e n t phase s ince t h e zero- f low, LOCA

t r a n s i e n t i s i n i t i a t e d f rom t h i s phase by c l o s i n g the steam i n l e t va lve. Th i s

problem was chosen as a sample problem because i t r e q u i r e s us ing bo th water and

steam i n the same model ( b u t no t i n the same computat ional c e l l s ) and a l s o

i n d i c a t e s t h e use o f t h e heated w a l l model.

The des ign o f t he NRU t e s t assembly and i t s i n t e r f a c e w i t h t h e r e a c t o r

c losed loop i s i l l u s t r a t e d by F igu re E.9. The NRU t e s t assembly i s composed

o f the f u e l p i n bundle, t he shroud, and t h e pressure tube w i t h t he two duc ts

j o i n e d t o common i n l e t hardware below t h e p i n bundle. The l i n e r i s t h e i n n e r

boundary o f the r e a c t o r c losed l o c p and i s surrounded by a 1 arge volume o f

water mainta ined a t an approx imate ly cons tan t temperature o f 100'~. The

geometry o f t h e 32-rod bundle i s based on a B&W 17 x 17 a r ray . The f o u r co rner

rods o f an o therw ise square m a t r i x have been removed.

The COBRA-WC model used t o s imu la te t h i s exper iment i s shown i n F i g -

u re E . l O . The NRU assembly has been modeled w i t h 41 channels i n t h e p i n bundle

and f o u r i n t h e shroud-pressure tube annulus. The geometry o f these channels

and t he numbering scheme i s a l so shown i n F igu re E . l O . The shroud and pressure

tube were modeled as t h e r m a l l y conduct ing w a l l s w i t h a heat gene ra t i on o f

0.2 w/gm i n each. The l i n e r was n o t modeled separa te ly , b u t i t s thermal

r e s i s t a n c e was combined w i t h t h a t o f t h e a i r gap i n t o a f i l m c o e f f i c i e n t o f

6.0 ~ t u / h r - f t ' - O ~ . Th is f i l m c o e f f i c i e n t was assigned t o t he duct -water

i n t e r f a c e by model ing t h e surrounding water as a second assembly and s p e c i f y i n g

t he f i l m c o e f f i c i e n t . Near ly constant - temperature

JRE TUBE

NRU EXPERIMENTAL ASSEMBLY

FIGURE E.9. NRU Experimental Assembly

water was maintained by specifying a large mass flow ra te of water over the

outside duct. The radial pin power profi le i s given as Figure E.11 and the axial power prof i le i s given as Table E.7. One rod, marked by an "xu in Fig- ure E . l l , i s used for instrumentation and has zero power.

The analysis of t h i s t e s t required the use of both steam and water with a

single phase code. The problem was circumvented by using a property table,

(Table E.8), as input with low-temperature (100 '~ to 125'~) water proper-

t i e s a t 1500 psi and 40-psia steam properties a t higher temperatures (267.3'~

to 1500'~). Since the temperatures of water and steam never overlap, t h i s

permitted both phases in the same model. For th i s problem the check on saturation temperature based on the system pressure i s meaningless, and so the

pressures do not necessarily correspond with the saturation temperatures in

Table E.8. The only requirement i s that the temperature a t the highest pres-

sure be above any temperature encountered during the calculation. The operat-

ing conditions for the simulation are l is ted in Table E.9.

A l i s t ing of the computer output of t h i s sample problem (provided here)

shows the input cards, the edited input, and the calculated resul ts .

TABLE E.7. A x i a l Power Profile

NRU R A D I A L POWER PROFILE

FIGURE E . l l . R a d i a l Power Profile for N R U Assembly

PLIQ (PSIA)

TEMLIQ 0

HLIQ ( B t u / l bm)

TABLE E.8.

CONL IQ ( B t u / h r - f t - f )

F l u i d P r o p e r t y

CPLIQ VLIQ VIS IQ (B tu / lbm- f ) ( f t 3 / l b m ) ( l b m / h r - f t )

TABLE E.9. S imula t ion Operat ing Condi t ions

Cool ant Steam

F 1 ow 3000 H/hr

Pressure 40 p s i a

I n l e t temperature 471°F

Water temperature 1 0 0 ~ ~

* * * + . ~ * * * e ~ ~ ~ * * * e * t e * e t * ~ ~ ~ * * * c * * * * + * c * i ~ ~ 1 3 13 T r E cn3Rb-WHl~E C O R E CODE F U R H I ~ L T I * J S E M R L Y LMFRQ A h t A ~ Y q I q

'JRlTTEtI bT P A C I F I C N O R T Y + * E Y T L A M O R ~ T ~ R Y O?IRIFIG 1977-19~0 oOF CUIITRACT AG1')ZOUU AND cR@Ro COb.tT PACT D l 81 3.00761

CORPA D T M F N S ~ ~ N PAREMCTFRS MA. I Mr. 50 t.1. 5 M,18 1 k t n m ?9 E(M8

t * 36 M$. 1 Y W S 32 MY. 2'5 rim 1392 NT8 fl JE. I J IP. u T V . b IN. ,'

ME. 25 t!<s 370 !108 7 t rT . 1 8 U rltm T

I T . 2 I H W h

MG. 90 M L m 1 MP8 31 Y V . 1 MZ. 10 1nm 36 IU. 1 x 8

? 1 NRU SAMPLE PQrlBLF" z I 13 11 1 99,999 b7.99 .363'J .998 . 0161 I; en . IZO. 67.97 .q701 , 998 .0142 c s o I ?so. 590, 0 1s .son 10.3 7 "0. 2h7.3 116'4.8 ,0166 .521 10.50 P 50. 300. 11n0 .b ,7169 ,509 I i . n ~ o 60. ~ 0 0 . 1236.1 ,0196 .‘'go 12.62 In 70. 5017. I 2PS.O -0228 ,405 10 .1 ) 1 1 80. 600. 1331.b ,0262 ,007 15.69 1 ? 90. 700. I38?.5 ,0299 . 090 17.20 I 1 i o n . eon. ! 03~2, 1 ,0337 ,500 1 R .TO l o 110. 9 0 0 , IWR2.5 m3577 ,508 20 .20 I s 120. lnoo. 1534.7 ,0019 .917 21.79 1 i- 230. 1500. 1803 .1 ,0638 , 560 Pq.17 I? ? 2 ? 1 P , 164 ..20 6". - 1 S O

l o ,316 -.25 61. * I S O ?; rs so21 .R * l l 0. 2 9 0, 0. 0.5S.55 ;? ? t 1 26 ? 7 0 . ~ o 2 0 8 ~ @ b ~ 5 . 1 0 U 2 , l a 5 ~ ~ 1 ~ 7 ~ ~ ? ? ~ 2 ~ ~ 7 0 ~ ~ ~ 1 2 5 ~ ~ ~ 0 2 . 3 9 ~ ~ ~ ~ 3 ? 5 ? 11 . 4 7 ~ ? . ~ 2 0 P , 5 b ~ s . h 0 1 1 2 . 6 ~ 1 5 A , b ~ 7 5 ~ 7 ? ~ 2 . 7 7 0 R . 8 1 ~ 5 ~ ~ ~ ~ ~ ~ ~ ~ 5 n , 9 3 7 5 2' .~?~?l.OOO ?6 0 . ~ 1 7 3 ? 3 . 0 4 0 6 ~ ? 7 ? 7 . ~ ~ ~ ~ ~ 6 ~ ? 3 ~ ' ~ ~ b ~ Q 3 3 0 1 ~ 0 ~ ~ 1 * 2 ~ ~ ! ~ 3 0 ~ 1 . 3 9 2

3 ? 57 9 11

5 s -6 * 7 5 n 5 0 CP 0 1 h? 67 h 11 6 P'

6 6 6 7 h P 6 0 ? n 7 1 7 ? 7 r 7 Ll

7 4

7 C 1 7 7 f 7 0

8 0 8 1

a ? 87 P F

e- ar- 07 C P no q I' 9 1 9 ? P 7

V 18 9. '46 97 9 P 0 0

1 0t' I 09 1 0 2 1 fl- 1 0 b 1 0G

9.8

9.8 n.8

n.R n.a n.8 3 . n n. 9

n, R 0 R n.q n.3 0.9 n. n n. n.8 n.f ' 0.n n.fl 0. 9.R 0.8 0 . R r). 8 n.R n. 9 0.8 n.4 n.9 0.8 7.9 n.8 n." 0.P n. 8 0.P n. o 7 .0 'I. 0 n.7 n. r)

n.R r ) . * 0.q n. 8 9. 4 n. 9 n.8 n.q

0 1 2 3 U 5 b 7 B ~ ~ ~ U 5 ~ ~ ~ 9 n ~ ~ ~ U ~ 6 7 ~ ~ 0 ~ 2 l ~ 5 b 7 R O 0 ~ ~ t ~ S f . 7 d 9 0 ~ ~ 3 1 1 ~ b ? 8 ~ O i 2 3 U ~ 4 7 ~ ~ 0 ~ 2 ~ U ~ b 7 B ~ 0 1 2 t U ~ b 7 ~ 0 ~

1 1~ ,556 n.p 1 I ? e59h 0.4 1 16 m45h 9.8 1 17 .sSb n . 11 I 18 .55h 0.9 1 19 ,556 0 R 1 20 .:sh 0.4 I 21 , 5 5 6 0.8 1 2 2 .55h n. n 1 23 ,556 0.0 I 24 ,556 n. e 1 25 .59h 0 . R J 26 . 55h 0.n

1 27 .55h n.R 1 2P .59h n. R 1 29 .5Sh n.R 1 30 .43h n. 8 1 31 ,556 9.8 1 32 .54h R e 8 1 33 .55h n.8 1 34 m55h r), 8

1 35 .qSh 0. B I 56 .53b n. R 1 37 .5Sb n.0 1 38 . sqh n. R 1 39 .55h n e e

40 .5Sh 0 . 8 1 U I ,556 n. R I 42 556 0.0 I 43 .55h 0 .0 I 110 .55h r). 0 1 03 .556 n. '3 P 1 ,556 n.n 1 1 . Q B * n. 4 1 2 .On4 n.8 f 3 . Q R ~ n.3 1 1 1 ,996 n. R 1 ' 5 .QRh 0. 9 1 b . ? a h 0.8 1 7 . Q * 6 n.4 1 R .96h r). R

1 9 . ~ b h r). 8 I 10 . Q R ~ n.9 I 11 .Q"h r ) .R

1 1 2 .Qqh 0.9

! 13 .='Rh 'I." 1 I U . ~ e h n.8 I 15 . Q n h 0.8 1 l b .oqh ?. 8 I 17 . Q * h 0.9 I 1 8 .oat, 1 19 , q 4 h n. * 1 20 .QRh , l a n

1 21 . 7 R h 9.Y

n I z 3 u 5 b I R , ~ ~ U ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ I ~ ~ ~ ~ ~ ~ U ~ ~ ~ ~ Q , I ~ ~ ~ ~ S ~ ~ ~ Q I ~ ~ ~ U ' ~ ~ ~ P Q ~ ~ ~ ~ U C ~ ~ ~ Q O ~ Z ~ U ~ ~ ~ Y Q ~ ) I ? T ~ + ~ T ~ ~ ~

I N P I ~ T F@R C A S F 1

115 Uh t l ? '44 -0 -0 - 0 - 0 -0 -n - 9 -0 -0 -n o - n -n -11 .O -n .n n -0 -0

n n o c r 0 1 o 0

-n I - 0 -n o n 0 7 n 2 1 0

GC

IC

CC

CC

C

CC

CC

CC

C

PC

CC

Ct

r

A,

..

..

..

..

..

..

.

CC

OC

CC

CC

CO

CC

C

'2

OC

CC

CC

CC

CC

CC

C

r

rn O

CC

Cn

CC

CC

OC

G

2~

OS

C~

Cc

CC

CC

cC

C

Wb

t

ra

m

Z.

*

cv

c

-.N

O

CC

O

4.

.

IL - N

.

? 0

CW

W

tn

a

I+

)

>

"Ct

P

P

..

..

.

-- L-

-.

..

..

-.

..

--

.-

..

.-

--

-.

.-

.-

.-

LI

I-

.-

--

~3

0m

3~

33

CO

CO

C3

63

C3

0S

C;

o9

O3

C3

9~

C,

3o

33

OC

i3

OO

Cc

oo

o~

~

RC

GN

QC

CC

CO

CC

CC

CC

CO

CC

CC

CC

CC

CC

CC

OC

CC

CC

CC

CC

CC

CC

O

400-0000000C0CC000000c0C000000000000000c00000 -

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

18

1

&I

11

1

88

1

81

81

81

81

18

88

88

81

11

81

11

81

88

---------..--.-------.------------.-------.--

~.

+~

CC

CC

~O

CC

CC

Q

CC

C~

C~

CC

CC

CG

CC

~C

~C

CC

CC

C~

C~

C~

ccc

c

mn

n=

n

lr v

n

- - C

----u

LV

u-IU

-----IC

---"

---"

-L

------------*----

L

CC

C C

CC

CC

PC

C-

C

P-

--

-r

PP

FC

C-

mm

-P

*C

C

CC

C~

~C

CC

C~

~~

C

4

nn

nw

nn

n~

an

.~

nr

uu

on

~n

~o

ou

u

oc

cc

nc

cc

cc

=c

co

cc

oc

cc

cc

cc

c

CC

CC

CC

~C

CC

CC

C~

~~

~~

~~

CC

CC

C~

-c

cc

cc

cc

cc

cc

cc

cc

cc

cc

0

v

,v

.Y

mv

vm

~u

,Y

Y.

YP

OY

u.

CO

PJ

PC

,C

IO

CL

c~

Gc

cc

Co

cc

cG

GC

cc

cc

c

...................................................... .....**....*.

88

18

8

81

88

~1

18

88

88

~8

~8

81

..I... ........ .......

.........................I...-.. C

.....-...-.......I...

r.

C

I.

I

L

LL

uC

b"

uL

b-b

L~

r-c

bu

bu

b-r

-*

b--u

uL

bL

-L

--u

bL

bb

Lb

C

-C

C-

C-

LI

--

C-

CC

CI

IC

--

--

P-

-P

-C

--

--

--

--

--

~~

~~

--

-

+

nn

ac

nn

nn

nn

nn

nn

nn

na

nn

a-

~~

ci

nn

nn

nn

nn

nn

nn

nn

nc

c~

cc

=

CC

~C

C~

C~

CC

CC

CC

SC

G~

CC

~P

~-

-~

C-

~~

C-

CC

C-

-C

~-

~~

~~

~

~u

viu

~~

~m

w~

v.

r~

~m

rr

um

v~

w~

~w

.v

.a

r~

nv

v.

~u

r-

~v

v.

cr

uw

r~

vu

c

cc

co

c

U

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

c 9

88

18

1

..--.-.----------.---------.---.------------.

CS

C C

OO

O

CO

CC

C

OO

OC

OC

OC

OC

OO

C

CC

OC

CO

C

c.C

CO

CG

Oc

0 C,

0 C

m 4

- 4

u. -

as-

. .

00

0C

'o

e0

0

CC

OC

CO

OC

-

nr

cL

m-

o

C, C

c

CO

C

OC

C

0 C

. C

0 2

0

C-

C'

... O

C3

CC

C

00

0

ca

t

--- o

w0

, -- - ...

,-

--

CC

CC

CC

C

Oc

OO

C:

CO

O

CC

OC

CO

CC

CC

CC

C

00

00

0

OO

OO

CC

- -

La

-

CCCOCCCCCCOCCCCCCCCCCCCGGCGCCOGO

3000000003030000000000303003C)300o0003

ccCCGCCCCCCCCCCCCCCCCCCOCCCCCCCC

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

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

QC

CC

OG

OC

CO

CC

CC

CC

CC

CO

CO

CC

OC

OO

CG

CG

1

11

11

11

It

1#

I1

11

11

~1

II

II

1I

II

II

#I

l

OO

OO

OO

CO

oO

OO

OO

OO

OO

Oo

0O

OO

OC

OO

OO

OQ

C

CC

CC

CG

CC

CC

CC

CC

CC

CC

CC

CC

CC

CC

CC

CC

C

~C

CO

OO

OO

GO

O~

~C

~O

GC

O~

~~

OO

CC

CC

GC

O~

OO

C

CC

CC

CC

CC

C~

C~

CC

C~

CC

CC

C~

CC

CC

~C

~C

~

-----d#---------

CC

CC

CC

CC

CC

CC

CC

LC

C

Ct

CC

CC

CG

CC

CC

OC

C

..,....... C

* ...... .

.*

.r

..

..

z ................................ 3

SC

~U

N-

N~

~O

J~

OC

S~

DO

-~

~-

JV

IO

CE

ND

=-

V,

r

NN

NN

N

NN

n

--

-+

~-

--

--

~-

NN

N

C

', -

Uw

-U

u'-

u-

~-

-u

--

du

w-

-w

-w

"-

--

"-

--

d

J

m J

T

W

W7

. m

zm

I

EI

Z

e r

0

Q

0

tL Z

C

; -(L

C

CC

I-

- 0

-

CZ

kC

C

ZY

7cz-

0-0

-3

.0

C

- 30

~

tz

-~

~~

u~

~~

~c

-n

w~

ur

~u

u~

~n

~~

u

&C

=D

c-n

C m

-

--

--

--

--

-N

aN

NN

Nh

NN

Nm

Wq

W,

U

S0

O

JO

DO

C

tG

O

u J

U

S ~ J B ~ H A N N E L IVPUT ~ L T A FnR AJ3eHRL.Y EIIIWBER ? LOCEL ?LnRAL Fn lcTh I AREA l*'ETTFO HEATED HVDPAIILIC ( r P J n C E l l l r H n u r ~ F l NO;, O o l ~ I b ' f i , MOM. C, V. LENGTH) CH roo pn ~i FACTDO (91)-IN) P E R T M . PERIM, OI IMETC~

T vPE (1'1) ( I N ) ( I N ) I 4 6 2 1 0 . o n n 0 0 ~ n n o o.ooo0on u0.00nnon f n,-.nn(r.-.non)( O,-:oon;-:Onn1( n,-. ion,-.noO)( 0,-.one,-.nro\

THEPHAL P R D P E P T ~ E S I-IF FIIEL M d t E H I r L 3 'JQDER OF C [ l L L O r r T I n N FUFL PPOPERTIES CLAD PROPERTlEq

T Y P E C O Y O . SP. H F A T n ~ t ~ s ~ t v Q I I . COFIO. q ~ . H F L T 3EL191TV t u t r ~ ; G I P r o r ~ n . c n L C r o r S Y M IDTVP Nn. (R/H?-FT-F) ( 8 / ~ 8 - F ) f ~ n / F T y ( I N , ) , ( ~ / H Q - F T - F ) ( R / I R-F) (LR/FT.I l 1 ( R / ~ ( Q - C T ? - F ~

1 2.62 .n750 6 ~ 7 . 5 .3?3n 11.40 .nnUO uo5.0 .n>zl i r0a.nn 1 1 1 1

LOSS DIVEUlEI l FLOJ f l P T 7 0 ~ CuEFF I C ~ E N T GIP NO. c ~ n w

PCSTEIIT

. A 0 - . nono

. A 0 - . nOnO

.9 0 -.nor10

.9 n -. nOn0

.4 3 -.nOqO

. 9 0 -. nOnO . q 0 -.nnnO . q 0 -.qOnO

.q n -.on00 . J n -.nOlrO

. 9 0 -. nnnn - 4 D -.nOnO ." o -.nono .a 0 -.nono . @ 0 ..nnoo . 4 0 -.nun0 .a 0 -.nono ." 0 -.nOnO a n 0 -.?On0 . A n -.nOnO . @ 9 -. nono .n 0 -.-On0 .9 0 -.nono . A o -.nOnO . n r.qO1-10 . d O -.nOnO . 9 0 -.flOnO .@ n ..nOn@ .a O -.?On@ .A n -.?On0 .I\ n -.nOnO

500C0C00CC0000003CC0C~000000003000C03C0000c~cccc0G00c

=J

CJ

~a

1J

03

00

=0

0&

&&

&.

L&

*&

&&

&

&C

&&

&&

C&

CC

&&

<&

&~

&C

t&

C3

.J

Ct

C

--

--

~-

--

--

--

--

-U

UU

VW

YV

KL

~Y

YV

V

UF

~U

WU

V~

UK

V~

UW

KU

~~

~F

WV

iV

I~

~U

~U

G

CC

CC

CC

CO

C G

CO

CC

~U

~V

LT

VY

1Y

LT

Vm

K~

yl

UY

U~

W~

UU

UI

P~

yl

V~

VL

T.

YV

U~

IC

U~

yl

VI

V~

LT

U~

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

1 1 5 I I 1 I 1 2 I 1 9 1 1 " 1 1 5 1 16 I 1 7 1 1 8 1 1 9 ! 2 0 1 2 I 1 i?? 1 2 1 1 2 1 1 2 5 1 2 6 1 2 1 1 2 8 I 2 0 1 3 0 I 3 1 1 32 1 3 3 1 3 4 1 35 I 3 h 1 3 1 ! J P 1 3 9 1 43 1 U ! 1 4 2 I 3 I U 4 1 us F I

NOOF I h J T F G s b L N094L NO, H E I G H T ( I N . ) L E N G T H [IN.)

1 0.0- 6.0 h.0ofl U 1 P . C - 1 8 . 0 h.000 7 3h.0- u2.0 h ? n o n

in 54.0- 60.0 h . no0 1 3 I ? . @ - TR.0 h.090 I 6 9 0 . 0 - 96.0 6.000 19 1OR.O' 1tu.O 6.fl00 2 12h.o- 1ta.o h.000

M I X 7 N G p I R A H E T E g 9 A S ~ E M R L Y ~ I Y I N G H I Y I N G c O F F F I C T E Q T S T v P F Np. C O R Q E L A T I O Q A R F T ~ F R F T A

I 1 1 -0.000 2 I IS -0.n00

4 9 3 F Y P L Y M A 9 9 FLUY F R ~ C T I ~ N S ( A S J F M B L V 9 FLUY F Q A C T I [ ~ N ) r i - 1.onoFtonl ( 2 - ~ , T ~ ~ F + o o )

D A T E FRnW I T E P A T I V F S0LllTlnpl

E U U I L . Q U A L I T Y

(].@On 0.0on O.nOn 0. Don 0.00n 0. OOn 0. Onn 0.03n 0.oon 0. Don o.Oon 0.009 0.000 0.0o0 0 . onn O.Onn 0.000 O.Oon o.on0 O.00n 0.000 0.000 0.000 0.000 O.nnn

P O D P O ~ ~ E H PELIVEFED T O T H E CIIDl.ANT 1 3 3 . 9 9 3 BTU/SEC

VOIR r A A C T I O N

o.r)no 0.000 0.000 0.000 n.ocrn n,ono n . r ) n ~ o.on0 n.000 0.ono n,oqo n.000 o.ono 0.300 o.on0 n.ono o.onn 0.000 0.000 o.onO 0,ono n.ono 0.900 0.000 0.r)nn

.lo139 4 4

' E b ' P F R b T U a t O E N S T T Y ( D F C - F ) ( L ~ I C U - F T )

i n ~ . o a b2.31 19P.01 62.31 lOP.0 3 62.3? 1nn.oo 62.33 lOn.06 62.30 l n ~ ~ o q b2.30 1no.19 b2.3n 1no.13 h ? . 30 i n c . l h 62.30 !no.!? 6 2 - 3 0 1nn.2' 62.50 100.26 62.30 i no. 3 , ) 62.30 ln0.3n 62.30 ln(r.34 62.30 !nn.u2 62.30 loa.as 6 r : l n 1 0 0 . ~ 1 62.30 l ( I p . 5 9 62.29 100ebn h2.29 100.bu 6 2 - 2 9 l n 0 a b q 62.29 I OD.?? 6 2 - 2 9 1nO.lb 6Z.29 i n n . 7 ~ 62.29

EQU IL . o u r L I ~ y

O.DOn 0. Pun n.oon 0.090 oaOUn 0 . 0 0 ~ 1 O.OOn 0.OOn 0 * (100 O. n o 0 0.000 O.00n 0.000 0.900 OIOOn o.oun 0:Oon 0 . OOn O.OO(, 0.000 0.00n 0. 0 0 n 0. OOn 0.00n O.Onn

pDn D o w E R 0 E ~ 1 v E a E o 70 THF CnOl A N T O.000 R T U / 9 E C

FNTHALPV [ B l U / L P I

1 1 99.05 1199.25 1190.77 12n1 .TO l>OU.Pb 1 ~ 0 9 . 5 9 1213.76 l c ~ a . n 2 l ? ? ? .55 1?3$.h3 l ~ o u . 7 2 1 ~ 5 4 . 5 2 l?bU,nh lP75.60 128h.49 1297.71 1708.73 1319.119 112q.R2 1339.77 11uP.5b 13'36.65 17b3.h? 1 7b9.56 1 ~ 7 u . u n

T E M P E Q b T l l l ( E D E N S I T Y ( O E G - F ) (LHICU-FT)

~ ? s . ~ a .09 3 ~ 5 a 1 ,09 326wUU .O9 329.92 .C9 335.85 s o 9 3uO. lq a09 35u.54 - 0 9 367.11 .08 3R1 . R Z a09 39P.hU . O n 417.12 .OR 437 ~ 2 9 . n5 4SP.Sb .07 URO.67 .O? 503w2h .07 526 .13 - 0 7 94R.Bq .OT 57F.qb .0? 5'97.23 .Ob b lP .20 .Ob 670.6') .Oh 6 4 7 1 4 .Oh 6 h l .Ob 673.54 .Ob hA3.Oq .Oh

~c

00

0C

cO

CC

cC

cc

CO

CC

oC

Co

OO

0C

a-0CcOUOCOOOOOOCCooCc~GCo3O

U~

OC

CC

C~

CO

~C

OC

CC

C~

C~

~C

C~

OO

C~

~

QO

OC

00

00

00

00

0O

CO

C0

0O

OO

OO

Od

Q

OC

CC

C~

OC

CG

CC

CC

tC

cc

cC

cC

cC

CC

C

- ......................... CCCCCCCCCCCCCCCCCCCCCCCCC

+4

4------------------4

---

c,.........................

m3

n N

NN

nn

lN

NN

NN

n~

NN

NN

NN

NN

NN

NN

m

ZU

OC

9O

Ld

CO

Z4

SS

L~

09

SO

9O

SQ

O9

9

w\

r 1- u o r * - U s )

5 ? ? . 0 0 722 .ph q ? n . q q ?lbn.n5 35?.n7 ThS.75 - a n . T G 3 9 7 . i O ni5.74 ~ 3 0 . 5 2 115r,a2 U 7 3 . ~ 5 ~ 9 7 . 7 2 c l ? . > t l 5 3 1 .7R '55r.20 5 6 7 . 0 2 5 8 7 , n l

5 9 6 . 9 5 6Ur . r 6 c la . !u h 2 S . 7 5 h J P . 1 7 r ~ a . 0 2

C r L r u L A t E n R O D T E P P F P ~ T I I R F ~ b T T1"E = n.OonO l i E C O r D S R O D NO. I 3 AJJFFlnLv 1 (FUEL. T V P C 1 - c y ~ 1 N l ) E U )

FUEL T F Y P F D A T ~ I ~ F ~ ( F .) (QELATIVE Q ~ o ~ U u ( n / @ n ) ) T f 1 1 T f 2 )

( l , o n ? ) [o .nan) 330.- 771.5 3 . 1 1111 .q 7 . 6 qnp.3 on7.9 u ~ o . 2 0UU.I U46.5

~ 7 9 . h 516.1 qnb.? 549.2 57U.F 507.1 99J.7 675.0 h2P.a 670.8 b h l .Q 711.3 607.0 7UU,5 771.0 7714.3 7uh.7 Rqn.2 7hR.l q 3 l . u 7 P S . R 879.7 799.9 9 S 0 . 5 809.0 n57,b 810.7 959.3 P10.5 855.6 9 i n . 1 1186.4 900.6 871.4 TRR.7 P 1 3 . 5 776.2 7 0 6 . 3

19-PIN WIRE-WRAPPED ASSEMBLY

The COBRA-WC code r e t a i n s t h e COBRA-IV-I code 's c a p a b i l i t y t o model g r i d -

spaced o r wire-wrapped assemblies. A 19-p in wire-wrapped assembly i s modeled

here t o i 1 l u s t r a t e t h e use o f t h e wire-wrap model and t h e a u x i l i a r y program

GEOM f o r c a l c u l a t i n g the problem i npu t .

A c ross -sec t i ona l view o f the bundle i s g iven i n F igu re E.12. The sub-

channels have been numbered t o min imize t h e m a t r i x bandwidth f o r t h e d i r e c t

s o l u t i o n o f the momentum equat ion a t each l e v e l . The channel numbering i s

ob ta ined by us ing t h e GEOM Option, which a l lows t h e s tandard GEOM numbering

scheme t o be changed. The geometry o f t h i s sample bundle i s t y p i c a l o f an

LMFBR f u e l assembly. l i s t i n g o f t h e GEOM i n p u t i s g iven i n F i g u r e E.13 and t h e

computed i n p u t f o r Card Groups 4, 7, and 8 i s l i s t e d i n F igu re E.14. Th is

i n p u t i s g e n e r a l l y w r i t t e n t o a sc ra t ch f i l e f o r subsequent use by t h e COBRA-WC

code. F igure E.15 l i s t s the cards f o r the COBRA-WC run. Note t h a t i n p u t f rom

sources

FIGURE E.12. Cross-Sect ional View o f a 19-Pin Wire-Wrapped Assembly w i t h Subchannel Numbering

FIGURE E.13. Card I n p u t f o r GEOM f o r 19-Pin Wire-Wrapped Assembly Problem

1 1 ~ 0 1 ~ ~ ~ 3 b ~ f . 3 6 l ~ l7.0557.95U8 14.055T005u~ 6 ~ 0 5 ~ 1 . 0 ~ ~ 8 T n , b . 3 b 1 21.OTS7.n¶UR 12,05S7~05~4 ? l , D t ~ ~ ~ b ~ S . 3 ~ 1 1 2ba05S7q0148 ~7.059700548 Zb,01U6.gbiS.3h13 23,0557.0949 11.0557rU544 P I I , F I Q c . ~ ~ ~ ~ , ~ ~ , ~ I i089557,n!i48 25.055700548 14.61~b.3bj3.3h13 10*0997=0549 S;01~~.3613,3htt b.o5!57.05'J8 5.05570054~ 1;0551,05~8 b,blUh.36~5.3611 Unn551.n9u8 U.OlUP,3bjJ.3hl~ 7.0557.0548 2.05S7aP5~~ 7,01Q6.36! 3.361 3 12,0557.0544 9,05570054F (2.010bm36~3.3bt3 18.0557.05u8 18;014b,3bj3,Jbl3 ?U8n551,~5U8 16.0s5700548 ?4,0l~h+3b! 3,3613 27*0557.,0548 Z3.0S57*09~4 2T.O11h*3bl3*3613 32.0557*0S48 3~;01~6.36)3,361~ 34,0557,0548 29,0557m0544 ?U.01~6.561303613 31.6557.0546 56.0557*OSU~ Jl1010bas6, 3.3613 33.6557.n5lJ9 ~3,0in6,3blS.Sbts 10,0551.0~08 $5.0357~0548 30,olUb.3bi3.3bls 25.n5!%7.0348 28.0557*054~ ?S,nl4b,3bj3.3013 19,05S7,0548 IQ,ol&b.3bj3.3hll 13.055T.0548 02.~557a054r ~ 3 t 0 1 ~ 6 ~ 3 b i 3 m 3 h 1 ~ 10.05~7.0~lJ8 lS*OS9706548 ~ 0 , 0 i ~ h 1 3 b ~ 3 0 3 b 1 1 5,0557~0508 5,01~b.)6~3~36lf 8,O557.OqUA l,o~h5.78nb.u215 Z,@bOS.ob5a 8,0405.0652 2.3267a78?6.42l!j 9a0POSqfibS2 9t~2bf.78~b.U215 lbmOo05.O652

lb,O265,78~b.U215 23m000S.06SE '

? S l 0 ~ 6 ~ . 7 ~ ~ b . 4 , ? l ~ ?9,0405.f~652 ?9.0i?b~.78~6.4~15 3b.noOS.n6S2 5b;o~hs,~b~h.u?15 33,0005.0652 55,n265*788b.u~15 ~8.0o05.0652 2E,0265,78sb,U~15 22,oo05,oh52 ? ? , b . 7 8 6 1 \S,~&OS.OQS~ I S . O ~ ~ S . ~ ~ A L . U ~ ~ T 8,nrOS.~bS~ 8;0?b~,l8bb,4215

S n ~ U t l o Y OF THE M F ~ I E ~ I ~ N F P U A I I O N HILL REUIJIHE b M A T R I X OF B A N D W I T H 15

FIGURE E.14a. GEOM Computed I n p u t f o r Card Groups 4, 7, and 8

FIGURE E.14b. GEOM Computed I n p u t f o r Card Groups 4, 7, and 8 (contd)

FIGURE E .14~ . GEOM Computed I n p u t f o r Card Groups 4, 7, and 8 (contd)

* * * c r T r E ~ O L L O W ~ N G I a A N l n A n E L I S T I N G OF THE C n B R A r w C I N P I J T C i ~ n a r e * * * G E O M G ~ N E A A T E D I N P U T I b rlOT ~ N C L I J D E D

FIGURE E.15. Card I n p u t f o r COBRA-WC f o r 19-Pin Wire-Wrapped Assembly Problem

o the r than cards i s requested i n Card Groups 4, 7, and 8 t o r e t r i e v e t he GEOM

r e s u l t s . A l i s t o f t h e e d i t e d i n p u t and t h e r u n r e s u l t s i s g iven i n F i g -

u re E.16 f o r the s teady-s ta te s imu la t ion . Only t he heated l e n g t h of t he bundle

(36 i n . ) was modeled us ing 18 a x i a l nodes. The 0.056-in. w i r e wrap has a l e a d

l e n g t h o f 12 i n . A un i f o rm r a d i a l power p r o f i l e i s used w i t h a power d e n s i t y 3 of 160.48 MBtu /h r - f t . The i n l e t mass f l u x was s p e c i f i e d as 4.491 Mlbm/hr-

f t2 a t 680'~.

INP I IT f @ Q C A S F 1 fFt415A BUNOLE T F e T E RUN 1011

H E A T f'Ll1II O I S T R I B U T I O N X I L R E L A T I V E P I U Y ~ R n f t L E 8

FIGURE E.16a. COBRA-WC Output f o r 19-Pin Wire- Wrapped Assembly Problem

00

O0

00

G0

00

00

OC

OO

OO

OC

OO

OO

OO

CC

3O

CO

OO

OO

O

OOOOOOCOOCOOCOCOOOOOOOCOOCOCOOCOOOCO

o

mm

~m

m~

)m

mm

mm

mm

m~

~n

~)

mm

mm

yl

mm

m*

~m

m~

~~

mm

mm

m~

,

ROD I v P L ~ T D ~ l b Fl lR b6aCuRLY NtlMRER 9 LOCbL 6LOBbL TvPe D l A ? R A O I A L POWER ~ Q 4 C l I o v O r POuER i f l A O J A C E N T f !HlNr~Ei R ( A D J : CI~LI'NFL Nn.\ Rfl0 NO. ROO PD; NO. ( ! ) I ) F A C T ~ A

I I 1 .?So0 1 .UP06 . IbbT ( 1 1 ) . lhAT ( I ? ) . Ibh7 ( 2 7 ) ; I A ~ T ( 7 s ) . l h h l P ? t .?goo 1 .n!no .146? ( 11) . l r 6 1 ( IU) ,166) ( q) ,1667 f 6 ) . t6h7 3 1 1 .?Yo0 1 a @ ! 40 .1h6? ( 111 .1$67 ( 1 7 ) .I&&? ( 6) , l i b ? I 4 ) ,1667 (1 u I * ? l r ) O 1,0200 .166? ( 17) ' .I&CT ( 21) . l h h ? ( l l j I f I . t h b 7 3 9 1 .?YO0 ,9060 e l 6 b l ( 21) e l h 6 7 ( Zb) .1kh7 ( 2 7 ) ,1hh l ( 7 ? ) .1647 4 b I e?39b ,99b0 .1661 ( Zb) .1h67 ( Z O ) . l k h ? ( 3 i ,thh! ( 3 7 ) a l b h 7 7 7 1 .?Xoo 1 .n?no . IbbT ( . I667 ( i n ) . l hkT ( 2.1 ,16br ( 1.1 . i 6 6 7 e c I .?So0 1 . O P ~ O 1 1 6 b l ( 11 * l r 6 7 ( 5 ) I i ,333- r s) -6.n0nO P o I . P ~ O O 1 .no60 ,1667 ( 3 ) . )A&? ( 6 ) . I667 1 4 ) ,)?on ( j ) .r50O

1 0 i n 1 ,2100 l .no60 . I~L I ( 4) . ( 71 3 ( .3131 ( 9 ) -6.n0n0 1 1 1 ,2300 1.0190 . 1 b 6 ~ ( 7) . l ~ h ~ ( 12) , l h h ? ( I R ) ;??on ( o ) .?5nO ! c " 1 z 1 . ? I o n 1 .no00 ,1667 ( 18) . l h b 7 ( 2 1 ) . 3 ? 7 9 ( 11) , 3 3 5 ~ ( 23) - i .nono 1' 1 Y I .?yo0 ,9960 . 1 6 b ~ ( 24) .I&~T ( S T ) .16b7 ( 3 i j , E ~ O Q I ?:I . ? ~ o o !" I 0 t .?3OO ,0550 . l b b 7 ( 32) .1hh7 ( 3 4 ) .3333 ( LO) 1 3 6 - i .n0n0 9 1 5 i .?so0 ,0590 . l b b 7 ( 34) . Ihb7 ( J L ) . ! b b ~ ( f r l ,>+an t 3h1 .?so0 2 " ! b I . ? l o o ,0550 .1667 ( 3 5 ) , 1 6 6 ~ ( Y O ) ,1SqI ( 3 q j S T ( P -6.n0nO ! T 17 I .?3bO ,QQhD . ~ b b t [ 30) . I 6 6 7 ( ~ 5 ) .1hh7 ( f a ) ,?%on [ p a ) . s ~ n o ! 8 1 1 a2100 1.0300 l l b 6 T ( 1 9 ) . I667 ( 1 3 ) .3133 ( 2 i ! ,1731 1 5 ) -6.nOnO 19 10 1 * ? y o 0 1.0140 .!bb? ( 1 3 ) mlhb? ( 1 0 ) e l h h 7 ( TI .ZqllO ( 19) .>SO0

FIGURE E . 1 6 ~ . CORBA-WC Output f o r 19-Pin Wire- Wrapped Assembly Problem

. t A 6 1

.I b b ? . f 6 6 7

. l h b ?

. I 6 6 7

. l h b T 1hbT

-0.0000 -0.ooon -0.0n00 -0.onoo - o . ~ n o n -0.0000 -o.onon -o.onoo -o.onoo - o m o n o n -o.onon -0.0no0

( t n r ( s r ( c E l ( 37' ( -1 ) f 331 ( q01 ( 01 ( 0' ( 0' ( 01 ( n r ( 0 ) ( 0 ) ( 01 ( 01 ( 0 ) I o r ( 01

N [ I ~ I I ~ T F Q R A L NO, H E I G H T f I N . 1

1 0 .0 - 1.0 o 3 .0- P.0 7 6 .0 - 7 . 0

l o 9 .0- 10.0 I 3 12.0- ! 1.0 1 h l S r O * 1b.n 18 I1.0- !q .0 2 2 21 .0 - F2.O a5 2a.o- 35.0 il* E1.0- ?8.O 1 1 30.0- r ( l .0 3 4 3 3 r O * 3a.O

O P F P r r I r l G C O N ~ ~ I T I ~ N S S v P T E r PUESSUQE I3cl.r) P q I A I N L E T E N T H I L P V 150.7 911J/L3H I N L F T T E M P ~ U A T U R C hRO.1~00 0C1;PEES F N I ~ M I N I L P A P 3 FLUX 4.uqI MILLION L B W / F T ~ - H R N n A l N b L P o ~ E R D E N P I T V DIOY.ARPO " 1 L C I O N R T U / H E - F T ~

UNTFIIRC I N L E T TEMPFRATIJ@F

FIGURE E.16e. COBRA-WC Output f o r 19-Pin Wire- Wrapped Assembly Problem

.I I( O L P ~ F ~ P C C O . A T JY 3 z s b 1 1 l a t b 7 0 $1 s u Z T 3 1 3 s 3 0 3 9 44 U 54 3 3 4 9 10 1 9 1 8 1 9 9 2 z b 30 3 3 3 4 a! 5 3 4 3 2 7 ? I 7 fi I ? 13 1 7 ?I 3 5 ZII 29 Y Z 3b on 4 2 5 1 8 90 9 Z S b I t i U 1 6 ?O 2 1 p 4 ~7 31 3 3 3 P 3 9 a 9

1 0 u a 11 3 4 9 1 0 15 1 8 1 9 ~2 2h 30 1 3 3 4 37 a 1 a? ! ? u b 1 1 7 8 1 2 1 3 11 2 1 ? 3 20 2 9 32 3h 40 a ? a ¶ ! O * r J 1 5 + i? b 1 1 l U t b 2 0 ? 3 24 27 3 1 3 5 3 8 3 9 UU 1 0 s 4 17 c 3 o 9 1 0 i s t 8 1 8 ? a ?b 3 0 1 3 1 4 3 1 ar 5 s 1 4 q +? 1 9 + 1 t 8 1 ? 1 5 1 7 ? 1 $5 28 2 9 3 2 36 1 0 a? 5 1 ? O * - 0 ? l * Z 5 6 1 1 1 9 1 6 P O 2 1 24 37 I 1 35 36 3 9 0 9 $1 P R ?1 * 1 o 9 1 9 j S 1 8 1 9 pi? ~b 3 0 3 3 3 9 37 a1 47 24 U b ? 5 + 1 7 8 I 2 1 3 l ? ? 1 ?g 28 2 9 37 Sb 40 42 I S ? b * 0 3 ?? * ? 5 1 1 1 4 t b ? O ~3 24 ? I 3 1 3 5 36 1 9 04 p 4 + q u ? q * 3 0 9 90 1 s 1 8 1 9 P a 2b SO 11 3 4 3 1 41 3 3 - 0 + 32 a \ • 1 8 Ii? 1 3 17 ?1 2 5 Z8 2 9 f P Jb 0 0 a t 5 1 ? Z 30 - 1 r L S b 11 1 4 1 6 20 r 1 ? u 27 11 3 9 ~6 3 9 o Q ?U r 46 ? T r 3 4 9 10 ( 5 1 8 1 9 ?Z 2b 3 0 3 3 3 4 57 a 1 a7

I T E P A T l F N 1 0 1 4 ~ INTERNbL La92 WODF UUT PAYI"\IM EQ4111 NO. I T ~ R ~ l r ( r t t 8 OF C l l r J v E R G F N C t I N T t R N 4 L t ~ 1 r r ) ~ h i : ~ ~ n r F N T H A ~ PC

r r

FIGURE E.16f. COBRA-WC Output f o r 19-Pin Wire- Wrapped Assembly Problem

FIGURE E.16g. COBRA-WC Output f o r 19-Pin Wire- Wrapped Assembly Probl em

TEMPEPbTUQF DENSITY (OFG-r) (LB/CU-FT)

68o.on s a ,os h b 8 . 6 1 S3.07 b Q @ a 3 4 '13.89 7FP115 53.81 715.9s 53.7s 7 ? 5 * 6 Z 53.69 730.20 5J.63 717.5? '33.57 747.aa 53.49 7T5.71 53.42 767.15 53.33 777.35 s3.za ~ P T 104 S S , ~ L 7qh.47 53.06 FOR. 30 52.98 RZOmIh ¶E?bR n?s.se 52 .81 (117.bb qa.74 AQU.83 5 2 . 6 6 F ~ Z . S ~ s a ? b ? BhY.U? 32.5'1 P7Pa14 52.45 PPO.UU 52.35 P9'5.15 S ? . Z h 905.26 52 .18 91 P195 s2.10 9?7 a 2 1 92.00 Q ~ O m l 7 5 1 - 8 9 qes.bs 91.81 957.27 51 a74 9 5 6 . Q 9 5 1 ;7¶ 0 5 6 a90 '11 .75 9Sfi.39 3 l q 7 4 Q?iRm79 9 1 - 7 3 QhO.60 51 .Ti! 961 51.71

FIGURE E.16h. COBRA-WC Output f o r 19-Pin Wire- Wrapped Assembly Problem

CAL~ I ICATL !~ FLt l In C O N O I T I O N S A T 11l4E r 0.n000 ~ E c O N I I ! ~ PResauRc I 1Sn;n P n 1 i CHANNEL 5 AS3FMpLy 1

D 1 8 T b r r C ~ DELTA-P ENTHALPV T E ? ~ P E R A ~ U ~ F O t N S l l Y ~ ( J U ~ L . VllIb C L ~ N k4Aq9 F C I ! ~ ( 1 N . l (PSI) [BTIJILRJ (OEQ-PI (LB/CUIFTI ~ U A L I T V ~ R A C T I ~ N ( ~ ~ 3 1 3 ~ ~ 1 t ~ i R / ~ ~ R - c T , ) n ;Q 20.6007 759;73 ~ ( \ F . o o 54.0q 0.000 11,003 . l o 5 1 u ' u o l p

I t n 19.11577 763.49 hQ3.4'4 93.,94 0.000 0.000 ,1003 4 '6hh7 2.0 1 9 t 3 0 0 0 367.00 7FS.bT 53.05 oeO00 0.000 . l 0 7 t 4:519q 3;n 16.Sb70 710.36 7fU.67 53;7b 0.00n n;ooo ;I 3c.p a;sssq

to 10.1293 312.91 713.09 53.69 0.000 0,000 .105? U,59 4 5 4 ,r) 17,lOqc) q76.P9 715.90 53.60 0.000 0,000 ,1077 a ~ Q R ! h t o 16.9941 tT8,59 7 u j . s t 53.54 0.oon 0.000 ,1242 u : u l t ? 7.0 16.6551 381.13 t U S , 8 l 53.47 0.000 0.000 ,123: 4 3 7 9 1 8 ;O 1 3 . ~ 8 7 b ~ 8 o ; q ~ t b o . r b SJ;JL 0.000 0,000 ,! O E ~

to 15.bP99 38 l l .?b 7 7 1 e 2 3 53.E7 0.000 0.000 ,09Pr U , O ~ R S 10,n 1 4 , ~ ~ 2 1 39?,45 74h.93 53.16 0.000 0,000 ,12b! U 4 7 h t J 1 { o 14,q3?b 395, l l l 7 9 6 n Q 9 53.08 0.000 0.000 ,1221 4:7550 12,o J3.50a3 '199,OO 8ne.sn 5a.98 0.000 0.000 .I 051 4,529r 13.6 J E e u l 5 O u00.AO n ~ a . b n 52.95 O.OOn 0.0n0 .109! a,hPoq I 0;o la,! s s ? UOF,OJ P P F . ~ ~ s t . 8 ~ 0,000 o,ono . I ? Q ~ 4 * b o u t I S,O 11.?419 001.64 8401O'J 52.72 o.oon 0.0n0 . I 3 9 9 0:9017 1 b,o 1 1 e O t ? l U10.41 8Ub.07 52.67 0.000 0.000 . 1 0 7 ~ 0,3876 17 ,0 jr),O30? 413,1? 835.87 52.59 0.000 0,006 ,1091 4,6554 19,O 9eFq03 ul3,OO 861 r 2 1 5E.54 0.000 0,,000 .l 2 5 ~ I ICuS3? 19,n 9.5575 o l 7 .26 8bF.70 53.48 0.000 0.000 PUP u,uo4_a ?n,n Oq79p9 ~ 2 n . 3 9 9 7 Q e 6 3 5 2 , s ~ 0.006 0.000 ,I 0 s n u ,uoo l 2 1 ,O '1.5417 uZP.35 BQ? . l 5 92.29 0.000 0.060 ,0991 b,OO?7 ?E,O 7 . 6 5 ~ 6 u3n.81 906.91 52 . i b 0.000 n;ono , 1 0 7 3 u,S1@3 Z3,G 7 , ~ 5 8 9 4 3 I ,A0 91h.96 52.08 0.000 0,000 4, Iqbt P ~ , O b.uSnU u 3 S . u ~ 9 2 8 . 8 9 5 1 . ~ 8 0.009 0.000 .I n 6 9 u .qk?? ?5,0 5 . ~ 3 ~ 1 4 5 7 . ~ 0 o 3 e . t ~ 51.93 0.000 o;ooo , i l n ~ u ; ? t l p 2 6 ,n 5.1 l ? ~ o a t ,SP 9no.01 5 1 . ~ 1 o.ono 0,000 . I ~ O O u,bzqg ? T t n U.!b?n U'JS.20 Qb! rS9 5 . 7 0.000 6.000 , 1 3 9 ~ u,qhun

3,'41b 446,qt q66.?5 51,bb 0.000 0,0.00 ; l o 1 9 4 ' 601? rr'n 2 ,Qh lQ 29%') 049.R4 976.b9 51.5n 0.000 o , n ~ o ,I o o q 11:57c2 50,0 Z.PUS3 UuB.,fll 97Pob9 S 1 ? 6 1 0.000 0.000 ,155k U,460@ ? I ,0 2,'1220 ~ 4 7 9 2 6 9 b R 0 I n 3 1 . 6 0 . 0 ~ ~ 0 n,000 ,I E u ~ "41 O ? 3E:n 1 .?bO? ~ ' J 7 . 2 5 96P.09 51.66 Q e 0 0 0 0,000 . I 0 1 3 U t u l O 1 33,o 1,5171 4 0 7 t 2 1 9 ~ 7 . 9 3 5 l ? b b 0.0Q0 0.000 .09b- o l 1 3 n 34,O ,hob0 ~ 4 7 , 6 6 q10.09 51.64 0.000 0,000 . !?a? ~ ' 5 7 0 3 ?5,9 0.00n0 llUR.95 970.75 51.63 0.000 0.0f10 . I 323 11:b09?

FIGURE E.16i. COBRA-WC O u t p u t for 19-Pin Wire- Wrapped Assembly Problem

0

CI - - -I om-

h,

U

2-

-

rC

CO

CO

OO

OC

CC

OC

CC

CC

C C

C C

CC

CC

OO

C C

OC

OC

OO

C

*z

. e

..

*r

..

.d

..

..

*.

.0

#.

.#

#.

..

.I

.*

dd

.-

d.

rd

C.

.r

..

'l

dr

.d

r.

*.

c

~c

~~

~o

~Q

~o

~C

~N

~~

~~

C(

~D

~C

N~

C~

~Z

C~

Q~

~~

~~

~

I

Y

--

m-

d-

--

--

~~

~~

n.

,n

,~

~a

&n

~n

w~

mn

a

c r L r u ~ h t c o FLIIID C O ~ O I ~ I O N S AT CHANNEL 2 6 ASSFMRLY 1

TLI~PFR~TURE D E N S I T Y (DEB-F) (LB /CU-FT)

68F.00 SO705 bQ! as3 55 .95 IO leU '1 93.85 71( .sb l 53.74 7?9.?9 93.64 7 1 0 a l l 53.55 7 5 1 - 2 3 55.0h 763a49 53.36 ~ T U D Z ~ ~ 5s.27 IAIJ.IR 53.18 7Q3.70 33,10 9OSm01 53.01 R l J a 4 1 52.94 8??eb? SZqE7 83u.23 SE.77 AIJ7 .?l 32.66 obn.71 5 t .55 871 .OQ 52,Ob 889 e7S 52.37 893.20 52 .?8 9(1?.35 5 2 - 1 9 Q ! J e l l 52.11 9?0.5? sz .05 Q30.87 5 1 a97 937.54 5 1 - 9 1 Qu(.mO! 5 1 .nu 957.91 51.7u 970.U¶ 5 1 .bU 9811.09 5 1 :FIE 9Qll.33 31 . u a P Q Y . O ~ . r 5 909 0 2 9 51 ;Ub 9R9mb1 31.48 981.99 s l .Us PRu.?u 5 1 - 5 1 ~ n p . 5 5 51.5 3

LQLIIL. Q U A L I T Y

O.OOn U.00n O.0On 0.000 0.000 0.000 o m O @ n 0.009 O*OO@ 0.000 o.oon 0.00r) 0.000 o r n o n o 0.00n O.OOn ornono 0.000 om000 0.000 0 . 0 0 0 010On o s o o o O. o n n 0.0on 0. o n 0 O.OOn 0.0'Jo ~ . 0 0 0 0.Ol'o 0.090 0 0 0 0 0.000 0. OOa o.000 0.000

FIGURE E.16k. COBRA-WC O u t p u t f o r 19-Pin Wire- Wrapped Assembly Problem

T F t l P E U A T U 4 E D E N S I T Y (OEG-Fl ( L R / C U + F T )

6A0.00 54.05 h ~ t . . 9 e 53.99 6011.59 '33.9) ?r)?.Uu 55.85 715.27 5 3 ; ~ ~ T??mZh 53.70 7 3 1 e l u SS.bt Tcl?.bQ 53.53 7'51 .BI T J ? 4 5 7EP.11 53.37 ThQeUu 53.31 7 7 b e R t 93.24 7RU.91 53.19 793.10 5 3 ? 1 1 d03.9u s3.02 RI 3.7a 5 2 - 9 5 b d U b i l 52.85 b 3 0 e b U 52.77 6UU.lU 52.69 RSI .2b 52.58 8 6 1 .i?0 52.4q L\?Pe47 S 2 ? 4 0 RRb.O'J S ? . 34 PqSmbi? S2,2? qnp.07 52,20 910.49 52.13 9 2 ) .no sa.00 930.82 51.97 Q 0 3 e l u 51.86 957.94 5 1 .79 950.89 51.77 9 3 1 e 7 i 51.73 960.59 51 . I ? 9h?.7Q 31.70 963. lP 5 1 .TO 9(,?,OQ 51.69

FIGURE E.161.

EOU I C . O U A L I T V

0.000 0.000 0.000 0.000 0.000 0.00n 0.oon o e O o n U . 0 0 0 0 0 0 0 0. OOn 0.000 o.ono 0.000 0.000 0 . 0 0 0 0.000 0.0ofl o.onn 0.000 0.000 0.000 0.000 o e o n n 0.000 O.OOn 0.000 a.oon u.oon 0.000 0.000 0.000 o * o o o 0.000 c.000 0.00n

vo rn P L ~ W F Q A C T I ~ N t ~ n t o e c j

9.000 .??94 0,000 . ? Z t a 0.000 ,2742 O.Ob0 ? 2 ? ? b n.000 . 2 1 2 5 0.000 . I 9 9 1 6.000 ,145 l l 0,000 .21b? n,ooo .znan 0;000 ,Z 147 0,900 .P?E- n.000 .esor, 0:oco . e l ? ; 0,OOO . ? I 8 4 n,ooo ,23211 0.000 .22ncr n,ono . i ? l i o 0.000 ,1987 0.000 .I R s i o.on0 . 2 1 b l 0.000 :?ozo 0.090 . e l 0 7 9,000 , 2 2 2 7 0.000 ,ZJOh 0.000 .EETn o.'ono . 21 *u 0.000 . 23?n 0,000 .220$ o,noo . e l 11 0.000 , I Q @ r l 0;ooO .I qua 6.000 .21qR 0.oon ,201 i n.ono , 2 1 3 ~ 0.000 . e z l r 0.000 .22bP

COBRA-WC O u t p u t f o r 19-Pin Wire- Wrapped Assembly Problem

FIGURE E.16m. COBRA-WC Output f o r 19-Pin Wire- Wrapped Assembly Problem

W ( LP, a s ) w c 10, 14) u( 1, 61 w c 3 , 5 ) u r i, 3) r ( U, b \ w ( n; 7 1 1.1 9451 .I7?P.1 .?OR44 -.ZqbS7 -.nZRIE -.1Q?3T a ! ? ; ? 3

. D Q l O ' 1 , l o 8 ? t - 1 .nn?oz ,43616 - , ~ u 9 3 n , U f U A l . . t rnbb -.nSU59 .,1?877 -.TlbUb .2Ol59 -.uh00? . l o 1 69 - . h b r 9 ? -.F923q -,Ihb08 - . 1 ~ ~ 4 1 1 . 6 ~ 9 3 9 . e l l 2 5 .7U101 . i r s j 5 0 - .0bl79 -.59127 -.US014 .b5175 eF4U5h - 5 4 0 n q -.-47TZ .f 127? ,@-TO0 .u2570 -,OsbO? .q6853 -.OR931 ,112n2Q m'tUPlT ,OTi?F@ .005bB .3384S a133Zo .34336 .01?31!

-en4015 .67109 .161%0 1,42329 -.99f,S7 -,USET4 .?bl;SS mmob181 ;a1920 9.01529 -.00835 - . 1 1 1 9 ~ -.oII~) . f l U 4 4 r e 6 7 7 6 4 -.SRb?? - . ~ 5 1 0 Q r.35636 -.!319b -.20335 US US^ - m a ~ ~ 9 0 -;oh618 .00139 -.lb99U -,?09SY -,0¶1T3 ..!on24

. s 0 5 1 ~ - . a 3 o ~ e -.a5159 wbEIZO - .n29g9 ,9 toPo -.nul;6n

.~ lbbB? .0308b .31737 .U9601 .as742 - . 1 ~ 5 7 9 -.p!t,sn mOlb41 , O J ~ Q S - . 9 2 0 ~ 9 -44027 r.pJbSR .4U4J'! - e@9?09

-.030un , 0 3 1 ~ ~ -.?abet . a l s 5 e - .?~TsI . l ~ S 9 u - . ~ u T ~ E m.0555~ w.11836 r .oqu11 ,89064 .a 1 4 4 1 .7a60a .n9!aa - .F3lb5 -,5h201 -,u1246 .bU?90 e ? 5 5 3 9 m5QSOU 0.331 17 .! l o Z a .Uh169 .029b1 -.os251 . !~339 -.one74 . N ? Q S ~ mfi4lbb .OhbaE • nz l 08 .J3278 a15660 * 3 l l b 4 .nloRA

- e u 4 ? ~ n ;bnlqS .1 8898 3 - .~19321 -.u'14~'! .!hh?? -eF6(1('1 .4?OJU -.nObld -.Ol8U3 m . 1 1 2 5 ~ -.dqCta6 . I 7 7 1 1 r rn681 f i ? r,5RSTb -.UU?6? -,Shbb4 - . ~ 3 5 7 1 - ,ZlU39 -.hln?R - m n 2 q 1 g -,Oh365 . n o 5 3 2 m.17709 - . r i y a q -.OSRPT -.n9110h

.qR33q .,45732 -.uSQ45 . b l 7 8 9 -.o391Q .90h40 -.?hhYh

.0b36! ,0?874 . g l h4a .09U28 . a 5 i 3 s -.1901 E - . z i n74 ea fT1b .a5504 - . ~ 2 3 0 8 . U ~ b 3 1 - . ? ~ b 0 t .44b l l -.&0?71

-.0%932 .,OXOR0 -.7093F .2180O -e *7023 . I 8 7 7 1 -.?48YR -mO55U4 w , l t 939 -.0'4u60 - 8 9 1 12 t 3 5 1 .7UddS . f iUnW -.n3190 r . 5 ~ 0 ~ 8 -.41229 ,be701 .?53A4 .Sob21 - . ! t a h ~

. l l h ~ 8 ,4f l?Sl .a299a -.05066 .?7313 -.On1 95 . !~?a?? .01013

gq38bL .t.nj,s .0Z1408 ,33179 73875 ,13731 .n2[47

-afiU3T? , t 8 q l 0 -m f i29J9 -.u9174 -.4403? . t h ~ R h - . o ? u ~ u .4?1b2 *.f1lo83 - .02101 - . i1530 -.09fJ?h . i h 0 8 Q -.610R3 -.5Q7?'4 -.05h80 r .37212 -.aS9qR -.20ST? - . r 1 ~ ? 7 - .*El77 -;J?nlQ -.?lSQS -,13h47 -.10135 -.Oh050 - . l l ~ q h

FIGURE E.16n. COBRA-WC Output f o r 19-Pin Wire- Wrapped Assembly Problem

U ( I ? , 1 8 ) W ( 1 8 , 2 4 ) W ( l b , 1 0 1 W ( 24, 21 ) W t 2 i , 2 4 ) W ( Z7, 3 t \ ~t 3 k y 34; W I P O ' ; 3 2 1 \ I ( 31, 3 0 ) w l 34, 36 ) . n 9 2 I q -,ObgQS -.f ib219 -,189eZ c.96249 -.ITISS - . ??pu l -,ORST? el 7140 -.05U 5 P

1.116480 .Z l aAb .US209 .45169 .!IOP¶O a 0 5 h 6 1 el111 11 ,h1547 1.nhh5o . hZ3hU 0.ab26h -,Z?770 .a1998 . 0 ~ 2 8 9 .?boa! -.371E7 . n l ? ? l ,39577 . ~ ~ R O R . l Q S 1 9

. n919u ,451 1 0 .Sflo30 . 1 7 l b 5 -.sEOIZ .ugh72 .!4791 -,?0?#1 .a'30n! ,43859 -.?aU02 .O! (\35 3 - ,01493 r . i 2 5 7 1 .08921 . i n ! l u , onn r9 ,.nos14 ,21910

.11302~ ,37319 - .?846s 0,44184 r . 0 ~ 6 2 1 . 219os ..hcnhe - , U U ~ Y R .a539? , 0 4 n 3 1

.nn1R9 . I Bnh? ,00746 - 0 1 101 -.?128'5 ,05692 - . ? ~ p 3 0 * % l ~ b ? ~ ~ . ? 3 1 1 ~ 0 . 4 6 3 ~ 6

. ? ! I 9 9 -.6?625 -.44i?62 -.45364 ..?3624 ..92h?b -.(IU~OA .206k7 .o205! .PJ382

. n S s l n - , O Q T ~ ~ - . l0599 ,3?448 .n6337 , I A 2 1 0 ,.?1nuQ -;353a5 . r l n l l ,37489 * .9200? -,44503 .?b219 1.92027 -.JJSII - .44610 -.no117 r , ? ~ h a t .n9129 - . U l u l b

e l 8 1 2 2 - .2!831 -..1970b - ,?0809 r .q7727 -.1P67E - .40q30 -,3hOb7 . a t 1 2 0 -.2q?97 - , o u s 5 ~ - . B Q ? ~ o ash^@ 1.09256 . U I ~ O R - . ? ~ b P o . n5351 P Z O Y Z . . a e ~ e s - .57232 - . ! F ~ S T - ,bath7 r .35989 0,40989 .?Shoo -,5a3?0 ,.q?nhS ; ! O R ~ Q ,.n?2u0 - ,31h78 - . 7 a s s l ,05361 .u2101 .u2993 .q7269 , 0 8 5 3 ~ . i ~ ? p ~ b , ~ R P J Z . . ibn09 . 4 9 1 r 4 ~ - . s a r 2 ~ -.:3?qnI .19917 .02369 .11617 - . 3 3 6 t l . n212q . Y l e r 4 e .no072 .I 1 5 9 1

e0625? ,UFOIIU . ¶ a S P l ! . l a 9 4 7 -.119&1¶ .4795b . T ~ & Q T - ; 2 ~ 1 h 8 .nUli5S .4363b - . r ~ 7 7 ) .0?104 .11974 0.00526 - . i t u s 1 ,09209 . j T ? 9 6 - .onz7h ,.nOsUo .21301

. 0 3 9 0 ~ , 5 6 7 ~ 3 -,e9050 - ,44006 - . ~ 3 6 0 4 ,21525 . . ~ f n 3 7 -;au??3 , .u5441 . 0 3 9 @ 5

. ~ 9 n 9 1 ,17812 - . n o i o ~ .0038Z -.?IJSI .05R25 -.n97JO - t l ~ ~ ? ~ , , ? I V ~ P -.UT157 w? l4b f i - . b I b41 -.Uu?ub r .45474 r .n39h7 m.9n737 -.!IP!U~ .2a7Q2 .S20 l l r . 231R I .05?59 -,'Ood41 - . I8656 . 5 I F 6 0 .n'33237 .I 9135 ,.z1790 -;3h0?h .7 1 n‘ln .37905

- l a 0 7 1 i -.Uuh?O .?4801 -.9?359 -.23bUR -.UU591 -.*OJSQ -,EJ715 . n ~ i 1 5 ~ - .41398 a l 9 0 6 ? -.2!614 -.YhOO? 9,11034 -.?78F9 , 1 6 5 7 - . ~UR+?? - , S h l n I , .01?91 -.253P9

-,oUSul - , bq t92 -.?3b7U -.09448 . u l ~ b n -,711bU1 .n5?7? ,U?Obl , . a 2 4 5 3 - .9716b - 0 1 867q 0.60181 0.36039 r , u l i ? b U .?55?9 -.5'15Jh - . T Y B ~ ~

1 7 - ,n215b -.JJ77O -.7U7?0 .05138 .4?@ZO .U2996 ,57257 .ORSJP .11?03l ,592FS - . l s P 3 3 .U9402 -.-usbn 0.3J172 . i Q O U l ,02279 . v J 7 4 9 - .J lbUT .n?nOq , J t 6 9 1 .f lO?P$ . l l u 9 1

.0O28r, . a t 9 4 0 .SBTl i? . I 0 7 9 6 -.?93Uh .4 l '?h9 .Th3!5A -,2oSQ3 . f 1 4 ~ 7 1 ,43553 0.?3?51 . o ? I ; ? l . ~ l e 5 5 ..no583 I J Q O .093T? . j ? s ? ~ - .on?&? ..no161 .2 13e4

e f l3923 3 -.?9H00 - . ~ 4 7 1 1 -.$3b75 . 21uA1 - .h1594 - ; U O Z ~ ~ S .115?9R . O U ~ O U *( r919> ,179PU .0002? . 0 0 5 ~ 9 - . ? 1 0 ~ ? .Oh020 - . ~ 9 > q 1 7 ..?1?76 - .49068 .?13"u -,b1Qn4 -.u4103 - ,uSSlo -.n3895 - .90141 . . ~4q94 ;zu65h .02?2? .?37(13 .0099& -,lObob r . 18879 l 30922 . l ? b u 7 ..pSnOh -,35171 . ? ( " 3 S ? ,37637 .NSOBO

-.o0190 - , u P ~ ~ s . i ? j I Y I -.B83b8 -.?130h -.4fli??n -.16h4Q - , ? ~ 6 4 9 .nbQ95 r .41 1 2 1 -.5luO? - ,ZSblB . ?Qq93 -,Sf1596 - .?0414 -.ETQR2 -.TI t 95 - :?pel 1 . i 2 1 21 m.73923

F I G U R E -- E.160. COBRA-WC Outpu t f o r 19-Pin Wire- Wrapped Assembly Problem

CRossFLoU BETWEEN APJACCNT C H L N ~ I E L S AT T I M F . 0.0000 8 E c n ~ n S

A3JFMFLy NUCBPR 1 9 1 1 1 1 1 q 1 1

A Y l A L ?!WE w f Y j , 31 ) w ( SO, 31 ) v t 33, 3 3 1 w ( 25, 3 0 ) w f 211, 30) w t 19, 2 5 i \.I[. I?; , l s i u r i 9 ; ? P ) r ( , l n , 1 3 ) w ( 13, 15) 0;0 1,F -.!9060 ,13139 -.g1263 -,0323S ep727Z .1169@ ,.pqy01 -,Dhbqn - . ( 008q -.O?09h - 2.0 .n3720 -.ZJ361 .UZPUl . 58&31 -.?0039 -.OT191 . ? A t 7 0 % U U ~ ~ R .uuh91 -. 1 1 0 0 3 ZtO 1 e O e ~ 9 1 0 t , r .08353 .lo1102 1 1 ~ 2 9 6 -.PU630 .0420U .P l PPO .156h5 ,.PIfZP - 0 6 6 0 7 2 3 , 4.0 e ? l 4 3 0 .b?351 .4u39J ,45063 v.nS8u1 .91951) .33Q13 - ; ? 9 5 ~ 6 mPQ7bl ,ZF3OE

0 5.0 * 6 5 2 0 6 .oQ??5 - 1 8 5 5 4 -. 3 5 2 8 1 .nabbT -.19302 . aF tuU .354US .TOt?Ul .JTCEZ 5,O 6.0 -.a2196 .UP677 -.a6281 , 9 1 9 l S -.?3507 ,44477 , ~ l l h T ;?33h0 .nA951 0.41035 0 7.0 * ! Q 1 7 b ,211161 .13904 ,70908 - . tn?8R . l ~ l e f .+0??7 , S h l ? l .U!*SD - .24hZ5 7.0 * 8.0 -.Obbs) , 8 0 1 9 7 .? l5trO ,OQS43 - 0 1 1 6 3 .7441b ,.n3!b0 - .Of695 ,.u?U2O - .56*41 0 9,O -e18996 .ho7?1 .Thli?O .U1465 q ? P 9 O R ,54?o7 .77q17 - 1 ,.qn0f7~ - . 3 3 l b b Q,O 10,O - . T 4 7 l f r t 0 S 2 8 0 -.U1973 -.48bTZ . -7139 r .Onb99 .,IJ?P?~ -,SROhR - . l P l O h ,494A6

fO,0 - f1,O r e q & 3 8 ? ,JS laS - .19653 r . 0 1 8 3 2 . *1459 .32SPV ,.r11h37 r ,S f J f lS . ~ l ? h I . I 1 357 ) I ,o - 12.0 .nos26 -,4?493 -.9826b - . I n 5 8 1 - . fq600 - .43?Qq - . ? h ? ~ h ? o ~ n r , , . 1 ~ 9 n 7 ~ . o t s o b 12,O - 13.0 - 4 -,'O?d29 - . J l b72 ,00902 9.1 l h 5 A -,O9133 ..17!139 :004?? ..n936? .21108 t o - 14.0 .ass33 -,3b660 . C ~ Z O U ,44886 - . ~ s ~ o u - .2127n . ? t r ? ~ , ~ U ~ T J . I I ~ P U J . O ~ C S ~ 1"O r 15.0 . 0 9 2 7 j -.17Anb .0031? -.00Sz3 r . 21321 -.05795 .fiSqu7 . i n 9 a n , . ~ ~ s l n - .u3u68 i5,n 16.0 . ? t u 9 i ,6181 8 .a4251 .U33bQ - ,n3951 . 9n574 .O?I 40 . 2 3 ? ? 2 .!IOIIUR - ; E Q F ~ ~ lS,.n - 17.0 ... . F 5 8 3 ~ .0Q3!53 . . 1 8 b l 9 -.3198Y.. .a5356 . m.19319.. . z ! suQ - . . 1 5 9 ~ . o . ?on69 , 3 7 9 1 9 . IT,.O 18.0 - . a o b S ~ . U U ~ O U -.?4739 .q2392 -.2379n . 4uu?e .PP!OQ ;a3780 ,PQUSI -.UIJBI 18,0 ' 19.0 . 9 9289 ,2/ 697 . t b n 9 2 .7!047 - . lAO lU . h e r b 5 ,36136 , .I A51 O ,41333 - .25329 lVIO - PO.0 -.04539 . # Q l d D . s J ? O P .09u5? e ~ 1 3 5 1 ,74714 - .05(18 -.U19P* ,.112869 9.57305 ZO,O - 21,O r .16597 , 6 4 7 ~ 2 .36091 .U133d *?S?bN .Sob70 ,73299 -;197?1 - . n l q Y 9 -.?31U6 21,0 22.0 - .Ta?h t - .05 t19 - . u l 9 8 9 -.U2963 , T T E T T -.n8u21 - . u p n s ~ - , 5 ~ 2 i 5 -. t 8 7 8 2 . u9s15

m 0 - 73.0 -.*1472 .S3?bZ -.197US r . 0 2 1 2 1 .-ST41 ,33087 - , n i n 2 7 - t 3 1 0 S n .cln192 . l l U b l +' ? x i 0 9 24.0 .On387 -,:4?~bE -.91379 - .1802% -.0931h *.U591* -.vb-n!i ,2s3r P ./lU(rYU .US555 0 CI Z U , ~ 25.0 -.3373h -,o?ono - . ~ 1 7 ? 3 ,00595 - . i !305 m.09201 - . i 7587 .onup, - .n i l360 .?130b

F5,O - 26.0 .U391# -.3h793 ,78960 . Y u ? U ~ r . p3b@3 w.21457 . h l T l O ;PO?PT ./1S77 h .03n59 ? 6 , 0 - 27.5 .n9147 - , l 7 8 ~ O .n(j091 -,On577 -.a1355 -.0590b .n9117 , lRbhh ,.1169h - .45?51 7 - 2a.o .?134t, . b ! l a a . u4161 ,Us447 -.n3965 . sosns .!18&31 - \ 2 0 h a ~ .oi!?iot .?3001 ? c , O - 29.0 .P577o ,004 $ 3 .18677 - ,S f564 .&To45 -.!OD03 . ? f n ? ? , Y f V l f i ,100h3 .11n95 2 v S 0 - 30.0 -.an340 .UubuZ m . 2 ~ 5 2 4 ,92220 -.a311uo . u u h l l . 5 9 ~ 2 ? . 2 1 6 ~ n .n95T? -.u!495 3n.n s1,o .1 Qn52 .'219i?8 . ~ ' l n o 9 .To973 - . *76ns .IRRI? .hun95 ; T ~ ~ R O .a1209 - .?59o3 51,O - 32.0 -.UUu?? .9*001 .?!92S ,09449 -111 2 4 ? . ? 4 ~ 7 ? - . n a q 3 ~ -,uj 990 - . ~ T ~ o R - . 5 ? 5 6 5 32.0 - 53.0 - . f l~ l~ . 6u2h5 .35602 . ~ o 3 7 1 .?55'37 .54044 . r 2?TT - .?nzn3 ..n2h57 -.ST195 3 0 3U,0 1 -,0770b - .41860 - ,83179 .5¶205 - . l l f J U L . 1 ~ 3 r 4 2 -;Shhho - .1851h , uQ'36h 3 4 . 0 35.0 - . U O ~ J Z . 0 ? 1 ~ 5 - . ~ 2 8 6 1 r . 2 ~ 1 6 5 . z s n s z .051T0 -.i O P T I - . , ? ~ o T P .n5690 . z u P . ~ ~

FIGURE E . 1 6 ~ . COBRA-WC Output f o r 19-Pin Wire- Wrapped Assembly Problem

1 I t 'I 1 I

U ( 1, a ) w c 1, 8 ) b l f , 9 ) M I 9, 16; 1 4 ( 16; r s i w r ? ? ; > 9 ) .,IS99 - ,2511? .! 07 87 . 9 1 9 9 q ..nTsUe - , i ? h n l

-.a1015 .29b57 .?7ST2 - .?Tbh3 ..!na7s - 1 % I n l n 7 r . 07759 .ShSZb . p h i YP -. 3 9 4 1 1 ,.?Oh37 -,9652Q -.?J364 - .269b? - . ? b S l t r l . 2453 td -1 . t r r ! l 8 . I , Y b l h ? - . l7107 - .07445 *.?7433 - .9hP?Q - i . j R ? ~ h - ,91?n9

-1.22448 ,15581 1 . 8 - 1 .SR055 -1 ,?9n20 -;67195 - .Q5b70 .bbZ92 - l . !Bnbu - 1 9 5 0 3 5 - .?on07 v.403-U

-1.39472 1.7h967 - 1 , # 9 9 5 q 9. 6 n l J S 9. t f r 7 9 -;?n2hu - .QZ970 1.1b703 -.j930b -.UoA71 -.nkxuT -,3?777 - r b R 9 @ 1 1.24987 r a i 2 0 9 b - .21210 - . ~ n ! l n - . j a9 *R -.~1V983 ,164bb -.fib553 * . 3 P R 9 2 -.?4279 -:1?917 - .PZlbS ,12669 - . l O l b 6 - . l a f i 3n . ?hh0h - , 2 ~ ~ ? n r . 32931 .ObS71 -.?u110 - . I z?~o ,?n?np a - ; ~ h q z l -.1"812 ,30096 .?b199 -.?o?Rq w . 7 5 7 5 8 - I , ? \ b > S a. 12829 .3ubDS . ~ 0 3 9 1 -.Jh?n9 . . + h i 7 8 - I ~ u ? a 9 - . ? 4 l 2 9 - ,ah295 - . ~ 5 7 0 5 -1 . E l b Q 7 - ~ . ? q a l ? ,3431 1 r .36597 - , 0 8 2 ~ 0 r . fbZY7 - .948u3 - 2 - 91Rnn

- l . ? l 7 7 9 ,15631 -1 .!kICJ -1.3bi I77 - 1 -:b7070 -.9U963 * b 6 2 4 2 -1 .!bS16 - . 91991 - .?7975 -,Un?>h

- 1 . t c S b i i .76O9R -I . ? ~ 9 7 1 - .6@043 . . ~ P ~ Q P - ; a t s t - -.V204U 1 . l h 4 b 0 - .?8059 - .40350 - .nh?qh -.1>7?q -.hROUU 1 ,20014 - . i 2 d > 5 - . 215Qh ..rQ02b - ; lumbl - .0oY l2 .?n048 - . o b ~ ~ n - .3?74q n o -,Iz.R? - .?1110 . I ? b S b -.,9989 - . l b 7 7 * r 2 5 7 n n -,?4300 - . y?7 re . o b j s e 0.15913 - , l ~ 9 6 9 , ~ A P ~ U - ' f h 4 0 0 - . f 443? . 2491? . ~ 9 ? 4 t - .24355 C . 7 5 5 7 ~ 11 ; Z ~ U P ! - . f an88 .33800 . ? ~ o E c - .36454 : .hbl o n - ' 9 o l n s - .?P?9b - .29191 - .?554t l - 1 . E l b 2 2 -!.tqu97 -1 : 3 h ? * 5 -.3b421 1.08035 -.hhOOT 9.94789 0 -,9(ARS

-1 .F I3b3 , 1 5 5 5 8 - 1 . tS82b -1.36039 -1.21793 - :ba ln3 -.9'46bu .hb115 -1. !bnt7 -.919R1 . . t7n t? - . 4 n 2 ~ 6

-1 . fh089 1 ,?558b - l . ? S h b l - .bFLo l - . i ~ n 0 7 -;?210h -.Ql922 I . i s w 0 - . U I O R ~ ..rtl w -,3?69n - .6@879 1.21581 - .1U(87 -.?bSOS , . p Q ~ 8 ? - , lu696 - .u3?99 ,77294 - . r 1 5 2 0 ~ -,OPS57 . . i h ? l ~ . nu7nq

FIGURE ~ . 1 6 q . COBRA-WC Output f o r 19-Pin Wire- Wrapped Assembly Problem

FIGURE E.16r. COBRA-WC Output f o r 19-Pin Wire- Wrapped Assembly Prob l en1

BLOCKAGE SAMPLE PROBLEM

A 19-p in bundle s i m i l a r t o t h a t used f o r t h e wire-wrap sample problem i s

used t o i l l u s t r a t e the COBRA-WC blockage c a p a b i l i t y . F igure E.17 shows a cross

sec t i on o f t h e assembly and the l o c a t i o n o f a p l a t e blockage 4 i n . f rom t h e

assembly i n l e t . This bundle and blockage arrangement i s s i m i l a r t o t h e bundle

used i n t h e ORNL FFM-5A blockages t e s t s . The w i r e wraps i n t h e FFM-5A bundle

were no t inc luded i n t h i s s imu la t i on s ince some o f the wi res were shaved and

cou ld no t be modeled by COBRA-WC inpu t . The shaved w i res cou ld be modeled

us ing minor code mod i f i ca t i ons b u t were neglected f o r t h i s sample problem s ince

t h e i n t e n t o f t h e sample problems i s t o i l l u s t r a t e t h e use o f t h e code through

i n p u t only. An a x i a l l eng th o f 22 i n . i s modeled us ing 22 a x i a l nodes. The 3 power dens i t y i s un i fo rm r a d i a l l y a t 47.48 MBtu /hr - f t . An i n l e t mass f l u x

2 o f 4.491 M l bm/hr - f t i s s p e c i f i e d a t an i n l e t temperature o f 610'~. GEOM

was used t o generate i n p u t f o r Card Groups 4 and 8. The i n p u t cards, t h e

ed i t ed inpu t , and the ca l cu la ted problem r e s u l t s are prov ided i n t he computer

p r i n t o u t .

FFM - 5A B U N D L E

ZONE

F IGURE E.17. Cross Section and Location of Plate Blockage for Blockage Sample Problem

E . 105

7

1; y:N:F HEATED

:, ' 1 ' LOCATION OF FLOW f BLOCKAGE

B O l l O M OF HEATED

FLOW: 41.93 gpm POWER: 139.9 kw P/D: 1.24 SKEW: 1.0

BLOCKAGE P U T

- - - - - -

-

--- - - -

11.f6h7 14. i 567 17.1~57 21.1667 ?b.!h57 20.16~67 14.lhb7 5.1hh7 b.1567 t.!bbl 1Z.l'lhl 24.1 hh7 27.1bb7 3U.ib67 31 .) hbl 30.1667 25.1667 lY.lhb7 lO.lbh7

C O ~ P A D y M F N S I F N P A R ~ ~ E T F R ~ V A I I nrw 9 3 PIW ? MJI a PHI 60 MNw 5 PR. 61 1 rcw. 35 M I 3h rtm rllpS Nl. 17 YE. 2) /R. h J V I u IWI 7

I N P I I T f P R C I S F 9 FFM-5A R U N n l E l E 9 T 2 P U N l o l a

CC

Cr

CC

Cr

CC

CC

Cr

CC

CC

CC

-e

*C

er

rr

CC

r*

CC

Ce

OO

OO

GO

OO

GG

CO

OC

OO

OO

OO

CO

OC

OO

CO

OC

OC

OO

OO

C

CC

CC

CC

CL

CC

CC

CC

CC

CC

cC

CC

CC

CC

CC

CC

00COOGcOOOCOOCCOGCCOCoOOCOCCOOCOOOOO

.................................... 8

81

88

88

88

88

88

88

88

88

88

88

88

88

~8

~8

8~

88

8

---- C

CG

O

oc

mo

CCCC

.... 8

8

8 em

-----

OO

CO

OG

O

CO

OO

OO

O

0C

CO

CC

)C

....... 8

88

88

88

,---

CO

O

DC

O

OC

C

... 8

8 1

-.a

CC

C

00

0

3C

.C.C

----- O

OC

~O

C

OC

OC

G

CC

OC

O

..... 8

88

88

----- CCCCC

00

00

0

C.C

CIC C

E r

n

"0

-----------------..--.--.-----------

I-K

NU

ZC

~J

~B

CQ

WC

EC

CU

~.

L=

IC

P

&~

~L

UC

~~

Z(

P-

PC

-E

~

a P

L

d -dc-

NN

N-

-W

-N

Nd

Nm

NW

.W

~n

n~

hn

-1

W

W

wY

YY

--

--

"-

IU

Y-

-I

VI

VY

--

--

--

--

--

--

I-

--

a L

C

OOOOOOOOOOOOGOOOOtOOOOOOOOOCOOOOOOC~

C

OC

OC

CO

OO

CO

OO

OO

OO

OC

CO

CC

CC

OC

CC

OO

CC

CG

CC

+

W

c.

mm

nn

nn

r~

mw

nn

nn

nm

mn

nn

nm

mm

rn

nn

mm

mn

nm

nm

~

.J ,,,=

--

"-

--

--

--

--

--

--

--

--

--

--

--

-@

--

--

--

&-

wz

C

U-

NN

~~

~~

~N

N~

~~

~~

NN

OO

~~

CI

NN

Q~

~~

NN

~~

~.

G~

W~

~

I-

~~

~a

~m

~n

mn

~u

nn

~m

m~

an

nm

nn

~~

nn

nm

~~

mn

.n

~)

~.

)~

~

-u

rn

-.

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

.

x P

- CC

C

GO

O

me

n

IL e -

-D

O

.G

ZC

V-V

.

00

.2

C

OO

n

ne

--a

C

41 0

mm

t-

... CO

CC

CC

Co

Cc

C

GO

OO

OO

OO

OO

O

mn

nm

n~

m~

rn

n

=-----a,*---

D&

G4

44

mw

3&

C

cr

v.

~n

nc

cn

-n

r

........... C

PO

CC

:

co

oc

c

nn

ma

a

---=

a

42 3

. .I.

0 0

*

iV

PIC

tc

.....

I.

..

.d

Gza

(C

OW

o

O+

a-----&

&-d

---------------------------

LO

*

NW

OO

N

NO

O

-N

NO

O

.... -

-C

C

cc

ao

0

--

C

CCIC

.... 0

-

CC

LC

CL

CO

OC

CC

GC

CO

CC

C

00

69

00

43

00

00

00

03

33

0

4&

46

4C

4C

CC

CC

OC

CC

CC

C

-------0

00

00

00

00

00

0

CL

Cr

-C

CC

00

00

00

00

00

00

&

4.

L.

L4

CC

Cc

CC

CC

CO

CC

OC

C

CC

SC

Q~

OY

O~

Cm

Ow

~S

mC

ui

-

c-

-.

--

-c

nc

nc

nc

nc

fi

~n

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

CC

C

C'

C

c

@I

11

11

------------------- ~

&=

IC

~~

PU

R-

OO

R

~C

ZC

a

m-

n

-

PW

-

na

nr

v n

n.--

OC

CC

ON

OO

*O

O

C

0-

CC

O

CC

C

OO

OO

NC

I

9N

C

CC

C

CO

t

CO

CC

O

0

oo

c-

ooo

wm

oo

c

C

90

-c

C

C-

......I

-0

c.o

a

ms

o

cm

0

....... 1

en

, -

*

QU

W

P Z

C

Z

az

CJ

P W

".Z5 t

na

:

(W

'D

2+2u

>a\=

L-U

.D-

FIPDF: l r l T s ~ D A [ .n: H F ! G H t ( I N * )

3 2 .0- 3 .0 b 0 - 6.0 9 n,n- 9.0 i 2 1t.n- 12.0

1: 1 t . 0 - 15." 17.0- 1 8 , o

P 1 20 ." - 21.0

RESIILTS BoNnLF. T E S T L RllN i n l .

A!!sFM~Lv AVERAGF RE~IULT$ FOR A S ~ E M ~ L V 1 T I M E 8 0.n0000

D I 3 r A N C f DELTA-P ENTYILPV r E n P F Q r T u Q r D F N S I T V EOUKI.. cry.) (PSI) (BTU/LR) (DEG-F) (LI/CU-FTI QUPLITV

0.0 1 2 . b l l ~ 9 3317.1 i! 610.00 54.62 o e o 0 0 1 12.1 326 ~ 3 o . a u h t ? . b u 5u.59 0.000 2.O 11.7791 100.37 b17.29 54.56 0.0(10 3 c0 11.0868 501 - 5 0 hZP.99 5u.53 O.OOn 0.0 3e?497 J'J?.h3 674.57 50.51 O.00n

3.7031 143.58 5?7.6q 5a.35 0.000 6*.0 3.0876 ~ U O . R ? 631 1 8 1 5U.36 0.000 7,0 4.?2i A 74h.01 635.51 50.3h om000 8.0 3'17. 1 4 h J Q . l b 51.34 0.000

748.27 * l o 4 .n25u bup.81 54.32 0.000 !n,o 3.P093 lUq.U0 bUh.47 50,?9 0.000 11.0 3.5952 7'317.51 650.12 54 .21 O.OOn 1P;O 3.2757 151.65 655.79 54.24 0.000 I T t ' . ' 2.qrR6 35P.78 697 .11~ 54.21 0.000 10,o 2.0hn7 153.91 6 6 1 . i n 54.18 0.000 IT,O 2.31196 755.00 hh0 ,T l 90.15 O.o@n 16e.O 2.0214 75h . l7 668.02 54.12 0.000 17.0 1.6937 557.29 67?.04 54.10 O.00n 1 8 l o 1. '597 758.42 675.75 54.07 0.000 19.0 l . n r u 1 15A.4P h 7 5 r 7 5 54.07 O.OOn eo;o .6n57 7 5 6 . ~ 2 679.73 5u.07 0.00-0 ? I e.9 ,1009 15R . l l? 67'4.7q 54.07 0.000 22.0 0.n000 15P.42 675.73 54.07 0.000

POD POWER P E L ~ v E P E o TO THE CnOLbNT 132.563 B T U / ~ E C

E Q u I L . QUALITY

O.OOn 0.000 0.000 0.00,- 0.000 0.000 0.000 0. OOn 0. OOn 0.000 O.0na 0.0on 0.000 O.0On 0.000 0.00n n.onn 0. oon o.non o.onn 0.COn O.OOn o.non

ARFI (SO-IN) .03300 .n3300 .QJ700 .C3300 .nJ300 .n330o .n3300 .n3300 .03300 .n33on .n3300 .F3300 .03300

. ~ J ? O O

.0JZOO ,05300 .n3300 .03300 .0JS00 .a3300 ,03300 .n3zon .03700

.no

Y

N

C 0

u-2 - U.

a*-

... J J J

nn

n -C

ud

YS

Co

Cu

C<

N

CI

FO

OC

CN

r-

CN

C

.. R

.C

,--lf

-u

=

-0

-

UC

JY

~J

~C

,~

PN

~

............ m

rn

m~

mn

mm

mm

mm

n

nn

nw

mn

nn

nn

n

&, R

OW

dY

--

Pn

F-

IP

W-

-S

mC

hC

Cc

nc

>

-

GQ

V8

--

-b

RO

6

QM

mm

Ul

OC

O-

a

RO

O

tL

..

..

..

..

..

..

..

am

..

..

..

.

a I c

~.u

.c

- J -

0

R=

CC

W..D

O ~

~.

~R

,N

CC

CC

O

u

C-

--

-~

.L

&~

V~

P-

J

=~

*~

tr

nt

r

~&

c.

L.

c

kb

0b

4 ~

DC

CO

CC

&C

CC

Cu

SS

c~

aQ

C

U n

- Q

)-

WJ

e0

90

0C

P

OQ

CC

-m

-c

mJ

CIC

IO

J

iT

uz -

~C

~U

-J

~~

-U

P

CW

JO

I~

~~

CU

~~

P

9-0

i2 .......................

-u

OJ

-P

OC

QC

--

-O

rn

n&

Jm

CR

03

~J

C

Y C

T~

=C

LC

CC

~&

U-

C

co

ro

nn

c4

c

C~

~L

OC

C~

OO

~C

C~

FC

CN

U.

CC

~~

KP

A

*'

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

C~

N&

~C

O~

Y~

C~

QU

CC

--

--

~~

.T

U~

R

>-

nn

nn

-

--

--

--

nn

nh

n~

nn

nn

n

- - ~

~C

CC

CP

CC

C,

CC

CC

CL

CC

CC

CC

C

CC

-

-C

CC

CC

CC

CO

C=

OC

DC

3C

CC

3C

C=

I

3~

0C

00

CC

OO

OO

CG

G0

CG

00

CC

0C

OC

......................... W

3O

OO

OC

OO

OO

CO

GC

OC

OC

O3

3C

5G

w

0

I- -

>-

NC

CJ

~V

OC

CO

I-

-N

JS

EU

C

C~

IP

~Y

~

P~

-Y

C.

C,

UR

~C

CJ

W~

.~

c

na

.n

a -

v

oa

r-

=

-,

J .......................

z

a \

am

-n

n,

~-

~-

ar

~

sc

cu

c n

cn

.n

nn

o

s 3

nv

.~

~4

bm

mm

~.

mm

mm

mm

90

<

5.

0~

9

c

t t

~~

~r

nr

rr

.n

rr

.r

~w

rr

rr m

r r

8n

v.r

t -

z w

w

-

0

9

DISrAtlCF (XP!.) 0,o 1,o

3.0 a;o 5,o 6 ., 0 ; :: 9,o

10.0 Il;o l?,O IS, 0 14;o 15..0 16,O I 7,n IP,0 19,O PO,') 2l,0 22.0

OEL l r - P [PSI)

12.U8n1 12.1346 1 1 .FOOO 1 1 .???I 2.Oq9U 3.?93? 4.0032 4.?3na e.lorrq 4.02~0 3.8110 3.55hO 3.2766 2.q79z 2.hb9? i?.?)OO ~ . F C S T I .P970 1 .?boo 1 m02bP ehb99 .?a51

0.0000

EOLIIL. Q U A L I T Y 0.000 0.000 o.oo0 0.000 0.000 o.ono Q.000 oeoOo 0.00n 0.000 0.000 0.000 0.oon 0.000 0.000 0.000 O.OOn O.OOn 0.000 0.000 0.003 0.000 0.000

E U I I I L . Q ' J A L I T V 0.00n 0.0DQ O.onn @.0on 0.0on Q.00n O.0On 0.000 0.OOn 0.noo 0.000 0.001) o . nnn 0 . Oun 0.000 0. OOn U.00n 0.000 o.nnn 0.q11n 0. 000 o.ocrn 0.00n

D I R T A N C F

C A L ~ U L A T E D FL i I IO CONOITrONS 4 t TIHE a 0.0000 SECONDS PRES~UQE 8 130; t l P q I h C H A P ~ N E L 1 1 A S J F M R L v 1

TEHPFQATUYF DENSITY (DF6-F) ( L B / C U - F T )

610.00 54.62 610.92 54.98 b 1 9 . e ~ 5 4 . 4 ~ b?U.71 54.50 628 .17 50.47 63?.91 50.0s 676.31 54.41 b30.91 54.se 64?.77 50.34 647.77 50.31 bS! .@q 54.28 bTC.OQ 54.211 hh0.37 5 Q . Z t hh0.71 50.17 bh9.09 54.10 673.51 5 4 . l n 677.96 54.06 hP?.Ua 54.03 hA6 .9~) 53.99 AO6.67 53.99 hR6.00 53.99 hn6.12 50.00 6 A % . P ? 54.00

EO(I IL . v n r o F L O W Q U A L I T Y ra rcT InN f L s / S E t )

0 . 0 0 ~ 0,000 ,1291 0.000 0.000 .I209 0.OOn 0,0nO .1?70 0 . 0 0 ~ 9,ano .109n 0.000 0.000 0.00on 0.0on 0.000 -,0393 0.000 o.ono ,0077 O.OOn 0,000 . n n u 0.nnn 0.000 . ? u ~ Q O.0On 0,000 . O ~ O U 0.oOn o,ono .Ob9u 0.000 0.9no .07LQ 0.000 n,ono . 0 * 3 1 0.0Go 0,ono . O R Q I I 0.000 0.000 .0°31 O.OOn o,onQ . 0 9 ? 1 0.000 0.000 .I nnp o . @ Q n 0.000 .\(I111 0.000 0.0nO . I n7> 0 . 0 0 ~ n.on0 .11n t O.L'n0 0.0-0 . l l ? q O.ODn o,nno . I 1 5 u @,Don n,onO . 1 1 7 ~

E Q U I L , O U A L I T Y 0.00n 0.00n 0.00~1 0.000 0.0On 0.00~: 0.00n 0. OOn 0.000 0.000 0.000 0.000 0.000 o.onrr o.Oon 0.000 U.OUn O.0On 0.000 0,000 0.00n 0,OOn o.onn

rnrn FLD*I r r 1 - s F L I I Y F R A C T I O N ( L R / S E t ) (91 O/UR-FT?) 0.000 .1291 0'4010 0.OnO .1?9pl U:UATS 0.000 .127o 4.as01 0,000 .!16Q u;Cihbh o.on0 .I ~ r ? u;3qzr 0.000 .1?1q U,2?47 n.000 . I I T U P,ORSI 0.000 .llTq 0,0*?? 0.000 . I lQ9 4 '1161 o.ono . I?OI u'lP32 a, onn . I P ~ U 0'2350 0.000 ,12r?q u'ehoo 0.000 . I 2 3 4 u'?o?~ o.ono . I 247 P ~ I ? ~ O 0.000 . I ~ U I ) u'jurn 0, on0 ,1256 U:YT~? 0.000 .l?hT U 3950 0.000 .12to u l a i r r 0,ono .1?7h u;e?gr 0.000 .I Zb? 4.4hOU 0,000 . i e n 7 0;U781 0.000 .129? 4 UOUU o, ono ,17Qq u j3nbr

TE'4PFQbTUSF D E N S I T V ( D F G - F ) ( L R / C U - F T )

h l Or00 54.62 h l ? . b 9 54.60 615.39 5 4 - 5 0 blP.U? 54.55 029.61 50.5s 523.39 54.51 6 h P e l l 54.50 bP?.@? 54.48 619.0' 94.47 h79 a24 54.0'3 h37.5n 54.13 b75.RO 5u.41 638.33 54.39 h'J0.PE 54. 37 64?.4¶ 50.35 h06.09 54.33 hUP.R;! 54.30 659 .bP 54.28 634.43 54m2h b5T.OZ 5u.25 659.5' 5 4 - 2 5 655.99 50.20 hS6. U I '34.24

V E L n f I T Y ( F T I q E r ) ? ? . F - 8 1 P2.8S69 ? ? . o r 7 1 ?U ,O987 77.713n 7h,?nPR J3.7R09 - 1 .UP17 to.nq24 ?9.112C ?a.3717 ?7,kP79 ? ? , l l ~ S h 2h,h'2! ?h.?PDO ?5,QPb? ?5.6121 25,7703 ?5,n757 >U,RP31 ~ 4 . 5 ~ 7 ~ ?u,r lhbr 2u.16111

- 20

00

CC

OO

CO

CO

OO

OO

OC

CO

CO

OC

U

UU

0V

~V

VV

0V

V0

0V

VV

VU

VO

.V

V0

6

WI

~*

=J

~-

~O

J~

~P

B~

~~

JU

J~

~J

J

mr

n-----------------------

IV

JC

LC

CC

CC

CC

C G

CC

GC

GC

CC

CC

CC

.

..

..

..

..

..

..

..

..

..

..

..

.

C

- ~

-~

~~

Jo

o~

~~

~N

cJ

-o

~u

Ec

~~

~~

-

m

PC

-Z

-&

C-

-m

FC

aF

um

CO

~*

N-

Cm

a

Jd.. .................. r

..

z

0

a\

av

-n

~~

~a

u~

&n

~&

~e

~-

nn

n~

~

C

x3mnJJIJJJammmmmmma&4QQ*Q

cC

rr

mn

mn

mc

nr

nV

cr

.r

rC

r.

rm

rC

*1

+

I

Z

ffi w

-

0

2

0

U

a B

~N

Oo

O~

OQ

Om

mL

N"

-N

N~

C

OO

JO

NO

C

n

~

r~

~~

~~

a~

~a

~c

~~

uu

ur

no

oo

wo

~

~O

~N

O~

~~

~Q

NI

~L

CQ

ON

QQ

NV

OO

- -

An

* -

av

.e

no

n.-C

DY

.~

LO

J

C.C

&C

CC

C~

.C

.

A

WY

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

LC

-

O

NN

--

N~

nU

Oa

m~

nN

NN

N-

--

0

N

--I-

0

W +

>u

-Ad O

dw

a

Z-

3

ZE

~

OO

CO

CO

OO

OO

OO

OO

O0

CG

OO

C)

OC

LZL ....-..............................

2-n

~~

c-

N~

~~

~c

~~

o-

N~

~c

Qc

oo

o-

N

(I- --

----------N

fiN

UOU

0

-. Z

OO

OC

0O

CC

CO

OO

OO

C0

00

GO

OO

G

UW

06

00

0~

00

QO

O0

00

V0

PO

0P

00

0

bI~UJJOJO~=JPJIIPEJOSJJJJ

zm

*-

--

--

-+

-d

-d

--

--

e-

4-

--

-

~v

CC

CC

cc

CC

cC

CC

Cc

CC

Oc

cc

Gc

c

..

..

..

..

..

..

..

..

..

..

..

..

t-

~v

co

+-

n=

n~

~c

un

n~

cc

w~

d~

dc

~~

-

WF

-<

P-

N~

OG

~U

~J

C C

C~

ncu--*-*-&

UC

CS

-Y

O

OF

SZ

CW

KY

RI

C~

CC

-z

nz

C

~R

CC

CC

~~

~P

LO

~~

~-

~A

UC

CC

CP

~

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

28-

C.

.

WY

ru

nlw

b0

E C

4n.CO

L'r

C,-.z

dIn

Y~

tn

Y a

J

J

>-

nn

nn

w

~m

vw

.m

n~

nm

nn

nn

~n

nn

n

o Is r rb1c r DELIA-P ( 1 y . I (PSI)

0.0 12.U870 1.0 12. !Z iU E;O I I .6i??3 3,.0 9.750Q 4.0 3 . Q l h h s t n s.aous b , " 3.07?7 T,.n r .?on2 A < 0 U.170? 9,0 4.0106

10,.0 3 . P 0 5 3 I t , 0 3.<5?i! 1 C,0 3.?73" 13.0 2.QTh6 I U ; ~ 2,6671 i 3,n 7.34nr 16,o z.nz?e 17 ,O 1 . 6 ~ 1 7 10.0 i.35nn 19;n 1 . 0 2 ~ 1 20,O a6fiPq 2 l C n . t u r n 22.0 o.nooo

CDLIII.. Q U ' L I T Y

0.00n 0.000 @ * 0 0 0 0.000 o.Oon 0. OOn 0.000 O.OOn 0. GOO 0.000 0.000 O.0On O.OOn 0.000 0.oOn u.000 0.000 O.0On 0. 0On 0.003 0.000 O.DOn 0.000

PREJSURE rn 130;0

OELT A-P ( P S I )

12.4884 1 2 . 1 ~ n e ~ 1 . P 5 t J 12.nhn9

?.RUT? 3.?219 3,097 4 4.?377 4.1859 a.nZRP 3 . ~ 1 I 3 3,55h7 1.?7h9 2.07'25 2.6693 2.3502 2.nCoo 1.6932 1.36oF I ,024b

.68hC

.3u5e n.nono

TCMPEQbTURE D E N S I T Y (OEG-F) ( L B f C U - F T I

b l FeOrl 34.62 618.84 50 .58 h19ebU 54.5U h?4.22 5u.5t 6?7.19 54.48 bhn.17 34.14 bq5.69 34.29 bTU.26 94.26 b 5 6 e f h 54. 24 659.97 54.21 hhF.87 54.18 667.96 sU.15 C7? . lh 54.11 hT6.4O 54.08 b n n e b 7 54.00 614 .91 54.01 6 P 0 , l q 53.97 hP11.4I) 53.94 677.5r\ 93.017 696.53 53,qt h Q 5 e 5 1 53.92 h9u.b' 53.01 6Q3.77 53.93

LQUIL . QUALITY

O.00n 0.000 0.00n 0.0nn o.000 0.00fI 0.00n O.0On 0.000 0.000 o.nnn 0.000 O.OOn O.onr, 0.000 0.0Un o. OOn 0.000 @.OOn O.OOn @,on9 0. n u n D.0nn

PRESSURE 8 13n;n P - I ~ ,

AREA ( $ 0 - I N 1 .OlU90 ,01090 . r1 iu90 . n l n 9 0 ,01490 .n1a90 . ~ I U P O ,01490 .OlUPO ,01490 ,01490 ,01490 . n i u q n .n!usn . e l 4 9 0 . n l u 9 0 ,01490 .n1490 .OlU90 .n1u9n . n l a 9 0 . F l u 9 0 , n 1 u9O

EQUIL. O u A L I r r

0.000 0. QOn 0.000 0 . 0 0 ~ 0.0on 0. Oon 0.000 0.000 0.000 O.OOn 0.000 0. 000 0. OOn 0.000 o.0on 0.0on 0.000 O.O@n O.OOn 0.000 O.c'O0 O.OOn 0.000

w N CALCIJLAIE~ F L l l I n cONOIT~ONS AT T I H E 0.0000 SECONDS Cn CHAPNEL 2 7

A~SFMRLV 1

E Q L I I L . Q U * L I T V

0 . 0 0 ~ O.POn 0.0On 0.000 0.000 O.OOn U.000 U. no0 O. OOn O.00n 0.000 O.OOn 0 . Clan 0.0Qn O.0On O.FO0 0.00n 0.OOn 0.0On O.Ofln o.Onn 0.000 G.011(\

VOID FLOW F R A C T I O N fLR/SEtI

0,000 . I 2 9 1 n.0n0 .1701 0.000 ,l?r)n 0.000 . t 292 o.nno .1971 0 . 0 ~ 0 . I Q n n 0.000 .I757 0.OflO .lb5Q o.ono . l s q ~ 0.000 . 1 5 5 ~ O , O ~ O .1510 O.O'J0 .l uq1 0.000 .la47 0,000 ,lcrur, n.ono .lo20 e,ono .lulr 0.000 .l"00 0.000 .13nr 0.000 .I374 o.onn ,1364 0.000 .135h 0.000 .13U7 0.000 .lsse

FLOW I L n I q F C )

.12Ol

. 1 eo7

. 13no . I an- ,2231 .?lhh .1904 .lP72 .I7Rr .l l ? l . lhh. .16?1 . I =.n9 .I552 .192? .l U Q r .I071 . I 4 5 1 ,1031 . I " l T , I ? O r ,

.1779

.l 3691 --

DELTA-P (P 9 I )

12.u87E 12.1234 1 1 .Cub6

9.AS42 3 . ~ l h 7 3.P304 3.QIbT 'J.7039 4.1721 4.F207 3,8960 3.5527 3 .?T t? 2,0700 z.hb74 2.348u 2.n224 1.691 9 1 .?500 1 .n?Tu

0 6 9 5 0 .3U41

n,oona

T E M P € R A T U R ~ D E N S I T Y ( D E 6 - F ) ( L R / C U - F T )

610.07 511.62 b l P . 5 h 54.60 ht 5.22 S4.5P b l 8 1 2 ' 54.56 6 1 ) .or 54.5 3 6 2 3 . l l 54.5P h?U.B;! 54.50 b2bmbb 54.49 hPP.65 54.47 bqP.74 5 0 . 4 5 h3P.9h 54.03 h l 5 . 7 6 5 0 . ~ 1 b17.65 5U.40 bU(1.13 54.37 hd?.E@ 54.35 t.U';.31 5 4 - 3 1 hUa.On 5 4 - 3 1 b'30.74 54.20 b53.59 54.26 h5U. 1 4 54.Pb bSO.bq 54.25 h5G.19 54.2'3 h59.66 50.7'3

EOUII-. Q U A L I T V

o.OOn 0.000 0 . 000 O.OOn 0. OOn 0.000 0.000 0.00n 0.000 0. OOn 0. OOn 0.000 o.0On 0. c o n 0. OOP U.Oon 0.000 O.OOn n.nnn V. onn U.O"Q o.000 0 , n 11 0

V E L O C I T Y I F T / S E C ) ? e . a J e l ~ 2 ~ ~ 7 3 5 ??,608n 20.01178

0,Pnon 10.1715 11.9215 13.un7e l U , I T l R 15.9h6'i 96.n56u I 7 .hn5n 1 8.2U53 i n . n n i n 19.2931 1q.73z7 p0;110n ~ o . a s u z 20,nPnn 71.1292 ?1.410* $ 1 .*73r, 21.91 3q

AREA ( $ 0 - I N ) . n3300 .n3300 .O3300 .n3:00 .n3300 ,03300 .03300 .n33oo .n330@ .n3300 .n)snn . n ~ 3 o o

.03700 .03300

.n3300

.03301)

. O J ~ O O

.n3300

.03300

.03300 ,03300 .n3300 .n33on

E Q I I I L . Q U A L I T Y

O.OOn 0.000 o.ono 0.000 u,oon 0. o n n O.99n 0.0nr) 0. OOn 0. OOn 0.000 O.OOn o.non 0.OOn 0 . Oon 0 . OOn 0.oon o.no9 o. nqo o.noc C.@On 0,Oljn O.OOn

EQUIL, n u r L I r v

O.OOn 0.000 0.000 0.000 0.000 0.000 0.000 0.0(10 0,000 0.000 U.Oon O.OOn 0.000 0.000 0.009 0.000 0.000 o.oo0 0.000 0.000 0.000 0.000 0. oon

ELJUIL. QUAL ITY

0.000 0.COo O.09n 0.00n 0. OOn 0.000 0.000 0.OOn 0.00n o.onn O.00n 0.0On O.OOn 0.009 O.OOn 0.000 0.000 0.000 O.@OP 0,OOn 0.000 0.0rtn U.nc)n

e u u r ~ . Q U A L I T Y

0. OOn 0.000 0.000 0 . o o n 0.000 U.OOP 0.000 0.00n o.ono 0.oon 0.000 0. o n n o.000 0.00n O o O ~ o 0.o0n O.OOn 0.oon n.000 0.000 0.ono U.0nn ".O"r,

T F C P F Q b T U R E D E N S I T Y (DFG-Fl ( L B / C U - F T )

61n.00 54.62 612.5' 30.60 615.11 54.58 h l 7 . 6 3 54.56 62O.90 54.53 h??mb' SUm52 6 ? u * 5 2 54.50 6Z6.53 5U.UQ 628.b8 Sue07 6 3 @ * 9 a 94.45 b 3 3 a J ' J 54.43 b3q.74 5u.41 b l P 1 3 9 54.39 600.91 54.37 h U 3 . b Z 54.35 bU6.39 34.32 6119.2~ 9U.39 6 7 2 1 1 1 5u.28 b55mOY 54.25 653.71 54.25 656.33 54.24 b S b a 9 1 5 4 - 2 4 697.49 50.23

~ Q I J I L . Q U A L I T Y

0.000 o * 0 0 0 o.ono O.non O * O O @ 0.000 0,000 0.000 0.000 0.000 a, ooo 0.00n O.OO@ O.OO,, 0.oon 0 .OOO 0.0On 0.000 01000 0. OOn o.Oon O.OOn 0.oon

m CROpSFLFW R E T a E r N A ~ J A C E N T C H i N N F L S A T T I Y E 8

+ W IV 4 S s F M R I . v NU*SFR 1 1 1

r ! I b L ZONE H[ 12, I n ) u ( jB, ? a ) b ( 16, 101 o10 - 1.0 * 0 0 4 7 u .001n9 -.nu206 0 - 2.0 , 0 9 9 2 ~ .OjU41 - . ~ 2 0 0 9 a , o - 3.0 ,5593 R . 1 7 r t b -.17510 3,O * u,D 1,75203 .P i l l ?U - .u690? u,0 - 5.0 -.c3891 -.05599 .oJ113 5.0 - 6.0 -.bop83 * . ! ? 5 s l .I 1 0 5 s 6;o - 7.0 -.-352u -.091n0 . n t \ h l l ?,o - 8.0 - . ? ~ b 9 0 - . 0 ~ 1 0 ' 3 - 0 6 0 6 2 O ~ O - 9.0 - . c a u l 1 - . o s b ? l .n"h70 9,O - 10.0 - . j S 1 5 n - ,QUl55 .n3R22

10,o - 11.0 - . i ~ ~ 5 5 - . 0 ~ 1 1 9 .n3225 l l , o - 12.0 3 -.Olh?R .n21R5 1E;O - 13 .0 -.n9167 -,072U1 .nzU41 1 3 . 0 - l U * O -.08li!u -.0?930 la;" - 15.0

. n ? l 1 3 -.fi?R73 -,O?677 .D l956

15, .0- l h . O - 1 -.O?uhB .n118b 1 6 . 0 - 17.0 -. f ibh34 -.0??q4 . n l b h o 7 16.0 -.061Rs - ,O?l f l f ,01572 10.0 - 19.0 - . 0 5 ? 9 ~ -.0?016 . n l u 4 3 19;0 - 20.0 -.0¶UU5 -,OlA?4 . n l J 9 5 ?n,o - 21.0 -.0509n - .n ! th8 .r)1303 2 i . n - t 2 . 0 7 - . 0 t h ? @ . n l l M 5

1 1 f

W ( ?u, 2 7 ) n ( 2 v , 2111 W ( 21, 321 -.003Ja -.nO?b1 .O?nhl - .04100 -.024nfj .O- lhn -.376b2 - . > a y t , o .0?597

- 1 .On674 -.hJRU7 ,0902) . l n o 3 0 .nnb53 .Oqh57 .28143 eS1133 - .O lb?u .22118 . chhun - . O ~ O R E . I 5 8 6 0 .c .?y la -.UQ?UD . l 2 4 9 5 . t 0 0 2 " .OO20q .1 n u 2 1 . n ~ 5 6 0 .oou9h .OQ97U .0?51S .OOb9Q . D l 4P 3 .n5722 . e n a s 1 .07034 .nh09* .OOPhS .Oh360 .n5597 .0109? ,05820 .n91 R R . 0 l I 1 A .05303 .nORU9 .Of l h ? .osoze .0457u .01195 ,Ou737 .nUTU? ,01205 .OuU8Z .n01 2P . O l ? l h . nuzuu . P J ~ O ~ . o t ? ? r .OuOOO .n>h5? .OIP3? . 0 3 7 l l .nT393 . O 1 ?3U

A Y I A L ZONE I ( ln, 1 3 ) -.qO?o!! ,.n3?83 -,yon08

-i.70129 -.h5h26 a4449b ./I3770 . ? u @ o t .18~bR . i §no9 , l asoe rlO~l1 .n9120 en7922 .n69s? .*blbh ,nS521 .nSn00 , nUr 13 .nu.2? .nln9? .n3~70

CROPSCCnw BETWEEN I D J A C ~ U T C H A N N E L S AT T I Y E m 0.0000 S E C f l Y 0 S

INPUT T R A N S I F N T T I M E COMPLFTED

DISTRIBUTION

No. o f Copies

OFFSITE

A. A. Churm U.S. Department o f Energy Chicago Paten t Group Argonne, I L 60439

27 DOE Technica l I n f o r m a t i o n Center

U.S. Department o f Energy A s s i s t a n t D i r e c t o r f o r M a t e r i a l s Germantown, MD 20767

U.S. Department of Energy A s s i s t a n t D i r e c t f o r Eng ineer ing Germantown, MD 20767

U.S. Department o f Energy Ass i s tan t D i r e c t o r f o r Reactor

Sa fe t y Chief , Sa fe t y Ana lys is Branch Germantown, MD 20767

U.S. Department o f Energy Chief , Eng ineer ing Component

Branch Germantown, MD 20767

2 R. J. Neuhold U.S. Department o f Energy Reactor Ana lys i s Branch Germantown, MD 20767

Ca r l Ockert Department o f Energy Germantown, MD 20767

D. K. Magnus Chief , Fue ls Branch Department o f Energy Germantown, MD 20545

No. o f Copies

John Ford A c t i n g Ch ie f Chief Components Sec t ion Department o f Energy Germantown, MD 20545

W. Bennett Chief, Fuel Systems

Sec t ion Department o f Energy Germantown, MD 20545

10 Argonne Code Center Argonne Na t i ona l Labora to ry 9700 S. Cass Avenue Argonne, I L 60439

D i r e c t o r , Components Technology Argonne Na t i ona l Labora to ry 9700 S. Cass Avenue Argonne, I L 60439

P. Be t ten Argonne Na t i ona l Labora to ry 9700 S. Cass Avenue Argonne, I L 60439

R. Henry Argonne Na t i ona l Labora to ry 9700 S. Cass Avenue Argonne, I L 60439

P. L o t t e s Argonne Na t i ona l Labora to ry 9700 S. Cass Avenue Argonne, I L 60439

R. Singer Argonne Na t i ona l Labora to ry 9700 S. Cass Avenue Argonne, I L 60439

No. of Copies

No. o f Copies

Dr. John G. B a r t z i s Components Technology D i v i s i o n Argonne Na t i ona l Labo ra to r y 9700 S. Cass Avenue Argonne, I L 60439

L. F e l t e n Atomics I n t e r n a t i o n a l P.O. Box 309 Canoga Park, CA 91304

B i l l y Bingham Babcock and Wi lcox P.O. Box 1260 Lynchburg, VA 24502

C . Morgan Babcock and W i l cox P.O. Box 1260 Lynchburg, VA 24502

P. Lo renz fu i B e t t i s Atomic Power

Labo ra to r y P.O. Box 79 West M i f f l i n , PA 15122

A. Agrawal Brookhaven Na t i ona l Labo ra to r y B u i l d i n g 130 Upton, NY 11973

Bahman A t e f i Brookhaven Na t i ona l Labo ra to r y B u i l d i n g 130 Upton, NY 11973

B. Chan Brookhaven Na t i ona l Labo ra to r y B u i l d i n g 130 Upton, NY 11973

W. Wu l f f Brookhaven Na t i ona l Labo ra to r y Upton, Long I s l a n d , NY 11973

J. E. C a s t e r l i n e Department o f Chemical

Eng ineer ing Columbia U n i v e r s i t y New York, NY 10027

R. Noyes Combustion Eng ineer ing 1000 Prospect H i1 1 Road W i ndsor, CT 06095

G. d iLauro Combustion Eng ineer ing 1000 Prospect H i l l Road Windsor, CT 06095

P. Nor th EG & G P.O. Box 1625 Idaho F a l l s , I D 83401

T. Ferandez E l e c t r i c Power Research

I n s t i t u t e 3412 H i 11 view Avenue P.O. Box 10412 Palo A l t o , CA 94304

F. Gelhaus F a u l t Ana lys is & Model ing E l e c t r i c Power Research

I n s t i t u t e 3412 H i l l v i e w Avenue P.O. Box 10412 Palo A l t o , CA 94304

J. Kim E l e c t r i c Power Research

I n s t i t u t e P.O. Box 10412 P a l t o A l t o , CA 94303

R. Sehgal E 1 ec tr i c Power Research

I n s t i t u t e P.O. Box 10412 P a l t o A l t o , CA 94303

No. o f C o ~ i e s

No. o f Copies

K. Sun E 1 ec tr i c Power Research

I n s t i t u t e P.O. Box 10412 Palo A1 to , CA 94303

D r . Chandu Baxi General Atomic Co. P.O. Box 81608 San Diego, CA 92138

General E l e c t r i c Company Manager, Reactor Systems

Safe ty Development San Jose, CA 95114

P. McGee General E l e c t r i c Company Manager, Desi gn Engineering Breeder Reactor Development

Operat i on 310 Deguigne Dr i ve Sunnyvale, CA 94086

H. S. B a i l e y General E l e c t r i c Company 310 DeGuigne Dr i ve P.O. Box 5020 M/C 528 Sunnyvale, CA 94086

K. Horst General E l e c t r i c Company 310 DeGuigne Dr i ve P .O. Box 5020 Sunnyvale, CA 94086

D. Sere11 General E l e c t r i c Company 310 DeGuigne D r i v e P.O. Box 5020 Sunnyvale, CA 94086

G. H. Halsey Kno l l s Atomic Power Laboratory General E l e c t r i c Company P.O. Box 1072 Schenectady, NY 12301

N. Todreas Massachusetts I n s t i t u t e o f

Techno1 ogy 77 Massachusetts Avenue Cambridge, MA 02139

E. Davidson U.S. Nuclear Regulatory Commission D i v i s i o n o f Reactor Sa fe t y

Research Washington, DC 20555

S. Fabic U. S. Nuclear Regulatory Commission D i v i s i o n o f Reactor Safe ty

Research Washington, DC 20555

S. I s r a e l U. S. Nuc 1 ear Regu 1 a t o r y Commi s s i on D i v i s i o n o f Technical Review Reactor Systems Branch Washington, DC 20555

P. Norian U.S. Nuclear Regulatory Commission D i v i s i o n o f Technical Review Core Performance Branch Washington, DC 20555

Zo l tan Rostoczy U.S. Nuclear Regulatory Commission D i v i s i o n o f Technical Review Reactor Systems Branch Washington, DC 20555

D. F. Ross U.S. Nuclear Regulatory Commission D i v i s i o n o f Technical Review Core Performance Branch Washington, DC 20555

No. of Copies

No. o f Copies

L. Shotk in M. Cor rad in i U.S. Nuclear Regulatory Commission L i g h t Water Reactor Safe ty D i v i s i o n o f Reactor Safe ty D i v i s i o n

Research Sandi a Labora tor ies Washington, DC 20555 A1 buquerque, NM 87185

L. S. Tong G. E. G i l e s U.S. Nuclear Regulatory Commission Union Carbide Corp. D i v i s i o n o f Reactor Safe ty P.O. Box P

Research Bldg K-1007 MS-49 Washington, DC 20555 Oak Ridge, TN 37830

J. Dearing Oak Ridge Nat iona l Laboratory P.O. Box Y Oak Ridge, TN 37830

M. Fontana Oak Ridge Nat iona l Laboratory P.O. Box Y Oak Ridge, TN 37830

J. Want 1 and Oak Ridge Nat iona l Laboratory P.O. Box Y Oak Ridge, TN 37830

C. Wilson Oak Ridge Nat iona l Laboratory CRBRP P r o j e c t O f f i c e Oak Ridge, TN 37830

L. Peddicord Oregon Sta te U n i v e r s i t y Corva l l i s , OR 97331

R. Lahey Renssel aer Po ly techn ic I n s t i t u t e Department o f Nuclear Engineering Troy, NY 12181

D. S. Rowe Rowe and Associates 14400 Bellevue-Redmond Road,

Su i te 208 Be1 levue, WA 98007

J. Wei sman U n i v e r s i t y o f C i n c i n n a t i C inc inna t i , OH 45221

H. S. I s b i n Department o f Chemi ca 1

Engi neer i ng U n i v e r s i t y o f Minnesota Minneapolis, MN 55455

A. Bishop U n i v e r s i t y o f P i t t sbu rgh P i t tsburgh, PA 15261

D r . Robert Ber r inger Westinghouse Corporat ion Box 19218 Tampa, FL 33616

C. L. Caso Westinghouse E l e c t r i c

Corporat ion P.O. Box 355 P i t tsburgh, PA 15230

M. C a r e l l i Westinghouse E l e c t r i c Corporat ion Advanced Reactors Branch Waltz M i l l S i t e Box 158 Madison, PA 15663

No. of Copies

No. o f Copies

R. Mark ley Westinghouse E l e c t r i c Corporat ion Advanced Reactors Branch Waltz M i l l S i t e Box 158 Madison, PA 15663

E. Novendstern Westinghouse E l e c t r i c Corporat ion Advanced Reactors Branch Waltz M i l l S i t e Box 158 Madison, PA 15663

3 D. Spencer Westi nghouse E l e c t r i c Corporat ion Advanced Reactors Branch Waltz M i l l S i t e Box 158 Madison, PA 15663

Y. Tang Westinghouse E l e c t r i c Corporat ion Advanced Reactors Branch Waltz M i l 1 S i t e Box 158 Madison, PA 15663

B. Vegtor Westinghouse E l e c t r i c Corporat ion Advanced Reactors Branch Waltz M i l l S i t e Box 158 Madison, PA 15663

ONSITE

DOE Richland Operat ions O f f i c e

Westinghouse Hanford Company Hanford Engineer ing Development Laboratory

S. Additon R. Bennett H. B i rney C. Cox E. Evans J. Hanson T. Horning R. Jackson H. Johnson D. E. Mahagin/J. E. I r v i n J. Muraoka

54 P a c i f i c Northwest Laboratory

K. L. Basehore J. M. Bates R. L. Cheatham J. M. Creer J. M. Cuta T. L. George (30) C. R. Hann G. M. Hesson J. M. K e l l e y E. U. Khan W. W. L a i t y F. Panisko W. A. Prather A. M. Sutey C. W . Stewart M. J. Thurgood D. S. Trent C. L. Wheeler Technical I n fo rma t i on ( 5 ) Pub l i sh ing Coord inat ion ( 2 ) PA

H. E. Ransom

COBRA-WC: A Version of COBRA for Single-Phase … · Multiassem bly Thermal Hydraulic Transient...

Documents

Transcript of COBRA-WC: A Version of COBRA for Single-Phase … · Multiassem bly Thermal Hydraulic Transient...