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.

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