LS - 128@*Jnd A 1 i Khounsar y Tuncer Kuzay
Summary
A N S Y S Program and R e - v a l i d a t i o n o f t he SepteNE~FIVED Thermal A n a l y s i s of t h e C o r n e l 1 S i l i c o n C r y s t a l
SEP 2 3 1996
Thermal a n a l y s i s of t h e C o r n e l l t h r e e - c h a n n e l s i l i c o n c r y s t a l is carr ied
o u t u s i n g the A N S Y S f i n i t e e lement program. R e s u l t s a re i.n g e n e r a l agreement
wi th t h o s e p r e v i o u s l y o b t a i n e d u s i n g t h e T r a n s i e n t Heat T r a n s f e r , v e r s i o n B
(THTB) program. c11
The main t h r u s t of t h e p r e s e n t s t u d y h a s been t o ( a ) e x p l o r e the thermal
a n a l y s i s p o t e n t i a l s of the ANSYS program i n s o l v i n g thermal h y d r a u l i c problems
i n the APS beamline d e s i g n , (b) compare the ANSYS r e s u l t s wi th those o b t a i n e d
by T i T B f o r a s p e c i f i c tes t c rys ta l , and ( c > o b t a i n some cost benchmarks f o r
t he A N S Y S program.
On the basis of a l i m i t e d number of t e s t r u n s f o r the s i l i c o n c rys ta l
problem, c o n c l u s i o n s c a n be drawn t h a t ( a ) e x c e p t f o r c o n d u c t i o n problems w i t h
s i m p l e boundary c o n d i t i o n s t h e u t i l i t y o f A N S Y S for s o l v i n g a v a r i e t y of
three-d imens iona l thermal h y d r a u l i c problems is a t b e s t l i m i t e d , ( b ) i n
comparison wi th THTB program, ANSYS r e q u i r e s a more de ta i l ed modelim ( w i t h
i n c r e a s i n g computa t ion time) for comparably a c c u r a t e r e s u l t s , and (c> no firm
s t a t e m e n t r e g a r d i n g the cost f a c t o r c a n be made a t t h i s time a l t h o u g h the
ANSYS program a p p e a r s t o be more e x p e n s i v e t h a n any o t h e r code we have used so
far.
1 .O I n t r o d u c t i o n
I n t h e a n a l y s i s and d e s i g n of the v a r i o u s beamline components of t h e APS
p r o j e c t , a v a i l a b i l i t y of re l iab le and economical numerical codes f o r heat
t r a n s f e r and stress a n a l y s i s is very desirable . While i n t h e case of s i m p l e r
Problems approximate a n a l y t i c a l s o l u t i o n s or numer ica l codes c a n be developed ,
DISCLAIMER
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f o r more complex problems, i n house development , t e s t i n g , e v a l u a t i o n and
v e r i f i c a t i o n of numer ica l programs are not war ran ted .
A l a r g e number of commercial codes t o hand le thermal h y d r a u l i c problems
are a v a i l a b l e . Some of these codes are a l r e a d y i n s t a l l e d ( b u t no t s u p p o r t e d )
a t ANL. The T r a n s i e n t Heat T r a n s f e r , Ver s ion B (THTB) t h a t has been
e x t e n s i v e l y used i n our a n a l y s e s i s one such code. The System Improved
Numerical D i f f e r i n g Analyzer (SINDA) is ano the r c a p a b l e heat t r a n s f e r codes
a v a i l a b l e a t ANL. Other genera l -purpose , commercial ly a v a i l a b l e , thermal-
hydraul ic codes i n c l u d e PHOENICS, FLUENT, FLOTRAN. TAP2, THAP and
NASTRAN. [*
The c a p a b i l i e s o f these thermal codes vary wide ly and the c h o i c e o f one
over o t h e r s depends not o n l y on the s p e c i f i c a p p l i c a t i o n s bu t a l s o o n such
factors as familiar it y , r e l i a b i l i t y , use r - fr iend 1 i n e s s , docume n t a t i o n ,
s u p p o r t , t h e o p e r a t i n g machine envi ronment , and o f c o u r s e , c o s t .
For stress a n a l y s i s a p p l i c a t i o n s , s i m i l a r l y , a large number o f programs
are a v a i l a b l e . c 4 1
I n a d d i t i o n , there are a number o f broad-based g e n e r a l purpose numerical
programs tha t c a n s o l v e , among o t h e r s , bo th thermal and stress problems.
These programs are e s s e n t i a l l y s t r u c t u r a l a n a l y s i s codes and t h e i r thermal
p r o v i s i o n s are add-on features which, however, have l i m i t e d c a p a b i l i t i e s .
ANSYS is one such genera l -purpose program. It has been a v a i l a b l e a t ANL on
the IBM mainframe and its newest v e r s i o n (4.3A) has j u s t been i n s t a l l e d on the
VAX-8700.
*Some of our A N S Y S r u n s were done t o tes t t h i s new i n t e r a c t i v e v e r s i o n of A N S Y S . I d e n t i c a l programs were r u n at Fermi-Lab. We are not charged f o r these t e s t s a t ANL. A N S Y S 4.3A is expec ted t o be a v a i l a b l e ( b u t not s u p p o r t e d ) f o r g e n e r a l use i n September 1988.
*
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L i k e most o t h e r s t ruc tu ra l a n a l y s i s programs, A N S Y S is a f i n i t e e lement
codes. The f i n i t e e lement approach is now i n c r e a s i n g l y used i n thermal and
f l u i d a n a l y s i s C 5 ' where the f i n i t e d i f f e r e n c e methods have t r a d i t i o n a l l y been
u t i l i z e d . Since bo th the the rma l h y d r a u l i c f i n i t e d i f f e r e n c e program THTB and the
f i n i t e e lement A N S Y S code are a v a i l a b l e o n s i t e , a r e - e v a l u a t i o n o f the
thermal behav io r of t h e Corne l1 th ree -channe l s i l i c o n c r y s t a l was unde r t aken
t o ( 1 ) examine the thermal h y d r a u l i c c a p a b i l i t i e s o f ANSYS, (2 ) v e r i f y t h e
THTB s o l u t i o n , ( 3 ) deve lop a bas i s f o r c o s t comparison, and ( 4 ) carry o u t a n
a n a l y s i s o f the thermal stress i n t h e s i l i c o n c rys ta l u s i n g A N S Y S . The
r e s u l t s o f t h e first three t a s k s are b r i e f l y o u t l i n e d below and the las t item
is now be ing pursued.
2.1 Thermal C a p a b i l i t i e s o f A N S Y S
Typ ica l problems encountered i n t he APS beamline component a n a l y s i s and
d e s i g n invo lve heat t r a n s f e r i n th ree -d imens iona l complex geomet r i e s w i t h
convec t ive boundary c o n d i t i o n s and v a r i o u s flow reg imes . From a n e x t e n s i v e
examina t ion of t h e v a r i o u s ' e l emen t s ' i n ANSYS l i b r a r y , as well as d i s c u s s i o n
wi th t h e SWANSON ANALYSIS SYSTEMS, I N C . (ANSYS d e v e l o p e r ) p e r s o n n e l it seems
t h a t it is not p o s s i b l e , a t least d i r e c t l y , t o model a channe l f low wi th
r a d i a l t empera tu re g r a d i e n t s i n th ree -d imens iona l conduct ion-convect ion
problems. Tinis c a p a b i l i t y is e s s e n t i a l f o r our a n a l y s i s , and t h e matter has
been brought t o the a t t e n t i o n o f SWANSON c o n s u l t a n t s . The e f f ec t s o f f low
rates and mixing , t h e r e f o r e , cannot be modeled by ANSYS. THTB c a n simulate
t h e s e f e a t u r e s i n a s i m p l e f a s h i o n .
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2.2 ANSYS and V e r i f i c a t i o n o f t h e THTB A n a l y s i s
I n o r d e r t o e s t a b l i s h t h e accu racy o f t h e THTB code and t h e resu l t s there
o f , and a l s o t o examine the computa t iona l f e a t u r e s and merits of t h e THTB and
t h e ANSYS programs, t h e C o r n e l l t h ree -channe l ga l l ium-cooled s i l i c o n c r y s t a l
problem is f u r t h e r ana lysed . A uniform x-ray beam of 375 W t o t a l power
i n c i d e n t a t a 1 4 . 3 O C a n g l e is assumed.
T h i s problem is s o l v e d f o r a v a r i e t y o f f low regimes, boundary
c o n d i t i o n s , nodal c o n f i g u r a t i o n s , and code modes. S e v e r a l of these r u n s , t h e
ones most p e r t i n e n t t o our compara t ive a n a l y s i s o f t h e THTB and A N S Y S
programs, are summarily inc luded i n T a b l e 1 where the maximum observed
t empera tu re i n t he c r y s t a l f o r each case is also inc luded .
2.2.1 THTB R e s u l t s
I n Table 1 the summary d e s c r i p t i o n s of f o u r sets of THTB r u n s (Runs #I t o
8) are inc luded . Each se t co r re sponds t o a d i s t i n c t boundary c o n d i t i o n and/or
flow c o n d i t i o n for two t y p i c a l f l u i d (or wall) t empera tu res o f 30° and 5 O O C .
Runs #I & 2 are t h e s t a n d a r d r u n s : t h e y r e p r e s e n t r e a l i s t i c models f o r
t h e s i l i c o n c rys t a l cooled by g a l l i u m f lowing through the three channe l s a t a
ra te o f 1 . 0 gpm (4 .855 f t / s ec ) .
The maximum temperature i n the system f o r t h e 30°C ga l l ium i n l e t
t e n p e r a t u r e is 7O.l0C, and f o r t h e 5 O o C i n l e t t empera tu re is 92.7OC. The
22.6OC d i f f e r e n c e i n the maximum tempera tu res is s l i g h t l y above the 20°C
d i f f e r e n c e i n t h e f low t empera tu re . T h i s 2.6OC d e v i a t i o n r e s u l t s from t h e
t empera tu re dependency o f t he s i l i c o n p r o p e r t i e s .
Runs 83 & 4 d i f f e r from t h e s t a n d a r d case (Runs #l & 2 ) i n t h a t
a r t i f i c a l l y high v a l u e s of g a l l i u m flow r a t e and s p e c i f i c heat are
i n c o r p o r a t e d t o s i m u l a t e a c o n s t a n t bu lk f l u i d t empera tu re . Th i s case is
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necessa ry f o r
convect i o n i n
l a te r comparison wi th t h e ANSYS computa t ions . The improved
t h e s e r u n s r e d u c e s t he maximum system t empera tu re a few degrees
from t h e co r re spond ing s t a n d a r d Runs #1 & 2.
Runs #5 & 6 i n T a b l e 1 are d e r i v e d t o s i m u l a t e a c o n s t a n t channel -wal l
t empera tu re by a s s i g n i n g a v e r y large v a l u e f o r t h e hea t t r a n s f e r
c o e f f i c i e n t . The maximum tempera tu re i n the system is abou t 10°C less t h a n
the co r re spond ing t empera tu re i n t h e ga l l ium-cooled c o n s t a n t bu lk f l u i d
t empera tu re case (Runs #3 & 4 ) , and d i f fe rs from the s t a n d a r d case (Runs #l or
2 ) by abou t 1 5 O C .
I n t h e f i n a l THTB r u n s (Runs f7 & 8) c o n s t a n t channel -wal l t empera tu res
are e x p l i c i t l y imposed.
t h a n the co r re spond ing f i g u r e s f o r t he s imula t ed c o n s t a n t wall t empera tu re i n
Runs #5 & 6 (see Table 1 ) .
The r e s u l t i n g maximum tempera tu res are s l i g h t l y lower
Taken t o g e t h e r , the THTB Runs f l t o 8 d i s p l a y the expec ted behavior o f
the thermal sys tem c o n s i s t e n t l y , and i n p a r t i c u l a r show the heat removal
e f f i c i e n c y from the c r y s t a l from a moderately high convec t ive case ( s t a n d a r d
Runs W1 & 2 ) t o the maximum p o s s i b l e heat removal r a t e when t h e channe l W a l l
is kept a t a c o n s t a n t t empera tu re (Runs #7 & 8) . Noteworthy is t h e
co r re spond ing maximum tempera tu re r i se i n t h e c r y s t a l t h a t v a r i e s from 4 0 . 1 O C
(Runs # l > t o 23.4OC (Runs f 7 ) f o r t h e f l u i d and wall t e m p e r a t u r e o f 30°C
r e s p e c t i v e l y .
2 .2 .2 ANSYS R e s u l t s
The A N S Y S p re -p rocess ing f a c i l i t i e s are used t o produce a nodal
arrangement f o r t h e s i l i c o n c r y s t a l i d e n t i c a l t o t he one used i n THTB r u n s .
T h i s allows a d i rec t comparison between the t empera tu re d i s t r i b u t i o n s o b t a i n e d
by t h e A N S Y S and t he THTB programs.
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Cons ide r ing the l i m i t a t i o n s o f t h e A N S Y S code, o n l y two of t h e f o u r cases
ana lysed by t h e THTB code i n the las t s e c t i o n can be modeled and so lved . They
cor respond t o ( a ) c o n v e c t i o n a t a c o n s t a n t f l u i d bulk temperature, and ( b )
p r e s c r i b e d channel -wal l t empera tu res .
The A N S Y S Runs #9 & 10 i n Table 1 y i e l d the maximum t e m p e r a t u r e s i n t h e
s i l i c o n c rys t a l for c o n s t a n t f l u i d bulk t empera tu re o f 30 and 5 O o C
r e s p e c t i v e l y . While the d i f f e r e n c e between the two maxima o f 56.1°C and
7 8 . 1 O C i s 22.OoC and, therefore, c o n s i s t e n t w i t h t h e THTB r e s u l t s , t h e
t empera tu res themselves are no t . For a f l u i d bulk t empera tu re o f 30°C, THTB
y i e l d s a maximum sys tem t empera tu re of 66.8"C (Run IF31 w h i l e ANSYS g i v e s a
56.1OC (Run #9) t empera tu re , abou t 16% lower.
T h i s d ive rgence of s o l u t i o n , p a r t i c u l a r l y i n view o f the i d e n t i c a l system
s p e c i f i c a t i o n s and nodal arrangement used i n THTB and t h e A N S Y S r e q u i r e s a n
e x p l a n a t i o n ( n o t e t h a t t i g h t and i d e n t i c a l convengence c r i te r ia are used i n
bo th cases).
The d i f f e r e n c e i n the r e s u l t s stems from the fact t h a t ANSYS and THTB
u t i l i z e two d i f f e r e n t numerical scheme based o n two d i s t i n c t concep tua l
approach t o t he f o r m u l a t i o n and s o l u t i o n of t h e problem. That a firm and
g e n e r a l s t a t e m e n t r e g a r d i n g the accuracy of one s o l u t i o n ove r t h e o t h e r cannot
be made is due t o a m u l t i p l e o f f a c t o r s r a n g i n g from problem s p e c i f i c a t i o n s
and boundary c o n d i t i o n s t o t h e precise methodology and a l g o r i t h m used i n the
f i n i t e e lement and f i n i t e d i f f e r e n c e methods.
I n our p a r t i c u l a r problem of thermal a n a l y s i s o f t h e s i l i c o n c rys t a l t he
d i sc repancy between t h e THTB and ANSYS r e s u l t s is a t t r i b u t a b l e t o t h e
inaccuracy i n the ANSYS s o l u t i o n s i n c e we have e v e r y i n d i c a t i o n t h a t t h e THTB
r e s u l t s are bo th c o n s i s t e n t (as, f o r example, Runs 111 t o 8 i n Table 1
i n d i c a t e ) and a c c u r a t e ( a s i n d i c a t e d by our e x t e n s i v e checks and cross-checks
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o f t h e results as well as examina t ion o f ene rgy c o n s e r v a t i o n and convergence
c r i t e r i a 1. *
With t h e a s s u r a n c e o f accu racy i n the THTB r e s u l t s (which is f u r t h e r
v e r i f i e d a s descr ibed below) t h e source of d i s c r e p a n c y between THTB and t h e
ANSYS r e s u l t s may l i e i n the s i z e o f the e l emen t s used i n t h e ANSYS program.
A d d i t i o n a l l y , large aspect r a t io s are though t t o have d e t r i m e n t a l effects o n
t h e accu racy of t h e ANSYS r e s u l t s ; such effects are not expec ted i n THTB
program b a r r i n g s t e e p material p r o p e r t y and t empera tu re g r a d i e n t s .
Thus, for more a c c u r a t e r e s u l t s a n o t h e r A N S Y S r u n i n which the s i l i c o n
c r y s t a l is re-meshed t a k i n g a t o t a l of 8960 nodes ( ins tead of t h e p r e v i o u s
1232) is at tempted (Run # l l , Table 1 ) . I n doing so , we a lmos t double t he
number o f nodes i n each d i r e c t i o n and reduced some o f t h e large element a s p e c t
r a t io s . A s shown i n Table 1 , f o r a f l u i d bulk t empera tu re o f 30°C a maximum
sys t em t empera tu re of 64 .5OC is o b t a i n e d . T h i s is s h a r p l y d i f f e r e n t f rom the
56. loC o b t a i n e d w i t h fewer nodes, and shows t h a t i n t h i s p a r t i c u l a r case ( a )
t h e accu racy of t he ANSYS r e s u l t s is s u b s t a n t i a l l y improved when a v e r y large
number o f nodes is u t i l i z e d and, (b) the improved s o l u t i o n y i e l d s a maximum
tempera tu re i n the system which d i f f e r s from t h e co r re spond ing THTB s o l u t i o n
(Run a31 by o n l y 3%. T h i s is a n independent v e r i f i c a t i o n of the THTB r e s u l t s .
The improved accuracy i n t h e ANSYS r e s u l t s , however, comes a t t h e expense
o f a s u b s t a n t i a l i n c r e a s e i n the computa t ion time, from 200 t o 6000 CPU
seconds or a t h i r t y - f o l d i n c r e a s e . The c o s t of runn ing t h i s program o n t h e
VAX-8700 v a r i e s from $660 ( f o r daytime i n t e r a c t i v e ) t o a n a b s o l u t e minimum o f
$290 ( f o r weekend batch).
"Energy is a u t o m a t i c a l l y conserved i n t h e A N S Y S program and t h u s cannot be used as a means of checking t h e a c c u r a c y o f the r e s u l t s . energy , however, does p rov ide a n independent and ex t r eme ly u s e f u l means f o r examining t h e THTB r e s u l t s . **Figures are based o n a minimum r o y a l t y fees o f 4.lC/CPU seconds and $250/hr ($25/hr ) o f CPU time charge f o r i n t e r a c t i v e (weekend batch) programming o n the VAX-8700 machine.
** -
C o n s e r v a t i o n Of
t
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A s i n d i c a t e d elsewhere i n t h i s memorandum, no a t t e m p t h a s been made t o
op t imize t h i s l a s t ANSYS run . Appropr i a t e p r e p a r a t i o n of t h e problem c a n
s u b s t a n t i a l l y r educe the computa t ion expenses , b u t t h i s w i l l be a t the expense
o f s taff time r e q u i r e d i n t he t e d i o u s t a s k of d e v i s i n g o p t i m a l problem
d e s c r i p t i o n . Two a d d i t i o n a l A N S Y S r u n s (Runs W12 & 13) w i t h c o n s t a n t channel-
wall t e m p e r a t u r e s co r re sdpond ing t o t h e THTB Runs #?’ & 8 r e s p e c t i v e l y , are
inc luded i n Tab le 1 . The 8960 node v e r s i o n s are not r u n f o r these cases for
r e a s o n s of economy
T h i s s e c t i o n c a n be summarized by stating that ( a ) ANSYS canno t d i r e c t l y
s o l v e the s i l i c o n c r y s t a l problem r e a l i s t i c a l l y s i n c e it canno t treat the
channel f low i n t he problem bu t (b) it c a n s o l v e t h e problem i f s imple
convec t ive boundary c o n d i t i o n s o n the channe l walls are imposed, however, ( C )
t o o b t a i n compara t ive ly a c c u r a t e r e s u l t s a much f i n e r nodal d e s c r i p t i o n o f the
s i l i c o n c r y s t a l t h a n t h e one i n THTB a n a l y s i s m u s t be used and ( d ) t h i s
r e q u i r e s a much h igher computa t iona l expense which ( e ) c a n be somewhat reduced
a t t h e expense o f s t a f f time r e q u i r e d f o r problem o p t i m i z a t i o n .
2.3 THTB and A N S Y S Cost Basis
The approximate CPU seconds used i n t h e THTB and ANSYS runs are inc luded
i n Table 1 .
ANSYS runs .
Pre-and pos t -p rocess ing times are not i nc luded i n t he case Of
While no at tempt was made a t o p t i m i z i n g t h e de ta i led ANSYS program Run
811 ( T a b l e 1 ) i t s l o n g computa t ion time ( T a b l e 1 ) is i n d i c a t i v e of t he
expenses invo lved . We g u e s s t i m a t e t ha t by t a k i n g a p p r o p r i a t e o p t i m i z a t i o n
measures i n modeling and p r e p a r a t i o n , t h i s computa t ion time c a n be reduced ,
perhaps by two t h i r d . Our aim here has not been t o r u n a n e f f i c i e n t program,
ra ther t o o b t a i n a fee l f o r the computa t iona l expense.
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The s u b s t a n t i a l d i f f e r e n c e i n computa t ion time between THTB and A N S Y S
(for comparable a c c u r a c y i n resu l t s ) , a p a r t from t h e o p t i m i z a t i o n f a c t o r
a l l u d e d t o above , l i e s i n the fac t t h a t t h e s e two numerical codes e s s e n t i a l l y
u t i l i z e d i f f e r e n t f o r m u l a t i o n and s o l u t i o n approaches . A s mentioned b e f o r e ,
THTB uses a f i n i t e d i f f e r e n c e method whi le A N S Y S is a f i n i t e e lement
program. There seems t o be no g e n e r a l t h e o r y t o e x p l a i n why one approach
y i e l d s b e t t e r resul ts t h a n a n o t h e r f o r a g i v e n problem and c o n f i g u r a t i o n .
It very much depends o n the s p e c i f i c s o f the problem be ing c o n s i d e r e d and the
p r e c i s e manner i n which computa t ions w i t h i n t h e codes a r e performed, a l t h o u g h
under c e r t a i n c o n d i t i o n s , f i n i t e e lement s o l u t i o n s shou ld y i e l d b e t t e r
r e s u l t s .
C6l
THTB is a no-usage fee program bu t A N S Y S carries a minimum cha rge o f 4.1 c
per CPU second o n the V A X - 8 7 0 0 ( w i t h $1000 per month minimum c h a r g e , s i t e
wide ) . T h i s is, of c o u r s e , i n a d d i t i o n t o t h e computer time expenses .
I n summary, it is d i f f i c u l t t o assess c o s t f igures f o r A N S Y S o n the basis
of t h e l i m i t e d number o f tests r u n s , b u t the data i n Table 1 may be used as
rough y a r d s t i c k s .
3. Conclus ions
P r e v i o u s l y o b t a i n e d THTB resu l t s fo r a gal l ium-cooled s i l i c o n c r y s t a l are
v e r i f i e d u s i n g t h e A N S Y S program. A N S Y S c a n be used t o s o l v e v a r i o u s h e a t
t r a n s f e r problems, a l t h o u g h i ts c a p a b i l i t i e s are l i m i t e d n e c e s s i t a t i n g i n
c e r t a i n c a s e s t h e use of o t h e r , more s p e c i f i c , heat t r a n s f e r and f l u i d
codes. The maximum temperature rise i n a n expe r imen ta l 3-channel C o r n e l l
s i l i c o n c rys ta l s u b j e c t t o s y n c h r o t r o n r a d i a t i o n has been v e r i f i e d by both
ANSYS and THTB codes .
, <
TABLE 1: Varloua TilTB and ANSYS run8
Muxlmuin Syatem Approximate CI'U Coluineiit s F l u i d Solid-Fluid lieat Tranef r Coeff. Plow Kate No. of Nodes Temperature, 'C Secouda Used on 7
Temp. ('C) B.C. N(Btu1f tf-'P) f t l s e c i n Nodel VAX-8700 Run I Code Used
THTtl
TllTU
THTB
THTB
30, i n l e t Convective
50, i n l e t Convective
5
6
7
8
9
10
11
12
13
THTB
THTB
THTB
THTB
ANSYS
ANSYS
ANSY s
ANSYS
UJSYS
30, i n l e t Convective
50, i n l e t Convective
Not Applicable Tw-30.C
Not Applicable Ty-50.C
30, Constant Convective
50, Constant Convective
30. Constant Convective
bulk temp.
bulk temp.
bulk temp.
Not Applicable Tw-50.C
Not Applicable Tp50.C
10,ooq
10,000
10,000
10,000
99 ,999
9 9 , 9 9 9
Not Applicable
Not Applicable
10,000
10,000
10,000
Not Applicable
Not Applicable
4.9
4 .9
1,000
1,000
1,000
1,000
Not Applicable
Not Applicable
Not Available
Not Available
Not Available
Not Available
Not Available
1232
1232
1232
1232
1232
1232
1232
1232
1232
1232
8960
1232
1232
70.1
92.7
6 6 . 8
6 9 . 4
55.1
77.4
53.4
75.6
56.1
78.1
64.5
47.9
69.6
700
7 00
7 00
7 00
7 00
700
700
700
200
200
6000
200
200
Standard case8
high flow ra te and s p e c i f t c heat a r e used to simulate a constant f lu ld bulk temperature f o r f l u i d
samc as Runs I 3 and 4, excepc a Ii181i heat t ransfer coef f ic ien t value wall temperature
IS used t o simulate conatant channel-
No flow; channel walls a r e kept a t a constant temperature
ANSYS runs using the same nodal configuration a s i n THTB
de ta i led version of Run 1 9 ; almoat e ight times as many elemcnts a r e used
ANSYS counterparts of THTB r u n s 1 7 and 8
'A node is here defined aa a coordinate locat ion i n 'space. reconcile the d i f fe ren t terminology used i n f i n i t e element and f i n i t e difference methods.
This statement is necessary t o
11
References
1.
2.
3.
4.
5.
6.
A. Khounsary, T. M. Kuzay, and G. A. F o r s t e r , " S i l i c o n C r y s t a l Surface Temperature: Memorandum , June 30, 1 988.
Computat ional and Radiometr ic S t u d i e s , " ANL T e c h n i c a l
R. M. Lueptow, "Sof tware f o r Computa t iona l F l u i d Flow and Heat T r a n s f e r Ana lys i s ,1 t CINE, Vol. 6, No. 5, 1988.
COSMIC Sof tware I n f o r m a t i o n S e r v i c e s . C o l l e c t i o n , " Computer S e r v i c e s Annex, The Univ. of Georgia , Athens, GA. 1985.
"Heat T r a n s f e r and F l u i d Flow
E ng i n e w i ng I nf o r ma t i o n , I ne . E ng i nee r i ng a nd I ndus tr i a 1 Sof t war e D i r e c t o r y , Eng inee r ing In fo rma t ion , I n c . , 1985.
0. C . Z ienkiewicz and Y . K. Cheung, The F i n i t e Element Method i n S t r u c t u r a l and Continuous Mechanics, McGraw-Hill, 1967. - W. J. Minkowycz, e t a l . , Handbook o n Numerical Heat Transfer, Chapter 13, Wile y-I n t ersci e n c e s , 1 988.
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark,
I manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
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