ORNL-TM-2815.txt

)

)y

1wy

w k.

RECEV

 

: R E’\, PT! r—

-
r

 

 

OAK RIDGE NATIONAL LABORATORY

operated by
UNION CARBIDE CORPORATION = NUCLEAR DIVISION m
for the

U.S. ATOMIC ENERGY COMMISSION
ORNL- TM-~ 2815

COMPUTER PROGRAMS FOR MSBR HEAT EXCHANGERS

C. E. Bettis T. W. Pickel
W. K. Crowley M. Siman-Tov
H. A. Nelms W. C. Stoddart

NOTICE This document contains information of a preliminary noture
and was prepared primarily for internal use ot the Ook Ridge National
Loboratory. It is subject to revision or correction and therefore does

not represent a final report.

DISTRIBUTION OF THIS DOCUMENT 1S UNLIMITED
 

 

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 its use would not infringe privately owned rights,

 

 
OAK RIDGE NATIONAL LABORATORY

OPERATED BY
UNION CARBIDE CORPORATION
NUCLEAR DIVISION

UNION
CARBIDE

POST OFFICE BOX X
OAK RIDGE, TENNESSEE 37830

June 24, 1971

To:  Recipients of Subject Report

Report No. : ORNL-TM-2815 Classification: _ Unclassified

Author(s):E; E. Bettis, W. K. Crowley, H. A. Nelms, T. W. Pickel

Subject: Computer Programs For MSBR Heat Exchangers

 

Request compliance with indicated action:

Please affix the attached corrected pages 6, 7, 58, 62, 63, 86,87,88,89, 117, 124, 125
to pages with same numbers in your copy(ies) of the subject report. They are prepared
on gummed stock for your convenience. Also prepared on gummed stock is a correction
for the bottom two lines on page 9 of the report.

Please cerrect your copies promptly to avoid further errors. The corrected design data for
the primary heat exchanger agree with the data shown in Report No. ORNL-4541.

Laboratory Records/Department
Technical Information Division
Table 2.1. Design Data for MSBR Primary Heat Exchanger

 

Type

Number required

Rate of heat transfer per unit,
MW
Btu/hr

Tube-side conditions
Hot fluid
Entrance temperature, °F
Exit temperature, °F
Entrance pressure, psi
Pressure drop across exchanger, psi
Mass flow rate, 1lb/hr

Shell-side conditions
Cold fluid
Entrance temperature, °F
Exit temperature, °F
Exit pressure, psi
Pressure drop across exchanger, psi
Mass flow rate, 1b/hr

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

Tube sheet
Material
Thickness, 1in.
Sheet~-to-sheet distance, ft

Total heat transfer area, ft2
Basis for area calculation

Volume of fuel salt in tubes, ££3

Shell
Material
Thickness, in.
Inside diameter, in.

Central tube diameter, in.

Baffle
Type
Number
Spacing, in.

Shell-and-tube one-pass vertical
exchanger with disk and doughnut
baffles

Four

556.5
1.9 x 10°

Fuel salt
1300

1050

180

130

23.4 x 100

Coolant salt
850

1150

34

115.7

17.8 x 10°

Hastelloy N
5803

0.75

0.375

0.035

24.4

Hastelloy N
4,75
23,2

13,916
Outside of tubes

71.9

Hastelloy N
0.5
67.6

20.0

Disk and doughnut
21
11.23
Table 2.1 (continued)

 

Disk outside diameter, in. 54,20
Doughnut inside diameter, in. 45.3
Overall heaf transfer coefficient, U,
Btu/hr.ft*.°F 784.8
Tube
Maximum primary (P) stresses
Calculated, psi 683
Allowable, psi 4232

Maximum primary and secondary
(P + Q) stresses

Calculated, psi 12,484
Allowable, psi 12,696
Maximum peak (P + Q + F) stresses
Calculated, psi 13,563
Allowable, psi 25,000

 

wave configuration., The tubes are held in place by wire lacing in this
upper portion of the tube bundle. Since baffling is not employed in
this region, the bent-tube portion of the bundle experiences essentially
parallel flow and a relatively lower heat transfer performance.

Below the bent-tube region of the bundle, evenly spaced doughnut-
shaped baffles are used to hold the tubes in place and to produce cross
flow. The baffles spacings and cross-flow velocities are designed to min-
imize the possibility of flow-induced vibration. The tubes in this baf-
fled region of the heat exchanger have a helical indentation knurled
into their surface to enhance the film heat transfer coefficients and
thereby reduce the fuel salt inventory in the exchanger. No enhancement
of this nature was used in the upper bent-tube region because of present
uncertainty about the reliability of tubes that are both bent and

indented.
 

 

Bottom of page 9:

For completely turbulent flow with Reynolds numbers greater than
12,000,

Q.14

h.d ub
u—l") (EFl) (2.3)

i3

k.,
i

 

= 0*'8 1/3
0.0217(NRe) (NPr)

 
1047 FORMAT(31HGBERGLIN MODIFICATION FACTOR = ,F542) MSBR 500
1048 FORMAT(1HQ, 2X+1HIs7TX43HTCI,9X43HTCO,9X,3HCWT 99Xy 3HTFI,9X,3HTFG, MSBR 510
19Xy 3HF WT y 8X y4HTWDT/ /11Xy 1HF y11Xy1HF,11X,1HF 411X, MSBF 511
2 1HF 311X 91HFy 11 X3 1HF 311Xl HF // (1 X3 12,7TE1264)) MSBR 512
1049 FORMAT (1HCy 2X y1HI»9Xy2HV1y 9X,2HV2 ,9X,2HV3 ,9X,3HVW1 ,9X,3HVW2 , MSBF 520
1 8Xy4HPDSCy 8X y4HPLTC//32Xs 6HFT/SEC 33X THLB/SQFT//(1X,13,7F12.4)) MSBR 521
105C FORMAT(1HO, 2X s1HI s 5Xy5SHRENTO,7X+5HPRNTO s 7TX EHRENSOL ,€X ,6HRENSC2, MSBR 530

16X, 6HKENSC2 y7X933HHTO$ 8Xy 4HAHSO 39X 9 3HUCA y8X s 4HHEAT//TTX, MSBR 531

¢ 13HBTU/HR/SQFT/F4313X,6HBTU/HR// (1X:13,9E12e4)) MSBR 532
1051 FORMAT{(27FCTUBE WALL AVERAGE TEMPe = +F10e2) MSBR 54C
1052 FORMAT (28FCSHELL SIDE AVERAGE TEMPe = 4 F1lGe2) ' MSBR 55C
1053 FORMAT(1HO,24+P STRESS AT TUBE 0D AND TUBE ID = , 2F10.241Xy MSBR S6C
1 9H(LB/SQIN)//18H(SHOULD NOT EXCEEDsF1l0e243H 1)) MSBR 561
1054 FORMAT(1HC,36FP+Q STRESS AT TUBE OD AND TUBE ID = , MSBR 570
1 2F10e2+s1X49H(LB/SQIN}//18H{ SHOULD NOT EXCEEDyFlC.2, MSBR 571

2 3H 1)) MSBR 572
1055 FORMAT(1HC,38FP+Q+F STRESS AT TUBE OD AND TUBE ID = , MSBR 580
i 2F10e42s1X,SH(LB/SQIN)//18H(SHOULD NOT EXCEEDsFl0e2, MSBR 581

2 34 1)) MSBR £82
MSBR €50

READ IN ANC PRINT OUT INPUT DATA MSBR €6C
KEYT= 1 MSBR 610
VM1{1)=0e MSBR 620
VM2(1)=0. MSBR €30
VM3(1)=0. MSBR 640
VWO1(1l)=C, MSBR €50
VWO3(1)=0. : MSBR 660
RENSO1(1)=Ce MSBR 670
RENSGO2(1) =0, MSBR 680
RENSO3(1) =0, MSBR 690
HS01(1)=0. MSBR 700
HSO02(1)=0, MSBR 710
HS03(1)=0. MSBR 720

MSBR 810

8¢
10

IF(KEY1leEQe C)BSOI=Cs5*(BSL+BSH)
CURVES=C o C6S812%ARC* EXPRAD+ Oe4*(KAB—RAS)+625*%BSOI

IT =0
KFINAL =0
I=1
HEFI
HEFO
TSUM=C,
SSUM=C,
THEATO = Q.0
TPDTO = 0.0

1.
1.

i

TPDSO = 040

TFO(I)}=FTC

TCI(I)=CTC

TIF=~5,0

TIC2—500

CDTF=0,

FDTF=C.

BSO = BSQO1

BRL1 =

GBRL = Coe 77%BRL1%%(-,138)
AWO1l = BSC*xLAWOL

AWO3 = BSC*LAWO3

AWl = SQRT{AWO1*APO1l)
AWZ = {(AWO1l+AW03)/2
AW3 = SQRT(AWC3*APD3)
GSO1 = QC/AMW]

GS02 = QC/AW2

GS03 = QC/AW3
BSO=CURVES

EQVBSO= CURVES+ 13.,* (CIA+DIAT)
KEY4=C

KEY5=(

ATC TCI(I) + (TIC/260)

CFT = ATC +CDTF*HSFCT
ATF = TFO(I)+TIF/2.
FFT=ATF-FLT F*HSFCT
FI=1

own

TUBLN(I) =(FI-1,)%BSOI+CURVES

BSC/ ({RAB=(KAB=RAT)/26)=(RAS+(RAE6~RAS)/2.))

MSB
MSB
MSB
MSB
MSE

1850
1860
1870
188C
1890

MSBR 7320
MSBk 740

MSB
MSB
MSB
MS8B
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSE
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB

1900
1910
1920
193C
1940
1950
1960
1970
l98C
199G
2000
2010
2020
2030
204C
2050
2060
2C70
2C80
2090
21G0
2110
2120
2130
2140
2150
2160

2180

2200
2210

Z9
CVIS=Ce2l21%EXP(4032e/(4€04+ATC)) MSB 222C

CVISW=0e 2121%EXP(40324/(4604+CFT)) MSB 223C
CDEN=141,27-0.02466*ATC MSB 2240
CCON=Co24C MSB 2250
CSPH=0¢36 MSB 2260
FVIS=0e2637T*EXP(T3€24/(460.+ATF)) MSB 2270
FVISW=0e 2E3T*EXP(T2624/(460,+FFT)) MSB 228C
FDEN=234 ¢4 S7T~0,C2317*ATF MSB 229C
FCON=0,70 MSB 230C
FSPH=0e324 MSB 2310
VISK = (CVIS/CVISW)**(0,14 MSB 2320
FVISK=(FVIS/FVISW)**C,14 MSB 2330
DCVIS = DIA/CVIS | MSB 2340
CCDEN = 14/CCEN MSB 2350C
QCCDEN = QC*CCDEN MSB 2360
CALCULATE REYNOLS AND PRANDTL NUMBER TUBE SIDE MSB 2550
RENTO(I)=CIAI*GTO/FVIS MSB 2380
PRNTO(I)=FVIS*FSPH/FCCN MSB 239C
IF(KENTBe EQel e ANDeRENTC(I) ¢GTe1l00le eANDe IeNEol) MSB 2400
IHEF I=1 e+ { (RENTG(I)=1G00e)/90C0e )%%045 MSB 2401
POTO(I)={ «0C28+4 25%FENTO**(~4,32) ) *EQVBSO*GTQ**%2%HEF1/ MSB 2410
1l (DIAI*FDEN*4171824C0,) MSB 2411
CALCULATE HEAT TRANSFER COEFF TUBE SIDE MSB 2640

IF(RENTO(I)LT412CCC6 IGO0 TO 12
HTO(I ) =FCCON/CIA*eC217*{RENTO(I ) *%¢8)* (PRNTC(I)%%,3323)%FVISK*HEFI MSB 2430

GO TO 15 MSB 2440
12 IF(RENTO(I).LT421CCe) GO TO 14 MSB 245C
i3 HTO(I) = FCON/DIA¥eCB9% (RENTO(I )**467895-14141272)* (PRNTO(])
1%%¢ 3333 )% FVISK¥HEF I* (1e+e3233%(DIAI/TUBLN(I) ) %% ,6666)
GO TO 15 MSB 2470
14 HTO(I) = FCCN/CIA%*(4 426+ (0o025%RENTO(I)*PRNTO(I)I*DIAT/TUBLN(TI) MSB 2480
1 )1/(le+C 0C12%RENTC(I)*PRNTO(I)*DIAI/TUBLN(I)}) MSB 2481
i5 IF(I+EQe1)GC TO 1€ MSB 2490
CALCULATE FLCw AREAS SHELL SIDE MSB 248C
VWO1(I) = QCCLEN/AWOL MSB 2510
VWO3(I) = QCCDEN/AWC3 MSB 2520
VM1(I) = GSO1*CCDEN MSB 2530
VMe(I) = GSO2*CCDEN - MSB 2540
VM3(I) = GSGC3*CCDEN MSB 2550

€9
Computer Output for Reference MSBR Primary Heat Exchanger

TOTAL HEAT TRANSFERED = 18G€217984e (BTU/HR) ( 9949 PERCENT)

MASS FLOW RATE OF COOLANT = 1759C736. (LB/HR)

MASS FLOW RATE OF FUEL = 2345432C. (LB/HR)

SHELL-SIDE TOTAL PRESSURE CRCP = 115.75 (LB/SQIN) ( SGe¢7 PERCENT]}
TUBE-SIDE TOTAL PRESSURE CROP = 129,32 (LB/SQIN) ( 9S.,5 PERCENT)
NOMINAL SHELL RADIUS = 2e81€2 (FT)

UNIFORM BAFFLE SPACING = (eS386 (FT)

TUBE FLUID VOLUME CONTAINEC IN TUBES = 71.92 (CUBIC FEET)

TOTAL HEAT TRANSFER AREA BASED ON TUBE OeDe = 13916632 (SQFT)
TOTAL NUMBER OF TUBES = 58032,

TOTAL TUBE LENGTH = 24,43 (FT)

HEAT EXCHe APPROXe LENGTFH = 22422 (FEET)

STRAIGHT SECTICN OF TUBE LENGTH = 2Ce26 (FT)

RADIUS OF THERMAL EXPANSION CURVES = Oe86 (FEET)

BERGLIN MODIFICATION FACTOR = Q679
TUBE WALL AVERAGE TEMP, = 1116454

SHELL SIDE AVERAGE TEMP. = 1012, 6¢€

98
P STRESS AT TUBE OD AND TUBE ID = 683442 €46e47 (LB/SQINI
SHOULD NOT EXCEED 4232422 )
P+Q STRESS AT TUBE OD ANC TUBE IC = 12484439 8890,S7 (LB/SQIN)
SHOULD NOT EXCEED 126967C )
P+Q+F STRESS AT TUBE OD AND TUBE IC = 13562677 1098155 (LB/SQIN)
SHOULD NOT EXCEED 2500C.CO0 )
I TCI TCC CWT TF1 TFO FWT TWDT
F F F F F F F
1 D.1150E 04 0.,1i22E 04 (C,124CE C4 0Q.1276E 04 (.13COF 04 0.1256E 04 0Q.1549E
2 0el1i22E 04 061108E G4 0Qe61178E C4 Qe1265E 04 0e1276E 04 061223E 04 Co4528E
3 0e1108E G4 O0.1094E 04 O0.,1165E 04 O0ei254FE 04 0e012¢65E 04 0601210E 04 0.4516E
4 0.1094E (4 O0.1G81lE 04 (C.1152E 04 0.1242E 04 OQ.1254F 04 0.1198FE C4 0,4525E
5 0el08lE 04 0.,1067E C4 0ell3SE 04 0e1231E 04 0e1242E 04 C(Q.1185E 04 O044533E
6 0.1067E 04 04,1053E 04 0e112¢E 04 O0,1219E C4 061231F 04 Geo1172E C4 Ce4538E
7 0.1053E 04 0.1039E 04 0.1113E 04 (0.1208E 04 0.1219E 04 (0.1159E 04 0.4540E
8 0Uel039E 04 O061025E 04 (ellCGCE 04 O0e1196E 04 061208E 04 001146E 04 (0,4540E
9 D.1025E 04 0.1012E 04 C.l087E 04 O0.1185FE 04 0e119¢E 04 041133E 04 O0.4538E
10 0.1012E 04 0.9979E C3 O0.1074E 04 O0.1173E 04 O0.1185E 04 O0.1119E G4 (Qe.4532E
1l 0,9979E 03 0e9842E 03 (e01C61E 04 Cell62E C4 061173E 04 O061106E 04 O0.4F24E
12 0,9842E C2 0e9705E U3 0.1048E 04 O0.115CE 04 (Q.1162E 04 0,1093E 04 0.4513E
13 0.9705E 03 0.9569€ 03 C.1lC35E G4 O0.1139E 04 0.1150F 04 0.1080E G4 0e4499E
14 0¢9569E 03 0e9433E 03 0e1C22E 04 (Qe1l128E 04 0e1139E 04 O0.1067E 04 044482E
15 069433E 03 069297TE 03 CelOO9E C4 O0e01116E C4 0Qe61128E 04 061053E 04 Ce44€2E
16 0,9297E 03 0,9162E 03 0.9557E 03 0.1105E 04 O0.1116E 04 O0.1040E 04 0.444CE
17 0e9162E 03 069029E C3 CeSB27TE 03 0.10S4E 04 O0e1105E 04 O0.1027E 04 0Oe4414E
18 0.9C29E 03 068895E 03 Ce9€¢SGTE 03 0,1083E 04 061094E 04 0.1014E 04 C4%3285E
19 0C.8895E 03 C.8763E G3 (C.9568E C3 0.1072E 04 0.1C83E 04 O0.1000E 04 O0.4353E
20 0e8T7T63E 03 0e8632E 03 Ce943SE 03 0.1061E 04 0.1072E 04 0.9871E 03 0.4318E
2l 0e863ZE 03 O0e8503E (02 0e9311E (3 0,1050E 04 0.,1061E 04 O0.9739E 02 0.428CE

G2
02
02

02
02

G2
02
02
02
Cc2
02
02
C2
02
c2
02
02
02
02

L8
o o b
N OO D=0 WP o e

N N P et b e s
ROV~ WP W

V1

Oe0

641833
6e1646
6el467
bel286€
€.1106
be0G926&
60748
560570
6+03G4
640219
660045
59872
59702
5¢953¢
59365
59199
59035
58€73
58713
548555

V2

0.C

6e 9424
6e5 218
669Cl4
6.8810
6.8¢€08
6e 8406
6e 8206
6.8006
e 78C 8
beT7612
CeT41l6
6e 1223
6e 7031
6e 6 E41
€Ce 6E53
e 46T
666283
666101
6e 5521
6e 5144

V3
FT/SEC

C.0

N
6.7022
€. 6825
Ce 6628
Ee€4322
606236
606042
€.584S
60,5658
6o 54€7
65278
6o 5C91
6064905
6.4T21
604539
604358
64180
6.40C4
603830
6o 3€59

VWl

Oe.0

€e3719
63530
Ce3342
6e3155
642970
6e2785
642601
6.2418
6e2236
642055
6.1876
6e1699
6.1522
6.1348
661175
61004
6.0836
€. 0669
60504
60341

VW3

0.0

Te6251
T7.6025
745801
75577
7.5255
Te5133
74913
74694
Te44T7
Te4261
T.4046
Te3834
703623
72414
72208
73003
7.2801
72601
Te2404
7.2210

PDSO

LB/SQFT

84Te4312
84744312
841.4097
8354158
8294214
82344299
81lTe4436€
Blle 4666
805.501C
79S¢ 5500
7936187
787.7100
7818259
7759714
770.1499
76443652
7584 6204
752.9199
714762676
T41.,6660
736.1208

PDTO

286961321

86l.8818
85349421
84640403
83861379
83042402
82263506
8l4e4T4E
80666165
7987803
7902712
78341628
1754529
7677529
7600996
75244968
74449495
7137.4624
730.GC410
T2206892
715.4114

88
(5N
CWO®=~O VI WP

-
™ =

T s bt (o b Bt pd et
COHO~NOCWMEIW

n
-

RENTO

0.1138E
0.1091E
041061E
0.1031E
0.1001E
0.9721E
De9434E
0.9151E
0.8874E
0.8601E
0.8333E
0.8071E
0.7814E
D.7562E
0e.7316E
0.7075E
0.6840¢E
0.66l11E
D+6389E
0.6172E
Ue5961E

PRNTC

0.8232E
0.8589E
0.8835E
0.9092E
049360E
0.9641E
0.9934E
0.1024E
0.1056E
0+.1090E
0.1125E
Oe1l61E
0+1199E
041239E
0e1281lE
0.1325E
0.1370E
0.1417E
O.1467E
O«1518E
D0.1572E

o1

o1
01
01
01
o1
02
02
Q2
02
02
02
02
02
0e
0e
02
02

02

RENSC1

0.0

0.2887E
Ce2822E
0.,2758E
6,2695E
0e2631E
0.2568E
0. 2506E
0. 2443E
Ce2382E
Ce232CE
Ce226(E
0s2199E
0.2140E
0.2081E
0.2023E
Ce1G96€E
0.191CE
Cel854E
Cel8CCE
0el174¢E

05
05
05

05
05
¢S
05
05
05
05
05
05
05
05
05
05
05
05
05

RENSO2

0.0

0.3241E
0.3169t
0. 3097E
0.3026E
0+ 2955E
O« 2884E
0.2813E
0.2743E
Oe 26T74E
Q0. 2605E
042537E
O+ 2469E
0.2403E
0.2337€
0.2272E
0.2207E
0. 2144E
0.,2082E
0. 2021E
0e1961E

RENSO3

0.0

0.3138E
D«3068E
0+2999E
0.2930E
0.2861E
0.,2792E
0.27 24E
0.2656E
0.2589E
0.2523E
0. 2456E
0.2391E
0.2326E
0.2263E
0.,2199E
0.2137E
06207¢€E
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

HTO

0.1732E
0.3422E
0.3318E
0.3232E
0.3147E
0.3063E
0e2979E
0.2896E
0.281l4E
0.2T32E
0.2651E
0.2571E
0.2492E
0.2413E
0.2335E
0.2258E
0.2183E
0.2108E
0. 2034E
0.1961E
0.1889E

AHSO

0e5314E
0.2580E
0.2532¢
0.2507E
0.2481lE
0e2456E
0. 2430E
0.2403E
02377E
0.2351E
0.2324E
0«2298E
C.2271E
0.2245E
0e.2218E
0«2192E
0.2165E
0.2139E
0.2112E
0.2086E
0.2059E

BTU/HR/SQFT/F

03
04

UGA

0.3653E
0.1044E
0.1026E
0«1014E
0.1001E
0.9881E
0.9751¢E
0.9619E
O« 9485E
0.9349E
0.9211E
0.9071E
0.8929E
0.8786E
0.8640E
0.8493E
0.8345E
0.8194E
0.804 2E
0.7888E
0. 7733E

HEAT
BTU/HR

Ge1793E
C. 87COE
Ce 8678E
0.8695E
Ce8TI0E
Ce8T1SE
Co 8724E
0.8724E
0. 8719E
0. 87C8E
C.B8692E
0.8672E
0. 8645E
C.8612E
Oe 8574E
Ce 8521E
C.8481E
0. 8426E
Qe 8364E
0.82STE
0. 8224E

68
117

CALCULATE THE DIFFERENCE BETWEEN THE TOTAL TUBE SIDE DELTA-
P (SDPT) AND THE ALLOWABLE TUBE SIDE DELTA-P (DELPTA)

v

YES NO
CHECK TO SEE IF SDPT IS WITHIN 3% OF DELPTA >——
A 2
ADJUST THE NUMBER OF TUBES IN THE EXCHANGER (NUMT)
66 2

CALCULATE THE DIFFERENCE BETWEEN THE TOTAL SHELL SIDE DELTA-
P (SDPS) AND THE ALLOWABLE SHELL SIDE DELTA-P (DELPSA)

v

NO
CHECK TO SEE IF SDPS IS WITHIN 3% OF DELPSA )——“
ADJUST THE BAFFLE SPACING (BS(K)) #@

\\\\ ALL OF THE HEAT HAS BEEN TRANSFERRED--THE TOTAL PRESSURE DROPS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ON BOTH TUBE AND SHELL SIDE ARE WITHIN LIMITS. WE HAVE AN
ACCEPTABLE SOLUTION.

WRITE OUT THE RESULTS.

 

Fig. D.l. (continued)
16

161
162

17
18

19

MS=1

$X=0

S85=0

TC(l)=7C2

TH(1)=TH1
RWK=DTO*LCGF(LTO/DTI)/2,0
PCll)=PC2

CALL SVHIZyPCZ:TC2430UMHC(1))
BN=FLODATF (N)

QAX=QT/ BN

DECT=QX/ { WH*CPH)

DECH=QX/WC

I=1

K=1

SB = SBK*8SL

LOPT=0

TCON=TH(I)}=CTPB/2.C

IF(1eEQel) GO TO 161

VMUD=0,21 22*EXPF{40226/1TH#+460,.))
VMUB=0421 22*EXPF (40324 /( TCON+460. ) )
FACT=(VMUC/VMUB)**0,14

GO TO 162

FACT=1,0

CONTINUE

DENH=1414 2B8E+(C-2,4¢6E-02*TCON
VISH=0,2]1 22E+00*EXPF(4032.CE+CO/( TCON®4 60, CE+CO))
DHOT(K)=DENH

VHOT(K )=V ISF
CON1=(CPH*VISF/TCH)**Co6€YE+QQ
GM=WH/ 58

RECB=DTO*CM/V 1ISH
IF(RECB-800.0117,18,18
HJB=0, 571 /{RECB**C¢456)

GOTO19

HJB=0e 346 /( RECB**(0, 282)
HB=(HJB*CPH*GM/CON1 } *FACT
GW=WH/ SW

GS=SQRTF( CM*GNW)
RECW=DTO*CS/V ISH
IF(RECW-800,0)20,21,21

Sup
SUP
SUP
SupP
SUP
SUP
SUP
SUP
SUP
SUPpP
SUP
Sup
sue
SupP
SUP
suep
SUP

1020
103¢
1€ 4C
1050
1069
1074
1CRo
109C
1100
111¢
1120
1130
1140
1150
1160
1170
1180

sSup=*11°1
SUP%*1182
SUP#*1182
SUP*1184
SUpP=*1185
SUP*1186
SUP*1187

sue
SUP
SuUP
SUP
SUP
SUP
sup
SUP
SUP
Sup
SUP

1190
12CC
1210
1220
123C
124C
125C
1260
1270
1280
1290

SUP*1300

SuP
SUP
SUP
SuUP

1310
1320
133¢
1340

A
20

21
22

23

24

25

26

28

29
30
31
32

33

HIW=0,571 /{RECW*%) ,456)

6G0TO022

HIW=0e 346 /(RECW**0,382)

HW= (HJW*CPH*GS/CONL ) *FACT

HO=(HB*( 1 s0=2C¥PW) +HW*{ 2,0%PW) ) *BLFH
HO = HO*GEBRL

RO(K)=1s07/HC

THUI+1)=TH({ I)=-DECT

LOP5=0

HC{I+1)=HC{1)-CECH

DELPP=(0.0

PC{I+1)=PC{ I)+CELPP

LOP3=0

LOP4&=0

TC(I+1)=TC{ 1)-CECH

CALL SVH{2,PC(I+1),YC{I+1),DUM,HCG}
EH=ABSF(HC(I+1)-HLG)
[IF(EH-0.0C1#+-C(1+41)1})31,31,26
TRIAL=TC( 1+1)

HRIAL=HCG
TCUI+L)I=TC{I+1)+(HC (141 )=HCGI®R(TC(I)-TC{I+1))/{HCLI)=~HCG)
CALLSVH{2 PC{1I+1),TC(I¢1),DUM,HCG)
EH=ABSF(HC(I+1)-HCG)
IF{EH-0,0C1*HC(I+1))31,31,28

TNEXT=TC( I+1) +(HC(T+1)=HCG)*(TC(I+1)-TRIAL)/(HCG-HRIAL)
TRIAL=TC( I+1)

HRTIAL=HCG

TC(I+1)=TNEXY

LOP3=L0OP3+]

IF(LOP3-1C)30,30,29
WRITEQUTPUTTAPESL,1015,LCP3

GOTO80

GOTO27
DENOM=(TH(TI+1 )=TC{I+1 )/ (TH(I)-TC(I})
TOEN=ABSF (DENCM-1,0}

IF(TDEN-0,05) 32,33,33

DELTEM=0o SE4+QC*(TH(I+1)=TC{I+1)+TH(I)=TC(I)}
GO TO 34

sup
SuP
Sup

1350
1360
137¢C

SUP%x1380

SUP
sue
sup
SUP
sue
SUP
SUP
sSup
Sup
SuUP
SuUP
SuUP
Sup
sup
SUp
SuUP
SuUp
SUP
SuUpP
Sup
SupP
SuUPpP
SUP
sup
SuUP
SupP
Sup
Sup
sup
SupP
SUP
Sup
sup
sur

DELTLM=(TH{ 1+1)=TCUI¢L)=TH{I)I+TC(I))/LOGFUUTH{I+1)=TCCTI+1))/(TH(L)SUP

1-TC(I)))

sye

1390
140C
1410
1420
1430
1440
1450
1460
1470
1480
149C
1500
1510
1520
1530
154¢
155¢C
1560
157¢
158¢C
159C
1600
1610
162C
1630
164C
1650
1660
1670
1680
169G
1700
1710
1720
173¢
1731

Gel
ORNL TM-2815

Contract No. W-7405-eng-26

General Engineering Division

COMPUTER PROGRAMS FOR MSBR HEAT EXCHANGERS

C. E. Bettis T. W.

Pickel
W. K. Crowley M. Siman-Tov
H. A. Nelms W. C. Stoddart
APRIL 1971

 

 

LEGAL NOTICE
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 of implied, or assumes any
legal liability or responsibility for the accuracy, com-
pleteness 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
operated by
UNION CARBIDE CORPORATION

for the

U.S. ATOMIC ENERGY COMMISSION

DISTRIBUTION OF THIS DOCUMENT 18 UNLIMITED

Dot
AbStraCt 8 8 & S B SR E B ENSS S G s 8 Pt N R A AN N S et s e

INTRODUCTION ....QQ.Il.l....tl.'..‘.'......!l..l.'.'.l’.l‘.....

1.
2.

iii

CONTENTS

PRIMEX, THE PRIMARY HEAT EXCHANGER PROGRAM ..cetvtevcscasce

2.1 Description of Priméry Heat Exchanger .cceccecercecase

2.2 Design Calculations +eceseeesvsetresaccrssssncsonconsssans

2.3 Description of PRIMEX +.veevsrorosasoasoccns cesesacnae
2.4 Evaluation o0f PRIMEX cseceeeevoostososocosesnonnosscsas

RETEX, THE STEAM REHEATER EXCHANGER PROGRAM ........ ceatsess
3.1 Description of Steam Reheater +¢eoeeervnersocesceniosans

3.2 Design Calculations .+eeveievvcrecnccncnn cesresserennanns

3.3 Description of RETEX +cevveereceorsnoosnssssososssssss
3-4 Evaluation Of R-ETEX ® & & B 4 & 4 5 ¥ ¢ 8 & & & ¥ S B AR NE NS

SUPEX, THE STEAM GENERATOR SUPERHEATER PROGRAM ...ciivveeass
4.1 Description of Steam Generator «iesesisecscrasarsass ciraen
4.2 Design Calculations .......... Cree s aeeses e eirenaanne
4.3 Description of SUPEX .t..vtveriireiereecnnottsenesonnsnnns
Lol FEvaluation Of SUPEX s eeveeesnseonnneeansoeaneoenansnns

REFERENCES * 9 8 8 B 8 & 0PI 8 e e # 0 & & & 9 % s 0 2 s 0 0 4 © & 5 & 2 8 &8 & B 8 e 2 e s s * b o &
Appendix A: PHYSICAL PROPERTY DATA ...ccecerererecccnannnnns .o

Appendix

Appendix

B : THE PRImX PROGRAM @ 5 6 3 & ¢ ¢ 8 4 b 0 0 s a2 s ® & & & & & 0 & 8 8 8 s d & & 9 v 8
Appendix C: THE RETEX PROGRAM ...t rerenesttttnarasnassscsanns
D : THE SU PEX PROGRAM 4 ® &8 8 0 8 4 % 8 0 s 8 02 0o 4 5 2 & 8 5 2 % 9 8 0 8 0 s A s

0 W e

16
17
19
20
23
23
24
26
27
29
37
39
41
45
49
90
Figure

Number

2.1

2.2

3.1
4.1
B.1
C.1
D.1

LIST OF FIGURES

Title

Cross-Sectional Elevation of a Typical MSBR Primary
Heat Exchanger

Zones of Flow Between Two Baffles in the Shell Side
of the MSBR Primary Heat Exchanger

Typical MSBR Steam Reheater Exchanger

Typical MSBR Steam Generator Superheater Exchanger
Simplified Flow Diagram of the PRIMEX Computer Program
Simplified Flow Diagram of the RETEX Computer Program
Simplified Flow Diagram of the SUPEX Computer Program

Page

Number

12

21
27
50
91
115
Table
Number

2.1
3-1
4-1

4.2

4.3

A.l
A.2
A.3
B.1
B.2
C.1
C.2
D.1
D.2

vii

LIST OF TABLES

Title

Design Data for MSBR Primary Heat Exchanger
Design Data for MSBR Steam Reheater Exchanger

Design Data for MSBR Steam Generator Superheater
Exchanger

Preliminary Stress Calculations for MSBR Steam
Generator

Percentage Deviations Resulting From Calculational
Uncertainties Related to MSBR Steam Generator
Exchanger

Design Properties of MSBR Fuel Salt
Design Properties of MSBR Coolant Salt
Design Properties of Hastelloy N
Computer Input Data for PRIMEX Program
Output Data From PRIMEX Program
Computer Input Data for RETEX Program
Output Data From RETEX Program
Computer Input Data for SUPEX Program
Output Data From SUPEX Program

Page

Number

20
28

37

40

46
47
48
53
54
94
95
118
119
COMPUTER PROGRAMS FOR MSBR HEAT EXCHANGERS

Abstract

Three computer programs were developed to make design
calculations for the heat exchangers for Molten-Salt Breeder
Reactor concepts. They are the program for the primary heat
exchangers, PRIMEX; the program for the reheaters, RETEX;
and the program for the steam generator superheaters, SUPEX.
Each type of exchanger analyzed is described, the basic equa-
tions used in each analysis are given, and the logic used in
each program is discussed briefly in this report. Flow dia-
grams, lists of input required and output received, complete
program listings, and the nomenclature for the programs as
well as example computer input and output for the exchangers
described are appended.

1. TINTRODUCTION

The concept of a single-fluid Molten-Salt Breeder Reactor (MSBR)
with a thermal capacity of 2250 MW and a net electrical output of 1000 MW
has some very special heat exchange requirements. In the present concep-
tual design for the MSBR plant, there are four heat exchangers in the
primary system that transfer heat from the molten fluoride fuel-salt mix-
ture to the molten sodium fluoroborate coolant salt. In the secondary
system, there are eight reheaters and 16 steam generators that transfer
heat from the coolant salt. The manner in which these exchangers were
designed to meet the special heat exchange requirements and the computer
programs that were developed to calculate the design numbers are described
in this report.

The development of MSBR concepts passed through a number of stages
during which the plant layout was improved, core configurations were
optimized, and physical property data were refined. The first formal
study of a MSBR heat exchange system made by the authors was reported in
1967 (GE&C Division Design Analysis Section, "Design Study of a Heat-
Exchange System For One MSBR Concept,'" USAEC Report ORNL TM-1545, Oak
Ridge National Laboratory, September 1967). To analyze one exchanger at
each stage of its subsequent development without programming a large por-
tion of the necessary calculations would have meant almost continual rep-
etition of these calculations over a period of many months. With com-
puter programs available, the design for an exchanger could easily be
updated for changed capacity, physical properties, temperatures, pres-
sures, etc.

Three such computer programs were developed. One computer program
was written to make the design calculations for the primary heat
exchanger, and it is the PRIMEX program. This program was modified at
one stage of its development to perform the calculations for the steam
reheater exchangers. This modified version is the RETEX program. A
third computer program was wéitten to perform the design calculations for
the steam generator superheater exchangers, and it is the SUPEX program.
The design data for each of these three types of exchanger, the basic
equations used in each design analysis, and each of the computer programs
developed to perform the analysis are described in the following sections
of this report. Flow charts for each program, lists of the input
required and the output provided by each program, complete program list-
ings, nomenclature lists for each program, and the computer input and

output for each type of heat exchanger discussed are appended.
2. PRIMEX, THE PRIMARY HEAT EXCHANGER PROGRAM

There are four primary heat exchangers, which transfer heat from the
fuel salt to the coolant salt, in the conceptual design for a single-
fluid MSBR. Each of these exchangers has a thermal capacity of 556 MW
and each is of the same design. The fuel salt circuits for the primary
heat exchangers are in parallel, each having its own fuel pump. The
coolant salt from each exchanger is circulated through its own system of
two reheater exchangers and four steam generators.

At full design load, the fuel salt enters the top of the primary
heat exchanger at a temperature of 1300°F and exits from the bottom at a
temperature of 1050°F for return to the reactor. The coolant salt at a
temperature of 850°F enters the top of the primary heat exchanger and is
directed to the bottom of the exchanger through a central downcomer where
it enters the shell side of the exchanger, flows upward in counterflow
to the fuel salt, and leaves the top of the exchanger at a temperature of
1150°F. This coolant salt is circulated through the steam reheaters and
steam generators where its heat is transferred to the exhaust steam and
feedwater, respectively.

The design conditions for the primary heat exchanger were partially
dictated by the overall requirements of the MSBR system. The heat load,
entrance and exit temperatures of the fuel and coolant salts, and the
maximum or desired pressure drops across the shell and tube sides of the
exchanger were specified by the operating conditions of the system.
Design considerations for the overall system dictated the type of
exchanger, arrangement of nozzles to facilitate piping, minimum tube
diameter considered to be consistent with fabrication practices, and the
limit on the overall length of the exchanger. Certain criteria such as
the maximum allowable temperature drop across the tube walls and the need
to build in enough tube flexibility to compensate for differential ther-
mal expansion were established by the strength of the materials. Vibra-
tion considerations placed limits on flow velocities and the spacing
between baffles. In addition, it is highly desirable that the volume of

fuel salt be kept at a minimum to lower the doubling time of the reactor.
Within the framework of these requirements and guidelines, a
computer program was developed to perform a parameter study and select
the design for the primary heat exchanger that employs a minimum volume
of fuel salt. The design data and equations discussed in the following
subsections were used to develop the computer program for the primary

heat exchanger (PRIMEX).

2.1 Description of Primary Heat Exchanger

Each of the four primary heat exchangers is a vertical shell-and-
tube type with a single counterflow pass on both the tube and shell sides.
Each unit is about 6 ft in diameter and about 22 ft tall, not including
the coolant salt U-bend piping ét the top. A cross-sectional elevation
of a typical primary heat exchanger is illustrated in Fig. 2.1, and the
pertinent design data are given in Table 2.1.

The fuel (primary) salt enters the tube side of the primary heat
exchanger at the top and flows out the bottom of the exchanger after a
single pass through the 3/8-in.-0D tubes. The coolant (secondary) salt
enters at the top of the exchanger, flows to the bottom of the exchanger
through a central 20-in.~diameter downcomer where it enters the annular
shell containing the tubes, flows upward around modified disk and dough-
nut baffles, and exits through a 28-in.-diameter pipe concentric with the
inlet pipe at the top.

The tubes are arranged in concentric rings in the bundle with a con-
stant radial pitch and a circumferential pitch that is as constant as
can be obtained. The L-shaped tubes are welded into a horizontal tube
sheet at the bottom and into a vertical tube sheet at the top. The
toroidal-shaped top head and tube sheet assembly has a significant
strength advantage, simplifies the arrangement for coolant-salt flow, and
allows the seal weld for the top closure to be located outside the heat
exchanger.

To accommodate differential thermal expansion between the shell and

tubes, about 4 ft of the upper portion of the tubing is bent into a sine
ORNL-DWG 69-6004

SEAL WELD

N
A
3

SECONDARY
PRIMARY __ SALT

\

 

I

 

 

 

 

 

 

 

SECONDARY
SALT

 

 

 

 

 

 

 

 

 

Lt

 

 

T

  

 

PRIMARY
SALT

Fig. 2.1. Cross-Sectional Elevation of a Typical MSBR Primary
Heat Exchanger.
Table 2.1.

Design Data for MSBR Primary Heat Exchanger

 

Type

Number required

Rate of heat transfer per unit,
MW
Btu/hr

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

Shell-side conditions
Cold fluid
Entrance temperature, °F
Exit temperature, °F
Exit pressure, psi
Pressure drop across exchanger, psi
Mass flow rate, 1lb/hr

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

Tube sheet
Material
Thickness, in.
Sheet-to-sheet distance, ft

Total heat transfer area, ft<
Basis for area calculation

Volume of fuel salt in tubes, £t2

Shell
Material
Thickness, in.
Inside diameter, in.

Central tube diameter, in.

Baffle
Type
Number
Spacing, in.

Shell-and-tube one-pass vertical
exchanger with disk and dough-
nut baffles

Four

Fuel salt
1300

1050

180

130

23.45 x 10°

Coolant salt
850

1150

34

116.2

17.8 x 10°

Hastelloy N
5896
0.75
0.375
0.035
22.57

Hastelloy N
4.75
21.31

13,037
Outside of tubes

67.38

Hastelloy N
0.5
68.07

20.0

Disk and doughnut
21
11.23
Table 2.1 (continued)

 

Disk outside diameter, in. 54.56
Doughnut inside diameter, in. 45.54
Overall heat transfer coefficient, U,
Btu/hr.ft=«°F 838.3
Tube
Maximum primary (P) stresses
Calculated, psi 674
Allowable, psi 3912

Maximum primary and secondary
(P + Q) stresses

Calculated, psi 11,639

Allowable, psi 11,737
Maximum peak (P + Q + F) stresses

Calculated, psi 13,006

Allowable, psi 25,000

 

wave configuration. The tubes are held in place by wire lacing in this
upper portion of the tube bundle. Since baffling is not employed in
this region, the bent-tube portion of the bundle experiences essentially
parallel flow and a relatively lower heat transfer performance.

Below the bent-tube region of the bundle, evenly spaced doughnut-
shaped baffles are used to hold the tubes in place and to produce cross
flow. The baffle spacings and cross-flow velocities are designed to min-
imize the possibility of flow-induced wvibration. The tubes in this baf-
fled region of the heat exchanger have a helical indentation knurled
into their surface to enhance the film heat transfer coefficients and
thereby reduce the fuel salt inventory in the exchanger. No enhancement
of this nature was used in the upper bent-tube region because of present
uncertainty about the reliability of tubes that are both bent and

indented.
2.2 Design Calculations

 

Since experience with both the fuel and coolant salts is limited,
there was and still is a certain degree of uncertainty associated with
the transport properties of salt and its behavior as a heat transfer
medium. The design properties of the fuel salt, coolant salt, and of
Hastelloy N used in the concept of a single-fluid MSBR and incorporated
in the primary heat exchanger computer program are given in Appendix A.

As previously described, the tubes in the baffled portion of the
primary heat exchanger are helically indented to improve heat transfer
performance. Experiments performed by C. G. Lawson, R. J. Kedl, and R.
E. McDonald® indicated that this indentation is expected to result in an
improvement by a factor of 2 in the tube-side heat transfer coefficient.
An enhancement factor of 1.3 for the heat transfer coefficient outside
the tubes is suggested by Lawson™ although no experiments have been done
to support this recommendation. The experimental work” that was per-
formed was limited to Reynolds numbers greater than 10,000, and there is
some uncertainty about the degree of improvement that can be expected for
Reynolds numbers of less than 10,000. It was assumed that no improvement
can be expected in a truly laminar flow (Reynolds numbers less than 1000),
and the improvement expected for the intermediate range was extrapolated
by using a method suggested by H. A. McLain.> The resulting enhancement

factors (EF) are

EFi = 2.0 and EF_ = 1.3 for Reynolds numbers > 10,000
and
EF, = 1.0 and EFO = 1.0 for Reynolds numbers < 1000,
where
EFi = enhancement factor inside tube and
EFO = enhancement factor outside tube (cross flow).
For 1000 < Reynolds number < 10,000,
Np, - 1000 1/z
. = 1.0 + .
EF1 1.0 5000 (2.1)

 

 

and
 

 

Np, - 1000 1/2
= 1.0 + 0. 2.
EFO 1.0 + 0.3 9000 (2.2)
where N, = the corresponding Reynolds number.

Re
The enhancement factors for heat transfer resulting from the helical

indentation of the tubes in the baffled region were assumed to have a
proportionate effect on pressure drop. The shell-side pressure drop was
calculated by using the procedure reported by 0. P. Bergelin et al.,* and
the tube-side pressure drop was calculated by using the conventional
friction-factor method. An overall leakage factor of 0.5 was used for
the pressure drop in the shell side of the heat exchanger, and a factor
of 0.8 was used in the heat transfer calculations. These leakage factors
were selected on the basis of recommendations reported by Bergelin et al.”
The correct leakage factor, which is dependent upon various clearances
between tubes and baffles and between baffles and the shell, will have

to be calculated when the actual design for the primary heat exchanger
has been completed.

Since molten fluoride salts do not wet Hastelloy N, the containing
material of the heat exchanger, it was suspected that the usual heat
transfer correlations, which are normally based on experiments with water
or petroleum products, might not be valid. However, recent experiments
performed by B. Cox” indicated that basicaily the behavior of the fuel
salt is similar to that of conventional fluids. The correlations devel-
oped by Cox result in heat transfer coefficients somewhat lower than
those obtained from the Sieder and Tate cofrelations for turbulent
regions,7 Hansen's equation for transition regions,8 and the Sieder and
Tate correlations for laminar regions.7 The correlations used in this
study are those based on the data developed by Cox that were recommended
by H. A. McLain.® These are given in Eqs. 2.3, 2.4, and 2.5.

For completely turbulent flow with Reynolds numbers greater than

12,000,
0.14

(EF;) (2.3)

h.d,
i’i

kg

1/3 Eh

Hi

 

 

_ 0.8
= 0.217(Ng,) (N

 

Pr)
10

where
hi = heat transfer coefficient inside tube, Btu/hr.ft2-°F,
;= inside diameter of tube, ft,
k; = thermal conductivity of fluid inside tube, Btu/hr.ft-°F,

NRe = Reynolds number,
Npr = Prandtl number,
B = viscosity at temperature of bulk fluid, 1b/hr.ft,

By = viscosity of fluid at temperature of inside surface of tube,
1b/hr«ft, and

 

EF. = enhancement factor for helically indented tubes given in
Eq. 2.1.
Based on the inside diameter of the tube, the Reynolds number
Re By

where Gi = mean mass velocity of fluid inside the tube, lb/hr-ftg. For

completely laminar flow with Reynolds numbers less than 2100,

di)
NReNPr'E—

1 +0.0012

 

h.d. 0.023
= 14.36 +

 

 

di EFi (2.4)

Pr I_

 

 

NReN

where £ = length of tube from the entrance to the local point, ft. For

the intermediate region where 2100 < Reynolds number < 12000,

2/3 0. 14

b1y b (EFi)' (2.5)

1 1

k,
i

d,

1

£

= 0-089[(1\1&,_)2/3 - 125](Npr)3“/3 1+ %

 

 

 

 

 

i

The pressure drop inside the tubes was calculated by using the
expression
2

G

- ML Vg )y (2.6)

AP.
1 di Zpigc i

 

where

friction factor,

I."
"

length of tube, ft,

.
H

inside diameter of tube, ft,
11

mean mass velocity of fluid inside tube, lb/hr-fte,

G, =
i
p; = density of fluid inside tube, 1b/ft",
8. = dimensional conversion factor = 4.18 x 108 1bm-ft/lbf-hr2, and
EFi = enhancement factor for helically indented tubes given in

Eq. 2.1.
The friction factor for turbulent flow (Ng, > 2100) is given by the

expression

=-0Q.32 (2.7)

£ = 0.0014 + 0.125(Ng,) ’

and the friction factor for laminar flow (NRe < 2100) is given by the

expression

f=— . (2.8)

The heat transfer coefficient across the tube wall is given by the

expression
d -d
_ | k} o i
hw - (d t) d ’ (2.9)
© ln =2
d,
i
where
k = thermal conductivity, Btu/hr.ft:°F,

dO = outside diameter of tube, ft,
t = wall thickness, ft, and
d, = inside diameter of tube, ft.

No experiments have been performed to date to develop correlations
for the heat transfer behavior of a sodium fluoroborate coolant salt in
the shell side of the heat exchanger. The correlation developed byIO. P.
Bergelin et al.® was used for the baffled region of the MSBR primary heat

O

exchanger, and the correlation developed by D. A. Donohuel® was used for

the unbaffled region.
Although selected as being the most representative available for the

% is strictly for cross flow and

baffled region, Bergelin's correlation
his data were based on work with half-moon shaped baffles with straight

edges. Since disk and doughnut baffles are used in the MSBR primary heat
exchanger, the adaptation of Bergelin's data involved certain interpreta-

tions in determining the cross-sectional areas involved. The correlation
12

for cross flow was also modified by the introduction of a correction
factor. This correction factor is dependent upon the degree of actual
cross flow that exists as determined by the ratio between the baffle
spacing and the annular thickness of the vessel. Data from Bergelin's
original experiment4 were used to estimate the value of the correction
factor, which is expressed as

_00188

BCF = 0.77(3] (2.10)
where
BCF = correction factor for shell-side heat transfer coefficient as
proposed by Bergelin,4
= baffle spacing (as illustrated in Fig. 2.2), ft, and
Y = radial distance from center of window to center of opposing

window (as illustrated in Fig. 2.2), ft.

|
l
¢
|

 

T T S S S S S

 

|
S

_— OUTER SHELL

 

INNER SHELb—
[

 

 

 

() - WINDOW ZONE

 

(@ - BAFFLE ZONE (PURE CROSS FLOW)

(3 - WINDOW ZONE

Fig.k2.2. Zones of Flow Between Two Baffles in the Shell Side of
the MSBR Primary Heat Exchanger.
13

In the method advanced by Bergelin,? the region between two baffles
is considered as three parts: one pure cross-flow zone between two win-
dow zones, as illustrated in Fig. 2.2. The mass velocity in each zone
is based on the effective area of each zone. In a window zone, the

effective area is given by the expression

S, = (sWsB)1/2 (2.11)
where
SW = free cross-sectional area in baffle window, ftZ, and
SB = free cross-sectional area for cross flow between tubes applied

at lip of the baffle, ftZ.

The effective area of the pure cross-flow zone is given by the expression

S = 0-5(Sp + 5 ) (2.12)

B2

where the indices 1 and 2 indicate the sides of the pure cross-flow zone.
Based on this definition of the areas or zones used to calculate the mass

velocity, the Reynolds number for each zone is determined from the

expression
N = ng (2.13)
Re My ’
where
d = outside diameter of the tube, ft,

0
G = mass velocity of the fluid outside the tubes, lb/hr-ftZ, and

%

The relationship between the Reynolds number for each flow zone and

viscosity at temperature of bulk fluid, 1b/hr-ft.

an appropriate heat transfer factor (J) is developed in Bergelin's meth-

od.* The heat transfer factor for the window zone is determined from the

 

 

 

 

expression
hw C ub 2/3 . 0.14
I, =T = (EF_) (BCF) (LF) (2.14)
P m b
where |
hW = heat transfer coefficient for window zone, Btu/hr-ftZ.°F,

specific heat, Btu/1b.°F,

mean mass velocity of fluid, 1b/hr-ft=,
14

k = thermal conductivity, Btu/hr-ft-°F,
m = viscosity at temperature of bulk fluid, 1b/hr- ft,

viscosity of fluid at temperature of wall surface, 1b/hr-ft,

T
I

EFo = enhancement factor outside helically indented tube given by
Eq. 2.2,

BCF = correction factor for shell-side heat transfer coefficient
given by Eq. 2.10, and

LF = leakage factor for heat transfer taken as 0.8.
The heat transfer factor for the cross-flow zone (JB) is determined from
the expression

2/8 0.14

(EFO)(BCF)(LF) . (2.15)

3!
S

"

Equations 2.16 and 2.17 were derived from the graph of J versus NRe given

 

 

 

 

in Ref. 4 to determine the values of J. The values of J determined from
Eqs. 2.16 and 2.17 were then used in Eqs. 2.14 and 2.15 to determine the
heat transfer coefficients for the window zones and the cross-flow zone

(hw and hB).

For 800 < N_ < 10°, J = 0.346(NRe)°-382 (2.16)

For 100 < N__ < 800, J 0.571(NRe)°'456 (2.17)

The values of the heat transfer coefficients for the window zones (hW
and hwg) and the value for the cross-flow zone (hB) were then combined
in Eq. 2.18 to determine the total heat transfer coefficient for the
region between two baffles.

h, =h_a +h_ a +h

t B B Wi W1 W23W2 ? (2.18)

where a = the area of heat transfer surface in each zone, ft2/ft.

The data reported by D. A. Donochuel® were used for heat transfer
calculations involving parallel flow on the shell side of the MSBR pri-
mary heat exchanger. The heat transfer coefficient outside the tubes is
given by the expression

k_ [ 4,6\°°[C n
h = 0.128( )(12d )OO 2 e
o eq

do ub ko

0.33 0.14
(2.19)

 

 

o |oF

 
15

where
, = thermal conductivity of fluid outside tubes, Btu/hr-ft.°F,
do = outside diameter of tube, ft,
deq = equivalent diameter, ft,

G = mass velocity of fluid outside tubes, 1b/hr. £t2,

m = viscosity at temperature of bulk fluid, 1b/hr-ft,
Cp = gpecific heat, Btu/lb.°F, and
poo= viscosity of fluid at temperature of wall surface, 1lb/hr-ft.

The overall heat transfer coefficient was then calculated by using the

expression

 

U == —T (2.20)
+ = + —-9)

D‘Ir—l
D"r-—l

d

 

Sdin

0 ivii
where ho, hW’ and hi are the shell-side, wall, and tube-side heat trans-
fer coefficients, respectively.

The shell-side pressure drops in the baffled region of the MSBR
primary heat exchanger were calculated by using the equations reported by
0. P. Bergelin et al.* The pressure drop across the cross-flow zone is

given by the expression

v 2
cross floy = 0670 552 (PLF) (EF) (2.21)
where
rp = number of cross-flow restrictions,
o = density of fluid, 1b/ft2,
Vm = cross-flow velocity of fluid (based on effective area Sm given
by Eq. 2.12), ft/sec,
g, = dimensional conversion factor = 32.2 lby,-ft/lbf-sec®,

PLF = pressure drop leakage factor taken as 0.5, and
EF = enhancement factor outside helically indented tubes taken as 1.3.

The pressure drop across the window zone is given by the expression

2
DVZ
2gC

(PLF) (EF) (2.22)

= + 0.
window (1 0 6rw)
16

where
r, = number of restrictions in the window zone and
Vz = mean flow velocity (based on the effective area Sz given by

Eq. 2.11), ft/sec.

The number of restrictions was interpreted as being the number of rows
of tubes in the direction of cross flow. The full number was used for
the cross-flow zone, while only half of the number of rows was used for
each of the window zones. The shell-side pressure drop in the upper
bent-tube region of the exchanger was taken as being approximately equal

to the pressure drop across one baffled zone.

2.3 Description of PRIMEX

 

The computer program for the MSBR primary heat exchanger, PRIMEX,
is presented in Appendix B. 1In this program, each zone between two baf-
fles was considered as one increment length. The calculations are begun
on the hot side of the heat exchanger, and increments are added until a
complete heat balance is achieved. The dependence of each of the physi-
cal properties on temperature is given as an empirical equatibn, and
these equations are incorporated in the main program. If any of these
equations are changed, the appropriate data card must be replaced. The
physical property data as well as the other input data required for the
PRIMEX program are listed in Appendix B. A list of the output data
received from the computer is also presented.

A stress analysis subroutine, TUBSTR, is incorporated in the main
program. This subroutine performs a preliminary stress analysis of the
tubes with the assumption that the maximum tube stress will occur in the
upper bent-tube region of the heat exchanger. Pressure stresses, stresses
resulting from thermal expansion, and stresses resulting from the thermal
gradient across the tube wall are considered. The primary and secondary
stresses are computed, and these computed values are compared with the
allowable values given in Section III, Nuclear Vessels, of the ASME

Boiler and Pressure Vessel Code. A second subroutine, LAGR, is used for
17

interpolation of values from a given table. The complete listing for the
main program together with its two subroutines is given in Appendix B.

To illustrate the use of the PRIMEX program, the computer input data
for the MSBR primary heat exchanger discussed in Subsection 2.1 and the
output data printed by the computer are included in Appendix B. The time
required for a typical IBM 360/91 computer run of this program is about

2 minutes.

2.4 Evaluation of PRIMEX

 

It is believed that the use of the PRIMEX computer program will
result in a primary heat exchanger whose volume of fuel salt will be kept
to a minimum and whose design will be more reliable than can be achieved
with normal hand calculations. Variations in physical properties and
complicated geometries are handled easily, and an extensive parameter
study can be made in a very short time.

However, the output of a computer program cannot bé better than the
input. The input data which have a significant effect on the design of
the heat exchanger are the physical properties of the fuel and coolant
salts, the heat transfer correlations used, the enhancement factors
assumed for the helically indented tubes, and the leakage factors associ-
ated with fabrication clearances. The average deviations in the physical
properties of the fuel and coolant salts presently used in the program

1 The most notable uncertainties

are those reported by J. R. McWherter.?
in the physical property values presently are associated with the viscos-
ity and thermal conductivity of the fuel salt. The average deviation

for the fuel-salt heat transfer correlation is reported® as being about
5.7%. The deviation or error resulting from the use of Bergelin's cor-
relation® is not certain, but shell-side heat transfer coefficients nor-
mally have a deviation of about 25%. The leakage factor deviation for
the pressure drop might be about 20%, and the leakage factor deviation

for the shell-side heat transfer coefficient might be about 10%. The

enhancement factor deviation might be about 15%.
18

The two extreme cases were checked. All of the pessimistic values
were used in one case, and all of the optimistic values were used in the
other case. The result was a maximum estimated deviation in the overall
heat transfer area (or volume of fuel salt) of +38% (additional area

required) for the pessimistic case and -28% (less area required) for the

optimistic case.
19

3. RETEX, THE STEAM REHEATER EXCHANGER PROGRAM

The coolant salt circulating system in the conceptual design of a
single~-fluid MSBR consists of four independent loops, each containing
salt circulating pumps, steam generators, steam reheaters, and the shell
side of one of the four primary heat exchangers. There are two steam
reheater exchangers, which transfer heat from the coolant salt to pre-
heated exhaust steam from the high-pressure turbine, in each coolant salt
loop; with a total of eight reheaters to meet the total steam reheating
requirement of approximately 5.1 X 10% 1b/hr. Each reheater is of the
same design, and each has a thermal capacity of about 36.6 MW.

At full design load, the coolant salt from the primary heat exchanger
enters the shell side of the reheater at a temperature of 1150°F and
exits at a temperature of 850°F for return to the primary heat exchanger.
The preheated exhaust steam from the high-pressure turbine enters the
tube side of the reheater at a temperature of 650°F, flows through the
tubes in counterflow to the coolant salt, and leaves the reheater at a
temperature of 1000°F for delivery to the intermediate-pressure turbine.

Basically, the steam reheater exchangers must meet the same system
requirements prescribed for the primary heat exchangers that were dis-
cussed in Section 2 of this report. However, since no fuel salt is
involved, the desirability of keeping the fluid volume at a minimum is
not a critical factor in the design of the reheater. 1In addition, the
lower heat load and average temperatures permit more freedom in designing
the geometry of the reheater to avoid problems associated with vibration
or overstress.

Since the design for the steam reheater exchanger is similar to
that for the primary heat exchanger, an early version of the basic PRIMEX
computer program was modified to fit the requirements of the steam
reheater, thereby becoming the RETEX program. The design data and equa-
tions used to develop the RETEX computer program are discussed in the

following subsections.
20

3.1 Description of Steam Reheater

Each of the eight steam reheater exchangers is a horizontal shell-
and-tube unit with a single counterflow pass on both the shell and tube
sides.

22 in.

Each unit is about 30 ft long and has an outside diameter of
A typical reheater is illustrated in Fig. 3.1.

The preheated exhaust steam enters the tube side of the reheater at
a pressure of about 580 psi, flows through the 0.75-in.-0D tubes, and
exits at a pressure of 550 psi. There are 400 straight tubes arranged
in a triangular-pitch array in each reheater. The surfaces of these
tubes are not helically indented to enhance heat transfer, as are those
in the primary heat exchanger.

The coolant salt enters the shell side of the reheater at a pressure
of about 228 psi, flows around disk and doughnut baffles in counterflow
to the exhaust steam, and exits at a pressure of 168 psi. Other perti-

nent design data for the steam reheater exchanger are given in Table 3.1.

Table 3.1. Design Data for MSBR Steam Reheater Exchanger

 

Type Straight shell-and-tube one-pass
horizontal unit with disk and
doughnut baffles

Number required Eight

Rate of heat transfer per unit,
MW 36.6
Btu/hr 1.25 x 10°

Shell~side conditions

Hot fluid
Entrance temperature, °F

Coolant salt
1150

Exit temperature, °F 850
Entrance pressure, psi 228

Exit pressure, psi 168
Pressure drop across exchanger, psi 59.52

Mass flow rate, 1lb/hr 1.16 x 10°

Tube-side conditions

Cold fluid Exhaust steam
Entrance temperature, °F 650

Exit temperature, °F 1000

Entrance pressure, psi 580

Exit pressure, psi 550

Pressure drop across exchanger, psi 29.85

Mass flow rate, 1lb/hr 6.41 x 10°
21

ORNL Dwg 65-1238I
- STEAM OUTLET

“STUBE SHEET

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SALT INLET ; I
: I
*. i
i i ’
W; TIE ROD & SPACER
|
|
‘TT‘
A
;1
;
TUBULAR
SHELL
_ /"jfiflll[ L ——TUBES
////
| ——DISC BAFFLE
=
DOUGHNUT
BAFFLE
|

 

—SALT COUTLET

INSULATION BAFFLE i

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

~—_DRAIN LINE

““““““ ~STEAM INLET

Fig. 3.1. Typical MSBR Steam Reheater Exchanger.
22

Table 3.1 (continued)

 

Tube
Material
Number required
Pitch, in.
Qutside diameter, in.
Wall thickness, in.
Length (tube sheet to tube sheet), ft

Tube sheet material

Total heat transfer area, £t2
Basis for area calculation

Shell
Material
Thickness, in.
Inside diameter, in.

Baffle
Type
Number
Spacing, in.
Disk outside diameter, in.
Doughnut inside diameter, in.

Overall heat transfer coefficient, U,
Btu/hr. ft°

Tube

Maximum primary (P,) stress
Calculated, psi
Allowable, psi

Maximum primary and secondary

(P, + Q) stress

Calculated, psi
Allowable, psi

Shell

Maximum primary (P,) stress
Calculated, psi
Allowable, psi

Maximum primary and secondary

(P, * Q) stress

Calculated, psi
Allowable, psi

Hastelloy N

400

1.0 (triangular)
0.75

0.035

30.26

Hastelloy N

2376
Qutside of tubes

Hastelloy N
0.5
21.2

Disk and doughnut
21 each

8.65

17.75

11.61

306

4582
13,000

14,090
39,000

5016
9500

14,550
28,500

 
23

3.2 Design Calculations

When developing the computer program RETEX to analyze the steam
reheater exchanger, the properties of the steam were assumed to be essen-
tially constant along the length of the exchanger even though it was
recognized that some gain in the reliability of the estimates could have
been realized by incorporating the steam properties as a function of
pressure and temperature. The usual Dittus-Boelter equations were used
for the film heat transfer coefficient on the tube side of the exchanger.
The other procedures and correlations used in the analysis of the reheater
are basically the same as those used for the primary heat exchanger dis-
cussed in Subsection 2.2 of this report.

Manual computational methods were used to determine the stresses
in the steam reheater exchanger. This preliminary stress analysis was
based on the requirements of Section III, Nuclear Vessels, of the ASME
Boiler and Pressure Vessel Code; and the calculated values are compared
with the allowable wvalues in Table 3.1. However, a complete stress
analysis as required by Section III of the ASME Boiler and Pressure Ves-

sel Code has not been made.

3.3 Description of RETEX

 

The RETEX program, a modified version of the PRIMEX program, was
used to analyze the steam reheater exchanger. In the RETEX program, each
zone between two baffles is considered as one increment length. The cal-
culations are begun on the hot side of the exchanger, and increments are
added until a complete heat balance is achieved. The physical property
equations for the fuel salt in the PRIMEX program are replaced with the
physical property data for the exhaust steam in the RETEX program, and
these properties are considered as being essentially constant along the
length of the exchanger. The physical properties of the coolant salt are
evaluated at the average temperatfire of each increment. The dependence-

of the physical properties on temperature is presently expressed in the
24

form of empirical equations incorporated in the main program. If any of

these equations are changed, the appropriate data card must be replaced.

The RETEX computer program differs from the PRIMEX computer program
in that
1. the reheater tubes are not helically indented to enhance heat trans-

fer, and no enhancement factors are used in the RETEX program;

2. the reheater tubes are arranged in a triangular-pitch array rather
than in concentric circles, and certain geometric calculations are
therefore made differently in the RETEX program;

3. none of the reheater tubes are bent in a sine-wave configuration to
accommodate differential thermal expansion; and

4. no stress analysis subroutines are included in the RETEX program
(stresses were calculated by hand).

The computer program for the MSBR steam reheater exchanger, RETEX,
is given in Appendix C. A simplified outline of the program in block-
diagram form, a list of the input data required, a list of the output
received from the computer, and a complete listing of the main program
are presented. The RETEX program terms which differ from those of the
PRIMEX program are defined. To illustrate the use of the RETEX program,
the computer input data for the steam reheater exchanger discussed in
Subsection 3.1 and the output printed by the computer are also included
in Appendix C. The time required for a typical IBM 360/91 computer run

of this program is about 1 minute.

3.4 Evaluation of RETEX

 

Confidence in the design calculations for the steam reheater
exchanger is greater than that in the calculations for the primary heat
exchanger because the characteristics of steam are more familiar than
those of the fuel salt and because no enhancement factors are involved.
Vibration problems are not likely to be encountered in the steam reheater
because velocities are less than 6.5 fps and the tubes are supported by

baffles with a relatively close spacing.
25

The uncertainties associated with the coolant salt are involved in
the RETEX program, and the deviations applied for the primary heat
exchanger (discussed in Subsection 2.4) are also applicable to the steam
reheater. Again, two extreme cases were considered. All the pessimistic
values were used in one case, and all the optimistic values were used in
the other. The result was a maximum estimated deviation in the overall
heat transfer area of +23% (additional area required) for the pessimistic

case and -13% (less area required) for the optimistic case.
26

4. SUPEX, THE STEAM GENERATOR SUPERHEATER PROGRAM

There are four steam generator superheater exchangers, which transfer
heat from the coolant salt to feedwater, in each of the four coolant salt
circulating loops of the MSBR concept. The total steam generation require-
ment, which includes that needed for the feedwater and preheating the
exhaust steam, of about 10 X 10%® 1b/hr is provided by the 16 steam gener-
ators, each having a thermal capacity of about 121 MW.

These exchangers serve as both steam generators and superheaters.
They are operated in parallel with respect to the coolant salt and steam
flows, and they are identical in design and operation. At full design
load, preheated feedwater enters the exchanger at a temperature of 700°F,
and the supercritical steam exits at a temperature of 1000°F. The cool-
ant salt enters the exchanger at a temperature of 1150°F and exits at a
temperature of 850°F for return to the primary heat exchanger.

The factors influencing the design of the steam generator exchanger
are partially dependent upon the requirements for the overall MSBR system.
The exit temperature and pressure of the steam were dictated by the steam
power system selected. The inlet temperature of the steam was determined
by considerations relative to the liquidus temperature of the salt and
the rapid increase in heat capacity of the supercritical water at temper-
atures above 700°F. The inlet and exit temperatures of the coolant salt,
the pressure drop, and the total heat to be transferred were dictated by
the requirements for the reactor and primary heat exchange systems. In
addition to these system requirements, the design for the steam generator
exchanger must satisfy stress, stability, and space requirements.

Because of the marked changes in the physical properties of the feed-
water as the temperature is raised above the critical temperature at
supercritical pressures, the heat transfer and flow characteristics wvary
considerably throughout the exchanger. The SUPEX computer program was
developed to account for these changes by making the heat transfer and
pressure drop calculations for incremental tube lengths. The design data
and equations used to develop this computer program for analysis of the

steam generator exchanger are discussed in the following subsections.
27

4.1 Description of Steam Generator

Each of the 16 steam generator superheater exchangers is a U-tube,
U-shell unit mounted horizontally with one leg above the other. Each has
a single pass on the shell and tube sides with the flow in one side coun-
ter to that in the other. The overall length of each exchanger is about
40 ft, and the overall height from the feedwater inlet plenum to the
steam outlet plenum is about 12 ft. A typical steam generator is shown

in Fig. 4.1.

ORNL-DWG TO-1195¢

STeEAM
OUTLET

 

 

 

 

 

 

FEEDWATER
INLET

Fig. 4.1. Typical MSBR Steam Generator Superheater Exchanger.
28

The feedwater enters the tube side of the exchanger at a pressure
of 3754 psi, flows through the 0.50-in.-0D tubes, and the supercritical
steam exits at a pressure of 3600 psi. .The coolant salt enters the shell
side of the exchanger at a pressure of 233 psi, circulates in counterflow
to the supercritical fluid around segmental baffles, and exits at a pres-
sure of 172 psi. Segmental baffles are used to improve the heat transfer
coefficient for the salt film and to minimize salt stratification. A
baffle on the shell side of each tube sheet provides a stagnant layer of
salt to help reduce stresses resulting from temperature gradients across
the tube sheets.

Location of the steam generator exchanger in a horizontal position
reduces the possibility of unstable flow conditions for the supercritical
fluid in the tubes. The U-tubes are arranged in a triangular-pitch array
and the ends of the tubes are turned 90° to equalize the lengths of the
tubes in the exchanger. This equalization of tube lengths further
reduces the possibility of unstable flow conditions. The pertinent

design data for the steam generator exchanger are given in Table 4.1.

Table 4.1. Design Data for MSBR Steam Generator Superheater Exchanger

 

Type U-shell, U-tube one-pass hori-
zontal unit with cross-flow
baffles

Number required 16

Rate of heat transfer per unit,

MW 121

Btu/hr 4.13 x 10°
Shell-side conditions

Hot fluid Coolant salt

Entrance temperature, °F 1150

Exit temperature, °F 850

Entrance pressure, psi 233.0

Exit pressure, psi 172.0

Pressure drop across exchanger, psi 61.0

Mass flow rate, 1b/hr 3.82 x 10°
29

Table 4.1 (continued)

Tube-side conditions
Cold fluid
Entrance temperature, °F
Exit temperature, °F
Entrance pressure, psi
Exit pressure, psi
Pressure drop across exchanger, psi
Mass flow rate, 1b/hr
Mass velocity, 1b/hr-ft®

Tube
Material
Number required
Pitch, in.
Outside diameter, in.
Wall thickness, in.
Length (tube sheet to tube sheet), ft

Tube sheet
Material
Thickness, in.

Total heat transfer area, ft2
Basis for area calculation

Shell
Material
Wall thickness, in.
Inside diameter, in.

Baffle

Type
Spacing, ft
Number of spaces

Supercritical fluid
700

1000

3754

3600

154

6.33 x 10°

2.47 x 10°

Hastelloy N

393

0.875 (triangular)
0.50

0.077

76.4

Hastelloy N
4-5

3929
Outside of tubes

Hastelloy N
0.375
18.25

Cross flow
4002
19

 

4.2 Design Calculations

The heat transfer coefficient for the supercritical fluid film on

the inside of the tube walls is determined by using the correlation

reported by H. S. Swenson et al.'® This correlation is given in Eq. 4.1.

 

h.d, d,6\°"%2°MH. - H_
g ) T
1 1 g

 

 

e

 

0.231
) (4.1)

0.813
By

 

 

b
k. v,
i i
30

where
hi = heat transfer coefficient inside tube, Btu/hr-ftZ-:°F,
di = inside diameter of tube, ft,

k; = thermal conductivity of fluid inside tube, Btu/hr-£ftZ. °F per ft,

G = mass velocity of fluid, 1b/hr-ftZ,

By = viscosity of fluid at temperature of inside surface of tube,
Ib/hr. ft,

H, = enthalpy at temperature of inside surface of tube, Btu/lb,

H_ = enthalpy at temperature of bulk fluid, Btu/lb,

Ti = temperature of fluid at inside surface of tube, °F,

Tb = temperature of bulk fluid, °F,

v, = specific volume of bulk fluid, ft3/1b, and

v, = specific volume of fluid inside tube, ft3/1b.

The values of specific volume and enthalpy for the supercritical fluid
under various conditions of pressure and temperature are taken from data

13 A table look-up subroutine

reported by J. H. Kennan and F. G. Keyes.
is included in the SUPEX computer program for determination of these
values. The values of thermal conductivity and viscosity for the super-
critical fluid are determined from data reported by E. S. Nowak and

R. J. Grosh.’® These data were represented by Eqs. 4.2 and 4.3 in the

SUPEX computer program.

2

 

 

 

 

 

_ v T + 460|253 1478
BT 0’02191(v - 0.012 492 T + 1446) (4.2)
and
k = (1.093 X 10 ©)(T + 460)* 45 + (28.54 x 107 4)v™ 1285 (4.3)
where

v = specific volume, ft°/1b, and
T = temperature of fluid, °F.
The heat transfer coefficient for the salt film on the outside sur-
face of the tubes is determined by using the method proposed by 0. P.
Bergelin et al.*’® The experimental data* are presented as correlations
between a heat transfer factor (J) and the Reynolds number, with the

Reynolds number defined by the expression
31

N. = EQE 4.4)
Re ny
where
dO = outside diameter of tube, ft,
G = mass velocity of the fluid, lb/hr-ftg, and
B = viscosity at temperature of bulk fluid, 1b/hr-ft.

The shell side of the steam generator exchanger is divided into two types
of flow regions by the segmental baffles. These are the cross-flow and
window regions, and the heat transfer factor is determined for each. The

heat transfer factor for the cross-flow region (JB) is given by the

 

 

 

expression
2/3 0+14
_ hB Cgub uo
T8 = Co |k . (4-3)
p B "
where
hB = heat transfer coefficient for cross-flow region, Btu/hr-ftZ.°F,
Cp = gpecific heat, Btu/1b.°F, 4
GB = mass velocity of fluid in cross-flow region, 1lb/hr-ftZ,

= viscosity at temperature of bulk fluid, 1b/hr.ft,

~ o

= thermal conductivity, Btu/hr-ft-°F, and

 

 

 

 

n, = viscosity of fluid at temperature of outside surface of tube,
Ib/hr.ft.
The heat transfer factor for the window region is given by the expression
h (Cn 2/3 p 40-14
] =—¥ [Ppb -9 4.6)
w CG |k 1 (-
pm b
where
hW = heat transfer coefficient for window region, Btu/hr-ftZ.°F, and
G = mean mass velocity, 1b/hr- ft=.
The mean mass velocity is given by the expression
_ 1/2
G_ (GBGW , 4.7)

where Gw = mass velocity of fluid in window region, 1b/hr- ft=. Equations
for determining values of J were fitted to the graph of J versus NRe

given in Fig. 11 of Ref. 4 for use in the SUPEX computer program. The
32

values of J given by Eqs. 4.8 and 4.9 are used in Eqs. 4.5 and 4.6 to
determine the heat transfer coefficients for the cross-flow and window

regions (hB and hw)'

For 100 < N_ < 800, J = O.571(NRe)'°'456 (4.8)

Re
and

For 800 < N, < 10°, J

Re 0.346(NRe)‘°'582 (4.9)

In Bergelin's method,4 the heat transfer coefficient for the shell side

of the exchanger is a linear combination of the heat transfer coefficients
for the cross-flow and window regions weighted by the amount of heat
transfer surface in each region and corrected for bypass leakage.

Because of the large baffle-spacing-to-shell-diameter ratio (approximately
2.7) required for the steam generator exchanger, an additional correction
factor is applied to the shell-side heat transfer coefficient. The total

shell-side heat transfer coefficient (ho) is given by the expression

o.138/h

+
BaB hwaw
+
aB aw

h - 0.77B(§Z) , (4.10)

 

 

where
B = bypass leakage factor recommended by Bergelin,?

y = distance from the center line of the shell to the centroid of
the segmental window area, ft,

X = baffle spacing, ft,
h, = heat transfer coefficient for cross-flow region, Btu/hr.ftZ-°F

3

a, = area of heat transfer surface in cross-flow region per unit
length, ft2/ft,

hW = heat transfer coefficient for window region, Btu/hr-ft2-°F, and
a = area of heat transfer surface in window region per unit length,
ft2/ft.

The values of specific heat and thermal conductivity for the coolant
salt are treated as constants, independent of temperature, and are
included in the input information for the SUPEX computer program. The
density and viscosity of the salt are treated as functions of temperature

as determined by Eqs. 4.11 and 4.12.
33

o = 141.38 - 0.02466(T) (4.11)
and
p o= 0.2122 exp[fi%fifl , (4.12)
where
o = density of coolant salt, 1b/ft=,
T = temperature of salt, °F, and
n = viscosity of salt, lb/hr-ft.

The thermal resistance of the tube wall is calculated for each
increment of tube length by using the thermal conductivity of Hastelloy N
evaluated at the average temperature of the tube wall for each particular

increment. The thermal resistance of the tube wall is given by the

expression
=.EQ_(1n EQ) (4.13)
T\
where
Rw = thermal resistance of tube wall, hr-ft2'°F/Btu,
d0 = outside diameter of tube, ft,
k, = thermal conductivity of tube wall, Btu/hr.ft-°F, and
di = inside diameter of tube, ft.

The thermal conductivity of the tube wall is given by the expression
kw = 0.006375'1‘W + 4.06 (4.14)

where 'I'w = mean temperature of the tube wall, °F. The total thermal

resistance, based on the outer surface area of the tube, is given by the
expression

d

o
R =
t hidi

 

1
+ ho + Rw . (4.15)

The heat transferred per increment of exchanger length (AQ) is given by

the expression

7d_n(AL) (AT )
Mg = = — (4.16)
t
34

where

= outside diameter of tube, ft,
= number of tubes,

= increment of tube length, ft,

mean temperature difference between coolant salt and super-
critical fluid for the particular increment, °F, and

= total thermal resistance given by Eq. 4.15.

gfiw EBE:SOQ‘

e pressure drop per increment of tube length for the supercritical

fluid inside the tubes is given by the expression

e - 4EEDLE )
where
f = friction factor,
AL = increment of tube lengtfi, ft,
di = inside diameter of tube, ft,
G = mass velocity of fluid inside tube, 1b/hr-ftZ,
8, = gravitational conversion constant, lbm-ftllbf-hre, and
o = density of fluid inside tube, 1b/ft>3.
The friction factor is given by the expression4
p. 19-32
£ = 0.00140 + 0.125( 7% (4.18)
1

 

 

The pressure drops on the shell side of the steam generator exchanger
are calculated by using the equations recommended by Bergelin.® The

pressure drop across the i-th cross-flow region is given by the expression

 

. O.6rB(_E§_) 4.19)
Bi 144 2gcp ?
where
= number of restrictions in cross-flow region,
GB = mass velocity of fluid in cross-flow region, 1b/hr.ft=, and
o = density of fluid, 1b/ft>.
35

The pressure drop across the i-th baffle window is given by the

 

expression
. (2 +0.6r ) & 4. 20)
Wy 144 Zng ’ ’
where
r. = number of restrictions in window region and
G = mean mass velocity (given by Eq. 4.7), 1b/hr-ft=.

The total pressure drop on the shell side of the exchanger is given by

the expression

N+1 N
AP =B AP+ Z AP s (4.21)
s p By W
i=1 i=1
where
B_ = bypass leakage correction factor for pressure recommended by
P Bergelin* and
N = number of baffles.

Detailed stress calculations are not included in the SUPEX computer
program, but an approximate value of the allowable temperature drop across
the tube wall based on thermal stress considerations is determined for
each increment of tube length. This value of allowable temperature drop
can be compared with the value of the temperature drop across the tube
wall determined in the heat transfer calculations to provide some guid-
ance in selecting design parameters. The thermal stresses are treated
as secondary stresses. Based on the requirements set forth in Section
IIT, Nuclear Vessels, of the ASME Boiler and Pressure Vessel Code; the

permissible wvalue for the thermal stresses is given by the expression

Arh = arL < 38, - 8 s (4.22)
where

= hoop and longitudinal stress components caused by temper-

0. o
A >
Th™ AT L ature differences across the tube wall, psi,

S

allowable stress intensity based on rules prescribed in
Section III of the ASME Boiler and Pressure Vessel Code,
psi, and
36

S = total stress intensity resulting from primary membrane
stresses plus secondary stresses from all sources other
than thermal stresses, psi.

The value of S was conservatively estimated to be about 26,000 psi. The

tube wall material is Hastelloy N, and

for TW < 1015°F, Sm = 24,000 - 7.5(TW) (4.23)

and

for 1015°F < T,

< 1100°F, Sm = 57,000 - 4O(TW) . (4.24)
Based on data reported by J. F. Harvey,> the hoop and longitudinal
stresses resulting from temperature differences across the tube wall are

given by the expression

 

_QE(AEW) 2d° d
AT = ATOL T 3 | —;-——Tg( ) s (4.25)
In _9) dT - df

2(1 - v) 3

 

i
where
a = coefficient of thermal expansion, in./in.-:°F,
E = modulus of elasticity for Hastelloy N, psi,
AT . = temperature drop across tube wall, °F,
v = Poisson's ratio,
d = outside diameter of tube, in., and

d. = inside diameter of tube, in.

The estimated value of S and Eqs. 4.22, 4.23, 4.24, and 4.25 are used in
the SUPEX computer program to calculate the allowable value of AEW. The
values of E and & are determined in the computer program from Eqs. 4.26

and 4.27.
E = [31.65 - 0.005(Tw)3 X 108 (4.26)
and

o = [0.0031(Tw) + 5.91] x 1078 . (4.27)

Although detailed stress calculations are not included in the SUPEX
computer program, a preliminary stress analysis of the steam generator

exchanger was made by hand. This preliminary analysis was based on the
37

requirements of Section III, Nuclear Vessels, of the ASME Boiler and
Pressure Vessel Code; and the hand calculated values are compared with
allowable values in Table 4.2. The allowable stress values were taken
from data in code case interpretations 1315-3 (Ref. 16) and 1331-4
(Ref. 17).

Table 4.2. Preliminary Stress Calculations for MSBR Steam Generator

. . . a .
Maximum stress intensity, psi

Tube
Calculated P = 13,900; (Pm + Q) = 30,900
Allowableb Pm = 15,500; (Pm + Q) = 46,500
Shell
Calculated = 5800; (Pm + Q) = 13,200
Allowable® = 8800; (P +Q) = 26,400
Maximum tube sheet stress, psi
Calculated <17,000
Allowabled 17,000

 

%The symbols are those of Section III of the ASME Boiler and
Pressure Vessel Code where

Pm = primary membrane stress intensity, psi,
Q = éecondary stress intensity, psi,
Sm = allowable stress intensity, psi.

bBased on a temperature of 1038°F for the inside surface of the

tubes; this represents the worst stress condition.

“Based on the maximum or highest temperature of the coolant
salt of 1150°F.

dBased on a temperature of 1000°F for the steam and use of a
baffle on the shell side.

4.3 Description of SUPEX

 

The equations described in Subsection 4.2 are used in the SUPEX pro-
gram to size the steam generator exchanger for the specified input data.
A flow diagram of the SUPEX program, a list of the input required, and a

list of the output received from the computer are given in Appendix D.
38

In the SUPEX program, the total heat to be transferred in the
exchanger is divided into a specified number of equal increments. For
each increment, heat balance relations for the coolant salt and the
supercritical fluid and the heat transfer equations are used to determine
the change of temperature for each stream and the tube length required.
The pressure drop in the supercritical fluid for each increment and the
pressure drop in the coolant salt for each baffle space are calulated
and summed.

| Two major iteration loops are contained in the SUPEX program.

First, the baffle spacing is assumed and iterations are made until the
total calculated shell-side pressure drop agrees with that specified.
Internal to this loop, the number of tubes in the exchanger is estimated,
and iterations are made to give the total tube-side pressure drop speci-
fied. A simplified flow diagram of the SUPEX program, a complete list-
ing of the program, and a list of terms used in the program are given in
Appendix D.

Output from the program includes the number of tubes, inside diam-
eter of the shell, length of the exchanger, baffle spacing, number of
baffles, total heat transfer area, and the apparent overall heat transfer
coefficient. The method of calculation used in the program permits the
total length of the tubes to differ from the total length of the baffle
space by a fraction of the baffle spacing. Both lengths are given in
the output, as are the heat transfer area and apparent heat transfer
coefficient for each length. The output also includes pertinent informa-
tion for each baffle spacing and tube increment.

To illustrate the use of the SUPEX program, the computer input data
for the MSBR steam generator superheater exchanger described in Subsec-
tion 4.1 and the output data printed by the computer are included in
Appendix D. The time required for a typical IBM 360/91 computer run of

this program is about 30 seconds.
39

4.4 Evaluation of SUPEX

 

The problem of stability in the steam generator superheater was
considered. As indicated by K. Goldman et al.t® and by L. S. ’I‘ong,19
instabilities in steam generators can arise from two sources. First, a
true thermodynamic instability can exist where, for a given pressure drop
across the tube, the fléw rate through the tube may be changed from one
steady-state value to another by a finite disturbance. Second, a system
instability that is caused by resonant conditions in the fluid can exist.
Data related to the first type of instability have been reported by L. Y.
Krasyakova and B. N. Glusker,®° and data related to the second type of
instability have been reported by E. R. Quandt®' and by L. M. Shotkin.®?
A qualitative evaluation of these data indicates that the mass flow rate,
pressure drop, and heat flux used in the horizontal U-tube and U-shell
design will result in stable operation. Operation of a test module will
provide further information about the stability of this design concept.

An analysis was made to evaluate the various uncertainties involved
in the SUPEX computer program. Tolerances were placed on the physical
properties of the coolant salt, the heat transfer coefficients, and on
the pressure-drop correlation. The program was run for various cases to
determine the quantitative values of the favorable and the adverse effects
of the uncertainties. The favorable effects were defined as decreased
heat transfer area, decreased shell diameter, and decreased total tube
length. The adverse effects were defined as increased values for these
same three parameters. The selection of these parameters was based on
the belief that the heat transfer area is indicative of the total cost of
the exchanger, the diameter of the shell is indicative of the stress prob-
lem, and the total length of the tubes is indicative of the physical size
of the exchanger.

The range of uncertainties studied included the physical properties
of the coolant salt with a deviation of 12% for the specific heat and
density and a deviation of +10% for the viscosity and thermal conductivity,
the tube-side and shell-side heat transfer coefficients with a deviation

of + 20%, and the pressure-drop correlation with a deviation of +10%.
40

Scrutiny of the shell-side heat transfer coefficient revealed that
positive deviations (increases) in the specific heat and thermal conduc-
tivity of the coolant salt and negative deviations (decreases) in the
density and viscosity of the salt will produce favorable effects, while
opposite deviations will produce adverse effects. A negative deviation
(decrease) in the calculated pressure drop will produce favorable effects,
while a positive deviation (increase) will produce adverse effects.

The results of this analysis in terms of percentage changes relative
to the design case are given in Table 4.3. Case 1 is for an increased
specific heat and density of the coolant salt and a decreased viscosity
and thermal conductivity. Case 2 is for deviations opposite to those of
Case 1. Cases 3 and 4 are for increased and decreased, respectively,
shell-side heat transfer coefficients; Cases 5 and 6 are for increased
and decreased, respectively, tube-side heat transfer coefficients; and
Cases 7 and 8 are for decreased and increased, respectively, calculated
pressure drops. Case 9 for overall favorable conditions is for the com-
bined effect of all favorable changes, and Case 10 for overall adverse
conditions is for all adverse changes. Cases 1, 3, 5, and 7 represent

favorable changes; while Cases 2, 4, 6, and 8 represent adverse changes.

Table 4.3. Percentage Deviations Resulting From Calculational
Uncertainties Related to MSBR Steam Generator Exchanger

 

 

Heat Total
Transfer Shell Tube
Case Conditions Area Diameter Length
1 Favorable physical properties -8.2 -1.4 -5.6
2 Adverse physical properties +7.6 +1.2 +5.2
3 Increased shell-side heat transfer -10.1 -1.6 -7.0
4 Decreased shell-side heat transfer +13.5 +2.1 +8.8
5 Increased tube-side heat transfer -2.3 -0.5 -1.3
6 Decreased tube-side heat transfer +4.,2 +0.9 +2.3
7 Decreased calculated pressure drop -2.6 -0.5 -1.6
8 Increased calculated pressure drop +1.8 +0.7 +0.5
9 Overall favorable -21 -4 -15
10 Overall adverse +30 +5 +18

 
10.

11.

12.

13.

41

REFERENCES

C. G. Lawson, R. J. Kedl, and R. E. McDonald, '""Enhanced Heat Transfer
Tube for Horizontal Condenser With Possible Application in Nuclear
Power Plant Design,' Transactions of the American Nuclear Society,
Vol. 9, No. 2 (1966).

C. G. Lawson, Oak Ridge National Laboratory, personal communication
to C. E. Bettis, Oak Ridge National Laboratory.

H. A. Mclain, '"Revised Primary Salt Heat Transfer Coefficient for
MSBR Primary Heat Exchanger Design,' ORNL internal correspondence
MSR-67-70, July 31, 1969.

0. P. Bergelin, G. A. Brown, and A. P. Colburn, "Heat Transfer and
Fluid Friction During Flow Across Bank of Tubes -V: A Study of a
Cylindrical Baffled Exchanger Without Internal Leakage,' Trans. ASME,
76: 841-850 (1954).

0. P. Bergelin, K. J. Bell, and M. D. Leighton, ''Heat Transfer and
Fluid Friction Druing Flow Across Banks of Tubes -VI: The Effect of
Internal Leakages Within Segmentally Baffled Exchangers,'" Trans.
ASME, 80: 53-60 (1958).

B. Cox, "Preliminary Heat Transfer Results With a Molten Salt Mixture
Containing LiF-BeF»-ThF,-UF4 Flowing Inside a Smooth, Horizontal
Tube,'" ORNL internal document CF-69-9-44, September 25, 1969.

E. N. Sieder and G. E. Tate, 'Heat Transfer and Pressure Drop of
Liquids in Tubes,'" Industrial and Engineering Chemistry, 28(12):
1429-1435 (1936).

H. W. Hoffman and S. I. Cohen, ''Fused Salt Heat Transfer, Part III:
Forced Convection Heat Transfer in Circular Tubes Containing the
Salt Mixture NaNOp-NaNOz-KNOg,'" USAEC Report ORNL-2433, Oak Ridge
National Laboratory, March 1960.

H. A. McLain, "Revised Correlations for the MSBR Primary Salt Heat
Transfer Coefficient,'" ORNL internal correspondence MSR-69-89,
September 24, 1969.

D. A. Donochue, '"Heat Transfer and Pressure Drop in Heat Exchangers,"
Industrial and Engineering Chemistry, 41(11): 2499-2511 (November
1949).

J. R. McWherter, '"MSBR Mark I Primary and Secondary Salts and Their
Physical Properties,’ ORNL internal correspondence MSR-68-135,
Rev. 1, February 12, 1969.

H. S. Swenson, C. R. Kakarala, and J. A. Carver, "Heat Transfer to
Supercritical Water in Smooth-Bore Tubes,'" Transactions of the ASME,
Series C: Journal of Heat Transfer, 87(4): 477-484 (November 1965).

J. H. Keenan and F. G. Keyes, Thermodynamic Properties of Steam,
John Wiley and Sons, New York, 1936.
14.

15.

16.

17.

18.

19.

20.

21.

22.

42

E. §. Nowak and R. J. Grosh, "An Investigation of Certain
Thermodynamic and Transport Properties of Water and Water Vapor in

the Critical Region,' USAEC Report ANL-6064, Argonne National Labora-

tory, October 1959.

J. F. Harvey, Pressure Vessel Design, D. Van Nostrand Company, New

 

Jersey, 1963.

Case 1315-3, 'Nickel-Molybdenum-Chromium-Iron Alloy," Interpreta-
tions of ASME Boiler and Pressure Vessel Code, The American Society

of Mechanical Engineers, New York, April 25, 1968.

Case 1331-4, "Nuclear Vessels in High-Temperature Service,'" Interpre-
tations of ASME Boiler and Pressure Vessel Code, The American Society

of Mechanical Engineers, New York, August 15, 1967.
K. Goldman, S. L. Israel, and D. J. Nolan, 'Final Status Report:

Performance Evaluation of Heat Exchangers for Sodium-Cooled Reactors,'

Report UNC-5236, United Nuclear Corporation, Elmsford, New York,

June 1969.

L. S. Tong, Chapter 7 in Boiling Heat Transfer and Two-Phase Flow,
John Wiley and Sons, New York, 1965.

L. Y. Krasyakova and B. N. Glusker, "Hydraulic Study of Three-Pass
Panels With Bottom Inlet Headers for Once-Through Boilers,"

Teploenergetika, 12(8): 17-23 (1965), (UDC 532:

 

621.181.91.001.5).

E. R. Quandt, "Analysis and Measurement of Flow Oscillations,”
Chemical Engineering Progress Symposium Series, Vol. 57, No. 32,

1961.

L. M. Shotkin, '"Stability Considerations in Two-Phase Flow,'" Nuclear

Science and Engineering, 28:

 

317-324 (1967).
APPENDICES
45

Appendix A

PHYSICAL PROPERTY DATA

The design properties of the fuel salt used in the concept of a
single-fluid MSBR and incorporated in the PRIMEX computer program are
given in Table A.l. The design properties of the coolant salt used in
the MSBR concept and incorporated in the PRIMEX, RETEX, and SUPEX com-
puter programs are given in Table A.2; and the design properties of
Hastelloy N used in the MSBR concept and incorporated in these compfiter
programs are given in Table A.3.

Values for the density, viscosity, and thermal conductivity of the
fuel and coolant salts were taken from data reported in Ref. A.1l. The
value given for the heat capacity of the fuel salt is taken from Ref. A.2,
and the value given for the heat capacity of the coolant salt is taken

from Ref. A.3. These references are listed below.

A.1. Oak Ridge National Laboratory, "Molten-Salt Reactor Program Semi-
annual Progress Report August 31, 1969," USAEC Report ORNL-4449,
February 1970.

A.2. 0Oak Ridge National Laboratory, '"Molten-Salt Reactor Program Semi-
annual Progress Report August 31, 1968," USAEC Report ORNL-4344,
February 1969.

A.3. Oak Ridge National Laboratory, '"Molten-Salt Reactor Program Semi-
annual Progress Report February 29, 1969," USAEC Report ORNL-4254,
August 1969.
46

Table A.1. Design Properties of MSBR Fuel Salt

 

 

Fuel salt components 7LiF-BeFa—ThF4—UF4
Composition, mole % 71.7-16-12-0.3
Approximate molecular weight 64
Approximate melting point, °F 930
Vapor pressure at 1150°F, mm Hg <0.1
Density,”
g/cm3 o = 3.752 - (6.68 x 10-%)T°C
1b/ft3 o = 235.0 - 0.02317T°F
At 1300°F p = 204.9 1b/ft3
At 1175°F p = 207.8 1b/ft3
At 1050°F o = 210.7 1b/£ft®
Viscosity,
Centipoise = 0.109‘exp g?;o
1b/ft-hr n o= 0.2637(exp %%%2)
At 1300°F n = 17.29 1b/ft-hr
At 1175°F n = 23.78 1b/ft-hr
At 1050°F n = 34.54 1b/hr-ft
Heat capacity,® Cp = 0.324 Btu/1b-°F + 47
Thermal conductivityd
At 1300°F k = 0.69 Btu/hr-°F-ft
At 1175°F k = 0.71 Btu/hr.°F.ft
At 1050°F k = 0.69 Btu/hr-°F.ft

 

aFigure 13.6 on page 147 of Ref A.l.
Drable 13.2 on page 145 of Ref A.1.
“Page 163 of Ref. A.2.

dFigure 9.13 on page 92 of Ref. A.1. The value of k shown
is for salt with about 5% less LiF than in the reference salt.
Addition of LiF would increase the average value to about 0.72
to 0.74. The established and conservative value of 0.71 was
used in the calculations for the MSBR concept.
47

Table A.2. Design Properties of MSBR Coolant Salt

 

 

Coolant salt components NaBF4—NaF
Composition, mole % 92-8
Approximate molecular weight 104
Approximate melting point, °F 725
Vapor pressure at 1150°F, mm Hg 252
Density,a -4
g/cm3 p = 2.252 - (7.11 X 10 ")T°C
Ib/ft3 p = 141.4 - 0.0247T°F
At 1150°F o = 113.0 1b/ft3
At 1000°F p = 116.7 1b/ft3
At 850°F o = 120.4 1b/ft3
Viscosity,
Centipoise n = 0.0877(exp ifio
1b/ft-hr B = 0.2121(exp iggz
At 1150°F p=2.60 1b/ft-hr
At 1000°F n = 3.36 1b/ft-hr
At 850°F n=4.61 1b/ft-hr
Heat capacityc Cp = 0.360 Btu/1b.°F + 2%
Thermal conductivity,d
At 1150°F k = 0.23 Btu/hr.°F.ft
At 1000°F k = 0.23 Btu/hr. °F-ft
At 850°F k = 0.26 Btu/hr.°F.ft

 

a

b

Figure 13.6 on page 147 of Ref. A.l.
Table 13.2 on page 145 of Ref. A.1l.
CPage 168 of Ref. A.3.

dFigure 9.13 on page 92 of Ref. A.l.
48

Table A.3. Design Properties of Hastelloy N

 

Composition, wt %

Nickel Balance

Molybdenum 12

Chromium 7

Iron 0 to 4

Manganese 0.2 to 0.5

Silicon, maximum 0.1

Boron, maximum 0.001

Titanium 0.5 to 1.0

Hafnium or niobium 0 to 2

Cu, Co, P, S, C, W, Al 0.35
Density, 1b/ft3

At 80°F 557

At 1300°F 541
Thermal conductivity, Btu/hr-ft.°F

At 80°F 6.0

At 1300°F 12.6
Specific heat, Btu/lb-.°F

At 80°F 0.098

At 1300°F 0.136
Thermal expansion per °F

At 80°F 5.7 x 107°

At 1300°F 9.5 x 107°
Modulus of elasticity, psi

At 80°F 31 x 10°

At 1300°F 25 x 109
Tensile strength, psi

At 80°F ~115,000

At 1300°F ~75,000

Maximum allowable design stress
at 1300°F, psi
At 80°F 25,000
At 1300°F 3500

Melting temperature, °F 2500

 
49

Appendix B

THE PRIMEX PROGRAM

The PRIMEX computer program is outlined in block-diagram form in
Fig. B.1. The input data required for the program are given in Table
B.1, and the output received from the program are given in Table B.2.
A complete listing of the main program and its two subroutines is fol-
lowed by definitions of the intermediate variables used in the program.
To illustrate the use of the PRIMEX program, the input and output for
the MSBR primary heat exchanger discussed in Subsection 2.1 of this

report are presented as printed by the computer.
50

& C K )

READ AND PRINT
INPUT DATA

v

ASSUME BAFFLE
SPACING

© >}

ASSUME SHELL
DIAMETER

O, 2

CALCULATE NUMBER OF TUBES, FUEL AND COOLANT
FLONS AND VARIOUS GEOMETRIES

@ 2

ASSUME EXPANSION RADIUS REQUIRED FOR
ACCEPTABLE STRESSES

v

START WITH FIRST INCREMENT FROM HOT
SIDE OF HEAT EXCHANGER I=1

v

ASSUME TEMPERATURE OROP FOR THE INCREMENT

0, >y

EVALUATE ALL PHYSICAL PROPERTIES AT
AVERAGE TEMPERATURE OF INCREMENT

v

CALCULATE PRESSURE DROPS AND HEAT TRANSFER
COEFFICIENTS FOR THE INCREMENT, USING CORRECT
CORRELATION FOR DIFFERENT REGIMES

v

CALCULATE HEAT RATE AND TEMPERATURE
OROPS OF THE INCREMENT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. B.1l. Simplified Flow Diagram of the PRIMEX Computer Program.
51

 

 

     
 

DO INCREMENT
TENPERATURE DROPS AGREE

WITH OUR ASSUMPTION
?

 
    

 

 

CHANGE ASSUMED
INCREMENT TEMPERATURE
DROP

 

    

DOES END

 

    

  
 
 

TEMPERATURE OF
INCREMENT EQUAL TO SPECIFIED
END TEMPERATURE OF
HEAT EXCHANGER

    

 

G0 TO NEXT
INCREMENT
I=1+1

 

   
 

 

 

CALCULATE STRESSES
IN TUBES

 

 

 

 

    
 

ARE ALL

STRESSES ACCEPTABLE
?

 
 

 

 

CHANGE ASSUMED
EXPANSION RADIUS

 

 

 

     
 

DOES TOTAL TUBE
SIDE PRESSURE DROP
ACCEPTABLE

 
 

 

 

CHANGE ASSUMED
SHELL DIAMETER

 

   

?

Fig. B.l. (continued)

 

 

 

 
52

 

 

     
 

DOES TOTAL SHELL
SIOE PRESSURE DROP
ACCEPTABLE

    

 

 

CHANGE ASSUMED
BAFFLE SPACING

 

 

     
 

ARE THERE
ADDITIONAL CASES FOR

PARAMETER STUDY
?

 
 
    

 

PRINT OUTPUT

v

(: END _:)

Fig. B.1l. (continued)

 

 

 
53

 

 

Table B,1, Computer Input Data for PRIMEX Program
Card Columns Format Variable Term Units
A 1-10 E10.4 Heat load required HEATL  Btu/hr
11-20 F10.0 Allowable tube-side pres- PRDT 1b/ft?
sure drop
21-30 F10,0 Allowable shell-side PRDS 1b /2
pressure drop
31-40  F10.0  Tube-side inlet pressure TPIN 1b/ft?
41-50  F10.0  Shell-side outlet pressure SPOUT 1b/ft®
B 1-10 F10.0 Coolant outlet temperature CTO °F
11-20 F10.0  Fuel inlet temperature FTO °F
21-30 F10.0  Fuel outlet temperature ETF °F
31-40 F10.0 Coolant inlet temperature ETC °F
C 1-10 F10.0 Leakage factor for heat LK
transfer correlations
11-20 F10.0 Leakage factor for pres- PLK
sure drop calculations
21-30 F10.0 Tube material conductivity WCOND  Btu/hreft«°F
31-40 F10.0 Arc of bent tube for ther-  ARC Degrees
mal expansion
41-45 15 Number of pair points in ICNPT
Stress intensity table
for tube material
D ,0s. 1-10 F10.0  Stress intensity at CTM CASM psi
temperature
DicypT 11-20 F10.0  Temperature CTM °F
E 1-10 F10.0 Radius of coolant central RAS ft
downcomer
11-20 F10.0 Distance between shell DTR ft
wall and tube bundle
21-30 F10.0 Maximum anticipated heat RASMAX ft
exchanger radius
31-35 15 Number of cases to be run KASES
36-40 15 Index one if enhanced KENTB
tubes are used
41-45 I5 Index one if stress anal- KTBST
ysis is included 4
R”,E. 1-10  F10.0 Outside diameter of tubes DIA ft
. 11-20 F10.,0 Tube wall thickness WTHK ft
FKASES 21-30 F10,0 Radial pitch RPI ft
31-40 F10.0 Circumferential pitch BCPI ft
41-50 F10.0 Inner baffle cut CUT3 % of area
51-60 F10.0 Outer baffle cut CUT4 7% of area

 
54

 

 

Table B.2. Output Data From PRIMEX Computer Program
Term Variable Units
THEATO Total heat actually transferred Btu/hr
HTPERC Percentage of required heat load actually
transferred
QC Coolant (shell-side) mass flow rate 1b/hr
QF Fuel (tube-side) mass flow rate lb/hr
TTDSO Total tube-side pressure drop psi
SPPERC Percentage of allowed tube pressure drop
actually used
TTDTU Total shell-side pressure drop psi
TPPERC Percentage of allowed shell pressure drop
actually used
RAS8 Radius of heat exchanger shell ft
BSOTI Distance between baffles ft
VOL Fluid volume contained in tubes ft2
AREA Total heat transfer area in heat exchanger fto
SNT Total number of tubes
TUBLEN Actual tube length ft
HEXLEN Heat exchanger length from lower tube sheet ft
to upper nozzle of tubes
STRLEN Straight section length of tubes ft
EXPRAD Radius of tube bends for thermal expansion ft
BRL1 Modification factor for Bergelin's heat
transfer correlation
PSTO Primary stresses on outer surface of tubes psi
PQSTO Combined primary and secondary stresses on psi
outer surface of tubes
PQFSTO Combined primary, secondary, and peak psi
stresses on outer surface of tubes
PSTI Primary stresses on inner surface of tubes psi
PQSTI Combined primary and secondary stresses on psi
inner surface of tubes
PQFSTI Combined primary, secondary, and peak psi
stresses on inner surface of tubes
SAVT Shell average temperature °F
TAVT Tube average temperature °F
55

Table B.2 (continued)

 

 

Term Variable Units

TCI(I) Coolant outlet temperature from increment I °F

TCO(I) Coolant inlet temperature from increment I °F

CWT (1) Average tube wall temperature at coolant side °F

TFI(I) Fuel outlet temperature from increment I °F

TFO(I) Fuel inlet temperature from increment I °F

FWT(I) Average tube wall temperature at fuel side °F

TWDT (1) Average temperature drop across tube wall in °F
increment I

VMI(I) Fluid average velocity in outer window in ft/sec
increment I

VM2(1) Fluid average velocity in overlapping baffle ft/sec
zone in increment 1

VM3 (1) Fluid average velocity in inner window in ft/sec
increment 1

VWO1(I) Fluid velocity across tubes in outer edge of ft/sec
baffle in increment T

VW03 (1) Fluid velocity across tubes in inner edge of ft/sec
baffle in increment T

PDSO(I) Shell-side pressure drop for increment I 1b /ft?

PDTO(1) Tube-side pressure drop for increment I lb/ftg

RENTO(I) Tube-side Reynolds number for increment I

PRNTO(TI) Tube-side Prandtl number for increment I

RENSO1 (1) Reynolds number in outer window increment I

RENSO02 (1) Reynolds number in overlapping baffle zone in
increment I

RENSO03 (1) Reynolds number in inner window in
increment I

HTO(I) Tube-side heat transfer coefficient in Btu/hr-ft2-°F
increment I

AHSO(I) Shell-side heat transfer coefficient in Btu/hre ft° +°F
increment I

UOA(T) Overall heat transfer coefficient in Btu/hr-ft2-°F
increment I

HEAT (1) Heat transferred in increment I Btu/hr

 
*%FTN

1001
1002
1003
1604
1005
1006
1007
1008
1009

1010

1011
1012
1013
1014
1C15
1016
1617
1018
1019

The PRIMEX Program listing

’L'E’G’M-
PROGRAM MSBRPE-Z2
TYPE REAL LK s LAWO1l 4 LAWO3

DIMENSION TFOCT75), TCIC(T7E)4VML(T75) 4VM2(T75) yVWC1(T75)VWC3 (751},
IRENTO(75 ), PRNTO(75) 4RENSOL(75),RENSO2¢(75) yRENSC3(75),

2VM3(T75) 4 PDSO(75)sNT(100)4BJ(3)yHSOL(T75) yHSC2(75) +HSO3 (75) ,
BAHSO(T75) yHTO(T75) sUCALTS) 4 TCOLT5) o TFI (750 4HEAT(T75) s TWDT(T75)
4PDTO(75),y TUBLN{T75), VI(75)9sV2(T75)+V3(T75) 4VWL(T5) sVW3(T75),
5 R(100), FACT(100), TCPI{100), TOTAL(100) +CASM(E) LCTM(6)

6 CHWT(75)sFWT(T75),AVWT(75)

FORMAT( E10.4, 4F10.0)

FORMAT( 4F10.0)

FORMAT( 4F10.0,15)

FORMAT(2F10,4)

FORMAT( 3F10.0,315)

FORMAT( 6F10.0)

FORMAT (1H197X 91HI 4 8Xy3HCTMy TXy4HCASM//(4X41542F12.21))
FORMAT(22HOHEAT LOAD REQUIRED = +F12.0+2X,8H{(BTU/HR))

FORMAT (43HOALL OWABLE TOTAL TUBE-SIDE PRESSURE DRCP = 4F10.0+2Xy
1 10H(LB/SQ-FT) )

FORMAT (44HCALLOWABLE TCTAL SHELL-SIDE PRESSURE CRCP = ,F10.0,2X,
1 10H{LB/SQ-FT) )

FORMAT(23HOTUBE INLET PRESSURE = 4F10.0492X,1CH(LB/SQ-FT))
FORMAT (24HOSHELL OUTLET PRESSURE =¢F10.0,2X,10H(LB/SQ-FT))

FORMAT(33HOHIGH TEMP. OF SHELL SIDE FLUID =,F104242Xs3H(F))
FORMAT(33HOHIGH TEMP. OF TUBE SIDE FLUID = 4F10.2:2X+s3H(F))
FORMAT(32HCLOW TEMP. OF TUBE SIDE FLUID = 4F10.242Xs3H(F))

FORMAT({32HOLOW TEMP., OF SHELL SIDE FLUID =,F1C.2¢2Xs3H{(F))}
FORMAT(32HOHEAT TRANSFER LEAKAGE FACTOR = ,4F10.5)

FORMAT (27THOPRESSURE LEAKAGE FACTCR = LF10.5 )
FORMAT(35HCCONDUCTIVITY OF TUBE WALL METAL = +F10.5+2X,

1 13H(BTU/HR-FT-F) )

MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBRP
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR

10
20
30
31
32
33
34
35
36
40
50
60
70
80
90
100
110
120
121
130
131
140
150
160
170
180
190
200
210
220
221

9¢
1C20 FORMAT(37HOARC OF FOUR BENDS FOR FLEXIBILITY = ,F10.2 42X,
1 9H(DEGREES)}
1021 FORMAT(34HOINSIDE RADIUS OF OUTER ANNULUS = yF10.5,2X+6H(FEET))
1022 FORMAT(41HODISTANCE BETWEEN SHELL WALL AND TUBES =
1 +F10.5¢2X,6H(FEET) )
1023 FORMAT(4SHOMAXIMUM ANTICIPATED QUTER RADIUS CF EXCHANGER = ,
1 F10.542X+s6H(FEET) )
1024 FORMAT(23HONUMBER OF CASES RUN = ,414)

MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR

1025 FORMAT(25HOUSE OF ENHANCED TUBES = +14,2X+32H(ONE IF ENHANCED TUBEMSBR

1S ARE USED))
1026 FORMAT(1HO,36HUSE OF STRESS ANALYSIS SUBRCUTINE = ,

1 I442X419H(ONE IF TO BE USEDI}}
1027 FORMAT(29HOOUTSIDE DIAMETER OF TUBES = +F10.5,2Xy O6H(FEET) )
1028 FORMAT(27HOWALL THICKNESS OF TUBES = +F10e5+2Xy O6H(FEET) )
1029 FORMAT(1EHORADIAL PITCH = 4,F10.542Xy 6H(FEET))
1030 FORMAT{25HOCIRCUMFERENTIAL PITCH = 4F10.542Xy 6H(FEET})

1031 FORMAT(22HOINNER BAFFLE CUT3 = ,Fl0.5,2Xys 10H(PER CENT} }
1032 FORMAT(22HOOUTER BAFFLE CUT4 = 4F10.542Xy 1O0H(PER CENT) )
1033 FORMAT(25H1TOTAL HEAT TRANSFERED = 4F12.0+2X,8H(BTU/HR),

1 2Xy IH( 9+ F5.1+9H PERCENT})

1034 FORMAT(29HOMASS FLOW RATE OF COOLANT = ,F10.0,2X, 7H(LB/HR} )
1035 FORMAT(26HOMASS FLOW RATE OF FUEL = +F10.042Xy 7H(LB/HR} )

MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR

1036 FORMAT(34HOSHELL-SIDE TOTAL PRESSURE DROP = F1l0.292Xy 9H(LB/SQIN)IMSBR

1 12X ¢1H(4F5.1y9H PERCENT))

MSBR

1037 FORMAT(33HOTUBE-SIDE TCTAL PRESSURE DROP = 4F10.242X, S9H(LB/SQIN),MSBR

1 2Xy IH( 4 F5.149H PERCENT) )

1038 FORMAT(24HONOMINAL SHELL RADIUS = 4FT7.4+2X+4H(FT))

1039 FORMAT(2¢HOUNIFORM BAFFLE SPACING = +FT74442X4H(FTY})

1040 FORMAT(4OHOTUBE FLUID VOLUME CONTAINED IN TUBES = ¢F7.2+1X,
112H(CUBIC FEET))

1041 FORMAT(1FHO,46HTOTAL HEAT TRANSFER AREA BASED ON TUBE CeDe = o
1 F12.24+2Xs EH(SQFT) )

1042 FORMAT(25HOTOTAL NUMBER OF TUBES = ,Fé.0)

1043 FORMAT(Z21HOTOTAL TUBE LENGTH = ,F6.2 92X +s4H(FT})

1044 FORMAT(29HOHEAT EXCH. APPROX. LENGTH = F6.2+2Xs6H(FEET))

1045 FORMAT(35HOSTRAIGHT SECTICN OF TUBE LENGTH = sF6.242X +4H(FT))

MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR

1046 FORMAT(38HORADIUS GF THERMAL EXPANSION CURVES = +F6.2+2Xy6H(FEET) IMSBR

230
231
240
250
251
2 60
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
460
470
480
490

LS
1047

1048
1
2

1049

1 8X94HPDSO 18Xy 4HPDTO/ /32X 6HFT/SEC33X s THLB/SQFT//(1X41347F12.4))

FORMAT (3 1IHOBERGLIN MODIFICATION FACTOR = ,Ff5.2)
FORMAT (1HO 42Xy 1HI» 7TX¢3HTCI ¢9X¢3HTCOyGXs3HCWT 99X,
IXy 3FFWT ¢ 8Xy 4HTWDT//11 Xy 1HF 911X IHF 911X 9o1HF 411X,

BHTFI+9Xs3HTFOy

1FFy 11Xy IHF 9 11X 1HF 311X 1HF//7 (1 X913 47ELZe4))
FORMAT(1HO 92X 1HE» GXy2HV1 y 9X42HVZ +9X+2HV3 49X¢3HVWL +9X+3HVW3

1050 FORMAT(1HO+2Xy1HIL 95Xy 5HRENTO » 7Xy SHPRNTO ¢ 7X96HRENSCL 96 X9 6HRENS G2,
16Xy 6HRENSO3, 7TX33HHTO, 8X y4HAHSO,9X y3HUCA +8 Xy4HHEAT// 77 X,

2
1051
1052
1053

1

1054 FORMAT(1HO,36HP+Q STRESS AT TUBE OD AND TUBE ID =

1
2

1055 FORMAT(1HO,38HP+Q+F STRESS AT TUBE OD AND TUBE 1D

1
2

13HBTU/HR/SQFT/F 413Xy EHBTU/HR//(1X41349EL12.41))
FORMAT(27HOTUBE WALL AVERAGE TEMP. = +F10.2)
FORMAT (28HOSHELL SIDE AVERAGE TEMP., = 4, F10.2)
FORMAT(1HO,34HP STRESS AT TUBE 0D AND TUBE ID =
SH{LB/SQIN}//18H( SHOULD NOT EXCEED+F10424+3H 1))

'

2F10.241X,

2F104291X,9H(LB/SQIN) //1BH{SHOULD NCT EXCEED,F10.2,

3H 1))

2F10.291Xy9H{LB/SQIN) //18H(SHCOULD NCY
3H )

READ IN AND PRINT OUT INPUT DATA
KEY7= 1
VM1(1)=0.
VM2(1)=0.
VM3(1)=0.
VWO1(1)=0.
VWO3{1l)=C.
RENSOL1(11=0.
RENSO2(1)=0.
RENSO3(11=0.
HS01(1)=0.
HSO02(1)=0.
HSO3(1)=0.
HEF 1 1.
HEFO l.

-9

EXCEED+F10a2

?

MSBR
MSBR
MS BR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR

500
510
511
512
520
521
530
531
532
540
550
56C
561
570
571
572
580
581
582
650
660
610
620
630
640
650
660
610
680
690
700
716
720
730
740
810

8¢
READ
READ
READ
READ
READ

1001,
1002,
1003,

1005,

CONTINUE

READ

PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT

PRINT:

PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT

1006,

HSFCT=1O

IF(FTO.LT.CTO)

1008,
1C09,
1¢10,
1011,
1012,
1013,
1014,
1015,
1016,
1017,
1018,
1019,
1020,
1021,
1022,
1023,
1024

1025,
1026,
1027,
1028,

1029,

1030,
1031,
1032,

RA5,

DIA,

HEATL,
CT0,
LKy

HEATL
PRDT
PRDS
TP IN
SPOUT
CTO
FTO
ETF
ETC
LK
PLK
WCOND
ARC
RAS
DTR
RA 8MAX

+ KASES

KENTB
KTBST
DIA
WTHK
RPI
BCPI
CuT3
CuT4

+ TPIN, SPOUT
FTC, ETF,

PLK s WCONDyARC ,ICNPT

1004, (CASM(K) 4CTM(K) yK=1,ICNPT)

DTRy RABMAX,KASES,KENTB,KTBST

WTHK,

HSFCT==-1.
1007+ (KyCTM(K)4CASM{K) yK=1 ,ICNPT)

MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR

MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB

760
770
780
790
800
810
820

830
840
850
860
870
880
890
500
910
920
930
940
G50
960
970
980
990
10Co
1010
1020
1030
1040
1050
10 60
1C70
10 80
1650

39
BEGIN GECMETRY CALCULATIONS FOR SINGLE ANNULLS CCUNTER FLOW

DISC AND DOUGHNUT BAFFLED HEAT EXCHANGER
ARCR= C.017452%ARC

ATUBE = (3.14159% (DIA**%2.0))/4.0

GFTT = 1./3600.

GFT = 1./144.

DIAI=DIA-2.0%WTHK

FATUB =(3.14159%(DIAI**2.,0))/4.C

KEYl = 0

PERC1 = 0.99

IF{KEY1l. GT.C)IBSOI=0.5*(BSL+BSH)

KEYZ2 = C
PERCZ2 = C.99
RA8BL =RA5

RABH=RA8BMAX

RA8=0.5%¥(RASL +RABH )
RJB={(RAB8-RA5-2.*%DTR}/RPI+1.
I1J8=RJ8

RIJ8=1J8
IF(RJB-RIJB~0e5) 4y 445
J8=1J8
TRPI=(RA8~RAS5+-2.*%DTRI/(RI1J8-1.)
CPI=BCPI*RPI/TRPI

GO TO 6

J8=1J8+1
TRPI=(RA8-RAS5-2.*DTR)/RIJE8
CPI=BCPI*RPI/TRPI

DO 7 1I=1,J8
ROI)=RAS54DTR+TRPI*(I-1}
FACT(I)=6,28318*%R( 1)
NT(I)=FACT(I}/CPI
TCPI(II=FACT(I)/NT(I)
IF(I.EQ«1)TOTALCII=NT(I)
IFC(INE.1)TOTALCTI)=TOTALCI-1)+NT(I)
NTO=TOTAL(J8)

SNT=NTO

RAS52=RA5%%2

RAB2=RA8%*%2

MS8B
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
1210
1320
1330
1340
1350
1360
137C
1380
1390
1400
1410
1420
1430
1440
1450
1460
1470

09
RA6=(RA52+CUT4*(RAB2-RA52))%**,5
J6={RA6~R(1) }/TRPI+1,

RAG=R(JEI+.5%TRPI
RA7=(RAB82-CUT3*(RA82-RAE2) ) *%,5
J7=(RA7T-R(1)}/TRPI+1.

RAT=R(J7)+.5%TRPI

RA62=RA6X*x2

RAT2=RA7*%2

RB1=0,5%(J8-J7)

RB2=J7-J6

RB3=0.5%J6

SUM1=TOTAL(J8}-TOTAL(JT7)
SUM2=TOTAL(JT)-TOTAL(J6)

SUM3=TOTAL(Jé€)

ISUM1=5SUM1

ISUMZ2=SUM2

ISUM3=5UM3
BSMAX=1.5%((RAB~(RAB~RAT7) /24 )=(RA5+(RA6-RA5)/2.))
BSMIN=0. 2% (RA8~RA5)
IF(BSMIN.LT.0.1667)BSMIN=0,1667
APO1=3.14159%(RA82-RAT2)-ATUBE*SUMI]
AP03=3,14159%(RA62-RA52)-ATUBE*SUM3
LAWO1=6.28318%RA7T-¢S*DIAX(NT(JTI+NT(JIT+1))
LAWO3=6. 2831 8%RA6~S*DIAX(NT(J6)4NT(J6+1))
HW=2.*WCOND/ (DIA*(ALOG(DIA/DIAI)))
CSPHAV=0.36

FSPHAV=0.324

QC=HEATL/(CSPHAV*(CTO-ETC))

QF=HEATL/( FSPHAV*( FTO-ETF))

GTO = QF/(NTO*FATUB)

KEY3=0
XPRMAX=6,.,0
XPRMIN= 0.

EXPRAD= Q.5%(XPRMIN+XPRMAX)
IF(KTBST.EQ.Q)EXPRAD=1.77
IF(KEY1l.EQ.0)BSH=B SMAX
IF(KEY1.EQ.0)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
MSB
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

19
10
11

IF(KEY1.EQ.O)BSOI=0.5*%(BSL+BSH)

CURVES=0,069813%ARC*k EXPRAD+ Q.4*%(RAB-RAS)+,25%BS0I
IT =0
KFINAL=0
I=1
TSUM=0.
SSUM=0.
THEATO =
TPDTO
TPDSC
TFO(I)=F
TCI(I}=C
TIF=-5.0
TiIC=-5.0
CDTF=0.
FDTF=0.
BSO = BSOI

BRL1 BSO/({(RAB-(RA8-RAT7)/2.)-(RAS+ (RA6-RA5)/2.1)
GBRL C.7T7*BRL1**(-,138)

AWO1 BSO*LAWC1

AWO3 BSO*LAWO3

AWl SQRT(AWC1*APOL)

AW?2 (AWO1+AWO3) /2.

AW3 SQRTLAWO3*AP03)

GSO1 QC/AW1

GS02 QC/AW2

GSO3 QC/AW3

BSO=CURVES

EQVBSO= CURVES+ 13.*%(DIA+DIAIL)

KEY 4=0

KEY5=0

ATC

.0
0
0

it oH

0
0.
c.
10
10

Wi oot

TCI(I) + (TIC/2.0)

CFT ATC +CDTFXHSFCT

ATF TFO(I)+TIF/2,
FFT=ATF-FOTF*HSFCT

FI=1

TUBULN(I) =(FI-1.)*BSOI+CURVES
CVIS=0.2121%EXP(4032./(460.,+ATC))

Hon

MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS8B
MS B
MS B
RY
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS B

MSB
MSB

MS8
MSB

1850
1860
1870
1880
1890
1500
1910
1920
1930
1940
1950
1960
1970
1980
199C
2000
2010
2020

2030

2040
2G50
2060
20760
2C 80
2090
2100
2110
2120
2130
2140
2150
2160

2180
22C0

2210
2220

<9
C

12
13

14

15

1

1

1

CVISW=0.2121*%¥EXP(4032./(460,+CFT))
CDEN=141.37-0.02466*ATC

CCON=0.240

CSPH=0.36
FVIS=D0.263T*EXP(7362./(460.+ATF}))
FVISW=0.263T7T*EXP(7362./(460C.+FFT))
FDEN=234.97-0.02317*ATF

FCON=0.70

FSPH=0.224

VISK = (CVIS/CVISWI}*%0.14
FVISK=(FVIS/FVISWI**0,14

DCVIS CIA/CVIS

CCDEN 1. /CDEN

QCCDEN = QC*CCDEN

o

CALCULATE REYNOLS AND PRANDTL NUMBER TUBE SIDE

RENTO(I)=DIAI*GTO/FVIS
PRNTO( 1) =FVIS*FSPH/FCON

IF(KENTB+EQe¢ 1. AND.RENTO(I) .GT.1001.
IHEF I=14+((RENTO(I)-10004) 79000, ) **0. 5
POTO(I )=(,0028+. 25%RENTO%**(~,32) }*¥EQVBSC*GTO**2*HEFI1/

(DIAI*FDEN*4171824C0. )

CALCULATE HEAT TRANSFER CCEFF TUBE SIDE
HTO(I)=FCON/DIA* 0217 (RENTO(I ) **,8) *(PRNTO(I)*%43333 )*FVISK*HEFI

GO 10 15
IF(RENTO(I).LT.2100.) GC TO 14

HTO(I) = FCON/DIA*,089% (RENTO(I ) **,6666-125,)%(PRNTO(I)*%,3333)%
FVISK*HEFI*(1e+43333%(DIAL/TUBLN(I) )**,6666)

GO TO 15

HTO(I) = FCON/DIA*(4.36*(0.025*RENTO(Il*PRNTO(I)*DIAI/TUBLN(I)
)/(1.+0.0012*RENTO(I }*PRNTO(I ) *DIALI/TUBLN(I)))

IF(I.EQ.1)GO TO 16
CALCULATE FLOW AREAS SHELL SIDE

VWO1(I) = QCCDEN/AWOL
VWO3(I) = QCCDEN/AWO3
VML(I) = GSO1*CCDEN
VM2(I) = GSO2%CCDEN
VM3(I) = GSO3%CCDEN

eAND.TeNEel)

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
MS 8
MSB
MS8B
MSB
MSB
MSB
MSB
MSB
MSB
MSB

2230
2240
2250
2260
2270
2280
2290
2300
2310
2320
2330
2340
2350
2360
2550
2380
2390
2400
2401
2410
2411
2640
2430
2440
2450
2460
2461
2470
2480
2481
2490
2480
2510
2520
2530
2540
2550

t9
16

17

CALCULATE PRESSURE DROPS SHELL SIDE
DP1 (1.4.6*%RBY)IXCDEN*VML(I }*%2

DP2 s 6¥RB2*¥CLEN®VM2( I )*%2

DP3 (1.+.6*%RB3)*CDEN®VM3(] }*%*2
RENSOL(TI) GSG1*DCVIS

RENSOZ(I) GS02*DCVIS

RENSO3(I) GSO3*DCVIS
IF(KENTB.EQe1«AND.RENSC2(I)eGT.1001.)

oo

"

ton

PDSO(I) = (DP1+DP2+DP3)*PLK*HEFQ0/834624000.
IF(I.EQ.2)PDSO(1)=PDSO(2)

CALCULATE BJ FACTOR AND SHEL SIDE COEFFICIENT
BJ(1) =(0.346%RENSOL(I)**{-0,382))%GBRL

BJ(2) =(0.346%RENSO2(I ) **(-0,382) )*GBRL

BJ(3) =(0.346%¥RENSO3(I)*%*(~-0.382) )*GBRL

HSOL1(I) = (LK*CSPH*GSO1*BJ(1 I *( (CCON/(CSPH*CVIS) )*¥,66) )*VISK
HSO2{I) = (LK*CSPH*GSO2*BJ(2)*( (CCON/(CSPH*CVIS))*%x,66))*VISK
HSO3(I}) = (LK*CSPH*GSO3%BJ(3)*((CCON/(CSPH*CVIS) )*%k,66))*VISK
AHSOC(TI)=(((HSOLCT)*SUML1 )+ (HSC2(I)*SUM2)+(HSO3(I )*SUM3))/SNT)*HEFO
GO T0 17

PDSO(I)=0,

APO=3.14159%(RA82-RA52)~SNT*ATUBE

EQVDIA=4 .*AP0O/(3.,14159%SNT*D[A+6,24318%(RAB+RA5))
GS0=QC/APO

RENSO =GSO*DCVIS

PRESO =CVIS*CSPH/CCON
AHSO(I)=0.128%CCON*VISK*(12.*EQVDIA*RENSO 1 ¥%0,6

1 *PRESO *%¥0.33/DIA

UOA(I)=1.0/0(1.0/AHSO(I ) +(1.C/HTC(I))+(1.0/HW))

A = QF*FSPH
B = QC*CSPH

D = UOA(I)*SNT*BSO  *3,1415S*DIA
P = =HSFCT*(D*(A-B))/(A*B)

PBAR = EXP(P)
C = (B-A)*PBAR
TCOCI) = ((TCI(II*(B*PBAR-A))=-(TFC(I ) *AX{PBAR-1.})))/C

MSB
MSB
MSB
MS8
MSB
MSB
MSB
MSB
MSB
MSB
MS 8
MS B
MSB
MSB
MS B
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS B
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS8
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
21760
2770
2780
2790
2800
2810
2811
2820
2830
2840
2850

2870
2880
2890

79
18

19

IF((ABS(CYIF-TIF)eLE«{3e0))sAND. (ABS(CTIC~TIC).LE.(3.0)))G0O TO 18

=((TCOCTI-TCICI)I®*B/AY + TFOC(I)

= (HEAT(I)/NTO)*ALOG(DIA/DIAL)/(2.0%3,14159%BS0O*WCOND)

TFI(CI)

HEAT(I) ==AX(TFI(I) - TFO(I))
TWDT(I)

CTIF = TFI(I)-TFO(I)

CTIC = TCO(I)-TCI(I)

TIF = CTIF

TIC = CTIC

KEY5=KEYS+1

IF(KEY5.,GT .50)G0 TQO 37
GO TO 11}
THEATO
TPDTC
TPDSO
IF(I1.EQe 2) TPDSO=TPDSO+PDSO(1)

COTF=(((HEAT(I)})

THEATO + HEAT(
TPDTO + PDTO(I)
TPDSO + PDSO(I)

FDTF=CDT F*AHSO(I) /HTO
FWT(1)
CwrT(I)
AVWT(I)
TSUM=TSUM+AVWT(I)
SSUM=SSUM+ATC

[F(KFINAL.EQel .AND.I.EQ.IT) GO TO 20

IFCC(ABS(ETF=-TFI(I) M) LE.((ABS(TFI(I)-TFO(I)))/2.0)).0R.

=ATF-FDTF*HSFCT
=ATC+CDTF*HSFCT
=0 5% (FWT(1)

I)

/NTO)/BSO) /7(3.14159%DIA*AHSC(1))

(I}

+CWT(I))

1 (TFI(I)L.LE.ETF)) GO TO 169

I=1+

1

IF(I.GT.75) GO TO 30
IF(I.EQ.2) ATC1=ATC
TFOC(I)
TCI(I)
B8S0=BSOI
EQVBSO=B SO

KEY4=KEY 4+]

IF(KEY4.GT .501G0 TO 36
GO TO 10
KFINAL=1

IT=1
FIT

-—
-

IT

TFI(I-1)
TCO(I-1)

MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS B

MSB
MSB
MSB
MS B
MSB
MSB
MSB
MSB
MSB
MS8B
MSB
MSB

- MSB

MSB
MSB
MSB
MS B
MSB
MSB

2900
2910
2920
2930
2940
2950
2960
2970
2980
2990
aco0c
3010
3020
3030
3040
3090
3100

3130
3140
3150
3050
3060
3061
3070
3080
3160
3170
3180
3190
3200
321¢
3220
3230
3240
3250
3260

€9
20

21

22

23

24

DCURVE=CURVES*((HEATL-THEATO) /HEAT(1)})
CURVES=CURVES+DCURVE

GO TO 9

TUBLEN=( FIT~1. )*BSOI+CURVES

HEXLEN=( FIT-1.)%BSOI+4.*EXPRAD*SIN{ARCR) +DCURVE+0Q.25*BSMAX
STRLEN=(FIT=1. }*BSOI+DCURVE+.25%BSMAX
ITF( KTBST.EQ.Q)} GO TC 24
T1=FWT(1)

T2=CWT (1)

PDTO1=PDTO(1)

PDS01=PDSO(1)

- TSUM=TSUM-AVWT (1)

PN e

SSUM=SSUM-ATC1

TAVT=(CURVES*AVWT(1)+BSOI*TSUM) /TUBLEN

SAVT=((HEXLEN-BSOI*(FIT-1e) ) *ATCL+BSOI*SSUM) /HEXLEN

CALL TUBSTR(TPIN,SPOUT,PDTO1l ,PDSO1,TPDSO»yT1,T2,
HEXLEN, EXPRADyDIAT 4DIAWARCHETF4+FTO+ETC 4CTO4SAVT,,TAVT,
T11eT124T13,T244T254T364T737,T738,749,T7410,0T, BN,ASM,
ST+STPySQPySLPRySLPGySLLCySLLI »STTO,STTI +TM,CASM,CTM,
PlsP2+SAsR1,R2,TLsRB, AAl,AA2,AA3,AA4,AAS5,BE1,BB2,
883,8B4,+BB5)

KEY3=KEY3+1

IF(KEY3.GT.50)0G0 TO 35

IF(T24.LT.0.0,0R.T12.LT.0.0) GO TO 22
IF(T24.GT.(.08*%ASM) AND.T12.GT. (. C8%ASM)) GO TO 23

GO TO 24 |

XPRMIN=EXPRAD

GO 70O 8

XPRMAX=EXPRAD

GO T0 8 .

VOL = 0.7854%(DIATI**2,0)*NTO*TUBLEN

CHECK OF TUBE AND SHELL PRESSURE DROPS

KEYZ2 = KEYZ2 + 1

IF(PERC2.LE.Q0.1) GO TO 33

IF(TPDTO.LT.(PERC2*PROT)} GO TO 25

IF(TPDTO.GT.PRDT) GO TO 26

GO TO 27 ‘

MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS8
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
M5B
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
3440
3450
3460
3470
3480
3490
3500
3510
3520
3250
3540
3550
3560
3570
3580

99
25

26

27

28

29

30
1057

IF(RAB.LE.(RAS +0.005)) GO T0O 34
RABH =RAS8

IF(KEY2.NE.320)GO TO 3
RA8BL=RA8BL-C,?2

PERC2 = PERCZ2 - (.C1

KEYZ2=1C

GO TO 3

IF(RA8.GE.(RABMAX-0C.005)) GO TO 34
RA8L =RAS8

IF(KEY2.NE.30) GO 7O 3
RABH=RA8H+0./2

PERC2 = PERC2 - 0.01

KEYZ2=10

GO TO 3

KEY1l = KEY1l + 1

IF(PERCL.LE.O.1) GO TO 22
IFC(TPDSO.LT.(PERC1*PRDS)) GO TO 28
IF(TPDSO.GT.PRDS)IGO TO 29

GO 7O 38
IF(BSOI.LE.(BSMIN+0,005))G0 TO 31
BSH =BSOI

IF(KEY1.NE.30)GO TO 2

BSL=BSL-0.1

PERC1 = PERCl - (.01

KEY1=10

GO TO 2
IF(BSOI.GE.(BSMAX-0.,005})G0 TG 31
BSL =BSOI ‘

IF(KEY1.NE.30) GO TO 2
BSH=BSH+0.1

PERC1 = PERC1 - 0.01

KEY1=10C

GO TO 2

PRINT EXIT SIGNALS
PRINT 10°%1,BSO0

FORMAT(3GH1BAFFLE SPACINGS EXCEEDE 75 WITH BSC

GO TO 38

1F5.242X94H(FT) )

MSB
MS 8B
MS8
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS8
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB

3590
3600
3610
3620
3630
3640
3650
3660
3670
3680
3690
3700
3710
3720
3730
3760
3770
3780
3790
3800
3810
3820
3830
3840
3850
3860
3870
3880
3890
39C0
3910
3920
3930
3640
3650
3960
3970
3980

L9
31
1058

32
1059

33
1C60

34
1061

35
1062

36
1063

37
1064

38

39

PRINT 10E2

FORMAT(2CHIBSOI = MAX. OR MIN.)
GO TO 38

PRINT 1059

FORMAT(48H]1 PERC1 FOR SHELL PRESSURE DROP IS LESS THEN 0.1)

GO TG 38
PRINT 1060

FORMAT(48H1 PERC2 FOR TUBE PRESSURE DRGP IS LESS THEN 0.1)

GO TO 38

PRINT 1061
FORMAT(29H1 SHELL RADIUS = MAX. CR MIN.)
GO TO 38

PRINT 1062, KEY3
FORMAT(6HLIKEY3= ,15)
GO TO 38

PRINT 1063, KEY4
FORMAT(6H1KEY4= ,15)
GO TO 38

PRINT 10¢4, KEYS5
FORMAT(6H1KEY5= ,15)
GO TO 38

END OF CASE, PRINT QUTPUT
DO 39 I = 1,17

VI(I) = VMI(I)*GFTT

V2{I) = VM2(I)*GFTT

V3(I) = VM3{I)*GFTT

VW1(I) = VWOL(I)*GFTT
VW3(I) = VWO3B(I)*GFTT
CONTINUE

TTDSO = TPDSO*GFT

TTDTO = TPDTO*GFT
TPPERC=TPOTO%*100./PRDT
SPPERC=TPDSO*100./PRDS
HTPERC=100.*THEATO/HEATL
AREA=3,14159*DIA*SNT*TUBLEN

MSB
MSB
MSB
MSB
MSB
MS8
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS B
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS8
MS8B
MS8
MSB
MSB
MS8B
MSB
MSB
MSB
MSB
MSB

3990
4000
4010
40 20
4030
40 40
4050
4C €0
4C70
40 80
4090
4100
4110
4120
4130
4140
4150
4160
4170
4180
4190
3810
3820
4220
4230
4240
4250
4260
4270
4280
4290
4300
4310
4320
4330
4340

89
C
C

40

ASM3=3,%ASM
PSTO=AAl
PQSTO=AAZ2
PQFSTO=AA3
PSTI=BB1

PQSTI=

BB4

PQFSTI=BB5

PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINY
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
1
PRINT

1033, THEATO, HTPERC
1024, QC

1025, QF

1036,TTDSO, SPPERC
1027, TTDTO, TPPERC
1038,RA8

1039,BS01

1040,VCL

1041, AREA

10424 SNT

1043, TUBLEN

10444 HEXLEN

1045, STRLEN

1046 ,EXPRAD

1047, GBRL

1051 ,TAVT

1052 4 SAVT
1053,PSTO,PSTI,+ASM
1054,PQSTOL.PQSTI yASM3
1055,PQFSTO,PQFSTI 4 SA

1048y (L2 (TCICI)oTCOCI)4CWTLL) »

TWDTCI) Da1=1,1IT)

10494 (T4 (VI(I)sV2(T)4yV2(I) 4 VWI(I)VW3(I)},PDSO(I),PDTO(I))},

1 [=1,1IT)

PRINT 10Z20,(I, (RENTO(I)PRNTO(I) +RENSC1(I),RENSC2(I),RENSG3(I),

IHTOCI )y AHSO(I) JUCA(I) +HEAT(I)) +I=1,1IT)

LOOP FOR ADDITIONAL CASES IF REQUIRED

CONTINUE

TEICL) +TFC(I) oFWT(I),

MS8
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS B
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS8B
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
4500
4510
4520
4530
4540
4550
4560
4570
4580
4590
4600
4610
4620
4630
46 31
4640
4641
4650
4651
4240
4250
468C

69
4]

CcC

CcC

cC

KEY7=KEY7+1

IF(KEY7.GT.KASES)IGO TO 41

GO TO0 1

wm PN

CONTINUE
END

SUBROUTINE TUBSTR(TPINySPOUT.+PDTC1,PDSC1sTPDSOsT1,T2,
HEXLEN, EXPRADDIATI 4yDIAJARCETF4FTOLETC4CTOySAVTTAVT,
Tll!TlZvT].B'TZ‘f’TZS, T36,T371T38 1T49 'Tli'lO'DT' BF'ASM'
ST+STP+SQP 9 SLPRySLPG+SLLOySLLI +STTOLSTTI 4TM,CASHF,CTM,
PlyP2¢SAyR1,4,R2,TLyRBy AAl,AA2,AA3,AA4,AA5,BB1,BB2,
BB3,BB4,BB5)

DIMENSION CASM(6),CTM(6)

GFT=1./144.

Pl=(TPIN-.5%¥PDTO1l )*GFTY

P2=(SPOUT +.5%PDSO1  }*GFT
R1=64*%DIAI

R2=6.*DIA

TL =12 .%HEXLEN

RB=12.*EXPRAD
A=0.017452*ARC

MSB 4690
MSB 4700
MSB 4710
MSB 4720
MSB 4730

TUBST
TUBST
TuBST
TUBST
TUBST
TUBST
TUBST
TUBST
TUBST
TUBST
TUBST
TUBST
TUBST
TUBST
TUBS

DETERMINE AVERAGE CHANGE IN TEMPERATURE OF SHELL(DTS) AND TUBE(DTT)

DTS = SAVT-70.

DTT = TAVT-7C.

CALCULATE PRESSURE AND TEMPERATURE DIFFERENTIAL ACROSS TUBE WALL,
DP = P1-P2

DT = T1-T2
AND AVERAGE TEMPERATURE OF TUBE WALL
TM = (T1+T21})/72.

TUBS
TUBS
TUBS
TUBS
TuBS
TUBS
TUBS

10
11
12
13
14
15
20
30

50
60
70
80
S0
100
110
120
130
140
150
160
170
180

0L
CC
CcC

cC

cc

CcC

cC

CC

CALCULATE MOMENT OF INERTIA OF TUBE CRGSSECTICN{AMI)
AMI = 0.7853G68%(R2**¥4-R1%*%*4)

CALL SUBROUTINE TO DETERMINE ALLCWABLE STRESS(ASV)
CALL LAGR (CASMyCTM,ASM,TMy2,46 v+ IERR)

ESTABLISH MATERIAL PROPERTIES CONSTANTS

SA= 25000.0

EM = 25C00000.0
PR = 0,3

TE = 0.CN00078
SE = C.0C00076

CALCULATE AXIAL LOAD AND MOMENT DUE TO LCNGITUCNAL EXPANSION

DY = TLX(TE*DTT-SE*DTS)

RM = (R2+R1)/2.

TW = R2-R1

AL = TW*RB/RM*%x2

AL2 = AL%%Z2

AK = (1.+12.%AL2)/(10.+12.%AL2)
AA = 2.%A

P = 25000000.*AK*AMI*DY/(RB**3% (AAXCOS(AA) -3, *SIN(AA) +4,.%A))
BM = P*RB*(1.-CO0S(A))
CALCULATE Q STRESS DUE TO P

SQP = -P/(6.28318%RM*Th)
CALCULATE Q STRESS DUE T0O M
Bl = 6/ (Detb*AL2)

B2 = BM/(AK*AMI)

B3 = (R2/RM)*%x2

B4 = (R1/RM)*%x2

B5 = 1.5%RM*B2¥%AL*B1

SLLO = R2*BZ2*(1.-B1*B3)
SLLI = R1*B2*(1.-B1*B4)
STTO = B5%(1.-2.%B3)

STTI = B5%(1l.~2.%B4)
CALCULATE F STRESS DUE TO TUBE WALL TEMPERATURE CROP
ST = 13G.,%DT

SLI = -S7

ST = -S7

SLO = ST

STO = ST

TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TuBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TuBS
TUBS
TUBS
TUBS
TuBS
TUBS
TuBS
TuBS
TUBS
TUBS
TUBS
TusS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS

190
200
210
220
230
240
250
260
270
28C
290
300
310
320
33C
340
350
3€0
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560

1L
CC
cC
CC

cC

cC

CC

cC

cC
cC
cC
cc

ccC

CALCULATE STRESSES DUE TO PRESSURE

HOOP

STP = DP*RM/TW
LONGITUDNAL
SLPR = STP/2.
SLPG = 0
RADIAL

SRPI = =-P1
SRPO = =~P2

P STRESS TuBE OD BEND OD

All =AMAX1{(STP,SLPRySRPC)

Al2 =AMIN1{(STP+SLPR+SRPC)

AAl Al1l-A12

T11 ASM- ABS(AA]l)

P+Q STRESS TuBE OD BEND 0D

Al3 =AMAX1(STP+STTO,SLPR+5QP+SLLG,SRPO)

Al4 =AMINL(STP+STTO,SLPR+SQP+SLLC,SRPO)

AAZ2 = Al2-Al4

Tl2 = 3%ASM- ABS(AAZ2)

P+Q+F STRESS TUBE OD BEND 0D

Al5 =AMAX1(STP+STTO+STO+SLPR+SQP+SLLC+SLO,SRPC)
Al6 =AMIN1(STP+STTO+STOsSLPR+SQP+SLLO+SLO.SRPC)
AA3 = Al15-Al¢

T13 = SA - ABS(AA3)

P STRESS TUBE OD BEND 1ID

SAME AS P STRESS AT TUBE CD BEND 0D -- T11)

P+Q STRESS TUBE OD BEND ID
A22 =AMAX1{STP+STTO,SLPR+SQP-SLLC,4SRPO)
A23 =AMINL{STP4+STTO,SLPR+35QP-SLLC,SRPD)

AAG = A22-A23

T24 = 3%ASM- ABS{AA4)

P+Q+F STRESS TUBE 0D BEND ID

A24 =AMAX1{STP+STTO+STOsSLPR+SQP-SLLO+SLO,SRPOI
A25 =AMINI(STP+STTO+STO,SLPR+SQP-SLLO+SLO,SRFC)
AAS = A24-A25

T25 = SA - ABS(AA5)

TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TusS
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

<L
CC

cC

CC

ccC
CC

CcC

CC

CC

CC
CcC

P STRESS TUBE ID BEND OD

B1l =AMAX1(STP,SLPR,SRPI)

B12 =AMIN1(STP,SLPR,SRPI)

BBl = Bl1-Bl1

T36 = ASM- ABS(BB1)

P+Q STRESS TUBEID BEND OD

B13 =AMAX1(STP+STTI,SLPR+SQP+SLLI,SRPI)
Bl4 =AMIN1(STP+STTI,SLPR+SQP+SLLISRPI)

Hou

B82 = Bl3-Bl4

T37 = 3%ASM- ABS(BB2)

P+Q+F STRESS TUBE ID BEND 0D

B15 =AMAX1(STP+STTI+STISLPR+SQP+SLLI+SLI,SRPI}
Bl6 =AMINL(STP+STTI+STI SLPR+SQP+SLLI+SLI 4SRPI)
BB3 = Bl:5-Blé

T38 = SA - ABS(BB3)

P STRESS TUBE ID BEND ID
SAME AS P STRESS AT TUBE ID BEND OD -- T36

P+Q STRESS TUBE ID BEND ID ,
B23 =AMAX1(STP+STTI,SLPR+SQP-SLLI,SRPI)

B24 =AMINI(STP+STTI,SLPR+SQP-SLLI,SRPI}
BB4 = B23-B24
T49 = 3%ASM- ABS(BB4)

P+Q+F STRESS TUBE ID BEND ID

B25 =AMAX1(STP+STTI4+STI,SLPR+SQP-SLLI+SLI+SRPI)
B26 =AMINL(STP+STTI+STI, SLPR+SQP-SLLI+SLI,SRPI)
B85 = B2E5-B2¢€

T41l0 = SA - ABS(BBS)

RETURN
END

TUBS
TUBS
TUBS
TUBS
TUBS
TUBS
TuB
TUB
TUB
TUB
TUB
TUB
TuB
TUB
TUB
TUB
TUB
TUB
TUB
TuB
TuB
TUB
TUB
TUB
TUB
TUB
TUB
TuB
TUB
Tus
TUB
Tus
TUB

940

950

560

970

980

990
1000
1010
1020
1030
1040
1050
1060
1070
1080
1090
1100
1110
1120
1130
1140
1150
1160
1170
1180
1190
1200
1210
1220
1230
1240
1250
1260

€L
OO0 0COO0OO0O0O0

SUBROUTINE LAGR (FXysXyFXP ¢XP¢NyNPTyIER)

DIMENSION FX(NPT)y X(NPT)

SUBROUTINE USES LAGRANGIAN INTERPCLATICN TC A DESIRED DEGREE
POL INOMI AL

FX = FUNCTION OF INDEPENDENT VARIABLE

X = INDEPENTENT VARIABLE

FXP = ESTIMATE OF FX AT XP

XP = VALUE OF X FOR WHICH INTERPOLATICN [S DESIRED
N = DEGREE OF POLINOMIAL USED IN INTERPGLATICN
NPT = NUMBER OF POINT-PAIRS IN TABLE

TER = COUNTER TO REPORT TYPE OF EXECUTICN

CHECK TO SEE IF XP IS A TABLE ENTRY

DO 2 K = 1,4NPT

IF(XP.EQX(K))1,2

FXP = FX(K)

IER = 3

RETURN

CONTINUE

DETERMINE IF EXTRAPOLATICN IS REQUIRED
IF(XP.LTaX(1))4,43

IF{XP.GTX(NPT))5,6

L1 = 1

L2 = NPT

GO 1O 15

tl = NPT - N
L2 = NPT

GO TO 15

IER = 2

DETERMINE IF SUFFICINT DATA IS PRESENT FOR DEGREE OF POLINOMIAL
M =N®1

IF(MeGT.NPT)} 7, &

IER = 1

RETURN

DETERMINE NEXT HIGHEST POINT

D8 9 K = 2,NPT

Kl = K

IF(XPelLT X(K))10,9

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
10C
110
120
130
140
150
16C
170
180
190
200
210
220

230

240
250
260
270
280
290
300
310
320
330
340
350
360
370
380

L
10
11

12

13

14

15

16

17
18

CONT INUE

DETERMINE THE LOWER POINTS REQUIRED
L = M/2

LZ = K1 + L -1

IF(LZ2.LENPT)13,12

Kl = K1 -1

GO TO 11

Ll =K1 + L - M

IF(L1)14,14,15

Kl = K1 + 1

L2 = L2 + 1

GO TO 13

INTERPOLATION BY LAGRANGIAN METHCD (SEE MATHEMATICS OF PHYSICS

LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
LAGR

AND MODERN ENGINEERING o SOKOLNIKOFF AND REDHEFFER +PAGES 699,700)LAGR

FXP = 0,0
DO 18 K = L1,L2
PKX = 1.0
PKXK = 1.0

DO 17 I = Li,L2
IF(T.EQ.K)17416

PKX = PKX*(XP = X(I))

PKXK = PKXK*x(X(K) = X(I))
CONTINUE

FXP = FXP + FX(K)*PKX/PKXK
RETURN

END

LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
LAGR
L AGR
LAGR
LAGR

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

G/
LAWO1
LAWO3
NT(I)
BJ(I)

HSO01(1)

HS02(I)

HSO3(I1)

TUBLN(I)
V1(I)

V2(I)

V3(I)
VW1(I)

VW3 (1)

FTUB
KEY1
PERC1
KEY2
PERC2
RASL
RA8H
RJ8

138
RIJ8
R(I)
FACT(I)
TCPI(I)

76

Intermediate Variables

 

Net cross-flow circumference at inner edge of baffle, ft.
Net cross-flow circumference at outer edge of baffle, ft.
Number of tubes in ring I.

J factor for the heat transfer coefficient at the inner window
zone (I = 1), cross-flow zone (I = 2), and outer window zone
(I = 3).

Shell-side heat transfer coefficient for inner window zone in
increment I, Btu/hr.ftZ.°F.

Shell-side heat transfer coefficient for cross-flow zone in
increment 1.

Shell-side heat transfer coefficient for outer window zone in
increment I. :
Accumulated tube length up to increment I, ft.

Average velocity of fluid in outer window zone in increment I,
ft/sec.

Average velocity of fluid in overlapping baffle zone in incre-
ment I.

Average velocity of fluid in inner window zone in increment I.

Fluid velocity across tubes in outer edge of baffle in incre-
ment I, ft/sec.

Fluid velocity across tubes in inner edge of baffle in incre-
ment I.

Inside cross-sectional area of tube, ft=.

Flag for number of iterations on baffle spacing.

Fraction of input shell-side pressure drop considered acceptable.
Flag for number of iterations on outer radius.

Fraction of input tube-side pressure drop considered acceptable.
Current lower limit for outer radius.

Current higher limit for outer radius.

Temporary number of tube rings.

Integer form of RJS.

Real form of 1J8.

Radius of tube ring I, ft.

Circumference of tube ring I, ft.

Temporary circumferential pitch in tube ring I, ft.
TOTAL(T)
AVWT(I)
KEY7
HEFI
HEFO
HSFCT

ARCR
ATUBE
GFTT
GFT
DIAI
J8
TRPI
CPIL
NTO
RA52
RA82
RA6
J6
RA7
J7
RA62
RA72
RB1
RB2
RB3
SUM1
SUM2
SUM3
ISUM1
ISUM2
ISUM3
BSMAX
BSMIN

77

Accumulated number of tubes up to tube ring I.
Average temperature of tube wall in increment I, °F.
Flag for number of cases performed.
Tube-side enhancement factor.
Shell-side enhancement factor.

Flag: 1 = tube side hotter than shell side,
-1 tube side colder than shell side.

Arc of bent tube for thermal expansion, radians.
Outside cross-sectional area of tube, ftZ.
1/3600

1/144 .

Inside diameter of tube, ft.

Actual number of tube rings.

Actual radial pitch, ft.

Actual circumferential pitch, ft.

Integer form of TOTAL(I).

Square of RA5, ftZ.

Square of RA8, ftZ.

Radius of inner baffle edge, ft.

Number of tube rings up to RAG6.

Radius of outer baffle edge, ft.

Number of tube rings up to RA7.

Square of RA6, ft=.

Square of RA7, ft=.

Number of tube rings in inner window zone.
Number of tube rings in cross-flow zone.
Number of tube rings in outer window zone.
Number of tubes in inner window zomne.
Number of tubes in cross-flow zone.

Number of tubes in outer window zone.
Integer form of SUMI.

Integer form of SUMZ.

Integer form of SUM3.

Higher limit for baffle spacing, ft.

Lower limit for baffle spacing, ft.
APO1
APO3

CSPHAV
FSPHAV
GTO
KEY3
XPRMAX
XPRMIN
BSH
BSL
CURVES
IT
KFINAL
TSUM
SSUM
TPDTO
TPDSO
TIF

TIC

CDTF
FDTF
BSO
GBRL
AWO1
AWO3
AW1
AW2
AW3
GS01
GS02
GS03
EQVBSO

78

Net parallel flow in inner window zone, £t2,
Net parallel flow in outer window zone, £t2.
Heat transfer coefficient across tube wall, Btu/hr.ft=.°F.
Average specific heat in shell side, Btu/1b-°F.
Average specific heat in tube side.
Mass flow rate in tubes, lb/hr.ftZ.
Flag for number of iterations on tube expansion radius.
Higher limit on tube expansion radius, ft.
Lower limit on tube expansion radius, ft.
Current higher limit for baffle spacing, ft.
Current lower limit for baffle spacing, ft.
An approximate length of the curved section of the tubes, ft.
Number of baffle spacings.
A flag to indicate that the heat load requirement has been met.
Accumulated average temperature of tube wall.
Accumulated average temperature of shell fluid.
Accumulated tube-side pressure drop.
Accumulated shell-side pressure drop.

Assumed temperature difference in tube-side fluid between two
increments, °F.

Assumed temperature difference in shell-side fluid between two
increments, °F.

Tube-side bulk to wall temperature difference, °F.
Shell-side bulk to wall temperature difference, °F.
Current baffle spacing, ft.

Correction factor for Bergelin's heat transfer coefficient.
Net cross-flow area at inner edge of baffle, ft2,
Net cross-flow area at outer edge of baffle, ftZ.
Effective flow area in inner window zone, ftZ.
Effective flow area in cross-flow zone, ft2,
Effective flow area in outer window zone, ft=.

Mass flow rate in inner window zone, 1b/hr. £t2.
Mass flow rate in cross-flow zone, lb/hr.ft=.

Mass flow rate in outer window zohe, 1b/hr. ft=.

Length of heat exchanger in the curved tube region considered
as first baffle spacing.
79

KEY4 Inactive.

KEY5 Flag for number of iterations on average temperature in each
baffle spacing.

ATC Shell-side average temperature in each baffle spacing, °F.

CFT Average tube wall temperature on shell side in each baffle
spacing, °F.

ATF Tube-side average temperature in each baffle spacing, °F.

FFT Average tube wall temperature on tube side in each baffle
spacing, °F.

FI Numbeyr of baffle spaces.

CVIS Shell-side fluid viscosity, 1b/ft-sec.

CVISwW CVIS evaluated at wall temperature.

CDEN Shell-side fluid density, 1b/ftS.

CCON Shell-side fluid conductivity, Btu/hr.ft.°F.

CSPH Shell-side fluid specific heat, Btu/lb-:°F.

FVIS Viscosity of tube-side fluid, 1b/ft-sec.

FVISW FVIS evaluated at wall temperaturé.

FDEN Density of tube-side fluid, 1b/ftS.

FCON Conductivity of tube-side fluid, Btu/hr.ft.°F.

FSPH Specific heat of tube-side fluid, Btu/lb:°F.

VISK (CVIS/CVISW)**0.14 .

FVISK (FVIS/FVISW)**0.14 .

DCVIS DIA/CVIS

CCDEN 1/CDEN .

QCCDEN QC*CCDEN .

DP1 Velocity head in inner window zone.

DP2 Velocity head in cross-flow zone.

DP3 Velocity head in outer window zone.

APO Net flow area parallel to tubes in curved-tube region, ftZ.

EQVDTA Equivalent diameter to be used in Donohue's correlation, ft.

GSO Mass flow rate parallel to tubes in curved-tube region, 1b/hr-ftZ.

RENSO Reynolds number for shell-side of curved-tube region.

PRESO Prandt]l number for shell-side of curved-tube region.

CTIF Calculated temperature difference in tube-side fluid between

two increments, °F.

CTIC Calculated temperature difference in shell-side fluid between
two increments, °F.
ATC1
FIT
DCURVE
PDTO1
PDSO1
Tl

T2

T11

T12

T13

T24

T25

T36

T37

T38

T49

T410

BM
ASM
ASM3
ST
STP

SQP
SLPR

SLPG

80

Average temperature in shell side of curved-tube region, °F.

Final number of baffle spaces.

Additional straight length added to the curved-tube section, ft.

Tube-side pressure drop in curved-tube region, 1b/ft=.

Shell-side pressure drop in curved-tube region, 1b/ftZ.

Tube-side surface temperature of tube wall, °F.

Shell-side surface temperature of tube wall, °F.

Maximum

primary

bend 0D, psi.

Maximum
surface

Maximum
at bend

Maximum
surface
Maximum
at bend

Maximum

primary
of tube

peak (P

0D, psi.

primary
of tube
peak (P

ID, psi.

primary

bend OD, psi.

Maximum
surface

Maximum
at bend

Maximum
surface

Maximum
at bend
Average

determined,

primary
of tube

peak (P
OD, psi.
primary
of tube

peak (P
ID, psi.

(P) stress test on outside surface of tube at

and secondary (P + Q) stress test on outside
at bend OD, psi.

+ Q + F) stress test on outside surface of tube

and secondary (P + Q) stress test on outside
at bend ID, psi.
+ Q + F) stress test on outside surface of tube

(P) stress test on inside surface of tube at

and secondary (P + Q) stress test on inside
at bend 0D, psi.

+ Q + F) stress test on inside surface of tube

and secondary (P + Q) stress test on inside
at bend ID, psi.

+ Q + F) stress test on inside surface of tube

temperature of tube wall at point where stresses are

OFI

Bending moment resulting from restrained thermal expansion, in.-1b.

Allowable stress intensity determined in LAGR, psi.

Three times ASM, psi.

Magnitude of thermal stress resulting from DT, psi.

Hoop stress resulting from pressure differential across tube
wall, psi.

Longitudinal stress resulting from P, psi.

Longitudinal stress resulting from pressure differential across
tube wall, psi.

Longitudinal stress resulting from pressure differential across
lower tube sheet (currently set equal to zero), psi.
SLLO
SLLI
STTO
STTI

DT
P1
P2
SA
R1
R2
TL

AA3

AAL

BB1
BB2
BB3
BB4
BB>5

GFT

81

Magnitude of longitudinal stress resulting from BM on outside
diameter of tube, psi.

Magnitude of longitudinal stress resulting from BM on inside
diameter of tube, psi.

Magnitude of hoop stress resulting from BM on outside diameter
of tube, psi.

Magnitude of hoop stress resulting from BM on inside diameter
of tube, psi.

Temperature differential across tube wall, °F.
Tube-side pressure, psi.

Shell-side pressure, psi.

Allowable stress intensity for cyclic analysis, psi.
Inside radius of tube, in.

Outside radius of tube, in.

Length of tube (difference in elevation of tube ends; HEXLEN in
PRIMEX main program), in.

Radius of flexibility bend segments, in.

Maximum primary (P) stress intensity on outside surface of tube
at bend OD, psi.

Maximum primary and secondary (P + Q) stress intensity on out-
side surface of tube at bend OD, psi.

Maximum peak (P + Q + F) stress intensity on outside surface of
tube at bend OD, psi.

Maximum primary and secondary (P + Q) stress intensity on out-
side surface of tube at bend ID, psi.

Maximum peak (P + Q + F) stress intensity on outside surface of
tube at bend ID, psi.

Maximum primary (P) stress intensity on inside surface of tube
at bend OD, psi.

Maximum primary and secondary (P + Q) stress intensity on inside
surface of tube at bend OD, psi.

Maximum peak (P + Q + F) stress intensity on inside surface of
tube at bend OD, psi.

Maximum primary and secondary (P + Q) stress intensity on inside
surface of tube at bend ID, psi.

Maximum peak (P + Q + F) stress intensity on inside surface of
tube at bend ID, psi.

Conversion factor, feet to inches.

Arc of four bend segments in flexibility bend, radians.
DTS
DTT
DP
AMI
EM
PR
TE
SE

DY
RM
™
AL
AL2

AK
AA
P

82

Average change in temperature of the shell, °F.
Average change in temperature of the tubes, °F.
Pressure differential across tube wall, psi.
Moment of inertia of tube cross section, in.%
Modulus of elasticity for tube and shell material, psi.
Poisson's ratio for tube and shell material (0.3).

Coefficient of thermal expansion for tube material, in./in.°F.
Coefficient of thermal expansion for shell material.
Difference in thermal expansion of tubes and shell, in.

Mean radius of tube wall, in.

Thickness of tube wall, in.

Dimensionless parameter in Wahl's factor AK.

Square of AL.

Wahl's rigidity multiplication factor.

Two times A.

Axial load resulting from restrained thermal expansion, 1lb.

B1, B2, B3, B4, B5 Repeated factors used in calculating stresses result-

SLI

STIL

SLO

STO

SRPI

SRPO

All

Al2

Al3

Al4

ing from BM.

Longitudinal stress on inside diameter of tube resulting from
temperature differential across tube wall, psi.

Hoop stress on inside diameter of tube resulting from tempera-
ture differential across tube wall, psi.

Longitudinal stress on outside diameter of tube resulting from
temperature differential across tube wall, psi.

Hoop stress on outside diameter of tube resulting from tempera-
ture differential across tube wall, psi.

Radial stress on inside diameter of tube resulting from
pressure, Ppsi.

Radial stress on outside diameter of tube resulting from pres-
sure, psi.

Maximum value of primary (P) stress on outside surface of tube
at bend OD, psi.

Minimum value of primary (P) stress on outside surface of tube
at bend 0D, psi.

Maximum value of primary and secondary (P + Q) stress on out-
side surface of tube at bend 0D, psi.

Minimum value of primary and secondary (P + Q) stress on out-
side surface of tube at bend OD, psi.
Al5

Al6

A22

A23

A24

A25

B11l

B12

B13

B1l4

B15

B1l6

B23

B24

B25

B26

83 .

Maximum value of peak (P + Q + F) stress on outside surface of

tube at

Minimum
tube at

Maximum

Minimum value of primary and
side surface of tube at bend

value of peak (P +Q

Maximum
tube at
Minimum
tube at
Maximum
at bend
Minimum
at bend
Maximum
surface
Minimum
surface
Maximum
tube at
Minimum
tube at
Maximum
surface
Minimum
surface
Maximum
tube at
Minimum
tube at

bend OD, psi.

value of peak (P + Q
bend 0D, psi.

value of primary and
side surface of tube at bend

bend 1D,

value of peak (P + Q

bend 1D,

value of primary (P)

0D, psi.

value of

OD, psi.

primary (P)

+ F) stress on outside surface of

secondary (P + Q) stress on out-

ID, psi.

secondary (P + Q) stress on out-

ID, psi.

+ F) stress on outside surface of

+ F) stress on outside surface of

stress on

stress on

value of primary and secondary
of tube at bend 0D, psi.

value of primary and secondary
of tube at bend OD, psi.

inside surface

inside surface

(P + Q) stress

(P + Q) stress

of

tube

tube

inside

inside

value of peak (P + Q + F) stress on inside surface of

bend OD, psi.

value of peak (P + Q + F) stress on inside surface of

bend OD, psi.

value of primary and secondary (P + Q) stress on inside
of tube at bend ID, psi.

value of primary and secondary (P + Q) stress on inside
of tube at bend ID, psi.

value of peak (P + Q + F) stress on inside surface of

bend 1D, psi.

value of peak (P + Q + F) stress on inside surface of

bend ID, psi.
Computer Input for Reference MSBR Primary Heat Exchanger

I CTM CASM
1 800.00 18CC0.00C
2 S00.00 18C00.00C
3 1000.00C 17CCn.00
4 1100.0C 130€0.00
5 1200.00 6CC0.00
6 1300.00 3500.00
HEAT LOAD REQUIRED = 18997565808. (BTL/HR)
ALLOWABLE TOTAL TUBE-SIDE PRESSURE DROP = 18720. (LB/SQ-FT)
ALLOWABLE TOTAL SHELL-SIDE PRESSURE DROP = 16727. (LB/SQ-FT)
TUBE INLET PRESSURE = 25920« (LB/SQ-FT)
SHELL OQUTLET PRESSURE = 4896. (LB/SG-FT)
HIGH TEMP., OF SHELL SIDE FLUID = 115C.00 (F)
HIGH TEMP. OF TUBE SIDE FLUID = 130C.00 (F)
LOW TEMP. OF TUBE SIDE FLUID = 1050.C0 (F)
LOW TEMP. OF SHELL SIDE FLUID = 850.0C (F)
HEAT TRANSFER LEAKAGE FACTOR = ¢.8CC00
PRESSURE LEAKAGE FACTOR = - 0.52C00
CONDUCTIVITY OF TUBE WALL METAL = 11.60000 (BTU/HR-FT-F)

%8
ARC OF FQOUR BENDS FOR FLEXIBILITY = 60.00 (DEGREES)
INSIDE RADIUS OF OUTER ANNULUS = 0.83330 (FEET)

DISTANCE BETWEEN SHELL WALL AND TUBES = C.03125 (FEET)
MAXIMUM ANTICIPATED OUTER RADIUS OF EXCHANGER = 6.000C0 (FEET)
NUMBER OF CASES RUN = 1

USE OF ENHANCED TUBES = 1 (ONE IF ENHANCED TUBES ARE USED)
USE OF STRESS ANALYSIS SUBROUTINE = 1 (ONE IF TO BE USED)
OUTSIDE DIAMETER OF TUBES = 0.03125 (FEET)

WALL THICKNESS OF TUBES = 0.00292 (FEET)

RADIAL PITCH = 0.06250 (FEET)

CIRCUMFERENTIAL PITCH = 0.06250 (FEET)

INNER BAFFLE CUT3 0.40000 (PER CENT)

H

OUTER BAFFLE CUT4 0.400C0 (PER CENT)

¢8
Computer Output for Reference MSBR Primary Heat Exchanger

TOTAL HEAT TRANSFEREL = 189956480C. (BTU/HR) (100.0 PERCENT)

MASS FLOW RATE OF COOLANT = 17590736. (LB/HR)

MASS FLOW RATE OF FUEL = 23454320. (LB/HR)

SHELL-SIDE TOTAL PRESSURE DROP = 116.16 (LB/SQIN) (10C.0 PERCENT)
TUBE-SIDE TOTAL PRESSURE DROP = 125.€1 (LB/SQIN) ( 99.7 FERCENT)
NOMINAL SHELL RADIUS = 2.83¢4 (FT)

UNIFORM BAFFLE SPACING = 0.9256 (FT)

TUBE FLUID VOLUME CONTAINED IN TUBES = 67.38 (CUBIC FEET)
TOTAL HEAT TRANSFER AREA BASED ON TUBE G.D. = 13037.C2 (SAFT)
TOTAL NUMBER OF TUBES = 58%G6.

TOTAL TUBE LENGTH = 22.52 (FT)

HEAT EXCH. APPROX. LENGTH = 21.31 (FEET)

STRAIGHT SECTION OF TUBE LENGTH = 18.325 (FT)
RADIUS OF THERMAL EXPANSION CURVES = 0.86 (FEET)
BERGLIN MODIFICATICN FACTOR = 0.80

TUBE WALL AVERAGE TEMP. = 1113.04

SHELL SIDE AVERAGE TEMP. = 10C7.83

98
P STRESS AT TUBE OD AND TUBE ID =

SHOULD NGT EXCEED

3912.

53

P+Q STRESS AT TUBE OD AND TUBE ID =

SHOULD NGT EXCEED

11737,

58

P+Q+F STRESS AT TUBE OD AND

SHOULD NCT EXCEED

i

Vo0 Wmd N -

TCI

F

N.1150E
C.1129E
D0.1115E
0.1101€E
0.1087E
0.1074E
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
C.8638E

04
04
04
04
04
04
C4
04
04
Q4
04
03
03
03
03
03
03
03
03
03
03

25000.

TCO

F

0.1129E
0.1115E
0.1101E
0.1087E
0.1074E
0.1060E
0.1046E
0.1032E
0.1C18E
0.1004¢E
0.9895E
0.9754E
D.9614E
0.9474E
0.9334E
0.9194E
0.9054E
0.8915E
0.8776E
0.8638E
0.8500E

00

04
04
C4
04
C4
C4a
04
04
04
04
03
03
03
03
03
03
03
03
c3
03
03

€73.9C
)
11£39.02

)
TUBE ID =  13C06.32

)
CWT TFI

F F

C.1254E 04 0.1282E
0.1184E 04 0.1271E
0.1172E C4 0.1259E
C.1159E 04 0.1248E
0.1146E 04 0.1236E
C.1133E 04 0.1225E
0.1119E 04 0.1213E
0.1106E 04 0.1201E
0.1093E 04 0.1190E
0.1080E 04 O.1178E
0.1067€ 04 0.1166E
0.1054E 04 0.1155E
C.104CE 04 0.1143E
0.1027E 04 0.1131E
0.1014E 04 0.1119E
0.1001E 04 0.1108E
C.9874E 03 0.1C96E
0.S742E 03 0.1085E
C.S610E 03 0.1073E
0.9479E 03 0.1061E
C.9348E 03 0.1050E

6364593 (LB/SCIN)

8317.50 (LB/SGIN)

10551.26 (LB/SQIN)

04
C4
04
04
C4
04
04
C4
C4
04
04
04
04
04
C4
C4
04
C4
04
04
04

TFGC

F

0.1300E
0.1282E
0.1271E
0.1259E
0.1248E
0.1236E
0.1225¢E
0.1213E
0.1201E
0.1190E
0.1178E
0.1166E
C.1155E
0.1143E
0.1131E
0.1119E
0.11C8E
C.1096E
0.1085E
0.1073E
0.1061E

04
04
04
C4
04
04
04
04
04
04
04
04
Ca
04
04
04
04
C4
04
04
04

FWT

F

C.1271E
C.1229E
0.1216E
0.1204E
0.1191¢€
0.1178E
0.1165E
0.1152E
0.1139E
0.1126E
0.1112E
0.1099¢E
0.1086E
0.1073E
0.1059E
0.1046E
0.1033E
0.1C19E
0.1006E
0.9929E
0.9796E

04
04
04
04
04
04
04
04
04
04
04
04
04
04
04
04
04
04
04
03
63

TWDT

F

0.1681E
0.45C9E
0.4495E
O0.4512E
0.4526E
0.4538E
0.4549E
C.4557E
0.4564E
0.4568E
0.4571E
0.4571€E
0.4569E
0.4566E
0.4560E
0.4551E
0.4541¢E
0.4529E
0.4514E
0.4497E
0.4479E

02
02
2
02
02
02
02
02
02
02
02
02
02
02
c2
02
02
02
02
C2
02

L8
Vo~ N -

vl

0.0

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

vz

C.C *
7.0071
6.9861
6.5653
6.9445
6.9238
6.5032
6.8826
6.8621
6.8418
6.8215
6.8013
6.7613
6. 7415
6.7219
6.7024
6. 6830
6. 6638
6. 6448
6. 6260

V3
FT/SEC

0.0

6.7T107
6.6905
6.670¢€
6.6507
6.6306
6.6112
6.5915
6.5719
6.5523
6.5329
6.513¢
6.4944
€.4753
Ee45€4
6.4375
6.4189
6.40032
6.3819
6.3637
6.3457

VW1

0.0

6.4319
6.4126
6.3935
6. 3554
6.3365
6.3176
6.2G88
6. 2801
6.2615
6.2430
6.2246
6. 2063
6.1881
6. 1701
6.1522
6.1344
6.1168
6.0994%
6.0821

VW3

0.0

T.6953
T.6722
7.64G3
T.6265
7.6038
7.5812
7.5586
7.5361
745137
T.4914
T«4693
Te4413
T«4254
T.4036
7.3821
7.3394
7.3183
T.2974
T.2768

PDSO

LB/SQFT

851.3384
851.3384%
845,2434
839,1812
833.1099
827.0310
820,9490
814.8638
808.7805
802.6997
796.6255
790.5603
784.5063
T7T78.4670
T72.4438
716644417
760.4609
7154.5051
T48.5771
742.6804
736.8167

PDTO

3430.7144
834.3669
82646611
818.9949
811.3169
803.6326
795.9424
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

88
VO~NOWVMPH WN -~

RENTO

0.1129E
0.1090¢E
C.1059E
0.1029E
0.9998E
0.9706E
0.9418E
0.9134E
0.8854E
0.8578E
0.8307E
0.8041E
0.7779E
0.7523E
0.7271E
0.7025€
0.6784E
0.6548E
0.6318E
0.6094E
0.5874E

PRNTO

0.8172€
0.8463E
0.8707¢
0.8960E
0.9225¢E
0.9503¢E
0.9794E
0.1010E
0.1042€E
0.1075E
0.1110¢
0.1147E
0.1186¢€
0.1226¢
0.1268E
0.1313€
0.1360E
0.1409E
0.1460E
0.1514¢E
0.157CE

01
0l
0l
01
ol
o1
01
02
02
02
02
02

c2
02
02
02
02
02
02
02

RENSOL

0.0

0.2908E
C.2843E
0,2779E
C.2715E
0.2651E
0.2587E
C.2523E
0. 2460E
0.2397E
C.2335€
0.2273E
C.2211€
0.2150E
C.2089E
C.2029E
C.1970E
0.1912¢E
0.1854E
0.1797E
0.1740E

RENSO2

0.0

0.3304E
0.3231FE
0.3158¢
0. 3085E
0.3012€E
0. 2940E
0. 2868E
0.2796E
0.2724E
0.2653E
0.2583E
0.2513¢
D.2443E
0.2374E
C.2306E
0.2239¢E
0.2172E
0.2107€E
0.2042E
0.1978E

RENSC3

0.0

0.3164E
0.3094E
0.3024E
0.2954E
0.2885€
0.2815E
0.2746E
0.2677E€
0.2609E
0.2541E
0.2473E
0.2406E
0.2340E
0.2274E
0.2209E
0.2144E
0.2080¢E
0.2018E
0.1955E
0.1894E

HTO

0.2958E
0.3421F
0.3317E
0.3244E
0.3172€E
0.3100€E
0.3029E
0.2959E
C.2889E
0.2820E
0.2751€
0.2684E
0.2617E
0.2551E
0.2485E
0.2421E
0.2357¢
0.2295E
0.2233E
0.2172¢E
0.2112E

AHSO

0.5273E
0.2605¢
0.2552E
0.2526E
0.2500E
0.2474E
0.2448E
0.2421E
0.2395¢E
0.2368E
C.2341E
0.2314E
0.2287E
0.2259E
0.2232E
0.2204E
0.2177E
0.2149E
0.2122E
0.2094E
0.2067E

BTU/HR/SQFT/F

03
04
04
04
04
Ca
04
04
04
04

UoA

0.3980E
0.1048E
0.1029E
0.1018E
0.1C06E
0.9950E
0.9833E
0.9716E
0.9597E
0.9476E
0.9355€E
0.9233E
0.9109E
0.8985E
0.8860E
0.8733E
0.8607E
0.8479E
0.8351E
0.8223E
0.80S4E

HEAT
BTU/HR

0.1332E
0.8775¢€
0.8748E
0.8780E
N.86C7E
C.8832¢
0.8853E
0.8869E
0.8882E
0.8890E
0.8895E
0.8896E
0.8892E
0.8885€
0. 8873E
0.8857E
0.8837E
0.8813E
0.8785¢
0.8752E
0.8716¢

68
90

Appendix C

THE RETEX PROGRAM

The RETEX computer program is outlined in block-diagram form in
Fig. C.1. The input data required for the program are given in Table
C.1, and the output received from the program are given in Table C.Z2.
A complete listing of the main program is followed by definitions of
the intermediate variables used in the program. To illustrate the use
of the RETEX program, the input and output for the MSBR steam reheater
exchanger discussed in Subsection 3.1 of this report are presented as

printed by the computer.
91

. (s )
() >y
READ AND PRINT
INPUT DATA

v

ASSUME BAFFLE
SPACING

® >3

ASSUME SHELL
DIAMETER

® -y

CALCULATE NUMBER OF TUBES, FUEL AND COOLANT
FLOWS AND VARIOUS GEOMETRIES

v

START WITH FIRST INCREMENT FROM HOT
SIDE OF HEAT EXCHANGER I=1

v

ASSUME TEMPERATURE DROP FOR THE INCREMENT

() >

EVALUATE ALL PHYSICAL PROPERTIES AT
AVERAGE TEMPERATURE OF INCREMENT

v

CALCULATE PRESSURE DROPS AND HEAT TRANSFER
COEFFICIENTS FOR THE INCREMENT, USING CORRECT
CORRELATION FOR DIFFERENT REGIMES

v

CALCULATE HEAT RATE AND TEMPERATURE
DROPS OF THE INCREMENT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. C.1. Simplified Flow Diagram of the RETEX Computer Program.
92

 
     
 

00 INCREMENT
TEMPERATURE DROPS AGREE
WITH OUR ASSUMPTION

NO

 
   
 
  
  

YES

  
 
 
 

DOES END
TEMPERATURE OF
INCREMENT EQUAL TO SPECIFIED
END TEMPERATURE OF
HEAT EXCHANGER

NO

   
 

 
 
 
  
 

YES

  

DOES TOTAL TUBE
SIDE PRESSURE DROP

ACCEPTABLE
?

NO

 
   
   
 
   
 

YES

  

DOES TOTAL SHELL
SIDE PRESSURE DROP

ACCEPTABLE
?

NO

 
   
  
 

Fig. C.1. (continued)

 

 

CHANGE ASSUMED
INCREMENT TEMPERATURE
DROP

 

 

 

GO TO NEXT
INCREMENT
I 1-1

 

 

CHANGE ASSUMED
SHELL DIAMETER

 

 

CHANGE ASSUMED
BAFFLE SPACING

 

 

 

 

 
93

   

ARE THERE
ADDITIONAL CASES FOR

PARAMETER STUDY
?

     
     
 

 

PRINT OUTPUT

(: END :)

Fig. C.1. (continued)

 

 

 
94

 

 

Table C.1. Computer Input Data for RETEX Program
Card Columns Format Variable Term Units
A 1-10 E10.4 Heat load required HEATL  Btu/hr
11-20 F10.0 Allowable tube~side pres- PRDT 1b/ft3
sure drop
21-30 F10.0 Allowable shell-side pres-  PRDS 1b/ft?
sure drop
B 1-10 F10.0 Coolant outlet temperature CTO °F
11-20 F10.0 Fuel inlet temperature FTO °F
21-30 F10.0  Fuel outlet temperature ETF °F
31-40 F10.0 Coolant inlet temperature ETC °F
C 1-10 Fl1l0.0 Leakage factor for heat LK
transfer correlations
11-20 F10.0 Leakage factor for pres- PLK
sure drop calculations
21-30 F10.0 Tube material conductivity WCOND  Btu/hrefte°F
D 1-10 F10.0 Radius of coolant central RAS ft
downcomer ‘
11-20 F10.0 Distance between shell DTR ft
wall and tube bundle
21-30 F10.0 Maximum anticipated heat RABMAX ft
exchanger radius
31-35 I5 Number of cases to be run KASES
36-40 I5 Index one if enhanced KENTB
tubes are used
E ,Es, 1-10 F10.0 Outside diameter of tube DIA ft
cee 11-20 F10.0  Tube wall thickness WTHK ft
EKASES 21-30 F10.0 Triangular pitch TPIP ft
31-40 F10.0 Inner baffle cut CUT3 % of area
41-50 F10.0  OQuter baffle cut CUT4 % of area

 
95

 

 

Table C.2. Output Data From RETEX Computer Program
Term Variable Units
THEATO Total heat actually transferred Btu/hr
HTPERC Percentage of required heat load transferred
QC Coolant (shell-side) mass flow rate 1b/hr
QF Fuel (tube-side) mass flow rate 1b/hr
TTDSO Total tube-side pressure drop psi
SPPERC Percentage of allowed tube pressure drop
~ actually used

TTDTU Total shell-side pressure drop psi
TPPERC Percentage of allowed shell pressure drop

actually used
RA8 Radius of heat exchanger shell ft
BSOI Distance between baffles ft
VOL Fluid volume contained in tubes ft2
AREA Total heat transfer area in heat exchanger ft°
SNT Total number of tubes
TUBLEN Actual tube length ft
GBRL Modification factor for Bergelin's heat

transfer correlation
SAVT Shell average temperature °F
TAVT Tube average temperature °F
TCI(I) Coolant outlet temperature from increment I °F
TCO(I) Coolant inlet temperature from increment I °F
CWT(I) Average tube wall temperature at coolant side °F
TFI(I) Fuel outlet temperature from increment I °F
TFO(I) Fuel inlet temperature from increment I °F
FWT(I) Average tube wall temperature at fuel side °F
TWDT (1) Average temperature drop across tube wall in °F

increment I
V1(I) Fluid average velocity in outer window in ft /sec

increment I
V2(I) Fluid average velocity in overlapping baffle ft /sec

zone in increment T
V3(I) Fluid average velocity in inner window in ft/sec

increment I
96

 

 

Table C.2 (continued)
Term Variable Units

VW1(I) Fluid velocity across tubes in outer edge of ft/sec
baffle in increment I

VW3(I) Fluid velocity across tubes in inner edge of ft/sec
baffle in increment I

PDSO(I) Shell-side pressure drop for increment I 1b/ft°

PDTO(I) Tube-side pressure drop for increment I 1b/ft?

RENTO(I) Tube-side Reynolds number for increment I

PRNTO(I) Tube-side Prandtl number for increment I

RENSOL (1) Reynolds number in outer window in increment T

RENSO2 (1) Reynolds number in overlapping baffle zone
in increment I

RENSO3(1I) Reynolds number in inner window in increment I

HTO(I) Tube~side heat transfer coefficient in Btu/hr-ft2-°F
increment 1

AESO(I) Shell-side heat transfer coefficient in Btu/hr-ft2'°F
increment 1

UOA(TI) Overall heat transfer coefficient in Btu/hr-ft2°°F
increment I

HEAT(I) Heat transferred in increment I Btu/hr

 
The RETEX Program Listing

 

*¥FTNyLs E+ Gy M,

PROGRAM MSBRPE-2 MSBRP
TYPE REAL LK s LAWC1 , LAWC?Z - MSBRP
DIMENSION TFO(130),TCI(130),VMI(130),VM2(130),VWC1(130),VWO3(130),MSBRP
1 RENTO(130},PRNTO(130) ,RENSOL1(130),RENSO3(130), RENSC2(130}, MSBRP

2 VM3 (13C),PDSCG(130)4NT(100},B4(3),HS01(130)4,HS02(1301),HSO3(120}),MSBRP
3AHS0(1301),HTC(120),UCA(130),TCO(130),TFI(120),HEAT(130),TWDT(130),MSBRP
4 PDTO(1301,TUBLN(130),V1(130),V2(130}),V23(130),VW1(130}),VW3(130), MSBRP

5 R(100),FACT(1CO),TCPI(100),TCTAL(L100} MSBRP
6 CWT(130),FWT(130),AVWT (1320} MSBRP
1001 FORMAT( E10.4, 2F10.C) MSBRP
1002 FORMAT( 4F10.C) MSBRP
1002 FORMAT( 3F10.0]) MSBRP
1004 FORMAT( 3F10.0,215) MSBRP
1005 FORMAT( 5F10.0) MSBRP
1006 FORMAT(22HOHEAT LOAD REQUIRED = 4F12.04+2X,EH(BTU/HR) ) MSBRP
1007 FORMAT (43HOALLCWABLE TCTAL TUBE-SIDE PRESSURE DROP = ,F10.0,2X, MSBR
1 10H(LB/SQ~FT) ) MSBR
1008 FORMAT(44FOALLCWABLE TCTAL SHELL-SIDE PRESSURE DROP = ,F1l0.042X, MSBR
1 1O0H(LB/SQ-FT}) ) MSBR
1009 FORMAT(33FHCHIGH TEMP, CF SHELL SIDE FLUIC =,F10.2,2X+3H(F)) MSBR
1010 FORMAT(32HOHIGH TEMP., CF TUBE SIDE FLUIL = JF10.2:2X,3H(F)} MSBR
101! FORMAT(32HOLCW TEMP. CF TUBE SIDE FLUID = LF10.2,2Xs3H(F)) MSBR
1012 FORMAT(32HOLGW TEMP. CF SHELL SIDE FLUIC =4F10.2:2X,3H(F}) MSBR
1013 FORMAT(32FOHEAT TRANSFER LEAKACE FACTOR = ,F10.5) MSBP
1014 FORMAT(27FOPRESSURE LEAKAGE FACTOR = ,F10.5 ) MSBR
1015 FORMAT(25FOCCNCUCTIVITY OF TUBE WALL METAL = 4,F10.5,2X, MSBR
1 13H(BTU/HR-FT-F) ) MSBR
1016 FORMAT(34FOINSIDE RACILS OF CUTER ANNULULS = 2F10.5,2Xs6H(FEET)) MSBR
1017 FORMAT(41HFOCISTANCE BETWEEN SHELL WALL AND TUBES = MSBR
1 +F1045+42X%,€6H(FEET}) MSBR
1018 FORMAT (4SHOMAXIMUM ANTICIPATED QUTER RADIUS OF EXCHANGER = , MSBR
1 F1O0e542X46H(FEET) ) MSBR

10
20
30
31
32
33
34
35
36
&9
50
60
70
80
g0
100
101
110
111
120
130
140
150
160
170
180
181
150
200
201
210
211

L6
C

1019 FORMAT (23HONUMBER OfF CASES RUN = ,14)

MSBR

1020 FORMAT(25F0USE GOF ENHENCED TUBES = ,14,2X,32H(0ONE IF ENHENCED TUBEMSBR

1S ARE USEC))
1021 FORMAT(Z2SEQOCUTSIDE CIAMETER OF TUBES = LFI1C0.5,2Xs G6H(FEET) )
1022 FORMAT(27FOWALL THICKNESS OF TUBES = ,FiC.%42Xy 6H{FEET) )
1023 FORMAT(Z2O0FCTRIANGULAR PITCH = , ' F10.542Xy G6H(FEETH)
1024 FORMAT(22FOINNER BAFFLE CUT3 +yF10.5,2Xs 10H(PER CENT) 1}
1025 FORMAT(22FCCUTER BAFFLE CUT4 sy F10.542Xy 10H(PER CENT) )
1026 FORMAT(Z25FR1TCTAL HEAT TRANSFERED = 4yF1l2.042X,8H(BTU/HR),

] eXelFH{4F5.1,9H PERCENT))
1027 FORMAT (29FOMASS FLOW RATE OF CCOLANT = ,F1C.0y2X, 7TH(LB/HR) )
1028 FORMAT(26KCMASS FLOW RATE OF FUEL = 4F10.04+2Xs 7H(LB/HR) )

0

MSBR
MSBR
MSBR
MSBE
MSBR
MSBF
MSBR
MSBR
MSBR
MSBR

1029 FORMAT(24F0OSHELL-SIDE TOTAL FRESSURE DRCP = ,F10.2,2Xy SH(LB/SQIN)MSBR

1 12X 9 IH(,FE.,1,SH PERCENT))

MSBR

1020 FORMAT(33+OTUBE~-SIDE TCTAL PRESSURE DROP = ,F10.242X, SH(LB/SCIN),MSBR

1 2XyIF(,F5.1,SH PERCENT))

1031 FORMAT(24FCNCMINAL SFELL RADIUS = 4FT7.4,42X34H(FT))

1032 FORMAT(26HCUNTFORM BAFFLE SPACING = 4FTe b4y 2Xy&4HIFTY)

1032 FORMAT(40FOTUBE FLUID VOLUME CCNTAINED IN TUBES = 2F7.2+1X,
112H(CUBIC FEET))

1034 FORMAT(1HC,4€6HTOTAL HEAT TRANSFER AREA EASED CN TUBE 0.De =
1 Fl2.24+2XEH(SQFT))

1025 FORMAT(25FOTCTAL NUMBER CF TUBES = ,Fé.C}

1036 FORMAT(Z21HOTCTAL TUBE LENGTH = +F6es292X4H(FT))

1037 FORMAT(ZZHCBWINDOW 1 CROSSFLOW = 4F5.2,2Xy€H(SQFTY))

1038 FORMAT(31+0OBERGLIN MCDIFICATICN FACTOR = ,F5.2)

1029 FORMAT(1HC2X 31HI s 7X+2HTCI 46X, 3HTCCy9Xy3HCWT 49X, 2HTFI 9X,3HTFO,
16X s BHFWT § EXy4HTWDT// 11Xy 1HF 3 11X31HF,11 X, 1HF,11X,
2 IHF 311X, 1HF 3 11X IHFy 11X 1FF//(1X, 13, TE1Z24 %))

1040 FORMAT (L1HGC,2Xs1HI s 7X33HVMI ,G Xy ZHVMZ2 49X 4 2HVM2 48X, 4HVWO1 +8Xs4HVWO3,
1 8X44HPDSC,8X4HPDTO/ /32X, 6HFT/SEC33X,THLB/SQFT//(1X413,7F12.4))

1041 FORMAT(1HC,2X 31HI 35Xy SHRENTC, 7X35HPRNTO 47X +6HRENSOY1 46X 46HRENSCZ,
16Xy 6HRENSC3 37X 43HHT O 38X 9 4HAHSO 39Xy 3HUCA 3 8X 44HHEAT//TT7X y

2 13HBTU/HR/SQFT/F +13Xs6HBTU/HR//{1X,12,6E12.4))
1042 FORMAT(27HOTUBE WALL AVERAGE TEMP, = LF10.2)
1043 FORMAT (28FOSHELL SIDE AVERAGE TEMP., = , F1l0.2)

MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MS BR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
& 9
MSBR
MSBR

220
230
231
240
250
260
270
280
290
291
300
310
320
321
330
331
340
350
360
361
370
37%
380
360
400
410
420
421
422
430
431
440
441
4472

460
650

86
READ IN AND FRINT OUT INPUT LCATA
KEY7= 1
VM1(1)=0.
VM2(1) =0,
VM3 (1) =0,
VWO1(!)=0.
VW0O3(1)=0,
RENSO1(1)=0.
RENSOZ2(11=0,.
RENSO32(1) =0.
HS01(1)=0.
HS03(1)=0.

READ 1001y HEATL, PRDT, PRDS
READ 1002, CTO,y FTO, ETF, ETC
READ 1003, LK, PLK,WCCND

READ 1004, RA5, DTR, RABMAX,KASES,KENTB
CONTINUE ‘

READ 1005, CIA, WTHK, TRIP, CuT3, CUT4
HSFCT=1.

IF(FTOLLT.CTC) HSFCT=-1,
PRINT 100&, FEATL

PRINT 1007, FRCT

PRINT 100€&, PRLCS

PRINT 100¢, CTC

PRINT 1010, FTC

PRINT 1011, ETF

PRINT 1012, ETC

PRINT 1012, LK

PRINT 1014, PLK

PRINT 101£%, WCCND

PRINT 101€, RAE

PRINT 1017, CTR

PRINT 101E&, RAEMAX

PRINT 101¢S , KASES

PRINT 102C, KENTB

MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR

MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBK
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR
MSBR

660
490
500
510
520
530
540
550
560
570
580
590
600
81C
620
630
640
€50
660
670

680
690
700
710
720
730
740
750
760
770
780
790
800
810
820

66
PRINT 1021, CIA MSBR 830

PRINT 1022, WTFK MSBR 840
PRINT 1022, TR1P MSBR 850
PRINT 1024, CUT3 MSBR 860
PRINT 102%, CUT4 MSBR 870

MSB 1650
BEGIN GEOMETRY CALCULATICNS FCR SINGLE ANNULUS COUNTER FLOW MSB 1660
DISC AND COUGHNUT BAFFLEC HEAT EXCHANGER MSB 1670
ATUBE = (3.14159% (DIA*%2,01)/4.0 MSBR 910
GFTT = 1. /3€00, MSBR 920
GFT = 1./144. MSBR 930
DIAI=DIA-2.0%WTHK MSBR 940
FATUB =(2.14156%(DIAI**2,00)/4.0 MSBR 950
KEY1l = O MSBR 960
PERC1 = 0.99 MSBR 970
IF(KEY1. GT.0)BSOI=0. 5*(BSL+BSH) MSBF 980
KEY2 = 0 MSBR 990
PERCZ2 = 0.99 MSB 1000
RABL=RAS5 _ MSB 1010
RABH=RA8MAX MSB 1020
RA8=0. 5% ({RABL +RA8H ) MSB 1030
NTO = 4, 0¥ ((RAB**2,0)-(RAS*%2,0) )/ (Ll.12*(TRIP*%2.0})) MSB 1040
RAS52=RA5%*%2 MS8 1050
RAB2=RAB**2 MSB 1060
RA6=(RAS24CUT4*(RAB2-RA52) ) %*,5 MSB 1070
RA7=(RA82-CUT3*(RABZ-RA52) )**, & MSB 1080
RA62=RA6**2 MSB 1090
RA7Z2=RA7T**2 MSB 1100
APO1=3.1415G%( (RA8)**2,0-(RAT7)*%2, 0)%(1.0- (ATUBE/ MSB 11190
1(0, 866*( (TRIP)I*%2,0) 1)) ) MSB 1111
APO3=2,1415G%( (RA6 ) **2,0-(RA5)**2,0)*(1.C~(ATUBE/ MSB 1120
1(0. 866 TRIP**2.01) 1)) : MSB 1121
PLAV = (0.955%TRIP MSB 1130
RBl = (RAE-RA7)/(1.86¢*TRIP) MSB 1140
RBZ2 = (RA7-RA6)/(0.Q33%TRIP) MSB 1150
RB3 = (RA6-RA5)/(1,86€%TRID) MSB 1160

001
LAWO1=3.1415G6%2,0%FAT*(1.0-(DIA/PLAV))

LAWO3=3. 14156%2. 0%RA6*(1.0-(DIA/PLAV))

ISUM]L = 4,0*((RA8%*¥2,C)-(RAT*%2,0))/(1.12%(TRIP*%¥2,0)}
SUM1 = TSUM] ' B

ISUM2 = 4. 0*((RAT*%2_ 0)~-(RA6*%2,0))/(1.12%(TRIP*%2,01))
SUM2 = TSUM2 '

ISUM3 = 4,0*((RAGF*2,C)I=(RAS**2,0)} )1 /(1. 12%(TRIP*%24,0))
SUM3 = TSUM3

SNT = IStV + ISUM2 + ISUM3

BSMAX=1. 5*( (RAB-(RAE-RA7)/2. )-(RAS4(RA6-RA5)/2.))
BSMIN=0. 2*(R28-RA5)

IF(BSMIN.LT.0.,1€67)BSMIN=0.1667
HW=2.*WCOND/ (D IA*(ALOG(DIA/DIAI)})}

CSPHAV=0., 326

FSPHAV=0, £57}

QC=HEATL/ (CSPEAVX(CTO-ETC))

QF=HEATL/ (FSPHAVX(FTO-ETF})

GTO = QF/(NTC*FATUB)

CONTINUE

IF(KEY1l. EC. 0 )BSH=BSMAX

IF(KEY1l. EC.CIBSL=BSMIN

IF(KEY1.EC.OIBSCI=0.5*(BSL+BSF)

IT =0

KFINAL =0

I=1

TSUM=0,

SSUM=0,.

THEATO = (. C

TPDTO = 0
TPDSO = O
TFO(I)=FT
TCI(INI=CTC
KEY4 = 0
TIF=-5.0
TIC=-5.0
CDTF=90.
FDTF=0.
BSO = BSO1

MSB
MSB
MSB
MSB
MSB
MSB
MS8
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS8
MSB
mMs8
MSB
MSB
MS8
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB

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
1460
1470
1480
1490
1500
1510
1520
1530
1540

101
BRL1 =

GBRL = 0. 77*BRLI**(-.138)
AWOl = BSC*LAWC1

AW03 = BSC*LAWC3

AWl = SQRT(AWC1*APQOL)
AW2 = (AwO1+AW03)/2.
AW3 = SQRT(AWC3*APC3)
GSO1 = QC/AWl

GS02 = QC/AwW2

GSO3 = QC/An3

ATC = TCI(I) + (TIC/2.0)
CFT = ATC +CCTF*HSFCT
ATF = TFC(I)+TIF/2.
FFT=ATF-FLCT F¥HSFCT

FI=1

TUBLN(I) = FI*BSOI

CVIS=0.2121*%EXF(4032./(460.4ATC))
CVISW=0, 2121*EXP(4032. /(460.4CFT})
CDEN=141.427-C. C2466%ATC
CCON=0.24C

CSPH=N,3¢

FVIS=0.0¢€2

FVISW = 0.0€2

FDEN = 0,7622

FCON = 0,.,02¢

FSPH . £271

VI SK (CVIS/CVISWI**(0,14
FVISK=(FVIS/FVISW) %0, 14

DCVIS = CIA/CVIS

CCDEN = 1,.,/CCEN

QCCDEN = CC*CCCEN

CALCULATE REYNCLS AND PRANDTL NUMBER TUBE SIDE

RENTO(IV=CIAIXCTO/FVIS
PRNTO(I)=FVIS*FSPH/FCCN

HEFI=1.+((RENTC(I)~10C0.)/900C. )**0.5

TF(KENTB«NEL1IFEFI=1,
PDTO(I )=(.0028+.25%RENTO**(-,321) )%
(CIAT*FLCEN*417182400.)

BSC/((RAB-(RAB-RAT7)/2.)-(RA5+(RAE-RAS)/2.))

BSC*GTC**x2%xHEFI/

MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS8

MS 8

MSB
MSB
MSB
MSB
MS8
MSB
MSB
MS8B
MSB
MS8B
MSB
MSB
MSB
MSB
MS 8
MS8B
MSB
MSB
MSB
MSB
MS8
MSB
MSB
MS8

1550
1560
1570
1580
1590
1600
1610
1620
1630
1640
1650

1670

1690
1700
1710
1720
1730
1740
1750
1760
1770
1780
1790
1800
1810
1820
1830
1840
1850
2550
1870
1880
1890
13500
1510
1911

0T
g

10

il

1

1

CALCULATE HEAT TRANSFER COEFF TUBE SIDE

HiO(T)=FCON/CT A%, 022 7% (RENTO(T )**4 8)*% (PRNTC( I )%%*,2333)}*FVISK*HEFI

GO TO 10

IF(RENTO(I).LT,.2100.) GO TO 9

HTO(I) = FCON/CIA%, O89%(RENTO(I)}**%,666=-125., y*(PRNTO(] I**,3333)*
FVISK¥HEFI*(1,4.2233%(DIAI/TUBLN(I) )**,666€)

GO 70 10

HTO(I} = FCON/CIA*(4.36+(0.025%RENTO(I)#PRNTO(I)*DIATI/TUBLN(I)

}/(14+C.COLZH*RENTO(I)*PRNTO(I)*DIATI/Z/TUBLN(I) )
CONTINUE
CALCULATE FLCW AREAS SHELL SIDE
VWO1(I) = QCCCEN/AWC1
VWO3(1) = CCCCEN/AWC3
VM1(I) = GSC1*CCDEN
VM2 (I} = CSG2*CCDEN
VM3(1) = CSC3*CCDEN

CALCULATE PRESSURE DRCPS SHELL SIDE

DP1 (1.4, EXRELYXCDEN*VMI (T )*>*2

DpP2 e 6%RB2*CLENXVM2 (I )*%*2

DP3 (1. 4. E*RE3)*CDEN®VMI(T I*x%2

RENSO1(I) = CGSC1*DCVIS

RENSO2(TI} CSC2*%DCVIS

RENSN3(1) GSC3*DCVIS
HEFO=1,40.3*((RENSOZ2(1)-1000, )/900C, }**C.5
IF(KENTB, NEL 1 }IHEFDO=1.

PDSO(I) = (CF1+4DPZ+DP2)*PLK*FEFC/834624C00.
CALCULATE BJ FACTOR ANC SHEL SIDE COEFFICIENTY
BJ(1) =(0.24€*RENSOL(I)**(~-0.2E82) V*GBRL
BJ(2) =(0.324€*RENSOC2(I¥1**(-0.3€2))*GBRL
BJ(32) =(0e246*RENSOZ(I1**(~-0.2€2) )%*GBRL

it un

Hn

HSO1(I) = (LK¥CSPH®(GSC1*BJ(LI*((CCCN/(CSPH*CVIS) )I**,66))*VISK
HSO2(I) = (LK*CSPH*CSC2%BJ(2)*((CCON/ (CSPH*CVISH b**, 66 ) 1*VISK
HSO3(I) = (LK*CSPH*GSC3*BJ(3)*((CCCN/(CSPH*CVIS) b**,66))*VISK
AHSO(I b=( ((HSCI (T} *SUMLI+(HSC2(T)*SUM2 )+ (HST2(T)*SUM3) )/ SNT ) *HEFC
GO TO 12

CONTINUE

MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS8
MSB
MSB
MSB
MSB
MsSB
MSB
MSB
MSB
MSB
MSB
MS8B
MS8
MSB
MSe
MSB
MSB
MSB
MS8

2640
1930
1940
1850
1960
1961
1570
1680
1981
1590
2480
2010
2020
2030
2040
2050
2590
2070
2080
20690
2100
2110
2120
2130
2140
2150
273¢C
2170
2180
2190
2200
2210
2220
2230
2240
2250

£01
UDA(TI)=14C/((140/AHSO(I} )4+ (L.O/HTO(I})+(1.0/HW)) MsB8 22690

A = QF%FSFH MSR 2270
B = QC*CSFHE MSB 2280
D = UDA(I I*SNT*BSO #3,14159*CIA MSB 2290
P = “HSFCT*(C*(A-B) )/ (A%B)

PBAR = EXPI(P) MSB 2310
C = (B-A)*PBAR MSB 2320
TCO(I) = ((TCI(I}x(B*PBAR-A))-(TFO(I)%*A*(PRAR-1.)})/C MSB 2330
TFICI) =((TCC(I)=-TCI(I))I*B/A) + TFO(1) MSB 2340
HEAT(I) =-A%(TFI(I} - TFO(I}) MSB 2350
TWDT(I) = (FEAT(I)/NTC)*ALOG(DIA/DIAI }/(2.0%2,.14159%BSQ0%*WCOND) MSB 2360
CTIF = TFI(I)-TFO(I) MSB 2370
CTIC = TCC(IN-TCIC(I) MSB 2380
IF((ABS(CTIF-TIF)uLE«(1le5))aANDs (ABS(CTIC-TIC)I.LE. (1.5)))G0O0 TC 13 MSB 2390
TIF = CTIF MSB 2400
TIC = CTIC MSB 2410
GO TO 6 MSB 2420
THEATO = THEATC + HEATI(I) - MSB 2430
TPDTO = TEDTC 4 PDTO(I) MSB 2440
TPDSO = TFDSC + PDSO(1) MSB 2450
COTF=( ({HEAT(I)) /NTC)/BSO)/(3.14159%D[A%AHSO(I}) MSB 3090
FOTF=CDTF*AHSC(I) /HTC(1I) MSB 3100

FWT(1) =ATF-FCTF*HSFCT
CWT(I) =ATC+CLCTF*HSFCT

AVWHT(I) =0.5%{(FWT(I) <+CWT(I}) MSB 3130
TSUM=TSUM+AVWT(I) MSB 2140
SSUM=SSUM+ATC MSB 2560
IF(KFINAL.EQs1.AND.1.EQeIT) GO TO 15 MSB 2460
IF(({(ABSCETF-TFI(I)))a LE«{ (ABS(TFI(II-TFC(I}))/2e0))140R. MSB 2470
1 (TFI(I). LE.ETF))} GO TQ 14 MSB 2471
I=T+1 MSB 2480
IF{I.GT,129)GC TO 23 MSB 2490
TFO(I) = TFI(1I-1) MSB 2570
TCI(I) = TCO(I-1) MSB 2580
BSO=8S01 MSB 2550

GO TO 6 MSB 2600

H01
15

16
17

18

19

20

21

KFINAL=1

IT=1

FIT = IT

GO TO 5

TUBLEN= FIT%BSCI

TAVT=TSUM/FIT

SAVT=SSUM/FIT

CONTINUE

VOL = 0., 7854*(CTAI *%2,0)*NTOXTUBLEN
CHECK OF TUBE AND SHELL PRESSURE DROPS
KEYZ2 = KEYZ2 + 1

IF(PERC2.LE.O.1) GO TC 26
IF{TPDTO. LT« (PERC2%PRCT)) GO TC 18
IF(TPDTO. CT.PRCTY GO TC 19

GO TO 20

IF(RAB4LE.(RAS +0.0C8) ) GC TQ 27
RABH =RAS8

IF(KEY2«NE.20)CGC TO 3
RASBL=RA8BL-0.2

PERC2 = PERC2 - 0.01

KEYZ2=10

GO 7O 2

IF(RA8.GE.(RASBNMAX-0. 005})) GC TC 27
RABL =RAESg

IF(KEY2.NE.2C) GO TO 3
RASBH=RABH+0,2

PERC2 = PERCZ2 - 0.0C1

KEYZ2=10

GO TO 3

KEYl = KEY1 + 1

IF(PERC1.LE.O.1) GO TC 2%
IF(TPDSOLLT. (PERCI1*PRLCS)) GO TC 21
IF(TPDSO0.CT.PRLSIGO TC 22

GO TO 28

IF(BSOI-LE. (BSVMIN+O.QCENIGO TQ 24
BSH =BSCI1

IF(KEY1.NE.2C)ICC TO 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
MS8
MSB
MSB
MSB
MSB
MSB
MSB

2610
2620
2630
2640
2650

2680
2690
3250
2710
2720
2730
2740
2750
2760
2770
2780
2760
2800
2810
2820
2830
2840
2850
2860
2870
2880
2890
2900
2910
2920
2930
2940
29650
2960
2970

G01
22

23
1044

24
1045

25
1046

26
1047

27
1048

28

BSL=BSL-0.1

PERC1 = PERC1 - 0.01
KEY1l=10

GO T0 2

IF(BSOI.GE. (BSVAX-0.0C5) IGO0 TO 24
BSL =BSOI
IF(KEY1.NE.2C) GO TO 2
BSH=BSH+0.1

PERC1 = PERC1 - 0.01
KEY1=10

GO TO 2

PRINT EXIT SIGNALS
PRINT 1044,BSO

FORMAT (39F1BAFFLE SPACINGS EXCEEDE 129 WITH BSO =4F5.242Xy4H(FT))

GO TO 28

PRINT 104¢

FORMAT (20F1BSOT = MAX., OR MIN. )
GO TO 28

PRINT 104¢

FORMAT (48+1 PERC1 FOR SHELL FRESSURE DRCP IS LESS THEN 0.1}

GO TO 28
PRINT 1047

FORMAT(48H1 PERC2 FOR TUBE PRESSURE DRCP IS LESS THEN 0.1)

GO TO 28
PRINT 104¢€

FORMAT (2GF1 SHELL RADIUS = MAX. OR MIN,)

GO TO 28

END OF CASE, FRINT QUTPUT
DO 29 T = 1,IT7

VI(I) = VMI(I)*GFTT
V2{I)}) = VM2(II*GFTT
V3(I) = VM2(I)*GFTT
VW1(I) = VWOL(I)*GFTT
VW3 (I) = VWC2(I)*kGFTT

MSB
MS8
MSB
MSB
MS8B
MSB
MSB
MSB
MSB
MSB
MSB
MS8
MSB
MS8
MSB
MSB
MS8
MSB
MSB
MSB
MSB
MSB
MSB
MSB
Ms8
MSB
MSB
MSB
MSB
MSB
MsB
MSB
MSB
MSB
MSB
MS8

2980
2990
3000
3010
2020
3030
2040
2050
3060
2070
3080
3640
3650
3110
3120
3130
3140
3150
3160
3170
2180
3190
3200
3210
3220
3230
3240
3250
3810
3820
3280
3290
3300
2310
3320
3330

901
29

30

31

1
1

1

CONTINUE

TTDSO TFEDSC*CFT

TTDTO TEDTC*CFT
TPPERC=TPLTO*100,/PROT
SPPERC=TPLCSC*1C0./PRDS
HTPERC=10C. *THEATO/HEATL
AREA=341415S*CIA*SNT*TUBLEN

PRINT 102¢é,TFEATOyHTPERC
PRINT 1027, QC

PRINT 1028, CF

PRINT 102<,TTDSC,SPPERC
PRINT 103C, TTCTO, TPPERC
PRINT 1031,RA8

PRINT 1032,BSCI

PRINT 1032,VCL

PRINT 1034, AREA

PRINT 103%5,SNT

PRINT 103¢&,TUBLEN

PRINT 103€&, GBRL

PRINT 1042 ,TAVT

PRINT 1043 ,SAVT

PRINT 1036, (I (TCI(I)sTCOCI)9CWT(I)y TFI(I) TFO(I)4FWT(I),

TWET(I) },I=1,IT)

PRINT 104C,{I,(VYCT1},v2(T),V2(I),VWI(I) VW2(T),PESO(I),PDTO(I)),

I=1,IT)

PRINT 1041,(I, (RENTCG(I)4PRNTC(I),RENSO1(I),RENSO2(T),RENSQO3(T),
HTO(TI} +AHSO(I) JUOCA(IV},HEAT{(I)),I=1,1T)

LOOP FOR ADCITIONAL CASES IF REQUIRED

CONTINUE

KEY7=KEY7+1
IF(KEY7.GT.KASESIGO TC 31
GO 70 1

CONTINUE

END

MSB
MSB
MSB
MS8
MSB
MSB
MSB
MSB
MSB
MSB
MS8B
MSB

‘MSB

MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MSB
MS8

3340
3350
3360
32370
3380
3390
2400
1640
2420
3430
3440
2450
3460
3470
3480
3490
3500
3510
3520
3530
3540
3550
3560
3561
3570
3571
3580
3581
4240
4250
3610
3620
3630
3640
2650
3660

L0T
108

Intermediate Variables

The intermediate variable terms used in the RETEX computer program

are as defined for the PRIMEX program except for the two terms defined

below.
TRIP Uniform triangular pitch, ft.
PLAV 0.955*TRIP used in calculating the effective cross~-flow area

between the tubes, ftZ2.
Computer Input for Reference MSBR Steam Reheater Exchanger

 

HEAT LOAD REQUIRED = 125CC0CC0O. {(BTU/HR)

ALLOWABLE TOTAL TUBE-SIDE PRESSURE DRCP = ©220. (LB/SQ-FT)
ALLOWABLE TOTAL SHELL-SICE PRESSURE CROP = 8¢€40. (LB/SQ-FTI
HIGH TEMP., OF SHELL SIDE FLUIC = 1180.00 (F)

HIGH TEMP, OF TUBE SIDE FLUID = 1000.00 (F)

LOW TEMP., OF TUuBE SIDE FLUIC = 6£0.00 (F}

LOW TEMP., OF SHELL SIDE FLUIO = 850.00 (F}

HEAT TRANSFER LEAKAGE FACTCR = 0.80000

PRESSURE LEAKAGE FACTOR = C.5200C

CONDUCTIVITY OF TUBE WALL METAL = 11,6000C (BTUL/HR-FT-F)
INSIDE RADIUS CF OUTER ANNULUS = C.0 (FEET)

DISTANCE BETWEEN SHELL WALL AND TUBES = 0.C4167 (FEET)
MAXIMUM ANTICIPATED OUTER RADIUS OF EXCHANGER = 5.CC00C (FEETI
NUMBER OF CASES RUN = 1

USE OF ENHENCED TUBES = C (ONE IF ENHENCEC TUBES ARE USED)
OUTSIDE DIAMETER OF TUBES = 0.0625C (FEET)

WALL THICKNESS OF TUBES = €C.00292 (FEET)

TRIANGULAR PITCH = 0.C8232 (FEET)

INNER BAFFLE CUT2

C. 200C0 (PER CENT)

OUTER BAFFLE CUT4 €. 200C0 (PER CENT)

601
Computer Output for Reference MSBR Steam Reheater Exchanger

TOTAL HEAT TRANSFERED = 12€488992. (BTU/HR) (101.2 PERCENT)

MASS FLOW RATE OF COOLANT = 1157407. (LB/HR)

MASS FLOW RATE OF FUEL = €41075. (LB/HR)

SHELL-SIDE TOTAL PRESSURE CROF = 59.52 (LB/SQIN} ( 99.2 PERCENT)
TUBE-SIDE TOTAL PRESSURE DRCP = €9.85 (LB/SQIN} ( 69.5 PERCENT)
NOMINAL SHELL RADIUS = (C.E828 (FT)

UNIFORM BAFFLE SPACING = 0.,7205 (FT)

TUBE FLUID VALUME CONTAINEC IN TUBES = 30.€6C (CUBIC FEET)

TOTAL HEAT TRANSFER AREA BASEC ON TUBE CeD. = 237¢€.5€¢ (SQFTH
TOTAL NUMBER OF TUBES = 400.

TOTAL TUBE LENCTH = 20.z€¢ (FT}

BERGLIN MODIFICATION FACTOR = 0.75

TUBE WALL AVERAGE TEMF. = G42.<S

SHELL SIDE AVERAGE TEMP. = 1004. 44

OT1
J'*swuwwWUWWWUNNNNNNNNNNHHHFHO—‘FF‘MO‘
NFOOONIMVPIUVUNFMRODOVDENOVMEPEWUNFOOVOO NI VP RN ODODOO~NTWVEIWN

TC1

F

0.1150E
O« 1144E
0.1137E
0.1131E
0. 1124E
0.1118E
0.1111E
0.1104E
0.1098E
0. 1091E
0. 1084E
0.1077E
0. 1071E
0.1064E
0.1057E
0.1050€
0.1043E
0.1036E
0.1029E
0.1022E
0.1014E
0.1007E
Os 9999E
0. $926E
0.9853E
0.9779E
0.9705E
0.9631¢
0. 9556E
0. 9480E
0. 9405E
0. 9328E
0.9252€
0.9175E
0.9098€E
0.9020E
0. 8942E
0.8863E
0.8784E
0. 8705E
0. 8625E
0. 8545¢

TCC

¢

0. 1144E
0.1137E
0.1131E
0.1124E
0.1118E
0.1111E
0.1104E
0.1098E
0.1091E
0.1084E
0.1077E
0.1071E
0.1064E
0.1057E
0.1050€E
0.1043E
0.1036E
0.1029E
0.1022¢
0.1014E
0.1007E
0.9999E
0.9926E
0.9853E
0.9779E
0.970S5E
0.9631¢E
0.9556¢E
0.9480E
0.9405E
0.9328E
0.9252E
0.9175€
0.9098E
0.9020E
0.8942E
0.8863E
0. 8784E
0. 8705E
0.8625E
0. 8545E
0. 8464E

CWTY

F

C.1103E
0.1096E
C.1089E
C.1082E
Ce107SE
C.1068E
C.1061E
0. 1054E
C.1047E
C.1040E
C.1032E
0.1025E
€.1018E
C.1010E
€.1003E
C. 9956F
C.9881E
C.9806E
. 9730E
Ce9654E
C.9577E
€. 9500E

Ce9422E

0.9344E
C.9265E
C.9186E
C.9106E
C.9026¢
0.8945E
C.8864E
C.878B2E
€. 8700E
Ce8617E
C.8527E
Ca 84 44E
0.8360E
C.8275E
C.8190¢
C. 81 04E
C.8018BE
C.7932E
C.7845E

TF1

F

0.6925E
0. 9850k
0. S7175E
0. S699E
0. 6622E
0. S545E
0. S4€8E
0. S3S0E
0.9311E
0. S233E
0. S153E
0. SO73E
0. 89G3E
0.8612E
0. 8821E
0. 8749E
0. 8667E
0. 8585E
0. 85ClE
0. 8418E
0. 8334E
0. 824SE
O. 81 64E
0. 8079E
0. 7993€E
0. 7906E
0.7819E
0. 7722¢€
0. 7€44E
0. 7555E
0. T467E
0.72177E
0.7287E
0. 7197¢
0. 71C6E
0. 7015€E
0. £€924E
0.6821E
0. 6739E
0. £646E
0. £€552E
0.6458E

TFO

F

C.10COE
0.S925E
0.5$850E
0.5775E
0.66659¢E
0.6622E
0. S545E
0. S4€68E
0.6390E
0.S311E
0.S223E
0. S1E53E
0. S073E
0. 8993E
0.8912E
C. 8831E
0. 8749E
0.866TE
0. 8585E
0. 85C1E
C.8418E
0.8334E
0. 8249E
0. E1€4E
C. 8079E
0. 7993E
C.79C6E
C. 7819t
0.7722E
0. T644E
0. 7555E
C. T46TE
0.7377E
0.728TE
0. 71STE
C.71C6E
0. 7015€E
0. €924E
0.6821E
0. 6739¢
0.£E646E
0.6552E

FWT

F

0. 1090E
0. 1083E
0.1076E
0.1069E
0.1062E
0. 1055E
0.1048E
0. 1041€
0.1033E
0.1026E
0. 1019E
0.1012E
0. 1004E
0. 9967E
0.9892E
0.9817E
0. 9741E
0. 9665E
0.9589¢E
0. 9511E
0. 9434E
0.9356E

0.9277E -

0.9198FE
0. 9119E
0. 9039E
0. 8958E
0. 8877E
0. 8795E
0.8714E
0. 86 21F
0. 8548
O+ 8465E
0. 8373E
0. 8289E
0.8204E
0.8118E
0. 8032E
0. 7946E
0. 78 59E
0«77 712E
0.7684E

TWoY

F

0.1244E
0.1248E
0.1255E
0.1263E
0.1271E
0.1279€
0.1287E
0. 1295E
0.1302E
0.1310€
0.1318€E
0.1326E
0.1334E
0.1342E
0.1350E
0.1358E
0.1366E
0.1374E
0.1382E
0.1389E
0.1397E
0. 1405E
0.1413E
0.1421E
0.1429E
0.1437E
0.1445E
0.1453E
0. 1461E
Ce 1469E
0.1477E
0. 1485F
0. 1493E
0.1500E
0. 1508E
0.1515¢E
0.1523E
0.1531E
0.1539E
0.1546E
0. 1554E
0. 1561E

ITT
Pt i gt b b Pt it Pt
PN WNHROOODNTNSWUN-

VM1

5.5856
5.5778
5.570C
5.5622
55543
5.5465
5.5385
5.5306
5.522¢
551417
5.5066
5.4986
5. 4905
5.4825
S5.4744
5. 4662
5.4581
Se 4496
5.4417
5. 4335
5.4252
5.416%
S5¢ 4086
5.4002
Se 3920
5.3836
5.3753
5036665
5.3585
5.350C
5.3416
5. 3331
5.324¢
5.3154
5.3065
5.2983
5.2898
5.2812
5.2726
5.264C
5.2554
5.2468

VM2

4. 7831
4. 7764
4. TEST
4. 7£30
b4e T563
4o T495
4e 7428
40 T2€0
4. 7291
4. 7223
4e 71155
4e TC8B6
4. 1C17
4 6547
4. 6878
4o 6808
4o 6736
4o 6 €68
4. 6598
4. 6528
4. 6457
4. £28¢
4e 6215
4o 6244
4, 6172
4. 6101
4. 6C30
4. 5658
4. 5886
4. 5813
4s 5741
4e 5€€8
4. 5596
4 5517
4o 5444
40 5271
4. 5287
4e 5224
4. 5150
4. 5C77
4, 5C03
40 4529

VM3
FT/SEC

6. 6035
6. 8538
6.8842
6. 8745
6. 8648
6. 8550
6. 8453
6. 8354
6. 8256
6. 8157
6. 8058
6. 7959
6.7859
6. 7159
6. 7659
6. 7559
6. 7458
6. 1357
6. 7255
6. 7154
6.7052
6. 6950
6. 6847
6. 6744
6. 6641
6. 6538
6. 6435
6. 6231
6. 6227
6. 6123
6.6C18
6. 5914
6. 5809
6. 5654
6. 5589
6. 5484
6. 5278
6.5272
6. 5166
6. 5060
6. 4553
6. 4847

VWDl

3.9572
3.9516
2. 94¢€1
32,9406
3.,9350
32,9294
3.9238
3.9182
3.9125
2.9Cé9
3.9012
3,8985
3.8898
2.8841
2.8783
3.8726
2.8668
3.8610
3.8552
3.8494
3.8435
3.8377
3.8218
32,8259
3.8200
3.8141
3.8C¢el
3.8022
3.7962
3,7903
2, 7843
3.77€3
3.7723
2. 7€57
3. 7567
3.7536
3.7476
347415
3. 7354
3. 7293
3.7232
3.7171

VW03

€. 0447
6.0362
€.0278
€.0193
€.0108
&. 0023
5.9937
5.6851
5.6765
5. 6679
£.9592
5.6505
5.%418
5.€330
5.9243
5.6155
£.5066
£.8978
5.8889
5.8800
5. 8711
S.8621
5. 8532
5.8442
£.8351
5. 8261
5.8170
£.8C80
£.7988
5.7897
5.7806
5.7714
5.7622
5.7522
5. 7430
5.71338
S.7245
£.T152
5.7059
5, 6966
5.6873
£. 6780

PDSO

LB/SQFT

210. 3354
210.0414
209. 7476
209, 4527
209.1567
208. 8597
208, 5619
208, 2632
207.9633
207.6625
207. 3607
207. 0581
2064 7545
206.4502
20641448
2058386
205.5315
205, 2235
204. 9145
20446047
204.2942
203.9826
203.6705
203, 3576
202, 0438
202. 7291
202, 4137
202.0977
201.7808
201, 4633
201.1451
200. 8261
200. 5063
200.1584
199. 8376
199.5162
195. 1941
198, 8715
198,5483
198, 2244
197.9001
197.5751

PDTO

102.3585
102.3585
102. 3585
102, 3585
102.2585
102.3585
102.23585
102. 3585
102. 3585
102. 3585
102.3585
102. 3585
102.3585
102.3585
102.3585
102. 3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.3585
102.358g5
102.3585
102.3585
102.2585
102. 3585
102.3585
102.3585
102.3585
102. 3585

11
VRNV PWN

RENTO

0.5794¢E
0.5T794E
0.5794E
Oe 5T94E
0. 5794E
0. 5794E
0. 5794E
0. 5794E
0. 5794E
0. 5T94E
0. 5T94E
0. 5T94E
0.5794E
0. 5794E
O« 5T94E
0. 5794E
0. 5T94E
0.5794E
0. 5794E
0. ST94E
0. 5T794E
O« 5T794E
0. 5794E
Oe 5T94E
0. 5794E
0.5794E
O« 5T94E
0. 5794E
0. 5794E
0. 5794E€
0. 5794E
0. 5794E
0.5794E
0. 5794E
0. 5794E
0.5794E
0. 5794E
0.5794E
0. 5794E
0.5794E
0. 5T94E
0. 5794E

PRNTC

0.9594E
0. 9594 E
0. 9594
0. 95 94E
0.9594E
0.9594E
0.9594E
0.9594E
0.9594E
0.9594E
0. 9594E
0. 9594E
0. 9594E
0.9594E
0. 9594E
0.9594E
0.9594E
0. 9594 E
0.9594E
0.9594E
0.9594E
0.9594E
0. 9594E
0.9594E
0.9594E
0.9594E
0.9594E
0.9594E
0.9594E
0. 9594
0.9594E
0.9594E
0.9594E
0. 95 94E
0.9594E
0,9594E
0s 9594 E
0.9594E
0.9594E
0.9594E
0.9594E
0.9594E

RENSOlL

C. 544SE
C.5395E
Cs 5340E
C.5285E
C.5230E

C+517SE

C.512CE
C.5064E
C. 5008E
C.4952E
C.4896E
C.483SE
C.4782E
C.4T2¢E
C. 4669E
Ce4612E
C.4555E
C.4497E
C.4440E
Cs4282E
C.4324E
0. 4266E
C.4208E
C.4150E
C.4092E
C.4033E
C.3975E
0.391¢E
C.3858E
C.3799E
Ce3740E
C.3682E
C.3623E
C.3559E
C.3501E
C.3442E
0.3383E
C.3325E
C.3266E
C.3208E
0.314SE
C.3091E

RENSO2

0.4666E
0. 4620E
0. 4573E
0. 4526E
0. 447GE
0.4422E
0. 4384E
0.4336E
0. 4289E
0. 4241E
0.4162E
0. 41 44E
0.40S56E
0.4047E
0. 2998E
0. 3949E
0. 39Q0E
0. 328E1E
0.38C2€E
0.3752E
0.3703E
0.3653E
0. 36C3E
0.35E4E
0.35C4E
0. 3454E
0.34C4E
0.23€E4¢€
0.33C2E
0.2253E
0.2203E

- 0.3153E

0.3102E
O+« 2048E
0.2958E
0.2947E
0. 2897E
0.2847E
0.2797E
0.2747E
0. 2697E
0. 2647E

RENSO3

0. €T35E
0. €668E
C.£6COE
0.€522E
0, t464F
0. ¢3S6E
0.€228¢E
0.6259F
C.€1S0E
0.6120E
0.¢051E
0.5981E
0.5911E
0.5841E
0.5771E
C.57COE
0.5629E
0. 5558E
0.5487E
0.5416E
C. 5344E
0.5273E
C.5201E
0.5129E
0.5057E
0.4985E
0. 4913E
C.4840E
0.4768E
0. 46¢<5E
0e4623E
0. 4550E
0. 44 78E
0.4399E
0.4326E
0.42%4E
0.4181E
C.41C9E
0.4027E
0.39¢4E
0.3892¢E
0.2820E

HTO

0.5026E
0.50 26E
0. 50 26E
0. 50 26E
0.5026E
0. 50 26E
0.5026E
0.5026E
0. 50 26
0. 50 26E
0.5026E
0+ 50 26E
0.5026€
0.5026E
0.5026E
0. 50 26 €
0.5026E
0. 5026 E
0.5026E
0.50 26 E
0. 5026
0. 50 26 E

0.5026E

0.5026E
0. 5026E
0.5026E
0.5026E
0.5026E
0.5026¢E
0.5026E
0.5026E
0.5026E
0.5026E
0.5026E
0. 5026E
0. 5026E
0.5026E
0.5026¢E
0.5026E
0. 5026E
0.5026E
0.5026E

AHSO

0.1071E
0.1057E
0. 1054E
0.1051E
0.1048F
0. 1044E
0.1041E
0.1038E
0. 1034¢E
0.1031E
0.1027€
0.1024E
0. 1020E
0. 1016E
0. 1013E
0.1009E
0.1005E
0.1002E
0.9977€
0. 9938E
0. 9899E
0.9859E
0. 981 8E
0.S7T77E
0. 9736E
C. 9694E
0. 9652E
0. S609E
0.9565E
0. 9521E
0. 9476E
0.9431¢E
0. 9385¢E
0. $335E
C. 9288E
0. 9240E
0.9192E
0.9143E
0. 9094E
0.9044E

- 0. 8993E

0.8942E

BTU/HR/SQFT/F

UOA

0.3137¢
0.3126E
0.3123€
0.3120€
0.3117€
0.2114E
0.3111E
0.3108E
0.3105E
0.3102E
0.3099E
0.3096E
C.3092€
0.3089E
0. 3086E
0.2C82E
0.32079¢E
0.3075E
0.3071E
0.3068E
0.3064E
0. 3060E
0.3056E
0.3052E
0. 3048E
0.3044E
0.3040¢E
0.3036E
0.3031E
0.3027E
0.2022E
0.3018E
0.301 3¢
C.3008E
C.3003E
0.2%98E
0.2993E
0.2988E
0.2582E
0.2G77E
0.2971E
0.2966E

FEAT
BTU/HR

C. 2¢73E
0.2682E
0. 2€S8E
0.2715€
0.2772€
0. 2748E
0. 27¢5E
0.2782E
0. 27S9E
0. 281¢E
0.2823E
0.2850E
0.2867€
0. 2884E
0. 2SC1E
0. 2518F
0.2625€
0. 2552€
0. 2969E
0. 2586F
0. 3CC3E
0. 2C20€
C. 2C38E
0. 3C54E
0.32072E
0.3089E
0. 31C6E
0.2123E
0. 3140E
0. 3157E
0. 2174E
0.3191E
0. 22C8E
0. 2224E
0.3241E
0.3257€
0. 3274E
0. 3250E
0. 32C7E
0. 2323E
0.3329€
0. 325¢E

€11
114

Appendix D

THE SUPEX PROGRAM

The SUPEX computer program is outlined in block-diagram form in
Fig. D.1. The input data required for the program are given in Table
D.1, and the output received from the computer are given in Table D.2.
A complete listing of the main program and its subroutines is followed
by definitions of the intermediate variables used in the program and the
subroutines and their purposes. To illustrate the use of the SUPEX pro-
gram, computer print-outs of the input for the MSBR steam generator super-
heater exchanger discussed in Subsection 4.1 and the output of the SUPEX

program are presented.
115

(: START j)
\\\ READ N CASE VARIABLES //7

v

\\\WRITE OUT CASE VARIABLES///

 

 

 

CALCULATE AVERAGE PHYSICAL PROPERTIES FOR THE OVERALL EXCHANGER

 

v

 

CALCULATE GEOMETRIC PARAMETERS ASSOCIATED WITH THE BAFFLE WINDOW

 

v

 

KNOWING THE ALLOWABLE TOTAL PRESSURE DROP ON THE TUBE SIDE, USE
THE PRESSURE EQUATION TO CALCULATE A TUBE SIDE MASS FLOW
RATE. CALCULATE A REYNOLDS NUMBER AND FROM THIS A FRICTION
FACTOR. SUBSTITUTE THIS FRICTION FACTOR INTO THE PRESSURE
EQUATION TO CALCULATE A NEW TUBE SIDE MASS FLOW RATE; ITER-
ATE TO CONVERGENCE. THIS GIVES THE FIRST GUESS AT TUBE SIDE

 

MASS FLOW RATE.

 

USING THE TUBE SIDE MASS FLOW RATE, ESTIMATE THE TOTAL NUMBER
OF TUBES IN THE EXCHANGER.

 

 

>v

 

CALCULATE THE GEOMETRIC FACTORS NECESSARY TO CALCULATE THE
BERGELIN FACTORS, THEN CALCULATE THE BERGELIN FACTORS.

 

 

==

 

 

CALCULATE THE TUBE SIDE MASS FLOW RATE FOR AN INTEGER NUMBER
OF TUBES. CALCULATE THE GEOMETRIC PARAMETERS ASSOCIATED
WITH THE NUMBER OF RESTRICTIONS IN THE WINDOW AND CROSS

 

FLOW REGIONS.

 

 

SET TOTAL PRESSURE DROPS, TOTAL BAFFLE SPACINGS AND TOTAL TUBE
LENGTHS TO ZERO.

 

Fig. D.1.

Simplified Flow Diagram of the SUPEX Computer Program.

 

 
 

116

 

DIVIDE THE TOTAL AMOUNT OF HEAT TO BE TRANSFERRED INTO EQUAL
AMOUNTS FOR EACH INCREMENT.

 

v

 

BASED ON THE TOTAL HEAT TRANSFERRED IN AN INCREMENT, CALCULATE
THE DELTA-T AND DELTA-H FOR THE SHELL: SIDE FLUID FOR ANY

 

 

INCREMENT.

 

CALCULATE THE SHELL SIDE FILM RESISTANCE FOR THE GIVEN BAFFLE.

 

 

 

@)

YES

YES

62

Pye

 

BEGIN THE INCREMENT CALCULATION BY CALCULATING THE TUBE SIDE FLUID
TEMPERATURE AT THE END OF THE INCREMENT.

 

v

 

 

CALCULATE THE LOG-MEAN-DELTA T FOR THE INCREMENT
CALCULATE THE TUBE WALL RESISTANCE

CALCULATE THE TUBE SIDE FILM RESISTANCE

CALCULATE THE LENGTH OF THE INCREMENT

CALCULATE THE TUBE SIOE DELTA-P FOR THE INCREMENT

CALCULATE THE ALLOWABLE OELTA-T ACROSS THE TUBE WALL BASED ON
STRESS CONSIDERATIONS

CALCULATE THE SHELL SIDE DELTA-P FOR THE PARTICULAR BAFFLE
SPACE

SUM THE TUBE SIDE DELTA-P'S
SUM THE TUBE LENGTHS

 

v

NO
CHECK TO SEE IF ALL OF THE N-INCREMENTS HAVE BEEN USED. _i::>’--'

 

 

 

 

-

CHECK TO SEE IF THE NEXT INCREMENT WILL BE IN A NEW BAFFLE :: NO
SPACE.

 

Fig. D.1. (continued)

 
117

 

 

CALCULATE THE DIFFERENCE BETWEEN THE TOTAL TUBE SIDE DELTA-
P (SDPT) AND THE ALLOWABLE TUBE SIDE DELTA-P (DELPTA)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

YES v NO
CHECK TO SEE IF SDPT IS WITHIN 3% OF DELPTA _j::>>--=-
w
ADJUST THE NUMBER OF TUBES IN THE EXCHANGER (NUMT)
v
CALCULATE THE DIFFERENCE BETWEEN THE TOTAL SHELL SIDE DELTA-
P (SDPS) AND THE ALLOWABLE SHELL SIDE DELTA-P (DELPSA)
YES NO
CHECK TO SEE IF SOPS 1S WITHIN 3% OF DELSA
ADJUST THE BAFFLE SPACING (BS(K))

 

ALL OF THE HEAT HAS BEEN TRANSFERRED--THE TOTAL PRESSURE DROPS
ON BOTH TUBE AND SHELL SIDE ARE WITHIN LIMITS. WE HAVE AN
ACCEPTABLE SOLUTION.

WRITE OUT THE RESULTS.

 

Fig. D.1. (continued)

*(5)
118

 

 

Table D.1. Computer Input Data for SUPEX Program
Card Columns Format Variable Term Units
1 1-10 F10.,5 Tube outside diameter DTO in,
11-20 F10.5 Tube wall thickness THK in.
21-30 F10,5  Tube pitch P in.
31-40 110 Number of increments N
2 1-10 F10.1 Salt inlet temperature TH1 °F
11-20 F10.1 Salt outlet temperature TH2 °F
21-30 F10.1 Steam inlet temperature TC1 °F
31-40 F10.1  Steam outlet temperature TC2 °F
3 1-10 F10.1 Steam inlet pressure PC1 psi
11-20 F10.1 Steam exit pressure PC2 psi
21-30 F10.1 Allowable total shell- DELPSA psi
side pressure drop
31-40 F10.5 Bypass leakage factor for BLFP
pressure drop
4 1-20 E20.6 Mass flow rate of steam WwC 1b/hr
21-40 E20.6 Mass flow rate of salt WH 1b /hr
41-60 E20.6 Total heat transfer rate QT Btu/hr
61-70 F10.5 Bypass leakage factor BLFH
for heat transfer
5 1-10 F10.5 Specific heat of salt CPH Btu/1be°F
11-20 F10.5 Thermal conductivity of TCH Btu/ftehr«°F
salt (hot £fluid)
21-30 F10.5 Estimated number of GNB
baffle spaces
6 1-10 F10.5 Fractional window cut PW
11-20 F10.5 Estimated total tube SXG ft
length
21-30 F10,5 Estimated baffle spacing BSG ft

 
119

 

 

 

 

 

Table D.2, Output Data From SU?EX Computer Program
Term Variable Units
For Each Baffle Space
J Baffle number
IBK(J) Increment number of first increment which lies
completely in baffle space J
DELTW(J) Calculated temperature drop across tube wall °F
DELTWA(J) Allowable temperature drop across tube wall °F
based on allowable stress
TWALL (J) Temperature of wall material °F
DELPS(J) Calculated shell-~-side pressure drop for the psi
baffle space
DHOT(J) Mean density of hot fluid (salt) for the 1b/ft?
baffle space
VHOT (J) Mean viscosity of hot fluid (salt) for the 1b/ftehr
baffle space
For Each Increment
I Increment number
X1 Tube length for the increment ft
TH(I) Temperature of hot fluid (salt) °F
TC(I) Temperature of cold fluid (steam) °F
PC(I) Pressure of cold fluid (steam) psi
DELP(I) Tube pressure drop for the increment psi
RI(T) Thermal resistance of inside film for the hr-°F/Btu
increment
RW(TI) Thermal resistance of wall material for the hr-°F/Btu
increment
RO(I) Thermal resistance of outside film for the hr-°F/Btu
baffle space in which the increment lies
RT(I) Total thermal resistance between hot and hr-°F/Btu
cold fluids for the increment
For the Entire Exchanger
NUMT Total number of tubes
NBS Total number of baffle spaces
BSL Length of a baffle space ft
DS Inside diameter of exchanger shell in,
120

Table D.2 (continued)

 

 

Term Variable Units

SDPT Total pressure drop in tubes psi

SDPS Total pressure drop in shell psi

DTLME Log-mean delta-T °F

SX Total tube length ft

AREAX Total heat trénsfer area based on total tube fto
length

UEQX Overall heat transfer coefficient based on Btu/hr-ftB-°F
total tube length

SBS Total baffle space length ft

AREAB Total heat transfer area based on total ft2
baffle space length

UEQB Overall heat transfer coefficient based on Btu/hre ft? «°F

total baffle space length

 
The SUPEX Program Listing

 

*¥FTNyL oGy EsM,

PROGRAM SUPEX SUPEX 10
TYPE REAL NEW SUPEX 20
DIMENSION TC(2C1)s TH(201) 4PC(201) HC (201}, SUPEX 30
1DELPS(10C) yRW(201),RI(201),RO(100),RT(201),U(201), SUPEX 31
2X(201) yDELP(201),DELTWA(100) ;DELTW(100) sIBK(100) SUPEX 32
3DHOT(50) 3 VHOT( 50 ), TWALL (50) SUPEX 33
CALL SVH(1,P,T,V,H) SUPEX 40
READINPUTTAPES0,1007,DTCs THK 4P 4N | SUPEX 50
READINPUTTAPE50,1008, TH1,TH2,TC1,TC2 SUPEX 60
READINPUTTAPES0,1009,PC14PC2,DELPSA,BLFP SUPEX 70
READINPUTTAPES0, 10104 WC s WH, QT ,BLFH SUPEX 80
READINPUTTAPES0,1012,CPH, TCH,GNB SUPEX 90
READINPUTTAPE5041011,PWsSXG,BSG SUPE 100
DELPTA=PCLl-PC2 SUPE 110
LOP1=0 SUPE 120
LOP2=0 | SUPE 130
LOP3=0 SUPE 140
LOP4=0 SUPE 150
LOP5=0 SUPE 160
LOP6=0 SUPE 170
LOP7=0 SUPE 180
LOP8=0 SUPE 190
LOP9=0 SUPE 200
LOP10=0 SUPE 210
LOP11=0 SUPE 220
DELTH=QT/(WH%CPH) SUPE 230
DTPB=DEL TH/GNB SUPE 240
CALL RITEL(DTOsTHK,PsNsTHL,TH2,TC1,TC2,PC1,PC24DELPTADELPSAJWC, SUPE 250
1 WHyQT4CPHyTCHPW,BLFP,BLFH,GNBBSG,SXG) SUPE 251
BSL = BSG SUPE 260
DTI=(DT0-2.0%THK )/ 12.0 SUPE 270
P=P/12.0 SUPE 280

DTO=DT0/12.0 SUPE 290

1¢1
TCAV=(TC1+TC2)/2.0
PCAV=(PC1l+PC2)/2.0

CALL SVH(2,PC1l,TC1l,SPV1,DUM)
CALL SVH(2,PC2,TC2,SPV2,DUM)
CALL SVH(2,PCAV,TCAV,SPVAV,DUM)
SPVG=(2,0%(SPV1+SPVAV}+SPV2})/5.0
CALL VISCOS(TC1,PC1l,VISI)

CALL VISCOS{TCZ2,PC2,4VIS2)

CALL VISCOS(TCAV,PCAV,VISAV)
VISG=(2.0%(VIS1+VISAV)+VIS2})/5.0

CFG=C.014

THETAL = 0.8

PERCL = (THETAL = O0.5*SINF(2.0*THETAL)}/3.14159

THETAU = 1.5707

PERCU =(THETAU - O0.5%SINF(2.0*%THETAU))/3.14159

NEW = THETAL + (PW -PERCL)*(THETAU -THETAL)/(PERCU —-PERCL)

PNEW = (NEW — C.5%SINF(Z.0%NEW))/3.14159
EPNEW=ABSF(PW-PNEW)

IF(EPNEW-0.001)444,2

THETAL =NEW

PERCL = PNEW

LOP11=LOP11+1

IF(LOP11-10)1,1,3

WRITEOUTPUTTAPES1,1022,L0P11

601080

THETAC = THETAL
G=3600.0%SQRTF((DELPTA*64.4%144.0%DTI)/(CFG*xSXG*SPVG) )
REG=CTI*G/VISG
CFC=(0.00140+(0.125/(REG**0.32)}1*4,C
DIFA=ABSF(CFC-CFG)
IF(DIFA~Q.05%CFC )9+ 9,6

CFG=CFC

LOP1=L0OP1+1

IF(LOP1-10)8,8,7
WRITEOUTPUTTAPES1+1013,L0P1

G0TO080

SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
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

el
i1

12

13

14

15

CONT INUE
GOTOS

NUMT=XINTF(WC*4.0/ (G*3,1416%DTI%*%*2))
BNUMT=FLOATF(NUMT)

LOP10=0
DS=P*SQRTF(4.0%BNUMT*0,866/3.1416)
XBAR = (DS/2.0}*{THETAC - O0.5%SINF(2,0%THETAC)

(2. 0%(SINF(THETAC) )*%3,0)/3.0)/(THETAC-0.5*SINF({2.0%*THETAC))
BRL1 = BSL / (DS-2.C*XBAR)
GBRL = O0.77*BRL1**(-0,138)
AW=PW*3,1416%DS*%¥2/4,0
AX=(3. 1‘1‘16*05**2/400’”A“
THETA=(1.50%(3.1416-(4.0%AX/DS*%2)) ) **%0.333
AXC=(3.1416-THETA+(SINF(2.0%*THETA)/2.0) )*DS**2/4.0
DIFB=ABSF(AXC-AX) '
IF(DIFB-0.02%AX)15,15,12
THETAZ2=(1.50%(3.1416-(4.0%AXC/DS#*%2) ) )*%0,333
AXC2=(3.1416~THETAZ2+(SINF(2.0%THETA2)/2.0))*DS**2/4,0
THETA=( AX-AXC)*( THETA2-THETA) /(AXC2-AXC )+ THETA
LOP2=L0P2+1
IF(LOP2-10)14414,13
WRITEOUTPUTTAPES51,1014,L0P2
6GOT080
CONT INUE
GOTO1l1
GC=4.0%WC/(BNUMT*3 ,1416*DT[*%*2)
XB=DS*COSF(THETA)/ 2.0
CNB=2.0%XB/(0.866%PpP}
XH=(DS/2.0)-XB
CNW=(XH/ (0 866*P))~-1.0
XC=DS*SINF(THETA)
PCFB=(P-DTO) /P
SBK=PCFB*{(DS+XC) /2.0
SW=PW*BNUMT#*(0.866%P¥%2-(3,1416*%DTO**2/4,0) )
SDPT=0.0
SDPS=0.0
LOP8=0

SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE
SUPE

660
670
680
690
700
710
720
721
730
740
750
760
770
780
790
800
810
820
8 30
840
850
860
870
8 80
890
900
910
920
930
9 40
950
960
970
980
990

SUP 1000
SUP 1010

£Cl
16

17

18
19

20

21

MS=1

SX=0

$SBS=0

TC(1)=TCZ2

TH(1)=TH1
RWK=0TO*LOGF(DTO/D0TI)/2.C
PC(1)=PC2

CALL SVH(24PC2,TC24DUM,HC(1))
BN=FLOATF(N)

QX=QT/BN

DECT=QX/ (WH*CPH)

DECH=QX/WC

I=1

K=1

SB = SBK#*BSL

LOPT7=0

TCON=TH(I}-DTPB/2.0
DENH=141+38E+4+0C-2.466E~02%TCON
VISH=0.2122E+CO*EXPF(4032.CE+00/ (TCON+460.0E+00) )
DHOT (K} =DENH

VHOT(K)=VISH
CON1=(CPH*VISH/TCH)**0.667E+00
GM=WH/ SB

RECB=CTO*GM/VISH
IF(RECB-800.0}17,18,18
HJB=0.571/(RECB*%0,456)
GOTO019
HJB=0.34€¢/(RECB**0.382)
HB=HJB*CPH*GM/CON1

GW=WH/SW

GS=SQRTF (GM*GW)
RECW=DTO*GS/VISH
IF(RECW-800.,0)20,421,21
HJW=04571/(RECW**( 4456
G0T022
HJW=0.34€6/(RECW**(0,382)

SUP
SuUP
SUP
SUP
SUP
SUP
SUP
SupP
SUP
SUP
SuUP
SUP
SupP
SUP
SUP
SuUP
SUpP
SuUP
Sup
SUP
SUP
SUP
SupP
Sup
SUP
SUP
SUpP
SUP
SuUP
Sup
SUP
SUP
SUP
Sup
SUP
SUP

10 20
1030
1040
1050
1C60
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

7C1
22
23
24

25
26
27

28

29

30
31

32

33

HW=HJW*CPH*GS/CON1

HO=(HB*( 1,02, 0%PW)+HW*(2.0%PW) ) *BLFH
HO = HO*GBRL

RO(K)=1.0/HO

TH{I+1)=TH(I)-DECT

LOP5=0

HC(I+1)=HC{I)-DECH

DELPP=0.0

PC(I+1)=PC(I)+DELPP

LOP3=0

LOP4=0

TC(I+1)=TC(I)-DECH

CALL SVH(2,PC(I+1),7C(I+1),DUM,HCG)
EH=ABSF(HC(I+1)-HCG)
IF(EH-0,001%HC(1I+1))31,21,26
TRIAL=TC(I+1)

HRIAL=HCG
TCOI+L)=TC(I+1)+(HC(I+1)-HCG)*(TC(I)-TC(I+1))/(HC(I)-HCG)
CALLSVH(2,PC(I+1)sTC(I+1)+DUM,HCG)
EH=ABSF(HC(I+1)-HCG)

IF(EH-0.001*HC (I+41)1}31,31,28
TNEXT=TC(I+1)}+(HC(I+1)-HCG)*(TC(I+1)-TRIAL)/(HCG-HRIAL)
TRIAL=TC(I+1)

HRIAL=HCG

TCOE+1)=TNEXT

LOP3=L0OP3+1

IF(LOP3-10)30,30,29
WRITEQUTPUTTAPES1,1015,L0P3

GOTU80

GOT027

DENOM=(TH(I+1)-TC(I+1 ) /(TH(I)-TC(I))
TDEN=ABSF(DENCM-1.0)

IF(TBEN-C.05) 32,33,33
DELTLM=0.5E+00%(TH(I+1)-TC(I+1)+TH(I)~TC(I))
GO TO 34

SUP
SUP
SUP
Sup
Sup
SUP
SUP
SupP
SupP
SUP
SUP
SuUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SuUP
SuU°p
SUP
SUP
Sup
SUP
SUP
SuUP
SUP

SUP
SUP
SUP
SUP
SUP
SUP
SUP

DELTLM=(TH(I+1)=TCCI+1)-TH(I)+TC(I)) /LOGF ({TH(I+1)=TC(I+1))/(TH(I)SUP

1-TC(I)))

SUP

1380
1390
1400
1410
1420
1430
1440
1450
1460
1470
1480
1490
1500
1510
152¢C
1530
1540
1550
1560
1570
1580
1590
1600
1610
1620
1630
1640
1650

1660
1670
l168C
1690
1700
1710
1720
1730
1731

GC1
34

35

36

CONTINUE
TM=(TC(I+1)+TC(IL))/2.0
PM=(PC(I+1)+PC(I))/2.0

CALL SVH(2,PM,TM,SPVB,HFB)
PM=(PC({I+1)+PC(I))/2.0

CALL VISCOS(TM,PM,VISB)

TW=TM+0, 23%DELTLM

TCW=0,006375%TW+4, 06

RW{I)=RWK/TCW

DTFM=0.1%DELTLM

TMS=TM+DTFM

CALL SVH{2,PM,TMS, SPVIHFI)
CALLCONDT(TMS,PM,TCFI)

CALL VISCOS(TMS,PM,VISFI)
CRE=(CTI*GC/VISFI)*%0,923
CPR=(((HFI-HFB)/(TMS=-TM))*=(VISFI/TCFI))**0.613
CSV=(SPVB/SPVI ) *%%0, 231
HI=0.00459%(TCFI/DTI)}*CRE*CPR*CSV
RI(I)=DTO/(HI%DTI)
RT(IV=RO(K)I+RW(I)+RI(I)
DYFMC=RI{(I)*DELTLM/RT(I)
IF(ABSF{DTFM-DTFMC)-0.03%DTFMC)39,39,36
DTFM2=(DTFM+DTFMC ) *,5

TMS2=TM+DTFM2

CALL SVH(2,PM,TMS2,SPVI2,HFI2)

CALL CONDT(TMS2,PM,TCFI2)

CALL VISCOS(TMS2,PM,VISFIZ)
CRE2=(DTI*GC/VISFi2)%*0,.923
CPR2=(((HFI2~HFB)/( TMS2-TM} I *(VISFI2/TCFI2))*%0,613
CSV2=(SPVB/SPVI2}%%0,231
H2I=0.00459%TCFI2%CRE2%CPR2%CSV2/DTI
R2I=CTO/ (H2I*DTI)

R2T=RO(K)+RW(I)+R2I
DTFMC2=R2I*DELTLM/R2T
SLOPE=(DTFMC-DTFMC2)/(DTFM-DTFM2)
DTFM=(DTFMC-(SLOPE%DTFM) ) /(1.0-SLOPE)

SUP
Sup
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SuUP
SUP
SuUP
SUP
SUpP
SUP

SUP

Sup
SUP
SUP
SUP
Sup
SuUP
SUP
SUP
SUP
SUP
Sup
SUP
Sup
Sup
SUP
SUP
SuUP
SUP

1740
1750
1760
1770
1780
179C
1800
1810
1820
1830
1840
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090

9¢1
37
38

39

40

41
42

43
44

45

46

47

LOP4=L0OP4+1

IF(LCP4-10)38,38,37
WRITEOUTPUTTAPES1,1016,L0P4

GOTO8C

CONTINUE

GOTO35

UlII=1.0/RT(I)
X{I)=QX/(BNUMT=*3,1416*DTO*U(T)*DELTLM)
RE=DTI*GC/VISB

CFI=0.00140+0.125/ (RE*%*0, 32)
DELP(I)=(4.0%CFI*X(I)/DTI)%GC*%2,0%SPVB/(64.4%3600,%%2,%144,0)
DIFC=ABSF(DELP{(I}-DELPP)
IF(DIFC-C.O5%DELP(I}))43+43,40
DELPP=DELP(I)

LOP5=L0OP5+1

IF(LOP5-10)42,42,41
WRITEQOUTPUTTAPESL1,1017,L0P5

GOTO080

CONT INUE

GOT0Z24

IF(MS)53,53,44

IBK(K)=1I

TW=(RI(I)+0 5 RW(TI)I*(THC(L)-TC(I))/RTLI)+TC(I)
ALPHA=(0,0031%TW+5.6G1)
ETW=31.,65-0.,005%TH
CON2=ALPHA*ETW/{(1l.4*LOGF(DTG/DTI )}
CON3=1,0-(2.0%DTO**2%LOGF(DTO/DTI)/(DTO**2-DT[*%*2))
CON3=CON3*(-1.)

IF{TW=101543)45446446

B=24000.0

SL=7.5

GOTO47

B=57000.C

SL=40.0

CON4=3,0%(B-SL*TW)-2600C.C

TWALL(K) =TW

DELTWA(K )=CON4/(CONZ2*CON3)
DELTWIK)I=RW(II*(TH(TI-TC(I)}/RT(I)

SUP
SUP
SupP
SUP
SuP
SuUpP
SUP
SUP
sSue
SuPp
SUP
SUP
Sue
SUP
SUP
SuUpP
SUP
SUP
SUP
SUP
SUP
SUP
SupP
Sup
SUP
SUP
SUP
SUP
SuUP
SUP
SUP
SUP
SUP
SUpP
SuUP
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

Lel
48
49
50

51
52

53

54

55

56

57

58

59

60

61

62

63

64

IF(I-1151451,49
IF(N-I)51,51,50
BWN=1.0

GOTOS2

BWN=0,.,5

DELPSB=0.6*%CNB*{(GM/3600.0}**2/(64.4%144 .0%DENH)
DELPSW=BWN*{2.04¢0.6%CNW)*(GS/3600.0)*%2/(64,4%144.,0%DENH)

DELPS(K)=(DELPSB+DELPSW)*BLFP
SDOPS=SDP S+DELPS(K)

SBS = SBS+BSL
SDPT=SOPT+DELP(I)
SX=SX+X(1)

[FIN-1)162462,54

I=I+1

IF(SBS-SX)58458455

MS=0

LOP7=LOPT7+1
IF(LOP7-30157457+,56
WRITEOUTPUTTAPES51,1018,L0P7
GOTO80

CONTINUE

GO0TOZ23

MS=1

K=K+1

CONTINUE

LOP8=LOP8B+1
IF(LOP8-30)61461,+60
WRITEQUTPUTTAPES51,1019,L0P8
GOTO80

CONT INUE

GOTO16
EDPT=ABSF(SDPT-DELPTA)
IF(EDPY~C.03%DELPTA 66466463

NUMT=XINTF(BNUMT*(SDPT/DELPTA)*%0,35)

LOP9=L0OPS+1

IF{(LOPS~10)¢€5, 65,64
WRITEOUTPUTTAPES1,1020,L0CP9
G0TO80

SUP
Sup
SUP
SUP
SuP
SuUpP
SUP
SuUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
Sue
SuPpP
SUP
Sup
SUP
SuUp
SUP
Sup
SUP
SUP
SUP
SUP
SUP

SUpP
SuUP
SUP
SUpP
SUP
SUP
SUP

2480
2490
2500
2510
2520
2530
2540
2550
25€0
2570
2580
2590
2600
2610
2620
2630
2640
2650
2660
2670
2680
2690
2700
2710
2720
2730
2740
2750
2760
2770
2780

2790
2800
2810
2820
2830
2840
2850

8¢I
65

66

67

68

69

70

71

1001 FORMAT(1H19//+43X91HJ95Xs5H1ST-1+44X96HDELT-We3Xy8HDELT-W-A,3X,
6HT-WALL 93Xy 6HDELP-S+3Xs6HDENS-H+3 X4y6HVISC—-H)

1

1002 FORMAT(IH 54(1H=-)y3X946(1H=)s3XsT(1H=)43X,8(1H=)44(3X,6(1H=)),/)

1

1003 FORMAT(I5¢3XsI1€93XeF7e293X9FB84292(3X4F6.143X4F6.3))

12
73

74

CONTINUE

BSG=BSL

GOTO10

EDPS = ABSF(SDPS - DELPSA)
IF(EDPS - O O3%DELPSA)T70,70,67
BSL = BSL*SQRTF(SDPS/DELPSA)
LOP10=LOP10O+1
IF(LOP10-10)€94+69,68
WRITEOQUTPUTTAPES1,1021,L0P10
GOTO80

CONTINUE

GOTO15

CONTINUE

CALL RITEZ2

J=0

JN=J+1

JNC=49+JN

IF(JN.GT.K) GO TO 73
WRITEQUTPUTTAPES1,1001

WRITEQUTPUTTAPES1,1002

NBS = K
DO 72 J=JNyKsl

WRITEQUTPUTTAPES1,1003+JIBK(J)sDELTW(J) +DELTWA(J) yTWALL(J),

DELPS(J)DHOT(J )+ VHOT(J)

IF(J.EQ.JNC) GO TO 71
CONT INUE

CONT INUE

CALL RITE3

I=0

IN=I+1

INC=49+][N

IF(IN<GT.N) GO TO 76
WRITEOUTPUTTAPES1, 1C04

SUP
SUP
SUP
SUP
SUP
SUPpP
SUP
SUP
SUP
SuUp
SuUpP
SUP
SuUpP
SUP
SuUP
SUP
Sup
SUP
SUP
SUP
SUP
SUP
SUP
SuUP
SUP
SUP
Sup
SUP
SUP
SUP
SUP
SupP
SUP
SUP
SuUP
SUP
SUP

2860
2870
2880
2890
2900
2910
2920
2930
2940
2950
26960
2970
2980
299C
3000
3010
3020
3030
3040
3050
3051
3060
3070
3080
3090
3100
3101
3110
3120
3130
3140
3150
3160
3170
3180
3190
3200

YA
1004 FORMAT(1H14/7/7+3X9eIHIs5X6HLENGTH 34Xy SHT-HOT 45X y6HT=COLD ¢4 X
1 O6HP-COtDy4Xy 6HDELP-Cy4Xs6HRES=INy4Xs8HRES-WALL y4XTHRES~-0OUT,
2 4XyTHRES-TOT)
WRITEOUTPUTTAPES51,1005
1005 FORMAT(1H s5(1H=)43Xy6(1H=)43Xy2(7(1H=)43X)+48(1H=)+3X46(1H~-),
1 4(3Xs8(1H=))y/)
DO 75 I=INyN,1
RO(CII=RT(I)-RI(I)-RW(I)
WRITEOQUTPUTTAPESYy 1006919 X(I D)o TH(I) +TC(I)PCCI)DELP(I}4RI(I),
1 RWEIL)ROCI)SRT(I)
1006 FORMAT(I €y 3X9FEa393X92(FT74193X)1F8.193XsF6.394(3X4F8.61))
IF(I1.EQ.INC) GO TO 74
75 CONTINUE
16 CONTINUE
AREAX=BNUMT*SX*3,1416*DTO
DENOM=(TH1-TC2)/(THZ2-TC1)
TDEN=ABSF({DENOM-1.0)
IF(TDEN-0,05) 77,78,78
17 DTLME=0.5E+0C*(TH1-TC2+TH2-TC1)
GO TO 79
78 CONT INUE
DTLME=(TH1-TC2-TH2+TC1) /LOGF({(TH1-TC2}/(TH2-TC1}))
79 CONTINUE
UEQX=QT/ (AREAX*DTLME)
AREAB=AREAX*SBS/SX
UEQB=QT/ (AREAB*DTLME)
DS=DS*12.0
CALL RITE4(NUMT,DS,SDPTySCPSyDTLME,SX+AREAX,UEQX +SBS+AREAB,UEQB,
1 NBS,BSL)
80 CONTINUE
CALLEXIT
1007 FORMAT(F10.5,F10.5,F10.5,110)
1008 FORMAT(4F10.1)
1009 FORMAT(F10.1,F1C.1,F10.1,F10.5}
1010 FORMAT(E20.6,E20.69E20.¢€4F10.5)
1011 FORMAT(3F10.5)
1012 FORMAT(3F10.5)

SUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SUP
SupP
SUP
SUP
SupP
SUP
SUP
SUP
SUP
SuUpP
SUP
SupP
Sup
SUP
SUP
Sup
SUP
SUP
SUP
SUP
Sup
SUP
Sup
SUP
SUP
Sue
Sup

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

0¢l
1013
1014
1015
1016
1017
1018
1019
102C
1021
1622

FORMAT (8H
FORMAT (8H
FORMAT ( 8H
FORMAT(8H
FORMAT ( 8H
FORMAT ( 8H
FORMAT( 8H
FORMAT ( 8H
FORMAT ( 9H
FORMAT (9H
END

SUBROUTINE RITEL(DTOsTHKsP4N,TH1,TH2,TC1,TC2,4,PC14PC2,DELPTA,

LOP
LOP
LOP
LOP
LOP
LOP
LOP
LOP
LOP
LOP

=14)
=1 4)
=] 4)
=14}
=] 4)
=14)
=[4)
=] 4)
10 =14)
11 =14)

O o~

1 DELPSA+WC yWH, QT yCPHsTCHyPWBLFPsBLFH,GNB,BSG+SXG)
WRITEOUTPUTTAPES1,1001
WRITEQUTPUTTAPES51,1002,D7C
WRITEQUTPUTTAPES51,1003, THK
WRITEOUTPUTTAPES1,1004,P
WRITEQUTPUTTAPES1,1005,N
WRITEOQUTPUTTAPES1,1006, TH1
WRITECUTPUTTAPES], 1007, THZ2
WRITEQUTPUTTAPES51,1008,TC1
WRITEOUTPUTTAPES1,1009,TC2
WRITEOQOUTPUTTAPES51,1010,PC2
WRITEQUTPUTTAPES]1,1011,DELPTA
WRITEOUTPUTTAPES1,1012,DELPSA
WRITEOUTPUTTAPES1,1013,WC
WRITEQUTPUTTAPES1y 1614, WH
WRITEOUTPUTTAPES1,1C015,QT
WRITEQUTPUTTAPES51,1016,CPH
WRITEOUTPUTTAPES1,1017, TCH
WRITEOQUTPUTTAPES1,1018,PW
WRITEOQUTPUTTAPES51,1019,BLFP

SUP
SupP
SUP
SUP
SUP
Sup
SUP
SUP
SUP
SUP
SUP

RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE
RITE

3530
3540
3550
3560
3570
3580
3590
3600
3610
3620
3630

110
1 11
1 20
1 30
1 40
1 50
1 60
1 70
1 80
1 SO
100
110
120
130
140
150
160
17¢C
180
190
200

T€1
WRITEQUTPUTTAPES]1, 1020,BLFH RITE
NBSR = IFIX(GNB) RITE
WRITEOUTPUTTAPES1,1021,NBSR RITE
WRITEQUTPUTTAPES1,1022,BSG RITE
WRITEQUTPUTTAPES51,1023,SXG - RITE
RETURN RITE
1001 FORMAT(1Hl,//424Xy69H% * % THE FOLLOWING IS THE INPUT INFORMATIONRITE
1 FOR THIS PROBLEM * % %*,///) RITE
1002 FORMAT(1H ,36HOUTSIDE DIAMETER OF TUBES (INCHES)= ,F6.3) RITE
1003 FORMAT( 1HO,30HTUBE WALL THICKNESS (INCHES)= 4FT7.4) RITE
1004 FORMAT(1HO,21HTUBE PITCH (INCHES)= ¢F7.%) RITE
1005 FORMAT(1HO,58HNUMBER OF INCREMENTS INTO WHICH THE EXCHANGER IS DIVRITE
1IDED= 14477} RITE
1006 FORMAT(1HO,3E€HINLET TEMPERATURE QOF HCT FLUID (F)= 4F7.1) RITE
1007 FORMAT(1HO,37HOUTLET TEMPERATURE OF HOT FLUID (F)= +F7.1) RITE
1008 FORMAT(1HO,37HINLET TEMPERATURE OF CCLD FLUID (F)= ,F7.1) RITE
1009 FORMAT(1HO,38HOUTLET TEMPERATURE OF COLD FLUID (Fl= 4FT7ele//) RITE
1010 FORMAT(1HO,37HOUTLET PRESSURE OF COLD FLUID (PSIL)= 4F7.1) RITE
1011 FORMAT(1HO,50HALLOWABLE TOTAL PRESSURE DROP CN TUBE SIDE (PSI)= , RITE
1 F7.1) RITE
1012 FORMAT(1HO,51HALLOWABLE TCTAL PRESSURE DRCP CN SHELL SIDE (PSI)= LRITE
1 FT7.1477) RITE
1013 FORMAT(1HO,38HMASS FLOW RATE OF CCLD FLUID (LB/HR)= ,1PE10.3) RITE
1014 FORMAT(1HQO,37HMASS FLOW RATE OF HOT FLUID (LB/HR)= ,1PE10.3) RITE
1015 FORMAT(1HO, 35HTOTAL HEAT TRANSFER RATE (BTU/HR)= 41PE10.3) RITE
1016 FORMAT(1HO,39HSPECIFIC FEAT OF HCT FLUID (BTU/LB=F)= ,F6.3) RITE
1017 FORMAT(1HO 44SHTHERMAL CONDUCTIVITY OF HOT FLUID (BTU/HR-FT-F)= , RITE
1 Fé6.32) RITE
1018 FORMAT(1HO,23HFRACTIONAL WINDOW CUT= F5.24//7) RITE
1019 FORMAT(1HO,37HBY-PASS LEAKAGE FACTOR FOR PRESSURE= 4F6.3) RITE

1020 FORMAT(1HQ,42HBY-PASS LEAKAGE FACTOR FOR HEAT TRANSFER= 4F6.3,//) RITE
1021 FORMAT(1HC,50HESTIMATE OF THE NUMBER OF BAFFLE SPACES REQUIRED= , RITE

1 13} RITE
1022 FORMAT(1HO+46HESTIMATE OF THE LENGTH OF A BAFFLE SPACE(FT)= ,F5.2)RITE
1023 FORMAT(1HO,39HESTIMATE Of THE TOTAL TUBE LENGTH(FT)= ,F6.2) RITE

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
430
431
440
450
460
470
471
480
490
500

¢tl
SUBROUTINE RITEZ
WRITEOQUTPUTTAPES1,1001
WRITEOUTPUTTAPES1,1002
WRITEOQUTPUTTAPES1,1003
WRITEOUTPUTTAPES1, 1004
WRITEOUTPUTTAPES1,1005
WRITEOUTPUTTAPES1,1006
WRITECUTPUTTAPES1,1C07
WRITEOCUTPUTTAPES1,1008
WRITEOUTPUTTAPES1, 1009
RETURN

1001 FORMAT(1Hly//+12Xy95H* % * THE FOLLOWING TABLE GIVES INFORMATION RITE

1002 FORMAT(1HO,30HJ
1003 FORMAT(1HO+86H1IST-1

1004 FORMAT(1HO+59HDELT-W
1ALL (F))
1005 FORMAT{(1HO,84HDELT—-W-A

1006 FORMAT(1HO,40HT-WALL
1007 FORMAT(1HOy 68HDELP-S
1FFLE SPACE (PSI))
1008 FORMAT(1HO,7CHDENS~-H

1FLE SPACE (LB/FT3))
1009 FORMAT(1HO,74HVISC-H

RITEZ2
RITEZ2
RITEZ2
RITEZ2
RITEZ
RITEZ2
RITEZ
RITEZ2
RITEZ
RITE
RITE
lFOR EACH BAFFLE SPACE THROUGH THE EXCHANGER * * *,//435X,50HTHE CRITE
20LUMN LABELS FOR THIS TABLE ARE DEFINED BELGOWes/7///7) RITE
BAFFLE SPACE NUMBER) RITE
INCREMENT NUMBER OF FIRST INCREMENT WHICHRITE
1 LIES COMPLETELY IN BAFFLE SPACE J) RITE
CALCULATED TEMPERATURE CROP ACROSS TUBE WRITE
RITE
ALLOWABLE TEMPERATURE DROP ACROSS TUBE WARITE
1LL BASED ON ALLOWABLE STRESS (F)) RITE
WALL MATERIAL TEMPERATURE (¥)) RITE
CALCULATED SHELL PRESSURE DROP FOR THE BARITE
RITE
MEAN DENSITY OF THE HCT FLUID FOR THE BAFRITE
RITE
MEAN VISCOSITY OF THE HCT FLUID FOR THE BRITE
RITE

1AFFLE SPACE (LB/FT-HR))
END

RITE

10
20
30
40
5¢
60
70
80
90
100
110
120
121
122
130
140
141
150
151
160
161
170
180
181
130
191
2090
201
210

el
1001

1C02
1003
1004
1005
1006
1007

1008
10929
1010

1C11

SUBROUTINE RITE3
WRITECUTPUTTAPES1,100C1
WRITEOUTPUTTAPES1, 10202
WRITEOUTPUTTAPES1,1C03
WRITEOUTPUTTAPES1, 1004
WRITEOUTPUTTAPES]1, 1005
WRITEOUTPUTTAPES1, 1006
WRITEOQUTPUTTAPES1, 1007
WRITEQUTPUTTAPES1,1008
WRITEOGUTPUTTAPES1, 1009
WRITEOUTPUTTAPES1,41010
WRITEOUTPUTTAPES51,1011
RETURN

RITE3
RITE3
RITE3
RITE3
RITE3
RITE3
RITE3
RITE3
RITE3
RITE
RITE
RITE
RITE

FORMAT(1HLy// 414X, 91H* * * THE FOLLOWING TABLE GIVES INFORMATION RITE

1AT EACH INCREMENT THROUGH THE EXCHANGER * % *,//435X,50HTHE COLUMRITE
2N LABELS FOR THIS TABLE ARE DEFINED BELCW.////7) RITE
FORMAT(1HO,27HI INCREMENT NUMBER) RITE
FORMAT(1HOy 4 7THLENGTH TUBE LENGTH FOR THE INCREMENT (FEET)) RITE
FORMAT(1HO 4 43HT~-HOT TEMPERATURE OF THE HOT FLUID (F)) RITE
FORMAT( 1HO,44HT-COLD TEMPERATURE OF THE CCLD FLUID (F)) RITE
FORMAT( 1+0,43HP-COLD PRESSURE OF THE CCLD FLUID (PSI)) RITE
FORMAT(1HO 4 53HDELP~C TUBE PRESSURE DROP FOR THE INCREMENT (PSIRITE
1)) RITE
FORMAT (1HO, 77HRES-IN THERMAL RESISTANCE OF THE INSIDE FILM FGRRITE
1 THE INCREMENT (HR-F/BTU)) RITE

FORMAT(1HO, TOHRE S—WALL THERMAL RESISTANCE OF THE WALL MATERIAL FRITE

10R THE INCREMENT (HR-F/BTU)) RITE
FORMAT( 1HD,109HRES-0UT THERMAL RESISTANCE OF THE OUTSIDE FILM FRITE
10R THE BAFFLE SPACE IN WHICH THE INCREMENT LIES (HR-F/BTU)} RITE
FORMAT(1HO,90HRES-TOT TOTAL THERMAL RESISTANCE BETWEEN HOT & CORITE
1LD FLUTIDS FOR THE INCREMENT (HR-F/BTU)} RITE
END RITE

10

20

30

40

50

60

70

80

90
100
110
120
130
140
141
142
150
160
170
180
190
200
201
210
211
220
221
230
231
240
241
250

7E1
1601

1002
1003
1004
1005
1006
1007
1008
1009
1010

SUBROUTINE RITE4(NUMT, DSy SDPT4SDPS,DTLMEsSXsAREAXUEQX+SBS RITE4

AREAB,UEQB,NBS,BSL)
WRITEOUTPUTTAPES1,1001
WRITEQUTPUTTAPES]1, 1002, NUMT
WRITEOUTPUTTAPES1,1003,NBS
WRITEGUTPUTTAPES1,1004,8SL
WRITEQUTPUTTAPES1,1005,DS
WRITEGUTPUTTAPES1,1006,SDPT
WRITEOUTPUTTAPES1,1007, SDPS
WRITEQUTPUTTAPES1,1008,DTLME
WRITECQUTPUTTAPES1, 1009, SX
WRITEQUTPUTTAPES1,1010,AREAX
WRITEOUTPUTTAPES1,1011,UEQX
WRITEOUTPUTTAPES1,1012,SBS
WRITEOQUTPUTTAPES1,1013, AREAB
WRITEOUTPUTTAPES1,1014,UEQB
RETURN
FORMAT(1H1,//4+18Xs 84H%x * *

1PERTIES FOR THE ENTIRE EXCHANGER
FORMAT(1HO,23HTOTAL NUMBER OF TUBES=
FORMAT(1HO,31HTOTAL NUMBER OF BAFFLE SPACES=

RITE4
RITE4
RITE4
RITE4
RITE4
RITE4
RITE4
RITE4
RITE4
RITE
RITE
RITE
RITE
RITE
RITE
RITE

THE FOLLCWING ARE AVERAGE OR TOTAL PRORITE
* Kk Xoe//)

RITE

1 15) RITE
v14) RITE

eF6.3) RITE

FORMAT(1HO,32HLENGTH OF A BAFFLE SPACING(FT)=

FORMAT(1HO ,45HINSIDE DIAMETER OF EXCHANGER SHELL (INCHES)= ,F7.2) RITE
FORMAT(1HO,36HTOTAL PRESSURE DROP IN TUBES (PSI)= ,F8.2) RITE
FORMAT(1HO,36HTOTAL PRESSLRE DROP IN SHELL (PSI)= ,F8.2) RITE
FORMAT(1HO,23HLOG-MEAN DELTA-T (Fl= +FT7e2+4//7) RITE
FORMAT(1HG, 26HTOTAL TUBE LENGTH (FEET)= 2FT7.2) RITE

FORMAT(1HO,59HTOTAL HEAT TRANSFER AREA BASED CN TOTAL TUBE LENGTH RITE

1(FT2)= ,FB.11)

RITE

1011 FORMAT(1HO,77HOVERALL HEAT TRANSFER COEFFICIENT BASED ON TOTAL TUBRITE

1E LENGTH (BTU/HR-FT2-F)=

'F7-27//)

RITE

1012 FORMAT(1HO,34HTOTAL BAFFLE SPACE LENGTH (FEET)= , F7.2) RITE
1013 FORMAT(1HO,67HTOTAL HEAT TRANSFER AREA BASED CN TCTAL BAFFLE SPACERITE

1 LENGTH (FT2)= ,F8.1)

RITE

1014 FORMAT{1HO,85HOVERALL HEAT TRANSFER COEFFICIENT BASED ON TOTAL BAFRITE

1FLE SPACE LENGTH (BTU/HR-FT2-F)=

END

'FT.Z'

RITE
RITE

10

11

20

30

40

50

60

70

80

90
100
110
120
130
140
150
160
170
171
180
190
200
210
220
230
240
250
260
261
270
271
280
290
291
300
301
310

Gel
SUBROUTINE VISCOS(T,PL,ETAP}

TR = T+460.

ETAT = 189E-0O6é%(TR/492.) %%, C%(]1,+986./492.)/(1.4+4986./TR)
CALL SVH(Z24P+T4V,yHPT)

ETAP = 115920.*ETAT*(V/{(V-.012) ) *%2

RETURN

END

SUBROUTINE CONDT(T,P,COND)}

TR = T+460.

CALL SVH(Z4P+TyV4HPT)

COND = 1.093E-Q06%TR*%*1,45+28.5375E-04/V*%*1,25
RETURN

END

SUBROUTINE SVH(NyP,T,SVOL,HPT)
CCMMON/TP/PRESyTEMP 4M1 4 M24NC1yNC24XT,YT
GOTO(1ls2)4N

CALL TIPUT

RETURN

PRES=P

TEMP=T

CALL SPECvV(SvOL)

CALL H(HPT)

END

VISCO
VISCO
VISCO
VISCO
VISCO
VISCO
VISCO

CONDT
CONDY
CONDT
CONDT
CONDT
CONDT

SVH
SVH
SVH
SVH
SVH
SVH
SVH
SVH
SVH
SVH

10
20
30
40
50
60
70

10
20
30
40
50
60

10
20
30
40
50
60
70
80
90
100

9¢l
SUBRCUTINE SPECV(ANS)
COMMON/VOL/C(5,60)
COMMON/TP/PRESsTEMP yM1 4 N2 4sNCL1yNC24XT YT
T={TEMP-550.-1,0E~51/10.+1.
NC1l=T

XT=T-NC1

NC2=NCl+1
P=(PRES-3500.-1,0E~5})/7100.+1.
M1=P

YT=P=M1

M2=M1+1
IF(M1.LTo1.0ReM1aGTo4d192
CALL ERROR

IF(NC].-LT. l.OR.NCl.GTO 55, 1'3
CONTINUE

Z11=C(M1,NC1)

212=C{M1,NC2)

221=C(M2,NC1)

222=C(M2,NC2)
XA=Z11+4(212-7211)*XT
XB=221+4(7222«221)*XT
YSET=XA+(XB-XA}I*YT
YA=Z11+4(Z221-211)%YT
YB=212+4(122-212)*Y1
XSET=YA+{YB-YA)*XT
ANS=0,5%(YSET+XSET)

RETURN

END

SPECV
SPECV
SPECV
SPECV
SPECV
SPECV
SPECV
SPECV
SPECV
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC
SPEC

10
20
30

50

60

70

80

90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280

LeT
1001

1002

SUBROUTINE H(ANS}
COMMON/H/C(5460)
COMMON/TP/PRES+TEMP yM1 4 M2 4yNC1yNC24XT YT
£11=C{M1,NC1l)
£12=C(M1,NC2)
£21=C(M2,4NC1)}
£22=C(M2,NC2)
XA=Z114(212-2119%XT
XB=2214(£422-221)*XT
YSET=XA+(XB-XA)*YT
YA=Z114(221-211)%YT
YB=Z12+4(222-Z12)*YT
XSET=YA+(YB-YA)*XT
ANS=0,5%(YSET+XSET)
RETURN

END

SUBROUTINE TIPUT
COMMON/VOL/V (5,460)
COMMON/H/H(5,601)

DO 1 J=1,56
READ(50,1C0L)I(V(IsJ)syI=1,45)
FORMAT(5E10.0)

DO 2 J=1,56
READ(504 1002} (H{(I,+J),1I=1,5)
FORMAT(5E10.0)

RETURN .

END

IITIXIIIIIIXIIIIXTI

TIPUT
TIPUT
TIPUT
TIPUT
TIPUT
TIPUT
TIPUT
TIPUT
TIPUT
TIPU

TIPU

10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160

10
20
30
40
50
60
70
80
90
100
110

8ET
139

Intermediate Variables

The intermediate variables used in the SUPEX computer program are

listed below in the order in which the terms appear in the program. The

units in which the variables are expressed in the program are as follows.

DELPTA

Temperature, °F

Mass, 1b,
Length, ft
Pressure, lbg/in.=
Density, b /ft°

Viscosity, lbf/ft'hr

Total allowable pressure drop in the cold fluid (steam).

LOPl, LOP2, ... LOPI1 Counters used in the various iteration loops to

DELTH
DTPB

BSL
DTI
TCAV
PCAV
SPV1
DUM
SPV2
SPVAV
SPVG

VISl
VIS2
VISAV
VISG

determine whether the loop has converged within a certain pre-
set number of iterations.

Total temperature drop in the hot fluid (salt).

Temperature drop in the hot fluid (salt) per baffle space based
on the estimated number of baffle spaces (GNB).

Baffle spacing length.

Inside diameter of tubes.

Average temperature of the cold fluid (steam).
Average pressure of the cold fluid (steam).

Inlet specific volume of the cold fluid (steam).

A dummy variable.

OQutlet specific volume of the cold fluid (steam).
Average specific volume of the cold fluid (steam).

A guess at the mean value of the specific volume of the cold
fluid (steam) used in making an initial estimate of the mass
flow rate of the cold fluid.

Inlet viscosity of the cold fluid (steam).
Outlet viscosity of the cold fluid (steam).
Average viscosity of the cold fluid (steam).

A guess at the mean value of the viscosity of the cold fluid
(steam) used in making an initial estimate of the Reynolds num-
ber for the cold fluid.
CFG

THETAL

PERCL

THETAU

PERCU

NEW
PNEW

EPNEW

THETAC

CFC
DIFA

NUMT
BNUMT
DS

140

A guess at the value of the friction factor for the cold
fluid (steam).

The minimum value of the angle THETA (radians), where THETA
is half of the angle subtended by the chord that is formed
by the window region of the baffle, The value 0.8 corres-
ponds to § = 45°; this value is just a guess used to start
the iteration process.

  

BAFFLE

The ratio of the window area to the total cross-sectional
area at the baffle, based on THETAL.

The maximum value of the angle THETA. The value of 1.5707
corresponds to 8 = 90°.

The ratio of the window area to the total cross-sectional
area at the baffle, based on THETAU.

The value of THETA based on the iteration scheme,

The ratio of the window area to the total cross-sectional
area at the baffle, based on NEW.

The absolute difference between the desired fractional window
cut (PW) and the calculated fractional window cut (PNEW).

The calculated value of THETA that gives the desired value
of the fractional window cut.

Mass velocity (density times flow speed) for the cold
fluid (steam).

Reynolds number for the cold fluid (steam) based on an
estimate of the viscosity of the cold fluid.

Calculated friction factor for the cold fluid (steam).

Absolute difference between the calculated and guessed values
of the friction factor for the cold fluid (steam).

Number of tubes required.
Floating point conversion value of the integer NUMT.

Inside diameter of the shell of the heat exchanger.
XBAR

BRL1
GBRL

AW

AX
AXC
DIFB
THETA2
AXC2
GC

XB

CNB

141

Distance from the inside surface of the shell to the
centroid of the window area at a baffle,

 

 

 

 

 

 

 

 

/
S '’
[ ;m /// )
7
/// —+1 A~—XBAR

-~ %
BSL i p
-7 y

7
-\ /
R A

e \
+" IS <5
Y
A

{DS-2XBAR)

 

 

Tangent of the angle ¢, as illustrated in sketch above.

(0,77 /BRL1° **®3) This factor is a multiplicative correction
factor developed to modify Bergelin's correlation in cases
where the baffle spacing becomes large relative to the
diameter of the shell, 1In such cases, the flow in the
middle of the baffle region is essentially parallel.

Window area at a baffle.

Baffle area (total cross-sectional area minus window area).
A value of AX calculated from a value of THETA,

Absolute difference between AXC and AX.

A value of the angle THETA based on the value of AXC,

A value of AXC based on the value of THETAZ.

Mass velocity (density times flow speed) for the cold fluid
(steam) based on the current number of tubes in the
exchanger (NUMT).

Distance from the axial center line to the window edge of the
baffle.

Number of rows of tubes from the window edge of one baffle
to the window edge of the following baffle.
XH

CNW
XC
PCFB

SBK
SW
SDPT
SDPS
MS

SX
SBS
TC(I)

TH(I)

RWK

 

142

Inside radius of the shell minus XB.

 

L e bl A e

 

 

 

 

 

 

S
1)

 

 

ROWS OF TUBES (CNB)

Number of rows of tubes in one window.
Chord length of the window edge of the baffle,

Fraction of the distance between tube centers that is free
for cross flow.

Average free area in cross flow per unit baffle spacing.
Free hot-fluid (salt) area in the window region.

Summed pressure drop on the tube side,

Summed pressure drop on the shell side.

A counter which has a value of 1 for the first calculation
in each baffle space and a value of zero for the rest of the
incremental calculations in the baffle space.

Summed tube length.
Summed baffle space length.

Temperature of the cold fluid (steam) at the beginning of
the I-th increment.

Temperature of the hot fluid (salt) at the beginning of the
I-th increment.

A factor used to calculate the heat transfer resistance of
the tube wall material. It can be thought of as an effective
thickness of the tube wall. If

d d
- 2l1pq =2
Rw*zk( d.)’
i
where
thermal resistance of tube wall material,

= outside diameter of tube,

WOQJ
1l

thermal conductivity of wall material, and

o
I

inside diameter of tube; then

RWK = ka .
PC(I)

HC(TI)

BN

QX
DECT

DECH

SB

TCON

DENH

VISH

DHOT(K)
VHOT (K)
CONL

GM

RECB
HJB

HB

GS

RECW
HIW

143

Pressure of the cold fluid (steam) at the beginning of the
I-th increment.

Enthalpy of the cold fluid (steam) at the beginning of the
I-th increment.

Floating point conversion of the integer N (c.f. input
variables).

The amount of heat to be transferred in each increment.

The change in temperature per increment of the hot fluid
(salt).

The change in enthalpy per increment of the cold fluid
(steam).

Subscript index which refers to the increments,
Subscript index which refers to the baffle spaces.

Total cross-flow area for the hot fluid (salt) in a given
baffle space.

An estimate of the bulk temperature of the hot fluid (salt)
in a baffle space.

Density of the hot fluid (salt) based on the temperature
(TCON) .

Viscosity of the hot fluid (salt) based on the temperature
(TCON) .

Density of the hot fluid (salt) for the K-th baffle space.
Viscosity of the hot fluid (salt) for the K-th baffle space.

The Prandtl number for the hot fluid (salt) raised to the
2/3 power.

Masgs velocity (density times flow speed) of the hot fluid
(salt) in cross flow,

The cross-flow Reynolds number for the hot fluid (salt).

The effect of the cross-flow Reynolds number on the shell-
side convective heat transfer coefficient.

The shell-side convective heat transfer coefficient for
cross flow,

Mass velocity (density times flow speed) of the hot fluid
(salt) in parallel flow.

A kind of root-mean-square mass velocity for the hot
fluid (salt). It is used in the Bergelin correlations.

The parallel-flow Reynolds number for the hot fluid (salt).

The effect of the parallel-flow Reynolds number on the shell-
side convective heat transfer coefficient,
HW

HO
RO(K)

TH(I+1)

DELPP

HCG

EH

TRIAL
HRIAL
TNEXT

DENOM

TDEN
DELTLM

PM

SPVB

HFB

VISB

TCW
RW(I)
DTFM

™S

144

The shell-side convective heat transfer coefficient for
parallel flow.

The total shell-side convective heat transfer coefficient,

The film resistance to heat transfer on the outside of the
tubes for the K-th baffle space.

Temperature of the hot fluid (salt) at the end of the I-th
increment (i.e. the beginning of the I+l-th increment).

Tube-side change in pressure for a given increment.

An estimate of the enthalpy of the cold fluid (steam) at
the end of the I-th increment based on the estimated
pressure and temperature at the end of the I-th increment.

The absolute difference between HCG and the HC(I+1) which
has been calculated based on the heat transferred per
increment (QX/WC).

A trial value of TC(I+1) to be used for iteration.
A trial value of HC(I+1) to be used for iteration.

A value of TC(I+1l) which is determined by the iteration
scheme (i.e. a new estimate of TC(I+1) to start the next
iteration).

The antilog of the denominator of the defining equation for
a logarithmic mean temperature difference.

The absolute difference between DENOM and unity.
Logarithmic mean temperature difference,

Average temperature of the cold fluid (steam) in the I-th
increment.

Average pressure of the cold fluid (steam) in the I-th incre-
ment.

Specific volume of the cold fluid based on the average
temperature and pressure, TM and PM, in the increment.

Enthalpy of the cold fluid (steam) based on the average
temperature and pressure, TM and PM, in the increment,

Viscosity of the cold fluid (steam) based on the average
temperature and pressure, TM and PM, in the increment.

Temperature of the wall material in the increment.
Thermal conductivity of the wall material in the increment.
Thermal resistance of the wall material in the I-th increment.

Difference between temperature of inside wall and temperature
of bulk cold fluid (steam) for the increment.

Mean temperature of the tube wall surface in the increment.
SPVI

HFI

TCFI

VISFI

CRE

CPR

CSV

HI

RI(I)

RT(I)

DTFMC

DTFM2
T™MS2

145

Specific volume of the cold fluid (steam) based on the
average pressure and mean tube-wall surface temperature,
PM and TMS, in the increment.

Enthalpy of the cold fluid (steam) based on the average
pressure and mean tube-wall surface temperature, PM and TMS,
in the increment.

Thermal conductivity of the cold fluid (steam) based on the
average pressure and mean tube-wall surface temperature,
PM and T™MS, in the increment.

Viscosity of the cold fluid (steam) based on the average
pressure and mean tube-wall surface temperature, PM and TMS,
in the increment.

Reynolds number of the cold fluid (steam), based on the
inside tube wall conditions, raised to the 0.923 powver.

Prandtl number of the cold fluid, based on inside tube
wall conditions and a fictitious specific heat, raised to
the 0.613 power. The fictitious specific heat is defined

as
Hy - Hy
T, - T,

where H is enthalpy, T is temperature and the subscripts
"i" and ""b" refer to inside tube surface and bulk cold
fluid (steam), respectively. This definition of specific
heat is necessary since specific heat as normally defined
is indeterminant at the critical point, while enthalpy,
although discontinuous at the critical point, is not
indeterminant.

The ratio of the bulk specific heat of the cold fluid (steam)
to the specific heat of the cold fluid evaluated at inside
tube-wall conditions raised to the 0.231 power.

Convective heat transfer coefficient over the increment for
the inside surface of the tube wall.

The thermal resistance of the convective film on the inside
surface of the tubes, for the I-th increment, adjusted to the
outside diameter of the tube,

The total thermal resistance between the hot (salt) and
cold (steam) fluids for the I-th increment.

The temperature drop across the inside tube wall convective
film for the increment.

Arithmetic average of DTFM and DTFMC.

New estimate of the mean tube-wall surface temperature
based on DTFMZ.
SPVI2

HFI2

TCFIZ2

VISFIZ2

CRE2
CPR2
C8V2
H2T
R21
R2T
DTFMC2
SLOPE

U(1)

X(1)
RE

CFI
DELP(I)

DIFC

IBK(K)

146

New estimate of the specific volume of the cold fluid
(steam) based on average pressure (PM) and the new estimate
of the mean tube-wall surface temperature (TMS2) for the
increment.

New estimate of the enthalpy of the cold fluid (steam) based
on the average pressure (PM) and the new estimate of the
mean tube-wall surface temperature (TMS2) for the increment,

New estimate of the thermal conductivity of the cold fluid
(steam) based on the average pressure (PM) and the new
estimate of the mean tube-wall surface temperature (TMS2)
for the increment.

New estimate of the viscosity of the cold fluid (steam)

based on the average pressure (PM) and the new estimate

of the mean tube-wall surface temperature (TMS2) for the
increment.

New estimate of CRE based on VISFIZ,

New estimate of CPR based on HFI2, TMS2, VISFI2, and TCFIZ2.
New estimate of CSV based on SPVIZ2.

New estimate of HI based on TCFIZ, CRE2, CPRZ2, and CSV2.
New estimate of RI(I) based on HZI.

New estimate of RT(I) based on R2I.

New estimate of DTFMC based on R2I and RZT.

A ratio of two differences between various estimates of the
temperature drop across the inside tube wall convective film
for the increment. This is used to make a new estimate of
DTFM in order to continue the iteration process.

Overall heat transfer coefficient for the I-th increment
based on the outside diameter of the tube.

Tube length in the I-th increment.

Reynolds number for the cold fluid (steam) based on the bulk
viscosity (VISB) of the increment.

Fanning friction factor for the cold fluid (steam) for the
increment.

The pressure drop for the cold fluid (steam) in the I-th
increment.

The difference between two consecutive values of the pressure
drop for the cold fluid in the I-th increment as determined
by consecutive passes through the iteration loop.

The value of the index I at the beginning of the first
increment that is totally contained within the K-th baffle
space,
ALPHA

ETW
CON2, CON3

B, SL

CON4

TWALL (K)

DELTWA (K)

DELTW (K)

BWN

DELPSB
DELPSW
DELPS (K)
EDPT

EDPS

J, JN, JNC

NBS
IN, INC

RO(TI)

AREAX
UEQX

AREAB
UEQB

147

Coefficient of thermal expansion for the tube wall
material (x 10%).

Modulus of elasticity for the tube wall material (x 107¢).

Factors in the expression which calculate the stress
components in the tube wall,

Constants in the expression given in Section III of the ASME
Boiler and Pressure Vessel Code for calculating the allow-
able thermal stress components.

Term for the allowable thermal stress components given in
Section III of the ASME Boiler and Pressure Vessel Code.

Temperature of tube wall material for the K-th baffle
space,

Allowable temperature difference across the tube wall for
the K-th baffle space based on allowable thermal stresses.

Temperature difference across the tube wall for the K-th
baffle space.

Factor used in shell-side pressure drop calculations. The
factor takes the value 0,5 if the increment is at either end
of the exchanger, and it takes the value of unity for all
other increment positions.

Shell-side pressure drop in the baffle space area.
Shell-side pressure drop in the window area.
Total shell-side pressure drop for the K-th baffle space.

Absolute difference between the total calculated tube-side
pressure drop and the allowable total tube-side pressure
drop.

Absolute difference between the total calculated shell-side
pressure drop and the allowable total shell-side pressure
drop.

Counters to put the baffle space information out in groups
of 50 per page.

Total number of baffle spaces.

Counters to put the increment information out in groups of
50 per page.

The film resistance to heat transfer on the outside of
the tubes for the I-~-th increment.

Total heat transfer area based on total tube length.

Overall heat transfer coefficient based on total tube
length.

Total heat transfer area based on total baffle space length,

Overall heat transfer coefficient based on total baffle
space length,
148

Subroutines

There are ten subroutines in the SUPEX computer program. The terms

used for each of these subroutines are listed below with a brief

description of the purpose of each subroutine,

RITEL
RITE2

RITE3

RITE4

Writes out the input information.

Writes out definitions of the various columns in the table
of output for each baffle space.

Writes out definitions of the various columns in the table
of output for each increment.

Writes out information concerning the average or total
properties for the entire exchanger.

VISCOS(T, P, ETAP) Calculates the viscosity of the cold fluid (steam)

for a given temperature and pressure.

CONDT(T, P, COND) Calculates the thermal conductivity of the cold

fluid (steam) for a given temperature and pressure.

SVH(N,P,T, SVOL, HPT) Calls the subroutine TIPUT when N = 1 or calls

SPECV (ANS)

H(ANS)

TIPUT

subroutines SPECV and H when N = 2,

Calculates, using an interpolation of input data, the
specific volume of the cold fluid (steam).

Calculates, using an interpolation of input data, the
specific enthalpy of the cold fluid (steam).

Reads in an array of values of specific volume and specific
enthalpy as functions of temperature and pressure.
Computer Input and Output for Reference MSBR Steam Generator Superheater

* % % THE FOLLOWING IS THE INPUT INFORMATION FOR THIS PROBLEM @ = =

OQUTSIDE DIAMETER OF TUBES (INCHES)= 0.500
TUBE WALL THICKNESS (INCHES)= 0.0770
TUBE PITCH (INCHES)I= 0.875C

NUMBER OF INCREMENTS INTO WHICH THE EXCHANGER IS DIVIDED= 100

INLET TEMPERATURE OF HOT FLUID (F)= 1150.0
OQUTLET TEMPERATURE OF HOT FLUID (F)= 850.0
INLET TEMPERATURE OF COtLD FLUID (Fi= 700.0

OUTLET TEMPERATURE OF COLD FLUID (F)= 1C00.0

GUTLET PRESSURE OF COLD FLUID (PSI)= 2600.C
ALLOWABLE TOTAL PRESSURE DROP ON TUBE SIDE (PSI)= 150.0

ALLOWABLE TOTAL PRESSURE DROP ON SHELL SIDE (PSI)= 60.0

MASS FLOW RATE OF COLD FLUID (LB/HR)= 6.330E 05

MASS FLOw RATE OF HOT FLUID (LB/HR)= 2,820E 06

TOTAL HEAT TRANSFER RATE (BTU/HR)= 4.12CE 08

SPECIFIC HEAT CF HOT FLUID (BTU/LB-F)= C.3¢0

THERMAL CONDUCTIVITY OF HOT FLUID (BTU/HR-FT-F)}= 0.240

FRACTIONAL WINDOW CUT= 0,40

691
Computer Input

8Y-PASS LEAKAGE

BY-PASS LEAKAGE

ESTIMATE OF THE
ESTIMATE OF THE

ESTIMATE OF THE

Data for Reference MSBR Steam Generator Superheater (continued)

FACTOR FOR PRESSURE= 0,520

FACTOR FOR HEAT TRANSFER= 0.800

NUMBER OF BAFFLE SPACES REQUIRED= 18
LENGTH OF A BAFFLE SPACE(FT)= 3,00

TOTAL TUBE LENGTH(FT)= ¢€5,00

0¢1
* &« ®* THE FOLLOWING TABLE GIVES INFORMATICN FOR EACH BAFFLE SPACE THROUGH THE EXCHANGER * * »

THE COLUMN LABELS FOR THIS TABLE ARE DEFINED BELOW

J BAFFLE SPACE NUMBER
157-1 INCREMENT NUMBER OF FIRST INCREMENT WHICH LIES COMPLETELY IN BAFFLE SPACE J
DELT~w CALCULATED TEMPERATURE DROP ACROSS TUBE WALL (F)

DELT-w-A ALLOWABLE TEMPERATURE DROP ACROSS TUBE WALL BASED CN ALLOWABLE STRESS (F)

T-nALL WALL MATERIAL TEMPERATURE (F)
DELP-S CALCULATED SHELL PRESSURE DRCP FOR THE BAFFLE SPACE (PS1}
DENS~-H MEAN DENSITY OF THE HOT FLUID FOR THE BAFFLE SPACE (LB/FT3)
VISC-H MEAN VISCOSITY OF THE HOT FLUID FOR THE BAFFLE SPACE (LB/FT-HR)
J 157-1 DELT~-W DELT-W-A T-wWALL DELP-5 DENS=-H VISC~-H
1 1 53.05 S0.73 1Cel.5 1.785 113.2 2.630
2 5 6l.14 1C6.37 1¢3¢.8 3.391 113.5 2.681
3 10 70.73 121.2¢C 1007.0 3.3280 113.9 2.746
4 15 78.72 124.90 $7S.9 3.369 114.3 2.815
5 20 86.70C 128.€2 $53.0 3.358 114,6 2.886
6 26 94.22 132.70 S23.9 - 3.345 115.1 2.976
7 32 100.01 136.45 8S7.4 3.332 115.5 3.071
8 38 104.06 139.87 873.5 3.320 116.0 3.172
9 44 106.05 142.89 852.6 3.307 116.4 3.278
10 51 105.97 145.94 821.8 3.292 116.9 3.411
11 57 103.91 l148.16 Elé. 8 3.280 117.4 3.531
T 12 63 100. 40 150.07 803.9 3.268 117.8 3.660
13 69 95,38 151.64 793. 4 3.255 118.3 3.796
14 T4 90.69 152.83 785.5 3.245 118.6 3.917
15 79 85.40 153.88 778.5 3.235 119.0 4.044%
lé 84 80.07 154,92 771.7 3.225 119.4 4.178
17 89 T4.71 155.94 765.0 3.215 119.7 4.320
18 93 70.78 156.83 159.1 3.207 120.0 4.439

19 97 67.27 157.81 15247 3.199 120.3 4.564

161
¢St

* & * THE FOLLOWING TABLE GIVES INFORMATION AT EACH INCREMENT THROUGH THE EXCHANGER * » @
THE CCLUMN LABELS FOR THIS TABLE ARE DEFINED BELOW
I INCREMENT NUMBER
LENGTH TUBE LENGTH FOR THE INCREMENT (FEET)
T=-HOT TEMPERATURE OF THE HOT FLUID (F)
T-COLD TEMPERATURE OF THE COLD FLUID (F)
P-COLD PRESSURE OF THE COLD FLUID (PSI)
DELP-C TUBE PRESSURE DRCP FOR THE INCREMENT (PSI)
RES~IN THERMAL RESISTANCE OF THE INSIDE FILM FOR THE INCREMENT (HR-F/BTU)
RES~-WALL THERMAL RESISTANCE OF THE WALL MATERIAL FOR THE INCREMENT (HR-F/BTU)
RES-0UT THERMAL RESISTANCE OF THE OUTSIDE FILM FOR THE BAFFLE SPACE IN WHICH THE INCREMENT LIES (HR-F/BTU!}
RES-TOT TOTAL THERMAL RESISTANCE BETWEEN HOT & COLD FLUIDS FGR THE INCREMENT (HR-F/BTU}

—

I
i
!
1

Pt Pt Pt pumd Pt
S LWNNHMOYOOOJTNLEWN =

LENGTH

- — - —

1.076
1.038
1.002
0.975
0.951
0.924
0.899
0.882
0.859
0.839
0.824
0.809
0.794
0.780

1141.0
1138.0
1135.0
1132.0
1129.0
1126.0
1123.0
1120.0
1117.¢C
1114.0
1111.1

1€00.0
993.5
G82.9
576.4
567.9
96l.4
952.4
945.9
939.4
$30.3
923.8
917.3
S1C. 8
S04.3

P-COLD

3€00.0
3604.4
3608.5
3612.5
3€16.3
3620.0
3623.5
3626.9
3630.2
3€33.3
3636.4
3639.3
3é42.1
3644.9

DELP-C

——— - -

4.390
4.173
3.979
3.821
3.679
3.528
3.385
3.279
3.147
3.030
24937
2. 845
2.756
2.61Q

0.000476
0.000473
0.000469
0.000464
0.000460
0.000455
N0.000451
0.000447
0.000442
0.000438
0.000434
0.000429
0.000424
0.000420

RES—-WALL

0.000721
0.000724
0.000727
0.C00730
0.000733
0.000736
0.000739
0.000742
0.000745
0.000748
0.000751
0.000753
0.000756
0.000759

RES-0UT

- -

0.000842
0.000842
0.000842
0.000842
0.000847
0.000847
0.00C847
0.000847
0,000847
0.000853
0.000853
0.000853
0.000853
0.000853

RES-TOT

0.002039
0.002039
0.002039
C.002037
0.00203¢
0.002038
0.00203¢
0.002036
0.002034
0.002038
0.002037
0.002035
0.002033
0.002031
0.768
0.755
0.742
0.729
0.718
0.710
0.701
0.694
0.686
C.679
D.672
0.668
0.662
0.657
0.652
0.647
C.643
0.641
0.637
0.634
0.631
0.628
0.626
0.626
0.625
0.623
0.622
C.621
0.620
0.622
0.622
0.623
0.623
0.624
0.624
0.625
0.630
0.632
C.635
0.637
0.639
0.642
0.649
0.652
0.655
0.659
0.663
0.668

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
1023, 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
S88.2
985, 2
982, 2
979.2
976.2
973.2
970.2
967.2

897. 8
891.3
884.7
878.2
871.7
866.3
859. 8
855.0C
849, 8
844.5
839, 3
834.5
829.7
824.9
820.2
815.9
8l1.7
807.6
803.4
799.5
795.7
792.1
788.6
785, 2
781.9
778.9
T775.9
173.0
770.3
767.8
765.2
762.8
758.5
75644
T54.4
152.17
750.7
T49.3
T47.9
T46.5
745. 1
744.0
T42.7
T4l. 4
740.0
739.3
738.5

3647.6
365042
3652.7
3€55.1
3657.5
3659,7
3¢62.0
3664.1
3666.2
3668.3
3670.3
3¢72.2
3674.1
3676.0
3677.8
3¢e79.6
3¢81.3
3¢83.0
3684.7
368643
3687.9
3689.5
3¢691.0
3692.5
3€93.9
3€95.4
3696,8
3¢58.2
3€£99.5
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
3717.3
2718.3
3719.3
3720.3
3721.3

24592
2.510
2.430
2.350
2,282
2,223
2.161
2.109
2.054
2.002
1.950
1.909
l.862
1.818
1.775
1.734
1.694
1.662
1.626
1.590
1.556
1.523
1.490
l. 464
1.436
l1.407
1.379
1.353
1.328
1.307
1.282
l.260
l. 239
1.215
1.193
1.173
1.159
l.142
1.123
l.104
1.086
1.071
1. 061
l. 044
l.027
1.010
0.595
0.982

0.000414
0.000409
0.000404
0.000398
0.C000392
0.000387
0.000381
0.000376
0.000371
0.000366
0.000360
0.000354
0.000349
0.000344
0.000338
0.000332
0.000325
0.000319
0.00C314
2.000309
0.000303
0.000297
0.000290
0.000284
0.000280
0.CC0273
0.C00267
0.C00261
0.000254
0.000247
0.000241
0.000236
0.000230
0.000223
0.000216
0.000210
0.000205
0.00C199
0.000193
0.000186
0.000179
0.000174
0.000168
0.000163
0.000157
0.000152
0.000145
0.000139

0.000761
0.000764
0.000767
0.000770
0.000772
0.000775
0.000778
0.000780
0.000782
0.000785
0.000787
0.000789
0.000792
0.000794
0.000796
0.000798
0.000890
0.000802
0.000804
0.000806
€.000808
0.000810
0.000812
0.000814
0.000815
0.000817
0.000819
0.000820
0.000822
0.000823
0.000825
0.000826
0.000827
0.000829
0.000830
0.000831
0.000832
0.000834
0.000835
0.000836
0.000837
0.000838
0.000839
0.000840
0.000841
0.000841
0.000842
0.,000843

0.000859
0,000859
0.000859
0.000859
0.000859
0.000865
0.000865
0.000865
0.000865
0.000865
0.000865
0.000872
0.,000872
0.000872
0.000872
0.000872
0.000872
0.00C880
0.000880
0.000880
0.000880
0.00088C
0.000880
0.000888
0.000888
0.000888
0.000888
0.000888
0.000888
0.000897
0.00C897
0.000897
c.000897
0.000897
0.000897
0.000897
0.000907
0.000907
0.000907
0.000907
0.0009C7
0.000907
0.000916
0.00C916
0.000916
0.000916
0.000916
0.000916

0.002034
0.002032
0.002030
0.002026
0.002023
0.002027
0.002024
0.002021
0.002018
0.002015
0.002011
0.0020C16
0.002012
0.00201C
0.002006
0.002002
0.001996
0.002002
0.001998
0.001995
0.001991
0.001987
0.001982
0.001986
0.001983
0.001979
0.C01974
0.001969
0.001964
0.001967
0.001963
N.001558
0.001954
0.001949
0.001943
0.001938
0.001944
0.0C194C
0.001935
0.0C1928
0.001923
0.001918
0.001923
0.001918
0.001914
0.001909
0.001903
0.001898

£Cl
LENGTH

-

C.677
0.682
C.687
0.693
C.699
C.706
0.716
0.723
0.730
0.738
0.746
0.756
0.765
C.774
0.784
0.793
C.807
0.817
c.828
0.838
0.849
0.865
0.876
0.888
0.901
0.913
G.931
0.944
0.956
0.968
0.985
0.999
1.014
1.027
1.040
1.049
1.C57
1.066

T-HOT

964. 2
961. 2
958,32
955.3
952.3
949, 3
G46,.3
943.3
940.3
937.3
934.3
931.3
928.3
925.3
922.3
S19.3
916.3
913.2
910.3
907.3
904,32
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

T-COLD

- e i iy -

737.8
737.2
736.5
735.7
735.0
134,3
733.7
733.0
732.3
731.6
731.0
730.3
729.7
129.0
728.4
727.8
127.2
726.5
125.9
725.3
124.7
724.0C
123.4
722.7
722.0
721.4
720.7
720.1
718.6
717.1
T15.6
714.0
712.7
T11l.2
709,32
706.9
704.5
702.0

P-COLD

3722.3
2723.3
3724.3
3725.2
3726.1
3727.1
3728.¢C
3728.9
3729.8
3730.6
3731.5
3732.4
3733.2
3734.1
3734.9
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
3746.0
3746.8
3747.5
3748,.3
3749.0
3749.8
3750.5
3751.3
3752.0
3752.8

DELP~C

0.975
0. 963
0.948
0.935
0.922
0. 909
0.902
0.889
0.877
0.865
C. 853
N.845
0.838
0.831
0.826
0.821
0.818
0. 812
0.807
C. 802
0. 796
0., 794
0.787
0. 780
C.774
0.768
0. 765
C. 760
0. 758
0. 755
0. 756
0. 755
0. 754
0. 750
0. 750
0. 746
0.742
0. 739

- iy i — -

0.000134
C.000129
0.000123
0.000119
0.000115
0.000111
0.000107
0.000104
C.000101
0.000099
0.C00C96
0.000092
0.00CC91
0.000C90
0.00C089
0.000088
0.0C0087
0.00nC86
0.000C85
0.000084
0.C00083
0.000082
0.000C81
Cc.cCco0080
¢.000080
0.00C080
0.000C80
0.000082
0.0Cc0C88
0.CONCS4
0.000100
0.000107
0.000114
0.000122
0.000127
C.000134
C.000141
0.000149

RES-WALL

o ey N A

0.000844
0.000844
0.000845
0.000846
0.600847
0.000847
0.000848
0.000849
0.000849
0.000850
0.000851
0.000852
0.000852
€.000853
0.000854
0.000854
0.000855
0.000856
0.000857
0.000857
0.000858
0.€00859
0.000859
0.000860
0.000861
0.000862
0.000862
0.000863
0.000865
0.000866
0.000867
0.000868
0.000869
0.000870
0.000872
0.000873
0.000875
0.000877

0.000925
0.000925
0.000925
N.000925
0.000925
0.000925
0.00C935
0.000935
0.000935
0.000935
¢.000935
0.00n943
0.0C0943
0.000943
0.000943

‘0C00943

0.000952
0.000952
0.000952
C.000952
0.C00952
0.000961
0.000961
0.000961
0.000961
0.000961
0.000970
0.000970C
0.000970
0.000970C
0.000978
0.000978
0.000978
0.000978
0.000985
0.00C985
0.000985
0.000985

RES~-TOT

0.001903
0.001898
0.001893
0.001890
0.001887
0.001884
0.0C1890
¢.0Qlesse
0.0C1886
0.001884
0.0C1882
0.001887
0.co1887
N.,001886
0.001886
0.001885
0.001894
N.001894
0.001893
0.001893
0.001892
0.001901
0.001901
0.0C1901
0.001902
0.001902
0.001912
0.001915
0.001922
0.001929
0.001%45
0.CC1952
0.001961
0.001s70C
0.0019584
0.001992
0.C02001
0.002011

761
* * ¥ THE FOLLOWING ARE AVERAGE OR TOTAL

TOTAL NUMBER OF TUBES= 363

TOTAL NUMBER OF BAFFLE SPACES= 19

LENGTH OF A BAFFLE SPACING(FTI= 3,980
INSIDE DIAMETER OF EXCHANGER SHELL (INCHES)=
TOTAL PRESSURE DROP IN TUBES (PSIi= 1£3.53
TGTAL PRESSURE DROP IN SHELL (PSI)= €1.01

LOG~MEAN DELTA-T (F)= 150.0C

TOTAL TUBE LENGTH (FEET)= T76.38

TOTAL HEAT TRANSFER AREA BASED ON TOTAL TUBE LENGTH (FT2)=

18.21

PROPERTIES FOR THE ENTIRE EXCHANGER

3929,.3

CVERALL HEAT TRANSFER COEFFICIENT BASED ON TOTAL TUBE LENGTH (BTU/HR-FT2-F)= 699.02

TGTAL BAFFLE SPACE LENGTH (FEET)= 75.61

TOTAL HEAT TRANSFER AREA BASED ON TOTAL BAFFLE SPACE LENGTH

(FT2)= 3889.9

OVERALL HEAT TRANSFER COEFFJCIENT BASED ON TOTAL BAFFLE SPACE LENGTH (BTU/HR-FT2-F)= 706,10

%

*

*

6¢eI
93.

94.

95-96.

O NP YR TFEEOEANESLEORNUIIROEEORROC

. L.
. F.
. E.
. Bender

. Bettis
. Bettis

O S G ? DI IZTARORHEHEDOPOLIRE QN

157

Internal Distribution

 

Anderson
Baes
Beall

Bohlmann
Boyd
Briggs

. Cope (RDT Site Rep.)

Crowley
Distefano
Ditto
Duggan
Dyslin
Eatherly
Engel
Ferguson
Ferguson
Ferris
Fitzpatrick
Furlong
Gabbard
Gall

Grimes
Grindell
Haubenreich

. Helms

Kasten

Kedl

Keyes

Laughon (RDT Site Rep.)
Llewellyn

38.
39.
40.
41.
42.
43.
44 .
45,
46.
47.
48.
49.
50.
51-60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74-75.
76.
77.
78-90.
91.
92.

o o

n

SCRCEOEUFESRgROrmEmPOCm T ER

Gale

HOoORRPERERAREEOORSE 2P G0E P> &

ORNL TM-2815

. Lundin
. MacPherson

MacPherson
McCoy
McLain
McNees
McWherter
Meyer
Moore

Ne Ims
Nicholson
Perry
Pickel
Rosenthal

ap Scott
iman-Tov

. Stoddart
. Thoma

Trauger
Walker
Watson
Watts
Weir
Whatley
White

. Winsbro

Young

Central Research Library
Document Reference Section

GE Division Library
Laboratory Records Department
Laboratory Records, ORNL R.C.

ORNL

External Distribution

Patent Office

David Elias, USAEC, Division of Reactor Development and Technol-
ogy, Washington, D. C. 20545.

Ralph H. Jones, USAEC, Division of Reactor Development and Tech-
nology, Washington, D. C. 20545.

T. W. McIntosh, USAEC, Division of Reactor Development and Tech-
nology, Washington, D. C. 20545.
158

97. M. Shaw, USAEC, Division of Reactor Development and Technology,
Washington, D. C. 20545.

98-99. Division of Technical Information Extension.

100. Laboratory and University Division, USAEC, ORO.