ORNL-TM-2815 by Jon Morrow

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HELP OAK RIDGE N A T I O N A L LABORATORY operated by UNION CARBIDE CORPORATION for

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NUCLEAR DIVISION

the

U. S. A T O M I C E N E R G Y COMMISSION

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ORNL - TM - 2815

COMPUTER PROGRAMS FOR MSBR HEAT EXCHANGERS

C. E,

Bettis

W , K . Crowley H, A. Nelrns

T, W. Pickel M. Siman-Tov W. C. Stoddart

NOTICE This document contains information of a preliminary nature and was prepared primarily for internal use a t the Oak Ridge National Laboratory. I t is subject to revision or correction and therefore does not represent a final report.

This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that i t s use would not infringe privately owned rights. I

OAK RIDGE NATIONAL LABORATORY OPERATED

UNION CARBIDE CORPORATION NUCLEAR DIVISION

POST O F F I C E B O X X

O A K RIDGE, TENNESSEE 37830

June 24, 1971

To:

Recipients o f Subject Report

OR NL- TM-28 15

Report N o . :Author(s):_C_1

Classification:

Unclassified

Bettis, W. K. Crowley, H. A . Nelms, T. W . Pickel

Subject: Computer Programs For MSBR Heat Exchangers

Request c o m p l i a n c e w i t h i n d i c a t e d action: Please a f f i x the a t t a c h e d corrected pages 6, 7, 58,62 , 63, 86,87,88,89, 117, 124, 125 t o pages w i t h same numbers i n your copy(ies) of the subject report. They are prepared o n gummed stock for your c o n v e n i e n c e . Also prepared o n gummed stock i s a c o r r e c t i o n for the bottom t w o lines o n page 9 o f the report. Please ccrrect your copies promptly to avoid further errors.

The corrected design data for

the p r i m a r y heat exchanger agree w i t h the d a t a shown in Report N o . ORNL-4541.

LaGoratory RecordsIDepartment Technica I Information D i v i s i o n

6 Table 2.1,

Design Data for MSBR Primary Heat Exchanger Shell-and-tube one-pass vertical exchanger with disk and doughnut baffles

Number required

Four

Rate of heat transfer per unit, Mw

Btu/hr

556.5 1.9 109

Tube-side conditions Hot fluid Entrance temperature, OF Exit temperature, OF Entrance pressure, psi Pressure drop across exchanger, psi Mass flow rate, lb/hr

Fuel salt 1300 1050 180 130 23.4 x IO6

She11- side conditions Cold fluid Entrance temperature, O F Exit temperature, O F Exit pressure, psi Pressure drop across exchanger, psi Mass flow rate, lb/hr

Coolant salt 850 1150 34 115.7 17.8 x lo6

Tube Material Number required Pitch, in. Outside diameter, in. Wall thickness, in. Length, ft

Hastelloy N 5803 0.75 0.375 0.035 24.4

Tube sheet Materia 1 Thickness, in. Sheet-to-sheet distance, ft Total heat transfer area, ft2 Basis for area calculation

Hastelloy N 4.75 23.2 13,916 Outside of tubes

Volume of fuel salt in tubes, ft3

71.9

Shell Matertal Thickness, in. Inside diameter, in.

Hastelloy N 0.5 67.6

Central tube diameter, in.

20.0

Baffle Type Number Spacing, in.

Disk and doughnut 21 11.23

7 Table 2.1 (continued) Disk o u t s i d e diameter, i n .

54.20

Doughnut i n s i d e diameter, i n .

45.3

Overall hea t r a n s f e r c o e f f i c i e n t , U, Btu/hr. ft', O F

784.8

Tube Maximum primary (P) stresses Calculated, p s i Allowable, p s i Maximum primary and secondary (P + Q) s t r e s s e s Calculated, p s i Allowable, p s i Maximum peak (P + Q + F) stresses Calculated, p s i Allowable, p s i

wave c o n f i g u r a t i o n .

68 3 4232

12,484 12,696 13,563 25,000

The t u b e s are h e l d i n p l a c e by w i r e l a c i n g i n t h i s

upper p o r t i o n of t h e t u b e bundle.

S i n c e b a f f l i n g i s n o t employed i n

t h i s r e g i o n , t h e b e n t - t u b e p o r t i o n o f t h e bundle e x p e r i e n c e s e s s e n t i a l l y

p a r a l l e l flow and a r e l a t i v e l y lower h e a t t r a n s f e r performance. Below t h e b e n t - t u b e r e g i o n of t h e bundle, evenly spaced doughnutshaped b a f f l e s a r e used t o h o l d t h e t u b e s i n p l a c e and t o produce c r o s s flow.

The b a f f l e s s p a c i n g s and c r o s s - f l o w v e l o c i t i e s a r e designed t o min-

i m i z e t h e p o s s i b i l i t y of flow-induced v i b r a t i o n .

The t u b e s i n t h i s b a f -

f l e d r e g i o n of t h e h e a t exchanger have a h e l i c a l i n d e n t a t i o n k n u r l e d i n t o t h e i r s u r f a c e t o enhance t h e f i l m h e a t t r a n s f e r c o e f f i c i e n t s and t h e r e b y reduce t h e f u e l s a l t i n v e n t o r y i n t h e exchanger.

No enhancement

o f t h i s n a t u r e w a s used i n the upper b e n t - t u b e r e g i o n because o f p r e s e n t u n c e r t a i n t y about t h e r e l i a b i l i t y o f t u b e s t h a t a r e both bent and indented

Bottom of page 9 :

For c o m p l e t e l y t u r b u l e n t f l o w w i t h Reynolds numbers g r e a t e r than 12,000,

1047 F O P M A T ( 3 1 W B E R G L I N M O D I F I C A T I O N FACTOR = ~ F 5 . 2 ) 1 0 4 8 FORMAT ( 1HO, 2X , l H I 1 7 X 9 3 H T C I 9 9x9 3 H T C O 9 9 X 9 3HC kT t 9 X 9 3 H T F I9 9 X 93HT FO 9

MSBR MSBR 1 9 x 9 3HFWT9 8X r 4 H T W D T / / l l X , 1 H F , 1 1 X , l H F , P l X , l H F 9 1 1 x 9 MSBP 2 1 H F 9 1 1 X T ~ H 1F1X~9 1HF 9 1 l X 9 LHF / / (1X 9 I3 9 7 E 1 2 . 4 ) 1 MSBR 1049 F O R M A T ( l h C 9 Z X 9 1 H I , 9 X , 2 H V 1 9 9 X 9 2 H V 2 r 9 X 9 2 H V 3 ,9X,3HVW1 ,9X,3HVW3 9 MSBF 1 8 X 9 4 H P D S 0 9 8X , 4 H P C T C / / 3 2 X , 6 H F T / S E C , 3 3 X , 7 H L B / S Q F T / / ( 1 X 9 I 3 9 7 F l 2 04)1 MSBP 1 0 5 G F O R M A T ( l H 0 9 2 X , 1 H I ,5X,5HRENT0,7X95HPRNT0,7X1CHRENSO1 9 6 X 9 6 H R E N S 0 2 , MSBP 1 6 X 9 6HF EN S@3 9 7 x 9 3HHTO98X9 4HAHSOy 9 X 9 3 H U O A , 8 X , 4 H H E A T / / 7 7 X 9 MSBR 2 13HBTU/FR/SQFT/F,13Xr6HBTU/HR//(lX, 1399E12.41 1 MSBP P O 5 1 F O R M A T ( 2 7 P G T U E E WALL AVERAGE TEMP. = t F 1 0 0 21 MSBR 1 0 5 2 F O R M A T ( 2 8 W S h E L L S I D E AVERAGE TEMP. = 9 FlG.21 MSBR 1 0 5 3 F O R M A T ( l H 0 , 3 4 k P STRESS A T TUBE OD AND TUBE ID = T 2FlOo 2 9 1 x 9 MSBR 1 9 H ( L B / S Q I N ) / / 1 8 H ( S H O U L D NOT E X C E E D , F l O o 2 , 3 H 1) MSBR 1 0 5 4 F O R M A T ( L H C , 3 6 k P + Q STRESS A T TUBE 00 AND TUBE I D = 9 MSBR 1 2F 1 0 0 2 9 1 X ,9H( L B / S Q I N ) / / 1 8 H ( SHOULC NOT E X C E E D 9 F l C o 2 9 MSBR 2 3H 1 ) MSBR 1 0 5 5 FORMAT(PHC,38kP+Q+F STRESS A T TUBE OD AFID TUBE I D = 9 MSBR A ~ F ~ ~ o ~ ~ ~ X ~ ~ H ~ L B / S Q I N ~NOT / / ~E ~ X CHE E~ DS9 FHl O@ o 2U , L D MSBR 1) 2 3H MSBP C MSBR C READ I N A h C P R I N T OUT I N P U T DATA MSBP KEY7= 1 MSBR V M 1 ( 11 50 MSBR VM2(11=0. MSBR VM3(1)=0o MSBR VWOl(l)=C. MSBR v w 0 3 ( 1 )=O. MSBR REN SO 1( 1 1 =C MSBR RENSOZ(l)=Oo MSBR RENS03(1)=Oo MSBR HSOl(l)=Oo MSBR HSOZ(P)=Oo MSBR H S 0 3 ( 1) = O m MSBR C MSBR

500 510 511 512 52@ 522

530 531 532 54C 55C 56C 561 570 571 572 580 581 582 650 660

610 620 030

640 650 660 670 680

690 700 710 720 810

I F ( KEY 1 0 E Q o C 1 eSOI=G. 5 * ( BSL+BSH 1 CURVES=Co C6S812*ARC* EXPRAD+ 0 0 4 * ( k A 8 - R A 5 I T = 0 K F I N A L =O 1=1 HEFI = 1 0 H E F O = 1. TSUM=Co SSUM=Co THEATO = (3.0 TPDTO = G o 0 TPDSO = 000 TFO(I)=FTC! T C I ( I1 =C T C T I F =- 5 .O T IC =-5 0 CDTF=Oo FDTF=Oo

)+o25*BSOI

BSO = B S G X BRLl GBRL AWO1 AW03 AW1 AWZ AN3 GSOI.

= B S C / ( ( R A S - ( F A ~ - R A ~ ) / ~ O ) - ( R A ~ - R A ~ ) / ~ . 1)

= Gm77*BRLl**(-0138) = BSC*LAh01 = BSCsLAh03

= SQRT(Ak@l*APOl)

= = = GSO2 = GS03 =

(AbOl+Ak03)/2. SQRT ( A h C 3 * A P @ 3 ) QC/PWl QC/AW2 QC/AW3 BSO=CURV E S E Q V B S G = CURVES+ 13.* ( C I A + D I A I 1 KEY4=C KEY5=C ATC = T C I ( 1 ) + (TIC/Z.O) C F T = A T C +CDTF*HSFCT ATF = T F O ( I ) + l I F / 2 . FFT=ATF-FCTF*kSFCT FI=I T U B L N ( I) = ( F I - l . ) * B S O I + C U R V E S

MSB 1 8 5 0 MSB 1 8 4 0 MSB 1870 MSB 1 8 8 C MSB 1 8 9 0 MSBR 730 MSBk 740 MSB 1900 MSB 1910 MSB 1920 MSB 1 9 3 C MSB 1940 MSB 1 9 5 0 MSB 1960 MSB 1970 YSB 1 9 8 C MSB 1993 MSB 2 0 0 0 MSB 2010 MSB 2 G 2 0 MSB 2030 MSB 2 0 4 C MSB 2 C 5 0 MSB 2 0 6 G M S E 2C70 MSE! 2 C 8 0 MSB 2090 MSB 2100 MSB 2110 MSE! 2 1 2 0 MSB 2130 MSB 2140 MSB 2150 MS0 2 1 6 0 MSB 2180 MSB 2 2 0 0 MSB 2 2 1 0

CVIS=Co212l*EXF(40320/(460o+ATCI 1 C V ISk=Go 2 1 Z l * E X P ( 4 0 3 2. / ( 4 6 0 o + C F T ) I

P3 14

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

222C 2230 2240 2250 2260 2270 228C 229C 2300 2310

CDEN=141 37-Go02466sATC CCON=Co24C C SP H=O 36 FVIS=O.26 3 7 * E X P ( 7 3 6 2 o / ( 4 6 0 o + A T F 1 I F V ISW=Oo 2 637* EXP ( 736 2, / ( 460. + F F T 1 I FDEN=2 34 S7-OoO 2 3 1 7 * A T F FCON=0.70 F SP H=O 3 2 4 VISK = (CLIS/CVISW)**Oo14 2320 F V I SK= ( F V IS / F V ISW 1 * * O e 14 2330 DCVIS = D I A / C V I S 2340 2350 CCGEN = 1 o / C C E N QCCDEN = QC*CCDEN 2360 C A L C U L A T E REYKOLS AND PRANDTL NUMBER TUBE S I D E 2550 R E N T 0 ( I) = C I A I *GTO/ F V IS 2380 PRNTO ( I) = FV I S * F S P H / FCCN 239C I F ( K E N T B o E Q o l o A N D o R E N T C ( I)o G T 0 1 0 0 1 0 .AND. I o N E . 1 ) 2400 l H E F I = l o + ( (RENTG(I)-lGOOo )/9CCGo )**Oo5 2401 PDTO( I ) = ( o ~ G 2 ~ + o 2 5 * ~ E N T O * * ( - o 3 2I)* E Q V B S O s G T O * * Z * H E F I / 2410 1 ( D I A I*FDEN*4171824COo 1 2411 C A L C U L A T E H E A T TRANSFER COEFF TUBE S I D E 2640 I F ( R E N T O ( I) o L T o 1 2 C C C o )GO T O 1 2 HTO ( I1 =FCCN/C I A * o C 2 1 7 * ( R E N T O ( I ) * * 0 8 ) * (PRNTC ( I ) * * o 3 3 3 3 1 * F V I S K * H E F I MS6 2 4 3 0 GO TO 1 5 MSB 2440 I F ( R E N T O ( I ) o L T o 2 1 C C o ) GO TO 14 MSB 2 4 5 0 HTO( I 1 = F C O N / C I A * o C 8 9 * ( R E N T O ( I )**.67895-141.1172)*(PRNTO(I) 1 * % 3 3 3 3 l * FV ISK*HEF I*( l o + o 3 3 3 3 * ( D E A I / T U B L N ( I) )**06666) GO TO 15 M S B 2470 H T O ( 1 ) = F C C N / C I A ~ ( 4 ~ 3 6 + ~ 0 ~ 0 2 5 ~ R E N T O ( I ~ ~ P R N T @ ~ I ~ ~ D1I A I / T MSB UBL 2 4N8~0 I 1 )/(lo+CoO012*RENTOt I)*PRNTC(I )*DIAI/TUBLN(I) 1 ) MSB 2 4 8 1 I F ( I o E Q o 1 I G O TO 16 MSB 2 4 9 0 C A L C U L A T E F L O b ARFAS SHELL S I D E MS0 2480 VWO1( I 1 = QCCDEN/AWOI MSB 2 5 1 0 V W 0 3 ( I )= QCCDEN/AWC3 MSB 2 5 2 0 V M l ( 1 ) = GSOl*CCDEN MSB 2 5 3 0 MSB 2 5 4 0 V M 2 ( I ) = GS024CCDEN V M 3 ( I ) = GSG3WCDEN MSB 2 5 5 0

QI W

Computer Output f o r Reference MSBR Primary Heat Exchanger

TOTAL HEAT TRANSFERED =

18SE2179840

M A S S FLOW K A T E OF COOLANT = MASS FLOW R A T t OF F U E L = SHELL-SIDE TUBE-SIDE

1759Gi36.

2345432Go

UNIFORM BAFFLE SPACING =

(LB/SQIN)

129.32

(LB/SQIN)

71.92

HEAT EXCH.

APPROX.

(FT)

21022

S T R A I G H T S E C T I G N OF TUBE LENGTH =

(FEET) 20.26

R A D I U S O F THERMAL E X P A N S I O N CURVES = B E R G L I N M O D I F I C A T I O N FACTOR = TUBE WALL AVERAGE TEMP, SHELL S I D E AVERAGE TEMP.

13916032

58030

LENGTI- =

0.79 1116.54

99.5

PERCENT)

(CUBIC FEET)

TOTAL HEAT TRANSFER AREA BASED ON TUBE 0.D.

24.43

(

(FTI

TUBE F L U I D VOLUME C O N T A I N E C I N T U B E S =

TOTAL TUBE LENGTH =

9907 PERCENT)

(

(FT)

Lo5386

T O T A L NUMBER OF TUBES =

9 9 0 9 PERCENT)

tLB/HR)

115.75

T O T A L PRESSURE CROP =

2081t2

(

(LB/HR)

TOTAL FRESSURE CRCP =

NOMINAL SHELL RADIUS =

(BTU/HR)

10130 6 6

(FT) 0.86

(FEET)

(SQFT)

P STRESS AT TUBE O D A N D TUBE I D = SHOULD NOT EXCEED

4232.23

1269607C

1 2 3 4 5 6

7 8 9 10

11 12 13

14 15 16

17 18 19

20 21

2500C.CO

8890.97

12484.39

(LB/SQINI

P+Q+F STRESS A T TUBE OD AND TUBE IT; = SHOULD NOT EXCEED

(LB/SQIN)

P+Q STRESS AT TUBE OD A N C TUeE IC = SHOULD NOT EXCEED

646.47

683042

13562077

10981.55

(LBISQIN)

TCI

TCC

CWT

TF I

TFO

FWT

0.1150E 0o1122E 0o1108E 0o1094E 0o1081E 001067E 0.1053E Oo1039E 0o1025E Oe1012E 009579E OoY842E 0.9705E 0o9569E 009433E 0o9297E 009162E 009029E Co8895E 008763E 00863iE

04 04 G4 G4

04 04 04 04 04

04 03

C3 03 03

05 03 03

03 03 03

0o1122E 04 0 o 1 1 0 8 E G4 0 o 1 0 9 4 E 04 0olC81E 0olO67E 0o1053E 0.1039E 0o1025E 0o1012E G.9979E 0o9842E 0o9705E 0.9569E 009433E 0o9297E 0.9162E 009029E 008895E C.8763E 008632E 0o8503E

04 04 04 04 04

04 C3 03 03 03 03 03

03 G3 G3 C3 03 03

Co124CE 001178E 0o116SE 0o1152E 0oll39E Oo1126E 0.1113E Co11CCE 0.1087E 0.1074E 001061E 0o1048E ColG35E 0.1C22E 001009E (309S57E 009827E C09t97E 0.9568E (70943SE 00931l.E

C4 C4 04

04 04 04 04 04 04 04 04 04 04 04 C4 03 03 03

C3 03 C3

0.1276E 001265E 001254E O.1242E 001231E 001219E 0.1208E 001196E 001185E 001173E Oe1162E 001150E 0.1139E 001128E 001116E 001105E Oe1094E 001083E 0.1072E 0.1061E 0o1050E

04 04 04 04 04 04 04 04 04

04 C4 04

04 04 04 04

04 04 04

04 04

0.1300E 001276E 0o1265E 0.1254E 0of242E 0o1231E 0.1219E 001208E 0o1196E 0.1185E Oo1173E 0o1162E 0.115GE 001139E 001128E OolllOE 0o1105E 001094E 0olG83E 001072E 001061E

04 04 04 04 04 04 04 04 04 04

04 04 04 04 04 04 04 04 04

04 04

001256E 001223E OolZlOE Oo1198E 001185E Go1172E 0o1159E 0o1146E 0o1133E 0o1119E 001106E 0o1093E 0.1080E 0o1067E 001053E 0.1040E 0o1027E 0o1014E O.lG00E 009871E 0o9739E

TWDT

04 04

04 G4 04 C4

04 04 04 04 06 04

04 04 04 04 04 04 04

03 03

001549E Ca4528E 0o4516E Oo'i525E 004533E Co4538E 004540E 004540E 0o4538E 004532E 004524E 004513E 0o4499E 004482E 004462E Oo444CIE 004414E 004'385E 0.4353E 004318E 00428CE

C2 02 02 02 02

02 02 G2 02 02 02 C2

@2 02

C2 02

C2 02 02 02 02

o3 . I

VI1

v w3

FT/SEC

1 2 3 4 5 6 7

a 9 1G

11 12 13 14 15 16

17 18 19 20 21

0.0 6.1833 60 1 6 4 9 6. 1467 6.1286 6. I 1 0 6 6.0926 6,0748 60057G 600394 6.0219 6 0045 5.9672 5.9702 5.9532 5,9365 5.9199 5,9035 50 8 8 7 3 5.8713

5.8555

Om0 6.9424 6.S 21 8 6.9C14 6.8810 6.8t08 6.8406 6. 8 206 6,8006 6.78C 8 6.761 2 6.741 6 6.7 2 2 3 6. 7 0 3 1 6.6841 6.6653 6. 6 4 6 7 6.6 283 6.6101 6.5921 6. 5 744

0 6.7222 6.7022 606825 6.6628 6.6432 606236 6 06042 6.584s 60 5 6 5 8 6a 5467 6.5278 60 5C91 6,4905 6.4721 6,4539 6,4358 6.4180 6,4004 60 3 8 3 0 6.3659 Go

PDSO

PDTO

LB/SQFT

0.0 6.3719 6,3530 6.3342 6.3155 6.2970 6.2785 6.2601 6.2418 6. 2 236 6. 2 0 5 5 6.1876 6.1699 6.1522 6.1348 6,1175 6. 1 0 0 4 6,0836 6.0669 6.0504 6.0341

0.0 7.6251 7.6025 7.5801 7.5577 7.5355 7.5133 7.4913 7.4694 7 04477 7.4261 7.4046 7.3834 703623 7.3414 7.3208 7.3003 7.2801 7,2601 7. 2 4 0 4

7.2210

847.431 2 847.4312 841.4097 835.4158 8 2 9 , 4.214 823.4249 a 17.443 8 1 1.4666 805o5016 7990 5500 793.6187 787o7100 7 8 1 . a 259 775.9714 770.1499 704.365 2 758,6204 7 5 2.9199 747.2676 741.6660 736.1208

2869,1321 861.8818 853.9431 846.0403 a38.1379 8 a30.2402 2 2.3506 814.4746 806.6165 798.7803 7 9 0 , 971 2 783.1538 i 75.4529 967.75 29 760.0996 75 2.4968 '144.9495 737.4034 730oG410 722.6892 7 1 5 . 41 14

co co

RENT0

PRNTC

RENSOl

RENSOZ

REkS03

UOA

AHSO

HTO

HE AT

BTU/ HR / S QF T / F

1 2 a

4 5 6

7 8

9 10

11 12 13 14 15 16 17 18

20 21

0.1138E 0.1091E 0.1061E 0.1031E 0.100lE 009721E 0.9434E 0.9151E 008874E 008601E 008333E OoBO71E 0.7814E 0.7562E 007316E 007075E 0.6840E 0.6611E 0.6389E 0.6172E 3.5961E

05 05 05 05 05 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04

0.8232E 0.8589E 008835E 0.9092E 0.9360E 0.9641E 009934E 001024E 001056E 0.1090E 0.1125E 001161E 001199E 0.1239E 001281E 0.1325E 0.1370E 001417E 0.1467E 001518E 001572E

01 01 01 01 01 01 01 02 02 02 02 02 02 02 02 02 02 02 02 02 02

0.0 0m2887E C.2822E 0.2758E 0:2695E 0.2631E 0.2568E 002506E 0o2443E 0.2382E 0.232CE Co226CE 002199E 002140E 002081E 002023E 0.1966E 0.191CE 0.1854E C.18CCE 00174tE

05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05

0.0 0m3241E 0.3169E 0.3097E 0.3026E 002955E 002884E 0m2813E 0.2743E 002674E 0.2605E 002537E 002469E 0m2403E 002337E 0.2272E 0.2207E 0.2144E 0.2082E 0.2021E 001961E

05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05

0.0 0.3138E 003068E 0.2999E 002930E 002861E 002792E 0m2724E 002656E 0.2589E 0.2523E 0.2456E 0.2391E 002326E 0.2263E 0.2199E 0.2137E 0.207tc 0.2016E 0.1956E 0.1898E

05 05 OS 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05

0.17326 0.3422E 0.3318E 0.3232E 0m3147E Oo3063E 0.2979E 0.2896E 0.2814E 0.2732E 0m2651E 0.2571E 0.2492E 0m2413E 0.2335E 002258E 0m2183E 002108E 002034E 0m1961E 001889E

04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04

005314E 0.2580E 002532E 002507E 0.2481E 0.2456E 0.2430E 0m2403E 0.2377E 0.2351E 0m2324E 0.2298E 0m2271E 0m2245E 002218E 0.2192E 0m2165E 002139E 0.2112E 0m2086E 0.2059E

03 04 04 04 04

04 04 04 04 04 04 04 04 04 04 04 04 04

04 04 04

BTU/HR 003653E 0m1044E 0.1026E 0.1014E 0ml001E 009881E 009751E 0m9619E 0o9485E 0.9349E 0.9211E 0.9071E 0.8929E 0.8786E 008640E 0.8493E 0m8345E 0.8194E 0.804ZE 0m7888E 007733E

03 04 04

04 04 C3 03 03 03 C? C3 03 03 03 C?

03 03

C3 03 03

0.1793E 008700E 0.8678E 0.8695E Co8710E C.871SE 0.872*E 0.8724E 0.8719E 0.87CBE Cm86oZE 008672E 0.8645E C.8612E 0.8574E 0.8531E 0m8481E 008426E Ca8364E 0m8297E 008224E

09 Ce C8 08 08 C8 08 C8 08 C8 08 C8 C8 08 08 C8 08 08 C8 08 08

117

P (SOPT) AN0 THE ALLOWABLE TUBE SIDE DELTA-P (DELPTA) YES

CHECK TO SEE I F SOP1 I S WITHIN 3% OF DELPTA

A I I

ADJUST THE NUMBER OF TUBES I N THE EXCHANGER (NUNT) 1

CALCULATE THE DIFFERENCE BETWEEN THE TOTAL SHELL SlOE DELTAP (SOPS) AND THE ALLOWABLE SHELL S I D E DELTA-P (DELPSA)

CHECK TO SEE I F SOPS I S WITHIN 3% OF DELPSA

ADJUST THE BAFFLE SPACING (BS(K))

ALL OF THE HEAT HAS BEEN TRANSFERRED--THE TOTAL PRESSURE OROPS ON BOTH TUBE AN0 SHELL SIDE ARE WITHIN L I M I T S . WE HAVE AN ACCEPTABLE SOLUTION. WRITE OUT THE RESULTS. F i g . D. 1.

(continued)

MS=l SX=O

SBS=O TC( l ) = T C 2 TH( l)=TH1 R WK =DT O*LC.G F ( C TO/D T I 1 / Z O O P C ( 1)= P C 2 CALL S V H ( P p P C f t T C Z t C U C t H C ( 1 I 1 BN=FLOATf (N J QX=QT/ BN O E C T = Q X / ( hH*CPt-) DEC H= QX/ WC 1=1 16

K=1 SB = SBK*BSL LOP7=0 T C O N = T H ( I J-DTPE/2oC I F ( I o E O o 1 ) GO TO 162 VMUO=Oo2122*EXPF(4032o/(TW+460.))

VMUB~Oo2122*EXPF(4032o/(TCON+46Oo 1 1 FACT=( VH UC/ VH Ir 6 1 **0.14 GO TO 1 6 2 161 F A C T = l o O

162 CONTINUE DE"= 141 38 E + C C-2.4 t 6 E - 0 2* TC ON V I SH=O 0 2 1 2 2 € + 0 0 * E X P F ( 403 2oGE+bO / ( TCON+460o 0 E+GO 1 1 DHOT( K )=DE" VHOT( K 1=V 1SP C O N l = ( CPH *V IS )./TCH 1 * * G o 6 C 7 E +OU GM=WH/ Si3 RECB=DTO* EM/V ISH IF( R E C B - 8 0 0 . 0 l l 7 t 1 8 t l e 17 HJB=Om 5 7 1 /( R E C B * * O o 4 5 6 ) GOT019 18 H J t i = O o 3 4 6 / ( RECB**Oo 382) 19 H B = ( H J B*C PH*GC/CON 1 1 *FACT GW =WH/ SW G S = S Q R T f (GM*GbIl RECW=DTO* CS / V I S H I F 4 RECW-80G.O 1 2 0 p 2 1 9 2 1

1030 1030 1c4c 1050 SUP 1060 SUP SUP SUP SUP

SUP IO73 SUP l C P 0 SUP 1 0 9 C SUP 1100 SUP l l l C SUP 1 1 2 0 SUP 1130 SUP 1140 SUP 1 1 5 0 SUP 1 1 6 Q SUP 1170 SUP 1 1 8 0 SUP*11 e 1 SUP*l SUP*1183

la?

SUP* 1194 s u ~ i i a 5 SUP*1186 SUP*? 1 8 1 SUP 1190 SUP ? 2 C G SUP l 2 l G SUP 1 3 2 G SUP 1 2 3 C SUP 1 2 4 C SUP 1 2 5 C SUP 1 2 6 @ SUP 1 2 7 0 SUP 1 2 8 0 SUP 1290 SUP 1300 SUP 1310 SUP 1 3 2 0

SUP 1330 SUP 1340

H J Y = O o 571/ ( RECW**Oo456)

SUP SUP SUP SUP* SUP SUP SUP SUP

GO TO2 2 21 HJW=O. 346/(RECW**0.382 J 2 2 HW=(HJW*CPH*GS/CONl )*FACT HO=(HB*( 1oO02oC*PW J+HY*( 2.0*PWJ HO

wwew

)*BLFH

RO( K ) = l o 0 /HC TH( I + 1 ) = T k ( 1)-DECT LOP5=O HC( I + l )=HC( 1)-CECH OELPP=O.O PC ( I + l )=PC( I ) +CELPP LOP3=0 LOP4=O T C I 1+1) = T C ( I)=D€CH CALL S V H ( 29PC (I+1!r l C ( I + l ) rDUH9tKGJ EH=ABS F ( HC( I + 11-HC G1 I F ( EH-00 OC1*).C( 1+1 J J 3 1 9 3 1 9 2 6 TRIAL=TC( 1+1J

HR IAL=HCG TC ( I + 1 1 = T C ( I+ 11 +( HC ( I +1I-HCG 1 ( TC ( I 1- TC f I + I )1 / iHC ( I 1-HCG 1 CALLSVHt 2 9PC( I+l)rTC( I+1)rOUH9HCG1

EH=ABSF(HC( I + 1 J-HCG)

IF ( EH-O.OC1 *HC ( I+1) 1 3 19 3 19 2 8 T N E X T t TC 4 I + 1 J + (HCI I + 1I-HCG 1 ( TC ( I +1J-TR I P L J /(HCG-HR TRIAL=TC( I + l ) HRIALrHCG TC( 1+1 I=TNEXT

LOP3=LOP3+1

I F ( L O P 3 - 1 C J 3 0 r30r29 29

WR I TEOUTP UTTA P E S 1 9 1 0 15 9 LOP3

GOT080

30 31

SUP

GOT027

IALJ

SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP

SUP SUP SUP SUP SUP SUP SUP

1350 136U

137G 13 80 1390

140C 1410 1420 143@ 1440 1450 146@ 1470 1490 149c 1500 1510 1520 153C 154c 155C 1560 1570 158C 159C 1600 1610

162C 1630 1640 1650 1660

1670

DENOMs(TH(I+11-TC( I + l ) ) / ( T H ( I J - T C ( I 4 ) SUP 1680 TOEWABSF ( D E N C N - l o O ) SUP 169L I F (TDEN-0.051 32933933 SUP 1700 DELTLM=OoSE+OC*(TH( I + l ) - f C ( I + l J + T H ( I I - T C ( I IJ SUP 1710 GO TO 34 SUP 172@ DELTLM=(Tb( I + ] ) - T C ~ I + 1 ~ ~ ~ H ~ I ~ + T C ( I ) ~ / L O G F ~ ~ T H ~ I + l J - T C ~JSUP I + l ~ 1J7/3~CT H ~ l SUP 1731 l-TC(I J ) )

ORNL TM- 2815

Contract No. W-7405-eng-26

Genera 1 Engineering Divi s i o n

COMPUTER PROGRAMS FOR MSBR HEAT EXCHANGERS C. E . B e t t i s

T . W.

W. K. Crowley

M. Siman-Tov W. C. S t o d d a r t

H. A . Nelms

Pickel

APRIL 1971 LEGAL NOTICE This report was prepared as sponsored by the United States the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility 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.

OAK RIDGE NATIONAL LABORATORY

Oak Ridge, Tennessee o p e r a t e d by UNION CARBIDE CORPORATION f o r the U . S . ATOMIC ENERGY COMMISSION

D w m T i O N OF TEilS DOCUMENT IS UNLI-

" Y

iii

CONTENTS

v .

......................................................... 1. INTRODUCTION ................................................. 2 . PRIMEX. THE PRIMARY HEAT EXCHANGER PROGRAM ................... 2 . 1 D e s c r i p t i o n of P r i m a r y H e a t E x c h a n g e r ................... 2.2 Design C a l c u l a t i o n s ..................................... 2.3 D e s c r i p t i o n of PRIMEX ................................... 2 . 4 E v a l u a t i o n of PRIMEX .................................... 3 . RETEX. THE STEAM REHEATER EXCHANGER PROGRAM .................. 3 . 1 D e s c r i p t i o n of S t e a m R e h e a t e r ........................... 3 . 2 D e s i g n C a l c u l a t i o n s ..................................... 3 . 3 D e s c r i p t i o n of RETEX .................................... 3 . 4 E v a l u a t i o n of RETEX ..................................... 4 . SUPEX. THE STEAM GENERATOR SUPERHEATER PROGRAM ............... 4.1 D e s c r i p t i o n of S t e a m Generator .......................... 4 . 2 Design C a l c u l a t i o n s ..................................... 4 . 3 D e s c r i p t i o n of SUPEX .................................... 4.4 E v a l u a t i o n of SUPEX ..................................... REFERENCES ....................................................... A p p e n d i x A: PHYSICAL PROPERTY DATA .............................. A p p e n d i x B : THE PRIMEX P R O G h .................................. Abstract

Appendix C :

THE RETEX PROGRAM

A p p e n d i x D:

THE SUPEX PROGRAM

...................................

1 1 3

8 16 17 19 20 23 23 24 26 27 29 37 39

41 45 49 90

114

LIST OF FIGURES

Figure Number

Title

Page Number

2.1

C r o s s - S e c t i o n a l E l e v a t i o n of a T y p i c a l MSBR Primary H e a t Exchanger

2.2

Zones of Flow Between Two B a f f l e s i n t h e S h e l l Side of t h e MSBR Primary Heat Exchanger

3.1

T y p i c a l MSBR Steam Reheater Exchanger

4.1

T y p i c a l MSBR Steam Generator S u p e r h e a t e r Exchanger

B.l

S i m p l i f i e d Flow Diagram o f the PRIMEX Computer Program

c. 1

S i m p l i f i e d Flow Diagram of t h e RETEX Computer Program

D. 1

S i m p l i f i e d Flow Diagram of the SUPEX Computer Program

115

vii LIST OF TABLES

Tab l e Numb e r

Title

Page Number

2.1

Design Data f o r MSBR Primary Heat Exchanger

3.1

Design Data f o r MSBR Steam Reheater Exchanger

4.1

Design Data f o r MSBR Steam Generator S u p e r h e a t e r Exchanger

4.2

P r e l i m i n a r y S t r e s s C a l c u l a t i o n s f o r MSBR Steam Genera t o r

4.3

Percentage Deviations R e s u l t i n g From C a l c u l a t i o n a l U n c e r t a i n t i e s R e l a t e d t o MSBR Steam Generator Exchanger

A. 1

Design P r o p e r t i e s o f MSBR Fuel S a l t

A. 2

Design P r o p e r t i e s of MSBR Coolant S a l t

A. 3

Design P r o p e r t i e s of H a s t e l l o y N

B. 1

Computer I n p u t Data f o r PRIMEX Program

B.2

Output Data From PRIMEX Program

c. 1 c. 2

Computer I n p u t Data f o r RETEX Program

Output Data From RETEX Program

D. 1

Computer I n p u t Data f o r SUPEX Program

118

D. 2

Output Data From SUPEX Program

119

1 COMPUTER PROGRAMS FOR MSBR HEAT EXCHANGERS

Ab s t r a c t

Three computer programs were developed t o make d e s i g n c a l c u l a t i o n s f o r the h e a t exchangers f o r Molten-Salt Breeder Reactor concepts. They a r e t h e program f o r t h e primary h e a t exchangers, PRIMEX; t h e program f o r t h e r e h e a t e r s , RETEX; and t h e program f o r t h e steam g e n e r a t o r s u p e r h e a t e r s , SUPEX. Each type of exchanger analyzed i s d e s c r i b e d , t h e b a s i c equat i o n s used i n each a n a l y s i s a r e given, and t h e l o g i c used i n each program i s d i s c u s s e d b r i e f l y i n t h i s r e p o r t . Flow d i a grams, l i s t s of i n p u t r e q u i r e d and o u t p u t r e c e i v e d , complete program l i s t i n g s , and t h e nomenclature f o r t h e programs a s w e l l a s example computer i n p u t and o u t p u t f o r t h e exchangers d e s c r i b e d a r e appended.

INTRODUCTION

The concept of a s i n g l e - f l u i d Molten-Salt Breeder Reactor (MSBR) w i t h a thermal c a p a c i t y of 2250 MW and a n e t e l e c t r i c a l o u t p u t of 1000 MW h a s some very s p e c i a l h e a t exchange requirements.

I n t h e p r e s e n t concep-

t u a l d e s i g n f o r t h e MSBR p l a n t , t h e r e a r e f o u r h e a t exchangers i n the primary system t h a t t r a n s f e r h e a t from t h e molten f l u o r i d e f u e l - s a l t mixt u r e t o the m o l t e n s o d i u m fluoroborate coolant s a l t .

I n the secondary

system, t h e r e a r e e i g h t r e h e a t e r s and 16 steam g e n e r a t o r s t h a t t r a n s f e r h e a t from the c o o l a n t s a l t .

The manner i n which t h e s e exchangers were

designed t o m e e t t h e s p e c i a l h e a t exchange requirements and t h e computer programs t h a t were developed t o c a l c u l a t e the d e s i g n numbers a r e d e s c r i b e d i n this report

The development of MSBR concepts passed through a number of s t a g e s d u r i n g which t h e p l a n t l a y o u t was improved, core c o n f i g u r a t i o n s were optimized, and p h y s i c a l p r o p e r t y d a t a were r e f i n e d .

The f i r s t formal

s t u d y of a MSBR h e a t exchange system made by t h e a u t h o r s was r e p o r t e d i n 1967 (GE&C D i v i s i o n Design Analysis S e c t i o n , "Design Study of a HeatExchange System For One MSBR Concept," USAEC Report ORNL TM-1545, Oak

Ridge N a t i o n a l Laboratory, September 1967).

To analyze one exchanger a t

each s t a g e of i t s subsequent development w i t h o u t programming a l a r g e port i o n of the n e c e s s a r y c a l c u l a t i o n s would have meant almost c o n t i n u a l r e p e t i t i o n of t h e s e c a l c u l a t i o n s over a p e r i o d of many months.

With com-

p u t e r programs a v a i l a b l e , t h e d e s i g n f o r an exchanger could e a s i l y be updated f o r changed c a p a c i t y , p h y s i c a l p r o p e r t i e s , t e m p e r a t u r e s , p r e s sures, e t c . Three such computer programs were developed.

One computer program

was w r i t t e n t o make the d e s i g n c a l c u l a t i o n s f o r t h e primary h e a t exchanger, and i t i s t h e PRIMEX program.

This program was modified a t

one s t a g e of i t s development t o perform t h e c a l c u l a t i o n s f o r t h e steam r e h e a t e r exchangers.

This modified v e r s i o n i s t h e RETEX program.

t h i r d computer program was w r i t t e n t o perform the d e s i g n c a l c u l a t i o n s f o r the steam g e n e r a t o r s u p e r h e a t e r exchangers, and i t i s the SUPEX program. The d e s i g n d a t a f o r each of t h e s e t h r e e t y p e s of exchanger, t h e b a s i c e q u a t i o n s used i n each d e s i g n a n a l y s i s , and each of t h e computer programs developed t o perform the a n a l y s i s a r e d e s c r i b e d i n t h e f o l l o w i n g s e c t i o n s of t h i s r e p o r t .

Flow c h a r t s f o r each program, l i s t s of the i n p u t

r e q u i r e d and t h e o u t p u t provided by each program, complete program l i s t i n g s , nomenclature l i s t s f o r each program, and t h e computer i n p u t and o u t p u t f o r each type of h e a t exchanger d i s c u s s e d a r e appended.

3 V

PRIMEX, THE PRIMARY HEAT EXCHANGER PROGRAM

There a r e f o u r primary h e a t exchangers, which t r a n s f e r h e a t from t h e f u e l s a l t t o t h e c o o l a n t s a l t , i n t h e conceptual d e s i g n f o r a s i n g l e f l u i d MSBR.

Each of t h e s e exchangers h a s a thermal c a p a c i t y of 556 MW

and each i s of t h e same d e s i g n .

The f u e l s a l t c i r c u i t s f o r t h e primary

h e a t exchangers a r e i n p a r a l l e l , each having i t s own f u e l pump.

The

c o o l a n t s a l t from each exchanger i s c i r c u l a t e d through i t s own system of two r e h e a t e r exchangers and f o u r steam g e n e r a t o r s .

A t f u l l d e s i g n l o a d , t h e f u e l s a l t e n t e r s t h e t o p of t h e primary h e a t exchanger a t a temperature of 1300째F and e x i t s from t h e bottom a t a temperature of 1050째F f o r r e t u r n t o the r e a c t o r .

The c o o l a n t s a l t a t a

temperature of 850째F e n t e r s t h e top of t h e primary h e a t exchanger and i s d i r e c t e d t o t h e bottom of the exchanger through a c e n t r a l downcomer where i t e n t e r s t h e s h e l l s i d e of t h e exchanger, flows upward i n counterflow

t o the f u e l s a l t , and l e a v e s the top of t h e exchanger a t a temperature of 1150째F.

T h i s c o o l a n t s a l t i s c i r c u l a t e d through the steam r e h e a t e r s and

steam g e n e r a t o r s where i t s h e a t i s t r a n s f e r r e d t o t h e e x h a u s t steam and feedwater , r e s p e c t i v e l y

The d e s i g n c o n d i t i o n s f o r t h e primary h e a t exchanger were p a r t i a l l y d i c t a t e d by t h e o v e r a l l requirements of the MSBR system.

The h e a t l o a d ,

e n t r a n c e and e x i t temperatures of t h e f u e l and c o o l a n t s a l t s , and t h e maximum o r d e s i r e d p r e s s u r e d r o p s a c r o s s t h e s h e l l and tube s i d e s of t h e exchanger were s p e c i f i e d by t h e o p e r a t i n g c o n d i t i o n s of the system. Design c o n s i d e r a t i o n s f o r t h e o v e r a l l system d i c t a t e d t h e type of exchanger, arrangement of n o z z l e s t o f a c i l i t a t e p i p i n g , minimum tube diameter c o n s i d e r e d t o b e c o n s i s t e n t w i t h f a b r i c a t i o n p r a c t i c e s , and t h e l i m i t on t h e o v e r a l l l e n g t h of t h e exchanger.

C e r t a i n c r i t e r i a such a s

the maximum a l l o w a b l e temperature drop a c r o s s the tube w a l l s and t h e need t o b u i l d i n enough tube f l e x i b i l i t y t o compensate f o r d i f f e r e n t i a l t h e r mal expansion were e s t a b l i s h e d by t h e s t r e n g t h of t h e m a t e r i a l s .

Vibra-

t i o n c o n s i d e r a t i o n s p l a c e d l i m i t s on flow v e l o c i t i e s and t h e s p a c i n g between b a f f l e s .

I n a d d i t i o n , i t i s h i g h l y d e s i r a b l e t h a t the volume of

f u e l s a l t be k e p t a t a minimum t o lower the doubling time of the r e a c t o r .

Within the framework of t h e s e requirements and g u i d e l i n e s , a computer program was developed t o perform a parameter s t u d y and s e l e c t t h e d e s i g n f o r t h e primary h e a t exchanger t h a t employs a minimum volume of f u e l s a l t .

The d e s i g n d a t a and e q u a t i o n s d i s c u s s e d i n the f o l l o w i n g

s u b s e c t i o n s were used t o develop the computer program f o r t h e primary h e a t exchanger (PRIMEX).

2.1

D e s c r i p t i o n of Primary Heat Exchanger

Each of t h e f o u r primary h e a t exchangers i s a v e r t i c a l s h e l l - a n d tube type w i t h a s i n g l e counterflow pass on b o t h t h e tube and s h e l l s i d e s . Each u n i t i s about 6 f t i n diameter and about 22 f t t a l l , n o t i n c l u d i n g t h e c o o l a n t s a l t U-bend p i p i n g a t t h e top.

A cross-sectional elevation

of a t y p i c a l primary h e a t exchanger i s i l l u s t r a t e d i n Fig. 2 . 1 ,

and the

p e r t i n e n t d e s i g n d a t a a r e given i n Table 2.1. The f u e l (primary) s a l t e n t e r s the tube s i d e of t h e primary h e a t exchanger a t the top and flows o u t t h e bottom of t h e exchanger a f t e r a s i n g l e p a s s through the 3/8-in.-OD

tubes.

The c o o l a n t (secondary) s a l t

e n t e r s a t the top of the exchanger, flows t o the bottom o f t h e exchanger through a c e n t r a l 20-in.-diameter

downcomer where i t e n t e r s the a n n u l a r

s h e l l c o n t a i n i n g the t u b e s , flows upward around modified d i s k and doughn u t b a f f l e s , and e x i t s through a 28-in.-diameter

p i p e concentric with the

i n l e t p i p e a t the t o p . The t u b e s a r e arranged i n c o n c e n t r i c r i n g s i n t h e bundle w i t h a cons t a n t r a d i a l p i t c h and a c i r c u m f e r e n t i a l p i t c h t h a t i s a s c o n s t a n t a s can be o b t a i n e d .

The L-shaped tubes a r e welded i n t o a h o r i z o n t a l tube

s h e e t a t the bottom and i n t o a v e r t i c a l tube s h e e t a t the top.

The

t o r o i d a l - s h a p e d top head and tube s h e e t assembly h a s a s i g n i f i c a n t s t r e n g t h advantage, s i m p l i f i e s t h e arrangement f o r c o o l a n t - s a l t flow, and allows the s e a l weld f o r the top c l o s u r e t o be l o c a t e d o u t s i d e t h e h e a t exchanger. To accommodate d i f f e r e n t i a l thermal expansion between t h e s h e l l and t u b e s , about 4 f t of the upper p o r t i o n of t h e t u b i n g i s b e n t i n t o a s i n e

ORNL-DWG 69-6004

PRIMARY SALT

Fig. 2 . 1 . C r o s s - S e c t i o n a l E l e v a t i o n of a T y p i c a l MSBR Primary He a t Exchanger.

6 Table 2.1.

Design Data f o r MSBR Primary Heat Exchanger

Shell-and-tube one-pass v e r t i c a l exchanger w i t h d i s k and doughnut b a f f l e s Number r e q u i r e d

Four

Rate of h e a t t r a n s f e r p e r u n i t , Mw Btu/hr

556.5 1.9 x 10"

Tube-side c o n d i t i o n s Hot f l u i d Entrance temperature, OF E x i t temperature , O F Entrance p r e s s u r e , p s i P r e s s u r e drop a c r o s s exchanger, p s i Mass flow r a t e , l b / h r

Fuel s a l t 1300 1050 180 130 23.45 X lo6

Shell-side conditions Cold f l u i d Entrance temperature, O F E x i t temperature, "F Exit pressure, p s i P r e s s u r e drop a c r o s s exchanger, p s i Mass flow r a t e , l b / h r

Coolant s a l t 850 1150 34 116.2 1 7 . 8 x lo6

Tube Materia 1 Number r e q u i r e d Pitch, in. Outside d i a m e t e r , i n . Wall t h i c k n e s s , i n . Length, f t

Hastelloy N 5896 0.75 0.375 0.035 22.57

Tube s h e e t Materia 1 Thickness, i n . Sheet-to-sheet d i s t a n c e , f t

Hastelloy N 4.75 21.31

Total heat transfer area, f t 2 Basis f o r a r e a c a l c u l a t i o n

13,037 Outside of tubes

Volume of f u e l s a l t i n t u b e s , f t 3

67.38

She 11 Materia 1 Thickness, i n . I n s i d e diameter, i n .

Hastelloy N 0.5 68.07

C e n t r a l tube d i a m e t e r , i n .

20.0

Baffle Type Numbe 1: Spacing, i n .

Disk and doughnut

21 11.23

7 Table 2 . 1 ( c o n t i n u e d )

Disk o u t s i d e d i a m e t e r , i n .

54.56

Doughnut i n s i d e d i a m e t e r , i n .

45.54

Overall heat transfer coefficient, U, Btu/hr f t2 O F

838.3

Tube Maximum primary (P) stresses Calculated, p s i Allowable, p s i Maximum primary and secondary (P + Q) stresses Calculated, p s i Allowable, p s i Maximum peak ( P + Q + F) s t r e s s e s Calculated, p s i Allowable , p s i

wave c o n f i g u r a t i o n .

674 3912 11,639 11,737 13,006 25 ,000

The tubes a r e h e l d i n p l a c e by w i r e l a c i n g i n t h i s

upper p o r t i o n of the tube bundle.

Since b a f f l i n g i s n o t employed i n

t h i s r e g i o n , t h e b e n t - t u b e p o r t i o n of the bundle e x p e r i e n c e s e s s e n t i a l l y p a r a l l e l flow and a r e l a t i v e l y lower h e a t t r a n s f e r performance. Below t h e b e n t - t u b e r e g i o n of t h e bundle, e v e n l y spaced doughnutshaped b a f f l e s a r e used t o hold t h e tubes i n p l a c e and t o produce c r o s s flow.

The b a f f l e spacings and c r o s s - f l o w v e l o c i t i e s a r e designed t o min-

imize the p o s s i b i l i t y of flow-induced v i b r a t i o n .

The tubes i n t h i s b a f -

f l e d r e g i o n of t h e h e a t exchanger have a h e l i c a l i n d e n t a t i o n k n u r l e d i n t o t h e i r s u r f a c e t o enhance t h e f i l m h e a t t r a n s f e r c o e f f i c i e n t s and t h e r e b y reduce the f u e l s a l t i n v e n t o r y i n t h e exchanger.

N o enhancement

of t h i s n a t u r e was used i n t h e upper b e n t - t u b e r e g i o n because o f p r e s e n t u n c e r t a i n t y about t h e r e l i a b i l i t y of t u b e s t h a t a r e b o t h b e n t and indented.

8 W

2.2

Design C a l c u l a t i o n s

Since e x p e r i e n c e w i t h b o t h the f u e l and c o o l a n t s a l t s i s l i m i t e d , t h e r e was and s t i l l i s a c e r t a i n degree of u n c e r t a i n t y a s s o c i a t e d w i t h t h e t r a n s p o r t p r o p e r t i e s of s a l t and i t s behavior a s a h e a t t r a n s f e r medium.

The d e s i g n p r o p e r t i e s of t h e f u e l s a l t , c o o l a n t s a l t , and of

H a s t e l l o y N used i n the concept of a s i n g l e - f l u i d MSBR and i n c o r p o r a t e d i n t h e primary h e a t exchanger computer program a r e given i n Appendix A.

A s p r e v i o u s l y d e s c r i b e d , t h e tubes i n t h e b a f f l e d p o r t i o n of t h e primary h e a t exchanger a r e h e l i c a l l y indented t o improve h e a t t r a n s f e r performance.

E . McDonald

Experiments performed by C. G. Lawson, R. J . Kedl, and R. i n d i c a t e d t h a t t h i s i n d e n t a t i o n i s expected t o r e s u l t i n an

improvement by a f a c t o r of 2 i n the t u b e - s i d e h e a t t r a n s f e r c o e f f i c i e n t . An enhancement f a c t o r of 1 . 3 f o r the h e a t t r a n s f e r c o e f f i c i e n t o u t s i d e the tubes i s suggested by Lawson2 although no experiments have been done t o s u p p o r t t h i s recommendation.

The experimental work

t h a t was p e r -

formed w a s l i m i t e d t o Reynolds numbers g r e a t e r than 10,000, and t h e r e i s some u n c e r t a i n t y about the degree of improvement t h a t can be expected f o r Reynolds numbers of l e s s than 10,000.

I t was assumed t h a t no improvement

can be expected i n a t r u l y laminar flow (Reynolds numbers l e s s than l O O O ) , and t h e improvement expected f o r the i n t e r m e d i a t e range was e x t r a p o l a t e d by u s i n g a method suggested by H. A . M ~ L a i n . ~The r e s u l t i n g enhancement f a c t o r s (EF) a r e EFi = 2.0 and EFo = 1 . 3 f o r Reynolds numbers

10,000

1 . 0 f o r Reynolds numbers

1000,

and EFi = 1.0 and EF

= 0

where EFi = enhancement f a c t o r i n s i d e tube and

EFo = enhancement f a c t o r o u t s i d e tube ( c r o s s f l o w ) . For 1000

Reynolds number

10,000, 1I2

EFi = 1.0 i[Nk9~o~ooo] and

= 1.0

1000

+ 0.3( NRe 9ooo

)

JJ2

where N

= t h e corresponding Reynolds number. Re The enhancement f a c t o r s f o r h e a t t r a n s f e r r e s u l t i n g from t h e h e l i c a l

i n d e n t a t i o n of the tubes i n t h e b a f f l e d r e g i o n were assumed t o have a p r o p o r t i o n a t e e f f e c t on p r e s s u r e drop.

The s h e l l - s i d e p r e s s u r e drop was

c a l c u l a t e d by u s i n g the procedure r e p o r t e d by 0. P. B e r g e l i n e t a1.,4 and the t u b e - s i d e p r e s s u r e drop was c a l c u l a t e d by u s i n g the conventional f r i c t i o n - f a c t o r method.

An o v e r a l l leakage f a c t o r of 0.5 was used f o r

the p r e s s u r e drop i n t h e s h e l l s i d e o f the h e a t exchanger, and a f a c t o r of 0.8 was used i n t h e h e a t t r a n s f e r c a l c u l a t i o n s .

These leakage f a c t o r s

were s e l e c t e d on t h e b a s i s of recommendations r e p o r t e d by B e r g e l i n e t a l . The c o r r e c t leakage f a c t o r , which i s dependent upon v a r i o u s c l e a r a n c e s between tubes and b a f f l e s and between b a f f l e s and t h e s h e l l , w i l l have t o be c a l c u l a t e d when t h e a c t u a l d e s i g n f o r the primary h e a t exchanger has been completed

S i n c e molten f l u o r i d e s a l t s do n o t w e t H a s t e l l o y N , the c o n t a i n i n g m a t e r i a l of t h e h e a t exchanger, i t was suspected t h a t t h e u s u a l h e a t t r a n s f e r c o r r e l a t i o n s , which a r e normally based on experiments w i t h water o r petroleum p r o d u c t s , might n o t be v a l i d .

performed by B . Cox

However, r e c e n t experiments

i n d i c a t e d t h a t b a s i c a l l y t h e behavior of t h e f u e l

s a l t i s s i m i l a r t o t h a t of conventional f l u i d s .

The c o r r e l a t i o n s devel-

oped by Cox r e s u l t i n h e a t t r a n s f e r c o e f f i c i e n t s somewhat lower than those o b t a i n e d from t h e S i e d e r and Tate c o r r e l a t i o n s f o r t u r b u l e n t

region^,^

Hansen's e q u a t i o n f o r t r a n s i t i o n r e g i o n s ,

Tate c o r r e l a t i o n s f o r laminar

region^.^

and the S i e d e r and

The c o r r e l a t i o n s used i n t h i s

s t u d y a r e those based on the d a t a developed by Cox t h a t w e r e recommended by H. A. McLain.

These a r e given i n E q s . 2.3,

2.4, and 2.5.

For completely t u r b u l e n t flow w i t h Reynolds numbers g r e a t e r than 12,000,

10 W

where

- h e a t t r a n s f e r c o e f f i c i e n t i n s i d e t u b e , B t u / h r . f t 2 * OF, hi di - i n s i d e diameter of t u b e , f t , k.1

= thermal c o n d u c t i v i t y of f l u i d i n s i d e t u b e , B t u / h r . f t *

OF,

Reynolds number, NRe NPr = P r a n d t l number, v i s c o s i t y a t temperature of bulk f l u i d , l b / h r - f t ,

Fb= Pi -

v i s c o s i t y of f l u i d a t temperature of i n s i d e s u r f a c e of t u b e , l b / h r * f t , and

EFi = enhancement f a c t o r f o r h e l i c a l l y indented tubes g i v e n i n Eq. 2 . 1 . Based on t h e i n s i d e diameter of t h e t u b e , the Reynolds number diGi =-

NRe where Gi

mean mass v e l o c i t y of f l u i d i n s i d e t h e tube, l b / h r - f t 2 .

;1/

For

completely laminar flow w i t h Reynolds numbers l e s s than 2100,

hidi =

where

= l e n g t h of tube from the e n t r a n c e t o t h e l o c a l p o i n t , f t .

the i n t e r m e d i a t e r e g i o n where 2100

Reynolds number

For

12000,

The p r e s s u r e drop i n s i d e t h e tubes was c a l c u l a t e d by u s i n g the exp re s s i o n

where f = friction factor, L = length of tube, f t ,

di = i n s i d e diameter of t u b e , f t ,

11 2

= mean mass v e l o c i t y of f l u i d i n s i d e t u b e , l b l h r - f t Gi 'i = d e n s i t y of f l u i d i n s i d e t u b e , l b / f t 3 ,

lo8

gc = dimensional conversion f a c t o r = 4.18 X EFi

Ib,.ft/lbf.hr*,

and

enhancement f a c t o r f o r h e l i c a l l y indented t u b e s given i n E q . 2.1.

The f r i c t i o n f a c t o r f o r t u r b u l e n t flow (NRe

2100) i s given by t h e

e x p r e s si o n f = 0.0014 i0.125(NR,) and t h e f r i c t i o n f a c t o r f o r laminar flow (N

-0.32

2100) i s given by t h e

exp re s s i o n f = -16

NRe The h e a t t r a n s f e r c o e f f i c i e n t a c r o s s the tube w a l l i s given by the expression

where

k d

= thermal c o n d u c t i v i t y , B t u / h r - f t * O F , = o u t s i d e diameter of t u b e , f t ,

t = w a l l t h i c k n e s s , f t , and di

i n s i d e diameter of t u b e , f t .

No experiments have been performed t o d a t e t o develop c o r r e l a t i o n s

f o r t h e h e a t t r a n s f e r b e h a v i o r of a sodium f l u o r o b o r a t e c o o l a n t s a l t i n the s h e l l s i d e of t h e h e a t exchanger. Bergelin e t

The c o r r e l a t i o n developed by 0 . P.

was used f o r t h e b a f f l e d r e g i o n of t h e MSBR primary h e a t

exchanger, and the c o r r e l a t i o n developed by D. A. Donohuelo was used f o r the unbaffled region. Although s e l e c t e d a s b e i n g t h e most r e p r e s e n t a t i v e a v a i l a b l e f o r the b a f f l e d r e g i o n , B e r g e l i n ' s c o r r e l a t i o n * i s s t r i c t l y f o r c r o s s flow and h i s d a t a were based on work w i t h half-moon shaped b a f f l e s w i t h s t r a i g h t edges.

S i n c e d i s k and doughnut b a f f l e s a r e used i n t h e MSBR primary h e a t

exchanger, t h e a d a p t a t i o n of B e r g e l i n ' s d a t a involved c e r t a i n i n t e r p r e t a t i o n s i n determining the c r o s s - s e c t i o n a l a r e a s involved.

The c o r r e l a t i o n

12 f o r c r o s s flow was a l s o modified by the i n t r o d u c t i o n of a c o r r e c t i o n factor.

This c o r r e c t i o n f a c t o r i s dependent upon the degree of a c t u a l

c r o s s flow t h a t e x i s t s a s determined b y the r a t i o between t h e b a f f l e s p a c i n g and t h e a n n u l a r t h i c k n e s s of t h e v e s s e l .

Data from B e r g e l i n ' s

o r i g i n a l experiment4 were used t o e s t i m a t e the v a l u e of t h e c o r r e c t i o n f a c t o r , which i s expressed a s

BCF = 0 . 7 7 -

(2.10)

where BCF = c o r r e c t i o n f a c t o r f o r s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t a s proposed by Berge l i n , 4

X = b a f f l e spacing ( a s i l l u s t r a t e d i n Fig. 2 . 2 ) ,

f t , and

= r a d i a l d i s t a n c e from c e n t e r of window t o c e n t e r of opposing

window ( a s i l l u s t r a t e d i n Fig. 2 . 2 ) , f t .

- WINDOW Z O N E

- B A F F L E Z O N E ( P U R E CROSS FLOW)

- WINDOW Z O N E

Fig. 2 . 2 . Zones of Flow Between Two B a f f l e s i n t h e S h e l l Side of t h e MSBR Primary H e s t Exchanger.

I n the method advanced by

i s considered a s t h r e e p a r t s :

berg el it^,^ t h e r e g i o n between two b a f f l e s one pure c r o s s - f l o w zone between two win-

dow zones, a s i l l u s t r a t e d i n Fig. 2 . 2 .

The mass velo'city i n each zone

i s based on t h e e f f e c t i v e a r e a of each zone.

I n a window zone, t h e

e f f e c t i v e a r e a i s given by t h e e x p r e s s i o n (2.11) where Sw = f r e e c r o s s - s e c t i o n a l a r e a i n b a f f l e window, ft',

and

SB = f r e e c r o s s - s e c t i o n a l a r e a f o r c r o s s flow between tubes a p p l i e d a t l i p of t h e b a f f l e , f t 2 . The e f f e c t i v e a r e a of t h e pure cross-flow zone i s given by t h e e x p r e s s i o n

m '

= 0.5(S

SB2)

(2.12)

where t h e i n d i c e s 1 and 2 i n d i c a t e t h e s i d e s of t h e pure c r o s s - f l o w zone. Based on t h i s d e f i n i t i o n of t h e a r e a s o r zones used t o c a l c u l a t e t h e mass v e l o c i t y , t h e Reynolds number f o r each zone i s determined from t h e expression

-%e

(2.13)

where d

= o u t s i d e diameter of the t u b e , f t ,

G = mass v e l o c i t y of t h e f l u i d o u t s i d e t h e t u b e s , l b / h r . f t ' , p,,

and

v i s c o s i t y a t temperature of bulk f l u i d , l b / h r - f t .

The r e l a t i o n s h i p between t h e Reynolds number f o r each flow zone and

an a p p r o p r i a t e h e a t t r a n s f e r f a c t o r (J) i s developed i n B e r g e l i n ' s meth~

d The . ~h e a t t r a n s f e r f a c t o r f o r t h e window zone i s determined from the

expression

-(?)(%] h

213

Jw = C G P m

0.14

(EFo)(BCF) (LF)

where h

= h e a t t r a n s f e r c o e f f i c i e n t f o r window zone, B t u / h r * f t 2 . ' F , = specific heat, Btu/lb*"F,

Gm = mean mass v e l o c i t y of f l u i d , l b / h r - f t 2 ,

(2.14)

14 J

k = thermal c o n d u c t i v i t y , B t u / h r . f t * " F , p,,

= v i s c o s i t y a t temperature of bulk f l u i d , l b / h r * f t ,

= v i s c o s i t y of f l u i d a t temperature of w a l l s u r f a c e , l b / h r . f t ,

= enhancement f a c t o r o u t s i d e h e l i c a l l y i n d e n t e d tube given by

Eq. 2 . 2 ,

BCF = c o r r e c t i o n f a c t o r f o r s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t given by Eq. 2.10, and LF = leakage f a c t o r f o r h e a t t r a n s f e r taken a s 0.8.

The h e a t t r a n s f e r f a c t o r f o r the c r o s s - f l o w zone (J ) i s determined from B the expression

cppb k

J B = ? ? - (hB

) 213

(:) 0.14

(EFo) (BCF) (LF)

(2.15)

P B Equations 2.16 and 2 . 1 7 were d e r i v e d from t h e graph of J v e r s u s NRe given i n Ref. 4 t o determine t h e v a l u e s of J .

The v a l u e s of 3 determined from

E q s . 2.16 and 2.17 w e r e then used i n E q s .

2.14 and 2.15 t o determine t h e

h e a t t r a n s f e r c o e f f i c i e n t s f o r the window zones and the c r o s s - f l o w zone (hw and h B ) . For 800

NRe

For 100 _< NRe

5 lo5 ,

3 = 0.346 (NRe)0 -382

_< 800,

0.571(N

)0'456

(2.16) (2.17)

The v a l u e s of the h e a t t r a n s f e r c o e f f i c i e n t s f o r t h e window zones (h Wl

and h

) and the v a l u e f o r the c r o s s - f l o w zone (h ) were then combined w2 B i n E q . 2.18 t o determine t h e t o t a l h e a t t r a n s f e r c o e f f i c i e n t f o r t h e

r e g i o n between two b a f f l e s . h t = h a

B B

+ h

a WI

+ h

(2.18)

a w2 w 2

where a = t h e a r e a of h e a t t r a n s f e r s u r f a c e i n each zone, f t 2 / f t . The d a t a r e p o r t e d by D. A . Donohuelo were used f o r h e a t t r a n s f e r c a l c u l a t i o n s i n v o l v i n g p a r a l l e l flow on t h e s h e l l s i d e of t h e MSBR p r i mary h e a t exchanger.

The h e a t t r a n s f e r c o e f f i c i e n t o u t s i d e t h e tubes i s

given by t h e e x p r e s s i o n

(e)( d G

(12d

)O*s

0.6

1-1

pb ko

0.33

(?)

0.14

(2.19) W

15 v

where ko = thermal c o n d u c t i v i t y of f l u i d o u t s i d e t u b e s , B t u / h r . f t .

OF,

do = o u t s i d e diameter of tube, f t , d

= e q u i v a l e n t diameter, f t , eq G = mass v e l o c i t y o f f l u i d o u t s i d e t u b e s , l b / h r . f t 2 ,

bulk f l u i d , l b / h r - f t ,

= v i s c o s i t y a t temperature of

C = s p e c i f i c h e a t , B t u / l b . " F , and P = v i s c o s i t y of f l u i d a t temperature of w a l l s u r f a c e , l b / h r - f t .

FrS

The o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t was then c a l c u l a t e d by u s i n g the expression

= '

1 + -1 ho

where h o ,

(2.20)

L(2) hi di

and h . a r e t h e s h e l l - s i d e , w a l l , and t u b e - s i d e h e a t t r a n s 1

f e r coefficients, respectively

The s h e l l - s i d e p r e s s u r e drops i n the b a f f l e d r e g i o n of t h e MSBR primary h e a t exchanger were c a l c u l a t e d by u s i n g the e q u a t i o n s r e p o r t e d by

0. P. B e r g e l i n e t a l . *

The p r e s s u r e drop a c r o s s the c r o s s - f l o w zone i s

given by t h e e x p r e s s i o n

LIPcross flow

(2.21)

where r

= number o f cross-flow restrictions, B p = d e n s i t y of f l u i d , l b / f t 3 , = c r o s s - f l o w v e l o c i t y of f l u i d (based on e f f e c t i v e a r e a S

by Eq. 2 . 1 2 1 ,

ft/sec,

given

gc = dimensional conversion f a c t o r = 32.2 l b m . f t / l b f * s e c 2 , PLF = p r e s s u r e drop leakage f a c t o r taken a s 0.5, and EF = enhancement f a c t o r o u t s i d e h e l i c a l l y indented tubes t a k e n a s 1 - 3 0 The p r e s s u r e drop a c r o s s t h e window zone i s given by t h e e x p r e s s i o n

LIP window

(2.22)

16 W

where

= number of r e s t r i c t i o n s i n t h e window zone and

= mean flow v e l o c i t y (based on the e f f e c t i v e a r e a S

Eq. 2.11),

ft/sec.

given by

The number of r e s t r i c t i o n s was i n t e r p r e t e d a s b e i n g t h e number of rows of t u b e s i n the d i r e c t i o n of c r o s s flow.

The f u l l number was used f o r

the c r o s s - f l o w zone, while o n l y h a l f of t h e number of rows was used f o r each of t h e window zones.

The s h e l l - s i d e p r e s s u r e drop i n t h e upper

b e n t - t u b e r e g i o n of the exchanger was taken a s b e i n g approximately e q u a l t o t h e p r e s s u r e drop a c r o s s one b a f f l e d zone.

2.3

D e s c r i p t i o n of PRIMEX

The computer program f o r the MSBR primary h e a t exchanger, PRIMEX,

i s p r e s e n t e d i n Appendix B.

I n t h i s program, each zone between two b a f -

f l e s was considered a s one increment l e n g t h .

The c a l c u l a t i o n s a r e begun

on t h e h o t s i d e o f t h e h e a t exchanger, and increments a r e added u n t i l a complete h e a t b a l a n c e i s achieved.

The dependence of each of t h e p h y s i -

c a l p r o p e r t i e s on temperature i s given a s an e m p i r i c a l e q u a t i o n , and t h e s e e q u a t i o n s a r e i n c o r p o r a t e d i n the main program.

I f any of t h e s e

e q u a t i o n s a r e changed, the a p p r o p r i a t e d a t a c a r d must be r e p l a c e d .

The

physical property d a t a a s w e l l a s the o t h e r input d a t a required f o r the PRIMEX program a r e l i s t e d i n Appendix B .

A l i s t of t h e o u t p u t d a t a

r e c e i v e d from the computer i s a l s o p r e s e n t e d .

A s t r e s s a n a l y s i s s u b r o u t i n e , TUBSTR, i s i n c o r p o r a t e d i n t h e main program.

This s u b r o u t i n e performs a p r e l i m i n a r y s t r e s s a n a l y s i s o f t h e

t u b e s w i t h t h e assumption t h a t t h e maximum tube s t r e s s w i l l o c c u r i n t h e upper b e n t - t u b e r e g i o n of the h e a t exchanger.

P r e s s u r e s t r e s s e s , stresses

r e s u l t i n g from thermal expansion, and s t r e s s e s r e s u l t i n g from t h e thermal g r a d i e n t a c r o s s the tube w a l l a r e c o n s i d e r e d .

The primary and secondary

s t r e s s e s a r e computed, and t h e s e computed v a l u e s a r e compared w i t h t h e a l l o w a b l e v a l u e s given i n S e c t i o n 111, Nuclear Vessels, of t h e ASME B o i l e r and P r e s s u r e Vessel Code.

A second s u b r o u t i n e , LAGR, i s used f o r

17 U

i n t e r p o l a t i o n of v a l u e s from a given t a b l e .

The complete l i s t i n g f o r t h e

main program t o g e t h e r w i t h i t s two s u b r o u t i n e s i s given i n Appendix B . To i l l u s t r a t e t h e u s e of t h e PRIMEX program, the computer i n p u t d a t a

f o r the MSBR primary h e a t exchanger d i s c u s s e d i n Subsection 2 . 1 and t h e o u t p u t d a t a p r i n t e d by t h e computer a r e i n c l u d e d i n Appendix B .

The time

r e q u i r e d f o r a t y p i c a l IBM 360/91 computer run of t h i s program i s about

2 minutes.

2.4

E v a l u a t i o n of PRIMEX

It i s b e l i e v e d t h a t the use of t h e PRIMEX computer program w i l l

r e s u l t i n a primary h e a t exchanger whose volume of f u e l s a l t w i l l be k e p t t o a minimum and whose d e s i g n w i l l be more r e l i a b l e than can be achieved w i t h normal hand c a l c u l a t i o n s .

V a r i a t i o n s i n p h y s i c a l p r o p e r t i e s and

complicated geometries a r e handled e a s i l y , and an e x t e n s i v e parameter s t u d y can be made i n a very s h o r t t i m e . However, t h e o u t p u t of a computer program cannot be b e t t e r than t h e input.

The i n p u t d a t a which have a s i g n i f i c a n t e f f e c t on t h e d e s i g n of

t h e h e a t exchanger a r e the p h y s i c a l p r o p e r t i e s of t h e f u e l and c o o l a n t s a l t s , t h e h e a t t r a n s f e r c o r r e l a t i o n s u s e d , t h e enhancement f a c t o r s assumed f o r the h e l i c a l l y i n d e n t e d t u b e s , and t h e leakage f a c t o r s a s s o c i ated with fabrication clearances.

The average d e v i a t i o n s i n t h e p h y s i c a l

p r o p e r t i e s of t h e f u e l and c o o l a n t s a l t s p r e s e n t l y used i n the program a r e those r e p o r t e d by J. R. McWherter.â&#x20AC;?

The most n o t a b l e u n c e r t a i n t i e s

i n the physical property values p r e s e n t l y a r e associated with the viscosi t y and thermal c o n d u c t i v i t y of the f u e l s a l t .

The average d e v i a t i o n

f o r t h e f u e l - s a l t h e a t t r a n s f e r c o r r e l a t i o n i s r e p o r t e d 6 a s b e i n g about 5.7%.

The d e v i a t i o n o r e r r o r r e s u l t i n g from t h e u s e of B e r g e l i n â&#x20AC;&#x2122; s c o r -

r e l a t i o n 4 i s n o t c e r t a i n , b u t s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t s normally have a d e v i a t i o n of about 25%.

The leakage f a c t o r d e v i a t i o n f o r

t h e p r e s s u r e drop might be about 20%, and t h e leakage f a c t o r d e v i a t i o n f o r t h e s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t might be about 10%. The enhancement f a c t o r d e v i a t i o n might be about 15%.

18 The two extreme c a s e s w e r e checked.

A l l of t h e p e s s i m i s t i c v a l u e s

were used i n one c a s e , and a l l of t h e o p t i m i s t i c v a l u e s were used i n the other case.

The r e s u l t was a maximum e s t i m a t e d d e v i a t i o n i n t h e o v e r a l l

h e a t t r a n s f e r a r e a ( o r volume of f u e l s a l t ) of +38% ( a d d i t i o n a l a r e a r e q u i r e d ) f o r t h e p e s s i m i s t i c case and -28% ( l e s s a r e a r e q u i r e d ) f o r t h e o p t i m i s t i c case.

RETEX, THE STEAM REHEATER EXCHANGER PROGRAM

The c o o l a n t s a l t c i r c u l a t i n g system i n t h e conceptual d e s i g n of a s i n g l e - f l u i d MSBR c o n s i s t s of f o u r independent loops, each c o n t a i n i n g s a l t c i r c u l a t i n g pumps, steam g e n e r a t o r s , steam r e h e a t e r s , and t h e s h e l l s i d e of one of t h e f o u r primary h e a t exchangers.

There a r e two steam

r e h e a t e r exchangers, which t r a n s f e r h e a t from t h e c o o l a n t s a l t t o p r e h e a t e d e x h a u s t steam from t h e h i g h - p r e s s u r e t u r b i n e , i n each c o o l a n t s a l t loop; w i t h a t o t a l o f e i g h t r e h e a t e r s t o meet t h e t o t a l steam r e h e a t i n g requirement of approximately 5.1 X 10" l b / h r .

Each r e h e a t e r i s of t h e

same d e s i g n , and each h a s a thermal c a p a c i t y of about 36.6 MW. A t f u l l d e s i g n l o a d , t h e c o o l a n t s a l t from t h e primary h e a t exchanger e n t e r s t h e s h e l l s i d e of t h e r e h e a t e r a t a temperature of 1150째F and e x i t s a t a temperature of 850째F f o r r e t u r n t o t h e primary h e a t exchanger. The p r e h e a t e d e x h a u s t steam from t h e h i g h - p r e s s u r e t u r b i n e e n t e r s the tube s i d e of t h e r e h e a t e r a t a temperature of 650"F, flows through t h e tubes i n counterflow t o the c o o l a n t s a l t , and l e a v e s t h e r e h e a t e r a t a temperature of 1000째F f o r d e l i v e r y t o the i n t e r m e d i a t e - p r e s s u r e t u r b i n e . B a s i c a l l y , t h e steam r e h e a t e r exchangers must m e e t t h e same system requirements p r e s c r i b e d f o r t h e primary h e a t exchangers t h a t w e r e d i s cussed i n S e c t i o n 2 of t h i s r e p o r t .

However, s i n c e no f u e l s a l t i s

involved, t h e d e s i r a b i l i t y of keeping t h e f l u i d volume a t a minimum i s n o t a c r i t i c a l f a c t o r i n t h e d e s i g n of t h e r e h e a t e r .

I n a d d i t i o n , the

lower h e a t l o a d and average temperatures permit more freedom i n d e s i g n i n g the geometry of t h e r e h e a t e r t o avoid problems a s s o c i a t e d w i t h v i b r a t i o n or overstress.

Since the d e s i g n f o r t h e steam r e h e a t e r exchanger i s s i m i l a r t o t h a t f o r the primary h e a t exchanger, an e a r l y v e r s i o n of the b a s i c PRIMEX computer program was modified t o f i t the requirements of t h e steam r e h e a t e r , t h e r e b y becoming t h e RETEX program.

The d e s i g n d a t a and equa-

t i o n s used t o develop t h e RETEX computer program a r e d i s c u s s e d i n t h e following subsections.

3.1

D e s c r i p t i o n of Steam Reheater

Each of the e i g h t steam r e h e a t e r exchangers i s a h o r i z o n t a l s h e l l and-tube u n i t w i t h a s i n g l e counterflow pass on b o t h t h e s h e l l and tube sides.

Each u n i t i s about 30 f t long and h a s an o u t s i d e diameter of

22 i n .

A t y p i c a l r e h e a t e r i s i l l u s t r a t e d i n Fig. 3.1.

The p r e h e a t e d e x h a u s t steam e n t e r s t h e tube s i d e of t h e r e h e a t e r a t a p r e s s u r e of about 580 p s i , flows through the 0.75-in.-OD e x i t s a t a p r e s s u r e of 550 p s i .

t u b e s , and

There a r e 400 s t r a i g h t t u b e s arranged

i n a t r i a n g u l a r - p i t c h a r r a y i n each r e h e a t e r .

The s u r f a c e s of t h e s e

t u b e s a r e n o t h e l i c a l l y i n d e n t e d t o enhance h e a t t r a n s f e r , a s a r e those i n t h e primary h e a t exchanger. The c o o l a n t s a l t e n t e r s t h e s h e l l s i d e of t h e r e h e a t e r a t a p r e s s u r e of about 228 p s i , flows around d i s k and doughnut b a f f l e s i n counterflow t o the e x h a u s t steam, and e x i t s a t a p r e s s u r e of 168 p s i .

Other p e r t i -

n e n t design d a t a f o r t h e steam r e h e a t e r exchanger a r e given i n Table 3.1. Table 3.1.

Design Data f o r MSBR Steam Reheater Exchanger S t r a i g h t s h e l l - a n d - t u b e one-pass h o r i z o n t a l u n i t w i t h d i s k and doughnut b a f f l e s

Number r e q u i r e d

Eight

Rate of h e a t t r a n s f e r p e r u n i t , Mw Bt u /hr

36.6 1.25 X

She l l - s i d e c o n d i t i o n s Hot f l u i d Entrance temperature , "F E x i t temperature, "F Entrance p r e s s u r e , p s i Exit pressure, p s i P r e s s u r e drop a c r o s s exchanger, p s i Mass flow r a t e , l b / h r

Coolant s a l t 1150 850 228 168 59.52 1.16 X lo6

Tube-side c o n d i t i o n s Cold f l u i d Entrance temperature, "F E x i t temperature , "F Entrance p r e s s u r e , p s i Exit pressure, p s i P r e s s u r e drop a c r o s s exchanger, p s i Mass flow r a t e , l b / h r

Exhau s t s t e am 650 1000 580 550 29.85 6.41 x io5

lo8

ORNL Dwg 65 12381 - STEAM

OUTLET

-“TUBE

SHEET

SALT I N L E T

-TIE

ROD 8 SPACER

TUBULAR SHELL

-TUBES

DOUGHNUT BAFFLE

-DISC

----SA

B AFF:LE

,LT

ou T L E T

INSULATION BAFFLE-

1 . -‘--STEAM INLET Fig. 3.1.

Typical MSBR Steam Reheater Exchanger.

Table 3 . 1 (continued) Tube Materia 1 Number r e q u i r e d Pitch, in. Outside diameter , i n . Wall t h i c k n e s s , i n . Length (tube s h e e t t o tube sheet), f t

Hastelloy N 400 1.0 ( t r i a n g u l a r ) 0.75

0.035 30.26

Tube s h e e t m a t e r i a l

Hastelloy N

Total heat transfer area, f t 2 Basis f o r a r e a c a l c u l a t i o n

2376 Outside of t u b e s

She 11 Materia 1 Thickness, i n . Inside diameter, i n .

Hastelloy N 0.5 21.2

Baffle Type Number Spacing, i n . Disk o u t s i d e d i a m e t e r , i n . Doughnut i n s i d e d i a m e t e r , i n .

Disk and doughnut 2 1 each 8.65 17.75 11.61

Overall h e a t t r a n s f e r c o e f f i c i e n t , U , Btu/hr f t2

306

Tube Maximum primary (P,) s t r e s s Calculated, p s i A 1 lowab l e , p s i Maximum primary and secondary (Pm + Q) s t r e s s Calculated, p s i Allowable , p s i Shell Maximum primary (Pm> s t r e s s Calculated, p s i Allowable , p s i Maximum primary and secondary (Pm + Q) s t r e s s Calculated, p s i Allowable, p s i

4582 13 ,000

14 ,090 39 ,000

5016 9500 14 ,550 28 ,500

23 3.2

Design C a l c u l a t i o n s

When developing t h e computer program RETEX t o analyze t h e steam r e h e a t e r exchanger, t h e p r o p e r t i e s of t h e steam were assumed t o be e s s e n t i a l l y c o n s t a n t along t h e l e n g t h of t h e exchanger even though i t was recognized t h a t some g a i n i n t h e r e l i a b i l i t y of t h e e s t i m a t e s could have been r e a l i z e d by i n c o r p o r a t i n g t h e steam p r o p e r t i e s a s a f u n c t i o n o f The u s u a l D i t t u s - B o e l t e r e q u a t i o n s were used

p r e s s u r e and temperature.

f o r t h e f i l m h e a t t r a n s f e r c o e f f i c i e n t on t h e tube s i d e of t h e exchanger. The o t h e r procedures and c o r r e l a t i o n s used i n t h e a n a l y s i s of the r e h e a t e r a r e b a s i c a l l y the same a s those used f o r t h e primary h e a t exchanger d i s cussed i n S u b s e c t i o n 2 . 2 o f t h i s r e p o r t . Manual computational methods were used t o determine the stresses i n t h e steam r e h e a t e r exchanger.

This p r e l i m i n a r y s t r e s s a n a l y s i s was

based on t h e requirements of S e c t i o n 111, Nuclear Vessels, of t h e ASME B o i l e r and P r e s s u r e Vessel Code; and t h e c a l c u l a t e d v a l u e s a r e compared w i t h t h e a l l o w a b l e v a l u e s i n Table 3.1.

However, a complete s t r e s s

a n a l y s i s a s r e q u i r e d by S e c t i o n I11 of t h e ASME B o i l e r and P r e s s u r e Vess e l Code h a s n o t been made.

3.3

D e s c r i p t i o n of RETEX

The RETEX program, a modified v e r s i o n of t h e PRIMEX program, was

used t o analyze the steam r e h e a t e r exchanger.

I n t h e RETEX program, each

zone between two b a f f l e s i s considered a s one increment l e n g t h .

The c a l -

c u l a t i o n s a r e begun on t h e h o t s i d e of the exchanger, and increments a r e added u n t i l a complete h e a t b a l a n c e i s achieved.

The p h y s i c a l p r o p e r t y

e q u a t i o n s f o r t h e f u e l s a l t i n t h e PRIMEX program a r e r e p l a c e d w i t h the p h y s i c a l p r o p e r t y d a t a f o r the exhaust steam i n the RETEX program, and t h e s e p r o p e r t i e s a r e c o n s i d e r e d a s b e i n g e s s e n t i a l l y c o n s t a n t along t h e l e n g t h o f t h e exchanger.

The p h y s i c a l p r o p e r t i e s of t h e c o o l a n t s a l t a r e

e v a l u a t e d a t t h e average temperature of each increment.

The dependence.

of t h e p h y s i c a l p r o p e r t i e s on temperature i s p r e s e n t l y expressed i n t h e

form of e m p i r i c a l e q u a t i o n s i n c o r p o r a t e d i n t h e main program.

I f any of

t h e s e e q u a t i o n s a r e changed, the a p p r o p r i a t e d a t a c a r d must be r e p l a c e d .

The RETEX computer program d i f f e r s from t h e PRIMEX computer program i n that

t h e r e h e a t e r tubes a r e n o t h e l i c a l l y indented t o enhance h e a t t r a n s f e r , and no enhancement f a c t o r s a r e used i n t h e RETEX program;

t h e r e h e a t e r tubes a r e arranged i n a t r i a n g u l a r - p i t c h a r r a y r a t h e r than i n c o n c e n t r i c c i r c l e s , and c e r t a i n geometric c a l c u l a t i o n s a r e t h e r e f o r e made d i f f e r e n t l y i n t h e RETEX program;

none of t h e r e h e a t e r tubes a r e b e n t i n a sine-wave c o n f i g u r a t i o n t o accommodate d i f f e r e n t i a l thermal expansion; and

no s t r e s s a n a l y s i s s u b r o u t i n e s a r e included i n t h e RETEX program ( s t r e s s e s were c a l c u l a t e d by hand). The computer program f o r the MSBR steam r e h e a t e r exchanger, RETEX,

i s given i n Appendix C.

A s i m p l i f i e d o u t l i n e of t h e program i n block-

diagram form, a l i s t of t h e i n p u t d a t a r e q u i r e d , a l i s t of t h e o u t p u t r e c e i v e d from the computer, and a complete l i s t i n g of t h e main program a r e presented.

The RETEX program terms which d i f f e r from t h o s e of t h e

PRIMEX program a r e d e f i n e d .

T o i l l u s t r a t e t h e u s e of t h e RETEX program,

t h e computer i n p u t d a t a f o r the steam r e h e a t e r exchanger d i s c u s s e d i n Subsection 3 . 1 and t h e o u t p u t p r i n t e d by t h e computer a r e a l s o i n c l u d e d i n Appendix C.

The t i m e r e q u i r e d f o r a t y p i c a l IBM 3 6 0 / 9 1 computer run

of t h i s program i s about 1 minute.

3.4

E v a l u a t i o n of RETEX

Confidence i n the d e s i g n c a l c u l a t i o n s f o r t h e steam r e h e a t e r exchanger i s g r e a t e r than t h a t i n t h e c a l c u l a t i o n s f o r t h e primary h e a t exchanger because the c h a r a c t e r i s t i c s of steam a r e more f a m i l i a r than those of the f u e l s a l t and because no enhancement f a c t o r s a r e involved. V i b r a t i o n problems a r e n o t l i k e l y t o be encountered i n t h e steam r e h e a t e r because v e l o c i t i e s a r e l e s s than 6 . 5 f p s and the t u b e s a r e supported by b a f f l e s with a r e l a t i v e l y c l o s e spacing.

25 V

The u n c e r t a i n t i e s a s s o c i a t e d w i t h t h e c o o l a n t s a l t a r e involved i n t h e RETEX program, and t h e d e v i a t i o n s a p p l i e d f o r the primary h e a t exchanger ( d i s c u s s e d i n Subsection 2.4) a r e a l s o a p p l i c a b l e t o t h e steam reheater.

Again, two extreme c a s e s were c o n s i d e r e d .

A l l the p e s s i m i s t i c

v a l u e s were used i n one c a s e , and a l l the o p t i m i s t i c v a l u e s were used i n the o t h e r .

The r e s u l t was a maximum e s t i m a t e d d e v i a t i o n i n the o v e r a l l

h e a t t r a n s f e r a r e a of +23% ( a d d i t i o n a l area r e q u i r e d ) f o r t h e p e s s i m i s t i c c a s e and -13% (less a r e a r e q u i r e d ) f o r t h e o p t i m i s t i c c a s e .

SUPEX, THE STEAM GENERATOR SUPERHEATER PROGRAM

There a r e f o u r steam g e n e r a t o r s u p e r h e a t e r exchangers, which t r a n s f e r h e a t from the c o o l a n t s a l t t o feedwater, i n each of the f o u r c o o l a n t s a l t c i r c u l a t i n g loops of t h e MSBR concept. The t o t a l steam g e n e r a t i o n r e q u i r e ment, which i n c l u d e s t h a t needed f o r t h e feedwater and p r e h e a t i n g the exhaust steam, of about 10 X

lo6

l b / h r i s provided by t h e 16 steam gener-

a t o r s , each having a thermal c a p a c i t y of about 1 2 1 MW. These exchangers s e r v e a s b o t h steam g e n e r a t o r s and s u p e r h e a t e r s . They a r e o p e r a t e d i n p a r a l l e l w i t h r e s p e c t t o the c o o l a n t s a l t and steam flows, and they a r e i d e n t i c a l i n design and o p e r a t i o n .

A t f u l l design

l o a d , p r e h e a t e d feedwater e n t e r s the exchanger a t a temperature of 700"F, and t h e s u p e r c r i t i c a l steam e x i t s a t a temperature of 1000째F.

The cool-

a n t s a l t e n t e r s the exchanger a t a temperature o f 1150째F and e x i t s a t a temperature of 850째F f o r r e t u r n t o the primary h e a t exchanger. The f a c t o r s i n f l u e n c i n g t h e design of t h e steam g e n e r a t o r exchanger a r e p a r t i a l l y dependent upon t h e requirements f o r the o v e r a l l MSBR system. The e x i t temperature and p r e s s u r e of the steam were d i c t a t e d by t h e steam power system s e l e c t e d .

The i n l e t temperature of t h e steam was determined

by c o n s i d e r a t i o n s r e l a t i v e t o t h e l i q u i d u s temperature of t h e s a l t and the r a p i d i n c r e a s e i n h e a t c a p a c i t y of the s u p e r c r i t i c a l w a t e r a t t e m p e r a t u r e s above 700째F.

The i n l e t and e x i t temperatures of t h e c o o l a n t s a l t ,

t h e p r e s s u r e d r o p , and t h e t o t a l h e a t t o be t r a n s f e r r e d were d i c t a t e d by t h e requirements f o r the r e a c t o r and primary h e a t exchange systems.

a d d i t i o n t o t h e s e system r e q u i r e m e n t s , the d e s i g n f o r the steam g e n e r a t o r exchanger m u s t s a t i s f y s t r e s s , s t a b i l i t y , and space r e q u i r e m e n t s . Because of the marked changes i n t h e p h y s i c a l p r o p e r t i e s o f the feedw a t e r a s t h e temperature i s r a i s e d above t h e c r i t i c a l temperature a t s u p e r c r i t i c a l p r e s s u r e s , the h e a t t r a n s f e r and flow c h a r a c t e r i s t i c s vary c o n s i d e r a b l y throughout the exchanger.

The SUPEX computer program was

developed t o account f o r t h e s e changes by making the h e a t t r a n s f e r and p r e s s u r e drop c a l c u l a t i o n s f o r i n c r e m e n t a l tube l e n g t h s .

The d e s i g n d a t a

and e q u a t i o n s used t o develop t h i s computer program f o r a n a l y s i s of the steam g e n e r a t o r exchanger a r e d i s c u s s e d i n the f o l l o w i n g s u b s e c t i o n s .

27 V

4.1

D e s c r i p t i o n of Steam Generator

Each of t h e 16 steam g e n e r a t o r s u p e r h e a t e r exchangers i s a U-tube, U - s h e l l u n i t mounted h o r i z o n t a l l y w i t h one l e g above t h e o t h e r .

Each h a s

a s i n g l e p a s s on t h e s h e l l and tube s i d e s w i t h t h e flow i n one s i d e coun-

ter t o t h a t i n t h e o t h e r .

The o v e r a l l l e n g t h of each exchanger i s about

40 f t , and t h e o v e r a l l h e i g h t from t h e feedwater i n l e t plenum t o t h e steam o u t l e t plenum i s about 1 2 f t .

A t y p i c a l steam g e n e r a t o r i s shown

i n Fig. 4.1. ORNL-DWG 70-11951

STEAM OUTLET

4 FEEDWATER INLET

F i g . 4.1.

Typical MSBR Steam Generator S u p e r h e a t e r Exchanger.

28 \

The feedwater e n t e r s the tube s i d e of t h e exchanger a t a p r e s s u r e of 3754 p s i , flows through t h e 0.50-in.-OD steam e x i t s a t a p r e s s u r e of 3600 p s i .

t u b e s , and t h e s u p e r c r i t i c a l

The c o o l a n t s a l t e n t e r s the s h e l l

s i d e of t h e exchanger a t a p r e s s u r e of 233 p s i , c i r c u l a t e s i n counterflow t o t h e s u p e r c r i t i c a l f l u i d around segmental b a f f l e s , and e x i t s a t a p r e s s u r e of 1 7 2 p s i .

Segmental b a f f l e s a r e used t o improve t h e h e a t t r a n s f e r

c o e f f i c i e n t f o r the s a l t f i l m and t o minimize s a l t s t r a t i f i c a t i o n .

b a f f l e on the s h e l l s i d e of each tube s h e e t p r o v i d e s a s t a g n a n t l a y e r of s a l t t o h e l p reduce stresses r e s u l t i n g from temperature g r a d i e n t s a c r o s s t h e tube s h e e t s

Location o f the steam g e n e r a t o r exchanger i n a h o r i z o n t a l p o s i t i o n reduces t h e p o s s i b i l i t y of u n s t a b l e flow c o n d i t i o n s f o r the s u p e r c r i t i c a l f l u i d i n the t u b e s .

The U-tubes a r e arranged i n a t r i a n g u l a r - p i t c h a r r a y

and the ends of the t u b e s are turned 90" t o e q u a l i z e t h e l e n g t h s of t h e tubes i n t h e exchanger.

This e q u a l i z a t i o n of tube l e n g t h s f u r t h e r

reduces t h e p o s s i b i l i t y of u n s t a b l e flow c o n d i t i o n s .

The p e r t i n e n t

design d a t a f o r t h e steam g e n e r a t o r exchanger a r e given i n Table 4.1. Table 4.1.

Design Data f o r MSBR Steam Generator S u p e r h e a t e r Exchanger

TYP e

U - s h e l l , U-tube one-pass h o r i z o n t a l u n i t with cross-flow baffles

Number r e q u i r e d

Rate of h e a t t r a n s f e r p e r u n i t ,

Mw Btu /hr Shell-side conditions Hot fluid Entrance temperature, O F Exit temperature, "F Entrance p r e s s u r e , p s i Exit pressure, p s i P r e s s u r e drop a c r o s s exchanger, p s i Mass flow r a t e , l b / h r

121 4.13 X

lo8

Coolant s a l t 1150 850 233.0 172.0 61.0 3.82 X lo6

29 v

Table 4 . 1 ( c o n t i n u e d ) Tube-side c o n d i t i o n s Cold f l u i d Entrance temperature , OF E x i t temperature , "F Entrance p r e s s u r e , p s i Exit pressure, p s i P r e s s u r e drop a c r o s s exchanger, p s i Mass flow r a t e , l b / h r Mass v e l o c i t y , l b / h r - f t 2

Supercritical fluid 700 1000 3754 3 600 154 6.33 x io5

2.47 x

lo6

Tube Materia 1 Number r e q u i r e d Pitch, in. Outside d i a m e t e r , i n . Wall t h i c k n e s s , i n . Length (tube s h e e t t o tube sheet), f t

Hastelloy N 393 0.875 ( t r i a n g u l a r ) 0.50 0.077 76.4

Tube s h e e t Mate r i a 1 Thickness, i n .

Hastelloy N 4.5

Total heat transfer area, f t 2 Basis f o r a r e a c a l c u l a t i o n

3929 Outside of tubes

She 11 Material Wall t h i c k n e s s , i n . I n s i d e diameter , i n .

Hastelloy N 0.375 18.25

Baffle Type Spacing, f t Number of spaces

Cross flow 4.02 19

4.2

Design C a l c u l a t i o n s

The h e a t t r a n s f e r c o e f f i c i e n t f o r t h e s u p e r c r i t i c a l f l u i d f i l m on the i n s i d e of t h e tube w a l l s i s determined by u s i n g t h e c o r r e l a t i o n r e p o r t e d by H. S . Swenson e t a1.12

This c o r r e l a t i o n i s given i n Eq. 4.1.

30 W

where h . = h e a t t r a n s f e r c o e f f i c i e n t i n s i d e tube, Btu/hr.ft2SoF, 1

d. = i n s i d e diameter of tube, f t , 1

k i = thermal c o n d u c t i v i t y o f f l u i d i n s i d e t u b e , B t u / h r . f t 2 * O F p e r f t , G = mass v e l o c i t y o f f l u i d , l b / h r * f t 2 ,

pi = v i s c o s i t y of f l u i d a t temperature of i n s i d e s u r f a c e o f t u b e , lb/hr. f t ,

Hi = e n t h a l p y a t t e m p e r a t u r e o f i n s i d e s u r f a c e o f t u b e , B t u / l b ,

= e n t h a l p y a t temperature of b u l k f l u i d , B t u / l b ,

Ti = t e m p e r a t u r e o f f l u i d a t i n s i d e s u r f a c e o f t u b e , OF,

T = temperature o f b u l k f l u i d , OF, b v = s p e c i f i c volume o f b u l k f l u i d , f t 3 / l b , and b v = s p e c i f i c volume of f l u i d i n s i d e t u b e , f t 3 / l b . i

The v a l u e s o f s p e c i f i c volume and e n t h a l p y f o r t h e s u p e r c r i t i c a l f l u i d u n d e r v a r i o u s c o n d i t i o n s o f p r e s s u r e and t e m p e r a t u r e a r e t a k e n from d a t a r e p o r t e d by J . H. Kennan and F . G. Keyes.13

A t a b l e look-up s u b r o u t i n e

i s i n c l u d e d i n t h e SUPEX computer program f o r d e t e r m i n a t i o n o f t h e s e values.

The v a l u e s o f thermal c o n d u c t i v i t y and v i s c o s i t y f o r t h e s u p e r -

c r i t i c a l f l u i d a r e determined from d a t a r e p o r t e d by E . R. J . Grosh.14

Nowak and

These d a t a were r e p r e s e n t e d by E q s . 4.2 and 4.3 i n t h e

SUPEX computer program.

= 0*02191(v

0.012)2(

T + 460 492

T t4::46-)

(4.2)

and k

(1.093 X

460)1'45

(28.54 X 10-4)v-1*25,

(4.3)

where v = s p e c i f i c volume, f t " / l b ,

and

T = temperature o f f l u i d , "F. The h e a t t r a n s f e r c o e f f i c i e n t f o r t h e s a l t f i l m on t h e o u t s i d e s u r -

f a c e of t h e t u b e s i s determined by u s i n g the method proposed by 0. P. Bergelin e t al.4'5

The e x p e r i m e n t a l d a t a 4 a r e p r e s e n t e d a s c o r r e l a t i o n s

between a h e a t t r a n s f e r f a c t o r ( J ) and t h e Reynolds number, w i t h t h e Reynolds number d e f i n e d by t h e e x p r e s s i o n

dG 0

E-

where d

= o u t s i d e diameter of t u b e , f t ,

G = mass v e l o c i t y of t h e f l u i d , l b / h r . f t 2 ,

and

pb = v i s c o s i t y a t temperature of bulk f l u i d , l b / h r * f t . The s h e l l s i d e of the steam g e n e r a t o r exchanger i s d i v i d e d i n t o two types of flow r e g i o n s by t h e segmental b a f f l e s .

These a r e the c r o s s - f l o w and

window r e g i o n s , and the h e a t t r a n s f e r f a c t o r i s determined f o r each.

The

h e a t t r a n s f e r f a c t o r f o r the c r o s s - f l o w r e g i o n ( J B ) i s given by t h e expression h

B JB -=('k P B

2/3

Pl-b

) ):(

0.14

(4.5)

where hB = h e a t t r a n s f e r c o e f f i c i e n t f o r c r o s s - f l o w r e g i o n , B t u / h r . f t 2 .

OF,

= s p e c i f i c h e a t , Btu/lb."F, P GB = mass v e l o c i t y of f l u i d i n cross-flow r e g i o n , l b / h r . f t 2 ,

= v i s c o s i t y a t temperature of b u l k f l u i d ,

lb/hr.ft,

k = thermal c o n d u c t i v i t y , B t u / h r * f t - " F , and = v i s c o s i t y of f l u i d a t temperature of o u t s i d e s u r f a c e of tube, lb/hr f t

. .

The h e a t t r a n s f e r f a c t o r f o r the window r e g i o n i s given by the e x p r e s s i o n

where h

= h e a t t r a n s f e r c o e f f i c i e n t f o r window r e g i o n , B t u / h r . f t 2 .

OF,

and

Gm = mean mass v e l o c i t y , l b / h r . f t 2 .

The mean mass v e l o c i t y i s given by t h e e x p r e s s i o n

where Gw = mass v e l o c i t y of f l u i d i n window r e g i o n , l b / h r - f t 2 .

Equations

f o r determining v a l u e s of J were f i t t e d t o t h e graph of J v e r s u s NRe given i n F i g . 11 of Ref. 4 f o r u s e i n t h e SUPEX computer program.

The

32 v a l u e s of J given by E q s . 4.8 and 4.9 a r e used i n Eqs. 4 . 5 and 4.6 t o determine t h e h e a t t r a n s f e r c o e f f i c i e n t s f o r t h e c r o s s - f l o w and window r e g i o n s (hB and hw). For 100

NRe

800,

J = 0.571(NR,)-0*456

(4-8)

For 800

NRe

5 lo5,

J = 0.346(NRe)-0'382

(4.9)

and

I n B e r g e l i n ' s methodY4 the h e a t t r a n s f e r c o e f f i c i e n t f o r t h e s h e l l s i d e of t h e exchanger i s a l i n e a r combination of the h e a t t r a n s f e r c o e f f i c i e n t s f o r the c r o s s - f l o w and window r e g i o n s weighted by t h e amount of h e a t t r a n s f e r s u r f a c e i n each r e g i o n and c o r r e c t e d f o r bypass leakage. Because of the l a r g e baffle-spacing-to-shell-diameter r a t i o (approximately

2.7) r e q u i r e d f o r t h e steam g e n e r a t o r exchanger, an a d d i t i o n a l c o r r e c t i o n f a c t o r i s a p p l i e d t o the s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t .

The t o t a l

s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t (h 0 ) i s given by t h e e x p r e s s i o n

ho = 0.77B(

0.138

(

hgag + hwaw) a

+ a

(4.10) w

where B = bypass leakage f a c t o r recommended by B e r g e l i n , 4

Y = d i s t a n c e from the c e n t e r l i n e of the s h e l l t o t h e c e n t r o i d of t h e segmental window a r e a , f t ,

x = baffle h a h a

B B W W

spacing, f t ,

= h e a t t r a n s f e r c o e f f i c i e n t f o r cross-flow region, Btu/hr.ft2-OF, = a r e a of h e a t t r a n s f e r s u r f a c e i n c r o s s - f l o w r e g i o n p e r u n i t length, f t 2 / f t , = h e a t t r a n s f e r c o e f f i c i e n t f o r window r e g i o n , B t u / h r . f t 2 . OF, and = a r e a of h e a t t r a n s f e r s u r f a c e i n window r e g i o n p e r u n i t l e n g t h , f t2/f t

The v a l u e s of s p e c i f i c h e a t and thermal c o n d u c t i v i t y f o r t h e c o o l a n t s a l t a r e t r e a t e d a s c o n s t a n t s , independent of temperature, and a r e included i n t h e i n p u t i n f o r m a t i o n f o r the SUPEX computer program.

The

d e n s i t y and v i s c o s i t y of t h e s a l t a r e t r e a t e d a s f u n c t i o n s of temperature a s determined by Eqs. 4.11 and 4.12.

= 141.38

(4.11)

0.02466(T)

and 1-1 = 0.2122 exp [ ( : ~ t ~ ~ ) ]

(4.12)

where p = d e n s i t y of c o o l a n t s a l t , l b / f t 3 ,

T = temperature of s a l t , OF, and II =

v i s c o s i t y of s a l t , l b / h r - f t .

The thermal r e s i s t a n c e of the tube w a l l i s c a l c u l a t e d f o r each increment of tube l e n g t h by u s i n g the thermal c o n d u c t i v i t y o f H a s t e l l o y N e v a l u a t e d a t t h e average temperature of the tube w a l l f o r each p a r t i c u l a r increment.

The thermal r e s i s t a n c e of the tube w a l l i s given by the

e x p r e s si o n (4.13) where

%= d

thermal r e s i s t a n c e of tube w a l l , h r - f t 2 - O F / B t u ,

= o u t s i d e diameter of tube,

ft,

= thermal c o n d u c t i v i t y of tube w a l l , B t u / h r * f t . " F , and

d . = i n s i d e diameter of tube, f t . 1

The thermal c o n d u c t i v i t y of the tube w a l l i s given by the e x p r e s s i o n

= 0.006375Tw

4.06

where Tw = mean temperature of t h e tube w a l l , OF.

(4.14) The t o t a l thermal

r e s i s t a n c e , based on t h e o u t e r s u r f a c e a r e a of t h e t u b e , i s given by t h e expre s s i o n d (4.15)

The h e a t t r a n s f e r r e d p e r increment of exchanger l e n g t h (AQ) i s given by the e x p r e s s i o n (4.16)

where d

= o u t s i d e diameter of t u b e , f t ,

n = number of t u b e s ,

= increment of tube l e n g t h , f t ,

AT = mean temperature d i f f e r e n c e between c o o l a n t s a l t and superm c r i t i c a l f l u i d f o r t h e p a r t i c u l a r increment, O F , and R

= t o t a l thermal r e s i s t a n c e given by Eq. 4.15.

The p r e s s u r e drop p e r increment of tube l e n g t h f o r t h e s u p e r c r i t i c a l f l u i d i n s i d e t h e tubes i s given by the e x p r e s s i o n 4f(fi)

(4.17)

A P = 144di (2gcP) , where f = friction factor,

= increment of tube l e n g t h , f t , =

i n s i d e diameter of t u b e , f t ,

di G = mass v e l o c i t y of f l u i d i n s i d e t u b e , l b / h r - f t * ,

gc = g r a v i t a t i o n a l conversion c o n s t a n t , l b - f t / l b f . h r 2 , m p = d e n s i t y of f l u i d i n s i d e t u b e , l b / f t 3 .

and

The f r i c t i o n f a c t o r i s given by the expression* 0.125 (;;G)0'32 f = 0.00140 i-

(4.18)

The p r e s s u r e drops on the s h e l l s i d e of t h e steam g e n e r a t o r exchanger a r e c a l c u l a t e d by u s i n g t h e e q u a t i o n s recomended by B e r g e l i x ~ . ~The p r e s s u r e drop a c r o s s t h e i - t h c r o s s - f l o w r e g i o n i s given by t h e e x p r e s s i o n

(4.19) where

= number of r e s t r i c t i o n s i n c r o s s - f l o w r e g i o n , = mass v e l o c i t y of f l u i d i n c r o s s - f l o w r e g i o n , l b / h r . f t 2 ,

p = d e n s i t y of f l u i d , l b / f t 3 .

and

35 The p r e s s u r e drop a c r o s s t h e i - t h b a f f l e window i s given by t h e expression

n e =

(4.20)

144

where

= number of r e s t r i c t i o n s i n window r e g i o n and

= mean mass v e l o c i t y (given by E q . 4 . 7 ) ,

lb/hr*ft2.

The t o t a l p r e s s u r e drop on the s h e l l s i d e of t h e exchanger i s given by the expression

m~ =

mBi

Owi)

-k

i=l

(4.21)

i=l

where B

= bypass leakage c o r r e c t i o n f a c t o r f o r p r e s s u r e recommended by

Bergelin4 and N = number of b a f f l e s . D e t a i l e d s t r e s s c a l c u l a t i o n s a r e n o t included i n t h e SUPEX computer program, b u t an approximate v a l u e of the allowable temperature drop a c r o s s t h e tube w a l l based on thermal s t r e s s c o n s i d e r a t i o n s i s determined f o r each increment of tube l e n g t h .

This v a l u e of allowable temperature drop

can be compared w i t h the value of the temperature drop a c r o s s t h e tube w a l l determined i n t h e h e a t t r a n s f e r c a l c u l a t i o n s t o provide some guidance i n s e l e c t i n g d e s i g n parameters. a s secondary stresses.

The thermal s t r e s s e s a r e t r e a t e d

Based on t h e requirements s e t f o r t h i n S e c t i o n

111, Nuclear Vessels, of t h e ASME B o i l e r and P r e s s u r e Vessel Code; the p e r m i s s i b l e v a l u e f o r the thermal stresses i s given by t h e e x p r e s s i o n AT"h

- AT"L = 3 sm

- s ,

(4.22)

where AT"h

AT"L S

= hoop and l o n g i t u d i n a l s t r e s s components caused by temper-

a t u r e d i f f e r e n c e s a c r o s s t h e tube w a l l , p s i , = allowable s t r e s s i n t e n s i t y based on r u l e s p r e s c r i b e d i n

S e c t i o n I11 o f t h e ASME B o i l e r and P r e s s u r e Vessel Code, p s i , and

S = t o t a l s t r e s s i n t e n s i t y r e s u l t i n g from p r i m a r y membrane

s t r e s s e s p l u s secondary stresses from a l l s o u r c e s o t h e r than thermal s t r e s s e s , p s i .

The v a l u e o f S was c o n s e r v a t i v e l y e s t i m a t e d t o be about 26,000 p s i .

The

tube w a l l m a t e r i a l i s H a s t e l l o y N , and for , T

1015"F,

Sm = 24,000

7.5(Tw)

(4.23)

and

< T, <

f o r 1015째F

1100"F,

Sm = 57,000

40(Tw)

(4.24)

Based on d a t a r e p o r t e d by J . F. Harvey,15 t h e hoop and l o n g i t u d i n a l

stresses r e s u l t i n g from temperature d i f f e r e n c e s a c r o s s t h e tube w a l l a r e g i v e n by t h e e x p r e s s i o n

where 2 = c o e f f i c i e n t o f thermal e x p a n s i o n , i n . / i n . - O F ,

E = modulus o f e l a s t i c i t y f o r H a s t e l l o y N , p s i , ATw = temperature drop a c r o s s tube w a l l ,

OF,

v = Poisson's r a t i o , d

= o u t s i d e d i a m e t e r of t u b e , i n . ,

and

= i n s i d e diameter of tube, i n .

The e s t i m a t e d v a l u e of S and E q s . 4.22, 4.23, 4.24, and 4.25 a r e u s e d i n

t h e SUPEX computer program t o c a l c u l a t e t h e a l l o w a b l e v a l u e o f AT,. v a l u e s of E and

The

a r e determined i n t h e computer program from E q s . 4.26

and 4.27.

r31.65

0.005(Tw)]

lo6

(4.26)

and CI: =

[0.0031(Tw) + 5.911 x

lom6 .

(4.27)

Although d e t a i l e d s t r e s s c a l c u l a t i o n s a r e n o t i n c l u d e d i n t h e SUPEX computer program, a p r e l i m i n a r y s t r e s s a n a l y s i s o f t h e steam g e n e r a t o r exchanger was made by hand.

T h i s p r e l i m i n a r y a n a l y s i s was based on t h e

37 W

requirements of S e c t i o n 111, Nuclear V e s s e l s , of t h e ASME B o i l e r and P r e s s u r e Vessel Code; and t h e hand c a l c u l a t e d v a l u e s a r e compared w i t h allowable v a l u e s i n Table 4 . 2 .

The allowable s t r e s s v a l u e s were taken

from d a t a i n code case i n t e r p r e t a t i o n s 1315-3 (Ref. 16) and 1331-4 (Ref. 1 7 ) . P r e l i m i n a r y Stress C a l c u l a t i o n s f o r MSBR Steam Generator a Maximum stress i n t e n s i t y , p s i Table 4.2.

Tube Calculated b A 1 lowab l e

Pm = 13,900;

(Pm -I-Q) = 30,900

Pm = 15,500;

(Pm -I- Q ) = 46,500

She 11 Ca 1cu l a t e d

pm = 5800;

(Pm

+ Q)

= 13,200

A 1 lowab l e L

pm = 8800;

(Pm

+ Q)

= 26,400

Maximum tube s h e e t s t r e s s , p s i Ca 1cu l a t e d d A 1 lowab l e

C17,OOO 17,000

The symbols a r e those of S e c t i o n 111 of the ASME B o i l e r and P r e s s u r e Vessel Code where Pm = primary membrane s t r e s s i n t e n s i t y , p s i , Q = secondary s t r e s s i n t e n s i t y , p s i , Sm = allowable stress i n t e n s i t y , p s i .

bBased on a temperature of 1038째F f o r t h e i n s i d e s u r f a c e o f the t u b e s ; t h i s r e p r e s e n t s the worst s t r e s s c o n d i t i o n . C

Based on t h e maximum o r h i g h e s t temperature of t h e c o o l a n t s a l t of 1150째F. dBased on a temperature of 1000째F f o r t h e steam and u s e of a b a f f l e on the s h e l l s i d e .

4.3

D e s c r i p t i o n of SUPEX

The e q u a t i o n s d e s c r i b e d i n S u b s e c t i o n 4 . 2 a r e used i n the SUPEX program t o s i z e t h e steam g e n e r a t o r exchanger f o r the s p e c i f i e d i n p u t d a t a .

A flow diagram of t h e SUPEX program, a l i s t of the i n p u t r e q u i r e d , and a l i s t of t h e o u t p u t r e c e i v e d from the computer a r e given i n Appendix D.

38 I n t h e SUPEX program, t h e t o t a l h e a t t o b e t r a n s f e r r e d i n t h e exchanger i s d i v i d e d i n t o a s p e c i f i e d number o f e q u a l i n c r e m e n t s .

For

e a c h increment, h e a t b a l a n c e r e l a t i o n s f o r the c o o l a n t s a l t and t h e s u p e r c r i t i c a l f l u i d and t h e h e a t t r a n s f e r e q u a t i o n s a r e u s e d t o determine t h e change o f temperature f o r e a c h s t r e a m and t h e tube l e n g t h r e q u i r e d . The p r e s s u r e drop i n t h e s u p e r c r i t i c a l f l u i d f o r e a c h increment and t h e p r e s s u r e drop i n t h e c o o l a n t s a l t f o r e a c h b a f f l e space a r e c a l u l a t e d and summed. Two major i t e r a t i o n loops a r e c o n t a i n e d i n t h e SUPEX program. F i r s t , t h e b a f f l e s p a c i n g i s assumed and i t e r a t i o n s a r e made u n t i l the t o t a l c a l c u l a t e d s h e l l - s i d e p r e s s u r e drop a g r e e s w i t h t h a t s p e c i f i e d . I n t e r n a l t o t h i s loop, t h e number o f t u b e s i n t h e exchanger i s e s t i m a t e d , and i t e r a t i o n s a r e made t o g i v e t h e t o t a l t u b e - s i d e p r e s s u r e drop s p e c i fied.

A s i m p l i f i e d f l o w diagram of t h e SUPEX program, a complete l i s t -

i n g of t h e program, and a l i s t o f t e r m s u s e d i n the program a r e g i v e n i n Appendix D. Output from t h e program i n c l u d e s t h e number o f t u b e s , i n s i d e diame t e r o f t h e s h e l l , l e n g t h o f t h e exchanger, b a f f l e s p a c i n g , number o f

b a f f l e s , t o t a l h e a t t r a n s f e r a r e a , and t h e a p p a r e n t o v e r a l l h e a t t r a n s f e r coefficient.

The method o f c a l c u l a t i o n u s e d in t h e program p e r m i t s t h e

t o t a l l e n g t h of t h e t u b e s t o d i f f e r from t h e t o t a l l e n g t h o f t h e b a f f l e space by a f r a c t i o n of t h e b a f f l e s p a c i n g .

Both l e n g t h s a r e g i v e n i n

t h e o u t p u t , a s a r e t h e h e a t t r a n s f e r a r e a and a p p a r e n t h e a t t r a n s f e r c o e f f i c i e n t f o r each l e n g t h .

The o u t p u t a l s o i n c l u d e s p e r t i n e n t informa-

t i o n f o r each b a f f l e s p a c i n g and tube increment.

To i l l u s t r a t e t h e u s e o f t h e SUPEX program, t h e computer i n p u t d a t a f o r t h e MSBR steam g e n e r a t o r s u p e r h e a t e r exchanger d e s c r i b e d i n Subsect i o n 4.1 and t h e o u t p u t d a t a p r i n t e d by t h e computer a r e i n c l u d e d i n Appendix D.

The t i m e r e q u i r e d f o r a t y p i c a l I B M 3 6 0 / 9 1 computer r u n o f

t h i s program i s about 30 seconds.

4.4

E v a l u a t i o n of SUPEX

The problem of s t a b i l i t y i n the steam g e n e r a t o r s u p e r h e a t e r was considered.

A s i n d i c a t e d by K. Goldman e t a1.l'

and by L. S. Tong, 1 9

i n s t a b i l i t i e s i n steam g e n e r a t o r s can a r i s e from two s o u r c e s .

First, a

t r u e thermodynamic i n s t a b i l i t y can e x i s t where, f o r a given p r e s s u r e drop a c r o s s t h e t u b e , t h e flow r a t e through t h e tube may be changed from one s t e a d y - s t a t e v a l u e t o a n o t h e r by a f i n i t e d i s t u r b a n c e .

Second, a system

i n s t a b i l i t y t h a t i s caused by r e s o n a n t c o n d i t i o n s i n t h e f l u i d can e x i s t . Data r e l a t e d t o t h e f i r s t type of i n s t a b i l i t y have been r e p o r t e d by L. Y. Krasyakova and B . N . GluskerY2' and d a t a r e l a t e d t o t h e second type of i n s t a b i l i t y have been r e p o r t e d by E . R. Quandt21 and by L. M. Shotkin.22

A q u a l i t a t i v e e v a l u a t i o n of t h e s e d a t a i n d i c a t e s t h a t t h e mass flow r a t e , p r e s s u r e drop, and h e a t f l u x used i n the h o r i z o n t a l U-tube and U - s h e l l design w i l l r e s u l t i n s t a b l e operation.

Operation of a t e s t module w i l l

provide f u r t h e r i n f o r m a t i o n about the s t a b i l i t y of t h i s d e s i g n concept. An a n a l y s i s was made t o e v a l u a t e t h e v a r i o u s u n c e r t a i n t i e s involved i n t h e SUPEX computer program.

Tolerances were p l a c e d on t h e p h y s i c a l

p r o p e r t i e s o f t h e c o o l a n t s a l t , t h e h e a t t r a n s f e r c o e f f i c i e n t s , and on the pressure-drop c o r r e l a t i o n .

The program was r u n f o r v a r i o u s c a s e s t o

determine t h e q u a n t i t a t i v e v a l u e s of t h e f a v o r a b l e and t h e adverse e f f e c t s of t h e u n c e r t a i n t i e s .

The f a v o r a b l e e f f e c t s were d e f i n e d a s d e c r e a s e d

h e a t t r a n s f e r a r e a , decreased s h e l l d i a m e t e r , and decreased t o t a l tube length.

The adverse e f f e c t s were d e f i n e d a s i n c r e a s e d v a l u e s f o r t h e s e

same t h r e e parameters.

The s e l e c t i o n of t h e s e parameters was based on

t h e b e l i e f t h a t t h e h e a t t r a n s f e r a r e a i s i n d i c a t i v e o f t h e t o t a l c o s t of t h e exchanger, t h e diameter of t h e s h e l l i s i n d i c a t i v e of t h e s t r e s s probl e m , and t h e t o t a l l e n g t h of t h e t u b e s i s i n d i c a t i v e of t h e p h y s i c a l s i z e

of the exchanger. The range of u n c e r t a i n t i e s s t u d i e d i n c l u d e d t h e p h y s i c a l p r o p e r t i e s of t h e c o o l a n t s a l t w i t h a d e v i a t i o n of

22%f o r

the s p e c i f i c h e a t and

d e n s i t y and a d e v i a t i o n of 510% f o r t h e v i s c o s i t y and thermal c o n d u c t i v i t y , t h e t u b e - s i d e and s h e l l - s i d e heat t r a n s f e r c o e f f i c i e n t s w i t h a d e v i a t i o n

+ 20%, and t h e p r e s s u r e - d r o p c o r r e l a t i o n w i t h a d e v i a t i o n of of -

_+lo%.

40 S c r u t i n y of t h e s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t r e v e a l e d t h a t p o s i t i v e d e v i a t i o n s ( i n c r e a s e s ) i n the s p e c i f i c h e a t and thermal conduct i v i t y of the c o o l a n t s a l t and n e g a t i v e d e v i a t i o n s ( d e c r e a s e s ) i n t h e d e n s i t y and v i s c o s i t y of the s a l t w i l l produce f a v o r a b l e e f f e c t s , while o p p o s i t e d e v i a t i o n s w i l l produce adverse e f f e c t s .

A negative deviation

( d e c r e a s e ) i n t h e c a l c u l a t e d p r e s s u r e drop w i l l produce f a v o r a b l e e f f e c t s , while a p o s i t i v e d e v i a t i o n ( i n c r e a s e ) w i l l produce adverse e f f e c t s .

The r e s u l t s of t h i s a n a l y s i s i n terms of p e r c e n t a g e changes r e l a t i v e t o t h e d e s i g n case a r e given i n Table 4 . 3 .

Case 1 i s f o r an i n c r e a s e d

s p e c i f i c h e a t and d e n s i t y of t h e c o o l a n t s a l t and a decreased v i s c o s i t y and thermal c o n d u c t i v i t y . Case 1.

Case 2 i s f o r d e v i a t i o n s o p p o s i t e t o those of

Cases 3 and 4 a r e f o r i n c r e a s e d and decreased, r e s p e c t i v e l y ,

shell-side heat transfer coefficients;

Cases 5 and 6 a r e f o r i n c r e a s e d

and d e c r e a s e d , r e s p e c t i v e l y , t u b e - s i d e h e a t t r a n s f e r c o e f f i c i e n t s ; and Cases 7 and 8 a r e f o r decreased and i n c r e a s e d , r e s p e c t i v e l y , c a l c u l a t e d p r e s s u r e drops.

Case 9 f o r o v e r a l l f a v o r a b l e c o n d i t i o n s i s f o r t h e com-

bined e f f e c t of a l l f a v o r a b l e changes, and Case 10 f o r o v e r a l l adverse c o n d i t i o n s i s f o r a l l adverse changes.

Cases 1, 3 , 5 , and 7 r e p r e s e n t

f a v o r a b l e changes; while Cases 2 , 4 , 6 , and 8 r e p r e s e n t adverse changes. Table 4 . 3 . Percentage Deviations R e s u l t i n g From C a l c u l a t i o n a l U n c e r t a i n t i e s Related t o MSBR Steam Generator Exchanger

Case 1 2

4 5 6 7 8 9 10

Conditions

Heat Transfer Area

Favorable p h y s i c a l p r o p e r t i e s Adverse p h y s i c a l p r o p e r t i e s Increased s h e l l - s i d e h e a t t r a n s f e r Decreased s h e l l - s i d e h e a t t r a n s f e r Increased tube-side h e a t t r a n s f e r Decreased t u b e - s i d e h e a t t r a n s f e r Decreased c a l c u l a t e d p r e s s u r e drop I n c r e a s e d c a l c u l a t e d p r e s s u r e drop Overall favorable O v e r a l l adverse

-8.2 +7.6 -10.1 +13.5 -2.3 +4.2 -2.6 +1.8 -21 +3 0

Shell Diameter

-1.4 +1.2 -1.6

+2.1 -0.5 W.9 -0.5 +0.7

-4 +5

Total Tube Length

-5.6 +5.2 -7.0 +8.8 -1.3 +2.3 -1.6 4-0.5 - 15

+18

41 REFERENCES

C. G. Lawson, R. J. Kedl, and R. E . McDonald, "Enhanced Heat T r a n s f e r Tube f o r H o r i z o n t a l Condenser With P o s s i b l e A_ p_ p l i c a t i o n i n Nuclear Power P l a n t Design," T r a n s a c t i o n s of the American Nuclear S o c i e t y , Vol. 9 , No. 2 (1966).

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H. A. McLain, "Revised Primary S a l t Heat T r a n s f e r C o e f f i c i e n t f o r MSBR Primary Heat Exchanger Design," ORNL i n t e r n a l correspondence MSR-67-70, J u l y 31, 1969.

0. P. B e r g e l i n , G. A. Brown, and A. P. Colburn, "Heat T r a n s f e r and A Study of a F l u i d F r i c t i o n During Flow Across Bank of Tubes -V: C y l i n d r i c a l B a f f l e d Exchanger Without I n t e r n a l Leakage," Trans. ASME, 76: 841-850 (1954).

0 . P. B e r g e l i n , K.

J. B e l l , and M. D. Leighton, "Heat T r a n s f e r and F l u i d F r i c t i o n Druing Flow Across Banks of Tubes - V I : The E f f e c t of I n t e r n a l Leakages Within Segmentally B a f f l e d Exchangers," Trans. ASME, 80: 53-60 (1958).

B. Cox, "Preliminary Heat T r a n s f e r R e s u l t s With a Molten S a l t Mixture Containing LiF-BeFz-ThF4-UF4 Flowing I n s i d e a Smooth, H o r i z o n t a l Tube," ORNL i n t e r n a l document CF-69-9-44, September 25, 1969.

E . N. S i e d e r and G. E. T a t e , "Heat T r a n s f e r and P r e s s u r e Drop o f Liquids i n Tubes," I n d u s t r i a l and Engineering Chemistry, 2 8 ( i 2 ) : 1429- 1435 (1936) *

H. W . Hoffman and S.

H. A. McLain, "Revised C o r r e l a t i o n s f o r t h e MSBR Primary S a l t Heat T r a n s f e r C o e f f i c i e n t , " ORNL i n t e r n a l correspondence MSR-69-89 , September 24, 1969.

I. Cohen, "Fused S a l t Heat T r a n s f e r , P a r t 111: Forced Convection Heat T r a n s f e r i n C i r c u l a r Tubes Containing t h e S a l t Mixture NaNOz-NaNOs-KN03 , I t USAEC Report ORNL-2433 , Oak Ridge N a t i o n a l Laboratory, March 1960.

10.

D. A . Donohue, "Heat T r a n s f e r and P r e s s u r e Drop i n Heat Exchangers," I n d u s t r i a l and Engineering Chemistry, 41(11): 2499-2511 (November 1949).

11.

J. R. McWherter, "MSBR Mark I Primary and Secondary S a l t s and T h e i r P h y s i c a l P r o p e r t i e s , " ORNL i n t e r n a l correspondence MSR-68-135, Rev. 1, February 1 2 , 1969.

12.

H. S . Swenson, C. R. Kakarala, and J. A. Carver, "Heat T r a n s f e r t o S u p e r c r i t i c a l Water i n Smooth-Bore Tubes," T r a n s a c t i o n s of t h e ASME, Series C: J o u r n a l of Heat T r a n s f e r , 8 7 ( 4 ) : 477-484 (November 1965).

13.

J . H. Keenan and F. G. Keyes, Thermodynamic P r o p e r t i e s of Steam, John Wiley and Sons, New York, 1936.

14. E. S . Nowak and R. J. Grosh, "An I n v e s t i g a t i o n of C e r t a i n Thermodynamic and T r a n s p o r t P r o p e r t i e s of Water and Water Vapor i n t h e C r i t i c a l Region," USAEC Report ANL-6064, Argonne N a t i o n a l Laborat o r y , October 1959.

1s.

J . F. Harvey, P r e s s u r e Vessel Design, D. Van Nostrand Company, New J e r s e y , 1963.

16.

Case 1315-3, "Nickel-Molybdenum-Chromium-Iron A l l o y , " I n t e r p r e t a t i o n s of ASME B o i l e r and P r e s s u r e Vessel Code, The American S o c i e t y of Mechanical Engineers, New York, A p r i l 25, 1968.

17.

Case 1331-4, "Nuclear Vessels i n High-Temperature S e r v i c e , I' I n t e r p r e t a t i o n s of ASME B o i l e r and P r e s s u r e Vessel Code, The American S o c i e t y of Mechanical Engineers, New York, August 15, 1967.

18.

K. Goldman, S . L. I s r a e l , and D. J . Nolan, "Final S t a t u s Report: Performance E v a l u a t i o n of Heat Exchangers f o r Sodium-Cooled Reactors , I ' Report UNC-5236, United Nuclear Corporation, Elmsford, New York, June 1969.

19.

L. S. Tong, Chapter 7 i n B o i l i n g Heat T r a n s f e r and Two-Phase Flow, John Wiley and Sons, New York, 1965.

20.

L. Y. Krasyakova and B . N. Glusker, "Hydraulic Study of Three-Pass Panels With Bottom I n l e t Headers f o r Once-Through B o i l e r s , " T e p l o e n e r g e t i k a , 1 2 ( 8 ) : 17-23 (1965), (UDC 532: 621.181.91.001.5).

21.

E. R. Quandt, "Analysis and Measurement of Flow O s c i l l a t i o n s , " Chemical Engineering P r o g r e s s Symposium S e r i e s , Vol. 57, No. 32, 1961.

22.

L. M. S h o t k i n , " S t a b i l i t y C o n s i d e r a t i o n s i n Two-Phase Flow," Nuclear Science and Engineering, 28 : 317-324 (1967).

APPENDICES

45 Appendix A PHYSICAL PROPERTY DATA

The d e s i g n p r o p e r t i e s of t h e f u e l s a l t used i n t h e concept of a s i n g l e - f l u i d MSBR and i n c o r p o r a t e d i n t h e PRIMEX computer program a r e g i v e n i n Table A . l .

The d e s i g n p r o p e r t i e s of t h e c o o l a n t s a l t used in

t h e MSBR concept and i n c o r p o r a t e d i n t h e PRIMEX, RETEX, and SUPEX comp u t e r programs a r e given i n Table A.2;

and t h e d e s i g n p r o p e r t i e s of

H a s t e l l o y N used i n t h e MSBR concept and i n c o r p o r a t e d i n t h e s e computer programs a r e given i n Table A.3. Values f o r t h e d e n s i t y , v i s c o s i t y , and thermal c o n d u c t i v i t y of the f u e l and c o o l a n t s a l t s w e r e taken from d a t a r e p o r t e d i n Ref. A . l .

The

v a l u e g i v e n f o r t h e h e a t c a p a c i t y of the f u e l s a l t i s taken from Ref. A and t h e v a l u e given f o r t h e h e a t c a p a c i t y of the c o o l a n t s a l t i s taken from Ref. A.3.

These r e f e r e n c e s a r e l i s t e d below.

A. 1.

Oak Ridge N a t i o n a l Laboratory, %Molten-Salt Reactor Program Semiannual Progress Report August 31, 1969," USAEC Report OWL-4449, February 1970.

A.2.

Oak Ridge N a t i o n a l Laboratory, "Molten-Salt Reactor Program Semiannual P r o g r e s s Report August 31, 1968," USAEC Report ORNL-4344, February 1969.

A.3.

Oak Ridge N a t i o n a l Laboratory, "Molten-Salt Reactor Program Semiannual Progress Report February 29, 1969,'' USAEC Report ORNL-4254, August 1969.

Table A . 1 .

Design P r o p e r t i e s of MSBR Fuel S a l t

Fuel s a l t components

7 L i F- BeF2 ThF,

Composition, mole %

71.7-16-12-0.3

App r ox ima t e mo l e cu 1a r we i gh t

Approximate m e l t i n g p o i n t , OF

930

Vapor p r e s s u r e a t 1150"F, mm Hg

<0.1

- UF,

Density, g/cm3 l b / f t3 A t 1300째F A t 1175 "F A t 1050 OF b Viscosity, Centipoise

= 3.752

(6.68 X 10-4)T"C 0.02317T"F = 204.9 l b / f t 3 = 207.8 l b / f t 3 p = 210.7 l b / f t 3 p p p p

= 235.0

p = 0.109lexp

lb/f t .hr

p = 0.2637 exp 7

A t 1300째F

p = 1 7 . 2 9 lb/ft-hr p = 23.78 l b / f t * h r

A t 1175째F A t 1050 OF

T R

p = 34.54 l b / h r . f t C

He a t cap a c i t y ,

= 0.324 B t u / l b * " F -I- 4%

The rma 1 conduc t i v i t y A t 1300 "F k = 0.69 B t u / h r * " F . f t A t 1175째F k = 0.71 B t u / h r - " F * f t A t-1050 "F k = 0.69 B t u / h r . " F - f t a F i g u r e 13.6 on page 147 of Ref A . 1 . ~

~~~

bTable 13.2 on page 145 of Ref A . l . C

Page 163 of Ref. A . 2 .

The v a l u e of k shown dFigure 9.13 on page 92 o f Ref. A . l . i s f o r s a l t w i t h about 5% less L i F t h a n i n t h e r e f e r e n c e s a l t . A d d i t i o n of L i F would i n c r e a s e t h e average v a l u e t o about 0.72 t o 0.74. The e s t a b l i s h e d and c o n s e r v a t i v e v a l u e of 0.71 was used i n t h e c a l c u l a t i o n s f o r t h e MSBR concept.

47 Table A.2.

Design P r o p e r t i e s of MSBR Coolant S a l t

Coolant s a l t components

NaBF4-NaF

Composition, mole %

92-8

Approximate mole cu 1a r we igh t

104

Approximate m e l t i n g p o i n t ,

7 25

O F

Vapor p r e s s u r e a t 1150째F, mm Hg a Density ,

g / cm3

25 2

p = 2.252 ( 7 . 1 1 X lO-")T"C p = 141.4 0.0247T"F p = 113.0 l b / f t 3 p = 116.7 l b / f t 3 p = 120.4 l b / f t 3

l b / f t3 A t 1150째F A t 1000 OF A t 850 "F b Viscosity, Centipoise

p = 0.0877(exp

lb/ft.hr A t 1150 OF A t 1000 OF A t 850째F

Heat c a p a c i t y

1-1 = 2.60 l b / f t . h r p = 3.36 l b / f t . h r p = 4.61 l b / f t . h r C

Thermal c o n d u c t i v i t y , A t 1150 "F k A t 1000 OF k A t 850 OF k a F i g u r e 13.6 on page 147 of Ref.

= 0.360 B t u / l b . " F = 0.23 B t u / h r . " F . f t = 0.23 B t u / h r . " F . f t = 0.26 B t u / h r - " F . f t

A.l.

bTable 13.2 on page 145 o f Ref. A . l . C

Page 168 of Ref. A.3.

dFigure 9.13 on page 92 o f Ref. A . l .

-I- 2%

48 Table A.3.

Design P r o p e r t i e s of H a s t e l l o y N

Composition, w t % Nicke 1 Molybdenum Chromium Iron Manganese S i l i c o n , maximum Boron, maximum Titanium Hafnium o r niobium Cu, Coy P , S , C y W , A 1

Balance 12 7 0 to 4 0 . 2 t o 0.5 0.1 0.001 0.5 t o 1.0 0 to 2 0.35

Density, l b / f t 3 A t 80°F A t 1300°F

55 7 54 1

Thermal c o n d u c t i v i t y , B t u / h r * f t . O F A t 80°F A t 1300 "F

6.0 12.6

Specific heat, Btu/lbA t 80°F A t 1300 "F

0.098 0.136

O F

Thermal expansion p e r "F A t 80°F A t 1300 OF

5.7 x 9.5 x

Modulus of e l a s t i c i t y , p s i A t 80°F A t 1300 OF

31 x 25 X

Tensile strength, p s i A t 80°F A t 1300°F

-1 15 ,000 -75,000

Maximum a l l o w a b l e d e s i g n s t r e s s a t 1300"F, p s i A t 80°F A t 1300 "F

25 ,000 3500

M e l t i n g temperature , "F

2500

lo+ lo6 lo6

49 Appendix B THE PRIMEX PROGRAM

The PRIMEX computer program i s o u t l i n e d i n block-diagram form i n

Fig. B . l . B.l,

The i n p u t d a t a r e q u i r e d f o r the program a r e given i n Table

and t h e o u t p u t r e c e i v e d from t h e program a r e given i n Table B . 2 .

A complete l i s t i n g of t h e main program and i t s two s u b r o u t i n e s i s f o l -

lowed by d e f i n i t i o n s of the i n t e r m e d i a t e v a r i a b l e s used i n the program.

To i l l u s t r a t e t h e u s e of t h e PRIMEX program, t h e i n p u t and o u t p u t f o r the MSBR primary h e a t exchanger d i s c u s s e d i n Subsection 2 . 1 of t h i s r e p o r t a r e p r e s e n t e d a s p r i n t e d by t h e computer.

REA0 AN0 P R I N T INPUT DATA

ASSUME BAFFLE SPAC ING . I L

b4 ASSUME SHELL 0 IAMETER

CALCULATE NUMBER OF TUBES, FUEL AND COOLANT FLOWS AN0 VAR I OUS GEOMETR IES

ASSUME EXPANS ION RAD IUS REQU IREO FOR ACCEPTABLE STRESSES

START WITH F I R S T INCREMENT FROM HOT 1=1 S I D E OF HEAT EXCHANGER

ASSUME TEMPERATURE OROP FOR THE INCREMENT

EVALUATE ALL P H Y S I C A L PROPERTIES AT AVERAGE TFMPERATURE OF INCREMENT

CALCULATE PRESSURE DROPS AND HEAT TRANSFER COEFF I C I ENTS FOR THE INCREMENT, US I NG CORRECT CORRELAT ION FOR 0 I FFERENT REG IMES

CALCULATE HEAT RATE AN0 TEMPERATURE DROPS OF THE INCREMENT

Fig. B.l.

Simplified Flow Diagram of the PRIMEX Computer Program.

TEMPERATURE OROPS AGREE WITH OUR ASSUMPTION

CHANGE ASSUMED INCREMENT TEMPERATURE DROP

EN0 TEMPERATURE OF

GO TO NEXT INCREMENT

I=I+l

DOES TOTAL SHELL SIDE PRESSURE DROP

CHANGE ASSUMED BAFFLE SPACING

53 Table B.I.

Card

Columns

Format

1-10 11-20

E10.4 F10 .O

2 1-30

F10 .O

31-40 41-50 B

Term

Units

HEATL PRDT

Btu/hr lb/ft2

PRDS

lb/ft?

F10 .O F10 .O

TPIN SPOUT

lb/ft2 l b / f ?i

1-10 11-20 2 1-30 31-40

F10 .O F10 .O F1O.O F10 .O

Coolant o u t l e t t e m p e r a t u r e Fuel i n l e t temperature Fuel o u t l e t temperature Coo 1a n t i n 1e t t emp e r a t u r e

CTO FTO ETF E TC

OF OF OF OF

1-10

F10 .O

11-20

F10 .O

2 1-30 31-40

F10.0 F10 .O

41-45

Leakage f a c t o r f o r h e a t transfer correlations Leakage f a c t o r f o r p r e s s u r e drop c a l c u l a t i o n s Tube m a t e r i a l c o n d u c t i v i t y Arc1 o f b e n t t u b e f o r t h e r mal expansion Number o f p a i r p o i n t s i n Stress intensity table for tube material

1-10

F10 .O

DICNPT E

11-20 1-10

F10 .O

11-20

F10 .O

2 1- 30

F10 .O

31-35 36-40

I5 I5

41-45

1-10 11-20 2 1-30 31-40 41-50 51-60

F10 .O F10 .O F10 .O F10 .O F10 .O F10 .O

...

va r i a b 1e Heat l o a d r e q u i r e d A 1 lowab 1e t u b e- s i d e p r e s s u r e drop Allowable s h e l l - s i d e p r e s s u r e drop Tube-side i n l e t p r e s s u r e Shell-side o u t l e t pressure

h,&.

Fl,F2.

Computer I n p u t Data f o r PRIMEX Program

F10 .O

S t r e s s i n t e n s i t y a t CTM temperature Temp era t u r e Radius o f c o o l a n t c e n t r a l downcomer D i s t a n c e between s h e l l w a l l and t u b e bundle Maximum a n t i c i p a t e d heat exchanger r a d i u s Number o f c a s e s t o be run Index one i f enhanced t u b e s a r e used Index one i f s t r e s s a n a l y s i s i s included Outside diameter o f tubes Tube w a l l t h i c k n e s s Radial p i t c h Circumferential pitch Inner b a f f l e cut Outer b a f f l e c u t

PLK WCOND ARC

B t u / h r * f t *OF Degrees

ICNPT

CASM

psi

CTM

O F

RA5

DTR

RASMAX

KASES KENTB

KTBST

DIA WTHK RPI BCPI CUT3 CUT4

ft ft ft ft % of area % of area

54 Table B.2.

Term

Output Data From PRIMEX Computer Program Variab 1e

Units Btu/hr

THEATO

Total heat actually transferred

HTPERC

P e r c e n t a g e o f r e q u i r e d h e a t load a c t u a l l y transferred

Coolant ( s h e l l - s i d e ) mass flow r a t e

lb/hr

F u e l ( t u b e - s i d e ) mass flow r a t e

lb/hr

TTDSO

T o t a l t u b e - s i d e p r e s s u r e drop

psi

SPPERC

P e r c e n t a g e o f allowed t u b e p r e s s u r e drop a c t u a l l y used

TTDTU

T o t a l s h e l l - s i d e p r e s s u r e drop

TPPERC

P e r c e n t a g e o f allowed s h e l l p r e s s u r e drop a c t u a l l y used

RA8

Radius o f h e a t exchanger s h e l l

BSOI

D i s t a n c e between baffles

VOL

F l u i d volume c o n t a i n e d i n t u b e s

f P

AREA

T o t a l h e a t t r a n s f e r a r e a i n h e a t exchanger

fi?

SNT

T o t a l number o f t u b e s

TUBLEN

Actual t u b e l e n g t h

HEXLEN

Heat exchanger l e n g t h from lower t u b e s h e e t t o upper n o z z l e o f t u b e s

STRLEN

S t r a i g h t s e c t i o n length o f tubes

EXPRAD

Radius o f t u b e bends f o r thermal expansion

BRL1

Modification f a c t o r f o r B e r g e l i n ' s h e a t transfer correlation

PSTO

Primary s t r e s s e s on o u t e r s u r f a c e o f t u b e s

psi

PQSTO

Combined primary and secondary s t r e s s e s on o u t e r s u r f a c e o f tubes

psi

PQFSTO

Combined primary, secondary, and peak s t r e s s e s on o u t e r s u r f a c e of t u b e s

psi

PSTI

Primary s t r e s s e s on i n n e r s u r f a c e o f t u b e s

psi

PQSTI

Combined primary and secondary s t r e s s e s on i n n e r s u r f a c e of tubes

psi

PQFSTI

Combined primary, secondary, and peak s t r e s s e s on i n n e r s u r f a c e o f t u b e s

psi

SAVT

S h e l l a v e r a g e temperature

O F

TAVT

Tube a v e r a g e temperature

O F

psi

55 W

T a b l e B.2 ( c o n t i n u e d ) Term

Variable

Units

TCI ( I )

Coolant o u t l e t t e m p e r a t u r e from increment I

TCO( I)

Coolant i n l e t t e m p e r a t u r e from increment I

CWT ( I )

Average t u b e w a l l t e m p e r a t u r e a t c o o l a n t s i d e

TFI (I)

Fuel o u t l e t t e m p e r a t u r e from increment I

TFO ( I )

F u e l i n l e t t e m p e r a t u r e from increment I

FWT(I)

Average t u b e w a l l t e m p e r a t u r e a t f u e l s i d e

TwJlT (1)

Average t e m p e r a t u r e drop a c r o s s t u b e w a l l i n i n c r ement I

vM1(I)

F l u i d a v e r a g e v e l o c i t y i n o u t e r window i n increment I

ft/sec

vM2(I)

Fluid average v e l o c i t y i n overlapping b a f f l e zone i n increment I

ft/sec

v~3(1)

F l u i d a v e r a g e v e l o c i t y i n i n n e r window i n increment I

ft/sec

VWOl ( I )

F l u i d v e l o c i t y a c r o s s t u b e s i n o u t e r edge o f b a f f l e i n increment I

ft/sec

W03 (I)

F l u i d v e l o c i t y a c r o s s t u b e s i n i n n e r edge o f b a f f l e i n increment I

ft/sec

PDSO( I)

S h e l l - s i d e p r e s s u r e drop f o r increment I

lb/ft2

PDTO ( I)

Tube-side p r e s s u r e drop f o r increment I

lb/ft2

WNTO ( I)

Tube-side Reynolds number f o r increment I

PRNTO( I)

Tube-side P r a n d t l number f o r increment I

RENSOl (I)

Reynolds number i n o u t e r window increment I

ENS02 ( I )

Reynolds number i n o v e r l a p p i n g b a f f l e zone i n increment I

ENS03 (I)

Reynolds number i n i n n e r window i n increnent I

HTO ( I)

Tube-side h e a t t r a n s f e r c o e f f i c i e n t i n increment I

B t u / h r * f ? *OF

AHSO ( I)

Shell-side heat transfer coefficient i n increment I

B t u / h r * f r ? *OF

UOA ( I )

Overall h e a t t r a n s f e r c o e f f i c i e n t i n increment I

Btu/hr* f$ #OF

HEAT (I)

Heat t r a n s f e r r e d i n increment I

Btu/hr

The PRIMEX Program L i s t i n g

* * F T N T L t E TGTM. MSBRP 10 PROGRAM MSBRPE-2 MSBRP 20 TYPE REAL LK 9 L A W O l T L A N 0 3 MSBRP 30 D I M E N S I O N TFO( 7 5 1 T T C I ( 7 5 ) T V M L( 7 5 ) T V M( ~7 5 ) T V k C l ( 7 5 ) T V W C 3 ( 7 5 ) T MSBRP 3 1 l R E N T O ( 7 5 ) , P R N T O ( ~ ~ ) T R E N S O ~ ( ~ ~ ) T R E tNR SE hOS~O (3 ( ~7 5~) )T MSBRP 3 2 2 V M 3 ( 7 5 ) ~PDSO ( 7 5 ) T N T ( 1 0 0 1 f B J ( 3 1 T H S O (~7 5 ) T H S C ~ ( ? T~ H) S O (~7 5 1 T MSBRP 33 3AHSO( 7 5 ) t H T O ( 7 5 1 t U O A l 7 5 ) 9TCO ( 7 5 ) T T F I( 7 5 J r H E A T ( 7 5 T T W D T ( 7 5 I T MSBRP 34 7 5 ) T v 2 ( 7 5 ) T v 3 (75 ) T V W l ( 7 5 ) TVW3( 7 5 ) T 4PDT0(75), TUBLN(751, MSBRP 35 5 R ( 100 ) 9 F A C T ( 100 1 t TCP I( 100 J T TOTAL ( 1 0 0 1 tCASM( 6 ) T CTM ( 6 MSBRP 36 6 C H T ( ~ ~ ) T F W 7T5(j r A V W T ( 7 5 ) MSBRP 40 1001 FORMAT( E 1 0 0 4 1 4F10.0) MSBRP 50 1 O C 2 FORMAT ( 4 F 10 -0 1 MSBRP 60 1003 FORMAT( ~ F L O O O T I ~ ~ 100 4 FORMAT ( 2 F 10 4 1 MSBRP 70 MSBRP 80 1005 FORMAT( 3 F l O o O T 3 1 5 ) MSBRP 90 1006 FORMAT( 6F 10.0 1 1007 FORMAT ( ~ H ~ T ~ X T ~ H I T ~ X T ~ H C T M ~ ~ X ~ ~ H C A S) M / / ( ~ X ~ I MSBR ~ ~ ~ F100 ~ Z . ~ ) MSBR 110 1 0 0 8 FORMAT(22HOHEAT LOAD R E Q U I R E D = T F ~ ~ . O T ~ X T ~ H ( B T U /1 H R I MSBR 1 2 0 1009 FORMAT(43HOALLOWABLE T O T A L T U B E - S I D E PRESSURE DRCP = r F l O o O v 2 X t MSBR 1 2 1 1 lOH(LB/SQ-FT) 1 MSBR 130 1010 F O R M A T ( 4 4 H C A L L O W A B L E T C T A L S H E L L - S I D E PRESSURE CROP = r F 1 0 . O t 2 X t MSBR 1 3 1 1 lOH(LB/SQ-FT) 1 MSBR 140 1011 F O R M A T ( 2 3 H O T U B E I N L E T PRESSURE = T F ~ O . O T ~ X T ~ LCBH/ S( Q - F T J 1 MSBR 150 1012 FORMAT ( 2 4 H O S H E L L O U T L E T PRESSURE = t F ~ O ~ O T Z1OH X T(LBISQ-FT) I 1013 F O R M A T ( 3 3 H O H I G H TEMP. OF SHELL S I D E F L U I D = T F ~ O . ~ T ~ X T ~ H ( F ) ) MSBR 160 MSBR 170 1 0 1 4 F O R M A T ( 3 3 H O H I G H TEMP. O F TUBE S I O E F L U I D = T F ~ O * Z T Z X T ~ H ( F ) J T F ~ O . ~ T ~ X T ~ H ( F I ) MSBR 1 8 0 1 0 1 5 FORMAT(32HOLOW TEMP, OF TUBE S I D E F L U I D = MSBR 190 1016 FORMAT(32HOLOW TEMP. OF S H E L L S I O E F L U I D = T F ~ C ! . Z T Z X T ~ H ( F I ) MSBR 200 1017 FORMAT( 32HOHEAT TRANSFER LEAKAGE FACTOR = T F 1 0 . 5 ) MSBR 210 1 0 1 8 FORMAT(27HOPRESSURE LEAKAGE FACTCR = t F l O . 5 1 MSBR 220 1019 FORMAT(35HOCONOUCTIVETY OF TUBE kALL M E T A L = r F L @ . S ~ 2 x 9 MSBR 221 1 1 3 H ( BTU/HR-FT-F) 1

1C20 FORMAT(37HOARC OF FOUR BENDS FOR F L E X I B I L I T Y = r F 1 0 0 2 r 2 X r

MSBR 1 9H(DEGREES)) MSBR 1 0 2 1 F O R M A T ( 3 4 H O I N S I D E R A D I U S OF OUTER ANNULUS = r F l O o 5 r 2 X r 6 H ( F E E T ) 1 MSBR MSBR 1 0 2 2 F O R M A T ( 4 1 H O D I S T A N C E B E T k E E N S H E L L WALL AND TUBES = 1 rFlOo5r2Xr6H(FEET)) MSBR MSBR 1 0 2 3 FORMAT(4SHOMAXIMUM A N T I C I P A T E D OUTER R A D I U S CF EXCHANGER = 9 MSBR 1 F10*5r2Xr6H(FEET) 1 MSBR 1 0 2 4 FORMAT(23HONLMBER OF CASES RUN = 114) 1 0 2 5 FORMAT(25HOUSE OF ENHANCED TUBES = , 1 4 r 2 X r 3 2 H ( O N E I F ENHANCED TUBEMSBR 1s ARE U S E D ) ) MSBR 1026 FORMAT( l I ’ O r 3 6 H U S E OF STRESS A N A L Y S I S S U B R C U T I h E = 9 MSBR 1 I4,2Xr19H(ONE I F TO BE U S E D ) ) MSBR 1027 F O R M A T ( 2 9 H O O U T S I D E D I A M E T E R OF TUBES = r F l O o 5 9 2 X r 6H(FEET) ) MSBR 1 0 2 8 FORMAT(27HOWALL T H I C K N E S S OF TUBES = r F l O o 5 r 2 X r 6 H ( F E E T ) ) MSBR 1029 F O R M A T ( 1 6 H O R A D I A L P I T C H = r F l O o 5 r 2 X r 6H(FEET)) MSBR MSBR 1 0 3 0 FORMAT(25HOCIRCUMFERENTIAL P I T C H = 9 F 1 0 e 5 r 2 X r 6H(FEET) 1 1 0 3 1 FORMAT422HOINNER B A F F L E C U T 3 = r F L O o 5 , 2 X v 1 0 H ( P E R CEhTJ ) MSBR 1 0 3 2 FORMAT(22HOOUTER B A F F L E C U T 4 = r F l O o 5 r 2 X r 1 0 H t P E R C E A T ) MSBR 1 0 3 3 F O R M A T ( 2 5 H l T O T A L HEAT TRANSFERED = 9F12.0 r 2 X r 8 H ( B T U / H R ) 9 MSBR 1 2 x 9 1H( r F 5 o l r 9 H PERCENT) ) MSBR 1034 FORMAT(29HOMASS FLOW RATE OF COOLANT = , F l O o O r 2 X , 7 H ( L B / H R ) MSBR 1 0 3 5 FORMPT(26HOMASS FLOW RATE OF F U E L = r F 1 0 0 O r 2 X 1 7 H ( L B / H R ) 1 MSBR 1036 F O R M A T ( 3 4 H O S H E L L - S I D E TOTAL PRESSURE DROP = r F 1 0 . 2 9 2 X 1 9 H ( L B / S Q I N ) M S B R 1 r 2 X q l H ( , F 5 o l r 9 H PERCENT)) MSBR 1037 F O R M A T ( 3 3 H O T U B E - S I D E T C T A L PRESSURE DROP = r F l O o 2 r 2 X I 9 H ( L B / S Q I N ) r M S B R 1 2 X r l H ( r F 5 o l r 9 H PERCENT) MSBR 1 0 3 8 FORMAT( 24HONOMINAL SHELL R A D I U S = r F 7 . 4 , 2 X r 4 H ( F T ) 1 MSBR 1039 FORMAT(26HOUNIFORM B A F F L E S P A C I N G = , F 7 o 4 r Z X 1 4 H ( F T ) I MSBR 1040 FORMAT(40HOTUBE F L U I D VOLUME C O N T A I N E D I N TUBES = r F 7 0 2 1 1 X 9 MSBR llZH(CUB1C FEET)) MSBR 1041 F O R M A T ( l P 0 ~ 4 6 H T O T A L HEAT TRANSFER AREA BASED ON TUBE COD. = t MSBR 1 F12*2r2X16H(SQFT)) MSBR 1 0 4 2 F O R M A T ( 2 5 H O T O T A L NUMBER OF T L B E S = r F O . 0 1 MSBR 1043 FORMAT(21HOTOTAL TUBE LENGTH = r F 6 . 2 , 2 X r 4 H ( F T ) 1 MSBR 1044 FORMAT(29HOHEAT EXCH. APPROXe LENGTH = r F 6 o Z r 2 X 1 6 H ( F E E T I I MSBR 1045 F O R M A T ( 3 5 H O S T R A I G H T S E C T I G N OF TUBE LENGTH = r F 6 * 2 r 2 X 1 4 H ( F T ) 1 MSBR 1046 F O R M A T ( 3 8 H O R A D I U S G F THERMAL E X P A N S I O N CURVES = r F 6 0 2 r 2 X 1 6 H ( f E E T ) IMSBR

230 231 240 250 251 260 261 270 280 281 290 291 300 310 320 330 340 350 360 361 370 380 390 391 400 401 410 420 430 431 440 441 450 46C 470 480 490

cn U

1047 F O R M A T ( 3 1 H O B E R G L I h M O D I F I C A T I O N FACTOR = r F 5 . 2 ) MS BR 1 0 4 8 FORMAT ( l H 0 1 2 X r 1 H I 9 7 x 9 3 H T C I r 9 X t 3 H T C O r 9 X 9 3 H C k T r 9 X 9 3 H T F I r 9 X 9 3 H T F O t MSBR 19x1 3 F F W T r 8 X r 4 H T W D T / / l l X r 1HF r l l X r l H F 9 1 l X r l H F ~ l l X r MS BR MSBR 2 l k F , 11x1 1 H F r 1 1 X t l H F 9 1 1 X r l H F / / 4 1 X t I 3 r 7 E 1E * 4 1 ) 1049 FORMAT( l H 0 , 2 X , l H I 1 9 X r 2 H V l 9 9 X r 2 H V 2 v 9 X r 2 H V 3 r 9 X r 3 H V W l t 9 X r 3 H V W 3 r MSBR 1 8 X ~ 4 H P D S 0 ~ 8 X r 4 H P D T O / / 3 2 X 1 6 H F T / S E C 1 3 3 X ~ 7 H L B / S Q F l / / ~ l X t I 3 r 7 F )l 2 MSBR ~4~ 1 0 5 0 FORMAT( l H O r 2 X 9 l H I r 5 X r 5 H R E N T O r 7 X t 5HPRNTO r 7 X ~ 6 H P E h S C l r 6X r 6 H R E N S 0 2 r MS BR 16x9 6HREN SO39 7 X 3 H H T O r 8 X r 4 H A H SO 9 9 X r 3 H U O A 18 X p 4 H H E A T / / 7 7 X r MSBR 1 2 13HBTU/HR/SQFT/F r l 3 X , 6 H B T U / H R / / ( l X r I 3 r 9 E L 2 . 4 ) MS BR 1 0 5 1 F O R M A T ( 2 7 H O T U B E WALL AVERAGE TEMP. = rF10.2) MS BR T F10.2) 1 0 5 2 F O R M A T ( 2 8 H O S H E L L S I D E AVERAGE TEMP. = MSBR 1 0 5 3 F O R M A T ( l H O q 3 4 H P STRESS A T TUBE OD AND TUBE I D = 2F10*2rlXr MSBR MSBR 1 9 H ( L B / S Q I N ) / / 1 8 H ( SHOULD NOT E X C E E D r F l O o 2 r 3 H II 1 0 5 4 F O R M A T ( l H O r 3 6 H P + Q STRESS AT TUBE OD AND TUBE I D = 9 MSBR 1 2 F 1 0 . 2 , lX,9H(LB/SQIN)//18H(SHOULD NGT E X C E E D I F L O . 2 9 MSBR MSBR 2 3H 1) 1055 F O R M A T ( l P 0 , 3 8 H P + Q + F STRESS A T TUBE OD AND TUBE I D = 9 MSBR 1 2 F 1 0 , 2 9 1 X 9 9 H ( L B / S Q I N I / / 1 8 H ( SHOULD NGT EXCEED, F l O 2 9 MSBR 2 3H 1) MSBR MSBR C C R E A D I N AND P R I N T OUT I N P U T DATA MSBR KEY7= 1 MSBR VMl(l)=O* MSBR MSBR V M 2 ( 1)=0* V M 3 ( 1)=0. MSBR MSBR V W O l t 1150. VW03( l ) = C . MSBR R E N S O l t 1I=O. MSBR R E N S 0 2 ( 1) = O * MSBR MSBR R E N S 0 3 ( 1)=O* H S O 1 ( 1)=O. MSBR H S 0 2 ( 1)=0. MSBR H S 0 3 ( 1 j =0. MSBR H E F I = 1. MSBR HEFO = 1. MSBR C MSBR

500 5 10 5 11 5 12 5 20 521 530 53 1 532 5 40 5 50 5 6C 561 570 571 572 580 581 582 650 660 610 620 630

640 650 660 670 680 690 700 710 720 730 740 810

READ 1001, H E A T L , PRDT, PROS t T P 1 N v S P O U T READ 1 0 0 2 1 CTOI FTOI E T F , ETC READ 1003, L K , P L K , WCONDvARC , I C N P T R E A D 10049 ( C A S M ( K ) r C T M ( K ) r K = l * I C N P T l READ 1 0 0 5 9 RA5, DTRI R A ~ M A X I K A S E S I K E N T B I K T B S T CONTINUE R E A D 1006, D I A , WTHKI R P I , B C P I , C U T 3 9 C U T 4 HSFCT=l. I F ( FTO.LT.CT0) HSFCTZ-1. P R I N T 1007 ( Kc CTM( K 1 ,CA SM ( K ) t K = l t I C N P T ) P R I N T 1008, H E A T L P R I N T 1C091 PRDT P R I N T 1Cl0, PROS P R I N T 1011, T P I N P R I N T 1 0 1 2 , SPOUT P R I N T 1013, CTO P R I N T 1014, FTO P R I N T 10159 E T F P R I N T 1016, ETC P R I N T 10179 LK P R I N T 1018, P L K P R I N T 10 19, WCOND P R I N T 10209 ARC PRINT 1021, RA5 P R I N T 1 0 2 2 9 DTR P R I N T 1023, RA8MAX P R I N T 1 0 2 4 t KASES P R I N T 1025, KENTB P R I N T 1026, KTBST PRINT 10279 D I A P R I N T 1028, WTHK PRINT 1029, R P I P R I N T 1030, B C P I P R I N T 1031, CUT3 P R I N T 10132, CUT4

MSBR MSBR MSBR MSBR MSBR MSBR MSBR

760 770 780 790 800 810

820

MSBR 830 MSBR 840 MSBR 850 MSBR 860 MSBR 870 MSBR 880 MSBR 890 MSBR 900 MSBR 910 MSBR 9 2 0 MSBR 930 MSBR 940 MSBR 9 5 0 MSBR 960 MSBR 970 MSBR 9 8 0 MSBR 990 MSB l O C 0 MSB 1010 MSB 1 0 2 0 MSB 1@3@ MSB 1040 MSB 1050 M S B 1060 MSB 1C70 MSB 1080 MSB 1650

C C

B E G I N GEGMETRY C A L C U L A T I O N S FOR S I N G L E ANNULLS CCUNTER FLOW D I S C AND DOUGHNUT B A F F L E D H E A T EXCHANGER ARCR= @ . 0 1 7 4 5 2 * A R C ATUBE = (3.141598 (DIA**2.0))/4.0 G F T T = 1*/36C'r). GFT = 1./144. DIAI=DIA-2*0*WTHK I/4.C FATUB = ( 3 0 1 4 1 5 9 * ( D I A I * * 2 . 0 ) KEY1 = 0 P E R C l = 0.99 I F ( K E Y 1. GT .C ) B SO I=O 5 4 ( BSL+B SH) KEY2 = 0 P E R C 2 = (2.99 RA8L=RA5 R A8H=RA8 MAX RA8=0*5*(RA8L +RA8H I RJ8=(RA8-RA5-2.*DTRl/RPI+lo IJ 8 = R J 8 RIJ8=IJ8 I F ( R J 8-R I J 8-0 5 1 4 9 4 9 5 J8=iJ8 T RP I = ( RA 8-R A 5- 2 *D TR 1 / 4 R I J 8- 1 l CPI=BCP I*RP I / T R P I GO TO 6 J 8 = IJ 8 + 1 T RP I = ( R A 8-R A 5- 2 *D TR I /R I J 8 CPI=BCPI*RPI/TRPI DO 7 I = l * J 8 R ( I 1 =RA5+DTR +TRP I* ( I - 1 1 FACT( I I=6028318*R( I 1 NT(I)=FACT(II/CPI TCP I ( I ) = F A C T ( I I / N T ( I) IF( I.EQ*l)TOTAL(I1=NT(II I F ( I.NE 1)T O T A L ( II =TOTAL ( 1-1 1 +NT ( 1 1 NTO=TOTAC( J 8 I SNT=NTO RA52=RA5**2 RA82=RA8**2

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

1660 1670 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310

1320 1330 1340 1350 1360 1370 1380 1390 1400 1410 1420 1430 1440 1450 146@ 1470

**.

R A 6 = ( R A 5 2 + C U T 4 * ( RA 8 2 - R A 5 2 1 1 5 J 6 = ( R A 6 - R ( 1) ) / T R P I + l , R A 6 = R ( J 6 I + . 5*TRP I R A 7 = ( R A 8 2 - C U T 3 * ( RA 82-RA 52 1 I**. 5 J 7 = ( R A 7 - R ( 1) ) / T R P I + l . R A 7 = R ( J 7 I + 5*TRP I RA62=RA6**2 RA72=RA7**2 R B 1=O 5* ( J 8- J 7 RB2=J7-J6 R B 3 = 0 5* J 6 SUM l = T O T A L ( J 8 - T O T A L ( J7 j SUM2=TOTAL ( J 7 1 - T O T A L ( J 6 ) SUM 3=TOT AL ( J 0 1 ISUMl=SUMl I SUM2=SUM2 ISUM3=SUM3 BSMAX= 1 5* ( ( RA 8- ( R A 8-RA 7 1 /2 I - ( R A 5+ ( RA6-RA5 1 4 2 1 1 BSM IN=O. 2s ( R P8-RA5 1 IF(BSMINoLT.Oo 1667)BSMIN=0.1667 AP01=3.14159*(RA82-RA72 )-ATUBE*SUMl AP03=3. 14159W R A 6 2 - R A 5 2 )-ATUBE*SUM3 LAWO1=6.28318*RA75 * D I A * ( N T ( J 7 I+NT( J7+1) 1 LAW03=6.28318*RA6-.5*DIA*(NT( J 6 ) + N T ( J6+1) 1 HW=2.*WCOND/(DIA*(ALOG( DIA/DIAI 14 1 CSPHAV=0.36 FSPHAV=0.324 QC=HEATL/(CSPHAV*(CTO-ETC I ) QF=HEATL/( FSPHAV*( F T O - E T F ) GTO = Q F / ( NTO*FATUB 1 K E Y 3=0 X P RM AX= 6 0 X P R M I N = 0. E X P R A D z 0.5* ( X P R M I N+XPRMAX) IF( KTBST.EQ.0) E X P R A D = l . 77 IF ( K EY 1 EQ .O I B SH=B S M A X I F ( K E Y 1. EQ.O)BSL=BSMIN

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS0 MSB

1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660 1670 1680 1690 1700 1710 1720 1730 1740 1750 1760 1770 1780 1790 1800 1810 1820 1830 1840

IF(KEYl.EQ.O~BSOI=O.59(8SL+BSH) CURV ES=0 .O 69 813*ARC*

EXPRAD+

0.4*(RA8-RA51+.25*BSOI

= 0

KFINAL=O

I=1 TSUM=O. SSUM=O. THEATO = 0.0 TPDTO = 0.0 TPDSO = 0.0 TFO( I )=FTO

TCI(II=CTO TIF=-5.0 TIC=-5.0 CDTF=O. FDTF=O. BSO = BSOI BRL 1 = BSO/((RA8-(RA8-RA7)/2.)-(RA5+(RAb-RA5)/2.J) GBRL = 0.77*BRLl**(-,138) AWO 1 = BSO*LAWOl AW03 = BSO*LAW03 = SQRT(AWOl*APOl1 AWL AW2 = (AWOl+AW03)/2. AW3 = SQRT( AW03*AP03) GSOl = QC/AWl

GS02 = QC/AW2 GS03 = QC/AW3

10 11

BSO=CURV ES EQVBSO= CURVES+ 13.*iDIA+DIAI KEY4=0 KEY5=0 ATC = TCI(1) + (TIC/2.0) CFT = ATC +.CDTF*HSFCT

ATF = TFO(I)+TIF/2.

MSB MSB MSB MSB MSB MSB MSB MS8 MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8 MSB MS8 MSB MSB MS8 MSB MSB MSB MSB MSB MSB

1850 1860 1870 1880 1890 1910 1920 1930 1940 1950 1960 1970 1980 199C 2000 2010 2020 2030 2040 2050 2060 2070 2C80 2090 2100 2110 2120 2130 2140 2150 2160

MSB

2180

MSB MSB MSB

22C0 2210 2220

1900

m N

FFT=ATF-FOTF*HSFCT

FI=I TUBLN(1) =(FI-1. j*BSOI+CURVES CVIS=0.2121*EXP(4C32./(460.+ATC)I

(

1 (

12 13

CV I SW=O 2 1 2 1 * E X P ( 4 0 3 2 . / (460. + C F T 1 1 MSB 2230 CDEN=141.37-0.02466*ATC MSB 2240 CCON=O. 240 MSB 2 2 5 0 CSPH=0.36 MSB 2 2 6 0 FVIS=Oo2637*EXP( 7362o/1460.+ATF1 MSB 2 2 7 0 FVISW=O. 2 6 3 7 * E X P ( 7 3 6 2 . / ( 4 6 @ o + F F T ) 1 MSB 2 2 8 0 FDEN=234.97-O002317*ATF MSB 2 2 9 0 FCON=0.70 MSB 2 3 0 0 FSPH=0.324 MSB 2 3 1 0 VISK = (CVIS/CVISW)**0.14 MSB 2 3 2 0 14 MSB 2 3 3 0 FVISK=( fVIS/FVISW)**O. MSB 2 3 4 0 DCVIS = C I A / C V I S CCDEN = l./CDEN MSB 2 3 5 0 MSB 2 3 6 0 QCCDEN = QC*CCDEN C A L C U L A T E REYNOLS AND PRANDTL NUMBER TUBE S I D E MSB 2 5 5 0 RENTO( I ) = D I A I * G T O / F V I S MSB 2 3 8 0 MSB 2390 PRNTO( I l = F V I S * F S P H / F C O N I F ( K E N T B E Q o 1 AND. R ENTO ( I GT. 1001 AND, I hE 11 MSB 2400 l H E F I = l . + ( ( R E N T O ( I ) - 1 0 0 @ 0 ) /9OOOo ) * * g o 5 MSB 2 4 0 1 P D T O ( I ) = ( . 0 0 2 8 + . 25*RENTO**L-.321 )*EQVBSC*GT0*~2*HEFI/ MSB 2410 1 (DIAI*FDEN*417182400o 1 MSB 2 4 1 1 C A L C U L A T E HEAT TRANSFER COEFF TUBE S I D E MSB 2 6 4 0 H T O ( I ~ ~ F C O N / D I A ~ ~ 0 2 1 7 * ~ R E N T O ~ I ~ * * ~ 8 1 * ~ P R N T O ~ I ~ ~ * o 3 3 3 3 ~ *MSB F V I 2430 SK*HEfI GO TO 1 5 MSB 2 4 4 0 MSB 2 4 5 0 I F ( R E N T O ( I ) o L T o 2 1 0 0 . ) G C TO 14 H T O ( 1 ) = F C O N / D I A * ~ 0 8 9 * ( R E N T O ( I ~ * * 0 6 6 6 6 ~ 1 2 5) .* ( P P N T O i I ) * * . 3 3 3 3 ) * MSB 2 4 6 0 1 F V I S K * H E F I * ( l . + o 3 3 3 3 s ( D E A E / T U B L N ( I I )**e66661 MSB 2 4 6 1 GO TO 15 MSB 2 4 7 0 H T O ( 1 ) = F C O N / D I A * ~ 4 ~ 3 6 + ~ 0 ~ 0 2 5 * R E N T O ~ I ~ * P R N T O ~ I ) ~ D I A I / T U B L NMSB ~ I 1 2480 1 ) / ( l . . + 0 ~ 0 0 1 2 * R E N T O ( I 1*PRNTO(11*DIAI/TUBLN(I)1 1 MSB 2 4 8 1 MSB 2 4 9 0 I F ( I o E Q o 1 ) G O TO 16 C A L C U L A T E FLOW AREAS S H E L L S I D E MSB 2 4 8 0 V W O 1 ( I ) = QCCDEN/AWOl MSB 2 5 1 0 MSB 2 5 2 0 V W 0 3 ( I 1 = QCCDEN/AW03 MSB 2 5 3 0 V M l ( I 1 = GSOlsCCDEN V M 2 ( I J = GS02*CCDEN MSB 2 5 4 0 V M 3 ( I ) = GS03sCCDEN MSB 2 5 5 0

C A L C U L A T E PRESSURE DROPS S H E L L S I D E D P 1 = (1.+.6*RB11*CDEN*VMl(I)**2 D P 2 = .6*RBZ*CCEN*VM2( I1**2 D P 3 = (l.+.6*RB3)*CDEN*VM3(1 )**2 RENSOl( I ) = GSOl*DCVIS R E N S 0 2 ( I )= G S 0 2 * D C V I S R E N S 0 3 ( I) = G S 0 3 * D C V I S IF(KENTB.EQ. 1.AND. R E N S 0 2 ( I)GT. 1 0 0 1 . 1 lHEFO=1.+0.3*( ( R E N S 0 2 ( 1 1 - 1 0 0 0 . 1/9000. 1**0.5 P D S O ( 1 ) = (DPl+DP2+DP3)*PLK*HEF0/834624QOO* I F ( I . E Q . 2 ) P D S O ( l 1 ~ P D S O ( 91 C A L C U L A T E B J FACTOR AND S H E L S I D E C O E F F I C I E N T B J ( 1) = ( 0 * 3 4 6 * R E N S O l ( I ) * * ( - O 0 3 8 2 ) l*GBRL B J ( 2 1 =(Oo346*RENS02(11**(-0o382) )*GBRL B J ( 3 ) =(O0346*RENS03( 1)**(-0.3821j*GBRL H S O 1 ( I 1 = ( L K * C S P H * G S O l * B J ( l I*( ( C C O N / ( C S P H * C V I S ) )**.661 )*VISK HS02(11 = (LK*CSPH*GS02*BJ(Z)*((CCON/(CS~H*CViS1)~~o66~)*VISK HS03( I ) = (&K*CSPHsGS03*BJ(3J*( (CCON/(CSPH*CVIS) 1***66) ) * V I S K AHSO( I 1 = ( ( ( H S O 1 ( I ) * S U M 1 1 + ( H S C Z ( I)*SUM2 1 + ( H S 0 3 ( I )*SUM3 1 j / S N T ) *HEFO GO T O 17 P D S O ( I) = O m APO=3.14 159* ( R A 8 2 - R A 5 2 )-SNT*ATUBE EQV D I A = 4 .*APO/ ( 3 1 4 159* SN T*D I A+6 243 1 8 * 4 RA8+RA5 1 I GSO=QC/A PO RENSO =GSO*DCVIS PRES0 =CVIS*CSPH/CCON AHSO(I)=O.l28*CCON*VISK*(12o*€QVD~A*RENSO )**0.6 1 +PRES0 **0*33/DIA U O A ( I ) = 1e o / ( ( l , O / A H S O ( I 1 1+( l . O / H T O ( I1 I + (1. O / H k l ) A = QF*FSPH B = QC*CSPH D = UOA( I ) * S N T * B S O *3.1415S*DIA P = -HSFCT*(D*(A-B) )/(A*B) PBAR = E X P ( P 1 C = (8-A)*PBAR TCO( I ) = ( ( T C I ( I l*(B*PBAR-A1 1 - ( T F C ( I )*A*(PBAR-l. 1 1 )/C

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

2590 2570 2580 2590 2600 2610 2620 2630 2631 2640 2650 2730 2670 2680 2690 2700 2710 2720 2730 2740 2750 2760 2770 2780 2790 2800 2810 2811 282@ 2830 2840 2850

MSB 2870 MSB 2880 MSB 2890

T F I ( 1 I =((TCO( I ) - T C I ( I ) ) * B / A J + TFO(1) HEAT(1) =-A*(TFI(IJ TFO(1)) TWDT( I)= ( H E A T ( I) I N T O 1 *ALOG ( D I A / D I A I 1 / ( 2 * 0 * 3 . 14159*BSO*WCOND) CTIF = TfI(I)-TFO(I) CTIC = TCO(II-TCI(1) IF( I ABS ( CT I F-T I F 1 L E ( 3 0 1 1 AND. ( A B S ( C T I C - T I C 1 LE. ( 3 0 0 1 1 GO T 0 1 8 T I F = CTIF T I C = CTIC K E Y 5=K EY 5+ 1 IF(KEY5.GT.50)GO TO 3 7 GO TO 11 THEATO = THEATO + H E A T ( 1 ) TPDTO = TPDTO + P D T O ( 1 I TPDSO = TPDSO + PDSO(1) I F ( I EQ 2 1 TPDSO=TPD SO+PDSO ( 11 CDTF=(((HEAT(I)) /NTO)/BSO) / ( 3 . 1 4 1 5 9 * D I A * A H S C ( I J ) /HTO(I 1 FDTF=CDTF*AHSO(I 1 FWT ( 11 =ATF-FDTF*HSFCT =ATC+CDTF*HSFCT CWT( I ) AVWT 4 I 1 = O . 5* ( F WT ( I) + C h T ( II 1 TSUM=TSUM+AVWT( I) S SUM=SSUM+ATC IF ( K F I N A L . EQ 1.AND I EQ I T I GO TO 2 0 I F ( ( ( A B S ( E T F - T F I ( 1 ) ) ) . L E * ( ( A B S ( T F I ( I ) - T F O ( I ) I ) / 2 * 0 ) 1. OR. 1 (TFI(I).LE.ETF)I GO T O 15 I=I+l IF(I.GT.75) GO TO 3 0 I F ( I.EQ.21 ATClZATC TFO(1) = TFI(1-11 T C I ( 1 ) = TCO(1-11 BSO=BSOI E Q V B SO = B SO K EY4=KEY 4+ 1 IF(KEY4,GT.SO)GO TO 3 6 GO TO 10 KFINAL=l IT=I FIT = IT

MSB MSB MSB MSB MSB MS B MSB MSB MSB MSB MSB MSB

2900 2910 2920 2930 2940 2950 2960 2970 2980 2990

3000 3010

M S B 3020 MSB 3030 MSB 3040 MSB 3090 MSB 3100 m

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

3130 3140 3150 3050 3060 3061 3070 3080 3160 3170 3180 3190 3200 321@ 3220 3230

3240 3250 3260

DCURVE=CURVES*((HEATL-THEATO)/HEAT(l)l 2cI

22 23

24 C

CURVES=CURVES+DCURVE GO TO 9 T U B L E N = ( F I T - 1 . )*BSOI+CURVES +DCURVE+Oo25*BSMAX HEXLEN=( F I T - 1 . ) * B S 0 1 + 4 . * E X P R A D * S I N ( A R C R ) S T R L E N = ( F I T - 1. )*BSOI+DCURVE+. 2 5 * B S M A X IF( KTBST.EQ.0) GO TC 2 4 Tl=FWT( 1 ) TZ=CWT( 1) PDTOl=PDTO( 1 1 PDSOl=PDSO(l) TSUM=TSUM-AVWT ( 1 ) S SUM =S S U M- A T C 1 T A V T = ( CURVES*AVWT( 1) + B S O I * T S U M ) / T U B L E N S A V T = ( ( H EXLEN-BSO I * ( F 11-1 1 1 *ATC 1+B SOI*SSUly) / H E X L E N C A L L T U B S T R ( T P I N . SPOUT, P D T O 1 r P D S O L , T P D S O v T l r T 2 r 1 H E X L E N r E X P R A D v D I A I r D I A ,ARC, E T F r F T O r ETC r C T O r S A V T r T A V T 9 2 T 1 1r T 1 2 r T 1 3 r T 2 4 r T 2 5 r T 3 6 9 T 3 7 . 1 3 8 r T 4 9 r T 4 1 Q rOTr BF rASM9 3 S T r STP 9 S Q P , SLPR 9 S L P G r S L L O r S L L I 7 STTO r S T T I r T M r CASMrCTM 4 P 1 r P 2 r SA. R 1 r R 2 , T L .RBI A A l r A A 2 r AA3 r A A 4 r A A 5 r B E l 9 882 r 5 883rBB4rBB5~ K E Y 3=K EY 3+ 1 IF(KEY3.GT.50)GO T O 35 I F ( T 2 4 . L T . O . O ~ O R . T l 2 ~ L T o O o O ) GO TO 2 2 I F ( T 2 4 . G T . ( . 0 8 ~ A S M ) . A N D ~ T l 2 . G T . ( . @ 8 ~ A S M ~ ) GO T O 2 3 GO T O 2 4 XPRMIN=EXPRAD GO TO 8 XPRMAX=EXPRAD GO TO 8 VOL = 0 . 7 8 5 4 * ( D I A I * * 2 . O ) * N T O * T U B L E N CHECK OF T U B E AND S H E L L PRESSURE DROPS KEY2 = KEY2 + 1 IF(PERCZ.LE.O.1) GO TO 3 3 IF(TPDTO.LTo(PERCZ*PRDT)) GO TO 2 5 IF(TPDTO.GT.PRDT1 GO TO 2 6 GO TO 27

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

MS0 MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

3270 3280 3290 3300 3310 3320 3330 3340 3350 3360 3370 3380 3390 3400 3410 3420 3421 3422 3423 3424 3425 3430 344@ 3450 3460 3470 3480 3490 3500 3510 3520 3250 3540 3550 3560 3570 3580

cn cn

IF(RA8*LE.(RA5 + 0 . 0 0 5 ) ) GO TO 3 4 R A 8 H =RA8 TO 3 IF(KEY2.NE.30)GO RA8LzRA8L-C. 2 P E R C 2 = PERC2 @.Cl KEY2=10 GO TO 3 IF(RA8.GE.(RA8MAX-C~005J) GO TO 34 R A 8 L =RAE? I F ( K E Y 2 e N E . 3 0 ) GO TO 3 RA8H=RA8H+Oo2 0.01 PERC2 = PERC2 KEY2=10 GO TO 3 KEY1 = KEY1 + 1 IF(PERCl.LEoO.1J GO TO 3 2 IF(TPOSO.CTo(PERCl*PRDS)l GO TO 2 8 TO 2 9 IF(TPDSO.GT.PRDS)GO GO TO 3 8 I F ( BSO I LE. ( B S M I N + 0 . 0 0 5 1 )GO TO 3 1 BSH = B S O I I F ( K E Y L * N E * 3 0 1 G O TO 2 BSL=BSL-Oo 1 PERCl = PERCl 0.01 K EY 1=10 GO TO 2 I F ( B SO I G E ( B S MA X- 0 00 5 1 1 GO TO 3 1 BSL = B S O I I F ( K E Y l o N E o 3 0 ) GO TO 2 BSH=BSH+O. 1 PERCl = PERCl 0.01 KEY1=10 GO TO 2

PRINT EXIT SIGNALS 30 PRINT 1051tBSO 1057 F O R M A T ( 3 9 H l B A F F L E S P A C I N G S EXCEEDE 7 5 W I T H B S C = t F 5 0 2 r Z X t 4 H ( F T ) ) GO TO 3 8

M S B 3590 M S B 3600

MSB 3610 M S B 3620 M S B 3630 M S B 3640 M S B 3650 M S 0 3660 MSB 3670 M S B 3680 M S B 3690 M S B 3700 M S B 3710 M S B 3720 M S B 3730 MSB 3760 M S B 3770 M S B 3780 M S B 3790 MSB 3800 MSB 3810 M S B 3820 MSB 3830 M S B 3840 MSB 3850 MSB 3860 MSB 3870 M S B 3880 M S B 3890 MSB 3 9 C O M S B 3910 M S B 3920 MSB 3930 M S B 3640 M S B 3650 MSB 3960 MSB 3970 MSB 3980

31 PRINT 1052 1 0 5 8 F O R M A T ( 2 C H l B S O I = MAX. GO TO 3 8 32 P R I N T 1059

OR M1N.I

1C59 F O R M A T ( 4 8 H l P E R C 1 FOR S H E L L PRESSURE DROP IS L E S S T H E & 0.1) 33

1C.60 34 106 1

35 106 2 36

1@ 6 3 37 1064 C C 38

GO T O 3 8 P R I N T 1060 F O R M A T ( 4 8 H l P E R C 2 FOR TUBE PRESSURE DRGP IS L E S S T H E N 0.11 GO TO 3 8 P R I N T 1061 F O R M A T ( 2 9 H l S H E L L R A D I U S = MAX, CR M I N . 1 GO TO 38 P R I N T 1062, K E Y 3 FORMAT( 6 H l K E Y 3 = 9 I 5 1 GO TO 3 8 P R I N T 1063, K E Y 4 FORMAT(6HlKEY4z ,151 GO TO 3 8 PRINT 1064, KEY5 FORMAT( 6 H l K E Y 5 = 9 I 5 1 GO TO 3 8 END OF CASE, P R I N T OUTPUT DO 39 I = l r I T = VMl(I)*GFTT Vl(1I V2( 1 ) = V M 2 ( I I*GFTT = V M 3 ( I 1*GFTT V3( I J VW1( I 1 = V W O l ( I 1 * G F T T VW3( 1 ) = VW03( I I * G F T T CONTINUE T T D S O = TPDSO*GFT T T D T O = TPDTO*GFT T P P ERC=TPDTO*lOO./PRDT SPPERC=TPDSO*lOO./PRDS H T P ERC= 100 TH EA TO /HE A T L AR E A = 3 1 4 15 9 * D I A * SNT* TUBL EN

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

3990 4000 4010 4020 4030 4040 4050 4C60 4070 4C80 4090 4100 4110 4120 4130 4140 4150 4160 4170 4180 4190 381@ 3820 4220 4230 4240 4250 4260 4270 4280 4290 4300 4310 4320 4330 4340

m co

ASM3=3. *ASM P STO=AA 1 PQSTO=AA2 PQFSTO=AA3 PSTI=BBl PQSTI=BB4 PQFSTI=BB5

P R I N T 1033,TPEATO,HTPERC P R I N T 10349 QC P R I N T 1 0 3 5 9 QF P R I N T 1@36,TTDSO,SPPERC P R I N T 1037, TTDTO, TPPERC PRINT 1038rRA8 PRINT 1039rBSOI PRINT 1040rVCL P R I N T 1041, AREA PRINT 1042rSNT P R I N T 10 43 9 T U B L EN P R I N T 1044, HEXLEN P R I N T 1045, S T R L E N PRINT 1046vEXPRAD P R I N T 1 0 4 7 ~ GBRL P R I N T 1 0 5 1 VTAVT P R I N T 1 @ 5 2 9SAVT P R I N T 10 5 3 9 P STO, P S T I I A S M PRINT 1054tPQSTOqPQSTIrASM3 P R I N T 1055,PQFSTO,PQFSTI,SA P R I N T 1 0 4 8 , ( I , ( T C I ( I J , T C O ( I J rCWT(1 I T T F I (I J ,TFC(IJ rFhT( I ) v 1 TWDT(I1 I r I = l * I T ) P R I N T 1 0 4 9 9 ( I , ( V l ( I ) , V 2 ( 1 ) r V 3 ( I J t V W l ( 1 1 r V W 3 ( I J ,PCSO(I ),PDTO( I ) J , 1 I=l,ITI P R I N T 1@5Q,(Ir(RENTO(I)rPRNTO(I)tRENSOl(I JrREhSC2(I)rPENS03(IJ, 1HTO( I 1 ,AHSO( I J , U O A ( I 1 * H E A T ( 1 ) 1 t I = l v I T ) C C

LOOP FOR A D D I T I O N A L CASES I F R E Q U I R E D CONTINUE

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

4350 4360 4370 4380 4390 4400 4410 1640 4430 4440 4450 4460 4470 4480 4490 45C0 4510 4520 4530 4540 4550 4560 4570 4580 4590 4600 4610 4620 4630 4631 4640 4641 4650 4651 4240 4250 468C

K E Y 7 = K E Y 7+ 1 I F ( K E Y 7 o G T m K A S E S ) G O TO 4 1 GO TO 1 CONTINUE END

cc cc

4690 4700 4710 4720 4730

SUBROUTINE T U B S T R ( T P I N v S P O U T ~ P D T C l ~ P D S O l ~ T P D S O v T l v T 2 v TUBST 10 1 HEXLENv E X P R A D v D I A I t D I A ,ARC, E T F v F T O t ETC v C T O v S A V T v T A V T v TUBST 11 2 T l l , T 1 2 ~ T 1 3 v T 2 4 v T 2 5 v T 3 6 v T 3 7 v T 3 8 v T 4 9 v T 4 l O v D T v e)YvASMv TUBST 12 3 ST~STP~SQP~SLPR~SLPGvSLLO~SLLI~STTO~STTIvTMvCAS~vCTMv TUBST 13 4 P l v P 2 v S A v R 1 9 R 2 , T L ,RB v A A l v A A 2 vAA3 v A A 4 v A A 5 v B B l r B B 2 v TUBST 14 5 BB3rBB4,BB5) TUBST 15 DIMENSION CASM(6 rCTM( 6 1 TUBST 20 G F T = 1 144 TUBST 30 P 1 = ( TPIN-. 5*PDTO1 l*GFT TUBST 40 P 2= ( SPOUT +a 5*PDSO1 )*GFT T U B S T 50 R 1=6 * D I A I TUBST 60 R2=6 D IA TUBST 70 TL =12.*HEXLEN TUBST 80 RB=lZ.*EXPRAD TUBST 90 A=!Io017452*ARC TUBS 100 D E T E R M I N E AVERAGE CHANGE I N TEMPERATURE OF S H E L L ( D T S 1 AND T U B E ( D T T 1 110 DTS = SAVT-700 T U B S 120 DTT TAVT-70. TUBS 130 C A L C U L A T E PRESSURE AND TEMPERATURE D I F F E R E N T I A L ACROSS T U B E MALL. TUBS 140 DP = P l - P 2 TUBS 150 DT = Tl-TZ T U B S 160 AND AVERAGE TEMPERATURE OF T b B E kALL TUBS 170 TM = (Tl+T2)/2. TUBS 1 8 0

MSB MSB MSB MSB MSB

cc cc cc

cc cc

C A L C U L A T E MOMENT OF I N E R T I A OF TUBE C R O S S E C T I C h ( A H 1 ) AMI = Oo7853S8*(R2**4-R1**4) C A L L S U B R O U T I N E TO DETERMINE A L L C k A B L E S T R E S S ( A S V ) TIERR) C A L L LAGR (CASMT CTMqASM t T M t 2 T 6 E S T A B L I S H MATERIAL PROPERTIES COhSTANTS SA= 25000.r) EM = 25COOOOO.O PR = 003 T E = OoCOOOO78 SE = CoOCOOO76 C A L C U L A T E A X I A L LOAD AND MOMENT DUE TO L G N G I T U C h A L E X P A N S I O N DY = T L * ( T E * D T T - S E W T S I RM = ( R 2 + R 1 ) / 2 o TW = R 2 - R 1 = TW*RB/RM**2 AL A L 2 = AL**2 AK = (l.+12o*AL2)/(10o+lZo*ALZ) AA = 2o*A P = 2 5 @ 0 0 O O O *AK*AM I * D Y / ( RB **3* 4 AA*C 0 S ( AA ) -3 *S I h ( A A 1 +4. * A 1 I BM = P*RB*(lo-COS(A)I C A L C U L A T E Q ZTRESS DUE TO P SQP = -P/( 6 . 2 8 3 1 8 * R M * T k I C A L C U L A T E Q STRESS DUE TO M B l = 6o/(5.+6.*AL21 62 = BM/(AK*AMI) 63 = (R2/RM)**2 64 = (Rl/RM)**2 85 = 1.5*RM*BZ*AL*Bl SLLO = R2*B2*( l.-Bl*B3) SLLI Rl*B2*( 1o-B1*B4) STTO = 6 5 * ( 1 o - Z o * B 3 1 S T T I = B5*(1.-2.*84) C A L C U L A T E F STRESS DUE TO TUBE WALL TEMPERATURE CROP ST = 13So*DT S L I = -ST S T I = -ST SLO = S T STO = S T

TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS

190

200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560

C A L C U L A T E STRESSES DUE TO PRESSURE HOOP S T P = DP*RM/TW LONG I T U D N A L SLPR = STP/2. SLPG = 0 RADIAL SRPI = -P1 SRPO = - P 2 P STRESS T U B E OD BEND OD A l l = A M A X l ( STP 9 SLPRI SRPC) A 1 2 = A M I N l ( STP 9 SLPRI SRPC) AA1 = All-A12 T 1 1 = ASM- A B S ( A A 1 J P+Q STRESS T U B E OD BEND OD A 1 3 = A M A X l ( S T P + S T T O 9 SLPR+SQP+SLLC VSRPOJ A 14 =AM I N 1 ( STP+STTO 9 SLPR+ IQP+SLLC! 9 SR P O ) AA2 = A l 3 - A l 4 T 1 2 = 3*ASM- A B S ( A A 2 ) P + Q + F STRESS T U B E OD BEND OD A 1 5 =AMAX1 ( STP +STTO+STO 9 SLPR+ SQP+ S L L O+ SLO 9 SRPC I A 1 6 = A M I N 1 ( STP+STTO+STO 9 SLPR+ SQP+SLLO+SLO (SRPC) AA3 = A15-A16 T 1 3 = SA ABS(AA3) P STRESS T U B E OD B E N D I D T11) SAME AS P STRESS A T TUBE CD BEND OD

cc cc

cc cc cc cc

P+Q STRESS T U B E OD BEND I D A 2 2 = A M A X l ( STP+STTO, S L P R + S Q P - S L L C r S R P O I A 2 3 = A M I N l ( S T P + S T T O * SLPR+SQP-SLLOvSRPO) AA4 = A22-A23 T 2 4 = 3*ASM- A B S ( A A 4 J P+Q+F STRESS T U B E OD BEND I D A 2 4 =AMAX1 ( S T P + S T T O + S T O , S L P R + S Q P - S L L O + S L O 1 S R P O ) A 2 5 =AM I N 1 ( STP +STTO+STO 9 SLPR+ SQP-SL LO+ SLO 9 S R P C ) AA5 = A24-A25 ABS(AA5) T 2 5 = SA

I .

TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS TUBS

570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890

900 910 920

930

4 h)

cc cc cc cc

cc cc

P STRESS T U B E I D BEND OD 811 =AMAXl(STPTSLPR*SRPIj 812 = A M I N ~ ( S T P T S L P R * S R P I I B B l = B11-61 T 3 6 = ASM- A B S ( B B 1 ) P+Q STRESS T U B E I D BEND OD B 13 =AMAX1 ( SJP+STT I * SLPR+ SQP+SLL IT S R P I 1 814 = A M I N l ( S T P + S T T I * S L P R + S Q P + S L L I I S R P I ) B B 2 = 813-814 T 3 7 = 3*ASM- A B S ( B B 2 ) P+Q+F STRESS T U B E I D BEND OD 8 1 5 S A M A X l L S T P + S T T I + S T I r S L P R + S Q P + S L L I + S L I T S R P I1 B 1 6 = A M I N l ( S T P + S T T I + S T I p S L P R + S Q P + S L L I + S L I T S R P I1 883 = B l 5 - 8 1 6 ABS(BB3) T 3 8 = SA P STRESS T U B E I D BEND I D S A M E A S P STRESS AT TUBE ID BEND OD T36

P+Q STRESS T U B E I D BEND I D 823 =AMAXl( STP+STTI*SLPR+SQP-SLLI r S R P I j 824 = A M I N l ( S T P + S T T I T S L P R + S Q P - S L C I T S R P I I 884 = 823-824 T49 3*ASMABS(BB41 P+Q+F STRESS T U B E I D BEND I D 825 = A M A X l ( Z T P + S T T I + S T I T S L P R + S Q P - S L L I + S L I r S R P I 1 SLPR+SQP-SCLI+ S L I T S R P I 1 826 =AM I N l ( STP+STT I + S T IT 885 = 8 2 5 - 8 2 6 T410 = SA ABS(BB5l

RETURN END

T U B S 940 TUBS 950 TUBS 960 T U B S 970 TUBS 980 T U B S 990 T U B 1000 T U B 1010 T U B 1020 T U B 1030 T U B 1040 T U B 1050 T U B 1060 T U B 1070 T U B 1080 T U B 1090 T U B 1100 T U B 1110 T U B 1120 T U B 1130 T U B 1140 T U B 1150 T U B 1160 T U B 1170 T U B 1180 T U B 1190 T U B 1200 T U B 1210 T U B 1220 T U B 1230 T U B 1240 T U B 1250 T U B 1260

SUBROUT I N E LAGR ( F X TX 9 F X P r X P T N TN P T t IE R I DIMENSION FX(NP7 1, X(NPT) S U B R O U T I N E U S E S L A G R A N G I A N I N T E R P O L A T I C N T C A D E S I R E D DEGREE P O L I N O M I AL FX = F U N C T I O N OF I N D E P E N D E N T V A R I A B L E X = INDEPENTENT VARIABLE F X P = E S T I M A T E OF F X A T XP = V A L U E OF X F O R WHICH I N T E R P O L A T I C N I S D E S I R E D XP N = DEGREE OF P O L I N O M I A L USED I N I N T E R P C L A T I C h NPT = NUMBER O F P O I N T - P A I R S I N T A B L E I E R = COUNTER TO REPORT T Y P E OF E X E C U T I C N

C C C C C C

C C C C

C 3 4

5 6

C 8

CHECK T O SEE I F XP I S A T A B L E ENTRY DO 2 K = l 9 N P T I F ( XPeEQ o x ( K ) 1 1 9 2 FXP = F X ( K ) IER = 3 RETURN CONTINUE DETERMINE I F E X T R A P O L A T i C h I S REQUIRED I F ( X P o L T .X( 1) 14.3 I F ( X P o G T e X ( N P T 1I 59 6 L1 = 1 L 2 = NPT GO TO 1 5 L 1 = NPT N L 2 = NPT GO TO 15 IER = 2 D E T E R M I N E I F S U F F I C I N T DATA I S PRESENT FOR DEGREE OF P O L I N O M I A L M = N + l IF ( M GT e NPT ) 7 9 E IER = 1 RETURN DETERMINE NEXT HIGHEST P O I N T DO 9 K = 2 9 N P T K 1 = K IF( XP L T 0x4K ) I 1099

LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR

10 20 30

40 50 60

70 80

90 1OC 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 3CO 310 320 330 340 350 360 370 380

9 c 10 11

CONTINUE DETERMINE THE L = M/2 L2 = Kl + L IF(LZ.LE.NPT~13,12

LOWER

POINTS

REQUIRED

Ll = Kl + L - M IF(LlJ14,14,15 Kl = Kl + 1 L2 = L2 + 1 GO TO 13 INTERPOLATION BY LAGRANGIAN METHCD AND MODERN ENG INEER ING , SOKOLNIKOFF FXP = 0.0 DO 18 K = LlrL2 PKX = 1.0 PKXK = 1.0 DO 17 I = LlrL2

14 C C

=Kl-1 GO TO 11

IF(I.EQ.K)17,16 16 17 18

PKX = PKX*(XP - X( I )1 PKXK = PKXK*LX(K) - X(I)) CONTINUE FXP = FXP + FX(K)*PKX/PKXK RETURN END

LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR LAGR

390

400 410 420 430 440 450 460 470 480 490 500 (SEE MATHEMATICS OF PHYSICS 510 AND REDHEFFER rPAGES 699,700)LAGR 520 LAGR 530 LAGR 540 LAGR 550 LAGR 560 LAGR 570 L AGR 580 LAGR 590 LAGR 600 LAGR 610 LAGR 620 LAGR 630 LAGR 640

76 Intermediate Variables

LAW01

N e t c r o s s - f l o w circumference a t i n n e r edge o f b a f f l e , f t .

LAW03

Net c r o s s - f l o w circumference a t o u t e r edge o f b a f f l e , f t .

NT ( 1 )

Number o f t u b e s i n r i n g I.

BJ(I)

J f a c t o r f o r t h e h e a t t r a n s f e r c o e f f i c i e n t a t t h e i n n e r window zone (I = l ) , c r o s s - f l o w zone (I = 2 ) , and o u t e r window zone ( I = 3).

HSOl ( I )

S h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t f o r i n n e r window zone i n increment I , Btu/hr.ft'. O F .

HS02 ( I )

S h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t f o r c r o s s - f l o w zone i n increment I .

HS03 (I)

S h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t f o r o u t e r window zone i n increment I . Accumulated tube l e n g t h up t o increment I , f t .

TUBLN(1)

Average v e l o c i t y o f f l u i d i n outer window zone i n increment I , f tlsec. Average v e l o c i t y of f l u i d i n o v e r l a p p i n g b a f f l e zone i n i n c r e ment I . Average v e l o c i t y of f l u i d i n i n n e r window zone i n increment I . F l u i d v e l o c i t y a c r o s s t u b e s i n o u t e r edge of b a f f l e i n i n c r e ment I , f t / s e c . F l u i d v e l o c i t y a c r o s s t u b e s i n i n n e r edge of b a f f l e i n i n c r e ment I . I n s i d e c r o s s - s e c t i o n a l a r e a of t u b e , f t 2 . F l a g f o r number o f i t e r a t i o n s on b a f f l e s p a c i n g . F r a c t i o n o f i n p u t s h e l l - s i d e p r e s s u r e drop c o n s i d e r e d a c c e p t a b l e . F l a g f o r number o f i t e r a t i o n s on o u t e r r a d i u s . F r a c t i o n of i n p u t t u b e - s i d e p r e s s u r e drop c o n s i d e r e d a c c e p t a b l e . C u r r e n t lower l i m i t f o r o u t e r r a d i u s . Current higher l i m i t f o r o u t e r radius. Temporary number of tube r i n g s . I n t e g e r form of RJ8. Real form o f 158. Radius of tube r i n g I , f t . Circumference of tube r i n g I , f t . Temporary c i r c u m f e r e n t i a l p i t c h i n tube r i n g I , f t .

77 TOTAL(1)

Accumulated number of t u b e s up t o tube r i n g I .

AVWT(1)

Average temperature o f tube w a l l i n increment I , OF.

KEY7

F l a g f o r number of c a s e s performed.

HEFI

Tube-side enhancement f a c t o r .

HEFO

S h e l l - s i d e enhancement f a c t o r .

HS FCT

Flag:

ARCR

Arc o f b e n t tube f o r thermal e x p a n s i o n , r a d i a n s .

ATUBE

O u t s i d e c r o s s - s e c t i o n a l a r e a of t u b e , f t 2 .

GFTT

1/3600

GFT

1/144

DIAI

I n s i d e d i a m e t e r of t u b e , f t .

A c t u a l number of t u b e r i n g s .

TRPI

Actual r a d i a l p i t c h , f t .

CPI

Actual circumferential p i t c h , f t .

NTO

I n t e g e r form o f TOTAL(1).

RA5 2

Square o f R A ~ ,f t 2 .

RA8 2

Square o f

RA6

Radius o f i n n e r b a f f l e e d g e , f t .

Number of tube r i n g s up t o RA6.

RA7

Radius o f o u t e r b a f f l e e d g e , f t .

Number o f tube r i n g s up t o RA7.

RA6 2

Square o f RA6, f t 2 .

RG7 2

Square of R A ~ , f t 2 .

â&#x201A;Ź31

Number of tube r i n g s i n i n n e r window zone.

RB2

Number o f tube r i n g s i n c r o s s - f l o w zone.

RB3

Number of tube r i n g s i n o u t e r window zone.

SUM1

Number o f t u b e s i n i n n e r window zone.

SUM2

Number o f t u b e s i n c r o s s - f l o w zone.

SUM3

Number of t u b e s i n o u t e r window zone.

Ism1 Ism2

I n t e g e r form o f SUM1. I n t e g e r form of SUM2.

ISUM3

I n t e g e r form o f SUM3.

BSMAX

Higher l i m i t f o r b a f f l e s p a c i n g , f t .

BSMIN

Lower l i m i t f o r b a f f l e s p a c i n g , f t .

1 = tube s i d e h o t t e r than s h e l l s i d e , -1 = tube s i d e c o l d e r than s h e l l s i d e .

. .

Ma,

ft2.

78 APO 1

N e t p a r a l l e l flow i n i n n e r window zone, f t 2 .

AP03

N e t p a r a l l e l flow i n o u t e r window zone, f t 2 .

Heat t r a n s f e r c o e f f i c i e n t a c r o s s tube w a l l , Btu/hr*ft'.OF.

CSPHAV

Average s p e c i f i c h e a t i n s h e l l s i d e , B t u / l b * " F .

FSPHAV

Average s p e c i f i c h e a t i n tube s i d e .

GTO

Mass flow r a t e i n t u b e s , l b / h r - f t 2 .

KEY3

Flag f o r number of i t e r a t i o n s on tube expansion r a d i u s .

XPRMAX

Higher l i m i t on tube expansion r a d i u s , f t .

XPRMIN

Lower l i m i t on tube expansion r a d i u s , f t .

BSH

Current h i g h e r l i m i t f o r b a f f l e s p a c i n g , f t .

BSL

Current lower l i m i t f o r b a f f l e s p a c i n g , f t .

CURVES

An approximate l e n g t h of t h e curved s e c t i o n of t h e t u b e s , f t .

Number of b a f f l e s p a c i n g s .

KFINAL

A f l a g t o i n d i c a t e t h a t t h e h e a t l o a d requirement h a s been m e t .

TSUM

Accumulated average temperature of tube w a l l .

SSUM

Accumulated average temperature of s h e l l f l u i d .

TPDTO

Accumulated t u b e - s i d e p r e s s u r e drop.

TPDS 0

Accumulated s h e l l - s i d e p r e s s u r e drop.

TIF

Assumed temperature d i f f e r e n c e i n t u b e - s i d e f l u i d between two increments, OF.

TIC

Assumed temperature d i f f e r e n c e i n s h e l l - s i d e f l u i d between two increments, OF.

CDTF

Tube-side bulk t o w a l l temperature d i f f e r e n c e , O F .

FDTF

S h e l l - s i d e b u l k t o w a l l temperature d i f f e r e n c e , OF.

BSO

Current b a f f l e s p a c i n g , f t .

GB RL

Correction f a c t o r f o r Bergelin's h e a t t r a n s f e r c o e f f i c i e n t .

AWO 1

Net c r o s s - f l o w a r e a a t i n n e r edge o f b a f f l e , f t 2 .

AW03

Net c r o s s - f l o w a r e a a t o u t e r edge of b a f f l e , f t 2 .

Awl

E f f e c t i v e flow a r e a i n i n n e r window zone, f t 2 .

AW2

E f f e c t i v e flow a r e a i n c r o s s - f l o w zone, f t 2 .

AW3

E f f e c t i v e flow a r e a i n o u t e r window zone, f t 2 .

GSOl

Mass flow r a t e i n i n n e r window zone, l b / h r . f t 2 .

GS02

Mass flow r a t e i n c r o s s - f l o w zone, l b / h r . f t 2 .

GS 03

Mass flow r a t e i n o u t e r window zone, l b / h r . f t2.

EQVBSO

Length of h e a t exchanger i n the curved tube r e g i o n considered a s f i r s t b a f f l e spacing.

KEY4

Inactive.

KEY5

F l a g f o r number of i t e r a t i o n s on average temperature i n e a c h b a f f l e spacing.

ATC

S h e l l - s i d e average temperature i n e a c h b a f f l e s p a c i n g , OF.

CFT

Average tube w a l l temperature on s h e l l s i d e i n e a c h b a f f l e s p a c i n g , OF.

ATF

Tube-side average temperature i n each b a f f l e s p a c i n g , OF.

FFT

Average tube w a l l t e m p e r a t u r e on tube s i d e i n e a c h b a f f l e s p a c i n g , OF.

Number of b a f f l e s p a c e s .

CVIS

Shell-side f l u i d viscosity, lb/ft.sec.

CVISW

CVIS e v a l u a t e d a t w a l l temperature.

CDEN

Shell-side f l u i d density, lb/ft3.

CCON

S h e l l - s i d e f l u i d c o n d u c t i v i t y , B t u / h r . f t . OF.

CS PH

S h e l l - s i d e f l u i d s p e c i f i c h e a t , B t u / l b * OF.

FVIS

Viscosity of tube-side f l u i d , l b / f t . s e c .

FVISW

FVIS e v a l u a t e d a t w a l l t e m p e r a t u r e .

FDEN

Density of t u b e - s i d e f l u i d , l b / f t 3 .

FCON

C o n d u c t i v i t y of t u b e - s i d e f l u i d , Btu/hr.ft.OF.

FS PH

S p e c i f i c h e a t o f t u b e - s i d e f l u i d , B t u / l b - OF.

VISK

(CVIS /CVISW) *?kO. 14

FVISK

(FVIS/FVISW)**0.14

DCVIS

DIA/CVIS

CCDEN

~/CDEN

QCCDEN

QC*CCDEN

DP 1

V e l o c i t y head i n i n n e r window zone.

DP2

V e l o c i t y head i n c r o s s - f l o w zone.

DP3

V e l o c i t y head i n o u t e r window zone.

APO

Net f l o w a r e a p a r a l l e l t o t u b e s i n curved-tube r e g i o n , f t 2 .

EQVDTA

E q u i v a l e n t d i a m e t e r t o be u s e d i n Donohue's c o r r e l a t i o n , f t .

GS 0

Mass flow r a t e p a r a l l e l t o t u b e s i n curved-tube r e g i o n , l b / h r * f t 2 .

RENSO

Reynolds number f o r s h e l l - s i d e o f curved-tube r e g i o n .

PRES0

P r a n d t l number f o r s h e l l - s i d e of curved-tube r e g i o n .

CTIF

C a l c u l a t e d t e m p e r a t u r e d i f f e r e n c e i n t u b e - s i d e f l u i d between two i n c r e m e n t s , OF.

CTIC

C a l c u l a t e d temperature d i f f e r e n c e i n s h e l l - s i d e f l u i d between two i n c r e m e n t s , OF.

. .

ATC 1

Average t e m p e r a t u r e i n s h e l l s i d e o f curved-tube r e g i o n , OF.

FIT

F i n a l number o f b a f f l e s p a c e s .

DCURVE

A d d i t i o n a l s t r a i g h t l e n g t h added t o t h e curved-tube s e c t i o n , f t .

PDTO 1

Tube-side p r e s s u r e drop i n cunred-tube r e g i o n , l b / f t 2 .

PDSO 1

S h e l l - s i d e p r e s s u r e drop i n curved-tube r e g i o n , l b / f t 2 .

Tube-side s u r f a c e temperature of tube w a l l ,

S h e l l - s i d e s u r f a c e temperature of tube w a l l , OF.

T11

Maximum primary (P) s t r e s s t e s t on o u t s i d e s u r f a c e o f tube a t bend OD, p s i .

T12

Maximum primary and secondary (P s u r f a c e of tube a t bend OD, p s i .

T13

Maximum peak (P + Q a t bend OD, p s i .

T 24

Maximum surface Maximum a t bend

T25

+ Q)

OF.

s t r e s s t e s t on o u t s i d e

+ F) s t r e s s t e s t on o u t s i d e s u r f a c e o f t u b e

primary and secondary (P + Q) s t r e s s t e s t on o u t s i d e o f tube a t bend I D , p s i . peak ( P + Q + F) s t r e s s t e s t on o u t s i d e s u r f a c e o f tube ID, psi.

T36

Maximum primary ( P ) s t r e s s t e s t on i n s i d e s u r f a c e o f tube a t bend O D , p s i .

T37

Maximum primary and secondary (P s u r f a c e of tube a t bend OD, p s i .

T3 8

Maximum peak ( P + Q a t bend OD, p s i .

T49

Maximum primary and secondary ( P s u r f a c e o f tube a t bend I D , p s i .

T410

Maximum peak ( P f Q + F ) s t r e s s t e s t on i n s i d e s u r f a c e o f tube a t bend I D , p s i . Average temperature of tube w a l l a t p o i n t where stresses a r e determined, OF.

+ Q)

s t r e s s t e s t on i n s i d e

+ F) s t r e s s t e s t on i n s i d e s u r f a c e o f tube

+ Q)

s t r e s s t e s t on i n s i d e

Bending moment r e s u l t i n g from r e s t r a i n e d thermal e x p a n s i o n , i n . - l b .

ASM

Allowable s t r e s s i n t e n s i t y determined i n LAGR, p s i .

ASM3

Three t i m e s ASM, p s i .

Magnitude of thermal s t r e s s r e s u l t i n g from DT, p s i .

S TP

Hoop s t r e s s r e s u l t i n g from p r e s s u r e d i f f e r e n t i a l a c r o s s tube wall, psi.

SQ P

L o n g i t u d i n a l s t r e s s r e s u l t i n g from P, p s i .

S LPR

L o n g i t u d i n a l s t r e s s r e s u l t i n g from p r e s s u r e d i f f e r e n t i a l a c r o s s tube w a l l , p s i .

S LPG

L o n g i t u d i n a l s t r e s s r e s u l t i n g from p r e s s u r e d i f f e r e n t i a l a c r o s s lower tube s h e e t ( c u r r e n t l y set e q u a l t o z e r o ) , p s i .

81 v

sLLO

Magnitude of l o n g i t u d i n a l s t r e s s r e s u l t i n g from BM on o u t s i d e d i a m e t e r of tube , p s i .

sLLI

Magnitude of l o n g i t u d i n a l s t r e s s r e s u l t i n g from BM on i n s i d e d i a m e t e r of tube , p s i .

STTO

Magnitude of hoop s t r e s s r e s u l t i n g from BM on o u t s i d e d i a m e t e r of t u b e , p s i .

STTI

Magnitude of hoop stress r e s u l t i n g from BM on i n s i d e diameter of t u b e , p s i .

Temperature d i f f e r e n t i a l a c r o s s tube w a l l ,

Tube-side p r e s s u r e , p s i .

Shell-side pressure

Allowable s t r e s s i n t e n s i t y f o r c y c l i c a n a l y s i s , p s i .

I n s i d e r a d i u s of t u b e , i n .

Outside r a d i u s of t u b e , i n .

Length of tube ( d i f f e r e n c e i n e l e v a t i o n o f tube e n d s ; HEXLEN i n PRIMEX main program), i n .

Radius o f f l e x i b i l i t y bend segments, i n .

AA1

Maximum primary (P) stress i n t e n s i t y on o u t s i d e s u r f a c e of tube a t bend OD, p s i .

AA2

Maximum primary and secondary (P + Q ) s t r e s s i n t e n s i t y on o u t s i d e s u r f a c e of tube a t bend OD, p s i .

AA3

Maximum peak ( P + Q + F) s t r e s s i n t e n s i t y on o u t s i d e s u r f a c e of tube a t bend OD, p s i .

AA4

Maximum primary and secondary (P + Q ) s t r e s s i n t e n s i t y on o u t s i d e s u r f a c e of tube a t bend I D , p s i .

AA5

Maximum peak ( P + Q + F ) s t r e s s i n t e n s i t y on o u t s i d e s u r f a c e of tube a t bend I D , p s i .

BB 1

Maximum primary (P) stress i n t e n s i t y on i n s i d e s u r f a c e of tube a t bend OD, p s i .

BB 2

Maximum primary and secondary (P s u r f a c e of tube a t bend OD, p s i .

BB3

Maximum peak ( P + Q + F) s t r e s s i n t e n s i t y on i n s i d e s u r f a c e of tube a t bend OD, p s i .

BB4

Maximum primary and secondary (P s u r f a c e of tube a t bend I D , p s i .

BB5

Maximum peak (P + Q + F) s t r e s s i n t e n s i t y on i n s i d e s u r f a c e o f tube a t bend I D , p s i .

GFT

Conversion f a c t o r , f e e t t o i n c h e s .

Arc of f o u r bend segments i n f l e x i b i l i t y bend, r a d i a n s .

OF.

, psi.

+ Q)

s t r e s s i n t e n s i t y on i n s i d e

stress i n t e n s i t y on i n s i d e

DTS

Average change i n temperature of t h e s h e l l ,

DTT

Average change i n temperature of t h e t u b e s , OF.

P r e s s u r e d i f f e r e n t i a l a c r o s s tube w a l l , p s i .

AMI

Moment of i n e r t i a of tube c r o s s s e c t i o n , i n . 4

Modulus of e l a s t i c i t y f o r tube and s h e l l m a t e r i a l , p s i .

P o i s s o n ' s r a t i o f o r tube and s h e l l m a t e r i a l ( 0 . 3 ) .

C o e f f i c i e n t of thermal expansion f o r tube m a t e r i a l , in./in.OF.

C o e f f i c i e n t of thermal expansion f o r s h e l l m a t e r i a l .

D i f f e r e n c e i n thermal expansion of t u b e s and s h e l l , i n .

Mean r a d i u s o f tube w a l l , i n .

Thickness of tube w a l l , i n .

Dimensionless parameter i n Wahl's f a c t o r AK.

AL2

Square o f AL.

Wahl s r i g i d i t y mu1t i p l i c a t i o n f a c t o r .

Two times A .

Axial load r e s u l t i n g from r e s t r a i n e d thermal e x p a n s i o n , l b .

OF.

B 1 , B 2 , B 3 , B 4 , B 5 Repeated f a c t o r s used i n c a l c u l a t i n g s t r e s s e s r e s u l t i n g from BM.

sL I

L o n g i t u d i n a l s t r e s s on i n s i d e diameter of tube r e s u l t i n g from temperature d i f f e r e n t i a l a c r o s s tube w a l l , p s i .

ST I

Hoop s t r e s s on i n s i d e d i a m e t e r of tube r e s u l t i n g from temperat u r e d i f f e r e n t i a l a c r o s s tube w a l l , p s i .

sLO

L o n g i t u d i n a l s t r e s s on o u t s i d e d i a m e t e r of tube r e s u l t i n g from temperature d i f f e r e n t i a l a c r o s s tube w a l l , p s i .

S TO

Hoop s t r e s s on o u t s i d e diameter of tube r e s u l t i n g from temperat u r e d i f f e r e n t i a l a c r o s s tube w a l l , p s i .

SRPI

Radial s t r e s s on i n s i d e d i a m e t e r of tube r e s u l t i n g from pressure, p s i .

S RPO

R a d i a l s t r e s s on o u t s i d e diameter of tube r e s u l t i n g from p r e s sure, p s i .

A 11

Maximum v a l u e of primary (P) s t r e s s on o u t s i d e s u r f a c e of tube a t bend O D , p s i .

A12

Minimum v a l u e of primary ( P ) s t r e s s on o u t s i d e s u r f a c e of tube a t bend OD, p s i .

A13

Maximum v a l u e of primary and secondary (P s i d e s u r f a c e of tube a t bend OD, p s i .

+ Q)

A14

Minimum v a l u e of primary and secondary (P s i d e s u r f a c e of tube a t bend OD, p s i .

s t r e s s on o u t -

Q ) s t r e s s on o u t -

A 15

Maximum v a l u e of peak ( P tube a t bend OD, p s i .

+Q +

A16

Minimum v a l u e o f peak ( P tube a t bend OD, p s i .

+ Q + F)

A22

Maximum v a l u e of primary and secondary ( P s i d e s u r f a c e of tube a t bend I D , p s i .

+ Q)

s t r e s s on o u t -

A23

Minimum v a l u e of primary and secondary (P s i d e s u r f a c e of tube a t bend I D , p s i .

+ Q)

s t r e s s on o u t -

A24

Maximum v a l u e of peak (P tube a t bend I D , p s i .

A25

Minimum v a l u e of peak ( P tube a t bend I D , p s i .

+Q +

B11

Maximum v a l u e of primary (P) s t r e s s on i n s i d e s u r f a c e of tube a t bend OD, p s i .

B12

Minimum v a l u e of primary (P) stress on i n s i d e s u r f a c e of tube a t bend OD, p s i .

B 13

Maximum v a l u e of primary and secondary ( P s u r f a c e of tube a t bend OD, p s i .

+ Q) s t r e s s on i n s i d e

B 14

Minimum v a l u e of primary and secondary ( P s u r f a c e of tube a t bend OD, p s i .

+ Q) s t r e s s on i n s i d e

B15

Maximum v a l u e of peak ( P tube a t bend OD, p s i .

B16

Minimum v a l u e of peak ( P tube a t bend OD, p s i .

+ Q + F) s t r e s s on i n s i d e s u r f a c e of

B 23

Maximum v a l u e of primary and secondary ( P s u r f a c e of tube a t bend I D , p s i .

+ Q) s t r e s s on i n s i d e

B 24

Minimum v a l u e of primary and secondary (P s u r f a c e of tube a t bend I D , p s i .

+ Q)

B 25

Maximum v a l u e of peak (P tube a t bend I D , p s i .

+ Q + F) stress

B 26

Minimum v a l u e of peak ( P tube a t bend I D , p s i .

+Q +

F) stress on o u t s i d e s u r f a c e of

+ F)

s t r e s s on o u t s i d e s u r f a c e of

stress on o u t s i d e s u r f a c e o f

F ) s t r e s s on o u t s i d e s u r f a c e of

+ F ) s t r e s s on i n s i d e s u r f a c e of

s t r e s s on i n s i d e

on i n s i d e s u r f a c e of

F ) s t r e s s on i n s i d e s u r f a c e of

Computer I n p u t f o r Reference MSBR Primary Heat Exchanger

CT M

1 2 3 4 5

. 1ooo.oc

1100.00 1200.00

18OCO.O@ 18000 000 17C03.00 13oc0.00 6CC0.00

1300.00

3500.00

CASM

800 00 900 00

HEAT L O A D R E Q U I R E D =

1€!99795808.

ALLOWABLE T O T A L T U B E - S I D E ALLOWABLE T O T A L S H E L L - S I D E T U B E I N L E T PRESSURE = S H E L L OUTLET PRESSURE =

(BTL/HR)

PRESSURE DROP =

18720.

PRESSURE DROP =

25920

16727.

(LB/SC-FT)

H I G H TEMP.

OF S H E L L S I D E F L U I D =

1150.00

(F1

H I G H TEMP.

OF TUBE S I D E F L U I D =

130C.00

(Fj

OF T U B E S I D E F L U I D =

LOk TEMP.

OF S H E L L S I D E F L U I D =

HEAT TRANSFER L E A K A G E FACTOR = PRESSURE L E A K A G E FACTOR =

(LB/SO-FTI

(LB/SQ-FT 1

4896.

LOW TEMP.

(LB/SO-FT)

1050.CO

(FI

850.0C

tF1

0.8CCOO

0.52COO

C O N D U C T I V I T Y O F T U B E WALL M E T A L =

11.60000

(BTU/HR-FT-F)

ARC O F FOUR BENDS FOR F L E X I B I L I T Y =

I N S I D E R A D I U S OF OUTER ANNULUS =

60.00

(DEGREES) (FEET)

0.83330

D I S T A N C E BETWEEN S H E L L WALL AND T U B E S =

0.03125

MAXIMUM A N T I C I P A T E D OUTER R A D I U S OF EXCHANGER = NUMBER OF CASES RUN =

(FEET)

(ONE I F ENHANCED TUBES ARE USED)

USE OF STRESS A N A L Y S I S SUBROUTINE = O U T S I D E D I A M E T E R OF TUBES = WALL T H I C K N E S S OF TUBES =

0.06250

CIRCUMFERENTIAL P I T C H =

6.00000

USE OF ENHANCED TUBES =

RADIAL PITCH =

(FEET)

0.03125 0.00292

(ONE I F TO BE USED)

(FEET) (FEET)

(FEET) 0.06250

(FEET)

INNER BAFFLE CUT3

0.40000

( P E R CENT)

OUTER B A F F L E C U T 4

0.400CO

( P E R CENT)

Computer Output f o r Reference MSBR Primary Heat Exchanger

TOTAL HEAT TRANSFEREE = MASS FLOW R A T E

1899564800.

COOLANT =

MASS FLOW RATE O F FUEL =

SHEFL-SIDE TUBE-SIDE

17590736.

23454320.

UNIFORM BAFFLE SPACING =

(LB/HR)

129.61

67.38

TOTAL HEAT TRANSFER AREA B A S E D ON TUBE G.D.

HEAT EXCH,

APPROX.

21.31

S T R A I G H T S E C T I O N OF TUBE LENGTH = R A D I U S OF THERMAL

B E R G L I N M O D I F I C A T I O N FACTOR =

SHELL S I D E A V E R A G E TEMP.

13037.C2

(FEET) 18035

EXPANSION CURVES =

TUBE WALL A V E R A G E TEMP,

(FTI

LENGTH =

0.80 1113.04

99.7

FERCENT)

(CUBIC FEET)

58S6.

22.52

(

(FTI

TUBE F L U I D VOLUME C O N T A I N E D I N TUBES =

TOTAL T U e E LENGTH =

(LB/SBINI

PERCENT)

(FT)

0.9356

T O T A L NUMBER OF TUBES =

(ieo,o

(LBISQIN)

116.16

T O T A L PRESSURE DROP = 2.8364

(100.9 P E R C E N T )

(LB/HRJ

TOTAL PRESSURE DROP =

h O M I N A L SHELL R A D I U S =

(BTU/HR)

10~7.83

0.86

(FT) (FEET)

(SOFT)

P S T R E S S A T T U B E O D AND TUBE I D =

3912,53

SHOULD NCT E X C E E D

673.9C

11737.58

P+Q+F STRESS A T TUBE

SHOULD NGT E X C E E D 1

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21

11639.02

8317.50

(LB/SCINI

O D AND TUBE I D =

25000.00

(LB/SCIh)

P+Q S T R E S S AT TUBE O D AND TUBE I D =

SHOULD NCT E X C E E D

636.93

13C06.32

10551.26

(LB/SCIN)

TC I

T CO

CUT

TFI

TFO

FWT

901150E 0,1129E 0.1115E 0.1101E 0.1087E Oe1074E 0.1060E 0.1046E 0.1032E 0,1018E 0.1004E 0.9895E 0,9754E 0.9614E 0,9474E 0.9334E 0.9194E 0.9054E 0.8915E 0.8776E Co8638E

04 04 04 04 04 04 04 04 04 04 04 03 03 03 03 03 03 03 03 03 03

0.1129E 0.1115E Oe1101E Oo1087E 0.1074E 0.1Q60E 0,1046E 0.1032E 0.1C18E 0.1004E 9.9895E 0,9754E 0,9614E 0.9474E 0.9334E 9.9194E 009054E 0.8915E 0,8776E 0.8638E 0.850OE

Co1254E 0o1184E C4 001172E 04 Co1159E 0 4 0.1146E C4 C.1133E 0 4 0.1119E 0 4 0.1106E 0 4 Ce1093E 04 0.1080E @3 0.1067E 03 0.1054E 03 Co104CE 03 0,1027E 03 0.1014E 0 3 0.1001E Q3 Ce9874E 03 CIeS742E (33 Co4610E c13 0.9479E 03 Ce9348E

TWDT

vw1

vw3

FT/SEC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

0 00 6.1660 6.1475 6.1292 6.1109 6.0927 6.0745 6.0565 6.0384 6.0205 6.0027 5.9849 5.9673 5.9497 5.9323 5.9150 5.8979 5.8808 5.8639 5.8472 5.8306

0.0

7.0071 6.9861 6.9653 6.9445 6.9238 6.9032 6.8826 6.8621 6. a418 6.8215 6,8013 6.7812 6.7613 6.7415 6.72 19 6.7024 6. 6830 6. 6638 6.6448 6.6260

0.0 6.7107 6.6905 6.6706 6.6507 6.6309 6.6112 6.5915 6.5719 6.5523 6.5329 6.5136 6.4944 6.4753 6.4564 6.4375 6.4189 6.4003 6.3819 6.3637 6.3457

PDSO

PDTO

LB/SQFT

0.0 6.431 9 6.4126 6. 3935 6.3744 6.3554 6. 3365 6.3176 6.2’388 6.2 a01 6.2615 6.2430 6.2246 6.2063 6.1881 6. 1 7 0 1 6.1522 6.1344 6.1168 6.0994 6.082 1

O.@ 7.6953 7,6722 7.6493 7.6265 7.6038 7.5812 7.5586 7.5361 7.5137 7.4914 7.4693 7.4473 7.4254 7.4036 7.3821 7. 3606 7.3394 7.3183 7.2974 7.2768

8 5 1 3384

a 5 1 .3384

8 45 2434 8 39 1812 833.1099 8 27. 0310 8 20 9490 8 14.8638 808.7805 802.6997 796.6255 790.5603 784.5063 778.4670 772.4438 7 66 4417 7 60 4609 754.5051 748.5771 742.6804 736.8167

3430.7144 834.3669 826.6611 8 18 9949 8 11 3169 803.6326 795 9 4 2 4 788.2510 780.5627 772.8799 765.2080 757.5488 749.9067 742.2856 734.6880 727.1172 719. 5779 712.0718 704.6025 697.1743 689.7888

RENT0

RENSO2

RENSOl

PRNTO

RENSC3

HTO

AHSO

UOA

HEAT

BTU / HR/ SOFT/ F

1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21

0.1129E 0-1090E C01059E 0.1029E 009998E 0.9706E 0.9418E 0.9134E 0.8854E 0.8578E 0.8307E 0.8041E 0.7779E 007523E 007271E 0.7025E 0.67846 0.65486 0.6318E 0o6094E 005874E

05 05 05 05 @4 04 04 04 C4 04 04 04 04 04 04 04 04 04 04 04 04

0.8172E 008463E 0.8707E 0.8960E 0.9225E 0.9503E 0.9794E OelOlOE 0.1042E 0.1075E 0.lllOE 0.1147E 0.1186E 0.1226E 0.1268E 0.1313E 0.1360E 0.1409E 0.1460E 0.1514E 0.1570E

0.0

01 01

0.2908E 0.2843E 0.2779E 0.2715E 0.2651E 0.2587E 0.2523E 0.2460E C.2397E 0.2335E 0.2273E C02211E 0.2150E 0.2089E C.2029E C.1970E 0.1912E 0.1854E 0.1797E 0.1740E

61 01

01 01 02 02 02 02 02 02 C2 02 02 02 02 02 02 02

0.0 05 C5 05 05 05 05 C5 C5 05 05 05 05 05 C5 05 CC 05 05 05 05

0.3304E 0.3231E 0.3158E 0.3085E 0.3012E 0.2940E 0.2868E 0.2796E 0.2724E 0.2653E 0.2583E 0.2513E 0.2443E 0.2374E C.2306E 0.22396 0.2172E 0.2107E 0.20426 0.1978E

05 05 05 05 05 05 05 05 65 05 05

05 05 05 05 05 05 C5 05 05

.O .3164€ 1.3094E ' 3024 E -2954E 0.2885E 0.2815E 0.2746E 0.2677E 0.2609E 6.2541E 0.2473E 0.2496E 0.2340E 0.2274E 0.2209E 0.2144E 0.20806 @.2018E 0.1955E 0.1894E

05 05 05 05 C5 05 05 05 05 @5 05 05 05 05 05 05 05 C5 05 05

0.2958E 0.3421E 0.3317E 0.3244E 0.3172E 0.3100E 0.3029E 0.2959E 0.2889E 0.2820E 0.2751E 0.2684E 0.2617E 0.2551E 0.2485E 0.2421E 0.2357E 0.2295E 0.2233E 0.2172E 0.2112E

04 04 04 04 04 04 04

04 04 04 04 04 04 04 04 04 04 04 04 04 04

0.5273E 0.2605E 0.2552E 0.2526E 0.2500E 0.2474E 0.2448E 0.2421E 0.2395E 0.2368E 6.2341E 0.23146 0.2287E 0.2259E 0.2232E 0.2204E 0.2177E 0.2149E 0.2122E 0.2094E 0.2067E

03 04 04 04 04

04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04

0.3980E 0.1048E 0.1029E 0.1018E 0.1C06E 0.9950E 0.9833E 0.9716E 0.9597E 0.9476E 0.9355E 0.9233E 0.9109E 0.8985E 0.8860E 0.8733E 0.8607E 0.8479E 0.8351E 0.8223E 0.8094E

BTU/HR

03 04 C4 04 C4 03

03 C3 03

03 C3

03 03

C3 C3 03 03 03 03

0.1332E 0.8775E 0.8748E 0.87806 3086C76 C.8832E 0.8853E 0.8869E 0.8882E 0.8890E 0.88956 O.8896E 0.8892E 0.88856 0.88736 0.88576 0.88316 0o88136 0.8785E 0.81526 0.87166

09 08 08 08 08 08 08 08 08 08 08 08 08 C8 08 08 08 08 08 08 08

90 Appendix C THE RETEX PROGRAM

The RETEX computer program i s o u t l i n e d i n block-diagram form i n F i g . C.l.

The i n p u t d a t a r e q u i r e d f o r t h e program a r e given i n Table

C . 1, and t h e o u t p u t r e c e i v e d from t h e program a r e given i n Table C . 2.

A complete l i s t i n g o f t h e main program i s followed by d e f i n i t i o n s of t h e i n t e r m e d i a t e v a r i a b l e s used i n t h e program.

To i l l u s t r a t e t h e u s e

o f t h e RETEX program, t h e i n p u t and o u t p u t f o r t h e MSBR steam r e h e a t e r exchanger d i s c u s s e d i n S u b s e c t i o n 3 . 1 of t h i s r e p o r t a r e p r e s e n t e d a s p r i n t e d by t h e computer.

ASSUME BAFFLE SPAC ING

ASSUME SHELL D IAMETER

CALCULATE NUMBER OF TUBES, FUEL AND COOLANT FLOWS AND VAR I OUS GEOMETR I ES

START WITH F I R S T INCREMENT FROM HOT S I D E OF HEAT EXCHANGER I=1

ASSUME TEMPERATURE DROP FOR THE INCREMENT

EVALUATE ALL PHYSICAL PROPERT IES AT AVERAGE TEMPERATURE OF INCREMENT

CALCULATE PRESSURE DROPS AND HEAT TRANSFER COEFF I C IENTS fOR THE INCREMENT, US ING CORRECT CORRELATION FOR DIFFERENT REGIMES

CALCULATE HEAT RATE AND TEMPERATURE DROPS OF THE INCREMENT

Fig. C.l.

Simplified Flow Diagram of t h e RETEX Computer Program.

CHANGE ASSUMEO INCREMENT TEMPERATURE DROP

TEMPERATURE DROPS AGREE

GO TO NEXT INCREMENT I 1-1

END TEMPERATURE OF

OOES TOTAL TUBE S I D E PRESSURE DROP

CHANGE ASSUMEO SHELL 0 I AMETER

OOES TOTAL SHELL S I D E PRESSURE DROP

CHANGE ASSUMED BAFFLE SPACING

6 F i g . C.1.

(continued)

ADD I T I ONAL CASES FOR PARAMETER STUDY

P R I N T OUTPUT

Fig. C . l .

(continued)

Table C . l . Card

...

El,&,

Columns

Format

Computer I n p u t Data f o r RETEX Program Variab 1e

Term

Units

1-10 11-20

E10.4 F1O.O

2 1-30

F10 .O

1-10 11-20 21-30 31-40

F10 .O F10 .O F10 .O F10 .O

Coolant o u t l e t t e m p e r a t u r e Fuel i n l e t t e m p e r a t u r e Fuel o u t l e t t e m p e r a t u r e Coolant i n l e t t e m p e r a t u r e

CTO FTO ETF ETC

1-10

F1O.O

11-20

F10 .O

2 1-30

F10 .O

Leakage f a c t o r f o r h e a t transfer correlations Leakage f a c t o r f o r press u r e drop c a l c u l a t i o n s Tube m a t e r i a l c o n d u c t i v i t y

WCOND

Btu/hr*ft*OF

1- 10

F10 .O

RA5

11-20

F10 .O

DTR

21-30

F10 .O

RA8MAX

31-35 36-40

I5 I5

Radius o f c o o l a n t c e n t r a l downcomer D i s t a n c e between s h e l l w a l l and t u b e bundle Maximum a n t i c i p a t e d h e a t exchanger r a d i u s Number of c a s e s t o b e run Index one i f enhanced t u b e s a r e used

1-10 11-20 21-30 31-40 41-50

F10 .O F10 .O F10 .O

F10 .O F10 .O

Heat l o a d r e q u i r e d Allowable tube- s i d e p r e s s u r e drop Allowable s h e l l - s i d e p r e s s u r e drop

Outside diameter of tube Tube w a l l t h i c k n e s s Triangular pitch Inner b a f f l e cut Outer b a f f l e c u t

HEATL PRDT PRDS

PLK

USES KENTB DIA WTHK TPIP CUT3 CUT4

ft ft ft % of area % of area

95 T a b l e C.2. T em

Output Data From RETEX Computer Program Variable

Units Btu/hr

THEATO

Total heat actually transferred

HTPERC

Percentage o f required heat load t r a n s f e r r e d

C o o l a n t ( s h e l l - s i d e ) mass f l o w r a t e

lb/hr

F u e l ( t u b e - s i d e ) mass flow r a t e

lb/hr

TTDSO

T o t a l t u b e - s i d e p r e s s u r e drop

psi

SPPERC

P e r c e n t a g e of allowed t u b e p r e s s u r e d r o p a c t u a l l y used

TTDTU

T o t a l s h e l l - s i d e p r e s s u r e drop

TPPERC

P e r c e n t a g e o f allowed s h e l l p r e s s u r e d r o p a c t u a l l y used

RA8

Radius of h e a t exchanger s h e l l

BSOI

D i s t a n c e between b a f f l e s

VOL

F l u i d volume c o n t a i n e d i n t u b e s

ft3

AREA

T o t a l h e a t t r a n s f e r a r e a i n h e a t exchanger

ft"

SNT

T o t a l number o f t u b e s

TUBLEN

Actual tube length

GBRL

Modification factor f o r Bergelin's heat transfer correlation

SAVT

S h e l l average temperature

O F

TAVT

Tube a v e r a g e t e m p e r a t u r e

TCI ( I )

C o o l a n t o u t l e t t e m p e r a t u r e from increment 1

O F

TCO( I)

C o o l a n t i n l e t t e m p e r a t u r e from i n c r e m e n t I

CWT ( I )

Average t u b e w a l l t e m p e r a t u r e a t c o o l a n t s i d e

TFI (I)

F u e l o u t l e t t e m p e r a t u r e from increment I

O F

TFO( I)

F u e l i n l e t t e m p e r a t u r e from i n c r e m e n t I

FWT(I)

Average t u b e w a l l t e m p e r a t u r e a t f u e l s i d e

rnT(1)

Average t e m p e r a t u r e d r o p a c r o s s t u b e w a l l i n increment I

V1(1)

F l u i d a v e r a g e v e l o c i t y i n o u t e r window i n increment I

ft/sec

v2 (1)

Fluid average v e l o c i t y i n overlapping b a f f l e zone i n i n c r e m e n t I

ft/sec

v3 (1)

F l u i d a v e r a g e v e l o c i t y i n i n n e r window i n increment I

ft/sec

psi

Table C.2 Term

(continued) Var i a b 1e

Units

VWl(I)

F l u i d v e l o c i t y a c r o s s t u b e s i n o u t e r edge o f b a f f l e i n increment I

ft/sec

vw3 ( 1)

F l u i d v e l o c i t y a c r o s s t u b e s i n i n n e r edge o f b a f f l e i n increment I

ft/sec

PDSO( I)

S h e l l - s i d e p r e s s u r e d r o p f o r increment I

l b / f r?

PDTO( I)

Tube-side p r e s s u r e drop f o r increment I

l b / f ?i

RENTO( I)

T u b e - s i d e Reynolds number f o r increment I

PRNTO( I)

Tube-side P r a n d t l number f o r increment I

RENSOl (I)

Reynolds number i n o u t e r window i n i n c r e m e n t I

RENS02 (I)

Reynolds number i n o v e r l a p p i n g b a f f l e zone i n increment I

RENS03(I)

Reynolds number i n i n n e r window i n increment I

HTO (I)

Tube-side h e a t t r a n s f e r c o e f f i c i e n t i n increment I

AESO( I)

Shell-side heat transfer coefficient i n increment I

UOA( I)

Overall h e a t t r a n s f e r c o e f f i c i e n t i n increment I

HEAT (I)

Heat t r a n s f e r r e d i n i n c r e m e n t I

The RETEX Program L i s t i n g

**FTN,Lr E y G r M o QROGPAM MSBRPE-2 MSBPP 1 0 TYPE REAL LK r L A I J C l 9 L A k C 3 MSBRP 2 9 DIMENS I O N TFO( 1 3 0 1 T C I ( 1 3 0 I r V M l ( 1 3 0 ) ~ V M 2 ( 1 3 I0 r V k l G l ( 1 3 0 I , VW03 (1301 TMSBRP 3 0 1 R E N T 0 ( 1 3 O I r P R N T 0 ( 1 3 0 I r P E N S O l ( i 3 0 1 , R E N S O 3 ( 1 ~ 0 T~ R E N S 0 2 ( 1 3 0 ) 9 MSBRP 3 1 VM3 ( 1 3 C I ,PDSO(13O I (NT (100I r B J ( 3 I r H S O l ( 1 3 O IqHSO2( 130 I r H S O 3 ( 130 I T MSBRP 3 2 2 3AHSO( 130 1 HTC ( 110 I r UOA (130 I r TCO ( 1 3 0 I T TF I(1 3 0 I9 HEAT ( 1 3 @I r TkDT ( 130 I r MS BRP 3 3 MSBRP 3 L 4 P D T O ( 1 3 0 Ir T U B L N ( 1 3 0 I r V I ( 1 3 0 1 , V2( 1 3 0 ) t V 3 ( 1 3 0 J r V W 1 ( 1 3 0 J 9 V W 3 ( 1 3 0 ) I MSBRP 3 5 5 R (100I t FPCT( 1 C O I T T C P I (100 I r TCTAL (100I 6 CWT( I30 I , F k T ( 1 3 0 I YAVWT ( 1 3 0 I MSBRP 3 6 1 0 0 1 FORMAT( € l o o 4 9 2 F 1 0 - G I MSBPP 10 1 0 0 2 FORMAT( 4 F 1 0 . 0 ) MSBRP 5 0 1 0 0 3 FORMAT( 3 F l O e O l MSBRP 60 1 0 0 4 fOSMAT( 3 F 1 0 - 0 , 2 1 5 1 MSBRP 70 1 0 0 5 FORMAT( 5F10.0) MSBRQ 80 1006 FORMAT(22FOHEAT LOAD REQUIRED = r F 1 2 * O t 2 X r t ? H ( B T U / H R I I MSBRQ 90 1 0 0 7 FORMAT(43WOALLCWABL€ TCTAL TUBE-SIDE PRESSURE DROP = , F I O . O , Z X r MSBR 100 1 lOH(LB/SQ-FT) I MSBR 1 0 1 1 0 0 8 FORMAT(44kOALLCWABLE TCTAL SHELL-SIDE PRESSURE DROP = r F l O e O r 2 X r MSBR 1 1 0 1 lOH(LB/SQ-FTI I MSBR 111 1009 F O R M A T ( 3 3 b 0 P I G F TEMP. CF SHELL S I D E F L U I C = T F I O . ~ T Z X * ~ H (I F I MSBR 1 2 0 1,010 FORMAT(3?HOHIGl’ TEMP. CF TUBE S I D E F L U I C = r F 1 0 0 2 ~ 2 X r 3 H ( F 1I MSBR 1 3 0 1011 F O k M A T ( 3 2 k O L C k TEMP. CF TUBE S I D E F L U I D = t F 1 0 2 ? 2 X , 3 H ( F I ) MSBR 140 1 0 1 2 FORMAT(32l’OLCW TEMP. OF SHELL S I D E F L U I C = , F I O . Z T Z X , ~ H ( F J I MSBR 1 5 0 MSBP 1 6 0 1 0 1 3 FORMAT(32kOHEAT TRANSFER LEAKAGE FACTOR = 9F10.5 1 1014 FORMAT(27kOPRESSURE LEAKAGE FACTOR = , F l O . 5 1 MSBP 170 1 0 1 5 fORMAT(35kOCCNCUCTIVITY OF TUBE WALL METAL = , F 1 0 * 5 ~ 2 X r MSBR 1 8 0 MSBR 1 8 1 1 1 3 H ( BTU/HP-FT-F) J 1 0 1 6 F O R M A T ( 3 4 k O I N S I O E R A C I L S O F CUTEP PNNULQS = r F 1 0 - 5 r 2 X , 6 H ( F E E T ) I MSBR 190 MSBR 200 1 0 1 7 FORMAT(4ltJOCISTANCE BETWEEN SHELL WALL AND TUBES = MSBR 2 0 1 1 rFlO.5r2Xr6H(FEETI J MSBR 2 1 0 1 0 1 8 FORMAT(49POMAXIMUM A N T I C I P A T E D OUTER RADIUS OF EXCHANGER = 9 MSBR 2 1 1 1 F l o e 5 7 2 X ,6H( FEET I I

1 0 1 9 FOFMAT(23POhbPeES O F C A S E S RUN = 9 1 4 ) MSBR 2 2 0 1 0 2 0 FOSMAT(25kOUSE OF ENHENCEO TUBES = T I ~ T Z X , ? ~ H ( O NI EF ENHENCED TUBEMSBR 2 3 0 1s A R E U S E C ) ) MSBR 2 3 1 1 0 2 1 FORMAT(2GkOCLTZIDE PIAPETER OF TUBES = T F ~ P . ~ ~ 6 ~ HX( FEET) T I MSBP 2 4 0 6H(FEETl I MSBP 2 5 0 1 0 2 2 FORMAT(27kOkPLL THICKNESS OF TUBES = TFiC. 5 9 2 x 9 1 0 2 3 FOPMAT(20kGTPIbNGULbR P I T C H = 9 ' F ~ O I ~ , ~ X T6 H ( F E E T ) ) MSBP 2 6 0 1 0 2 4 FORMAT(22kOINNER BAFFLE CUT3 = T F L O . 5 9 2 x 9 1 0 H ( P E P CENT) I MSBE 2 7 0 MSBF 2 8 0 1 0 2 5 FCJRMAT(22kOOLTEP BAFFLE CUT4 = r F 1 0 . 5 ~ 2 X ~1 0 H ( P E R CENT) 1 1 0 2 6 F O P M A T ( 2 5 b l T C T A L HEAT TRPNSFEPED = T F ~ ~ . O T ~ X T ~ H ( B T U IT /HF MSBR 2 9 0 1 2 X T l k ( ~ F 5 . 1 y 9 H PERCENT) 1 MSBR 2 9 1 MSBR 3 0 0 1 0 2 7 FOFMAT(2QkONPSS FLOk RATE OF CCOLANT = , F Z C . O T ~ X , 7 H ( L B / H R L 1 1 0 2 8 FO'?MAT(26kOMPSS FLOP' R A T E OF FUEL = T F L O . O , ~ X T 7 H ( L B / H R I 1 MSBF. 3 1 0 1 0 2 9 FORMAT(?4kOSkELL-SIGE TOTAL FRESSUPE D R C P = t F l O o T r 2 X ~ 9 H ( L B / S Q I N I M S B F 3 2 0 1 , 2 X ~ l H ( r F 5 c l r 9 H PERCENT)) MSBR 3 2 1 1 0 3 0 FORMAT(33kOTL'BE-SIDE TCTPL PPESSUR€ D R O P t F 1 0 * 2 9 2 X T 9H(LB/SCINI,MSBR 3 3 0 1 2 X 9 1 b ( T F ~ o ~ T PERCENT) ' H 1 MSBR 3 3 1 1 0 3 1 FORMAT(24kChCMINAL SFELL RADIUS = t F 7 , 4 , 2 X ~ 4 H ( F T l I MSBP 340 \o 1 0 3 2 FORMAT(26bOUNIFORF BAFFLE SPACING = * F 7 0 4 9 2 X ~ 4 H ( F T I) MSBP 3 5 0 m 1 0 3 3 FORMAT(LOF0TUBE F L U I D VOLUME CChTAINEC I h TUBES = 9F7. 2 T l X T MSBR 3 6 0 MSBR 3 6 1 1 1 2 H ( C U B I C FFET I ) = T MSBR 3 7 0 1 0 3 4 F O R M A T ( ~ H C T ~ E I ' T O T A HEAT L TRANSFER A R E & E A S E D CN TUBE 0.D. 1 F I ~ . ~ T ~ X T ~ H ( S 1Q F T I MSBR 3 7 1 1 0 1 5 FORMAT(25kOTCTPL NUPBER CF TUBES = v F 6 o C ) MSBR 3 8 0 1 0 3 6 FORYAT(21kOTCTAL LEWGTH = T F ~ * ~ T ~ X T ~ I H ( F T I MSBP 3 9 0 M S B R 400 1 0 3 7 FORMAT(23k0BWINDOW 1 CROSSFLOW = T F ~ ~ ~ T ~ X ~ ~ HI ( S Q F T ) 1 0 3 8 FORMAT(31kOBERCLIN VCDTFICATICN FACTOR = 7 F5.2) MSBR 410 1 0 3 9 F O R M A T ( ~ H @ T Z X T ~ H I T ~ X T ~ ~ T C I I S X , ~ H T C ~S,H~T F X I , T?~~X~T~~THTT~F~CMSBR T! ~ 420 MSBF 4 2 1 19x t 3HFWT T E X r 4 H T h D T / / 1 l x T 1HF T 1 1 x T ZHF T 1 1 x T 1HF T 11X T 2 MSBR 422 1 H F ~ 1 1 X 1HFt t ~ ? X T ~ H F T ~ I X T ~ ~IF ~ /7 E / 1 ( 2T ~0 4 X )T 1 0 4 0 F O R M A T ( 1 HC T 2X T 1 H I T 7 X T 3EVP? T 9 X T 3HVM2 T 9 X T 3HV P? t 8X t 4HVWO: r 8 X ~ 4 H V k e 93 MSBR 4 3 0 1 8 X T ~ H P D S C8X T T 4 H P D f 0 / / 3 2 X T 6HFTlSEC 3 3 X t7l'LB/SQFT// ( 1 x 9 I3 T 7 F 1 2 - 4 I I MSBR 4 3 1 io41 F ~ R M A ? ( ~ ~ C T ~ X T ~ H I , ~ X T ~ H P E N T C ~ ~ X T ~ H P R N T O T ~ X T ~ H R E N S @MSBR Z T ~ 440 X T ~ H R E N S C ~ ~ 16X T 6HF ENSC3 t 7X r3HHTP T 8 X T 4HAHSC! t 9X T 3HUOA 7 8 X t 4 H H E A T / / 7 7 X T MSBR 441 Z 13HBTU/FR/SQFT/F 11 3 X t 6 H B T U / H P / / ( l X t I 3 t S E 1 ? - 4 ) I MSBR 4 4 2 1 0 4 2 FORMAT(27kOTURE WALL A V E R A G E TEMP. = ,F10.2) 4 9 1 0 4 3 FOSMAT(ZStOSl-ELL S I D E A V E R A G E TEMP. = 9 F10.21 MSBR 4 6 0 C MSBR 6 5 0

READ I N AhD F R I N T OUT I N P U T C A T B KEY7= 1 VM 1( 1L =O VM2 ( 11 = O VM3 ( 1I SO. V W O l ( 1 J=O. VW03 ( 1J=O R E N S O l ( 1 J =O. RENS02(1 I=O* RENS03 (1 J = O m H S O I ( 1 J=O, HS02(1 J = O . HS03(1 J = O ,

READ 1001, HEATLT PRDTT PRDS READ 1 0 0 2 , CTOT F T O T E T F t ETC REA0 1 0 0 3 ~L K T PLKtWCCND READ 1004, R P 5 9 OTRT R A ~ M A X T K A S E S T K E N T B CONTINUE READ 1005, C I A 9 WTHK, T R I P , C U T 3 1 CUT4 HSFCT=L. IF(FTOmLT.CTC1 H S F C T = - l s P R I N T 1006, PEPTL P R I N T 1 0 0 7 9 FRCT P R I N T 1 0 0 € ~PRES P R I N T 1 0 0 5 ~C T C P R I N T 1010, FTC P R I N T 1011, ETF P R I N T 1012, ETC P R I N T 1013, LK P R I N T 10149 PLK P R I N T 1 0 1 5 ~kCCND P R I N T 1016, P A 5 P R I N T 1017, CTP P R I N T 101€, RPEMAX KPSES PRINT 1 0 1 5 P R I N T 102C7 K E h T B

MSBR MSBP MSBP MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBP

MSRR MSBR MSBR MSBR MSER MSBR MSBR MSBR MSBR MSBR MSBR MSBR MSBP MSBR MSBR

660

490 500 510 520 530 540 550 560 570 580 590 600

83.0 620 630 640 650 660 670

680 690 700 710 720 730

740 750 760 770 780 790 800 810 820

W W

PRINT PRINT PRINT PRINT PRINT C C C

1021, 1022, 1023, 1024, 1025,

CIA kTl-K TRIP CUT3 CUT4

BEGIN GEOMETRY CALCULATICNS FOR SINGLE PNNULUS DISC AND COUGHbUT BAFFLEC HEAT EXCH4NGER ATIJBE = (3.14159* (DIA**2.01)/4.0 GFTT = 1./3600. GFT = 1. / 144. DIAI=DIA-f.O*kTHK =(3.14r59*(DIAI~‘s2.0))/4.0 FATUB

KEY1 = 0 PE R.Cl 2

= 0.99

IF(KEYl,GT.O~BSOI=O.

5*(@SL+BSHJ KEY2 = 0 PERCZ = 0.99 RASL=RAS RARH=PA8MPX RA8=0. 5* ( RABL +RA8H 1 NT0 = 4~0~~~PP8~~2.0~-~RA5~~2.0~~/~1~12~~T~1P~~2.0~~ RA52=PA5**2 RA82=RA8**2 RA6=(RASZ+CUT4*(RA82-RA521 I**. 5 RAi’=tRA82-CUT3*(RA82-RA521 I**,5 RA62=RA6**2 RA72=RA7**2 AP01=3.1415S*( (RA8J**Z.O-(RA7J**Z.OJ*~l.O-~ATUBE/ 1(0,866~((TRIP)4*2,0)))) AP03=3.34159*( (RA6J**Z.O-(RA5J**Z,Ob*tl.C-LATUBE/ l(O. 866*(r( TFIP**2.0) 1) 1 PL4V = O,955*TRIP RB1 = (RPt?-RP7)/(1.86t*TRIPI RB2 = (RP7-RA61/(0.933*TRIPJ RB3 = (RA6-RA5)/(1.86t*TRIpl

COUNTER

FLOW

MSBR MSBP MSBR MSBR MSBR MSB MSB MSB MSBR MSBR MSBR MSBR MSBR MSBR MSBP MSBF MSBF MSB MSB MSB MSB MSB MS8 MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

830 840 850 860 870 1650 1660 1670 910 920 930 940 950 960 970 980 990 1000

1010 1020 1030 1040 1050 ?Q60 1070 1080 1090

1100 1110 1111 1120 1121 1130 1140

1150 1160

LAHOl=S.

14155*2,0*FA7*(1.0-~01A/PLAV~

:~~~~=3.1415S*2.O+RA6,(1.0-(DIb/PLIV)) =

4.O~((FA8~~2.C)-(RA7~~2.0~~/(1.12~(TRIP~~2.0~~

SUM1 = ISUMl ISUMZ = 4.0*~~PA7~~2.0~-~PA6~~2.0~~/~1.12~~TR1P~~2.0~~ SUM2 = ISUM ISUM = 4.0~((RA6=~2.CI-(RA5~~2.0~~/(1.12~(TRIP~~2.0~~ SUM3 = ISUM SNT = ISCYl + ISUM + ISUM BSHAX=l,S*t (RAB-(RAE-RA71/2e )-(RA5+(RA6-RA5)/2.1) BStlIN=O. 2*c( RC8-RA5 1

IF(BSHIN.LT,O.~667~BSCIN=0.1667

HU=2.*NCOKD/(DIA*:ALOG(DIA/DIAI~~ CSPHAV=O, 36 FSPHAV=O, 5571 QC=HEATL/ (CSPFAV*( CTO-ETC) I QF=HEATL/ (FSPHAWL FTO-ETF) 1 GTO = QF/ (NTC*FATUB) CONTINUE IFtKEYl. ECwO)BEH=BSMAX IFLKEYl. ECmO1BSL=BSMIN IF(KEYl.EC.O~BSOI=O. 5*(BSL+BSF)

IT = 0 KFINAL=O I=1 TSUH=O, SSUM=O. THEATO = C. C TPDTO = 0.0 TPDSO = 090 TFO(I)=FTC TCI(I)=CTC KEY4 = 0

TIF=-5.0 TIC=+.0 CDTF=O, FDTF=O, BSO =

BSOI

MSB MSB MSB MSB MSB MSB MSB YSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

1170 1180 1190 1200 1210 1220 1230 1240 I.250 1260 1270 1280 1290 1300 1310 1320 1333 1340 1350

MSB 1360 MSB 1370 MSB 1380 MSB 1390 MSB 1400 MSB 1410 MSB 1420 MSB 1430 MSB 1440 MSB 5450 MSB 1460 MSB 1470 MS8 1480 MSB 1490 MSB 1500 MSB 1510 MSB 1520 MSB 1530 MSB 1540

Et w

R P L 1 = RZC/((GP8-(RA8-RA7)/2. )-(RA5+(Rb0-QP5)/2, ) ) GBRL = 0 . 7 7 * e ~ ~ 1 * * ( - . 1 3 8 ) A W O l = BSC*LAWCl AW03 = BSC*LAWC3 A W 1 = SQPT(PWCl.*APOl I A W 2 = ( A k O l + A k 0 3 ) /2. Ab43 = SQPT(PkC3*AP@31 GS91 = QC/Akl GSO2 = QC/ANZ GS03 = Q C / A k ? ATC = T C I ( 1 ) + ( T I C / % . O I CFT = A T C +CCTF*HSFCT ATF = T F G ( I ) + T I F / 2 . FFT=AT F- f CT F*H ZFCT FI=I TUBLN( I I = FI*E!SClI C V IE=O. 2 1 2 1* E X F ( 4 0 3 2 / ( 4 6 0 . + ATC ) 1 CVISW=O* 2121*EXP(4032. / ( 4 6 9 . + C F T ) 1 CDEN=141. 27-C. C 2 4 6 6 * A T C CCON=0.24C C S PH=O 3 6 FV IS=O e06 2 F V I S W = 0.062 FDEN = 0,7632 FCON = 0.036 FSPH = 0.5571 V!SK = ( C V I S / C L I S W l + * O . 1 4 F V I S K = ( F V I S / F V I S W I**O. 1 4 DCVIS = C I A / C V I S CCOEN = l./CCEh' QCCDEN = C C * C C C E N CALCULATE REYNCLS AND PRANDrL hUMBER TUeE S I D E RENTO( I I = C I AI*CTO/FVIS PRNTO( I) =FVIS*FSPH/FCCh H E F I = 1 * + ( ( R E h T C ( I I - 1 O C O - 1/900C. I * * O . 5 I F (KENTB. hE. 1 I k E F I = 1 . I* BSC*GTC**?*HEFI/ P D T O ( 1 I = (* 0 0 2 8 + . 2 5 * G E N T O * * ( - a 3 2 ) 1 (CIAI*fCEN*417182400. I

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

1550

1560 1570 1580 1590 1600 1610

1620 1630 1640 1650

M S B 1670 YSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS6 MSB MSB MSB MSB MSB MSB MSB MSB

1690

1700 1710

1720 1730 1740

1750 1760

1770 1750 1790 1800 1810 1820 1830 1840 1850 2550 1870

1880 1890 1900

1910 1911

7 8

'10 C

C A L C U L A T E HFPT T R A N S F E R C O E F F T U B E S I D E H T O ( T ) = F C C N / C I A** 0 2 1 7* ( R E N T 0 ( I) * * a 8 J * ( P R N T C ( II * * * 2 3 3 3 1 * F V I S K * H E F I GO T O 10 I F ( R E N T O ( I J , L T * 2 1 0 0 . 1 GO T O 9 H T O ( I I = FCCn/CIA*,089*(RENTO( I J**.C666-125* I*( PRNTO(1 )**.33331* 1 F V I S K * H E F I * ( l o + ,3 3 3 3 * ( D I A I / T U B L N ( I J J 3 4 . 6 6 6 6 ) GO TO 10 H T O ( 1 J = FCCN/CIA*(4o36+(0*025aRENTO( I)sPRNTO(I)4DIAI/TUBLN(I I 1 ~ / ~ 1 ~ + G ~ 0 0 1 2 * R E N T O ~ I ~ * P R N T O ~ I ~ * D ~ ~ I I 1/ T U B L N ~ I I CONTINUE C A L C U L A T E FLCW AREAS S k E L L S I D E V W g l ( 1 J = QCCCEN/AW@l V W 0 3 ( 1 I = CCCCEN/AW@3 V M l ( I 1 = CSOl*CCDEN V M 2 ( I I = CSC2*CCDEN V M 3 ( I J = CSC3*CCDEN C A L C U L A T E PRESSURE DRCPS S H E L L S I D E D P 1 = ( l o +@ . P @ l I * C D E N * V M l ( I) * * 2 D P 2 = * 6 * P B 2 * C C E N * V M 2 ( I) * * 2 D P 3 = (1. +. 6 * P e 3 ) * C D E N * V M 3 ( IL * * 2 RENSOI(1 1 = ESCl*DCVIZ R E N S 0 2 ( 1 J = GSCZ*DCVIS RENSr33(I J = GSC3*DCVIS HEF@=l.+O.3*( ( P E N S 0 2 ( I J - 1 0 0 0 ~ 1 / 9 0 0 C )**C*5 ~ IF(KENTBohEolJ~EFO=l. PDSO( I I = ( C F l + D P Z + D P Z ) * P L K * I - E F 0 / 8 3 4 6 2 4 C O O . C A L C U L A T E B J F b C T O R ANC S H E L S I D E C O E F F I C I E N T B J ( 1 ) = ( 0 , " 6 ~ P E N S ~ l ( I J * * ( - O o ~ ~ 2 ) I*GBRL BJ(21 = ( 0 . 3 L t * R E N S 0 2 ( 1 1**(-0.3E2I )*GBRL B J ( 3 ) = ( O 0 3 4 C * P E N S O 3 ( I l**(-0*3€21 ) * G B R L H S O l ( I = ( L K * C S P H * G S C l * @ J ( 1I*( ( C C C N / ( C S P H * C V I S I 1 4 8 . 6 6 I 1 W I S K H S 0 2 ( I 1 = ( LK*CSPH*CSC2*BJ ( 2 I * ( ( C C C N / ( C S P H * C V I S L 66 I l * V I S K H S 0 3 ( I J = (LK+CSPH*GSC3*BJ(3I*( (CCCN/(CSPH*CVIS) J**.66lI*VISK A H S ~ ( I I = ( ( ( H S G L ( I ) ~ S U ~ l ) + ( H S C 2 ( I ) ~ S U ~ 2 L + ( H S ~ ~ ( I ) *JS/ SUNM T J3* H J EFC GO TO 12 CONTINUE

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB PSB MSB MSB MSB MSB MSB MSE!

2640 1930 1940 1950 1960 1961 1970 1980 1981 1990

2480

2010 2020 2030 2040 2050 2590 2070 2080 2090 210Q 2110 2120 2130 2140 2150 M S @ 273C M S B 3170 MSB 2180 M S B 2190 MSB 2200 MSB 2210 MSB 2 2 2 0 MSB 2230 MSB 2240 MSB 2250

+ 0

1.2

UOA(I)=1.C/((1.C)/AHSO(I~~t(1.O/HTO(IJ~t(1.O/HW~~ A = QFSFSFH 6 = QC*CSFH 0 = UOA( I )+SNT*BSO *3,14159*CIA P -HSFCT*(C*(A-61 )/(A*%) PBiR = EXP(PI c = (B-AlsPEAR (I )*(B*P@AR-A) I-(TF’2(1 b*P*(PBAR-1. 11 l/C TCO(I1 = ((TCI TFItII =((TCC(I~-TCI(I1~*B/A~ + TFO(II HEAT1 I I =-A*(TFI(I) - TFO(I)b TWDT(1) = (HEAT(I~/NTC~*ALOG(DIA/DIAI ~/(2.0*3.14159*BSO*WCONDI CTIF = TF I( I I-TFO( II CTIC = TCC(II-TCI(Ib IF~~ABS~CTIF-TIFI.LE.~1.5~~.ANO.~ABS~CT!C-TIC~.LE.~1.5~~~GO TIF = CTIF TIC = CTIC GO TO 6 THEATO = THEATC + HEAT(I) TPDTO = TFDTC t PDTO(II TP OS0 = TFDSC t PDSOII) /NTC~/BS0)/(3.14159*DIA*AHSO(I~~ CDTF=(((HEAT(I)I FDTF=CDTF*AHSG (I 1 /HTO( I! FWT(I) =PTF-FCTF*HSFCT CWT(I) =ATC+CCTF*HSFCT AVWT( I I =0.5*(FWT(I 1 +CWT(I)) TSUM=TSUM+AVkT(I) SSUM=SSUMtATC IF(KFINAL.EQ.l.AND.I.EQ.ITi GO TO 15 IF~~~ABS~ETF-TFI~I~1),LE,~~ABS~TFI~I)-TFC~I~~~/2.O~~.OR. 1 (TFI(Ii,LE.ETFI1 Gr- TO 14 I=Itl IF ( I.GT. 129 IGG TO 23 TFO(I1 = lFI(I-11 TCI(1) = TC@(I-11 Bso=BsoI GO TO 6

MS% MSP MS% MS%

2260 2270 2280 2290

MS% MS% MS% MS% MS% MS% MS% MS% MS% MS% MS% MS0 MS% MS% MS% MS% MS%

2310 2320 2330 2340 2350 2360 2370 2380 2390 2400 2410 2420 2430 2440 2450 3090 3100

MS% MS% MS% MS% MS% MS% MS% MS% MS% MS% MS% MS%

3130 3140 2560 2460 2410 2471 2480 2490 2570 2580 2590 2600

zt -P

16 17 C

KFINAL=l IT=1 FIT = IT GO TO 5 TUBLEN= F IT*RSCI TAVT=TSUM/FIT SAVT=SSUM/FIT CONTINUE VOL = 0.7f!54*(CIAI**2.O~*NTO4TUBLEN CHECK OF TUBE AND SHELL PRESSURE DROPS KEY2 = KEY2 + 1 IF(PERC2.LE.O.11 GO TC 26 IF(TPDT0. LT. (PERC2*PRCTi 1 GO TO 18 IF(TPDTO.GT.PRCTI G@ TC 19 GO TO 20 IF(RA8,LE.(R45 +O- OC51 I GC TO 27 RA8H =RA@ IF(KEY2.NE.30iGO TO 3 RA8L=RABL-0.2 PERC2 = PERC2 - 0.01 KEY2=10 GO TO 3 IF(RA8.GE.(PA8CAX-0.0051 1 GC TC 27 RA8L =RPB IF(KEY2.NE.3CI GO TO 3 RA8H=RA8H+O. 2 PERC2 = PERC2 - 0.01 KEY2=10 GO TO 3 KEY1 = KEY1 t 1 IF(PERCl.LE.O.11 GO TC 25 IF(TPDSO.LT. (PERCl*PRCS) I GO TC 21 IF(TPDSO.ET.PRCSIGO TC 22 GO TO 28 IF(BSOI.LE. (BSb’INtO.OC51 bG0 TC! 24 8SH =BSOI IF(KEYl.NE.3C)CC TO 2

MSB MSB MSB MS8 MSB

261’3 2620 2630 2640 2650

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MS8 MS8

2680 2690 3250 2710 2720 2730 2740 2750 2760 2770 2780 2790

MS8 MS8 MSR MSB MSB MSB MSB MS6 MS8 MS8 MSB MSB MS0 MS6 MS8 MSB MSB MSB

2800 2810 2820 2830 2840 2850 2860 2870 2880 2890 2900 2910 2920 2930 2940 2950 2960 2970

z b-l

BS L=BSL-O. I. PERCl = P E P C l 0.01 KEYl=LO GO TO 2 I F ( B S O I * G E . (BSPAX-O.OC5J BSL = B S O I IF(KEYl.NE.3CI GO TO 2 BSH=BSH+O,l PERCl = PERCl 0.01 KEY1=10 GO TO 2

MSB MSB MSB MSB JGO TO 2 4 MSB MSB MSB MSB MSB MSf3 MSB MSB PRINT EX17 S I G h A L S MSB PRINT 1044,@SO MSB F O R M A T ( 3 9 F l E A F F L E SPACINGS EXCEEDE 1 2 9 k I T H BSO = 9 F 5 0 2 9 2 X , 4 H ( F T ) I MSB GO TO 2 8 MSB PRINT 1 0 4 5 MSB FORMAT(ZOk+lBSOT = M A X . OR MIN. J MSB GO TO 2 8 MSB PRINT 1 0 4 6 MSB FORMAT(48I-1 P E P C l FGR SHELL FRESSURE DRCP I S LESS THEN 0.1) MSB GO TO 28 MSB PRINT 1047 MSB F O R M A T ( 4 8 H l PEPC2 FOR TUBE PRESSURE ORCP I S LESS THEN 0.11 MSB GO TO 2 8 MSB PRINT 1 0 4 E MSB FORMAT(29t-1 SHELL R A D I U S = MAX. OR Y 1 N . J MSB GO TO 2 8 MSB MSB END OF C A S E , F P I N T CUTPUT MSB DO 29 I = 1 , I T MSB V l ( I I = VMl(IJ*GFTT MSB V2(IJ = VM2(IJ*GFTT MSB V3(I) = VM?(I)*GFTT MSB V W l ( 1 J = VWOl(II*GFTT MSB V W 3 ( I J = VWC3(1J*GFTT MSB

C C

23 1044

24 1045 25 1046 26 1047

27 1048 C

C 28

2980 2990 3000 3010 3020 3030 3040 3050 3060 3070 3080 3640 3650 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200 3210 3220 3230 3240 3250 3810 3820 3280 3290 3300

3310 3320 3330

CONTINUE TTDSO = TFDSC*CFT TTDTO = TFDTC*GFT TPPERCzT P CT ( 3 4 1OC, / P P DT SPPERC=TPCSO*lCO, / P P OS HTPERC=l OC. *THEATO/HEPTL AREAz3r 1 4 1 5 9 * C I A * S N T * T U B L E N

C PR INT PRINT PRINT PR I N T PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT PRINT

1 0 2 9 TI-EPTOT HTPEPC 1 0 2 7 7 QC 1 0 2 e 9 CF 10 2S9 TTDSOTS PP E R C 103C. TTCTOTTPPERC 10319RP8 1032~BSO1 10339VCL 10347 AREA 1035rSNT 1036rTUBLEN 103ET G B P L 1 0 4 2 TTALT 1 0 4 3 TSAVT TTFO( II T FWT( I I 9 1 0 3 5 , ( I 9 (TC I( I I ,TCO( I1 9 CWT ( 1 ) T T F I ( I) 1 TkCT(I1 ) T I = ~ ~ I T I P R I N T 1 0 4 c 9 ( I 9 ( V I . ( I I 9V2( I ) T V ? ( I I 9vw1( II 9 V W 3 ( I I ,PCSO( I ) 9PDTO( II I 1 I = ~ T I T ) P R I N T 10419 f 1, (RENTO(1 I , PRNTO( 1 ) T F E N S O ~ (1 I,RENSO2(? I ,RENS03( I1, l H T O ( X I t A H S O ( 1 I ,UOA( X I T H E A T ( I I I t I = l r I T )

C C 30

LOOP FOR b D C I T I O N A L C A S E S I F P E Q U I R E D CONTINUE KEY7=KEY7+1 TO 31 IF(KEY7.GT.KASESIGO GO TO 1 CONTINUE END

MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB MSB

3340 3350 3360 3370 3380 3390 3400 1640 '3420 3430 3440 3450 3460 3470 3480 3490 3500 3510 3520 3530 3540 3550 3560 3561 3570 3571 3580 3581

4240 4250 3610 3620 3630 3640 3650 3660

108

I n t e r m e d i a t e Variables

The i n t e r m e d i a t e v a r i a b l e terms used i n the RETEX computer program are a s d e f i n e d f o r t h e PRIMEX program except for t h e two terms d e f i n e d below.

TRIP

Uniform t r i a n g u l a r p i t c h , f t .

PLAV

0.955WRIP used i n c a l c u l a t i n g the e f f e c t i v e c r o s s - f l o w a r e a between t h e t u b e s , f t 2 .

Computer I n p u t f o r Reference MSBR Steam R e h e a t e r Exchanger

HEAT LOAD REQUIRED

IZSCCOCCO.

ALLOWABLE TOTAL T U B E - S I D E

P R E S S U R E DRCP

ALLOWABLE TOTAL S H E L L - S I C E

OF SHELL S I D E F L U I C

HIGH TEMP.

OF TUBE S I D E F L U I D

LOU TEMP.

OF TUBE S I D E F L U I C

LOU TEMP.

OF SHELL S I D E F L U I D =

HEAT TRANSFER LEAKAGE F A C T C R

Ot40.

1150.00

(F)

1000.00

(F)

. I

650.00

(F)

eCO.00

(FI

C.5200C

11.6000C

I N S I D E R A D I U S CF OUTER AhNULUS =

c.0

(BTL/HR-FT-F

0.04167

MAXIMUM A N T I C I P A T E D OUTER RADIUS OF EXCHANGER =

(FEET) 5.CCOOO

(FEET)

(ONE I F ENHENCEC TUBES A R E U S E D )

OUTSIDE DIAMETER OF TUBES = WALL THICKNESS OF TUBES = TRIANGULAR P I T C H =

(FEET)

D I S T A N C E BETUEEN SHELL k b L L Ah0 TUBES =

USE OF ENHENCED TUBES

(LB/SO-FTI

o.aoooo

C O N D U C T I V I T Y OF TUBE WALL METAL =

NUMBER OF CASES RUN =

tLB/SO-FT)

4120.

. I

PRESSURE CROP

HIGH TEMP.

PRESSURE LEAKAGE FACTOR

(BTU/HR)

0.0625C C.00292

0.C8331

(FEET) (FEET)

(FEETI

INNER BAFFLE CUT?

C.?OOCO

(PEP CENT)

OUTER BAFFLE CUT4

C.3OOCO

(PER C E N T )

Computer Output f o r Reference MSBR Steam R e h e a t e r Exchanger

TOTAL HEAT TRANSFERED =

MASS FLOW RATE OF COOLANT = MASS FLOW RATE OF FUEL = SHELL-SIDE TUBE-SIDE

(BTU/HP I

126488992. 1157407. 641075.

NOMINAL SHELL RADIUS

UNIFORM B A F F L E SPACING

59.52

0.7205

400.

?O.i6

B E R G L I N M O D I F I C A T I O N FACTOR TUBE WALL AVERIGE TEMF. SHELL

SIDE AVERAGE TEMP. =

(FT)

(

99.2 59.5

PERCENT) PERCENT)

(FT)

30.6C

TOTAL HEAT TRAhSFER AREA BASEC ON TUeE E.0.

TOTAL TUBE LENGTH

(

(FT)

TUBE F L U I D VOLUME C O N T A I h E C I h TIJBES *

TOTAL NUMBER OF TUBES =

(LB/SOIN) (LB/SQIN)

29.85

C.Ee3E 0

(LB/HRI

(LB/HR)

TOTAL PRESSURE GPOF = T O T A L PRESSURE DPCP =

(101.2 PERCENT)

0.75 $42.55

1004. 44

( C U B I C FEET)

237t.56

(SOFT)

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

40 41 42

TC I

TCC

CUT

TF I

1FO

F UT

0.1150E 001144E 001137E 0m1131E O.1124E Oo1118E OollllE 0.1104E 0.1098E 0.1091E 001084E Oml077E O.lO7lE 001064E 0.1057E OolO5OE 001043E 001036E 0.1029E 0.1022E 0o1014E 0.1007E 0m9999E 0-9926E 0m9853E 0.9779E 0.9705E 009631E 0.9556E 0.9480E 009405E 009328E 0m9252E 009175E 009098E 009020E 008942E 0m8863E 0o8784E 0.8705E 0m8625E 0m8545E

04 04 05 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03

0.1144E 04 0.1137E 04 Ool131E 04 0.1124E 04 O.1118E 04 O ~ l l l l E04 0.1104E C4 0m1098E 04 0.109lE 04 0.1084E 04 0m1077E 04 0.1071E 04 0.1064E 04 0.1057E 04 0,105OE 0 4 0.1043E 04 0.1036E 04 0.1029E 04 0.1022E 04 0.1014E 04 0.1007E 04 0.9999E 03 0.9926E 03 0.9853E 03 0m9779E 03 0.9705E C3 0.9631E 03 0.9556E 03 0.9480E 03 0.9405E 03 0.9328E 0 3 0m9252E 03 0.9175E 03 0m9098E 03 0.902OE 0 3 0.8942E 03 0.8863E 03 0.8784E 03 0.8705E 03 Oo8625E 03 0m8545E 03 0.8464E 03

C.1103E 001096E C.1089E C.1082E C.1075E C.1068E C.1061E C.1054E C.1047E C.1040E C.1032E 0-1025E C.1018E C.lO1OE Ce1003E C.9956E C.9881E C.9806E C.9730E C.9654E C09577E C.9500E C.9422E 0.9344E C.9265E Cm9186E C.9106E C.9026E 0.8945E C.8864E Co8782E Cm8700E Cm8617E C.8527E C.8444E 0.8360E C.8275E C.8190E C.8104E C.8018E Cm7932E 0.7845E

C4 04 04 04 C4 04 C4 C4 C4 C4 04 04 04 04 04 C3 C3 C3 03 C3 03 03 03 C3 03 C3 C3 C3 C3 C3 03 03 C3 03 C3 03 03 03 03 03 03 03

0-5924E 009850E 0.9775E 005699E OmS622E 0.5545E 0.94e8E 0oS390E 0.9311E 0.9233E 005153E 0.9073E 0.8993E 0.8912E 0.8831E 0.8749E 008667E 0.8585E 0.85ClE 0,@418E 008334E 0.8249E 0.8164E Ome079E 0.7993E 0.7906E 0.7819E 0.7722E 0-7644E 0.7555E 0.7467E 0m7377E 0.7287E 0.7197E 0.7lC6E 0.7015E OoC924E 0.6831E 0.6739E 0.6646E O.t552E 0.6458E

03 03 03 03 03 03 03 03 03 03 C3 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 C3 03 03 03 03 03 03 03 03 03 03 03 03

C - 1 O C O E 04 Om5925E 03 OmS850E 03 0.5775E 03 0.5659E 03 O.5622E 03 OoS545E 03 O.5468E 03 Oo5390E 03 O o S 3 1 1 E 03 0.5233E 0 3 0-5153E 03 O.5073E 03 0.8993E 03 O.@912E 03 0.8831E 03 0.8749E 03 008667E 03 0*85@5E 03 0m85ClE 03 C.8418E 03 0.8334E 03 Oo8249E 03 OeelC4E 03 C.8079E 03 0.79S3E 03 0.79C6E 03 0.7819E 03 0.7732E 03 0m7644E 03 0o7555E 03 C.7467E 03 0.7377E 03 0.7287E 03 0.71C7E 03 C.71C6E 03 0.7015E 03 Oot924E 03 0.6811E 03 0.6739E 03 0.t646E 03 0m6552E 03

0.1090E 0.1083E 011076E 0.1069E O.1062E 0.1055E 001048E 0.104lE 001033E Oml026E 0.1019E 0.1012E 0m1004E 0.9967E 0.9892E 0.9817E 0o9741E 0.9665E 0.9589E 0.95llE 0.9434E 0.9356E 0.9277E 0.9198E 0.91 19E 0.9039E 0.8958E 0.8877E 0.8795E 0.8714E 0.8631E 0.8548E 0m8465E 0.8373E 0.8289E 008204E 0.8118E 0-8032E 0m7946E 0.7859E 0.7772E 0.7684E

F 04 04 04 04 04 04 04

04 04 04 04 04

04 03 03 03 03 03 03

03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03

0.1244E 0.1248E 0.1255E 0.1263E 0.1271E O.1279E 0m1287E 0.1295E 0.1302E 0o1310E 0.1318E 0.1326E 0.1334E 0.1342E 0.1350E 0.1358E 0.3366E 0.1374E 0.1382E 0.13896 0-1397E 0.1405E 0.1413E O.1421E 0.1429E 0.1437E 0.1445E 0.1453E 0-1461E 0.1469E 0-1477E 0.1485F 0.1493E 0.1500E 0o1508E 0.1515E 0.1523E Oml531E 0.1539E 0.1546E 0.1554E 0m156'1E

02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 C2 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02

02 02 02 02 02

VMl

VH2

vw3

vu01

vu03

FTISEC 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 $0

41 42

5.5856 5.5778 5.570C 5.5622 5.5543 5.5465 5.5385 5.5306 5. 5226 5. 5 1 4 7 5.5066 5 . 4 9 a6 5. 4 9 0 5 5.4825 5.4744 5.4662 5.4581 5.4495 5.4417 5.4335 5.4252 5.4165 5.4086 5. 4003 5.3920 5.3836 5.3753 5.3665 5.3585 50 350C 5.3416 5.3331 5. 3 2 4 6 5.3154 5. 3 0 6 5 5. 2 9 8 3 5. 2 8 9 8 5. 2812 5. 2 7 2 6 5. 264C 5.2554 5.2468

4.7e31 4.7764 4.7657 4. ' 6 3 0 4. 7 5 6 3 4.7495 4.742e 4.73t0 4. 7 2 9 1 4.7223 4. 7 1 5 5 4. 7C86 4. 7 C l 7 4.6547 4. b e t 8 4.6808 4.6735 4. 6 6 6 8 4.6 598 4.6528 4. 6 4 5 7 4. t 3 8 t 4.6115 4. 6 2 4 4 4. 6 1 7 3 4. 6 1 0 1 4.6C30 4.5558 4.5E86 4.5813 4. 5741 4.5668 4. 5 5 9 6 4. 5517 4.5444 4.5171 4.5297 4. 5 2 2 4 4. 5 1 5 0 4.5c77 4.5C03 4.4529

6.4035 6 . 8S38 6.81342 6.8745 6.8648 6 . 8550 6 . 8453 6 . 8354 6 . 8256 6 . 8157 6. 8 0 5 8 6.7959 6.7859 6. 7759 6.7659 6.7559 6.7458 6.7357 6.7255 6.7154 6.7052 6 . 6950 6. be47 6.6744 6 . 6641 6.6538 6,6435 6. 6331 6.6227 6 . 6123 6 . 6C18 6 . 5914 6. 5809 6 . 5654 6. 5589 6. 5484 6 . 5378 6.5272 6. 5166 6 . 5C60 6.4953 6.4847

POSO

POTO

LB / S O F f 3.9572 3.9516 3. 9 4 6 1 3.9406 3.9350 3.9294 3.9238 3.91132 3.9125 3.9C69 3.9012 3.8955 3.8898 3.8841 3.8713 3.8726 3.8668 3. 8 6 1 0 3.8552 3.8494 3.8435 3.8377 3.8318 3. 8 2 59 3.8200 3.8141 3.8C e1 3.8022 3.7962 3.7903 3.7843 3.77f3 3.7723 3.76 57 3.7557 3.7536 3.7476 3.7415 3.7354 3.7293 3.7232 3. 7 1 7 1

6.0447 6.0362 6.0278 6 . 0193 6.0108 6.0023 5.9937 5. 5851 5. S765 5. 5679 5.9592 5. S505 5.541 8 5.5330 5.9243 5.4155 5. SO66 5.8978 5.8889 5.8800 5.8711 5.8621 5.8532 5.8442 5. 8 3 5 1 5.8261 5.8170 5.8C80 5.7988 5.7897 5.7806 5.7714 5.7622 5.7522 5.7430 5. 7 3 3 8 50 7 2 4 5 5. 71 52 5.7059 5,6966 5.6873 5. 6 7 8 0

21 0.3354 210.0414 209.7476 209.4527 209.1567 208.8597 2 0 8.561 9 208.2632 207.9633 20 7. 6 6 2 5 20 7. 3607 207.0581 206.7545 206. 4502 2060.1448 205. 8386 20 5. 531 5 20 5. 2235 2 0 4 - 9145 204.6047 204-2942 2 0 3 . 9826 203.6705 203-3576 20 3.043 8 202.7291 20 2.4137 202-0977 201.7808 20 1. 4633 201. 1 4 5 1 200. 8 2 6 1 200.5063 2 0 0 . 1584 199-8376 199.5162 19% 1941 198-8715 1 9 8 . 5483 198.2244 19 7.9001 197.5751

1 0 2 . 3 5 85 102.3585 102.35e5 102.3585 102.3585 102.3585 102.3585 102.3585 1 0 2 . 3 5 85 102.3585 102.35 85 102.3555 102.35 e5 102.3585 1 0 2 . 3 5 e5 102.3585 1 0 2 . 35 8 5 102.3585 1 0 2 . 3 5 85 1 0 2 . 3 5 e5 io2.35e5 102.3585 102. 3585 102-3585 102.35 e5 1 0 2 . 3 5 85 102.3585 102.3585 102.3585 102.3585 102.3585 102.35 85 1 0 2 . 3 5 85 102. 35e5 1 0 2 . 3 5 85 ioz.35a5 1O?. 33 85 102.3585 102.35 e5 102.'3585 102.3585 102.3585

RENT0

R EN S O 1

PRNTC

R ENS02

R ENS03

HT 0

UOA

AHSO

PEAT

BTU/HR/SQFT/F 1 0.5794E 2 0.5794E 3 0.5794E 4 005794E 5 Oo5794E 6 0.5794E 7 015794E 8 O.5794E 9 0,51946 10 005794E 11 005794E 12 005794E 13 0o5794E 14 0.5794E 15 005794E 16 005794E 17 005794E 18 0.57946 19 0-5794E 20 0.5794E 2 1 005794E 22 005794E 23 0.5794E 24 005794E 25 0.5794E 26 0.57946 27 0.5794E 28 0.5794E 29 0.5794E 30 0 0 5794E 3 1 0-5794E 32 O.5794E 33 0.5794E 34 0.5794E 35 O05794E 36 005794E 37 0.5794E 30 005794E 39 0.5794E 40 0-5794E 41 005794E 42 0.5794E

06 Ot Ot 06 06 Ot 06 Ot Ot Ot Ot Ot Ot Ot Ot Ot 00 06 O t O t Ot O t Ot O t Ot O t Ot O t Ot 0.t O t Ot O t O t O t O t O t O t O t Ot Ot O t

0.9594E 0.9594E 0.9594E Oe9594E 0.9594E 0.9594E 0.9594E 0.9594E 0.9594E 0.9594E 0e9594E 0.9594E 009594E 0.9594E 0o9594E 0e9594E 0.9594E 0.9594E 0.9594E 0.9594E 0.9594E 0.9594E 0.9594E 0.9594E 0.9594E 0e9594E 0.9594E 0.9594E 0.9594E 0.9594E 0o9594E 009594E 009594E 009594E 009594E 0.9594E 0.9594E 0.9594E 0.9594E 0.9594E 0e9594E 0.9594E

00 00 00 00 00 90

00 00 00 00 00 OC 00 00 00 00 OC 00 00 00 00 00 OC 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

0.5445E Ce5395E C.5340E C.5205E C.5230E C.5175E C.5120E C.5064E C.5008E C.4952E C.4896E G.4835E C04783E C.472tE Ce4669E 0.4612E Ca4555E C04497E C.4440E C.4282E C.4324E 0.4266E Ca4208E C.4150E C.4092E C04033E C03975E 00391tE C.3858E C.3799E Ce3740E Co3682E C.3623E 003559E C.3501E C.3442E 0.3383E Ce3325E Ce3266E Co3208E 0e314SE C.309iE

05 05 C5 C5 05 C5 05 05 05 C5 C5 05 C5 C5 05 C5 C5 05 C5 C5 C5 05 05 05 05 C5 C5 05 C5 05 05 C5 05 05 C5 05 05 C5 05 C5 05 05

0.4666E 0.462OE 0.4573E 0.4526E 0.4479E 0-4432E 0.4384E 0.4336E 0.4289E 0.4241E 0.4152E 0.4144E 0.40F6E 0.4047E 0-3998E 0.3949E 0.3400E 0.385lE 0.38C2E 0.3752E 0.3703E 0e3653E 0.36C3E 0.35f4E 0.35C4E 0e3454E 0.34C4E 0.3354E 0033C3E 0e3253E 0.3203E 0.3153E 0.3102E 0.3048E 0e2958E 0.2947E 092897E 0.2847E 0.2797E 0.2747E 0.2697E 0.2647E

05 05 C5 05 C5 C5 C5 C5 C5 05 C5 C5 C5 05 05 05 C5 05 C5 C5 C5 C5 C5 05 C5 C5 C5 C5 C5 C5 C5 05 C5 05 05 C5 05 05 05 C5 C5 C5

Oot735E Oet668E Cot6COE Oet532E 0 . t464E Oet3S6F Oot328E Oet259E C-ClSOE 006120E O.CO51E 0.5981E 0.5911E 0.5841E 0.5771E C.57COE 0.5629E 0.5558E 0.5487E 0.5416E C.5344E 0.5273E 0.5201E 0.5129E 0.5057E 0.4985E 0e4913E C.4840E 0.4768E 0-46S5E 004623E 0.4550E 094478E 0.4399E 0.4326E 0.4254E 0.4iei~ C.41C9E 0.4037E 0e3964E 003892E 013820E

05 05 C5 05 05 C5 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 05 C5 05 05 05 05 05 05 05 05 05 05 c5 05 05 05 05 05

0.5026E 0.5026E 0.5026E 0e5026E 005026E 0-5026E 0.5026E 0.5026E 0.5026E 0.5026E 0.5026E 0e5026E 0.5026E 0.5026E 0.5026E 0.5026E 005026E 0.5026E 0.5026E 0.5026E 0.5026E 0.5026E 0.5026E 0.5026E 0.5026E 0.5026E 0-5026E 0.5026E 0.5026E 0.5026E 0.5026E 0.5026E 0e5026E 0.5026E 0.5026E 0.5026E 0.5026~ 0.5026E 0.5026E 0.5026E 0.5026E 0e5026E

03 03 03

03 03 03 03 03 03 03 03

03 03 03 03 03

03 03

03 03 03 03 03

03 03 03 03 03 03 03 03

03 03

03 03 03

0e1071E 0.1057E 0.1054E 0.1051E 0.1048E 0.1044E 0.1041E 0.1038E 0.1034E 001031E 0.1027E 0.1024E 0.1020E 001016E 0.1013E 0.1009E 0,1005E 0.1002E 009977E 0.9938E 0.9899E 0.9859E 0.9818E 0.9777E 0.9736E 0.9694E 0.9652E 0.9609E 0-9565E 0-9521E 0.9476E 0.9431E 0.4385E 0.9335E 0.9288E 0.9240E 0.9192E 0.9143E 0.9094E 0.9044E 0.8993E 0-8942E

04 04 04 04 04

04 04 04 04 04 04 04 04 04 04 04 C4 04 G3 03

03 03 03

C3 03 C3 03 03 03 03 03

03 03

03 03 03 03

03 03

BTU/HP

0.3137E 0.3126E 003123E 0.3120E 0.3117E 0-3114E 0.3111E 0.3108E 0.3105E 0.3102E 0.3099E 0.3096E C.3092E 0.3089E 0.3086E 0.33082E 0.3079E 0.3075E 093071E 0.3068E 0.3064E 003060E 0.3056E 0.3052E 0.3048E 0.3044E 0.3040E 093036E 0.3031E 0.3027E 0e3022E 0.3018E 0.3013E 0.3008E C.3003E 0.2'298E 0-2493E 0.2988E 0.2582E 0.2577E 0.2971E 0.2966E

03 03 03 03 03

03 C3 03 03 03 03 03

03 02 03 03 03 03 03 03 03

03 03 03 03

G3 03 03 03 03

03 03 03 03 03 03

C.2t73E 0.26e2~ Oo2tS8E 0.2715E 0.2732E 0.2748E 0.2765E 0.27e2~ 0.2759E 0.281tE 0.2833E 0.2@50E O.?t?67E 0.2ae4~ 0925OlE

07 07 07 07 07 07 07 07

07 07 07 07 07 07 0.2S18F 07 O.ZS35E 07 0.2552E 07 0.2969E 07 0125@6E 07 0.3CC3E 07 0.3C20E C7 C.?C38E 07 0.3C54E 07 0..3072€ 07 0.3089E 07 0-31C6E C 7 0.2123E 07 0.3140E 07 0 . 3 1 5 7 ~ 07 0.3174E C7 0.319l.E 07 0. 32C8E 07 0.3224E 07 0.3241E 07 0.3257E 07 003274E 0 7 0.3250E 07 0-31C7E 07 0.3323E 07 0.3339E 07 0.335CE 07

114 Appendix D

THE SUPEX PROGRAM

The SUPEX computer program i s o u t l i n e d i n block-diagram form i n Fig. D . l .

The i n p u t d a t a r e q u i r e d f o r t h e program a r e g i v e n i n Table

D.l, and t h e o u t p u t r e c e i v e d from t h e computer a r e g i v e n i n Table D . 2 . A complete l i s t i n g of the main program and i t s s u b r o u t i n e s i s followed

by d e f i n i t i o n s of t h e i n t e r m e d i a t e v a r i a b l e s used i n t h e program and t h e s u b r o u t i n e s and t h e i r purposes.

To i l l u s t r a t e t h e u s e of t h e SUPEX pro-

gram, computer p r i n t - o u t s o f t h e i n p u t f o r t h e MSBR steam g e n e r a t o r s u p e r h e a t e r exchanger d i s c u s s e d i n S u b s e c t i o n 4.1 and t h e o u t p u t of t h e SUPEX program a r e p r e s e n t e d .

115

START

READ I N CASE V A R I A B L E S

WRITE OUT CASE V A R I A B L E S

CALCULATE AVERAGE P H Y S I C A L P R O P E R T I E S FOR THE OVERALL EXCHANGER

CALCULATE GEOMETRIC PARAMETERS ASSOCIATED W I T H THE B A F F L E WINDOW

KNOWING THE ALLOWABLE TOTAL PRESSURE DROP ON THE TUBE S I D E , USE THE PRESSURE E Q U A T I O N TO CALCULATE A TUBE S I D E MASS F L O I RATE. CALCULATE A REYNOLDS NUMBER AN0 FROM T H I S A F R I C T I O N FACTOR. S U B S T I T U T E T H I S F R I C T I O N FACTOR I N T O THE PRESSURE E Q U A T I O N TO C A t C U L A T E A NEW TUBE S I D E MASS FLOW RATE; I T E R ATE TO CONVERGENCE. T H I S G I V E S THE F I R S T GUESS AT TUBE S I D E MASS FLOW RATE.

U S I N G THE TUBE S I D E MASS FLOW RATE, E S T I M A T E THE TOTAL NUMBER OF TUBES IN THE EXCHANGER.

1 1

CALCULATE THE GEOMETRIC FACTORS NECESSARY TO CALCULATE THE BERGEL I N FACTORS, THEN CALCULATE THE BERGEL I N FACTORS.

CALCULATE THE TUBE S I D E MASS FLOW RATE FOR AN INTEGER NUMBER

OF TUBES. CALCULATE THE GEOMETRIC PARAMETERS ASSOCI A T E 0 W I T H THE NUMBER OF R E S T R I C T I O N S I N THE WINOOW AN0 CROSS FLOW REGIONS.

S E T TOTAL PRESSURE DROPS, TOTAL B A F F L E S P A C I N G S AN0 TOTAL TUBE LENGTHS TO ZERO.

Fig. D . l .

S i m p l i f i e d Flow Diagram of the SUPEX Computer Program.

116 e

D I V I D E THE TOTAL AMOUNT OF HEAT TO B E TRANSFERRED I N T O EQUAL AMOUNTS FOR EACH INCREMENT.

BASED ON THE TOTAL HEAT TRANSFERRED I N AN INCREMENT, CALCULATE THE D E L T A - T A N 0 D E L T A - H FOR THE SHELL, S I D E F L U I D FOR ANY INCREMENT.

B E G I N THE INCREMENT C A L C U L A T I O N BY C A L C U L A T I N G THE TUBE S I D E F L U I D TEMPERATURE AT THE END OF THE INCREMENT. ~

CALCULATE THE LOG-MEAN-DELTA

T FOR THE INCREMENT

C A L C U L A T E THE TUBE WALL RES ISTANCE CALCULATE THE TUBE S I D E F I L M R E S I S T A N C E C A L C U L A T E THE LENGTH OF THE INCREMENT CALCULATE THE TUBE S I D E D E L T A - P FOR THE INCREMENT CALCULATE THE ALLOWABLE D E L T A - T ACROSS THE TUBE WALL BASED ON STRESS CONS IDERAT I O N S CALCULATE THE SHELL S I D E D E L T A - P FOR THE P A R T I C U L A R B A F F L E SPACE SUM THE TUBE S I D E D E L T A - P ' S SUM THE TUBE LENGTHS

F i g . D. 1.

(continued)

117

P ( S D P T ) AND THE ALLOWABLE TUBE S I D E DELTA-P (DELPTA)

ETWEEN THE TOTAL SHELL S I D E DELTA-

IS W I T H I N 3% OF

ALL OF THE HEAT HAS BEEN TRANSFERRED--THE TOTAL PRESSURE DROPS ON BOTH TUBE AND SHELL S I D E ARE W I T H I N L I M I T S . WE HAVE AN ACCEPTABLE SOLUTION. WRITE OUT THE RESULTS.

Fig. D.l.

(continued)

118

Table D.l. Card

Columns

1-10 11-20 2 1-30 31-40

F10.5 F10.5 F10.5

Format

Computer I n p u t Data f o r SUPEX Program Variable

Term

Units

DTO THK P N

in. in. in.

I10

Tube o u t s i d e d i a m e t e r Tube w a l l t h i c k n e s s Tube p i t c h Number o f increments

1-10 11-20 21-30 31-40

F10.1 F1O.l F10.1 F10.1

S a l t i n l e t temperature S a l t o u t l e t temperature Steam i n l e t t e m p e r a t u r e Steam o u t l e t t e m p e r a t u r e

TH1 TH2 TC 1 TC 2

OF OF OF OF

1-10 11-20 21-30

F1O.l F1O.l F1O.l

PC 1 PC2 DELPSA

psi psi psi

31-40

F10.5

Steam i n l e t p r e s s u r e Steam e x i t p r e s s u r e Allowable t o t a l s h e l l s i d e p r e s s u r e drop Bypass l e a k a g e f a c t o r f o r p r e s s u r e drop

1-20 21-40 41-60 61-70

E20.6 E20.6 E20.6 F10.5

Mass flow r a t e o f steam Mass flow r a t e of s a l t Total heat t r a n s f e r r a t e Bypass l e a k a g e f a c t o r for heat t r a n s f e r

1-10 11-20

F10.5 F10.5

CPH TCH

21-30

F10.5

S p e c i f i c heat of s a l t Thermal c o n d u c t i v i t y o f s a l t (hot fluid) Estimated number o f b a f f l e spaces

1-10 11-20

F10.5 F10.5

21-30

F10.5

F r a c t i o n a l window c u t Estimated t o t a l t u b e length Estimated b a f f l e s p a c i n g

BLFP

WH QT BLFH

lb/hr lb/hr Btu/hr

B t u / l b OF Btu/ft*hr*OF

GNB

SXG

BSG

119 T a b l e D.2.

Output Data From SUPEX Computer Program Va r i a b 1e

Term

Units

F o r Each B a f f l e Space J

B a f f l e number

IBK( J)

I n c r e m e n t number o f f i r s t i n c r e m e n t which l i e s completely i n b a f f l e space J

DELTW (J)

C a l c u l a t e d temperature drop a c r o s s t u b e w a l l

DELTWA (J)

Allowable temperature drop a c r o s s t u b e w a l l based on a l l o w a b l e s t r e s s

TWALL(J)

Temperature o f w a l l m a t e r i a l

DELPS (J)

C a l c u l a t e d s h e l l - s i d e p r e s s u r e drop f o r t h e b a f f l e space

psi

DHOT (J)

Mean d e n s i t y o f h o t f l u i d ( s a l t ) f o r t h e b a f f l e space

lb/ff?

VHOT ( J )

Mean v i s c o s i t y o f h o t f l u i d ( s a l t ) f o r t h e b a f f l e space

lb/ft *hr

O F

For Each Increment

Increment number

Tube l e n g t h f o r t h e increment

TH(I)

Temperature o f h o t f l u i d ( s a l t )

TC(I)

Temperature o f c o l d f l u i d (steam)

PC(1)

P r e s s u r e o f c o l d f l u i d (steam)

psi

DELP ( I)

Tube p r e s s u r e d r o p f o r t h e increment

psi

RI (1)

Thermal resistance o f inside film for the

'F/ Btu

increment RW( 1)

Thermal r e s i s t a n c e o f w a l l m a t e r i a l f o r t h e increment

h r OF/Btu

RO( 1 )

Thermal r e s i s t a n c e o f o u t s i d e f i l m f o r t h e b a f f l e s p a c e i n which t h e increment l i e s

h r * OF/Btu

RT(I)

T o t a l t h e r m a l r e s i s t a n c e between h o t and c o l d f l u i d s f o r t h e increment

hr*OF/Btu

F o r t h e E n t i r e Exchanger NLJMT

T o t a l number o f t u b e s

NBS

T o t a l number o f b a f f l e s p a c e s

B SL

Length o f a b a f f l e s p a c e

I n s i d e d i a m e t e r o f exchanger s h e l l

in.

120

T a b l e D.2 ( c o n t i n u e d ) ~~

Units

Variable SDPT

T o t a l p r e s s u r e drop i n t u b e s

psi

SDPS

T o t a l p r e s s u r e drop i n s h e l l

psi

DTLME

Log-mean d e l t a - T

O F

Total tube length

AREAX

T o t a l h e a t t r a n s f e r a r e a based on t o t a l t u b e length

ft?

UEQX

O v e r a l l h e a t t r a n s f e r c o e f f i c i e n t based on t o t a l tube length

Btu/hr*ft"

SBS

T o t a l b a f f l e space length

AREAB

T o t a l h e a t t r a n s f e r a r e a based on t o t a l b a f f l e space length

ft2

UEQB

O v e r a l l h e a t t r a n s f e r c o e f f i c i e n t based on t o t a l b a f f l e space l e n g t h

Btu/hr*ft"

* O F

The SUPEX Program Listing

**FTN ,L T G , EvMo PROGRAM SUPEX T Y P E R E A L NEW D I M E N S I O N T C ( 2 0 1 J , TH( 2 0 1 ) ,PC ( 2 0 1 1 (HC ( 2 0 1 J 9 l D E L P S ( 100) ,RW( 2 0 1 J (RI ( 2 0 1 1 r R O ( l O O 1 ( R T ( 2 0 1 J r U ( 2 0 1 1 9 2X ( 20 1J 9 DELP ( 2 0 1 1 ,DELTWA ( 100 1 ,DELTW( 100 1 , I B K ( 100 1 3DHOT( 50 J ,VHOT( 50 J 9 T k A L L ( 50) CALL S V H ( ~ V P V T T V T H J READINPUTTAPE~O~~O~~,DTO*THKTP,N READ I N P U T T A P E 5 0 1 1008 9 TH1, TH2 9 TC 19 TC2 READINPUTTAPESO, 1OC9,PC 1, PC2 9DELPSA B L F P READINPUTTAPE50,lOlOtWCtWHtQTIBLFH READINPUTTAPESO, 1 0 1 2 r C P P , TCH rGNB READ I N P U T T A P E 5 0 10 11 P W SXG T B SG D EL P T A=P C 1-PC 2 LOPl=O LOP2=0 LOP3=0 LOP4=0 LOP5=0 LOP6=0 LOP7-0 LOP8=O LOP9=0 LOPlO=O L O P 1 1=0 DELTH=QT/( WH*CPH J DTPB=DELTH/GNB CALL R I T E l ( DTOeTHK T P t N, T H l r T H 2 9 T C l v T C 2 PC 1pPC2 ,DELPTA ,DELPSA, WC, WHt UT ,CPH,TCHTP W V B L F P TB L F H ,GNB,BSG, SXG J 1 BSL = B S G D T I = ( DTO-Z.O*THK I / 12.0 P=P/1200 DTO=DTO/l2oO

SUPEX 10 SUPEX 20 SUPEX 30 SUPEX 3 1 SUPEX 32 SUPEX 33 SUPEX 40 SUPEX 50 SUPEX 60 SUPEX 70 SUPEX 80 SUPEX 90 SUP€ 100 SUP€ 110 SUPE 120 SUPE 130 SUPE 140 SUPE 150 SUP€ 160 SUPE 170 SUPE 180 SUPE 190 SUPE 200 SUPE 210 SUPE 220 SUPE 230 SUP€ 240 SUPE 250 SUPE 2 5 1 SUP€ 260 SUPE 270 SUPE 280 SUPE 290

T C A V = ( T C 1 + T C 2 1 / 2 .O PCAV=(PCl+PC21/2.0 C A L L S V H ( 2 r P C l r T C 1 , SPV1,DUMI CALL S V H ( ~ T P C ~ ~ T C ~ ~ S P V ~ ~ O U M ) C A L L S V H ( 2 9 P C A V v TCA V, SP VAV 9 DUM) S P V G = ( 2.0* ( S P V l + S P V A V ) + SP V 2 I /5.0 C A L L V ISCOS ( T C 1, PC 1 9 V I S 1 I C A L L V I S COS( TC 2 t PC 2 t V I S 2 1 CALL VISCOS( TCAVvPCAVt V I S A V ) V I S G = ( 2.0*( V I S 1 + V I S A V I + V I S2 1 / 5 . @ C FG=O e 0 1 4 THETAL = 0.8 PERCL = (THETAL 005*SINF(2.0*THETAL))/3.14159 THETAU = 1.5707 PERCU =(THETAU O . S * S I N F ( 2 . 0 * T H E T A U ) I/3.14159 NEW = T H E T A L + (PW -PERCLI*(THETAU -THETALI/(PERCU PNEW = (NEW @.5*SINF(2oO*NEW) I/3.14159 E P N E W = A B SF ( P W- PNE W 1 IF(EPNEW-O.OOlI4r4~2 T H E T A L =NEW P E R C L = PNEW LOP11=LOP11+1 IF(LOPll-1011~1t3 WRITEOUTPUTTAPE519 1 0 2 2 r L O P l l GOT080 THETAC = THETAL G=3600.O*SQRTF((DELPTA*64.4*144. O*DTI )/(CFG*SXG*SPVG) R E G = C T I * G / V I SG

3 4

C F C = ( 0 o 0 0 1 4 0 + ( 0 ~ 1 2 5 / ~ R E G * * O o 3 2 1I ) * 4 o C 6

DIFA=ABSF(CFC-CFGI I F ( D I F A - O ~ O ~ * C F C I ~ V ~ ~ ~ CFG=CFC L O P l = L O P 1+1 I F( L O P 1- 10 I 89 8 9 7 WRITEOUTPUTTAPE51,1013rLOPl GOT080

-PERCL1

SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUP€ SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE SUPE

300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530

540 550 560 570 580 590 600 610 620 630 640 650

N N

8 9

CONTINUE GOT0 5 N UMT=X I N TF ( WC*400/ ( G* 3 14 168 D T I **2 1 BNUMT=FLOATF(NUMT) LOPlO=O DS=P*SQRTf ( 4oO*BNUMT*Oo 8 6 6 / 3 1 4 16 1 XBAR = (DS/2*01*(THETAC Oo5*SINF(ZoO*THETAC) -( 2 OS ( S I N F ( THETAC ) * * 3 * 0 1 /3 01 / ( THETAC-0- 5 *S I NF ( 20O*THET AC 1 1 1 B R L l = BSL / ( D S - 2 * C * X B A R ) GBRL = O o 7 7 * B R L l * * ( - O o 1 3 8 ) AW=PW*3o 1 4 1 6 * D S * * 2 / 4 * 0 A X = ( 3 1416*DS**2 /4.0 )-A k THETA=( 1050*( 3 1416-( 4. @*AX/DS**Z 1 ) 1 **0.333 AXC=( 30 1 4 1 6 - T H E T A + ( SI NF ( 2 * 0 * T H E T A ) / 2 0 )) * D S * * 2 / 4 * 0 DIFB=ABSF(AXC-AX) IF(DIFB-O*02*AXlI,5~15r12 T H E T A 2 = ( lo50*(3ol416-(4oO*AXC/DS**2) 1 l**C0333 AXC2=( 3 0 1 4 1 6 - T H E T A 2 + ( S I N F ( 2 o O*THETA2 1 / 2 * 0 1 I * D S * * 2 / 4 o O THETA=( AX-AXC 1 * ( TH ETA2-THETA 1 / ( A XC2-AXC 1 + THETA LOPZ=LOP2+1 IF(LOP2-10)14r14r13 WRITEOUTPUTTAPE519 1 0 1 4 9 LOP2 GOT080 CONTINUE GOT011 GC=4.0*WC/(BNUMT*3.1416*DTI**Z) X B=DS*CO SF ( THETA 1 / 2.@ CNB=2oO*XB/( 0 0 8 6 6 * P ) XH=( D S / 2 o O ) - X B CNW= ( X H / (0 R 6 6 4 P ) ) - l o 0 XC=DS*SINF(THETA) PCFB=(P-DTOI/P SBK=PCFB*(DS+XC)/Z.O SW=PW*BNUMT*(Oo866*P**Z-( 3o1416*0T0**2/4*0) ) S DPT=Oo 0 SDPS=O,@ LOP8=0

13 14

SUPE 660 SUPE 670 SUPE 6 8 0 SUPE 690 SUPE 700 SUPE 710 SUPE 720 SU PE 7 2 1 SUPE 730 SUPE 740 SUPE 7 5 0 SUPE 760 SUPE 770 SUPE 780 SUPE 790 SUPE 800 SUPE 8 1 0 SUPE 820 SUPE 830 SUPE 840 SUPE 850 SUPE 860 SUPE 8 7 0 SUPE 880 SUPE 890 SUPE 900 SUPE 910 SUPE 920 SUPE 930 SUPE 940 SUPE 9 5 0 SUPE 960 SUPE 970 SUPE 980 SUPE 990 SUP 1000 SUP 1010

MS=1

sx=o

SBS=O TC( 1I = T C 2 TH( 1) = T H l R WK= DTO*LOGF( DTO/DT II / 20 0 PC( 1) = P C 2 C A L L SVH ( 2 r P C 2 r T C 2 r DUM. HC ( 1 I 1 BN=FLOATF(NI QX=QT/BN DECT=QX/ 4 WH*CPH 1 DECH=QX/WC

1=1 K=l 16

17 18 19

20 21

SB = SBK*BSL LOP7=0 TCON=TH( I )-DTPB/Zo 0 D E N H z 1 4 1 3 8 E +OC-2 466E-O2*TCON V ISH=O .2 122E+CO*EXPF( 4 0 3 2 .CE+OO/ DHOT(KJ=DENH VHOT ( K 1 = V I SH C O N l = ( C P H * V I SH/TCH I * * O o 6 6 7 E + 0 0 GM= W H/ SI3 RECB=CTO*GM/VISH IF(RECB-800.0) 179 1 8 9 1 8 HJB=O 5 7 1/( RECB**@ 4 5 6 ) GOT019 H J 8 = 0 0 3 4 t / ( RECB**@. 3 8 2 I HB=HJB*CPH*GM/CONl G W= WH/ SW GS=SQRTF(GM*GW 1 R ECW=DTO*GS/ V I SH IF(RECW-800.0I20r21r21 HJW=O 571/ ( R EC W**O 4 5 6 I GOT022 HJW=C!o 34C/ ( R E C W**O 382 1

(TCON+460.OE+00 )

SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP

1020 1030 1040 1050 1@60 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1350 1360 1370

25 26

HW=HJW*CPH*GS/CONl SUP HO=(HB*( l.O-Z,O*PW)tHW*(Z.O*PW) )*BLFH SUP HO = HO*GBRL SUP RO( K ) = l o O/HO SUP T H ( I + l ) = T H ( I )-DECT SUP LOP5=0 SUP HC( I + l ) = H C ( I ) - D E C H SUP OELP P=Oo 0 SUP PC( I + l ) = P C ( I )+DELPP SUP LOP3=0 SUP L OP 4=0 SUP T C ( I + l ) = T C ( 1)-DECH SUP C A L L S V H ( Z t P C ( I+1)t T C ( I + 1 )t D U M t H C G l SUP EH=ABSF( HC( 1+1I-HCG I SUP SUP I F ( EH-0 00 1* HC 4 I + 11 1 3 1t S 17 2 6 TRIAL=TC(I+l) SUP HRIAL=HCG SUP T C ( I + 1 ) =TC ( I + 1 ) +( HC ( I + 1I-HCG ( TC ( I1 -TC ( I + 1) 1 / ( HC ( 1 -HCG 1 SUP C A L L $ V H ( 2,PC( I + l ) t T C ( I+1)(DUMtHCG) SUP EH=ABSF( H C ( I + l ) - H C G I SUP IF(EH-O.OOl*HC(I+l) )31,31t28 SUP SUP TNEXT=TC ( I + 1 )+ I HC( I + l ) - H C G ) * (TC ( I+1)- T R I A L ) / (HCG-HRI A L 1 TRIAL=TC(I+l) SUP HRIAL=HCG SUP TC( I + l ) = T N E X T SUP L OP3=LOP3+1 SUP SUP I F ( LOP3- 10 1 3 0 9 30 t 29 W R I TEOUTPUTTAP E5 1 , 1 0 1 5 , L O P 3 SUP GOT080 SUP GOT027 SUP DENOM=(TH( I + l ) - T C ( i t 1 1 ) / ( T H ( I ) - T C ( I 1 ) SUP TDEN=ABSF( DENOM-1.0 I SUP I f ( T DEN-G. 0 5 I 3 2 t 3 3 9 3 3 SUP DELTLM=0.5E+OO*(TH( I+l)-TC(I+l)+TH(I )-TC(I) I SUP GO TO 34 SUP DELTLM=( TH( I + l ) - T C ( I+1) - T H ( I I + T C (I) 1 /LOGF ( ( T H ( I + l ) - T C ( I + 1 ) I / ( T H ( I ) S U P 1-TC ( I 1 I I SUP

27 28

30 31

32 33

1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490

1500 1510 1520 1530 1540

1550 1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660 1670 168C 1690 1700 1710 1720 1730 1731

CONTINUE TM=(TC(I+lI+TC(II)/2.0 PM=( P C ( I + 1 I + P C ( 1 ) I / Z O O C A L L S V H ( 21 P M T TM I S P V B TH F B ) PM=(PC( I + l I + P C ( I ) I / 2 . 0 C A L L V I S COS ( TM T P M T V I SB TW=TM+O 2 3 * D E L T L M TCW=0.006375*TW+4.06 RW( I I = R W K / T C W DTFM=O.l*DELTLM TMS=TM+DTFM C A L L S V H ( ~ T P M T T M SSTP V I T H F I I C A L L C O N D T ( T M S T P M T T C F I1 C A L L V I SCOS( TMST PM T V I S F 1 ) CRE=( C T I * G C / V I S F I )**0.923 C P R = ( ( ( H F I - H F B I / ( T M S - T M I ) * ( V I S F I / T C F I 1 I**0.613 C S V = ( SPV B / S P V I I **O 2 3 1 H I =O .0@459*( T C F I / D T I I *CRE*CPR*CSV R I ( I I=DTO/(HI*DTI) R T ( I I =RO ( K 1 +RW ( I ) + R I( I 1 DTFMC=RI(I)*DELTLM/RT(I 1 I F ( A B S F ( DTFM-DTFMC ) - 0 * 0 3 * D T F M C I 3 9 ~ 3 9 ~ 3 6 D T F M 2 = ( DTFM+DTFMC I *.5 TMS Z=TM+DTFMZ C A L L S V H ( 2 T P M f TM S 2 T SP V I 2 T H F I 2 I C A L L CON DT ( T M S 2 9 PM T T C F I 2 I C A L L V I S C O S ( T M S ~ T P M T V I S F2 I) CRE2=( D T I * G C / V I S F I 2 ) * * 0 . 9 2 3 C PR 2= ( ( ( HF I 2-H F B I / ( TM S 2-TM I ( V I SF I 2 / T C F I 2 I I **O C S V 2 = ( S P V i 3 / S P V I 2 )**0.231 H 2 I =O. 00 4 5 9 * T C F I 2 * C R E 2*CPR2*C S V 2 /DT I R 2 I = CTO/ ( H2 I * D T I I RZT=RO(KI+RW(I I + R 2 I DTFMCZ=R 2 I * D E L T L M / R 2 T SLOPE=(DTFMC-DTFMCZ)/(DTFM-DTFMZI DTFM=(DTFMC-(SLOPE+DTFMI I / ( l . O - S L O P E I

6 13

SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP

1740 1750 1760 1770 1780 179C 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 192@ 1930 1940 1950 1960 1970 1980 1990

200@ 2010 2020 2030 2040

2050 2060 2070 2080 2090

w h,

37 38 39

40 41 42 43 44

45 46

LOP4=LOP4+ 1 I F ( LOP4-10 I 3 8 13 8 1 3 7 W R I TEOUTPUTTAPE5 It 10161L O P 4 GOT080 CONTINUE GOT035 U( I )=loO/RT( I ) X ( I J=QX/( BNUMT*3o 1 4 1 6 * D T O * U ( I 1 * D E L T L M I RE=DTI*GC/VISB C F I = O . O 0 1 4 0 + 0 o l 2 5 / ( R E * * ~ o 32) D E L P ( I J = ( 4 o O * C F I * X ( I J / D T I ) * G C * * 2 o O * S P V B / ( 6 4 o 4 ~ 3 6 O O o * ~ 2 . ~ ~ 4 4 oJO D I F C = A B S F ( D E L P ( I J-DELPP J I F ( D I F C - G o 0 5 * D E L P ( I )43943140 DELPP=DELP( I ) LOP5=LOP5+1 I F ( LOP 5- 10 J421 4 2 r 4 1 WRITEOUTPUTTAP E 5 1 1 1 0 1 7 9 L O P 5 GOT080 CONTINUE GOT024 I F ( M S 153 9 531 44 IBK(KJ=I TW= ( R I ( I J+Oo 5*RW ( I 1 1 ( T H ( I I TC ( I 4 1 / R T ( I ) + TC ( I ) ALPHA=(OoO031*TW+5o 9 1 ) E T W = 3 1 * 6 5-00 00 5*TW C O N 2 = A L P H A * E T k / ( 1,4*LOGF( D T O / D T I 1 ) CON3=1.0-(2.O*DT0**2*LOGF(DTO/DTI )/(DTO**Z-DTI**2)) CON3=CON3*(-l0 I IF(TW-lCl5o3 J45.46~46 B=24000,0 SL=705 GOT047 B=5700@.C SL=4C0O C O N 4 = 3 0 * ( B- SL*T W )-26O(?C C TWALL(KJ=TW D E L T W A i K )=CON4/(CON2*CON3 1 DELTW(KI=RW( IJ*c(TH( I ) - T C ( I ) ) / R T ( I )

SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP

2100 2110 2120 2130 2140 2150 2160 2170 2180 2190 2200 2210 2220 2230 2240 2250 2260 2270 2280 2290 2300 2310 2320 2330 2340 2350 2360 2370 2380 2390 2400 2410 2420 2430 2440 2450 2460 2470

IF( I-1151.51.49 IF(N-1)51,51,50 BWN=l.O

48 49 50

GOT052 BWN=O. 5 DELPSB=0.6*CNB*(GM/3600.0~**2/~64.4*144.O*DENH~ DELPSW=BWN~~2.0+0.6~CNW~~~GS/36@0.0~~~2/~64.4~144.0~DENH~ DELPS(K)=(DELPSB+DELPSWJ*BLFP SDPS=SDPS+DELPS(K) SBS = SBS+BSL SDPT=SDPT+DELP ( 11

51 52

SX=SX+X(IJ IF(N-I162r62.54 I=I+l IF( SBS-SX) 58,5a,

55 MS=0 LOP7=LOP7+1 IF(LOP7-30157,57,56 WRITEOUTPUTTAPE5lr101arLOP7 GOT080 CONTINUE GOT023

56 57 58

MS=1

K=K+l CONTINUE Lopa=Lopa+l

IF(LOP8-30)61,61,60 60

WRITEOUTPUTTAPE51,10l9,LOPa GOT080 CONTINUE

GOT016 62

EDPT=ABSF(SDPT-DELPTAJ IFtEDPT-0.03*DELPTA166,66.63 NUMT=XINTF(BNUMT*(SDPT/DELPTA1**0.35) LOP9=LOP9+1 IF(LOP9-10)65,65,64 WRITEOUTPUTTAPE5lrlO2O,LOP9 GOT0 a0

(

sup SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP

2480 2490 2500 2510 2520 2530 2540 2550 2560 2570 2580 2590 2600 2610 2620 2630 2640 2650 2660

SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP sup SUP sup sup sup sup sup sup

2670 2680 2690 2700 2710 2720 2730 2740 2750 2760 2770 2780 2790 2800 2810 2820 2830 284c 2850

, (

SUP 2 8 6 0 CONTINUE SUP 2 8 7 0 BSG=BSL SUP 2 8 8 0 GOT0 10 66 EDPS = ABSF(SDPS DELPSA) SUP 2 8 9 0 0*03+DELPSAJ70,70,67 SUP 2 9 0 0 IF(EDPS 67 BSL = BSL*SQRTF( SDPS/DELPSAJ SUP 2 9 1 0 LOP10=LOP10+1 SUP 2 9 2 0 SUP 2930 I F ( L O P I O - 1 0 1 6 9 ~ 6 %68 68 WRIT EOUT PUTTAP E5 1T 102 1T LOP 10 SUP 2940 GOT080 SUP 2 9 5 0 69 CONTINUE SUP 2 9 6 0 GOT015 SUP 2970 70 CONTINUE SUP 2 9 8 0 CALL R I T E 2 SUP 299C J=O SUP 3000 71 JN=J+1 SUP 30 10 JNC=49+J N SUP 3020 IF(JN.GT*K) GO TO 7 3 SUP 3030 WRITEOUTPUTTAPE5 1 9 100 1 SUP 3040 100 1 FORMAT( l H l , / / ? 3x9 1 H J , 5 X 1 5 H l S T - I 9 ~ X ~ ~ H D E L T - W ~ ~ X ~ ~ H D E L T - W - A T ~SUP X T 3050 1 6HT-WALL T 3x1 6HDELP-St 3 x 1 6HDENS-H,3 X & H V I SC-H 1 SUP 3 0 5 1 W R I TEOUTPUTTAP E 5 1 1 0 0 2 SUP 3060 1002 FORMAT( 1H , 4 ( l H - ) , 3 X , 6 ( 1 H - J r 3 X 1 7 o r 3 X 1 8 ( 1 H - ) , 3 X ~ 8 ( ~ H - ) ~ 4 ( 3 X , 6 ( l H - ) ) ~ / ~ SUP 307@ NBS = K SUP 3080 DO 7 2 J=JN,K,l SUP 3090 W R I T E O U T P U T T A P E ~ ~ ~ ~ O O ~ , J ~ I B K ( J ~ T D E L T W ~ J ) , D E L T W A ~ J ~ ~SUP T ~ A3100 LL~J~~ 1 OELPS ( J J DHOT( J J ,VHOT( J 1 SUP 3101 SUP 3110 1 0 0 3 FORMAT( 1 5 9 3 X * 1 6 ~ 3 xF7.2 1 , 3 X * F 8.2 ~ 2 ( 3 X rF6e 1 93X~F6.3 J ) IF(J.EQ*JNC) GO TO 7 1 SUP 3 1 2 0 72 CONTINUE SUP 3130 73 CONTINUE SUP 3140 CALL R I T E 3 SUP 3 1 5 0 I =c) SUP 3160 74 IN=I+l SUP 3170 INC =49+ I N SUP 3 1 8 0 SUP 3190 I F ( I N * G T . N J GO TO 7 6 W R I TEOUT PUTTAP E5 1 , 1 0 0 4 SUP 3 2 0 0 65

+ N

SUP 1004 FORMAT ( 1 H 1 9 / / T 3 x 9 1 H I 9 5 X 96HLENGTH 9 4 x 9 5HT-HOTq 5 X ~ ~ H T - C O L D I ~ X ~ SUP 1 6HP-CO L D 9 4 X 9 6HDE L P-C 9 4 X 9 6HR ES- I N 9 4 X 9 8HR ES- hAL L 94X T 7 HRES-OUT 9 2 4 X 9 7HR ES-TOT I SUP W R I TEOUTPUTTAPE519 l C 0 5 SUP 1005 FORMAT( 1 H ,5(1H-Ir3X16(1H-I13X,2(7(lH-) , 3 X I ~ 8 ( 1 H - ) r 3 X ~ 6 ( 1 H - ) r SUP 1 4( 3 x 9 8 ( 1H- I 1 9 / I SUP DO 7 5 I = I N , N v l SUP SUP RO( I ) = R T ( I I - R I ( II - R W ( I) WRITEOUTPUTTAPE519 10069 1, X ( I I 9 T H ( I ) r T C ( I ). P C ( I I r D E L P ( II 9 R I ( I I T SUP 1 RW( II r R O ( I J r R T ( II SUP 1006 F O R M A T ( I ~ ~ ~ X ~ F ~ . ~ T ~ X t F ~8 . ~1 9( 3FX 9~ F.6 .~3 9 , 4~ ( 3X XI9 F 8 . 6 I I SUP SUP I F ( 1 o E Q a I N C I GO TO 74 SUP 75 CONTINUE 76 CONTINUE SUP AREAX= BNUMT* SX*3 14 16*DTO SUP D ENOM=( TH1-TC2 I / ( TH2-TC 1) SUP TDEN=ABSF( DENOM-1.0 I SUP SUP I F ( T DEN-0 0 5 1 77 9 7 8 9 7 8 SUP 77 DTLME=O* 5E+OC*( T H L - T C Z + T H 2 - T C l ) GO TO 79 SUP 78 CONTINUE SUP SUP DTLME=(THL-TC2-THZ+TClI/LOGF( (THl-TCZI/(TH2-TCl) I 79 CONTINUE SUP SUP UEQX=QT/ ( AREAX*DTLME I SUP AREAB=AR EAX*SBS/SX UEQB=QT/ ( AREABsDTLME 1 SUP DS=DS*lZoO SUP ~ C A L L R I T E 4 ( NUMT, DST S D P T TS C P S ~ D T L M E I S X I A R E A X I U E Q X ~ S B S ~ A R E A B ~ U E Q BSUP SUP 1 NBSvBSL) SUP 80 CONTINUE SUP C A L L EX I T SUP 1007 FORMAT ( F 10.57 F 10.5 9 F 1 0 * 5 9 I 1 0 1 SUP 1 0 0 8 FORMAT( 4 F 1 0 . 1 ) 1009 FORMAT( F l O ~ l ~ F 1 @ ~ 1l , ~F lFO ol 5O) ~ SUP 1010 FORMAT( E 2 0 . 6 9 E 2 0 . 6 9 E Z O ~ C ~ F l O * 5 ) SUP SUP 1011 FORMAT( 3 F l O o 5 ) SUP 1012 FORMAT( 3 F 1 0 . 5 )

3210 3211 3212 3220 3230 3231 3240 3250 3260 3261 3270 3280 3290 3300 3310 3320 3330 3340 3350 3360 3370 3380 3390

3400 3410 3420 3430 3440 3441 3450 3460 3470 3480 3490 3500 3510 3520

FORMAT(8H FORMAT(8H FORMAT(8H FORMAT(8H FORMAT(8H FORMAT(8H FORMAT(8H FORMAT(8H FORMAT(9H 1022 FORMAT(9H END

1013 1014 1015 1016 1017 1018 1019 1020 1021

LOP LOP LOP LOP LOP LOP LOP LOP LOP LOP

1 =I41 2 =I41 3 =I41 4 =I4) 5 =I41 7 =I41 8 =I4J 9 =I41 10 =I41 11 = I 4 1

SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP SUP

SUBROUT I N E R I T E 1 ( D T O , T H K , P T Nv T H 1 1 T H 2 r T C l , T C 2 t P C l r P C 2 9 DELPTA, D E L P S A t WC 9 WHp QT TCPH, TCHIP W 96L FP, B L F H rGNB 9 BSG SXG J W R I TEOUTPUTTAP E 5 1 * 1 0 0 1 WRITEOUTPUTTAP E 5 1 9 1C02, D T C WRITEOUTPUTTAPE519 1003, THK W R I TEOUTPUTTAP E 5 1 9 1004 9 P W R I T EOUT PUTTAP E5 1,109 5 9 N WR I TEOUTPUTT AP E 5 1 1006 9 TH 1 WRITEOUTPUTTAPE51, 1 0 0 7 9 T H 2 WRITEOUTPUTTAPE51,1!l@8,TCl W R I TEOUTPUTTAP E5 1 , 1 0 0 9 , TC 2 WRI TEOUTPUTTAP E 5 1,1010 P C 2 W RX TEOUTPUTTAP E 5 1, 1 0 11, DE L P T A WRI TEOUTPUTTAP E 5 1,1012 9 DELPSA W R I T E O U T P U T T A P E 5 l r l e 1 3 9 WC WRITEOUTPUTTAPE51,1014,hH WRITEOUTPUTTAPE51,1015rQT WR I TEOUTPUTTAP E5 1 , 1 0 1 6 9 CPH WRI TEOUTPUTTAP E 5 1 9 10179 TCH W R I TEOUTPUTTAP E 5 1 , 1 0 1 8 PW WRITEOUTPUTTAPE51,1019, B L F P

3530 3540 3550 3560 3570 3580 3590 3600 3610 3620 3630

R I T E l 10 R I T E l 11 R I T E l 20 R I T E l 30 R I T E l 40 R I T E l 50 R I T E l 60 R I T E 1 70 R I T E l 80 R I T E l 90 R I T E 100 R I T E 110 R I T E 12C R I T E 130 R I T E 140 R I T E 150 R I T E 160 R I T E 17@ R I T E 180 R I T E 190 R I T E 200

w w

WRITEOUTPUTTAPE5lr 1 0 2 0 r B L F H RITE NBSR = I F I X ( G N B ) RITE RITE W R I TEOUTPUTTAP E 5 1 , 1 0 2 1 9 NB SR WRITEOUTPUTTAPE5lrlC22rBSG RITE WRITEOUTPUTTAPE51,1O23, S X G RITE RETURN RITE 1001 FORMAT( l H 1 , / / , 2 4 X , 6 9 H * THE FOLLOWING I S THE I N P U T I N F O R M A T I O N R I T E 1 FOR T H I S PROBLEM *,///I RITE 1002 FORMAT( 1 H r 3 6 H O U T S I D E D I A M E T E R OF TUBES ( I N C H E S ) = r F 6 . 3 ) RITE 1003 FORMAT( l H 0 9 3 0 H T U B E WALL T H I C K N E S S ( I N C H E S ) = ~ F 7 . 4 ) RITE 1004 FORMAT( l H O r 2 1 H T U B E P I T C H ( I N C H E S ) = rF7.4) RITE 1 0 9 5 FORMAT( l H 0 v 5 8 H N U M B E R OF INCREMENTS I N T O WHICH THE EXCHANGER I S D I V R I T E lIDED= ~ 1 4 r / / ) RITE 1006 FORMAT( 1 H 0 , 3 t H I N L E T TEMPERATURE OF H C T F L U I D ( F ) = r F 7 . 1 ) RITE RITE 1007 FORMAT( l H O r 3 7 H O U T L E T TEMPERATURE OF HOT F L U I D ( F ) = 1 F 7 . 1 ) 1008 FORMAT( 1 H O r 3 7 H I N L E T TEMPERATURE OF CCLD F L U I D ( F ) = r F 7 . 1 ) RITE 1009 FORMAT( 1 H O r 3 8 H O U T L E T TEMPERATURE OF COLD F L U I D ( F ) = , F 7 o l ~ / / ) RITE 1010 FORMAT(lHO,37HOUTLET PRESSURE OF COLD F L U I D ( P S I ) = vF7.1) RITE 1011 F O R M A T ( l H O r 5 0 H A L L O k A B L E TOTAL PRESSURE DROP CN TUBE S I D E ( P S I ) = 9 R I T E 1 F7.1) RITE 1 0 1 2 F O R M A T ( l H O , 5 1 H A L L O k A B L E T C T A L PRESSURE DRCP CN SHELL S I O E ( P S I ) = r R I T E 1 F7.1~//) RITE 1013 F O R M A T ( l h O v 3 8 H M A S S FLOW RATE OF CCLD F L U I D ( L B / H R ) = r l P E 1 0 . 3 ) RITE 1014 FORMAT( ~ H O T ~ ~ H M AFLOW S S RATE OF HOT F L U I D ( L B / H R ) = r l P E 1 0 . 3 ) RITE 1015 FORMAT( l H O v 3 5 H T O T A L HEAT TRANSFER RATE ( B T U / H R ) = r l P E 1 0 . 3 ) RITE 1016 FORMAT( l H O r 3 9 H S P E C I F I C F E A T OF HCT F L U I D ( B T U / L E - F ) = rF6.3) RITE 1017 FORMAT( l H O r 4 9 H T H E R M A L C O N D U C T I V I T Y OF HOT F L U I D ( B T U / H R - F T - F ) = 9 RITE 1 F6.3) RITE 1 0 1 8 FORMAT( l H O r 2 3 H F R A C T I O N A L kINDOW CUT= r F 5 + 2 r / / ) RITE 1019 FORMAT( l H O r 3 7 H B Y - P A S S LEAKAGE FACTOR FOR PRESSURE= r F 6 . 3 ) RITE 1020 FORMAT( ~ H O I ~ ~ H ~ Y - P A LEAKAGE SS FACTOR FOR HEAT TRANSFER= , F 6 . 3 r / / ) RITE 1 0 2 1 F O R M A T ( l H O , 5 0 H E S T I M A T E OF THE NUMBER OF B A F F L E SPACES REQUIRED= T R I T E 1 13) RITE 1 0 2 2 FORMAT( l H 0 , 4 6 H E S T I M A T E OF THE LENGTH OF A B A F F L E S P A C E ( F T I = r F 5 . 2 ) R I T E RITE 1 0 2 3 FORMAT( L H O T ~ ~ H E S T I M A TOF E THE TOTAL TUBE L E N G T H ( F T ) = r F 6 . 2 ) END RITE

* *

210 220 230 240 250 260 270 271 280 290 300 310 311 320 330 340 350 360 370 371 380 381 390

400 410 420 43@ 431

440 450

460 470 471 480 490 500

w 10

SUBROUTINE R I T E 2 R I T E 2 10 W R I TEOUTPUTTAP E5 1r 1001 R I T E 2 20 W R ITEOUTPUTTAP E 5 1r 1 0 0 2 R I T E 2 30 W R I TEOUTPUTTAP E 5 1T 1 0 0 3 R I T E 2 40 WRI TEOUTPUTTAP E 5 1 9 1 0 0 4 R I T E 2 5C WRITEOUTPUTTAPE51rl005 R I T E 2 60 W R I TEOUTPUTTAP E5 191006 R I T E 2 70 WRI TEOUTPUTTAP E 5 1 T 1@07 R I T E 2 80 WRI TEOUTPUTTAP E 5 1T 1 0 0 8 R I T E 2 90 WRI T E O U T P U T T A P E S l r 1009 R I T E 100 RETURN R I T E 110 1001 F O R M A T ( ~ H L T / / T ~ ~ X T ~ ~ H * THE FOLLOWING TABLE G I V E S I N F O R M A T I O N R I T E 120 l F O R EACH B A F F L E SPACE THROUGH THE EXCHANGER * t / / r 3 5 X r 5 O H T H E CRITE 121 20LUMN L A B E L S FOR T H I S T A B L E ARE D E F I K E D B E L O h r / / / / ) R I T E 122 1002 FORMAT( l H O r 3 O H J B A F F L E SPACE NUMBER) R I T E 130 1003 FORMAT( l H O r 8 6 H l S T - I INCREMENT NUMBER OF F I R S T INCREMENT W H I C H R I T E 140 1 L I E S COMPLETELY I N B A F F L E SPACE J ) R I T E 141 1004 FORMAT( lHO959HDELT-W CALCULATED TEMPERATURE CROP ACROSS T U B E W R I T E 1 5 0 lALL ( F f ) RITE 151 1 0 0 5 FORMAT( 1 H O v 84HDELT-W-A ALLOWABLE TEMPERATURE D R O P ACROSS T U B E WARITE 160 1LL BASED ON ALLOWABLE STRESS ( F ) 1 R I T E 161 1006 FORMAT( l H O p 4 0 H T - W A L L kALL M A T E R I A L TEMPERATURE ( F ) 1 R I T E 170 1007 FORMAT( 1 H O r 08HDELP-S CALCULATED SHELL PRESSURE DROP FOR T H E B A R I T E 1 8 0 l F F L E SPACE ( P S I ) ) RITE 181 MEAN D E N S I T Y OF THE HCT F L U I D FOR T H E B P F R I T E 190 1 0 0 8 FORMAT( l K O r 7 C H D E N S - H l F L E SPACE ( L B / F T 3 ) 1 R I T E 191 1009 FORMAT( l H O 9 7 4 H V I S C - H MEAN V I S C O S I T Y OF THE HCT F L U I D FOR THE B R I T E 200 l A F F L E SPACE ( L B / F T - H R I 1 R I T E 201 END R I T E 210

w w

SUBROUTINE R I T E 3 R I T E 3 10 WR ITEOUTPUTTAP E 5 1 9 1O@ 1 R I T E 3 20 WRI TEOUTPUTTAP E 5 l q l C ’ 0 2 R I T E 3 30 WR ITEOUTPUTTAP E 5 I q 1C 0 3 R I T E 3 40 W R I TEOUTPUTTAP E 5 191004 R I T E 3 50 WRI T E O U T P U T T A P E 5 1 q 1 0 0 5 R I T E 3 60 WRI TEOUTPUTTAP E 5 1 9 1 0 0 6 R I T E 3 70 WRITEOUTPUTTAPE519 10C7 R I T E 3 80 W R I TEOUTPUTTAPE5 1 9 1008 R I T E 3 90 W R I TEOUTPUTTAP E 5 1 9 1009 R I T E 100 W R I TEOUT PUTTAP E 5 1 9 1 0 10 R I T E 110 W R I T E O U T P U T T A P E 5 l r 1011 R I T E 120 RETURN R I T E 130 1001 FORMAT( l H l , / / r 1 4 X , 9 1 H * THE FOLLOWING TABLE G I V E S I N F O R M A T I O N R I T E 140 1 A T EACH INCREMENT THROUGH THE EXCHANGER *r//v35X950HTHE COLUMRITE 141 2N L A B E L S FOR T H I S TABLE ARE D E F I N E D B E L C k r / / / / ) R I T E 142 1 0 0 2 FORMAT( 1 H 0 9 2 7 H I INCREMENT NUMBER) R I T E 150 1 0 0 3 FORMAT( l H O v 4 7 H L E N G T H TUBE LENGTH FOR THE INCREHENT ( F E E T ) ) R I T E 160 1004 FORMAT( l H 0 9 4 3 H T - H O T TEMPERATURE OF THE HOT F L U I D ( F ) ) R I T E 170 1005 FORMAT( l H 0 , 4 4 H T - C O L D TEMPERATURE OF THE CCLD F L U I D ( F I ) R I T E 180 100 6 FORMAT ( 1k0 9 4 3HP-CO L D PRESSURE OF THE CCLD F L U I D ( P S I I I R I T E 190 1007 FORMAT( l H O 9 5 3 H D E L P - C TUBE PRESSURE DROP FOR THE INCREMENT ( P S I R I T E 200 1) 1 RITE 201 1 0 0 8 FORMAT ( 1HO 9 77HRES- I N THERMAL R E S I S T A N C E OF THE I N S I D E F I L M F G R R I T E 210 1 THE INCREMENT ( H R - F / B T U ) ) R I T E 211 1 0 3 9 FORMAT( l H O t 7 9 H R E S - W A L L THERMAL R E S I S T A N C E OF THE WALL M A T E R I A L F R I T E 2 2 0 1 0 R THE INCREMENT ( H R - F / B T U ) ) R I T E 221 1010 FORMAT( l H Q v 1 0 9 H R E S - O U T THERMAL R E S I S T A N C E OF THE O U T S I D E F I L M F R I T E 230 1 0 R THE B A F F L E SPACE I N h H I C H THE INCREMENT L I E S ( H R - F / B T U ) ) R I T E 231 l C l l FORMAT( l H 9 9 9 0 H R E S - T O T TOTAL THERMAL R E Z I S T A N C E BETWEEN HOT E C O R I T E 240 1LD F L U I D S FOR THE INCREMENT ( H R - F I B T U ) ) R I T E 241 END R I T E 250

* *

R I T E 4 10 SUBROUT I NE R I T E 4 ( NUMT 9 D S T SDP T 9 SDPS ,DTLME T SX AREAX (UEQX t S b S 9 1 AREABTUEQBTNBSTBSL~ R I T E 4 11 WRITEOUTPUTTAPE519 1001 R I T E 4 20 W R I TEOUTPUTTAP E 5 1 1 10@29NUMT R I T E 4 30 W R I TEOUTPUTTAPE51,1003 9 NB S R I T E 4 40 W R I TEOUTPUTTAP E 5 IT 10049 B S L R I T E 4 50 WRI TEOUT PUTTAP E 5 1 9 1 0 0 5 9 OS R I T E 4 60 W R I TEOUTPUTTAP E 5 1 9 1 0 0 6 9 SDPT R I T E 4 70 W R I TEOUTPUTTAP E5 1 9 1 0 0 7 9 SDPS R I T E 4 80 WRITEOUTPUTTAPE5lr 1008rOTLME R I T E 4 90 W R I TEOUTPUTTAP E 5 1 9 10099 SX R I T E 100 W R I T EOUT PUTTAP E5 1 9 1 0 10 AR EA X R I T E 110 W R I TEOUTPUTTAP E 5 1 9 10119 UEQX R I T E 120 WRI TEOUTPUTTAP E 5 1 1 1 0 1 2 SB ~ S R I T E 130 W R I TEOUTPUTTAP E 5 1 9 1 O 1 3 9 AREAB R I T E 140 WRI TEOUTPUTTAP E5 1910149 UEQB R I T E 150 RETURN R I T E 160 1001 F O R M A T ( ~ H L ~ / / , ~ ~ X T4~ ~ H *THE FOLLCWING ARE AVERAGE OR T O T A L P R O R I T E 170 l P E R T I E S FOR THE E N T I R E EXCHANGER **//I R I T E 171 1002 F O R M A T ( l H 0 , 2 3 H T O T A L NUMBER OF TUBES= , 1 5 1 R I T E 180 1003 FORMAT( l H 0 9 3 1 H T O T A L NUMBER OF B A F F L E SPACES= 9 1 4 1 R I T E 190 R I T E 200 1004 F O R M A T ( l H 0 9 3 2 H L E N G T H OF A B A F F L E S P A C I N G ( F T I = r F 6 . 3 ) 1005 FORMAT( l H O p 4 5 H I N S I D E D I A M E T E R OF EXCHANGER S P E L L ( I N C H E S ) = 9 F 7 . 2 1 R I T E 210 1006 F O R M A T ( l H O 9 3 6 H T O T A L PRESSURE DROP I N TUBES ( P S I ) = ~ F 8 . 2 ) R I T E 220 1007 FORMAT( l H O 9 3 6 H T O T A L PRESSLRE DROP I N S H E L L ( P S I ) = 9F8.2) R I T E 230 R I T E 240 1 0 0 8 FORMAT( lHO923HLOG-MEAN DELTA-T ( F ) = 9F7. Z T / / ~ 1009 FORMAT( l H 0 9 2 6 H T O T A L TUBE LENGTH ( F E E T I = 9F7.21 R I T E 250 1010 FORMAT(lHO,59HTOTAL HEAT TRANSFER AREA BASED CN TOTAL TUBE LENGTH R I T E 2 6 0 1 ( F T 2 1 = 9F8.11 R I T E 261 1011 FORMAT( l H 0 9 7 7 H O V E R A L L HEAT TRANSFER C O E F F I C I E N T BASED ON TOTAL T U B R I T E 270 1E LENGTH ( B T U / H R - F T Z - F I = rF7.2,//) R I T E 271 1 0 1 2 FORMAT( l H 0 1 3 4 H T O T A L B A F F L E SPACE LENGTH ( F E E T ) = 9 F 7 . 2 ) R I T E 280 1013 FORMAT( l H 0 9 6 7 H T O T A L HEAT TRANSFER AREA BASED CN TCTAL B A F F L E S P A C E R I T E 290 1 LENGTH ( F T 2 ) = 9 F 8 . 1 1 R I T E 291 1014 FORMAT( 1HO985HOVERALL H E A T TRANSFER C O E F F I C I E N T BASED ON T O T A L B A F R I T E 300 l F L E SPACE LENGTH ( B T U / H R - F T Z - F ) = rF7.2) R I T E 301 END R I T E 31@

* *

' (

F W

u l

1 2

SUBROUT I N E V ISCOS( T i P ETAP 1 TR = T + 4 6 0 o ETAT = . 1 8 9 E - O 0 * ( T R / 4 9 2 o ) s * o ~ * ( 1 , + 9 8 6 o / 4 9 2 . ) / ( 1 o + 9 8 6 o / T R J CALL S V H ( 2 r P e T i V i H P T ) 1982 ETAP = 1 1 5 9 2 0 o * E T A T * ( V / ( V - . O l 2 ) RETURN END

VISCO VISCO VISCO VISCO VISCO VISCO VISCO

SUBROUTINE C O N D T ( T i P i C 0 N D ) TR = T + 4 6 0 . CALL S V H ( 2 i P t T i V i H P T ) COND = 1 . 0 9 3 E - 0 6 * T R * * 1 . 4 5 + 2 8 . RETURN END

CONDT CONDT CONDT CONDT CONDT CONOT

5375E-04/V**l025

SUBROUTINE S V H ( N i P 9 T i S V O L i H P T C C M M O N / T P / P R E S ~ T E M P T Mi ~M 2 i N C l i N C 2 , X T i Y T GOTO(li2)iN CALL TIPUT RETURN PRES=P TEMP=T CALL SPECV(SVOL1 CALL H(HPT1 END

SVH SVH SVH SVH SVH SVH SVH SVH SVH SVH

10 20 30

40 50 60

10 20

30 40 50 60

20 30 40 50 60 70

80 90 100

w a\

SUBROUT IN E S P E C V ( A N S I COMMON/VOL/C ( 5 1 6 0 ) COMMON/TP/PRES 1TEMP 1M 1 1 P 2 T N C 1 1 N C 2 1 x 1 r Y T T = ( T E M P - 5 5 0 0 - 1 OE-5 1 / 1 0 10 NCl=T XT=T-NCl NC2=NCl+ 1 P=( P R E S - 3 5 0 0 . 1 OE-5 1 / 100 o + 1 Ml=P YT=P-Ml M2=Ml+l I F ( M 1 o L T 1oOR. M 1 oGT 4 ) 112 C A L L ERROR I F ( N C L . L T o l o O R o N C l o G T , 5 5 ) 113 C O N 1I N U E Z 1l = C ( M 1 i N C l ) 2 12=C( M 1i N C 2 1 Z21=C(M2vNCI) Z 2 2 = C ( M 2 rNC2 1 XA=Z11+( Z12-Z11)*XT X B=L 2 1+(222-2 2 11 *X T YSET=XA+(XB-XA l*YT Y A= Z 11+ ( 22 1-Z 11 1 *Y T Y B=Z12+( Z22-Z12)*YT X S E T = Y A+ ( Y B - Y A ) * X T ANS=O, 5* ( Y S E T + X S E T ) RETURN END 0 +

1 2 3

’ (

S P E C V 10 S P E C V 20 S P E C V 30 S P E C V 40 S P E C V 50 S P E C V 60 S P E C V 70 S P E C V 80 S P E C V 90 S P E C 100 S P E C 110 S P E C 120 S P E C 130 S P E C 140 S P E C 150 S P E C 160 S P E C 170 S P E C 180 S P E C 190 S P E C 200 S P E C 210 S P E C 220 S P E C 230 S P E C 240 S P E C 250 S P E C 260 S P E C 270 S P E C 280

SUBROUTINE H ( A N S 1 C OMMON/H/C ( 5 960 I COMMON/TP/PR ES T T EMP t M 1 9 P 2 9 NC 1t NC 2 T X T t YT Zll=C(MlvNCl) Z12=C(MLrNC21 Z 2 l = C ( M2 T NC 1J Z 2 2 = c ( M 2 T NC2 1 X A=Z 11+( Z L 2 - Z l l I * X T X B= 2 2 1+(2 2 2 - 2 2 1) * X T Y SET =XA+ ( XB-XA 1 YT Y A=Z11+( 2 2 1 - 2 1 1 ) * Y T Y B= Z 12+ ( 2 2 2- Z 12 1 * Y T XSET=YA+ ( Y 6 - Y A )*XT ANS=Oe5*(YSET+XSET) RETURN END

SUBROUTINE T I P U T COMMON/VOL/V (5 960) COMMON/H/H( 5 . 6 0 ) DO 1 J r 1 . 5 6 1 R E A D ( 509 1001 1 ( V ( I t J ) t I = ~ 5 T) 1001 FORMAT(5E10.01 DO 2 J s l . 5 6 2 J 1 , I = l t 5) R E A D ( 5 0 r 1 0 0 2 1 ( H ( IT 1002 FORMAT( 5E10.0) RETURN END

H H H H H H H H H H H H H H H H

10 20 30

40 50 60 70 80

90 100 110 120 130

140 150

160

J I P U T 10 T I P U T 20 T I P U T 30 T I P U T 40 TIPUT 50 T I P U T 60 J I P U T 70 T I P U T 80 T I P U T 90 T I P U 100 T I P U 110

139

I n t e me d i a te Va r i ab le s

The i n t e r m e d i a t e v a r i a b l e s u s e d i n t h e SUPEX computer program a r e l i s t e d below i n t h e o r d e r i n which t h e terms a p p e a r i n t h e program.

The

u n i t s i n which t h e v a r i a b l e s a r e e x p r e s s e d i n t h e program a r e a s f o l l o w s

DELPTA

Temperature

O F

Massy Lengthy

1bm ft

Pressure,

lbf/in.

Density,

lbm/f t3

V i s cos i t y

lb /f t * h r

T o t a l a l l o w a b l e p r e s s u r e drop i n t h e c o l d f l u i d ( s t e a m ) .

...

LOP11 Counters used i n t h e v a r i o u s i t e r a t i o n loops t o LOP1, LOP2, d e t e r m i n e whether t h e loop h a s converged w i t h i n a c e r t a i n p r e s e t number of i t e r a t i o n s . DE LTH

T o t a l t e m p e r a t u r e drop i n t h e h o t f l u i d ( s a l t ) .

DTPB

Temperature drop i n t h e h o t f l u i d ( s a l t ) p e r b a f f l e s p a c e b a s e d on t h e e s t i m a t e d number of b a f f l e s p a c e s (GNB).

BSL

Baffle spacing length.

DTI

I n s i d e diameter of tubes.

TCAV

Average t e m p e r a t u r e o f t h e c o l d f l u i d ( s t e a m ) .

PCAV

Average p r e s s u r e of t h e c o l d f l u i d ( s t e a m ) .

SPVl

I n l e t s p e c i f i c volume o f the c o l d f l u i d ( s t e a m ) .

DUM

A dummy v a r i a b l e .

SPV2

O u t l e t s p e c i f i c volume o f t h e c o l d f l u i d ( s t e a m ) .

SPVAV

Average s p e c i f i c volume o f t h e c o l d f l u i d ( s t e a m ) .

S PVG

A g u e s s a t the mean v a l u e of the s p e c i f i c volume of the c o l d f l u i d (steam) u s e d i n making an i n i t i a l e s t i m a t e o f t h e mass flow r a t e of the cold f l u i d .

VIS 1

I n l e t v i s c o s i t y of t h e c o l d f l u i d (steam).

VIS2

O u t l e t v i s c o s i t y of the cold f l u i d (steam).

VISAV

Average v i s c o s i t y of t h e c o l d f l u i d ( s t e a m ) .

VISG

A g u e s s a t t h e mean v a l u e o f t h e v i s c o s i t y o f t h e c o l d f l u i d ( s t e a m ) u s e d i n making an i n i t i a l e s t i m a t e o f t h e Reynolds number f o r the cold f l u i d .

140

C FG

A guess a t t h e v a l u e o f t h e f r i c t i o n f a c t o r f o r t h e cold f l u i d (steam).

THETAL

The minimum v a l u e o f t h e a n g l e THETA ( r a d i a n s ) , where THETA i s h a l f o f t h e a n g l e subtended by t h e c h o r d t h a t i s formed by t h e window r e g i o n o f t h e b a f f l e . The v a l u e 0.8 c o r r e s ponds t o 0 = 4 5 " ; t h i s v a l u e i s j u s t a g u e s s used t o s t a r t t h e i t e r a t i o n process.

PERCL

The r a t i o o f t h e window area t o t h e t o t a l c r o s s - s e c t i o n a l a r e a a t t h e b a f f l e , based on THETAL.

THETAU

The maximum v a l u e o f t h e a n g l e THETA. corresponds t o 6 = 90'.

PERCU

The r a t i o o f t h e window area t o t h e t o t a l c r o s s - s e c t i o n a l area a t t h e b a f f l e , based on THETAU.

NEW

The v a l u e o f THETA based on t h e i t e r a t i o n scheme.

PNEW

The r a t i o o f t h e window a r e a t o t h e t o t a l c r o s s - s e c t i o n a l a r e a a t t h e b a f f l e , based on NEW.

EPNEW

The a b s o l u t e d i f f e r e n c e between t h e d e s i r e d f r a c t i o n a l window c u t (PW) and t h e c a l c u l a t e d f r a c t i o n a l window c u t (PNEW).

THETAC

The c a l c u l a t e d v a l u e o f THETA t h a t g i v e s t h e d e s i r e d v a l u e o f t h e f r a c t i o n a l window c u t .

Mass v e l o c i t y ( d e n s i t y times flow speed) f o r t h e c o l d f l u i d (steam).

REG

Reynolds number f o r t h e c o l d f l u i d (steam) b a s e d on a n estimate of t h e v i s c o s i t y of t h e cold f l u i d ,

CFC

C a l c u l a t e d f r i c t i o n f a c t o r f o r t h e c o l d f l u i d (steam).

DIFA

A b s o l u t e d i f f e r e n c e between t h e c a l c u l a t e d and g u e s s e d v a l u e s o f t h e f r i c t i o n f a c t o r f o r t h e c o l d f l u i d (steam).

NUMT

Number o f t u b e s r e q u i r e d .

BNUMT

F l o a t i n g p o i n t c o n v e r s i o n v a l u e o f t h e i n t e g e r NUMT.

I n s i d e d i a m e t e r o f t h e s h e l l of t h e h e a t e x c h a n g e r ,

The v a l u e o f 1.5707

14 1 XBAR

D i s t a n c e from t h e i n s i d e s u r f a c e o f t h e s h e l l t o t h e c e n t r o i d o f t h e window a r e a a t a b a f f l e .

XBAR

BRLl

Tangent of t h e a n g l e @,

a s i l l u s t r a t e d i n s k e t c h above.

GBRL

This factor i s a multiplicative correction f a c t o r developed t o modify B e r g e l i n ' s c o r r e l a t i o n i n c a s e s where t h e b a f f l e s p a c i n g becomes l a r g e r e l a t i v e t o t h e d i a m e t e r o f t h e s h e l l . I n such c a s e s , t h e flow i n t h e middle of t h e b a f f l e region i s e s s e n t i a l l y p a r a l l e l .

Window a r e a a t a b a f f l e .

B a f f l e a r e a ( t o t a l c r o s s - s e c t i o n a l a r e a minus window a r e a ) ,

AXC

A v a l u e o f AX c a l c u l a t e d from a v a l u e o f THETA.

DIFB

A b s o l u t e d i f f e r e n c e between AXC and AX.

THETA2

A v a l u e o f t h e a n g l e THETA based on t h e v a l u e of AXC.

Axc2

A v a l u e o f AXC based on t h e v a l u e o f THETA2.

Mass v e l o c i t y ( d e n s i t y times flow speed) f o r t h e c o l d f l u i d (steam) based on t h e c u r r e n t number o f t u b e s i n t h e exchanger (NUMT)

(0.77/BRL1째

D i s t a n c e from t h e a x i a l c e n t e r l i n e t o t h e window edge o f t h e baffle.

CNB

Number o f rows o f t u b e s from t h e window edge o f one b a f f l e t o t h e window edge o f t h e f o l l o w i n g b a f f l e .

142 XH

I n s i d e r a d i u s o f t h e s h e l l minus XB.

CNW

Number of rows o f t u b e s i n one window.

Chord l e n g t h o f t h e window edge o f t h e b a f f l e .

PCFB

F r a c t i o n o f t h e d i s t a n c e between t u b e c e n t e r s t h a t i s f r e e f o r c r o s s flow.

SBK

Average f r e e a r e a i n c r o s s flow p e r u n i t b a f f l e s p a c i n g .

Free hot-fluid

SDPT

Summed p r e s s u r e d r o p on t h e t u b e s i d e ,

SDPS

Summed p r e s s u r e d r o p on t h e s h e l l s i d e .

A c o u n t e r which h a s a v a l u e o f 1 f o r t h e f i r s t c a l c u l a t i o n i n each b a f f l e s p a c e and a v a l u e o f z e r o f o r t h e r e s t of t h e incremental c a l c u l a t i o n s i n t h e b a f f l e space.

( s a l t ) a r e a i n t h e window r e g i o n .

Summed t u b e l e n g t h . Summed b a f f l e s p a c e l e n g t h . Temperature o f t h e c o l d f l u i d (steam) a t t h e b e g i n n i n g o f t h e I - t h increment. Temperature of t h e h o t f l u i d ( s a l t ) a t t h e b e g i n n i n g o f t h e I - t h increment.

RWK

A f a c t o r used t o c a l c u l a t e t h e h e a t t r a n s f e r r e s i s t a n c e o f t h e t u b e w a l l m a t e r i a l . It can b e t h o u g h t o f a s a n e f f e c t i v e thickness of the tube wall. I f d

d 1

where

%= d

thermal r e s i s t a n c e o f t u b e w a l l m a t e r i a l ,

= o u t s i d e diameter of tube, = thermal c o n d u c t i v i t y of w a l l m a t e r i a 1 , a n d

d . = i n s i d e diameter o f t u b e ; then 1

RWK = %k

143

P r e s s u r e o f t h e c o l d f l u i d (steam) a t t h e b e g i n n i n g o f t h e I- t h i n c r e m e n t . E n t h a l p y o f t h e c o l d f l u i d (steam) a t t h e b e g i n n i n g o f t h e I - t h increment.

F l o a t i n g p o i n t c o n v e r s i o n of t h e i n t e g e r N ( c . f . variables).

input

The amount o f h e a t t o b e t r a n s f e r r e d i n each i n c r e m e n t .

DECT

The change i n t e m p e r a t u r e p e r increment o f t h e h o t f l u i d (salt).

DECH

The change i n e n t h a l p y p e r increment o f t h e c o l d f l u i d (steam).

S u b s c r i p t i n d e x which r e f e r s t o t h e i n c r e m e n t s .

S u b s c r i p t i n d e x which r e f e r s t o t h e b a f f l e s p a c e s .

Total cross-flow area f o r t h e h o t f l u i d ( s a l t ) i n a given b a f f l e space.

TCON

An e s t i m a t e o f t h e b u l k t e m p e r a t u r e of t h e h o t f l u i d ( s a l t ) i n a b a f f l e space.

DENH

D e n s i t y o f t h e h o t f l u i d ( s a l t ) based on t h e t e m p e r a t u r e (TCON)

VISH

V i s c o s i t y o f t h e h o t f l u i d ( s a l t ) b a s e d on t h e t e m p e r a t u r e (TCON)

DHOT (K)

D e n s i t y o f t h e h o t f l u i d ( s a l t ) f o r t h e K-th b a f f l e s p a c e ,

VHOT (K)

V i s c o s i t y o f t h e h o t f l u i d ( s a l t ) f o r t h e K-th b a f f l e s p a c e .

CON 1

The P r a n d t l number f o r t h e h o t f l u i d ( s a l t ) r a i s e d t o the 213 power.

Mass v e l o c i t y ( d e n s i t y times flow speed) o f t h e h o t f l u i d

(salt) i n cross flow.

RECB

The c r o s s - f l o w Reynolds number f o r t h e h o t f l u i d ( s a l t ) .

HJB

The e f f e c t o f t h e c r o s s - f l o w Reynolds number on t h e s h e l l s i d e convective heat t r a n s f e r coefficient.

The s h e l l - s i d e c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t f o r c r o s s flow.

Mass v e l o c i t y ( d e n s i t y times flow s p e e d ) o f t h e h o t f l u i d ( s a l t ) i n p a r a l l e l flow.

A k i n d o f root-mean-square mass v e l o c i t y f o r t h e h o t f l u i d ( s a l t ) . It i s u s e d i n t h e B e r g e l i n c o r r e l a t i o n s .

mcw

The p a r a l l e l - f l o w Reynolds number f o r t h e h o t f l u i d ( s a l t ) .

HJW

The e f f e c t o f t h e p a r a l l e l - f l o w Reynolds number on t h e s h e l l s i d e convective heat t r a n s f e r coefficient.

144

The s h e l l - s i d e c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t f o r p a r a l l e l flow.

The t o t a l s h e l l - s i d e c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t . The f i l m r e s i s t a n c e t o h e a t t r a n s f e r on t h e o u t s i d e of t h e t u b e s f o r t h e K-th b a f f l e space. TH( I+1)

Temperature o f t h e h o t f l u i d ( s a l t ) a t t h e end of t h e I - t h increment ( i . e . t h e beginning of t h e I + 1 - t h increment).

DELPP

Tube-side change i n p r e s s u r e f o r a given increment.

HCG

An e s t i m a t e o f t h e e n t h a l p y of t h e c o l d f l u i d (steam) a t t h e end of t h e I - t h increment based on t h e e s t i m a t e d p r e s s u r e and temperature a t t h e end of t h e I - t h increment.

The a b s o l u t e d i f f e r e n c e between HCG and t h e HC(I+l) which has been c a l c u l a t e d based on t h e h e a t t r a n s f e r r e d p e r increment (QX/WC)

TRIAL

A t r i a l v a l u e o f TC(I+l) t o be used f o r i t e r a t i o n .

HRIAL

A t r i a l v a l u e o f HC(I+l) t o b e used f o r i t e r a t i o n .

TNEXT

A v a l u e o f TC(I+l) which i s determined by t h e i t e r a t i o n

scheme ( i . e . iteration),

a new estimate of TC(I+l) t o s t a r t t h e n e x t

DENOM

The a n t i l o g of t h e denominator of t h e d e f i n i n g e q u a t i o n f o r a l o g a r i t h m i c mean temperature d i f f e r e n c e .

TDEN

The a b s o l u t e d i f f e r e n c e between DENOM and u n i t y .

DELTLM

Logarithmic mean temperature d i f f e r e n c e .

Average temperature of t h e cold f l u i d (steam) i n t h e I - t h increment

Average p r e s s u r e of t h e c o l d f l u i d (steam) i n t h e I - t h i n c r e men t

S PVB

S p e c i f i c volume of t h e cold f l u i d based on t h e a v e r a g e temperature and p r e s s u r e , TM and PM, i n t h e increment.

HFB

Enthalpy of t h e cold f l u i d (steam) based on t h e a v e r a g e temperature and p r e s s u r e , TM and PM, i n t h e increment,

VISB

V i s c o s i t y of t h e c o l d f l u i d (steam) based on t h e average temperature and p r e s s u r e , TM and PM, i n t h e increment.

Temperature of t h e w a l l m a t e r i a l i n t h e increment. Thermal c o n d u c t i v i t y of t h e w a l l m a t e r i a l i n t h e increment. Thermal r e s i s t a n c e of t h e w a l l m a t e r i a l i n t h e I - t h increment. D i f f e r e n c e between temperature o f i n s i d e w a l l and t e m p e r a t u r e of b u l k c o l d f l u i d (steam) f o r t h e increment. TMS

Mean temperature of t h e t u b e w a l l s u r f a c e i n t h e increment. I

145

SPVI

S p e c i f i c volume o f t h e c o l d f l u i d (steam) based on t h e a v e r a g e p r e s s u r e and mean t u b e - w a l l s u r f a c e t e m p e r a t u r e , PM and TMS, i n t h e i n c r e m e n t .

HFI

E n t h a l p y o f t h e c o l d f l u i d (steam) based on t h e a v e r a g e p r e s s u r e and mean t u b e - w a l l s u r f a c e t e m p e r a t u r e , PM and TMS, i n t h e increment.

TCFI

Thermal c o n d u c t i v i t y o f t h e c o l d f l u i d (steam) b a s e d on t h e a v e r a g e p r e s s u r e and mean t u b e - w a l l s u r f a c e t e m p e r a t u r e , PM and TMS, i n t h e i n c r e m e n t .

VISFI

V i s c o s i t y o f t h e c o l d f l u i d (steam) b a s e d on t h e a v e r a g e p r e s s u r e and mean t u b e - w a l l s u r f a c e t e m p e r a t u r e , PM and TMS, i n t h e increment.

CRE

Reynolds number o f t h e c o l d f l u i d ( s t e a m ) , based on t h e i n s i d e t u b e w a l l c o n d i t i o n s , r a i s e d t o t h e 0.923 power.

CPR

P r a n d t l number o f t h e c o l d f l u i d , based on i n s i d e t u b e w a l l c o n d i t i o n s and a f i c t i t i o u s s p e c i f i c h e a t , r a i s e d t o t h e 0.613 power. The f i c t i t i o u s s p e c i f i c h e a t i s d e f i n e d

where H i s e n t h a l p y , T i s t e m p e r a t u r e and t h e s u b s c r i p t s "ill and "b" r e f e r t o i n s i d e t u b e s u r f a c e and b u l k c o l d f l u i d (steam), respectively. This d e f i n i t i o n of s p e c i f i c h e a t i s necessary since s p e c i f i c h e a t a s normally d e f i n e d i s indeterminant a t t h e c r i t i c a l point, while enthalpy, although discontinuous a t t h e c r i t i c a l point, i s not indeterminant.

csv

The r a t i o o f t h e b u l k s p e c i f i c h e a t of t h e c o l d f l u i d (steam) t o t h e s p e c i f i c h e a t of t h e cold f l u i d evaluated a t i n s i d e tube-wall c o n d i t i o n s r a i s e d t o t h e 0.231 power. C o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t o v e r t h e increment f o r the inside surface of the tube wall. The t h e r m a l r e s i s t a n c e of t h e c o n v e c t i v e f i l m on t h e i n s i d e s u r f a c e of t h e t u b e s , f o r t h e I - t h i n c r e m e n t , a d j u s t e d t o t h e o u t s i d e diameter of t h e tube. The t o t a l t h e r m a l r e s i s t a n c e between t h e h o t ( s a l t ) and c o l d (steam) f l u i d s f o r t h e I - t h i n c r e m e n t .

DTFMC

The t e m p e r a t u r e d r o p a c r o s s t h e i n s i d e t u b e w a l l c o n v e c t i v e f i l m f o r t h e increment.

DTFM2

A r i t h m e t i c a v e r a g e o f DTFM and DTFMC.

TMs2

New estimate o f t h e mean t u b e - w a l l s u r f a c e t e m p e r a t u r e b a s e d on DTFM2.

146

SPVI2

New estimate o f t h e s p e c i f i c volume o f t h e c o l d f l u i d (steam) b a s e d on a v e r a g e p r e s s u r e (PM) and the new estimate o f t h e mean t u b e - w a l l s u r f a c e t e m p e r a t u r e (TMS2) f o r t h e increment

HFI2

New e s t i m a t e o f t h e e n t h a l p y o f t h e c o l d f l u i d (steam) based on t h e a v e r a g e p r e s s u r e (PM) and t h e new estimate o f t h e mean t u b e - w a l l s u r f a c e t e m p e r a t u r e (TMSZ) f o r t h e i n c r e m e n t .

TCFI2

N e w e s t i m a t e of t h e thermal c o n d u c t i v i t y o f t h e c o l d f l u i d

(steam) based on t h e a v e r a g e p r e s s u r e (PM) and t h e new e s t i m a t e o f t h e mean t u b e - w a l l s u r f a c e t e m p e r a t u r e (TMS2) f o r t h e increment. VISFI2

New e s t i m a t e o f t h e v i s c o s i t y o f t h e c o l d f l u i d (steam) based on t h e a v e r a g e p r e s s u r e (PM) and t h e new estimate o f t h e mean t u b e - w a l l s u r f a c e t e m p e r a t u r e (TMS2) f o r t h e increment.

cRE2

New e s t i m a t e o f CRE based on VISFI2.

CPR2

New e s t i m a t e o f CPR based on HFI2, TMS2, VISFI2, and TCFI2.

csv2

New e s t i m a t e o f CSV based on SPVI2.

H2 I

New e s t i m a t e o f H I based on TCFI2, CRE2, CPR2, and CSV2.

R2 I

New e s t i m a t e o f R I ( 1 ) b a s e d on H2I.

U T

New estimate o f RT(1) based on R2I.

DTFMCZ

New e s t i m a t e o f DTFMC b a s e d on R Z I and R2T.

SLOPE

A r a t i o o f two d i f f e r e n c e s between v a r i o u s e s t i m a t e s o f t h e temperature drop a c r o s s t h e i n s i d e t u b e w a l l c o n v e c t i v e f i l m f o r t h e i n c r e m e n t . T h i s i s used t o make a new e s t i m a t e o f DTFM i n o r d e r t o c o n t i n u e t h e i t e r a t i o n p r o c e s s .

O v e r a l l h e a t t r a n s f e r c o e f f i c i e n t f o r t h e I - t h increment b a s e d on t h e o u t s i d e d i a m e t e r o f t h e t u b e , Tube l e n g t h i n t h e I - t h i n c r e m e n t . Reynolds number f o r t h e c o l d f l u i d (steam) b a s e d on t h e b u l k v i s c o s i t y (VISB) o f t h e i n c r e m e n t , CFI

Fanning f r i c t i o n f a c t o r f o r t h e c o l d f l u i d (steam) f o r t h e increment,

DELP( I)

The p r e s s u r e d r o p f o r t h e c o l d f l u i d (steam) i n t h e I - t h increment,

DIFC

The d i f f e r e n c e between two c o n s e c u t i v e v a l u e s o f t h e p r e s s u r e drop f o r t h e c o l d f l u i d i n t h e I - t h increment a s determined by c o n s e c u t i v e p a s s e s through t h e i t e r a t i o n l o o p .

IBK(K)

The v a l u e o f t h e i n d e x I a t t h e b e g i n n i n g o f t h e f i r s t i n c r e m e n t t h a t i s t o t a l l y c o n t a i n e d w i t h i n t h e K-th b a f f l e space.

147 ALPHA

C o e f f i c i e n t of thermal expansion f o r t h e t u b e w a l l m a t e r i a l (x 106).

ETW

Modulus o f e l a s t i c i t y f o r t h e t u b e w a l l m a t e r i a l (x

CON2, CON3

F a c t o r s i n t h e e x p r e s s i o n which c a l c u l a t e t h e s t r e s s components i n t h e t u b e w a l l .

B, SL

C o n s t a n t s i n t h e e x p r e s s i o n g i v e n i n S e c t i o n I11 o f t h e ASME B o i l e r and P r e s s u r e Vessel Code f o r c a l c u l a t i n g t h e allowa b l e thermal s t r e s s components.

CON4

T e r m f o r t h e a l l o w a b l e thermal s t r e s s components given i n S e c t i o n I11 o f t h e ASME B o i l e r and P r e s s u r e Vessel Code.

TWALL (K)

Temperature o f t u b e w a l l m a t e r i a l f o r t h e K-th b a f f l e space.

DELTWA(K)

Allowable t e m p e r a t u r e d i f f e r e n c e a c r o s s t h e t u b e w a l l f o r t h e K-th b a f f l e s p a c e based on a l l o w a b l e thermal stresses.

DELTW (K)

Temperature d i f f e r e n c e a c r o s s t h e t u b e w a l l f o r t h e K-th b a f f l e space.

BWN

F a c t o r used i n s h e l l - s i d e p r e s s u r e drop c a l c u l a t i o n s . The f a c t o r t a k e s t h e v a l u e 0.5 i f t h e increment i s a t e i t h e r end o f t h e exchanger, and i t t a k e s t h e v a l u e o f u n i t y f o r a l l o t h e r increment p o s i t i o n s .

DELPSB

S h e l l - s i d e p r e s s u r e drop i n the b a f f l e s p a c e a r e a .

DELPSW

S h e l l - s i d e p r e s s u r e drop i n t h e window a r e a .

DELPS (K)

T o t a l s h e l l - s i d e p r e s s u r e drop f o r t h e K-th b a f f l e space.

EDPT

A b s o l u t e d i f f e r e n c e between t h e t o t a l c a l c u l a t e d t u b e - s i d e p r e s s u r e drop and t h e a l l o w a b l e t o t a l t u b e - s i d e p r e s s u r e drop.

EDPS

A b s o l u t e d i f f e r e n c e between t h e t o t a l c a l c u l a t e d s h e l l - s i d e pressure drop and the allowable total shell-side pressure

drop. J, J N ,

Counters t o p u t t h e b a f f l e s p a c e i n f o r m a t i o n o u t i n groups of 50 p e r page. T o t a l number o f b a f f l e spaces.

NBS IN,

JNC

INC

Counters t o p u t t h e increment i n f o r m a t i o n o u t i n groups of 50 p e r page. The f i l m r e s i s t a n c e t o h e a t t r a n s f e r on t h e o u t s i d e o f t h e t u b e s f o r t h e I - t h increment.

AREAX

T o t a l h e a t t r a n s f e r a r e a based on t o t a l t u b e l e n g t h .

UEQX

Overall h e a t t r a n s f e r c o e f f i c i e n t based on t o t a l t u b e length.

AREAB

T o t a l h e a t t r a n s f e r a r e a based on t o t a l b a f f l e s p a c e l e n g t h .

UEQB

O v e r a l l h e a t t r a n s f e r c o e f f i c i e n t based on t o t a l b a f f l e space l e n g t h .

148

Subroutines

There a r e t e n s u b r o u t i n e s i n t h e SUPEX computer program.

The terms

used f o r each o f t h e s e s u b r o u t i n e s a r e l i s t e d below w i t h a b r i e f d e s c r i p t i o n of t h e purpose of each s u b r o u t i n e . RITE1

Writes o u t t h e i n p u t i n f o r m a t i o n .

RITE2

W r i t e s o u t d e f i n i t i o n s o f t h e v a r i o u s columns i n t h e t a b l e o f o u t p u t f o r each b a f f l e space,

RITE3

Writes o u t d e f i n i t i o n s o f t h e v a r i o u s columns i n t h e t a b l e o f o u t p u t f o r each increment.

RITE4

W r i t e s o u t i n f o r m a t i o n concerning t h e a v e r a g e o r t o t a l p r o p e r t i e s f o r t h e e n t i r e exchanger.

VISCOS(T, P, ETAP) C a l c u l a t e s t h e v i s c o s i t y of t h e c o l d f l u i d (steam) f o r a given t e m p e r a t u r e and p r e s s u r e . C a l c u l a t e s the thermal c o n d u c t i v i t y of t h e c o l d f l u i d (steam) f o r a g i v e n t e m p e r a t u r e and p r e s s u r e .

CONDT(T, P, COND) SVH(N,P,T,

SVOL, HPT) C a l l s t h e s u b r o u t i n e TIPUT when N = 1 o r c a l l s s u b r o u t i n e s SPECV and H when N = 2.

SPECV(ANS)

C a l c u l a t e s , u s i n g an i n t e r p o l a t i o n o f i n p u t d a t a , t h e s p e c i f i c volume o f t h e c o l d f l u i d (steam).

H (ANS 1

C a l c u l a t e s , u s i n g an i n t e r p o l a t i o n o f i n p u t d a t a , t h e s p e c i f i c e n t h a l p y of t h e c o l d f l u i d (steam).

TIPUT

Reads i n an a r r a y o f v a l u e s of s p e c i f i c volume and s p e c i f i c e n t h a l p y a s f u n c t i o n s o f t e m p e r a t u r e and p r e s s u r e .

Computer I n p u t and Output f o r R e f e r e n c e MSBR Steam G e n e r a t o r S u p e r h e a t e r

***

0.500

O U T S I D E DIAMETER OF TUBES (INCHESI;. TUBE M A L L T H I C K N E S S TUBE P I T C H

(

INCHES t =

INCHES I =

IS THE I N P U T I N F O R M A T I O N FOR T H I S PROBLEM

THE FOLLOWING

0.0770

0.8750

NJM6ER OF INCREMENTS I N T O WHICH THE EXCHANGER I S D I V I D E D =

1150.0

I N L E T TEMPERATURE OF HOT F L U I D ( F t = W T L E T TEMPERATURE OF HOT F L U I D ( F t =

850.0

I N L E T TEMPERATURE OF COLD F L U I D ( F t =

700.0

W T L E T TEMPERATURE OF COLD F L U I D ( F t =

lCOO.O

W T L E T PRESSURE OF COLD F L U I D ( P S I ) =

3603.C

ALLOWABLE TOTAL PRESSURE DROP ON TUBE S I D E ( P S I t ALLOWABLE TOTAL PRESSURE DROP O N SHELL S I D E ( P S I ) =

MASS FLOW RATE OF COLD F L U I D ( L B / H R ) =

4.12CE

S P E C I F I C HEAT CF HOT F L U I D ( B T U / L B - F t =

0.40

C.360

THERMAL C O N D U C T I V I T Y OF HOT F L U I D (BTU/HR-FT-F F R A C T I O N A L WINDOW CUT=

60.0

2 . 8 2 0 E 06

MASS F L O k RATE OF HOT F L U I D ( L B / H R I = TOTAL HEAT TRANSFER R A T E ( B T U / H R t =

6.330E

150.0

0.240

100

Computer

Input

Data

for

Reference

BY-PASS

LEAKAGE

FACTOR

FOR

PRESSURE=

BY-PASS

LEAKAGE

FACTOR

FOR

HEAT

ESTIMATE

THE

NUMBER

BAFFLE

ESTIMATE

THE

LENGTH

ESTIMATE

THE

TOTAL

TUBE

MSBR Steam

0.520

TRANSFER=

BAFFLE LENGTH(FTl=

Generator

SPACES

0. BOO

REQUIRED=

SPACE(FTJ=

18 3.00

C5.00

Superheater

(continued)

***

T H E F O L L O W I N G T A B L E G I V E S I N F O R M A T I O N FOR E A C H B A F F L E S P A C E THROUGH T H E EXCHANGER THE COLUMN L A B E L S FOR T H I S T A B L E ARE D E F I N E D BELOW

B A F F L E S P A C E NUMBER

1ST-1

I N C R E M E N T NUMBER OF F I R S T I N C R E M E N T W H I C H L I E S C O M P L E T E L Y I N B A F F L E S P A C E J

DELT-d

C A L C U L A T E D TEMPERATURE DROP ACROSS TUBE WALL ( F J

DELT-U-A

A L L O W A B L E T E M P E R A T U R E DROP ACROSS T U B E WALL B A S E D C h A L L O W A B L E S T R E S S ( F J

T-*ALL

W A L L M A T E R I A L TEMPERATURE ( F 1

DELP-S

C A L C U L A T E D S H E L L PRESSURE DROP F O R T H E B A F F L E SPACE ( P S I )

DENS-H

M E A N D E N S I T Y O F T H E HOT F L U I D F O R T H E B A F F L E SPACE ( L B I F T 3 )

V I SC-H

M E A N V I S C O S I T Y O F T H E HOT F L U I D FOR THE B A F F L E SPACE ( L B / F T - H R J

DELT-W-A OELT-W DELP- 5 DENS-H ------------- -1 ---h A--L L- -----------

1 2 3 4 5 6

7 8 9 10 11 12 13 14 15 16 17 18 19

1 5 10 15 20 26 32 38 44 51 57 63 69 74 79 84 89 93 97

53.05 61.14 70.73 78.72 86.7@ 94.22 100.01 104.06 106.05 105.97 103.91 100 40 95.38 90.69 85.40 80.07 74.71 70.78 67.2 7

S0.73 1C6.37 121.2c 124.90 128.62 132.70 136.45 139.87 142.89 145.94 148.16 150.07 151.64 152.83 153.88 154.92 155.94 156.83 157.81

1061.5 1036.8 1007.0 579.9 S53.0 923.9 857.4 873.5 e52.6 831.8 €16.8 803.9 793.4 785.5 778.5 771.7 765.0 7 59.1 752.7

1.785 3.391 3.380 3.364 3.358 3.345 3.332 3.320 3.307 3.292 3.280 3.268 3.255 3.245 3.235 3.225 3.21 5 3.207 3.1 99

113.2 113.5 113.9 114.3 114.6

115.1 115.5 116 -0 116.4 116.9 117.4 117.8 118.3 118.6 119.0 119.4 119.7 120.0 120.3

-----V I SC-H

2.630 2.681 2.746 2.815 2.886 2.976 3.071 3.172 3.278 3.411 3.531 3.660 3.796 3.917 4.044 4.178 4.320 4.439 4.564

* **

‘ (

** *

THE FOLLOWING TABLE G I V E S I N F O R M A T I O N AT EACH INCREMENT THROUGH THE EXCHANGER

THE CCLUMh L A B E L S FOR T H I S T A e L E ARE D E F I N E D BELOW

INCREMENT NUMBER

LENGTH

TUBE LENGTH FOR THE INCREMENT ( F E E T )

T-HOT

TEMPERATURE OF THE HOT F L U I D ( F I

1-COLD

TEMPERATURE OF THE COLD F L U I D ( F I

P-COLD

PRESSURE OF THE COLD F L U I D ( P S I 1

OELP-C

T U B E PRESSURE ORCP FOR THE INCREMENT ( P S I 1

RES-I N

THERMAL RESISTANCE OF THE I N S I D E F I L M FOR THE INCREMENT ( H R - F / B T U )

RES-WALL

THERMAL RESISTANCE OF THE WALL M A T E R I A L FOR THE INCREMENT ( H R - F / B T U )

RES-OUT

THERMAL RESISTANCE OF THE O U T S I D E F I L M FOR THE B A F F L E SPACE I N WHICH THE INCREMENT L I E S ( H R - F / B T U l

RES-TOT

TOTAL THERMAL R E S I S T A N C E BETWEEN HOT E COLD F L U I D S FGR THE INCREMENT ( H R - F / B T U )

----I

LENGTH -a_---

1.016

2 3 4 5 6 1 0 9 10

1 e038 1 .0c 2

11 12 13 14

0.975 00951 00924 00899 0.882 00859 0.839 0.824 0.809 0.794 0.180

T-HOT -.-----

1150.0 1141.0 1144.0 1141.0 1138.0 1135.0 1132.0 1129.0 1126.0 1123.0 1120.0 1117.C 1114.0 1111.1

-T-COLD 1c00.0 993.5 $82.9 576.4 967.9 961.4 952.4 945.9 939.4 930.3 923.8 917.3 9112.8 $04.3

P-COLD

3600.0 3604.4 3608.5 3612.5 3616.3 3620.0 3623.5 3626.9 3630.2 3633.3 3636.4 3639.3 3642.1 3644.9

DELP-C RES-IN RES-WALL RES-OUT RES-TOT ----------------------------------

4.390 4.173 3.979 3.021 3.619 3.520 3.385 3.279 3.147 3.030 2.937 2.845 2.156 2.670

0.000476 0 0 0 0 4 13 0.000469 0.000464 O.OQ0460 0.000455 ‘3.00@451 0. 0 0 0 4 4 1 0.000442 0.000430 0.000434 0.000429 0. 000424 0.000420

0.000721 0.000724 0 00012 7 0.000130 o.ooai33 0.000736 0.000139 0.000142 a. 0 0 0 7 4 5 0.000740 0 00015 1 0 00015 3 0 000156 0-000759

0 -000842 0.000842 0.000042 0.000042 0.000 847 0.000047 0 000 847 0 o000841 0 000 0 4 1 0,000853 0.000853 0.000853 0.000853 0.000053

0 - 0 0 2039 0 -002039 @ -002039 C 0 0 2037 0.002039 0.002038 0 0 0 2036 0.002036 0 00 2034 0 .@02@30 0oO02031 0.002035 O.QQ2033 0 .OQ2@3L

’ I

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

0.768 0.755 0 0742 0.729 0.110 0.710 0 -70 1 0 -694 0.606 0 e679 0.672 0.660 0.662 0.657 0.652 0.647 0.643 0.641 0.637 0 e634 0.631 0.620 0.626 0 -626 0.625 0.623 0.622 C,.621 0 e620 0.622 0.622 0 623 0 e623 0.624 0.624 0.625 0.630 0.632 0.635 0.637 0 -639 0 e642 0 649 0.652 0.655 0.659 0 663 0.660

1108.1 1105. 1 1102.1 1099. 1 1096. 1 1093.1 1090 1 1087.1 1084.1 1081.1 1078.1 1075.1 1072.1 1069.1 1066. 1 1063.1 1060.1 1057.1 1054.1 1051.1 1048.1 1045 1 1042.1 1039.1 1036.1 1033.2 1030.2 1027.2 1024.2 1021.2 1018.2 1015.2 1012.2 1009 2 1006.2 1003. 2 1000.2 997.2 994.2 991 2

see. 2

985.2 982.2 979.2 976.2 973 2 970.2 967.2

897.8 891.3 084.7 078.2 871.7 866.3 059.8 855. c e49.0 844.5 839.3 834.5 829.7 824.9 820.2 815.9 811.7 807.6 803.4 799.5 795..7 792.1 780.6 785.2 781.9 178.9 775.9 773.0 770.3 767.8 765.2 762.8 760.6 750.5 756.4 754.4 752.7 750.7 749.3 747.9 746.5 745.1 744.0 742.7 741.4 740. o 739.3 730.5

3647.6 3650.2 3652.7 3655.1 3657.5 3659.7 3662.0 3664.1 3666.2 3668.3 3670.3 3672.2 3674.1 3676.0 3677.8 3C79.6 3C81.3 3683.0 3604.7 3686.3 3687.9 3689.5 3691.0 3692.5 3t93.9 3695.4 3696.8 3698.2 3699.5 3700.9 3702.2 3703.4 3704.7 3705.9 3707.2 3708.3 3709.5 3710.7 3711.8 3712.9 3714.0 3715.1 3716.2 3 717.3 3710.3 3719.3 3720.3 3721.3

2.592 2.510 2.430 2.350 2.202 2.223 2.161 2.109 2.054 2.002 1.950 1.909 1 862 1.818 1.775 1.734 1.694 1.662 1 626 1.590 1.556 1.523 1.490 1.464 1.436 1.407 1.379 1.353 1.328 1.307 1.282 1 260 1.239 1.215 1.193 1.173 1.159 1.142 1.123 1.104 1.086 1 071 1.061 1.044 1.027 1.010 0.995 0.982

0 0004 14 0 000409 0.000404 0.000398 0.000392 0.00038 7 0.000381 0.000376 0.0003 71 0.000366 0.000360 0.000354 0.000349 0.000344 0 0003 38 0 .000332 0 0003 25 0 0003 19 0.00C314 9.000309 0 000 30 3 0.000297 0 000290 0.C00204 0 .000 2 80 0 . COO2 73 OeC00267 0. COO26 1 0.0002 54 0.000247 0 *OO0241 0.000236 O.OC’O230 0 000 223 0.000216 0 .0002 10 0 000205 0 . 00C 199 0.000193 0.000186 0.000179 0.000174 0 000 160 0.000 163 0.000157 0.0001 52 0 000 145 0.000139

0 00076 1 0.090764 0.000767 0.000770 O.CO0772 0.000 775 0.000778 0.00070C 0.000702 0.000185 0.000787 0.000789 0 00079 2 0.000794 0 . 000796 0.000798 0 000 80 0 0.000 80 2 0.003804 0 000 80 6 c.000808 0.000810 0.om81 2 0 000814 0.00081 5 0.0008 17 0.000819 0.1)00020 0*000822 0.000 82 3 0.000825 0 000 026 0.000027 0 . C0 0029 o .000830 0.00003 1 0.000832 0 e000834 0.000835 0.000836 0.000837 0.009838 0 . QOO039 0.000840 0 . COO841 0.90084 1 C 00004 2 0 000843

0 -000859 0 eOOO059 0.000859 0 -000859 0 -000859 0 000 86 5 0.000065 0.000065 0 e000865 0 e000865 0 -000 065 0.@00872 0 .OOO872 o.oaoa72 0 e000072 0 000 07 2 0.000072 0 00‘28 80 0 ooa88o 0.000880 0.000880 0 000 0 80 0 000800 0.000888 0 000008 0.000888 0.000088 0 .000888 0 .000 8 0 8 0 -000897 0 0000897 0 000 897 0.000897 0.000897 0.000897 0 -000 897 0.000907 0 .00@907 0 A0090 7 a ooo 907 0 e000 9C 7 0 000907 0.000916 0 eQOC916 0 0009 16 0.000916 0 000916 0.000916

. .

0 0 0 20 34 0.002032 0 e 0 0 2030 0.002026 0.002023 0.002027 0 - 0 0 2024 0.002021 0.00 2018 0 - 0 0 20 15 0.00201 1 0 .002C16 0.002012 0.00201c 0 002006 @ 00 2002 0 00 1996 ‘0. Q@ 2002 0.0 91998 0 . 0 0 1995 0 0 C 1991 00001907 0 - 0 0 1981 O.OC1986 0 CO 1983 0.0 C 1979 O.CO1974 0.00 1969 0 - 0 0 1964 0.00 1967 0.00 1963 9.0 01558 C. C 0 1954 0.0 C 1949 0 - 0 0 1943 0 - 0 0 1938 0 0 0 1944 0.0 0194C 0.001935 0.0 C 1928 0 0 0 1923 0.001918 0 - 0 0 1923 0.001918 0 001914 0 00 1909 0 00 1903 0 e 0 01898

RES-IN -------63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 8C 81 82 83 04 85 86 87 88

89 90 91 92 93 94

95 96 97 98 99

100

C.677 0.682 C.687 0.693 0.699 C.706 0.716 0.723 0.73C 0.738 0.746 0.756 0.765 0.774 0.784 0.793 C.807 0.817 C.828 0.838 0.849 0.865 0.876 00888 0.901 0.913 C.931 0.944 0.956 0.968 0.985 0.999 le014 1.027 1.040 1.049 1eC57 1.066

964.2 961.2 958.3 955.3 952.3 949.3 946.3 943.3 940.3 937.3 934.3 931.3 928.3 925.3 922.3 419.3 916.3 913.3 910.3 907.3 904.3 901.3 898.3 895.3 892 3 889.3 886.3 883.3 880 4

877.4 874.4 871.4 868.4 865.4 862.4 859.4 856.4 853.4

737.8 737.2 736.5 735.7 735.0 734.3 733.7 733.0 732.3 731.6 731.0 730.3 729.7 729.0 728.4 727.8 727.2 726.5 725.9 725.3 724.7 724. C 723.4 722.7 722.0 721.4 720.7 720. 1 718.6 717.1 715.6 714.0 712.7 71 1.2 709.3 706.9 704.5 702. 0

3722.3 3723.3 3724.3 3725.2 3726.1 3727.1 3728.C 3728.9 3729.8 3730. 6 3731 5 3732.4 3733.2 3734.1 3134.9 3735.7 3736.5 3737.3 3738.2 3739.0 3739.8 3740.6 3741.4 3742.1 3742.9 3743.7 3744.5 3745.2 3 746.0 3746.8 3747.5 3748.3 3749.0 3749.8 3750.5 3751.3 3752.0 3752.8

0.975 0.963 0.948 0.935 0.922 0.909 0.902 0.889 0.877 0.865 0.. 853 n. 845 0.838 0.831 0.826 0.821 0.818 0.812 0.807 a. 802 0.796 0.794 0.787 0.78@ 0.774 0.768 a. 765 c. 760 0.758 0.755 a. 7 5 6 0.755 a. 754 0.750 0.750 0.746 0.742 0.739

0e 000 1 3 4 0 0001 2 9 0 COO 1 2 3 0.000119 O.OCO1 1 5 0.009111 0 OOOlO7 0.000 1 0 4 0. coo 1 0 1 0 OOOO99 O.COOC96 0. COO092 O.OOCC91

O.QOOC90 0.00C089 0.0000 8 8 0.OG0087 0 OOQC 86 0.000085 0 . 0000 8 4 a .coo083 0 a000 0 2 0.000c 8 1 0 . coo0 80 0.0000 80 0. 0oc 0 80

O.OGOC80 0 000@82

oooc 88 0. COnOSft 0.000 1 0 0 a. 000 i o 7 0.000 1 1 4 0.000 1 2 2 0.000 127 C. 000 1 3 4 0 000 1 4 1 0.000149 0.

RE S-TOT --------

0.000 8 4 4 o.oooa44 0 000845 0.000846 0.000 8 4 7 0.000847 0.000848 0.000849 0 .a00849 o.ooa85a 0.009851 o. 0 0 0 8 5 2 0.000852 c. c o o 0 5 3 Oo000854 0.000 854 0.000855 o.000856 0 000857 Oo000857 0.0008 50 O.COO859 0 000859 0.000860 0.000861 0 000062 C 000 8 6 2 0.000863 0.000865 0.000866 0.000867 0,000868 0.000869 0.000870 0*000872 0.000073 0.000075 0.000877

0.000925 0.000925 0.00092 5 0 COO9 25 0 000925 @ oOOO92 5 0.000935 0.000935 0 eOOC935 0.000935 G e000935 0 OOn943 0 000943 00000943 0 .COO943 0 COO943 0.000952 0.000952 0.000952 0.COO9 52 O.CO0952 c1.000961 0 e00096 1 0 . 0 0 @ 9 61 0 .000961 0.00096 1 0.000970 0.0009m 0.000970 0.000970 o .om 9 7 8 O.CO0978 0 e000978 0 e000978 Po000985 O.OC0985 0.000985 0.000985

0 e 00 1903 0 e00 1 8 9 8 0 -001 8 9 3 0 .OC 1890 OoOO1 887 0 001 8 8 4 0.0 Cle90 0.001888 O.GC1886 0.00 1884 0.001882 0.00 1887 O.FO1887 3 0001886 0 0001 8 8 6 0.001885 0.00 1 e 9 4 0 .oa 1894 0 . OC1893 O.OC1893 0.001892 0 00 190 1 0 00 1901 0 .OC 1901 0 00 1902 0 .001902 0.001912 0.001915 0 . 0 0 1922 0 0 0 1929 0 -00 1945 0.0 C1953 0.001961 9-00197P 0 00 1 9 8 4 0 001992 0 c 02 0 01 0.00201 1

* * *

THE FOLLOWING ARE AVERAGE O R T O T A L P R O P E R T I E S FOR T H E E N T I R E EXCHANGER

393

TOTAL NUMBER O F TUBES=

T O T A L NUMBER O F @ A F F L E SPACES=

LEhGTH O F A BAFFLE S P A C I N G ( F T ) =

3.980

I N S I D E D I A M E T E R OF EXCHANGER S H E L L ( I N C H E S ) = TOTAL PRESSURE DROP IN TUBES ( P S I ) =

153.53

TGTAL PRESSURE DROP I N SHELL ( P S I ) =

61.01

LOG-MEAN

DELTA-T

(F)=

18.21

150.0C

TOTAL TUBE L E N G T H ( F E E T ) =

76.38

TOTAL HEAT TRANSFER AREA BASED ON TOTAL TUBE LENGTH ( F T 2 ) =

3929.3

G V E R A L L HEAT TRANSFER C O E F F I C I E N T BASED ON T O T A L TUBE LENGTH ( B T U / H R - F T Z - F l =

TGTAL B A F F L E SPACE LENGTH ( F E E T ) =

699.02

75.61

TOTAL H E A T TRANSFER AREA BASED ON TOTAL B A F F L E SPACE LENGTH ( F T Z ) =

3889.9

OVERALL HEAT TRANSFER C O E F F I C I E N T BASED ON TOTAL B A F F L E SPACE LENGTH (BTU/HR-FTZ-F

706.10

***

157 ORNL TM-2815

Interna 1 Distribution

1. 2. 3. 4. 5-9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

J. C. S. M. C. E. E. G. R. D. W. J. S. H. D. W. J. D. W. L. F. W. C. W. W. A.

31.

32. 33. 34. 35. 36. 37.

R. P.

R. J. K. G.

L. Anderson 38 * F. Baes 39. E. Beall 40. Bender 41. E. B e t t i s 42. S . Bettis 43. G . Bohlmann 44. E . Boyd 45 B . Briggs 46. F. Cope (RDT S i t e Rep.) 47 K. Crowley 48 R. D i s t e f a n o 49. J. D i t t o 50 51-60. G. Duggan A. Dyslin 61. P. E a t h e r l y 62. R. Engel 63. E . Ferguson 64. F. Ferguson 65. M. F e r r i s 66. C. F i t z p a t r i c k 67. K. Furlong 68. H. Gabbard 69 R. G a l l 70. R. Grimes 71. G. Grindell 72. N . Haubenreich 73. E . Helms 74-75. R. Kasten 76. J . Ked1 77. J . Keyes 78-90 0 . Laughon (RDTSite Rep.) 91. H. Llewellyn 92. 0

M. H. R. H. H. L. J.

I . Lundin G. MacPherson E . MacPherson E . McCoy

A . McLain E . McNees R. McWherter A . S . Meyer R. J . Moore H. A. N e l m s E . L. Nicholson A. M. P e r r y T. W. P i c k e l M. W. Rosenthal Dunlap S c o t t M. Siman-Tov W. C. Stoddart R. E. Thoma D. B . Trauger H. K. Walker G. M. Watson H. L. Watts J . R. Weir M. E. Whatley J . C . White W. R. Winsbro Gale Young C e n t r a l Research L i b r a r y Document Reference S e c t i o n GE D i v i s i o n L i b r a r y Laboratory Records Department Laboratory Records, ORNL R.C. ORNL P a t e n t O f f i c e

External Distribution

93.

David E l i a s , USAEC, D i v i s i o n of Reactor Development and Technology, Washington, D. C . 20545.

94.

Ralph H. J o n e s , USAEC, D i v i s i o n of Reactor Development and Technology, Washington, D. C. 20545.

95-96.

T. W. McIntosh, USAEC, D i v i s i o n of Reactor Development and Technology, Washington, D. C . 20545.

158

97. 98-99. 100.

M. Shaw, USAEC, Division of Reactor Development and Technology, Washington, D. C. 20545. Division of Technical Information Extension. Laboratory and University Division, USAEC, ORO.