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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
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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
Card Group I n p u t
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 )
Card Group I n p u t
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 ; maxi- mum: 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 .
Card Label Var iab les
SETUP .4 4,NlYN2,N3,N4
N 1
N 2
SETUP.4.1 RHODF , W IDTDF RWALLDF . WTHDF
RHODF
WIDTDF
RWALLDF
WTHDF
Format and Expl anat i o n
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
Card Label Var iab les
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.
Card Label Var iab les
AFACT
Format and Explanat ion
= 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.
Card Label Var iab les Format and Explanat ion
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.
Card Label Var iab les
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 and Expl anat i o n
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.
Card Label Var iab les Format and Explanat ion
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
Card Label Var iab les
SETUP. 8.5 ZEND
IZTYPE
Format and Expl anat i o n
= 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
Card Label Var iab les
SETUP .9
Format and Exp lana t ion
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.
Card Label Var iab les
SETUP .9 N 5
( con td )
Format and Exp lana t ion
= 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)
Format and E x ~ l a n a t i o n
= 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)
Op t i ona l i n p u t : N6 > 0
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 and E x ~ l a n a t i o n
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.
N 1 = 3: use equat ion 3.
N 1 = 4: use equat ion 4.
= 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
Card Label Var iab les Format and Expl anat i on
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)
Format and Explanat ion
= 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
Card Label Var iab les
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)
Opt ional i npu t : N5 > 1
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 )
Opt ional i npu t : N5 > 1
= 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)
Opt ional i npu t : N9 > 1
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))
Opt iona l i npu t : N9 > 1
= 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)
Op t i ona l i n p u t : N8 > 1
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.
Card Label Var iab les Format and Expl anat i on
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 )
Opt ional i npu t : N2 > 0
= 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 )
Opt iona l i npu t : N3 > 0
= 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
Opt ional i npu t : N5 > 0
= 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)
Opt iona l i npu t : N7 > 0
= 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
Card Label Var iab les
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
Format and Expl anat i o n
= 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
Card Label Var iab les
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 mov- ing. 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
Card Label Var iab les Format and Expl anat i on
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
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 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
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
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 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
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 . )
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
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 )
P r i n c i p l e D e f i n i t i o n
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 )
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
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
P r i n c i p l e D e f i n i t i o n
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
P r i n c i p l e D e f i n i 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
P r i n c i p l e D e f i n i t i o n
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)
P r i n c i p l e D e f i n i t i o n
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
P r i n c i p l e D e f i n i t i o n
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)
P r i n c i p l e D e f i n i t i o n
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)
P r i n c i p l e D e f i n i t i o n
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 )
P r i n c i p l e D e f i n i t i o n
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 )
P r i n c i p l e D e f i n i t i o n
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
P r i n c i p l e D e f i n i t i o n
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 )
P r i n c i p l e D e f i n i t i o n
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 . )
P r i n c i p l e D e f i n i t i o 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 para- meters 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 spec- decks
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
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Q
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m
a
a a
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10 1u.o- 2n.n ?.no0 TTMF ~ T E P VbRIATInN TIRLE
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( 1- u i l ( 7- l n )
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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
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2.0 . n 0 7 ~ 4, n -1257 B 6.0 . ? l U b i' 8.0 e l 367 ?
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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
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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
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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
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A R F A (PO-IN1 .n56u0 .n5640 .n§hPO ,05640 .n5huO , n ~ b u o .nfhoO ,nShoO .n5bUO *IrSbOO .OSbUO .OShUO .P54UO
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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
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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
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rn ITEPATI ( !N PPEJSURF r ~ n u FNERBV Ft@. SWEEPS E R R O R FQROR CMAYX E M 4 X J
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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
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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 satu- ration 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 ~ ~
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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
..
..
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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
- - - - - -
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A!!sFM~Lv AVERAGF RE~IULT$ FOR A S ~ E M ~ L V 1 T I M E 8 0.n0000
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POD POWER P E L ~ v E P E o TO THE CnOLbNT 132.563 B T U / ~ E C
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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
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