ORNL-TM-1545.txt

 

 

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ORNL-TM- 1545

Contract No. W-7405-eng-26

General Engineering and Construction Division

DESIGN STUDY OF A HEAT-EXCHANGE SYSTEM
- FOR ONE MSBR CONCEPT

by the
GE&C Division Design Analysis Section

 

LEGAL NOTICE

! .
This report was prepared as an account of Gove nt sponsored c:or:fl:@::::er the United
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. Makes an ty or repre v o eat tho usa

" rac Ammpleteneiu, or usefulnesa of the information contained in this rop::‘t m:y bt e e

T of Iy.l;y information, apparatus, method, oF process -!leolod in this repo! ‘

R wned rights; or -y . e

: priva:ly‘;:mm‘ any liabllluou with respect to the use of, or for damages r:ulting from o
e e, e o Gt i 1 o
the above, ‘‘person &¢ on T
L loy::er conit:wh!‘ of fll’e Commission, or employ:ée of such eonm:lo;;n mromnm“"s.
' :nch employee or contractor of the Commission, © employe: ;t h::cemm or peerarer,

. disseminates, or provides access to, any informati F‘"““w!.. 7 oymen ‘

with the Commiasion, or his employment with such contractor. )

 

SEPTEMBER 1967

OAK RIDGE NATIONAL LABORATORY
Oak Ridge, Tennessee
operated by
UNION CARBIDE CORPORATION
for the
U.S. ATOMIC ENERGY COMMISSION

o A S

DISTRIBUTION OF THTS DOCUMENT IS UNTTMITED

 
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iii

The individuals who participated in this study performed by the
General Engineering and Construction Division Design Analysis Section

are listed below.

Bettis

. Braatz
Cristy
Dyslin
Kelly
Pickel
Shobe
Spaller
Stoddart

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CONTENTS

Abstract - * L] - ® . . . * - . . . . o . - L ’ .

INTRODUCTION . . & ¢ v o ¢ ¢ ¢ o o s o 22 o
SUMMARY . & ¢ ¢ v o ¢ a ¢« ¢ o s s s 2 o o s
DESIGN APPROACH . .+ + v v v v v o 0 v o v .
Heat-Exchange System . . « « « « « « o o « &
Factors Affecting Design of Heat Exchangers
Materials . . . . . ¢« « ¢ s ¢ o 4 .
Maintenance Philosophy . . . . . . .

Feasibility . . . . . « « + « « . .

Heat-Transfer and Pressure-Drop Calculations .

Stress Analyses . . . ¢« ¢« 4 4 4 e 4 e 0 e
DESIGN FOR PRIMARY HEAT EXCHANGERS .,
Case A . . . v ¢ v o 4 v e 4 e e e e e e e
Case B . v ¢« ¢ o & o o o o s o o s = o o
Désign Variables . . . . . . . . . . .
Calculatory Procedures . . . « « « .+ o
Results of Calculations . . . . . . .
DESIGN FOR BLANKET-SALT HEAT EXCHANGERS .
Case A . . v & ¢ ¢« o ¢ o o o o o o o o @
Case B . ¢ ¢ o ¢ ¢ v o ¢ ¢ o o o o ¢ o o o o
DESIGN FOR BOILER-SUPERHEATER EXCHANGERS .

Case A . - .. » . o - . «© . . . * » . . . . -

) Case B * . » * o . * * - L * * . ) . * o . * .

Case C B ) . . . .0 . . . . . L . - . - - .
DESIGN FOR STEAM REHEATER EXCHANGERS . . . .
Case A * » - - - . » . » » - - L4 v * * * o [ ]

caseB. . » . 4 -0 . l.l o.c . - e e . . .

- Case C * .9 - . . L . - .' .V . ', . . - . . -

Sy N W o= =

12
12
12
13
14
20
22
22
26
28
30
32
35
35
39
46
46
52
53
56
56
62
63

 
 

vi

 

Page

8. DESIGN FOR REHEAT-STEAM PREHEATERS . . . « « « & « o « 65
Appendix A. CALCULATIONS FOR PRIMARY HEAT EXCHANGER . . . . 71
Appendix B. CALCULATIONS FOR BLANKET-SALT HEAT EXCHANGER . 111
Appendix C. CALCULATIONS FOR BOILER SUPERHEATER | -

EXCHANGER . &« v v ¢ v ¢ ¢ o o v o o o o o s 140
Appendix D. CALCULATIONS FOR STEAM REHEATER EXCHANGER . 164
Appendix E., CALCULATIONS FOR REHEAT-STEAM PREHEATER . . 184
Appendix F. NOMENCLATURE .« &+ « « o « s o o « o« « « o & 198

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LIST OF TABLES

Title
Values for Fuel-, Blanket-, and Coolant-Salt -
Properties Used in Preliminary Calculations

for MSBR-Heat-Transfer Equipment

Primary Heat Exchanger Design Data for Case A
Primary Heat Exchanger Design Data for Case B
Blanket-Salt Heat Exchanger Design Data for Case A
Blanket~Salt Heat Exchanger Design Data for Case B
Boiler-Superheater Design Data for Case A
Boiler=-Superheater Stress Data for Case B
Boiler-Superheater Design Data for Case C
Steam Reheater Exchanger Design Data for Case A
Steam Reheater Stress Data for Case B

Steam Reheater Exchanger Design Data for Case C

Design Data for the Reheat-Steam Preheater

Page

Number

15

24

33

38

43

50

53

54

62

63

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LIST OF FIGURES

Title

Flow Diagram for the Case-A Heat-Exchange System
Flow Diagram for the Case-B Heat-Exchange System

Primary Fuel-Salt-to-Coolant-Salt Heat Exchanger
for Case A

Primary Fuel-Salt-to-Coolant-Salt Heat Exchanger
for. Case B

Blanket-Salt Heat Exchanger for Case A
Blanket-Salt Heat Exchanger for Case B
Boiler-Superheater Exchanger

Steam Reheater Exchanger

Reheat-Steam Preheater Exchanger

Page

Number

10

23

27

36
40
47
57

66

 
 

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DESIGN STUDY OF A HEAT-EXCHANGE SYSTEM
FOR ONE MSBR CONCEPT

Abstract

The heat-exchange system for one concept of a 1000-Mw(e)

nuclear power plant using a molten-salt breeder reactor has

- been studied. The system has five types of heat exchangers
to transfer the heat generated in the reactor core to the
supercritical steam energy required to drive the turbine for
the generation of electrical power. The two major design
approaches reported here are for flow circuits in which heat

- is transferred from the molten core fuel and fertile blanket
salts to the molten coolant salt and then to the supercriti-
cal fluid. The Case-A system involves relatively high fuel-
and blanket-salt pressures in the reactor core. These pres-
sures are reduced in the Case-B system by reversal of the
flows of the fuel and blanket salts through the reactor core
and the respective pumps and exchangers, while the operating
pressures of the coolant-salt system are raised above those
in the Case-A system., The criteria used, assumptions made,
relationships employed, and the results obtained in the de-
sign for each of. the five types of exchangers used in these
cases are reported. Although the resulting design for the

- Case-B heat-exchange system and the exchangers appears to
be the most workable one, further experimental and analytical
investigations are needed before the designs for these ex-
changers can be finalized.

1. INTRODUCTION

Thermal -energy molten-salt breeder reactors (MSBR) are being studied

'to assess their economic and nuclear performance and to identify important

design problems. One such study made at Oak Ridge National Laboratory
(ORNL) was of a conceptual_lOOO-Mw(e)iMBBR power plant.’ The initial

- reference design for this plant employs a molten-salt breeder reactor

with a two-region fluid-fuel ccncept that has fissile material in the

 

lp. R.'Kasten, E. S. Bettis, and R. C. Robertson; "Design Studies of
1000-Mw(e) Molten-Salt Breeder Reactors,' USAEC Report ORNL-3996, Oak
Ridge National Laboratory, August 1966,

 
 

 

core stream and fertile material in the blanket stream. This study
encompassed all of the major equipment required for a complete power
station, including the components of the heat-exchange system. The
design studies for the heat exchangers are presented here in greater
detail to document some of the unique considerations involved in the
transfer of heat between different molten-salt systems and between
molten salt and water or steam.

The reference 1000-Mw (e) plant1 has four heat-exchange loops, and
the design for this heat-exchange system is referred to here as Case A.
Five types of heat exchangers are used in this system to accomplish the
two principal transfers of heat: (1) from the fuel and blanket salts to
the coolant salt and (2) from the coolant salt to supercritical fluid.
After an evaluation of this concept was made, the possibility of'improv-
ing the system by changing the operating pressures of the fuel-, blanket-,
and coolant-salt systems became apparent. The resulting design for a
reverse-flow system with lower fuel- and blanket-salt pressures in the
reactor core and higher operating pressures in the coolant-salt system
is presented here as Case B. Because of the possibility of developing
a coolant salt with a lower and more favorable freezing-point tempera-
ture, another modification of the Case-A system was considered briefly.
This is referred to as the Case-C design. The design criteria, assump-
tions, calculatory procedures, and the resulting design data are dis-
cussed for each of the five types of exchangers in these heat-exchange

systems.

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2.  SUMMARY

In the Case-A design of the heat- exchange system for the reference
1000-Mv(e) MSBR power plant, five types of heat exchangers are used in
each of the four heat- exchange loops. Each loop has one primary fuel-
salt-to- coolant salt exchanger, one blanket-salt exchanger, four boiler
superheater exchangers, two steam reheater exchangers, and two reheat-
steam preheaters to transfer the heat in the fuel and blanket salts to
the coolant salt and from the coolant salt to the supercritical fluid.

The fuel salt circulates through graphite tubes in the reactor core
with a maximum pressure of 95 psi, leaves the core, and passes through
the'primary exchanger‘where some of its heat is transferred to the cool-
ant salt. Upon leaving the primary exchanger, the fuel salt enters the
suction side of the fuel-salt pump and is_discharged back to the reactor
core. The blanket salt circulates through the reactor core outside the
graphite tubes with a maximum pressure of 115.8 psi{ Upon.leaving the
core, it passes through the blanket-salt exchanger to release some of its
heat to the coolant salt, enters the suction side of the blanket-salt
pump, and is discharged back to the reactor.

 Coolant salt is circulated through the primary exchanger and the

blanket-salt exchanger in series. ‘A major portion (87%) of the coolant
salt is then circulated through the boiler superheater exchangers where
its heat is released to the supercritical fluid, while a smaller portion
(137%) of the coolant salt is circulated through the reheaters. Reheat -
steam preheaters are required in the steam system to raise the tempera-
ture of the exhaust steam from the highapressure turbine before it enters
the reheaters.

A modification of the Case-A design that would eliminate the need
for the ‘reheat-steam preheaters and_for direct-contact heating of the
supercritical'fluid before it entersuthe boiler superheaters was consid-
ered:brieflv, Case C involves lowering the 1nlet temperatures of the
steam reheaters and the boiler superheaters to study the effects of a
coolant salt with a lower freezing-point temperature.

As the studies progressed and more understanding of the overall

system was obtained, the}fact that the-pressure of the fuel salt is

 
 

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higher than that of the coolant salt at the same point in the primary
exchanger and the relatively high pressures of the molten salts in con-

tact with graphite in the reactor core caused concern. The Case-B system

 

was developed to obtain a more desirable pressure arrangement.

In the Case-B system, the operating pressures of the coolant-salt
system were raised to assure that any leakage in the overall system
would be from the coolant-salt system into the fuel- or blanket-salt
systems. To lower the pressure on the graphite tubes in the reactor core
and keep salt penetration at a minimum, the flows of the fuel and blanket
salts through the reactor core and the respective pumps and exchangers are
reversed from those in Case A. The result is that the maximum pressure
of the fuel salt in the reactor core is 18 psi, and the maximum pressure
of the blanket salt is 32.5 psi.

The Case-B heat-exchange system involved redesign of tfie'primary,
blanket-salt, boiler superheater, and steam reheater exchangers.' The
design for the Case-B primary exchanger is an improvement over that for
Case A because the expansion bellows was eliminated and differential
thermal expansion between the inner and outer tubes is accommodated by
the use of sine-wave shaped tubes in the inner annulfis. The blanket-
salt exchanger was improved in Case B by the addition of a floating head
to accommodate differential thermal expansion between the tubes and shell
and to reduce cyclic fatigue. These improvements seem well suited for

ultimate application in the power-plant heat-exchange system.

Lo

The design criteria, calculatory procedures, and the results of the

o)

calculations for each type of exchanger are given in this report, and
many of the detailed calculations for the Case-B exéhangers are appended.
While no optimization can be claimed for these exchanger designs, we feel
that the concepts are sound and reasonable. However, there are two major
uncertainties in the heat-transfer calculations. Accurate values of the
molten-salt physical constants are not known, and the heat-transfer cor-
relations for our application need further verification. The values for
physical constants and tolerances for values of viscosity, density, and
thermal capacity that we used were provided us by the designers of the
'MSBR during the early stages of the study. Recent developments have Qfi)

revealed uncertainties in viscosity and thermal conductivity that could
 

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invalidate the existing designs. Therefore,.before final designs for the

heat exchangers can be presented with confidence, experimental investiga-

tions should be made to i

1. accurately determine the physical properties of molten fluoride salts;

2. investigate the heat-transfer properties of molten salts to extend
the work of MacPherson and Yarosh‘1

3. check and extend the heat transfer and pressure -drop equations devel-
oped by Bergelin et al.®’® to include disk and doughnut baffles;

4. 1investigate heat transfer from molten salt to supercritical fluid, in
particular the heat transfer during the transition from pressurized
water to supercritical fluid, if a practical experiment can be devised;

5. determine the tendency of both bent and straight tubes to vibrate
under various conditions of diameter, pitch,‘support, length, and
baffle shape and spacing; and to

6. determine the possible vibration effects of direct mixing of super-
critical fluid with pressurized water.

Analytical studies should also be made of the

1. possible errors to arrive at the amount of contingency that should be
designed into each exchanger to provide a trustworthy'design,

2. cyclic conditions in the system, -

3. wvibration in each exchanger to assure adeQuate tube life,
possibility of applying recently developed knowledge of tube config-
urations that enhance heat transfer,

5. 1loads on exchangers imposed by methods of support and the piping
restraints, and. R '

6. the maintenance consideratrOns.'

 

1R. E. MacPherson and M, M. Yarosh, 'Development Testlng'and Per-
formance Evaluation of Liquid Metal and Molten-Salt Heat Exchangers "

"Internal Document, Oak Ridge Natlonal Laboratory, ‘March 1960.

20. P. Bergelin, G. A, Brown, and A. P. Colburn, "Heat Transfer and
Fluid Friction During Flow Across Banks of Tubes -V: A Study of a Cylin-

drical Baffled Exchanger Without Internal Leakage, " Trans. ASME, 76: 841~

850 (1954).

3. Pp. Bergelin, K. J Be11 and M. D. Leighton, ”Heat Transfer and
Fluid Friction During Flow Across Banks of Tubes -VI: The Effect of Inter-
nal Leakages Within Segmentally Baffled Exchangers," Trans. ASME, 80:

53-60 (1958).

 
 

 

3. DESIGN APPROACH

The reference designl for the 1000-Mw(e) MSBR power plant involves
a two-region two-fluid system with the fuel salt and the blanket salt in
the reactor core separated by graphite tubes. The fuel salt consists of
uranium fluoride dissolved in a carrier salt of lithium and beryllium
fluorides, and the blanket salt contains thorium fluoride dissolved in a
similar carrier salt. The energy generated in the reactor fluid is trans-
ferred to a coolant-salt circuit that couples the reactor to a supercrit-
ical steam cycle. This reference design employs one reactor with four
heat-exchange loops. |

Since a high plant-availability factor in the'power plant is impor-
tant to the maintenance of low power costs, a modular-type design for the
MSBR plant was also considered. This modular plant would havé four sep-
arate and identical reactors with their separate salt circuits. The
desirability of the modular-type design and consideration of the size of
the components and pipe required for the reference plant influenced the
selection of the number of heat exchangers to be used in the system.
Regardless of the number of reactors to be used in the 1000-Mw(e) plant,
the study reported here is based on the use of four heat-exchange modules

in the system.

Heat-Exchange System

 

Each of the four modules or loops of the reference heat-exchange
system contains one primary fuel-salt-to-coolant-salt exchanger, one
blanket-salt exchanger, four boiler superheater exchangers, two steam
reheater exchangers, and two reheat-steam preheater exchangers. These
exchangers are housed in temperature-controlled shielding cells that can

be heated to temperatures up to l000°F with either gas or electric

 

1p. R. Kasten, E. S. Bettis, and R. C. Robertson, "Design Studies of
1000-Mw(e) Molten-Salt Breeder Reactors,'' USAEC Report ORNL- 3996 Oak
- Ridge National Laboratory, August 1966.

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heaters. This simplifies the system considerably by eliminating the need
for auxiliary heaters on each piece of equipment and the need to insulate
each individual component.

The flow diagram of the heat-exchange system for the reference
design,l Case A,.is shown in Fig. 1. Each.heat transfer stage. consists
of a number of identical exchangers represented in Fig. 1 as a single
typical exchanger. The temperature values shown in Fig. 1 constitute
the basis from which development of the designs for the various heat
exchangers was bégun. Some of these,values‘were derived from known prop-
erties of molten-salt systems, and some were derived from simple heat
and material balances. Values in the steam system were selected to make
use of the existing steam-cycle design in the Tennessee Valley Authority's
900-Mw(e) Bull Run steam plant. This design was modified to increase the
power rating to 1000 Mv(e).

In the resu1ting design for the CaSe-A'system, the fuel salt leaving
the reactor core at a pressure of 90 psi enters the primary exchanger at
a temperature of 1300°F and a pressure of 85.8 psi and is circulated
through the tubes in the'exchanger where some of its heat is released to

the coolant salt. It then enters the suction side of the fuel-salt pump

and is dischafged back to the reactor at a temperature of 1000°F and a

pressure of 95 psi. The heat from the blanket salt is transferred to the
coolant salt in the blanket-salt heat exchanger. The blanket salt leav-
ing the reactor at a préssure of 95.8 psi enters the exchanger at a tem-
perature of 12506F afid'a pressure of 90.3 psi, is circulated through the
tubes of the exchangéf whereWSOme of its heat is given up to the coolant
salt, enters the suction sidéfbf fihe blanket-salt pump, and is discharged
back to Efierféactof_at'aitéfipefature of 1150°F and a pressure of 97.8 psi.

These transfers of heat to the coolant-salt system represent one of

the two direct stéps involvé& in converting the heat generated in the
?reactorrfiore. tO'the'energyfrqui:ed to drive the steam turbine. The

‘coolant salt in the system entérs the primary exchanger at a temperature

of'850°F and a'préssure'of779.2 psi and leaves it at a temperature of
1111°F and pressure of 28.5 psi. This coolant salt is then circulated
through the blanket-salt exchanger, entering at a temperature of 1111°F

and pressure of 26.5 psi and leaving at a temperature of 1125°F and a

 

 
ORNL DWG 67-6817

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L e e e —————
i f
- P — s e e — e — . —)
! COOLANT 4 | .
| | SALT PUMP | T
| " " w
} 1 1125°F f
| . 2K Y 1 ; '
I a usoor \ GASEOUS FISSION | 5 [ |
* { - g - PRODUCTS DISPOSAL | ‘ | l
(/A . | ' SYSTEM i I
|__<‘~ ‘ ) te2s0°F Y : . I | :
n2seF | | : ' ' :] ‘
i | | : I
T | T } | ! o~ J;: I | . |
| | | | CONDENSATE
( Lo JlE o 7» I | 8 MAKE-UP
\ ~ | | REHEAT STEAM
il Y L/ | | J | PREHEATER
| | NIeF = — |000°F ' l _
¢ : ‘l 1300°F 1000°F ‘ I . :
| —— | heser 1 |
* REACTOR VESSEL  1300°F =TA
LT e R I " :
TR | : 7 BOILER REHEATER BOOSTER MIXING
BLANKET SALT \ | SUPERHEATER e PUMP  TEE
HT. EXCHG. & PUMP .
A -LEGEND -
FUEL SALT

 

 

BLANKET SALT - ===

| COOLANT SALT ———~—
FUEL SALT HT. STEAM  em=m=m=——-

EXCHG. & PUMP I B

Fig. 1. Flow Diagram for the Case-A Heat-Exchange System.
 

 

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pressure of 9 psi. The second direct heat-conversion step is performed
when the major portion (87%) of the coolant salt is circulated through
the boiler superheater exchangers where its heat is released to the
supercritical fluid.

The remaining portion (137%) of the coolant salt in the system is
used to reheat the exhaust steam from the high-pressure turbine in the
steam reheater éxchanger. There is a possibility that the coolant salt
in the steam reheater could be cooled to a temperature too close to its
freezing point by the much cooler steam fed directly from the turbine
exhaust. To avert possible freezing of the coolant salt, a reheat-steam
preheater was included in the system wherein heat from a relatively small
quantity of the high-temperature supercritical fluid raises the tempera-
ture of the reheat steam. For the same reason, the temperature of the
supercritical fluid is raised before it enters the boiler superheaters
by direct-contact heating. |

The studies of the MSBR heat-exchange system progressed to a point
where a better evaluation of the temperatures and pressures in the over-
all system could be made. The most objectionable single feature of the
Case-A system is that thére are points in the primary heat exchanger
where the pressure of the fuel salt is higher than that of the coolant
salt, particularly where the fuel salt enters at a pressure of 85.8 psi
and the coolant salt exits at a pressure of 28.5 psi. When efforts were
directed toward correcting this feature, other areas where improvements
in the system could_be'made became evident. The revised design that we
refer to as thé Case-B systéfi;was_developed by the reactor designers to
improve the overall operatiqh'of the heat-exchange system. The Case-B
system required the redéSigfi'éf the primary, blanket-salt, boiler super-
heatér,'and steam reheatéf exchéngers, and the resulting flow diagram
for the system is shown'in_F;g;VZ.

The operatingpressures of the coolant-salt system in the Case-B

design were raised to assure that any leakage in the overall system

- would be from the coolant-salt system into the fuel or blanket salt

system. The Case-B systém'has'a further advantage over the Case-A system
in that the pressures of the molten salts in contact with the graphite

tubes in the reactor core are lower. At the top of the reactor where

 

 
10

ORNL DWG 67-68I8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

     
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

? 260 PSI (mmmmmmmmmmm e ;
| 1125°F P m— o oe— e pm—— e a |
— - ! } 1’ Y
| \7 PSI l - “ | ) { nptd P T |/ GeN
ll25 F 5 i : --——-—L—__ i ; L)-I_(\'J_k___j
| COOLANT . l L@ Of—l
REACTOR VESSEL |
PUMP . —
| SALT PU '942&}{ -~ | ) Y 1 Y y
850°F 252psl |\ | Y| | |
|'25POS,' | 1125°F | | : LRT
| F ;
| | 208psi}/ | | |
| | 125°FJ| | , . : |
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l | P-' I i : l\ U | t
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' 8 MAKE-UP
| 9pS | E | REHEAT STEAM !
| apsi \,/) 1300F 46 P! : | PREHEATER +
* J i l3gc‘)3,| 1300°F | U | | | .
| KD 203531,_!2 ' l__:‘ Y l
) 850°F i
I000°F SOF I W _  _ F s A ____
129 pqu' 3PS | sopsi] Giilll [l BOILER | g .
1125°F BLANKET SALT IO00°F I000F | . . I98F‘:SI SUPERHEATER REHEATER BOOSTER MIXING
| HT. EXCHG. & PUMP 850°F PUMP TEE
I |64f$|}/ |
HH°F
-LEGEND-
I GASEOUS FISSION 1 '
PRODUCTS DISPOSAL | e—
| SYSTEM | FUEL SALT
\ BLANKET SALT  =——=em——
| FUEL SALT HT. COOLANT SALT ==———
e 4e——_1 EXcHG.B PUMP STEAM e
WATER ————

Fig. 2. Flow Diagram for the Case-B Heat-Exchange System.
 

 

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pressures are at a minimum, the pressure of the fuel salt in the graphite
tubes in the Case-A system is 83.5 psi, while that of the blanket salt
outside the tubes is 95.8 psi. At the bottom of the reactor where the
pressures are makimum; the pressure of the fuel salt is 95 psi and the
corresponding préssure of the blanket sélt 1s 115.8 psi.

In the Case-B system, where the pressures are at a minimum at the
top of the reactor, the pressure of the fuel salt circulating through
the graphite tubes is 6.5 psi, while the pressure of the blanket salt
outside the tubes at that point is 12.5 psi. At the bottom of the reac-
tor where the pressures are maximum, the pressure of the fuel salt is
18 psi and the corresponding pressure of the blanket salt is 32.5 psi.

This lowering of the pressure of the fuel and blanket salts in the
reactor for the Case-B system is accomplished by reversing the flow of
the fuel and blanket salts through the respective pumps and exchangers
and through the reactor core. The fuel salt leaving the reactor core at
a temperature of 1300°F and a pressure of 13 psi enters the suction side
of the fuel-salt pump and is discharged into the primary heat exchanger
at a pressure of 146 psi. It is circulated through the tubes of the
exchanger and then reenters the reactor at a temperature of 1000°F and
a pressure of 18 psi. The blanket salt leaving the reactor core at a

temperature of 1250°F and a pressure of 12.5 psi enters the suction side

of the blanket-salt pump and is discharged into the blanket-salt exchanger

at a pressure of 111 psi. It is circulated through the tubes in the

exchanger and then reenters the reactor at a temperature of 1150°F and a

pressure of 14.5 psi.

- To study the effects of having-a coolant salt with a lower and more
favorable freezing-pointtemperatufe in the system, another modification
of the Case-A heat—exchange systéthas developed. Case C involves lower-
ing thezifilet temperatures of the steam reheaters and the boiler super-
heaters, eliminating the reheataSteém preheaters and the need for direct-
contact heating of the superc:iticalvfIUid before it enters the super -
héatérq;*IThe tfirbine,exhafiSt-steam is fed directly to the steam reheaters
at a temperature of 552°F,'éhd the supercritical fluid enters the boiler

superheaters at a temperature of 580°F

 
 

 

 

 

12

Factors Affecting Design of Heat Exchangers

Several factors other than operating temperatures and pressures also
had to be taken into account before the designs for the various compo-
nents of the heat-exchange system could be developed. Those factors
included consideration of the materials that could be used to construct
the components, the maintenance philosophy to be followed, and the feasi-

bility of the concept as a whole.

Materials

Metal surfaces in ffequent contact with molten fluoride salts must
have corrosion resistance not provided by conventional materials. Hastel-
loy N, originally developed as INOR-8 specifically for use with molten
fluoride salts, was designated by the designers of the MSBR as the struc-
tural material for all components in the fuel, blanket, and coolant
systems that are in contact with molten salts.

The preheater and high-temperature steam piping will be made of
Croloy, 2 1/4% chrome and 17 molybdenum, Carbon steel can be used for
those surfaces in contact with water at temperatures below 700°F, as

specified in Section III of the ASME Boiler and Pressure Vessel Code.2

Maintenance Philosophy

Certain features of the designs for the heat exchangers are governed
by the maintenance philosophy to be applied to them. We believe that the
reliability of the exchangers can be held at a high level through quality
control in design and fabrication. Therefore, the maintenance philosophy
we adopted predicates that defective exchangers will be replaced with
new ones rather than being repaired in place. This attitude is neces-

sary for the primary and blanket exchangers because of the high level

 

2uASME Boiler and Pressure Vessel Code, Section III, Nuclear Ves-
sels,"”" The American Society of Mechanical Engineers, New York, 1965.

10

C

¥

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C
 

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13

of radioactivity_that’thej will incur during operation at full power.
When an exchanger must be removed from its temperature-controlled shield-
ing cell, it will have to be placed in another shielded cell for an
indefinite period.

Those exchangers that contain no fuel or blanket salt are not likely
to reach as high a level of radioactivity during operation as the primary
and blanket exchangers, but the level reached will probably be high enough
to prevent direct repair in place. If they fail, these exchangers will
also be repleped, and after the required decay time, they will be repaired.
Removal and subsequent repair of the exchangers in the steam system con-
stitute major operations, but no provisions for repairing them have yet
been made. 1In the final design, such provisions would be based on indus-
trial experience and practice with conventional heat exchangers that are
0pereted in the same pressure and temperature range as those used in this

application,

Feasibilitz

Some of the features of the designs for the heat exchangers that had
to be investigated to demonstrate the feasibility of the concept are worth
mentioning here. 1In each of the exchangers that have molten salt on the
shell side, a baffle extends across the entire cross-sectional area of
the shell at a distance of 0.5 in. from the tube sheet. This provides
a stagnant layer of malten salt between the tube sheet and the circulating
molten salt, and this 1nsu1at1ng-1ayer of salt serves to reduce the tem-
perature drop across the'tfibe sheet As conceived the tube-to-tube-
sheet connection is to be made by rolling at two places within the thick-
ness of the tube sheet and welding at the end of the’ tube. Trepanning

the tube sheet around eech tube makes a relxable tube-to-tube-sheet weld

','possible.;

In cases where the she114s16e fluid travels for considerable distance

- without baffling, small ring_baffles are used toubreak the flow between

the outermost tubes and the shell. In some cases, long tube lengths are
unsupported by baffles. Although the drawings do not show it, these tubes

can be held in place by some form of wire-mesh tube support.

 
 

 

 

14

Heat-Transfer and Pressure-Drop Calculations

The values for the physical properties of the fuel, blanket, and
coolant salt that were used in the preliminary calculations were prb-
vided by the designers of the MSBR, These are given'in Table 1. Because
of the unusual situations involved in this heat-exchange system, we
searched the literature to determine correlations between reported con-
ditions and those of our pafticular application and to select the physical
properties most nearly suited to those involved in our application. From
the material searched, we developed the bases for our heat-transfer and
pressure-drop calculations.

' For calculations involving heat transfer by forced convection
through a molten-salt film inside a tube with a small diameter, we used
data reported by MacPherson and Yarosh.® From the data, the following

equation was written.

 

 

hidi = 0.000065(NRe)1-43(NPr)°-4 , | (1)
where
; = heat transfer coefficient inside tube, Btu/hr- £t2 - °F,
di = inside diameter of tube,
k = thermal conductivity, Btu/hr-ft®-°F per ft,
NRe = Reynolds number,
NPr = Prandtl number,
Equation 1 was used when NRe < 10,000 and Eq. 2, the Dittus-Boelter
equation, was used when NRe > 10,000.
2% g 023(Ng) (N ) 2)
k - Re Pr * |

 

3R. E. MacPherson and M. M. Yarosh, "Development Testing and Perfor-
mance Evaluation of Liquid Metal and Molten-Salt Heat Exchangers," Internal
Document, Oak Ridge National Laboratory, March 1960.

w

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1

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<} a1 «) ¢ ! )

~ Table 1. Values for Fuel-, Blanket-, and Coolant-Salt Properties
Used in Preliminary Calculations for MSBR-Heat-Transfer Equipment

 

 

_ . Fuel Salt Blanket Salt Coolant Salt
Reference temperature, OF‘: 1150 1200 988
Composition o o L1iF-BeE, ~UF, LiF-ThF, - BeF, NaF-NaBF,
Molecular Weight, approximate 34,3 102.6 68.3
Liquidus temperature, QF | 842 1040 579

Density, 1b/ft3 . L 127 + 6@ 277 + 14® about 125
Viscosxty, lb/hr ft ) 27 + 3 : 38 + 19(a) 12
mfi:fi?firc;guc;ixiy& 1.5 1.5¢) 1.3

Heat capacity, Btu/1b+°F 0.55 = 0.14 0.22 + 0.055 about 0.41

 

r ( )Ifiternal memo MSBR-D-24 from Stanley Cantor to E, S. Bettis July 15, 1965, Subject:
Physical Property Estimates of MSBR Reference-Design Fuel and Blanket Salts.

(b)

A value of 4.0 Btu/hr-£ft2.°F per ft was used for the thermal conductivity of the
fuel salt in the calculations for the Case-A primary exchanger. Subsequent to the calcu-

‘latory work done for the Case-A primary exchanger, the improved estimated value of 1.5
was obtained and used.

| (C)W. R. Gambill, "Prediction of Thermal Conductivity of Fused Salts,' Internal
Document, Oak Ridge National Laboratory, August 1956,

ST

 
 

 

 

16

In all instances of baffled flofi, we made use of the work of 0. P.
Bergelin et al.*»® for both the heat-transfer and the pressure calculations.
Four out of five of the heat exchangers have coolant salt onrthe shell
side, and in each of these four exchangers, the flow of the coolant salt
is directed by baffles. A relation between a heat transfer factor J and
the Reynolds number for such baffled flow is illustrated in graphic form
~in Fig. 11 of Ref. 4. Based on the outside diameter of the tube, the
Reynolds number,

doG
Nee = -;; ’ (3)
where
d = outside diameter of the tube,

o

G = mass velocity of fluid, 1b/hr-£ft?, ,
W, = viscosity at temperature of bulk fluid, 1b/hr* ft.
The heat transfer factor for the window area,

14

h CIJ- 3 o
_ v (_pb _i |
JW_CG< k3/ C:l) ? (%)
p m

where
hw = heat transfer coefficient for window area, Btu/hr'fta-oF,
Cp = specific heat,

Gm = mean mass velocity of fluid, lb/hr-fte,
k = thermal conductivity, Btu/hr:ft®.°F per ft,
= viscosity at temperature of bulk fluid, 1b/hr-ft,

M, = viscosity at temperature of tube surface, lb/hr-ft.

 

0. P. Bergelin, G. A. Brown, and A. P. Colburn, "Heat Transfer and
Fluid Friction During Flow Across Banks of Tubes -V: A Study of a Cylindri-
cal 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 During Flow Across Banks of Tubes -VI: The Effect of
Internal Leakages Within Segmentally Baffled Exchangers," Trans. ASME,
80: 53-60 (1958).

(;)

8

i
 

 

 

 

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)

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%

b culate r.

17

The heat transfer factor for the cross-flow area,

EESET

In some instances, values of J were read from the graph® and the
heat transfer coefficients were determined from the equation. 1In other
instances, particularly where machine computation was used, the following

approximate equations derived from the graph were used to determine J.

For 800 < N, < 105, J

-0 ,382
Re 0.346 NRe . (6)

- -0 ,458
For 100 < Neo 800, J = 0.571 Np . (7)
The value of the heat transfer coefficient for the window area, hw’ and
the value for the cross-flow area, hB’ were then combined in Eq. 8 to

determine the total heat-transfer coefficient.

htat hBaB + h o 2 (8)

where a = the heat transfer surface, £t /ft.

These relationships were used to determine values for the heat
transfer coefficients on the shell side of baffled exchangers. The data
reported by Bergelin,*>5 and therefore the relationships given above,
were based on work with half—noon shaped baffles with straight edges,

whereas in the study reported here, disk and doughnut baffles were used

in all the exchangers except the superheater. The adaptatlon of Bergelin's

data to disk and doughnut baffles involved certaln 1nterpretatlons. The

"number of major restrictlons encountered in cross flow“ referred to in

-Bergelin's ‘work was interpreted for tubes arranged in triangular array as

being the number of rows of tubes, Ty 1n cross flow. Cross flow for disk

éand doughnut baffles varies in dlrectlon through 360 ~ For 30° of change

"1n direction, the distance between tube rows will vary from the pitch p

to 0. 866p. Therefore,.an‘average,of‘these_two extremes was used to cal-

_;eross-flofi distance o | 9)
- 1 + 0.866 :
2

 
 

18

Where an arrangement has the tubes placed in concentric circular rings,
r is simply the number of rings in the cross-flow area.

In calculating the flow area, Aw’ for the fluid moving outward from
the doughnut opening of diameter D,, we made use of the approximate
equation for the number of tubes, n, in a circular band with a width
equal to 1 pitch, p. 7
PP ™y
" 0.9p® 0.9
involved, the factor 0.9 lies between 0.8 and 1;

n . | _(10)

For the values of D

d
our choice of 0.9 was arbitrary. Then,

A /X =mD, - nd_,

where
X
d

o
The number of tubes of given size and pitch arranged in triangular

the baffle spacing,

the outside diameter of the tube.

array that can fit into a cylindrical shell,

0=t (l;) , a1

where
K = correction factor,
D = the diameter of the cylindrical shell,v
p = pitch of the tubes.

The value of K decreases with the increasing ratio between D and p. The
value K = 1.15 is sometimes used for triangular array, and the value

K = 1.12 was used in the calculations for the reheater exchanger. This
compromise value has been checked by graphic methods and found reasonable
for our applications.

The number of tubes passing through the window in a doughnut baffle,

In this case, there is no space devoid of tubes near the outside of the

circular window as is found in the case of the cylindrical shell.

w

K1

W

O
 

 

.

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-

19

For heat transfer calculations involving parallel flow on the shell
side, we used the data reported by Short.® The heat transfer coefficient

outside of the tubes,

ey ()R

This equation was used in the design calculations for the reheat-steam
preheater and the parallel-flow portion of the Case-A primary exchanger.
The superheater and the preheater both involve supercritical fluid,
and the data reported by Swenson et al.” was used extensively in calcu-
lating the heat transfer coefficients for those components. The corre-

lation recommended in this work is given below.

ome ()RR w

h, = heat transfer coefficient inside tube, Btu/hr-ft3°°F,

S13

 

d, = inside diameter of tube,

ki = thermal conduct1v1ty inside tube, Btu/hr ft2 °F per ft,
G = mass velocity of fluid, lb/hr ffia,

T viScoeity_of fluid at temperature inside tube, 1b/hr-ft,

H, =_enthe1py at temperature inside tube, Btu/lb,

H = enthalpy at temperature of bulk fluid, Btu/1b,

= temperature of f1u1d in81de tube, F,

t,
i
't = temperature of bulk fluid, °F,
vy ;_sPeciflc volume of bulk f1u1d, £t3 /1b,
_v, = specific volume of fluid in31de tube, ffi3/1b

.

 

. 6B. E. Short, "Flow Geometry and Heat Exchanger Performance " Chem.
En . Pro r., 61(7) 63- 70 (July 1965) , .

- 7H. S. Swenson, C. R. Kakarala, and J. R. Carver, "Heat Transfer to
Supercrltical Water in Smooth-Bore Tubes," Trans. ASME Ser. C: J. Heat

Transfer, 87(4): 477- 484_(November 1965) .

 
 

 

 

 

 

 

B e e 1 e 2 s et

20

The physical properties of supercritical fluid under various conditions
of pressure and temperature were taken from data reported by Keenan and
Keyesa. and by Nowak and Grosh.?

The pressure drops in the shell side of the exchangers were calcu-

lated by using Bergelin's equatidns.4

 

Vv 2 i
B
AP rossflow - 0'6er-2-g_c and (14)
OV
AR = (2 +0.6r) T - (15)
where
r = number of restrictions,

V_ = mean velocity, ft/sec,
Vg = cross-flow velocity, ft/sec.

Stress Analyses

Stress calculations were made for each of the heat exchangers. Where
possible, the shear stress theory of failure was used as the failure
criterion, the stresses were classified, and the limits of stress intensity
were determined in accordance with the methods prescribed in Section III
of the ASME Boiler and Pressure Vessel Code.?

The analyses were performed by treating thermally induced stresses
as secondary stresses in a single-cycle analysis rather than in a multi-
cyclic analysis. This procedure should assure adequate strength so that
future analyses based on cyclic considerations should not result in
severe revisions to the geometries of the exchangers. A departure from

the maximum shear stress theory of failure occurred in the analysis of

 

8J. H. Keenan and F. G. Keyes, Thermodynamic Properties of Steam,
John Wiley and Sons, New York, 1936.

2E. S. Nowak and R. J. Grosh, "An Investigation of Certain Thermo-
dynamic and Transport Properties of Water and Water Vapor in the Critical
Region," USAEC Report ANL-6064, Argonne National Laboratory, October 1959

¥
 

‘)

. o

o)

-

21

the tube sheets of the exchangers. These were analyzed by using the
maximum normal stress theory of failure and the allowable stress intensity
values applicable to an analysis based on the maximum shear stress theory
of failure. No consideration was given to the support of these vessels

or to the loads induced by piping restraints.

The thicknesses of the heads, shells, tube sheets, and tubes were
chosen to withstand the maximum pressure and thermal stresses at the
respective temperatures in the material. The exchangers were tentatively
designed, and the stresses caused by differential expansion and discon-
tinuities were checked to be sure that the allowable stress at the maximum
temperature had not been exceeded.

These analyses reported here are preliminary, but their extent is
considered sufficient to appraise'the‘integrity of the conceptual designs
for the heat exchangers. More rigorous analyses would be required to
investigaté cycling and off-deéign-point operations such as startup or a

hazardous incident.

 
 

 

 

 

 

 

22

4. DESIGN FOR FRIMARY HEAT EXCHANGERS

The four primary fuel-salt-to-coolant-salt heat exchangers are
shell-and-tube two-pass exchangers with disk and doughnut baffles. The
basic geometry of the top-supported veréical‘exchangers, the matefial to
be used to fabricate them, énd the size of the tubes were established by
the designers of the MSBR. The struéturél materiai selected for the pri-
mary exchangers was Hastelloy N, and the tube chosen was one with an out-
side diameter of 3/8 in. and a wall thickness of 0.035 in.

‘Case A

The criteria governing the design for the prifiary heat exchangers
for Case A that were fiied by the system are |
1. the temperatures and pressures of the incoming and outgoing coolant

salt,
2. the temperatures and pressures of the incoming and outgoing fuel salt,
3. the flow rates of the coolant salt and the fuel salt, and

the total heat to be transferred.

The design developed for the Case-A primary heat exchanger is shown
in Fig. 3. The exchanger is about 5.5 ft in diameter and 18.5 ft high,
including the bowl of the circulating pump. The inlet of the fuel-salt
pump is connected to the exchanger, and the fuel salt from the reactor
enters the exchanger from the 18-in.-diameter inner passage of the con-
centric pipes connecting the reactor and exchanger. The fuel salt flows
downward in the exchanger through the rows of tubes in the outer annular
section, and upon reaching the bottom of the shell, it reverses direction
and moves upward through the tubes in the center section.

The coolant salt enters the exchanger at the top and flows downward,
countercurrent to the flow of the fuel salt, through the center section.
Upon reaching the bottom of the shell, the coolant salt turns and flows
upward around the tubes in the outer annular section and leaves the

exchanger through the annular collecting ring at the top.

1

“6

.
 

 

 

 

 

 

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23

ORNL Dwg. 65-12379

     
  

| ]
R ',

FUEL SALT DUMP TANK

REACTOR | = ;4
;\\\\&“\\

FUEL SALT PUMP

4 "IIIII/"'
A7 7T

 

      
   

[/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

COOLANT SALT
->— FROM STEAM
‘ \ HEAT EXCHANGER
\_/ — -
FUEL SALT TO - I
REACTOR T 1]
; COOLANT SALT
. TO BLANKET
: HEAT EXCHANGER
/J’/
z & i :
DOUGHNUT BAFFLE L (I DISK BAFFLE
| LONGITUDINAL BAFFLE
LONGITUDINAL | [ TuBEs
BAFFLE L !
. [;:;7—7& RODS & SPACERS
CORE TUBE - il _ ANNULAR
SHEET -\ ! UBE SHEET
| :
N
I
N
. | N
EXPANSION __ - \
BELLOWS . . SHROUD
. . | T ’
COOLANT SALT DRAIN-" _ —FUEL DRAIN

Fig. 3. Primary Fuel-Salt-to-Coolant-Salt Heat Exchanger for Case A,

 
 

 

N

24

During the preliminary stages of the design for the Case-A primary
heat exchangers, a computer study was made to determine the effects on
the area of the heat-transfer surface of varying the pitch, the baffle |
size and spacing, and the ratio of the number of tubes in the two sections.
The computer code established the minimum baffle spacing limited by ther-
mal stress in the tubes and then increased the spacing as necessary to
remain within the pressure-drop limitations. The thermal-stress criteria
for the computer code were based on the worst possible conditions in
each section of the exchanger, and as a result, the annular section was
designed without baffles. It was therefore necessary to make 'hand"
calculations for an exchanger with several baffles in the bottom of the
annular section. This changed the baffle spacing in the center section,
the ratio of the tubes in the two sections) and the length of the
exchanger. The resulting design data for the Case-A primary exchanger

are given in Table 2.

Table 2. Primary Heat Exchanger Design Data for Case A

 

Type Shell-and-tube two-pass
vertical exchanger with
disk and doughnut baffles

3

 

Number required 4
Rate of heat transfer, each,

Mw 528.5

Btu/hr 1.8046 x 10°
Shell-side conditions

Cold fluid Coolant salt

Entrance temperature,oF

850

Exit temperature, °F 1111

Entrance pressure, psi 79.2

Exit pressure, psi 28.5

Pressure drop across exchanger, psi 50.7

Mass flow rate, lb/hr 1.685 x 107
Tube-side conditions

Hot fluid Fuel salt

Entrance temperature, °F 1300

Exit temperature, °F 1000

Entrance pressure, psi 85.8

Exit pressure, psi 0

Pressure drop across exchanger, psi 85.8

Mass flow rate, 1b/hr 1.093 x 107
 

 

T AL e g o

v po Rl R gt L € LR AR N L e

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Table 2 (continued)

 

Mass velocity, lb/hr ft?
Center section '
Annular section

Velocity, fps
Center section
Annular section

Tube material
Tube OD, in.
Tube thickness, in.

‘Tube length, tube sheet to tube sheet, ft

Center section
Annular

Shell material
Shell thickness, in.

| Shell ID, in.

- Center section
Annular section

Tube sheet material

Tube sheet thickness, in.
Top annular section '
Bottom annular section
Top and bottom center séction

Number of tubes
Center section
Annular section

Pitch of tubes, in.
Center section
Annular section

Total heat transfer area per exchanger,
£t° _ _

Center section
Annular section
Total a

Basis for area calculation
Type of baffle o

rNumber of baffles

' Center section -
Annular .section .

‘Baffle spacing, in.

Center section
Annular section

5.95 x 10°
5.175 x 10®

13.0
11.3
Hastelloy N
0.375
0.035

13.7
11.7

Hastelloy N
0.5

40.25
66.5

Hastelloy N

62
.75
0

oW

3624
4167

0.625

- 0.750

4875
4790
9665

Tube outside diameter

Disk and doughnut

27 .4
21

 
 

Table 2 (continued)

 

Disk OD, in.

 

Center section 30.6
Annular section 55.8
Doughnut ID,
Center section 25.0
Annular section 51.0
Overall heat transfer coefficient, U,
Btu/hr- ft2 ' 1106
Maximum stress intensity,a psi
Tube
Calculated P = 413; (Pm + Q) = 12,017
Allowable P =8 =4600; (P + Q) =
m m m
3s = 13,800
m
Shell
Calculated P = 6156; (Pm + Q) = 21,589
Allowable Pm = Sm = 12,000; (Pm + Q) =
3s_ = 36,000
m
Maximum tube sheet stress, psi
Calculated 10,750
Allowable 10,750

 

4The symbols are those of Section III of the ASME Boiler and
Pressure Vessel Code, where

Pm = primary membrane stress intensity,
Q = secondary stress intensity,
Sm = allowable stress intensity.

Case B

In the reverse-flow heat-exchange system of Case B, the fuel-salt
and blanket-salt flows were reversed from those of Case A, and the oper-
ating pressures of the coolant-salt system were increased. This involved
redesign of the primary heat exchanger, as well as some of the other
components of the system. The design for the primary heat exchanger for

Case B is illustrated in Fig. 4.

 
 

o

27

ORNL DWG 67-68!9

  
   
     
  
 
 

 

FUEL SALT DUMP TANK FUEL SALT LEVEL (DUMP)

FUEL SALT LEVEL

FUEL SALT FROM (OPERATING)

REACTOR

FUEL SALT PUMP

”»

EL SALT TO DRAIN TANK

od

FUEL SALT TO
REACTOR

COOLANT SALT FROM
STEAM HEAT EXCHANGER

DOUGHNUT BAFFLE

 

BAFFLE

")

TUBES

 

—COOLANT SALT TO
DRAIN TANK

: ; - COOLANT SALT
‘ ' TO BLANKET
HEAT EXCHANGER

 

i Fig. 4. Prifiary Fuel-Salt-to-Coolant-Salt Heat Exchanger for Case B.

 
 

 

 

 

28

As may be seen in Fig. 4, the flow of the fuel salt in the exchanger
for Case B is reversed from that in Case A, with the outlet of the fuel-
salt pump connected to the exchanger. Fuel salt enters the exchanger in
the inner annular region, flows downward through the tubes, and then
upward through the tubes in the outer annulér region before entering the
reactor. The coolant salt enters the exchanger through the annular
volute at the top. It then flows downward through the baffled outer
region, reverses to flow upward through the baffled inner annular region,
and exits through a central pipe. _

In this design, a floating head is used to reverse the flow of the
fuel salt in the exchanger. This was done to accommodate the differential
thermal expansion between the tubes and the shell and central pipe. The
expansion bellows of the Case-A design was eliminated, and.differential
thermal expansion between the inner and outer tubes is accommodated by
using sine-wave type bent tubes in the inner annulus and straight tubes
in the outer annulus. Doughnut-shaped baffles are used in both annuli.
Those in the inner annulus have no overlap so that the bent tubes have

a longer unrestrained bend.

Design Variables

 

Before making any detailed calculations for the design of the
primary heat exchanger for Case B, we fixed a number of the design vari-
ables on the basis of our own judgment.

Tube Pitch. As previously stated, the tubes in the inner annulus
are bent and those in the outer annulus are straight. To simplify the
bend schedule for the tubes in the inner annulus, these tubes are placed
in concentric circles with a constant delta radius and a nearly constant
circumferential pitch. The bends in the tubes are made in the cylindri-
cal surface that locates each ring of tubes. A radial spacing of 0.600
in. was selected for these bent tubes in the inner annulus as being the
minimum spacing practical for assembly. The spacing was increased to
0.673 in. in the circumferential direction because the distance between

the tubes at the bends is somewhat less than the circumferential pitch.
 

 

 

 

S gy e e

 

e

LY

[

Y

29

The tubes in the outer annulus are located on a triangular pitch.
The dimension for this pitch, 0.625 in., was selected on the basis of
the calculations done for the Case-A primary exchanger. This spacing
resulted in an efficient use of the shell-side pressure drop.

Number of Tubes. The number of tubes in each annular region is

 

determined by the allowable pressure drop on the inside of the tubes.
Since for Case B, the heat-transfer efficiency of the inner annulus
needed to be lowered to minimize the temperature drop across the tube
walls, the number of tubes chosen for the outer annulus was less than
the number chosen for the inner annulus. This number of tubes in the
outer annulus was further reduced until all of the allowable pressure
drop for the fuel salt was utilized. The resulting number of tubes in
the outer annulus was 3794 with 4347 tubes in the inmer annulus.

Lengths of Annular Regions. The length of the exchanger and the
number and size 6f the baffles determines the flow conditions for the
coolant-salt pressure drops and the heat-transfer coefficients. Prelim-
inary calculations showed that the exchanger would be approximately
15 ft long, with a recess of about 1 ft for the pump. A l4-to-15 ratio
was established for the lengths of the inner and outer annuli.

Baffle Spacing and Size. The baffle spacing in the inner annulus
is limited by the length required for the unrestrained bends in the
tubes and the maximum allowable temperature drop across the tube wall.
The use of smaller distances between baffles results in larger outside
film coefficients and-therefére’smallef'film drops. This increases the
temperature drop across'the'ffibe wall. The number of baffles selected
for use in the inner annulus was four.

In the outer annulus, an atfiempt'was made to select the baffle size

- and spacing combinations that wbuld result in efficient use of the avail-

able shell-side pressure drOp,?xTen baffles were used in the outer

annulus.

 
 

 

30

Calculatory Procedures

 

After selecting the just-described design variables, the pressure
drops, the required length of the exéhanger, and the stresses in the
tubes were calculated for the selected conditions, and these conditions
were adjusted where necessary. Then the thicknesses required for the
shell, skirt, tube sheets, and head of the exchanger were calculated.

The detailed heat-transfer, pressure-drop, and stress-analysis calcula-
tions are given in Appendix A.

Pressure Drops. The pressure drops for the selected conditions were
calculated, and where necessary, these conditions were adjusted to obtain
the allowable pressure drops. The pressure drops inside the tubes were

calculated by using Fanning's equation,
4fL G
di ngc

P = pressure, psi,

 

where

f = friction factor
= 0,0014 + (0.125/NRe° 32}
L = length of tube, ft,
d. = inside diameter of tube,
G = mass velocity, 1b/hr-ft?,
p = density, lb/ffi3,

g = gravitational conversion constant, 1bm-ft/1bf-sec?.

The pressure drops in the coolant salt outside the tubes were calcu-

lated by using Bergelin's equatioms.?

 

v 2
B
= 0.6rp =— and
Pcrossflow e ch
oV
APwindow =(2+ O'GrW) ch ?

 

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

"

v
 

 

 

a

o

°

31

number of restrictions,

2]
i

V_ = mean velocity, ft/sec,

Vp = cross-flow velocity, ft/sec.

These equations déveloped by Bergelin were the result of his experimental
work with straight-edged baffles. However, we decided that the flow
conditions for doughnut baffles would be similar to those for straight-
edged baffles and that the same pressure-drop equations would be appli-
cable.

Length of Exchanger. The required length of the exchanger for the

 

selected conditions was calculated, and the selected conditions were
adjusted until the calculated length equaled the assumed length. Six
equations that state the conditions necessary for heat balance in the
exchanger were combined, which resulted in a single equation with the
length of the exchanger as a function of all the other variables. The
development and use of this length equation is given in more detail in
Appendix A.

Stress in Tubes. The stresses in the tubes were calculated, and if

 

the allowable stresses were exceeded, the selected conditions were

changed to lower the stress. The conceptual design for the exchanger

was analyzed to determine the stress intensities existing in the tubes

of the exchanger that were caused by the action of pressure, thermal

gradients, and restraints imposed on the tubes bj other portions of the

exchanger. The’majorrstresées_pr@dueed in the tubes are

1. primary membrane stresses caused by pressure,

2. secondary stresses causédrbthemperature gradients across the tube
 wall, . | |

3. discontinuity'stfesses'at the junction of the tube and tube sheet, and

'4, secondary stresses at the mid-height of the inner tubes caused by

differential expansion of the inner and outer tubes.

The analysis of the 1nnér_tubeé,fias*made by using an energy method with

a simplified model of the tubes. These calculations for the stresses

are given in more detail in Appendix A.

 
 

 

 

 

 

32

Thicknesses. The thicknesses required for the shell, skirt, tube
sheets, and head were calculated. The conceptual design for the
exchanger was analyzed to determine the stress intemnsities or maximum
normal stresses existing in the heat exchanger shells and tube sheets
that are caused by the action of pressure and to determine the loads
caused by the action of other portions of the exchanger. The major
stresses in the shell are
l. primary membrane stresses caused by pressure and
2. discontinuity stresses at the junction of the tube sheets and shell.
The inlet and exit scrolls or toroidal turn-around chamber were not con-
sidered in this analysis. The shear stress theory of failure was used
as the failure criterion, and the stresses were classified and the limits
of stress intensity were determined in accordance with Section III of
the ASME Boiler and Pressure Vessel Code.

The tube sheets were designed by using the maximum normal stress
theory of failure and ligament efficiencies based on Section VIIXI of the
ASME Boiler and Pressure Vessel Code. The tube sheets were considered
to be simply supported, and the pressure caused by the tube loads and
pressures were used to determine a uniform effective pressure to be used

in this analysis.

Results of Calculations

 

The calculations described in the preceding paragraphs are given in
detail in Appendix A, and the resulting design data for the primary heat

exchanger for Case B are given in Table 3.
 

¢

»

oy

)

Table 3. Primary Heat Exchanger Design Data for Case B

 

Type

Number required

Rate of heat transfer, each

Mw
Btu/hr

Shell-side conditions
Cold fluid

o
Entrance temperature,

Exit temperature, ©OF
Entrance pressure, psi
Exit pressure, psi

Pressure drop across exchanger, psi

Mass flow rate, lb/hr

Tube~side conditions
Hot fluid

Entrance temperature, °F

Exit temperature, OF
Entrance pressure, psi
Exit pressure, psi

Pressure drop across exchanger, psi

Mass flow rate, 1b/hr
Tube material
Tube OD, in.

Tube thickness, in.

Tube length, tube sheet to tub

Inner annulus
Quter annulus

Shell material
Shell thickness, in.
Shell ID, in.

Tube sheet material

Tube sheet thickness, in.

Top outer annulus
- Top inner annulus
Floating head

Number of tubes
Inne: annulus
Outer annulus

e sheet, ft

Shell~and-tube two-pass
vertical exchanger with
doughnut baffles

Four

528.5
1.8046 x 1¢°

Coolant salt
850

1111

198

164

34

1.685 x 107

Fuel salt
1300

1000

146

50

96

1.093 x 107

Hastelloy N
0.375
0.035

15.286
16.125

Hastelloy N
1

66.7 _
Hastelloy N

W N~
« .
W nin

4347
3794

 
 

 

 

Table 3 (continued)

34

 

Pitch of tubes, in.
Inner annulus
Radial 0.600
Circumferential 0.673
Outer annulus, triangular 0.625
Type of baffle Doughnut
Number of baffles
Inner annulus 4
Outer annulus 10
Maximum stress intensity,a psi-
Tube
Calculated Pm = 285; (Pm + Q) = 6504
Allowable .Pm = Sm = 5850; (Pm + Q) =
3s = 17,500
m -
Shell
Calculated P = 6470; (Pm-+ Q) = 9945
Allowable P =8 =18,750; (p_+ Q) =
SSm = 56,250
Maximum tube sheet stress,
calculated and allowable, psi
Inner annulus 3500
Outer annulus 17,000
Floating head 10,000

 

%The symbols are those of Section III of the ASME Boiler and

Pressure Vessel Code, where

Pm primary membrane stress intensity,

Q

S
m

1l

secondary stress intensity, and

allowable stress intensity.

 

 
 

 

o

C

i

4Y

-

)

35

5. DESIGN FOR BLANKET-SALT HEAT EXCHANGERS

Heat accumulated in the blanket salt while it is circulating around
the reactor core is transferred to the coolant salt by means of four
shell-and-tube one-shell-pass two-tube-pass exchangers with disk and
doughnut baffles. The basic geometry of the top-supported vertical
exchangers, the material to be used to fabricate them, the tube size,
and the approximate pressure drops were established by the designers of
the MSBR. All surfaces of the blanket-salt exchanger that contact
fluoride salts were to be made of Hastelloy N, the outside diameter of
the tubes was specified as 0.375 in., and the wall thickness as 0.035 in.
The blanket salt would circulate"inside the tubes and the coolant salt
through the shell. ‘The pressure drop in the tubes was to be approximately
90 psi,-an& the pressure drop in the shell would be about 20 psi.
Physical-property data pertalnlng to the blanket salt and the coolant
salt were also Supplled by the designers of the MSBR.

Case A

The criteria governing the design for the blanket-salt exchangers for
Case A that were fixed by their function in the overall system are the
inlet temperature of the blanket salt,
outlet temperature of the. blanket salt,
mass flow rate of the blanket salt, |
inlet temperature of the coolant salt,r
. .outlet temperature of the coolant salt,.

mass flow rate of the coolant salt, and

-~ O Ut P W N e

~ the total heat to be transferrred

®

~As shown in Flg. 5, the configuratlon of the blanket-salt heat exchanger
for Case A is simllar_to that ‘of the primary heat exchanger for Case A;
that is, two passee were used on the tube side with the tubes arranged in
two concentric regions'an& with,the'olanket-salt pump located at the top

of the inner annulus. The inlet of the blanket-salt pump is connected to

 
 

 

36

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

™ - ‘ ORNL Dwg. €5-12380

COOLANT SALT

TO STEAM HEAT
EXCHANGER

COOLANT SALT
FROM PRIMARY
EXCHANGER

BLANKET SALT ———— BLANKET SALT PUMP
FROM REACTOR
-~
=
X
BLANKET SALT l
TO REACTOR [
i =
il
f | !
HHinA
DISK BAFFLE |
;L | DOUGHNUT BAFFLE
L | !
i
1 i .
R
il -
DRAIN

TO BLANKET DRAIN TANKS

Fig. 5. Blanket-Salt Heat Exchanger for Case A.

4

]
 

 

 

 

 

 

'Y

‘:f

”n

£

%

37

the exchanger, and the blanket salt from the reactor enters the exchanger
and moves downward through the tubes in the outer annular region and then
upward through the tubes in the inner annular region to the pump suction.
Stralght tubes Wlth two tube sheets are used rather than U-tubes to permit
drainage of the blanket salt.

The coolant salt passes through the primary heat exchangers and the
blanket-salt heat exchangers in series. However, unlike the primary
exchanger, a single coolant-salt pass on the shell side of the blanket-
salt exchanger was judged adequate on the basis of the heat load, tempera-
ture conditions, and the adwantage offered by the simplificatioh of the
design for the exchanger. | :

Before any values could be generated for the designeof the blanket-salt
heat exchanger for Case A, it was necessary to tentatively-fix the values
of some additional design variables. From several approximations, a
triangular tube pitch of 0.8125 in. was chosen, and it was also decided
that there would be an equal number of tubes in.each annulus. Disk and
doughnut baffles were selected to improve the shell-side heat transfer
coefficient and to provide the necessary tube support. Baffles on the
shell side of the tube sheets reduce the temperature difference across
the sheets to keep thermal stresses within tolerable limits. An open-
area-to-shell~cross-sectional-area ratio of 0.45 was selected for the
baffles. o

With these data fixed, values were calculated for the

number of tubes per annulus, . . .
diameter of the shell,

size and spacing of the baffles,

thlckness of the_ tube sheEts,

1
2

3

4. length of the tubes,,

5

6. - thickness of the ‘shell, and
7.

1th1ckness and shape of the heads..

'These design values were dependent upon calculatlons -and upon an analysis
'of_the;ind1v1dua1 heat-transfer_coeff1c1ents,»she11-51de and tube-side

pressure drops,-andjthe;thefmal and mechanical stresses. The resulting

design data developed for the blanket-salt heat exchanger for Case A

are given in Table 4,

 
 

38

Table 4. Blanket-Salt Heat Exchangér Design Data for Case A

 

 

Type | | - Shell-and-tube one-shell-
- pass two-tube-pass exchan-
ger, with disk and doughnut

 

baffles
Number required 4
Rate of heat transfer per unit, - '
Mw | . 27.75
Btu/hr 9.47 x 107
Shell-side conditions _ '
Cold fluid ~~ Coolant salt
Entrance temperature, °F : 1111
Exit temperature, F 1125
Entrance pressure, psi , 26.5
Exit pressure, psi ' %
Pressure drop across exchanger, psi 17.5
Mass flow rate, 1b/hr 1.685 x 107
Tube-side conditions
Hot fluid Blanket salt
Entrance temperature, °F 1250
Exit temperature, F | 1150
Entrance pressure, psi 90.3
Exit pressure, psi 0
Pressure drop across exchanger, psi 90.3
Mass flow rate, lb/hr 4.3 x 10°
Mass velocity, 1lb/hr:ft3 10.48 x 10°
Velocity, fps 10.5
Tube material Hastelloy N
Tube OD, in. 0.375
Tube thickness, in. 0.035
Tube length, tube sheet to tube sheet, ft §.25
Shell material Hastelloy N
Shell thickness, in. 0.25
Shell ID, in. 36.5
Tube sheet material Hastelloy N
Tube sheet thickness, in. 1.0
Number of tubes 1641 (~820 per pass)
Pitch of tubes, in, 0.8125
Total heat transfer area, ft? 1330

Basis for area calculation Outside diameter
 

»

(fl

ar

"

39

Table 4 (continued)

 

Type of baffle
Number of baffles
Baffle spacing, in.
Disk OD, in,
Doughnut ID, in.

Overall heat transfer coeff1c1ent, u,
Btu/hr* ft°

Maximum stress 1ntensity, psi
Tube
Calculated

Allowable

Shell
Calculated

Allowable

Maximum tube sheet stress, psi
Calculated
Allowable

Disk and doughnut

3
24,75
26.5
23
1016
P =411; (P_+ Q) = 7837
P =85 =6500; (P_+Q) =
3s_ = 19,500
. m
= 1663; (P_+ Q) = 11,140
W = Sy = 12,0005 (P + Q) =
3s = 36,000
m
2217

5900 at 1200°F

 

2The symbols are those of Section III of the ASME Boiler and

Pressure Vessel Code, where

Pm = primary membrane stress intensity,
Q = secondary stress intensity, and
Sm = allowable stress intensity.

 Case'B

In'the re§erse-f1ow'heat exchange
blanket salt through the exchanger was

redesigned blanket-salt heat exchanger

*sysfen of Case B, the flow of the

reversed from fhafrof Case A, The

is 111ustrated in Fig, 6., The out-

let of the blanket-salt pump 1s connected to the exchanger and the blanket

salt enters the tubes in the 1nner annulus, flows downward, reverses:

: dlrectlon, and flows upward through the tubes in the outer annulus and

out to the reactor. The coolant salt from the primary exchanger enters

the bottom of the blanket-salt excharger to flow upward through a central

 
 

 

BLANKET SALT
TO REACTOR

BLANKET SALT
FROM REACTOR

12"NPS

 

 

8"NPS— T

 

DISK BAFFLE o

9'-¢ 34"
8'-3lo"

DOUGHNUT BAFFLE —]

 

22"NPS
\’

TO COOLANT
SALT PUMP

AND STEAM
HEAT -,j

EXCHANGERS
—_

 

   

 

 

 

 

40

 

ORNL DWG 67-6820

BLANKET SALT PUMP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

%
‘. 4" 1D,
) anffpan
,-4~\\ ,/
I'-10'0.D. A
;
. 1
|
|
— — 24" NPS
/-',”
| i
—
:EEf/
1 nll!l'” H
L TO BLANKET SALT
DRAIN TANKS
| (]I |

COOLANT SALT FROM FUEL

SALT HEAT EXCHANGER"

Fig. 6. Blanket-Salt Heat Exchanger for Case B.
 

 

¥

SR 41 0

pipe and then make a single pass downward on the shell side of the
exchanger before going out to the coolant-salt pumps.

A significant improvement over the Case-A design for the blanket-
salt heat exchanger uas the inclusion of a floating head in the Case-B
design to reverse the flow of the blanket salt in the exchanger. This
was done to accommodate thermal expansion between the tubes and the shell
and the central pipe. However, unlike the Case-B primary exchanger,
straight tubes are used‘in'both annuli of the blanket-salt exchanger for
Case B. Doughnut and disk baffles are also used in the design for the
Case-B blanket-salt heat exchanger. o |

The reversal of the flow direction of the blanket salt, the increase
in operating pressures, and the physical changes in the blanket-salt heat
exchanger did not influence its heat-transfer or pressure -drop character-
istics. Therefore, the calculatory procedures used to determine the
design variables for the Case-B blanket-salt heat exchanger were basi-
cally the same as those used for the Case-A exchanger. The heat-transfer
and pressure-drop calculations and the calculations performed for the
stress analjsis for the Case-B design are given in Appendix B.

The calculations performed to determine the number of tubes to be
used in each annulus of the Case-B blanket-salt exchanger were based on
the straightforward relationship between the mass flow rate, tube size,
linear velocity,'an& density. The number of tubes per pass resulting
from these caiculations was'810. Determination of the geometry of the
shells and baffles followed readily once the number of tubes was estab-
lished. | ‘ AT |

Calculating the baffle spacing and tube 1ength that fulfills the
heat-transfer and pressureedrop requirements-was,quite involved. The
heat transfer coefficient'for;the-hlanket'salt inside the tubes was
calculated by using an equation derived from heat transfer data on
molten salt prov1ded by MacPherson and Yarosh. - In this equation, the

heat transfer coefficient of the blanket salt 1nside the tubes,

 

'””IR;“E}iMacPhérsonrand'M; M}'Yarosh, "Development Testing and Per-
formance Evaluation of Liquid Metal and Molten-Salt Heat Exchangers,"
Internal Document, Oak Ridge National Laboratory, March '1960.

 
 

 

 

42

- k '\ .43 ]
h; = 0.000065 -&-i-(nma)1 Np, ¥ *

where
k = thermal conductivity, Btu/hr}ft2-°F per ft,
d; = inside diameter of tube,
Nke = Reynolds number,
Ny, = Prandtl number,

The value determined for h; was 2400 Btu/hr.ftZ.°F. The resistance
across the tube wall was then easily evaluated by using the conductivity
equation, and this was found to be 2.8 x 1074, | |

The first step in determining the heat transfer coefficient and the
pressure drop for the coolant salt outside the tubes was to plot a curvé
of the outside film resistance as a function of the baffle spacing. Data
for the curve were generated by calculating the outside film resistance
for various assumed baffle spacings. The method used was based on an
adaptation of the work on cross-flow exchangers done by Bergelin et al.®’
At this point, it was possible to establish whether the baffle spacing
was limited by thermal stress in the tube wall or by the allowable shell-
side pressure drop. The outside film resistance, R,» was evaluated for
the maximum temperature drop (46°F) across the tube wall, and the cor-
responding baffle spacing from the curve was approximately 6 in. The
pressure drop at a baffle spacing of 6 in. exceeded the allowable of
20 psi. Therefore, the pressure drop was limiting and the baffle spacing
was greater than 6 in.

The next step in the calculatory procedures was to develop the
equations given below that relate the baffle spacing, the outside film

resistance, and the shell-side pressure drop.

= 6.74 + (0.85 x 104)R0 »

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

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

 

»

Aj

43

where o |

L = length of the tube, ft, and

Ro = thermal fiifi'reSistance outside tubes,

1 c. 12 c \®
P =-§(0.32 x 10-6)(3336) + (%.- 1) (2.40 x 10'6)(3333) 5

where | '

P = shell-side pressure drop, psi,

L = length of tube, ft,

X = baffle spacing,

Gy = cross-flow mass velocity, 1b/hr- ft2,

G = mean mass velocity, 1b/hr- £t
These equations and the curve were then used to determine a baffle
spacing at which the shellFside pressure drop was within the maximum
allowable of 20 péi; Using four baffles at a spacing of 1.65 ft, the
pressure drop across the shell was 14.55 psi. With the tube length
established at 8.3 ft,‘the pressure drop through the tubes was determined
from the Darcy equation and‘found‘to be 90.65 psi.

Analysis of the thermal stresses in the exchanger required determina-
tion of the temperature of the salt between the tube passes. The tempera-
ture was evaluated by a trial-and-error calculation involving a heat
balance between the two tube passes, and its value was determined as
1184°F. |

The design data for the blanket-salt heat exchanger for Case B

that resulted from these calculations are given in Table 5.

Table 5. ’Blanket-Salt_Heat Exchénger;Design'Data for Case B

 

Type T T Shell-and-tube one-shell-

pass two-tube-pass exchanger
with disk and doughnut

| baffles
Number reduiréd-' -- ;1:_  o 4 |
Rate of heat transfer per unif,“ |
Mw . T - 27.75
But/hr _ - 9.471 x 107

 
 

 

44

Table 5 (continued)

 

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

b psi
Tube~side conditions

Hot fluid

Entrance temperature, °F

Exit temperature, OF

Entrance pressure,? psi

Exit pressure,? psi

Pressure drop across exchanger,

Mass flow rate, lb/hr

Velocity, ft/sec

b psi

Tube material

Tube OD, in.

Tube thickness, in.

Tube length, tube sheet to tube sheet, ft
Shell material

Shell thickness, in.

Shell ID, in.

Tube sheet material

Tube sheet thickness, in.

Number of tubes
Inner annulus
OQuter annulus

Pitch of tubes, in.

Total heat transfer area, ft2
Basis for area calculation
Type baffle

Number of baffles

Baffle spacing, in.

Disk 0D, in.

Doughnut ID, in.

Overall heat transfer coefficieht, U,
Btu/hr- £t

Coolant salt

1111

1125

138

129

15

1.685 x 107

Blanket salt

1250
1150

111

20

91 e
4.3 x 10°
10.5

- Hastelloy N

0.375

0.035

8.3
Hastelloy N
0.25

40.78
Hastelloy N
1

810
810

0.8125
1318
Tube OD

Disk and doughnut

4
19.80
33.65
31.85
1027
 

 

o

0

45

Table 5 (continued) -

 

Maximum stress intensity,€ psi

Tube -
Calculated . , , . P = 841; (Pm + Q) = 4833
~Allowable , P =5 = 11,400; (P + Q =
- 38 = 34,200
Shell "
Calculated - ‘ P = 3020; (Pm + Q) = 7913
Allowable o = 5. =12,000; (P +Q =
o 3s_ = 36,000
m
Maximum tube sheet stress,
calculated and allowable, psi
Top annular 8500
Lower annular 6500

 

ncludes pressure caused by gravity head.
bPressure loss caused by friction only.

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

primary membréne stress intensity,

P =

m - - -

Q = secondary stress intensity, and
Sm = allowable stress intensity. |

 
 

 

 

46

6. DESIGN FOR BOILER-SUPERHEATER EXCHANGERS

Sixteen, four in each heat-exchange module, vertical U-tube U-shell
superheater exchangers are used to transfer heat from the coolant salt
to feedwater. The feedwater enters the superheater at a temperature of
700°F and a pressure of 3766 psi and leaves at a temperature of 1000°F7
and a pressure of 3600 psi as supercriticai fluid. The four superheater
exchangers in each module of the heat-exchange system are supplied by

one variable-speed coolant-salt pump. ' : | , .

Case A

The location of the four'9uperheater exchangers in each module of
the heat-exchange system for Case A is illustrated in Fig. 1. The
criteria governing the design for the boiler-superheater exchangers for
Case A that were fixed by the system are the
l. temperature and pressure of the incoming salt,

2. temperature and pressure of the outgoing salt,

3. temperature of the incoming feedwater,

4. temperature and pressure of the outgoing supercritical fluid,

5. maximum drop in pressure of the supercritical fluid acrbss the
exchanger,

6. flow rate of the salt, | : -

7. flow rate of the feedwater, and

8. the total heat transferred.

The type exchanger chosen for the system is a vertical U-tube one-
shell-pass and one-tube-pass unit, as illustrated in Fig. 7. The thbes
and shell are fabricated of Hastelloy N because of its compatibility with.
molten salt and the supercritical fluid. The U-shaped cylindrical shell
of the exchanger is about 18 in. in diameter, and each vertical leg is
about 34 ft high, including the spherical head. Segmental baffles were
used to improve the heat-transfer coefficient on the shell side to the ‘;;

extent permitted by pressure drop in the salt stream and thermal stresses
 

 

47

ORNL Dwg. 65-12383

SUPER CRITICAL SUPER CRITICAL
FLUID OUTLET - g FLuiD INLET

—TUBE SHEET

 

|||||n|n|,1,;1isf

|

 

BAFFLE

COOLANT SALT
OUTLET

  
 

COOLANT SALT _

INLET e

TIE ROD & SPACER

 

Ill

 

 

 

 

BAFFLES

 

|I

wn

 

 

 

 

" Fig. 7. Boiler-Superheater Exchanger.

 
 

48

in the tube wall. A baffle on the shell side of each tube sheet provides
a stagnant layer of salt that helps reduce stresses in the sheet caused
by temperature gradients. The coolant salt can be completely drained:
from the shell, and the feedwater can be partially removed from the tubes
by gas pressurization or by flushing. Compiete dféinability was not con-
sidered a mandatory design requirement. | _'
Design variables that had to be determined for the boiler-superheater
exchanger were the | :
1. number of tubes,
2. tube pitch,
3. 1length of tubes,
4. thickness of the wall,
5. thickness of tube sheet,
6. baffle size and spacing,
/7. diameter of shell,
8. thickness of shell, and
9. thickness and shape of head.
Because of marked changes in the physical properties of water as its
temperature is increased above the critical point at supercritical pres-
sures, the temperature driving force and heat-transfer coefficient vary
considerably along the length of the exchanger. This conditions required
that the heat-transfer and pressure-drop calculations for the superheater
exchanger be made on incremental lengths of the exchanger. N | s
Since the heat balances, heat transfer equations, and pressure drop
equations had to be satisfied for each increment and for the entire o
exchanger, an iterative procedure was programmed for the CDC 1604 com-
puter to perform the necessary calculations. Thisrprocedure varies fhe
number of tubes, the total length of the exchanger, and the number and
spacing of baffles to satisfy the heat-transfer, pressure-drop,iahd_
thermal-stress requirements. The input information, a simplified outline
of the program, and the output information are given in Appendix C. | |
The values for the physical properties of the coolant salt used in
the calculations were provided by the MSBR designers and are given in '
Table 1. The calculations of physical properties for supercritical ' QEJ

steam were included in the ¢omputer program as subroutines.  The values
 

 

n

o

"

49

for specific volume and enthalpy as functions of temperature and pressure
were taken from the work of Keenan and Keyes,! and the values for thermal
conductivity and viscosity were taken from data reported by Nowak and
Grosh.? | |

An adaptation of Eqs. 3 through 11 and Eqgs. 14 and 15 discussed in
Chapter 3 was used to calculate the shell-side heat transfer coefficients
and pressure drops. The heat transfer coefficient on the inside of the
tubes was calculated by using Eq. 13 given in Chapter 3. The pressure
drop on the inside of the tubes was calculated by using Fanning's equation,

with the friction factor,®

o Hi
f = 0.00140 + 0.125 F]_—G>

where
by = viscosity of fluid at temperature inside tube, 1b/hx-ft,
d. = inside diameter of tube, -
G = mass velocity, 1b/hr-£t®,

The thermal resistance of the tube wall was calculated for each
increment of tube length by using the thermal conductivity of Hastelloy N
evalnated at the average temperature of the tube wall of each particular
increment, The procedure.used to determine the allowable tefiperature
drop across the tube wall was based on the requirements set forth im
Section III of the ASME Boiler and Pressure Vessel Code. The thermal
stresses were treated as secondary membrane plus bending stresses with
the makifium'a11OWable'Galne"béinéiequal to three timesethe-alloweble

membrane'stresé for Hastelloy N minus the stresses caused by pressure.

 

. I7.:! HQ Keenan”and'F; G.'KeYes, Thermodynamic Properties of Sream,
John Wlley and Sons, ‘New York, 1936,
2E. §. Nowak and R. J. Grosh, "An Investigation of Certain Thermo-

‘dynamic and Transport. Properties of Water and Water Vapor in the Critical

Region," USAEC Report ANL-6064, Argonne National Laboratory, 0ctober 1959.

2J. H., Perry, Editor, P. 383 in Chemical Englneer s Handbook, 3rd
d.,. McGraw-Hill, New York, 1950.

 
 

 

50

From an equation reported by Harvey,4 the thermal stress,

aE(t - t) | 24 3
- —r—f(m-)]
2(1 - v) (}n -

 

w =

Oy = tangential or axial thermal stress in tube wall, psi,
@ = coefficient of thermal expansion, in./in.:°F,
= modulus of elasticity of tube, psi,
t. = temperature outside tube, °F,

t; = temperature inside tube, °F,

v = Poisson's ratio, '

d = outside diameter of tube,

d. = inside diameter of tube.
This equation and the allowable thermal stress as defined above were
used to calculate the allowable temperature drop across the tube wall.

The computer program was run for several cases to investigate the
parameters, and '"hand" calculations were made to check the program.
However, it should be noted that this work did not constitute a complete
parameter study or optimization of the design variables. The resulting
design data for the boiler-superheater exchanger for Case A are given

in Table 6.

 

4J. F. Harvey, P. 63 in Pressure Vessel Design, D. Van Nostrand
Company, New Jersey, 1963.

Table 6. Boiler-Superheater Design Data for Case A

 

Type U-tube U-shell exchanger with
cross-flow baffles
Number required 16
Rate of heat transfer, each,
Mw 120.9
Btu/hr 4.13 x 10°

 
 

 

o

51

Table 6. (continued)

 

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

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, 1lb/hr
Mass velocity, 1b/hr.ft?

Tube material
Tube OD, in.
Tube thickness, in.

Tube length, tube sheet to tube sheet,
ft

Shell material

Shell thickness, in.
Shell ID, in.

Tube sheet material

Tube sheet thickness, in.
Number of tubea o
Pitch of tubes, in.

Total heat transfer area, ffg

Basis for area calculation =

Type of baffle
Number of baffles
Baffle spacing

Overall heat ‘transfer - coeff1c1ent, U,

Coolant salt
1125

850

149

90.9

58.1

3.6625 x 10°

Supercritical fluid
700

1000

3766.4

3600

166.4

6.3312 x 10°

2.78 x 108

Hastelloy N
0.50

0.077

63.81

Hastelloy N
0.375

18.25
Hastelloy N
4.75

- 349

0.875
2915

‘Outside surface -
"~ Crossflow |
-9
- Variable
1030

 
 

52

Table 6 (continued)

 

' - - a
Maximum stress intensity, psi

Tube | o '
Calculated Pm = 6748; (Pm,+ Q) = 40,665
Allowable Pm = Sm = 16,0003 (Pm +Q =

3s = 48,000
m

Shell |
Calculated | P =3775; (P + Q) = 8543
Allowable o Sm = 10,500; (Pm + Q) =

3s = 31,500
m
Maximum tube sheet stress, psi
Calculated _ <16,600
Allowable 7 16,600

 

4The symbols are those of Section III of the ASME Boiler and
Pressure Vessel Code, where

Pm = primary membrane stress intensity,
Q = secondary stress intensity,
Sm = allowable stress intensity.

Case B

As previously discussed, the operating pressures of the coolant-
salt system were raised in the Case-B design for the heat-exchange
system. The coolant salt enters the superheater exchanger at the same
temperature as in Case A but at a pressure of 251.5 psi, a;d_it leaves
the exchanger at the same temperature as in Case A but at a pressure of
193.4 psi. Thus, the pressure drop across the exchanger, 58.1 psi, and
the heat transfer are the same for Case B as they are for Case A. How- |
ever, the difference between the pressure level in Case B and that for
Case A resulted in different stress intensities for the two cases. The
maximum pressure drop through the tubes was specified as 200 psi, but
this value had to be reduced to prevent exceeding the limitation placed on

the maximum height of the exchanger.
 

 

»)

9

o

bl

53

An analysis was made of the stress intensities in the tube sheets,
tubes, shells, high-pressure heads, shell-to-tubé-sheet junctions, and
tube-to~tube-sheet junctions. However, the discontinuity stresses were
not analyzéd atwthe'junctions of the high-pressure heads and shells or
at the junctions involving the entrance and exit of coolant salt or
supercritical fluid. These calculations performed for the Case-B
boiler-superheater exchanger are given in Appendix C, and the resulting
design data ére_given in Table 7. All other superheater design data

for Case B are the same as for Case A.

Table 7. Boiler-Superheater Stress Data for Case B

 

Maximum stress_intensity,a psi

Tube ,
Calculated A Pm = 13,843; (Pm + Q) = 40,662
Allowable o = Sm_= 16,000; (Pm + Q) =
38 = 48,000
m
Shell
Calculated o = 6372, (Pm + Q) = 14,420
Allowable o = Sm = 10,500; (Pm + Q) =
38 = 31,500
m |
Maximum tube sheet stress, psi
Calculated | ‘ <16,600
Allowable 16,600

 

aThe symbols are those of Section III of the ASME Boiler and
Pressure Vessel Code, where

P = primary membrane stress intensity,
Q =,sééfindafy_stress'inténsity, and
'S@ = allowable'stress-intensity.

- Case C .

VrnCase C-is'basically a modification of the Case-A heat-exchange system
that was studied briefly td_determiné the effect of having a coolant salt

with a lower liquidus point;' To study this condition, the temperature

 
 

 

54

of the feedwater entering the boiler superheater was lowered from'?OOoF‘»
to 580°F, and the entrance pressure was set at 3694 psi. ,With the feed-
water leaving the superheater as supercritical fluid at a témperaturé of
1000°F and pressure of 3600 psi, the coolant salt'ehtéring at.a tempera-

ture of 1125°F and a pressure of 149 psi leaves the exchanger at a tem-'

perature of 850°F and pressure of approximately 145 psi.

The computer program was used to size an exchanger for thesé condi-

tions, and the resulting design data for the Case-C boiler superheater

are given in Table 8.

Table 8. Boiler Superheater Design Data for Case C

 

Type

Number required

Rate of heat transfer, each
Mw
Btu/hr

Shell-side conditions
Hot fluid
Entrance temperature, °F
Exit temperature, °F
Pressure drop across exchanger, psi

Tube-side conditions
Cold fluid
Entrance temperature, °F
Exit temperature, °F
Entrance pressure, psi
Exit pressure, psi
Pressure drop across exchanger, psi

Tube material
Tube OD, in.
Tube thickness, in.

Tube length, tube sheet to tube
sheet, ft

Shell material
Shell thickness, in.

Shell ID, in.

Tube sheet matérial

 U-tube U-shell exchanger with

cross=-flow baffles
16

114.7
3.914 x 108

Coolant salt
1125
850
3.9

Supercritical f1u1d
>80

1000

3694

3600

9.4

Hastelloy N |
0.50

0.077

62.64

Hastelloy N
0.375

17
Hastelloy N
 

 

 

w}

[

n

"

55

Table 8 (continued) '

 

Number of tubes

Pitch of tubes, in.

Total heat transfer area, fto
Basis for area calculation
Type of baffle

Numbef of baffles

Baffle spacing, in.

Overall heat transfer coefficient, U,
Btu/hre ft®

323

0.875

2648

Qutside of tubes
Cross flow

3

Variable

785

 

 
 

 

56
7. DESIGN FOR STEAM REHEATER EXCHANGERS

Eight, two in each module of the heat-exchange eystem, vertical
shell-and~tube exchangers transfer heat from the.coolant salt to the
exhaust steam from the high-pressure turbine. The coolant salt enters.
the exchanger at a temperature of 1125°F and leaves at a temperature of

850° F, having elevated the temperature of the steam from 650 F to 1000°F.

Case A

The location of the two steam reheater exchangers in each module of
the heat-exchange system for Case A is illustrated in Fig. 1. The criteria
- governing the design for the reheater exchangers for Case A ‘that were
fixed by the system are the
1. temperature and pressure of the incoming salt,

2. temperature and pressure of the outgoing salt,
3. temperature and pressure of the incoming steam,
4. temperature and pressure of the outgoing steam,
5. flow rate of the salt,

6. flow rate of the steam, and

7 total heat transferred.

Following a procedure outlined by Kays and London,' we selected the
general type of exchanger to be used for these conditions. The reheater
exchangers are straight counterflow ones with baffles, as shown in Fig. 8.
The straight shell occupies less cell volume than a U-tube U-shell design
and requires slightly less coolant-salt inventory. The steam enters the.
bottom of the exchanger at a pressure of 580 psi, flows upward through
the tubes, and leaves the top of the exchanger at a pressure of 567.1
psi. The coolant salt enters the upper portion of the exchanger at a

pressure of 106 psi, flows downward around the tubes, and leaves the

 

1W. M. Kays and A. L. London, Compact Heat Exchangers, 2nd ed.,
McGraw Hill, New York, 1964.
»)

57

ORNL Dwg.65-12381:
STEAM OUTLET

TUBE SHEET

 

SALT INLET—

 

 

TIE ROD & SPACER

 

 

 

 

 

 

o
42 L

 

 

O

 

TUBULAR
SHELL

 

 

é | ('
218l TUBES

il

A ]

n’ %
1 ——DISC BAFFLE

; H==£‘

 

 

DOUGHNUT
. BAFFLE

 

 

 

 

 

—SALT OUTLET

 

 

 

 

 

 

 

 

 

 

 

 

 

 

| ~insucaTion BarrLe—il 1l
DRAIN LINE-
. \STEAM INLET

Fig. 8. Steam Reheater Exchanger.

L1

 

 

 

 
 

 

58

bottom portion of the exchanger at a pressure of 89.6 psi. A special
drain pipe at the bottom of the exchanger permits drainage of the coolant
salt.

Disk and doughnut baffles were selected for the exchanger because,
in our opinion, this design results in a more efficient exchanger than
one in which straight-edged baffles are used. Baffles on the‘shell side
of the tube sheets provide a stagnant layer of coolant salt to reduce
the thermal stresses in the sheets. The outside diameter of the tubes
stipulated by the designers of the MSBR is 3/4 in., and the tubes and
shell are fabricated of Hastelloy N because of its compatibility with
molten salt and steam.

The design variables that had to be determined for the steam reheater
exchanger were the
1. number of tubes,

2. tube length,

3. wall thickness of tubes,

4. baffle size and spacing,

5. thickness of tube sheets, and

6. thickness and shape of head.

To determine these variables, it was necessary to calculate the heat
transfer coefficients, pressure drops, and the thermal and mechanical
stresses. These calculations are given in Appendix D.

From a consideration of stresses caused by the temperatures and
pressures to be encountered, a tube wall thickness of 0.035 in. was cho-
sen. From the stipulated tube size (3/4 in. OD), the steam pressure drop,
and an assumed tube length, the number of tubes required was calculated.
This calculated value was corrected by iteration, and the number of tubes
was fixed at 628. A triangular tube pitch of 1 in. was selected, and the
- inside diameter of the shell was calculated to be 28 in. Then, by using
the Dittus-Boelter equation, Eq. 2 of Chapter 3, the heat transfer coeffi-
cient for the steam inside the tubes was calculated as 409 Btu/hr-ftZ.°F.

Design calculations for the shell-side flow of coolant salt were
somewhat more involved. Turbulent flow is desirable for good heat
transfer on the shell side. We therefore arbitrarily chose a Reynolds
number of 7500 for parallel flow through both the interior and exterior

»
 

 

 

"

o)

s

59

baffle windows. The Reynolds number chosen is well above the number at
the threshold of turbulence, and the resulting size of the exchanger is
not extreme. From this number and the mass flow rate fixed by the system,
the flow area in the two baffle windows was determined as 0.764 ft°.
Because we judged it to be good design practice and because it simplified
calculation of the shell-side heat-transfer coefficient, we made the
cross-flow area equal to the flow area through the baffle windows: 0.764
ft® . . Knowing the baffle sizes and pitch, we were then able to determine
the baffle spacing, which is 12.4 in. ‘

' The shell-side heat-transfer coefficient was calculated by using an
adaptation of Eqs. 3 through 11 discussed in Chapter 3, and this coeffi-
cient is 2240 Btu/hr'fta'oF. Knowing the shell-side heat~-transfer coef-
ficient, the heat-transfer coefficient for the steam inside the tubes
(409 Btu/hr £62.°7) the thermal conduct1v1ty of the Hastelloy N, and
the total heat transferred per hour in the exchanger, the length of the

tubes was calculated.

 

L = length of tube, ft,
U = overall heat-transfer coefficient, Btu/hr:ft®
a, = total heat transfer surface, ft®/ft,

t
n = number of tubes,
hi = heat-transfer coeffic1ent for steam inside tubes,

a; = heat,transfer surface inside tubes, ft2/ft,
k = thermal conductivity, Btu/hr.ft®.°F per ft,
T = thickness bf.tuBeifiéil5 in.,
. a_ =fmean heat-transfer surface, £t° [ft,
‘“ho #eheat -transfer coefflcient for coolant salt in shell,
ao-='she11-side heat transfer surface, £22 [fe.

-7.78 x 108
628

21.70 ft.

L . 01373 + 0.00150 + 0. 00227) ,

I

 
 

 

 

 

60

Conventional means were used to calculate the steam-side pressure
drop for the reheater exchanger, and the total was found to be 12 psi.
The pressure drop on the salt side was calculated by making use of an
adaptation of Eqs. 14 and 15 discussed in Chapter 3. The salt-side
pressure drop is 11.4 psi.

In designing the exchanger, a length of shell was allowed for the
inlet and outlet pipes that was somewhat larger than the bafflé sPacing.
This increased the overall length of the tubes from 21.7 and 22.1 ft.
This small increment in the length was neglected insofar as its effect
upon pressure, velocity, etc., is concerned. The Case A design data for

the steam reheater exchanger are given in Table 9.

Table 9. Steam Reheater Exchanger Design Data for Case A

 

Type - Straight tube and shell with
disk and doughnut baffles
Number required 8
Rate of heat transfer per unit,
Mw 36.25
Btu/hr 1.24 x 10°
Shell-side conditions
Hot fluid Coolant salt
Entrance temperature, °F 1125
Exit temperature, OF 850
Entrance pressure, psi 106
Exit pressure, psi 94.6
Pressure drop across exchanger, psi 11.4
Mass flow rate, lb/hr 1.1 x 10°
Mass velocity, lb/hr-ft® 1.44 x 108
Tube-side conditions
Cold fluid Steam
Entrance temperature, °F 650
Exit temperature, °F 1000
Entrance pressure, psi 580
Exit pressure, psi 568
Pressure drop across exchanger, psi 12
Mass flow rate, lb/hr 6.3 x 10°
Mass velocity, 1b/hr-ft® 3.98 x 10°
Velocity, fps 145
Tube material Hastelloy N
Tube OD, in. 0.75
 

 

 

)

n

B

61

Table 9 (continued)

 

Tube thickness, in.

Tube length, tube sheet to tube sheet, ft
Shell material

Shell thickness, in.

Shell ID, in. |

Tube sheet material

Tube sheet'thickness, in.
Number of tubes

Pitch of tubes, in.

Total heat transfer area, ft°
Basis for area calculation
Type of baffle

Number of baffles

Baffle spacing, in.

Disk OD, in.

Doughnut ID, in.

Overall heat transfer coefficient, U,
Btu/hr- £t2

’ * a’ -
Maximum stress intensity, psi
Tube
Calculated

Allowable

Shell
Calculated
Allowable

, Maximum tube sheet stress, p51

Calculated
Allowable_

0.035

22.1
Hastelloy N
0.5

28
Hastelloy N

4.75

628

1.0

2723

Outside of tubes
Disk and doughnut

10 and 10
12.375
24,3
16.9
285
P = 5243; (P + Q) = 15,091
P =S =14,500; (P + Q) =
3S_ = 43,500
m
P = 43505 (P +Q) = 14,751
P =8 = 10,600; (Pm +Q) =
3s = 31,800
m
9600
9600

 

" 2The symbols ‘are those of Section I11
~ Pressure Vessel Code, where

of the ASME Boiler and

primary membrane stress intensity,

P =

m

Q = secondary stress intensity,
S = allowable stress intensity.

m

 
 

 

 

62

Case B

In the Case-B design for the heat-exchange system, the operating
pressures of the coolant salt were raised. The coolant salt enters the
steam reheater exchanger at the same temperature as in Case A (1125°F)
but at a pressure of 208.5 psi, and it leaves the exchanger at fhe same
temperature as in Case A (850°F) but at a pressure of 197.1 psi. Thus,
the pressure drop across the exchanger, 11.4 psi, and the heat transfer
are the same for Case B as for Case A? but the difference between the
pressure levels of Case A and Case B resulted in different stress inten-
sities for the two cases. A

An analysis was made of the stress intensities existing throughout
the reheater for the higher pressure conditions, but the effects of the
design for the coolant-salt entrance and exit pipes and the steam delivery
and exit plenums upon the shell stresses were not considered. These cal-
culations are given in Appendix D, and the resulting stress data are given
in Table 10. All other steam reheater design data for Case B are the

same as for Case A.

Table 10. Steam Reheater Stress Data for Case B

 

Maximum stress intensity,@ psi

Tube
Calculated P = 4349; (Pm + Q) = 13,701
Allowable P, = S, = 14,5005 (_+ Q) =
35 = 43,500
Shell
Calculated Pm = 6046.5; (Pm + Q =17,165
Allowable Pm = Sm = 10,600; (Pm + Q)=
BSm = 31,800
Maximum tube sheet stress, psi
Calculated <10,500
Allowable 10,500

 

#he symbols are those of Section III of the ASME Boiler and
Pressure Vessel Code, where

Pm = primary membrane stress intensity,

Q

S
m

secondary stress intensity, and

allowable stress intensity.

 
 

 

»)

n

»

&

"’

63

Case C

The Case-C modification of the Case-A design for the heat-exchange

system was studied to determine the effect of having a coolant salt with

a lower liquidus point. To effect this, the temperature of the steam

entering the reheater exchanger was lowered from 650 to 551°F, and the

entrance pressure was set at 600 psi.

With the steam leaving the reheater

at a temperature of 1000°F and pressure of 584.8 psi, the coolant salt

entering at a temperature of 1125°F and pressure of 106 psi leaves at a

temperature of 850°F and a pressure of 92.2 psi. The design data for the

Case=C reheater are given in Table 11.

Table 11. Steam Reheater Exchanger Design Data for Case C

 

Type

Number required

Rate of heat transfer, each
Mw
Btu/hr

Shell-side conditions
Hot fluid
Entrance temperature, F
Exit temperature, °F
Pressure drop across exchanger, psi

Tube-side conditions
Cold fluid _
Entrance temperature, OF
Exit temperature, °OF -
Entrance pressure, psi
Pressure drop across exchanger, psi

Tube material

‘Tube OD, in.

Tube thickness,-in.r , B

Tube length; tubé sheet to tube
- sheet, ft - - '

Shell materiél,

Shell thickfiess, in.

Shell ID, in.

Straight tube and shell with
disk and doughnut baffles

8

48.75
1.66 x 10°

Coolant salt
1125
850
13.8

Steam
551
1000
600
15.2

Hastelloy N
0.75

0.035

23.4

Hastelloy N
0.5
28

 
 

64

Table 11 (continued)

 

Tube sheet material

Number of tubes

Pitch of tubes, in.

Total heat transfer area, ft®
Basis for area calculation
Type of baffles

Number of baffles

Béffle spacing, in,

Disk OD, in.

Doughnut ID, in.

Overall heat transfer coefficient, U,
Btu/hr'fta

Hastelloy N
620
1

2885

Qutside of tubes
Disk and doughnut
13 and 14

10 |

21.3

18.5

289

 
 

 

 

+

£

65

8. DESIGN FOR REHEAT~STEAM PREHEATERS

Eight reheat—steam.preheaters; two in each module of the heat-exchange
system, are used-to heat the exhaust steam from the high-pressure turbine
before it enters the reheaters to assure that the coolant salt will not be
cooled below its liquidus point. The preheaters are part of the steam
power system, andsinee they do not come into contact with molten salts,
they are fabricated of Croloy. Being a part of the steam system, the
preheaters are unaffected By the Case-B design for the heat-exchange
system, and their design is the same for both Case A and Case B. Thus,
their location in a module of the system may be seen in either Fig. 1 or
2. However, the need for'the preheaters is eliminated in the Case-C
modification of the Case-A heat exchange system.

Throttle steam'or supercritical fluid at a temperature of 1000°F
and a pressure of 3600 psi is used to heat the exhaust steam from the high-
pressure turbine, and the preheaters had to be designed for this high
temperature and pressure; A conceptual drawing of the reheat-steam pre-
heater is shown in Fig. 9. The exchanger selected is a one-tube-pass
one-shell-pass counterflow type with U-tubes and U~shell. Selection of
a U-shell rather than‘a divided cylindrical shell permits the use of
smaller diameters for the heads and reduces the thicknesses required for
the heads and the tube sheets. Each vertical leg of the U-shell is about
21 in, in diameter and the overall height is about 15 ft, including the
spherical heads. Therétubes heve'an outside diameter of 3/8 in. and a

wall thickness of 0.065 in. They are located in a triangular array with

a pitch of 3/4 in. No baffles are used in this design, but the tubes are

supported at intervals. :
The supercr1tica1 fluid enters the head region, flows down through

the tubes, back up, and exits from the opposite head at a temperature of

869°F and a pressure of 3535 psi. The turbine exhaust Steam enters a side

rrinlet below the head at a temperature of 551°F and a pressure of 595 4 psi,

flows around the tubes countercurrent to the flow of the supercrit1ca1

fluid, and leaves the exchanger through a side outlet on the opposite leg

‘below the head at a temperature of 650°F and a pressure of 590 psi.

 
 

SUPER -CRITICAL
FLUID OUTLETY

STEAM INLET

reheat-steam preheater are given in Appendix E.

-
b

 

L

 

]
! l'
170590

 

 

Fig. 9.

 

3y

 

66

- (@) ? @ ‘ it'.j,f: s

 

 

\\
O
-

 

ORNL Dwg 6512382

  
  
  
  
    
      

TUBE SHEET

STEAM OUTLET

BY-PASS RING
TIE ROD & SPACER

TUBES

RING

  

Reheat-Steam Preheater Exchanger.

The heat-transfer and pressure-drop calculations made for the

The heat transfer coef-

ficient for the supercritical-fluid film inside the tubes was calculated

by using the Dittus-Boelter equation, Eq. 2 discussed in Chapter 3 of

this report. The reheat steam flows outside and parallel to the tubes,

and the heat-transfer coefficient for the film outside the tubes was cal-

culated by using both Eq. 2 and Eq. 12 of Chapter 3. Equation 12 gave the

most conservative value and it was used in the design calculations.

Pressure drops in the tubes and in the shell were calculated by using

the Darcy equation for the friction loss; four velocity heads to account

e g e ant i e bin

 

 
 

"

-

"

67

for the inlet, exit,iéfifl reversal losses; and a correction factor for
changes in kinetic energy between the ifiief and exit of the exchanger.

An analysis of fhe stress intensities in the tubes, tube sheets,
shells, and high-pressure heads and of the discontinuity-induced stresses
at their junctions was made. The discontinuity stresses at the junction
of the high-pressure head and the shell, the entrance line, and the exit
line were not considered in this analysis. These stress calculations are
also given in Appendix E, and the resulting design data for the reheat-

steam preheater are given in Table 12,

Table 12. Design Data for the Reheat-Steam Preheater

 

Type : One-tube-pass one-shell-pass
U-tube U-shell exchanger
with no baffles

Number required 8
Rate of heat transfer, each
Mw ' 12.33
Btu/hr 4.21 x 107
Shell-side conditions
Cold fluid Steam
Entrance temperature, °F 551
Exit temperature, °F 650
Entrance pressure, psi 595.4
Exit pressure, psi 590.0
Pressure drop across exchanger, psi 5.4
Mass flow rate, 1lb/hr 6.31 x 10°
Mass velocity, 1b/hr ft2 3.56 x 10°

Tube-31de condltlons.

Supercritical water

- Hot. fluid oL
Entrance temperature, F 1000
Exit temperature, °F 869
‘Entrance pressure, psi 3600
'Exit pressure, psi ' _ 3535
- Pressure drop across exchanger, psi 65
Mass flow rate, 1lb/hr. : 3.68 x 10°
Mass velocity, 1b/hr-ft® 1.87 x 10°
Velocity, fps 93.5
Tube material | | ' Croloy
Tube OD, in. | a | 0,375
Tube thickness, in., | 0.065
Tube length, tube sheet to tube sheet, 13.2

ft

 
 

 

68

- Table 12 (continued)

 

Shell material

Shell thickness, in.

Shell ID, in,

Tube sheet material

Tube sheet thickness, in.
Number of tubes

Pitch of tubes, in.

Total heat-transfer area, ft2
Basis for area calculation
Type of baffle

Overall heat transfer coefficient, U,
Btu/hr* £t2

Maximum stress intensity,? psi
Tube
Calculated

Allowable

Shell
Calculated

Allowable

Maximum tube sheet stress, psi
Calculated
Allowable

Croloy
7/16
20.25
Croloy
6.5
603
0.75
781
‘Tube OD
None
162

rJ
g
W

10,503; (P + Q) = 7080
s_ = 10,500 @ 961°F;
(Pm +Q = 3Sm = 31,500

g
]

14,375; (p_ + Q = 33,081
S = 15,000 @ 650°F;

m m

(¢, + Q = 35 = 45,000

i

7800
7800 @ 1000°F

 

SThe symbols are those of Section
Pressure Vessel Code, where

Pm = primary membrane
Q = secondary stress
Sm = allowable stress

III of the ASME Boiler and

stress intensity,
intensity, and
intensity.
 

 

H

 

APPENDICES

 
 

 
 

 

*y

 
 

o

0

”

H

71

Appendix A

CALCULATIONS FOR PRIMARY HEAT EXCHANGER

Pressure-Drop and Heat-Transfer Calculations for Case B

The Case B desigfi for the primary fuel-salt-to-coolant-salt heat
exchanger is illustrated in Fig. 4 of Chapter 4. The values assumed to
determine the design variables for this two-pass sheil-and-tube exchanger
with disk and dougfinut_baffles are tabulated below.

z(oa) = length of outerrannulus,= 16.125 ft,

z(ia) = length of inner annulus = 15.050 ft,

10,

N(ia) = number of baffles in inner annulus = 4,

N(oa) = number of baffles in outer annulus

X(oa) = baffle spacing in outer annulus = 1.466 ft,

X(ia) = baffle spacing in inner annulus = 1.466 ft and 3.396 ft,

P(oa) = tube pitch in outer amnulus = 0.625 in. (triangular),

P(ia) = tube pitch in inner annulus

= 0.600 in. radial and 0.673 in. circumferential,

tn(oa) = number of'tubes in outer annulus = 3794,

Deja) = number of tubes in innmer annulus = 4347.
The assumed length for £(g,5) of 16.125 ft resulted in a calculated length
of 16.11 ft., Therefore, the 16,125-ft length was used for the outer
annulus, and the resultiné length fer tfie-inner annulus was 15 050 ft.
With these variables establlshed, the pressure-drop and heat-transfer
calculatlons ‘were made, and the terms used in these calculations are

defined in Appendlx F.

Pressure-Drop Calculations

Calculation of the total pressure drop inside the tubes involved
the determinatlon of the pressure drop inside the tubes of both the outer
and inner annuli, and calculation of the total pressure drop outs1de the
tubes or on the shell side involved the determination of the shell-side

pressure drop in both the outer and inner annuli.

 
 

72

Pressure Drop Inside Tubes. The pressure drop inside the tubes in

the outer annulus,

 

AP 4fl.+2)c;2

i(o0a) = ( di p2gc )

f = the friction factor = 0.0014 + 0.125/(NRE)°'33,
L = length of tubes, ft, ‘
d; = inside diameter of tubes,
G = mass velocity of fluid inside tubes, 1b/hr-ft®,
p = density of fluid inside tubes, 1b/ft®, and

g = gravitational conversion constant, 1L ft/lbf sec® .

To determine the friction factor, the Reynolds number,
. _'diG
Re p '’

where

(=N
|
i

0.0254167 ft,

27 1b/ft hr, and

flow rate of fluid inside tubes/flow area,

where the flow area, A = 3794 tubes (5.07374 x 107* £t® [tube)
1.9250 £t2,

Q T
il

~1.093 x 107 1b/hr
- 1.9250 ft°
Therefore, Neo = 5345, and the friction factor,
f = 0.0014 + 0.125(5345)°° 32 = 0.009416.

5.678 x 10° )2
AP _ 14€0.009416) (16.125) 3.6 x 10°
i(oa) ™ 0.02542 -——-——-——(127)(144)64 7

= 5.678 x 10° 1b/ft? *hr.

54,69 psi.

For the pressure drop inside the tubes in the inner annulus,

Loja = 15:286 f¢,
Deia) = 4347, -
A = the flow area inside the tubes = 2.2056 ftZ,
Gy(im) = 4-956 x 10° 1b/ft® .hr,
Npe = 4665, and
f = 0.0014 + 0.125(4665)° 32 = 0.00981.

C

i
 

 

1]

F )

b

73

The total pressure drop inside the tubes,

8P4 (total) 54.69 + 41.19 = 95.88 psi .

Pressure Drop OQutside Tubes., The shell-side flow pattern of the cool-

 

ant salt in the primary heat exchanger is illustrated in Fig. A.1. The
horizontal cross-sectional portion of this illustration shows the outer
annulus, oa, to be divided into three types of flow regions, and these are
numbered 1 through 3 from the outside in. Flow region 2 or the middle
region is established by the overlap of the alternately spaced baffles,
and there is only cross flow in this region. Regions 1 and 3 consist of
baffle windows in which there is a combination of parallel and cross flow.

+

ORNL OWG 67-6566

  

 

! l_ INNER ANNULUS OUTER ANNULUS
' {ia) ~ {o@)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. A.1. Shell-Side Flow Pattern of Coolant Salt in Primary Exchanger.

 
 

 

74

From Eq. 15 in Chapter 3, the shell-side pressure drop in the window

region of the outer annulus,

 

, pv;f
APo(oa)s-l = (2 + 0.6rw3-1) ch s
where ,
r, = the number of restrictions in the window region,
p = the density of the coolant salt = 125 1b/ft®,
, = mean velocity of the fluid, ft/sec, and
. = gravitational conversion constant, 1bm°ft/1bf-sec3.

The volumetric flow rate of the coolant salt,

_1.685 x 107 1b/hr

q = 125 1b/EC (3600 sec/hr) = 37.444 £t [sec .

With the parallel-flow areas being based on a velocity of 15 ft/sec, the
average flow area in the outer annulus is the average of the cross-flow

and the parallel-flow areas.

Am = [SW(SB)P 5 2

where
Sw = the cross-sectional area of the window region
= parallel-flow areas in regions 3 and 1 = 2.496 ft3,
SB = the cross-sectional area of the cross~flow region
= cross-flow area in region 2 = 7,708 ft2.
Therefore,

Am = [2.496(7.708) °-% = 4.386 ft2 ,

and the mean velocity of the coolant salt in the outer annulus,

| 37.444
Vm = 386 = 8.537 ft/sec .

The number of restrictions in the window region,
D - D,
r = el
W~ 1.866p ’
where

the outside diameter of the outer annulus region,

o l-'-u Otj
wonou

the inside diameter of the inner annulus region, and

the pitch of the tubes,

AL
 

 

.

6

75

For outer.annulus region 3, _
__59.11 - 53.05

Ty = 1.866(0.625) ~ °-19%
and for the outer énnulus région 1,
66.70 - 61.39 _ 4.553 .

Tw = 1.866(0.625)
Therefore, the number of cross-flow restrictions in regions 1 and 3,

r, = (5,196 + 4.553)0.5 = 4.875 ,

3-1
The shell-side pressure drop in the outer annulus baffle window flow

regions 3 and 1,

125(8.537)3
2(32.2) (144)

+ 0.6(4.875
APo(oa)3_1 2 0.6(4.875)

I

4.838 psi .

From Eq. 14 in Chapter 3, the shell-side pressure drop in the cross-

flow region of the outer annulus,

NP =0.6rp—"""
o(oa)2 B ch

The velocity of the coolant salt in region 2,

37 .444 ft3 [sec

V="7.708 &

= 4.858 ft/sec ,

and the number of cross-flow restrictions in region 2,

_"}161;39‘- 59.11 -
Tp ©1.866(0.625) ~ 977 -

Therefore,
. 4.858)%
32.4) (144)

_APo(oa)z?qf6(1'955)(125) 2(

= 0.373 psi .

 As may be seen ih'Fig. A.1, the horizontal cross-sectional area of
the inner.annulus, ia, is diVided'roughly into two flow regions caused
by the alternate spacing of the'doughnfit baffles with virtually no
6ve£1ap. These two regions;'4 and 5, consist of baffle windows in which
there is a combination of parallel and cross flow. The cross-flow area

in the inner annulus is 15.856 ft2. The parallel-flow area in region 5

 
 

 

76

of the inner annulus is 4.529 ft®, and the parallei-flow area in region 4
of the inner annulus is 4.559 ft®, The average flow areas in region S

and &,

S5 = |4-529(15.856)]° ® = 8.474 £ and
s, = [4.559(15.856)| 5 = 8.502 £e2 .
m&4 ,
The mean velocities of the coolant salt in regions 5 and 4,
37.444 ‘ '
Vs = 5475 = 4-419 ft/sec, and

 

37.444
Vo = 5502 4.404 ft[sec .

The pressure drop in the window areas 5 and 4 of the inner annulus,
125(4.419)?

APO(ia)S = 2 + 0-6(15) 2(32.2) (144) = 2.895 pSi and
_ 125(4.404)%  _
o(1a), - 2 +0.6(10) 3533y (12 = 2-091 Psi -

To determine the total shell-side pressure drop in both the outer
and inner annuli, assume the pressure drop at the entrance and the turn-
arounds to be proportional to &P (0a) /restrictions. Thus,

2
r _+r
en turn

Men & turn = T, (AP2)

2.689 + 3.029
- 75 —(0.373) = 1.868 psi .

Assume a leakage factor of 0.52 for leakage between the tubes and baffles
and between the baffles and the shell. Then the total shell-side pressure

drop for both the outer and inner annuli,

= (ZAPOS + 2A.Po4 + 10AP0(3,1) + 11AP02 + 2AP )0.52

APo(l:ot:::x].) en & turn

[2(2.895) + 2(2.091 + 10(4.838) + 11(0.373) + 2(1.868)10.52
34,42 psi .

 

C
 

 

 

#

»)

L

77
Heat-Transfer Calculations

The heat transfer coefficients inside the tubes, across the tube
wall, and outside the tubes were determined for both the outer and inmer
annuli of the Case-B primary heat exchanger. The overall heat transfer
coefficients were then determined for both annuli, and these values were
used with the mass-flow and heat~transfer equations developed to deter-

mine the required length of the tubes for the primary exchanger.

Heat-Transfer Coefficients. From Eq. 1 in Chapter 3, the heat

transfer coefficient inside the tubes in the outer annulus,

d
_ k_ 1 .43 0.4 i
hi(oa) = 0.000065 di(NRe) ‘ (NPr) do

1.5 1.43[, 9;22) .4 0.30>
0.000065 Gg527(5345)t 42 {27 (1=22)] " (G538

1672 Btu/hr-£t2 -°F .

The heat transfer coefficient inside the tubes in the inner annulus,

1.43
hi(ia) 0'007806(NRe)

0.007806 (4665)* +43
1377 Btu/hr-£t?.°F ,

The heat transfer coefficient across the tube wall for both annuli,
d k

m
™ =qT
- __.0

- where

T = thickness,of.the'tubexwallnand x
d -4, |
sl 1
m . do
' lan;-. e
0.375 - 0.305
= 1',0.375
. _ . *"0.305
My = 70.375(0.0029167)

(11.6)

1

3602 Btu/hr-ft2-°F ,

 
 

78

From Eq. 4 in Chapter 3 where p, /u =1 for this case, the heat

transfer coefficient outside the tubes,

 

L% _ouer
o J[cul®/ " [0.41(012 ‘3/3
B 1.3
k ) _
= 0,1688GJ ,
where
— -0 382
for 800 < NRe < 10°, J = 0.346(NRe) .
— \ =0 456
for 100 < NRe < 800, J = 0.571(NRe) .

A leakage factor of 0.80 was assumed for leakage between the tubes and
baffles and between the baffies and shell. Thus, the heat transfer

coefficient outside the tfibes,
ho = 0.13504GJ .

For the heat transfer coefficient outside the tubes in the window regions

3 and 1 of the outer annulus, the mass velocity of the coolant salt in

 

 

the shell,
¢ - 168 x 10 Ib/br _ 3 8418 x 10° 1b/£6 hr
Gds  (3.8418 x 10°)0.03125
Npe = 22 = - = 10,005, and
J = 0.346(10005)=C 282 - 0.01024 .
Therefore,
ho(oa)3,1 = 0.13504(3.8418 x 10°)(0.01024)

5312 Btu/hr-£fe2-°F .

In the cross-flow region 2 of the outer annulus, the mass velocity of

the coolant salt in the shell,

1.685 x 107 1b/hr

 

 

G = =208 2 = 2.1860 x 10° 1b/ft® :hr ,
_2,1860(0.03125) _ -
Npe = 12 = 5693, and fiifi
J = 0.346(5693)° 382 - 0,01272 .
 

 

 

0

»

[

"

“annulus,

79

The heat transfer coefficient outside the tubes in region 2 of the outer

annulus, _
0.13504(2.1860 x 10°)(0.01272)

f

ho(oa)2
3755 Btu/hr-£t2-°F .

i

To determine the heat transfer coefficient outside the tubes in the
inner annulus, the average of the mean flow areas in regions 5 and 4 of

the inner annulus,
8.474 + 8,502

 

 

Am(ia) = > = 8.488 ft2
Therefore,
1.685 x 107 1b/hr ;
G = 2488 IS = 1.9852 x 10° 1b/ft? -hr ,
(1.9852 x 10°)0.03125
NRe T2 = 5170, and

J = 0.346(5170)° -382 - 0,01322 .

The heat transfer coefficient outside the tubes in the inner annulus,

ho(ia) 0.13504(1.9852 x 10°)(0.01322)

3544 Btu/hr-ft®.°F ,

Overall Heat Transfer Coefficients. The overall heat transfer

coefficient in the outer annulus,
1

1
My

The average heat-transfer coéffi¢iént'outside the tubes in the outer

,U(oa) I T L
h h

_ n(°a)311h°(°a)3 1 +n(°a)2h°(¢a)z
total n '

Cav 1" - (o0a)

_ 3155(5312) + 639(3755)
- 3794 L

 

5050Btu/hr- £2-°F .

 
 

80

Therefore,

1

Yoa) " T . _1 .1
1672 * 3602 ' 5050

= 931 Btu/hr-£¢2-°F .

The overall heat transfer coefficient in the inner annulus,

U _ 1
(ia) ~ _ 1 + 1 + 1
1377 ~ 3602 ° 3544

= 778 Btu/hr-£t2*°F .

Determination of Length of Tubes

The heat~transfer and mass-flow equations developed in the following

material were used to calculate the required length of the tubes in the

Case-B primary heat exchanger. The heat transfer rate in the outer

annulus,

e . = Uoa)A(oa) trx = tox) * C(F our = fc in)]
(oa) ~ 2

where

Btu/hr- £t2 - °F,

A = heat flow area in outer annulus, ft2,
(oa)

J

(A.1)

U(oa) = the overall heat transfer coefficient in the outer annulus,

tFx = temperature of the fuel salt at turnaround point in exchanger,
°F, ]
tCX = temperature of coolant salt at turnaround point, oF,
tF out = temperature of fuel salt at outlet, oF, s
! te in = temperature of coolant salt at inlet, °F.

@ The heat transfer rate in the inner annulus,

o 2 uats [CF 10 ° te our) * Crx - tor)]
(ia) 2

The total heat transfer rate,

Qtotal - Q(oa) * Q(ia) ’

e e i s e R e R 1 & e e

(A.2)

(A.3)
 

 

 

e e 11 e 8 B8 B0 5 5P 0111

L

»

»

o}

B

81

The heat transfer rate in the outer annulus,

Q(oa) = (ch)F(tFX - tF out) ?
and
Q(oa) - (ch)C(tCX - tC in) ?
where
(WCP)F = product of the flow rate, W, and the specific heat, CP,
»  for the fuel salt,
(WCP)C = product of the flow rate, W, and the specific heat, Cp,

for the coolant salt,
The heat flow area of the outer annulus,

where K; = a constant used for these equations only. By definition,

 

 

At C Ctpy -t (g our T BC i)
m(oa) 2 ’
and
At C(tp gn o oue? T (g 7t
| m(ia) 2 *

Substituting in Eq. A.1,

Q(oa) - U(oa)A(oa)Atm(oa) ?

and substituting Eq. A.6 intd'Eé. A.la,

 oay = Y(oa)®A(ia) tn(oa)

Similarly,

‘:- .Q(ia5giU(ia)A(ia)Atm(oa)'

Combining Eqs. A.1lb and A.2a and éliminating Acia)?
oy Qa)

'U(oa)Kiétm(oa) - U(ia)Amm(ia)

(A.4)

(A.5)

(A.6)

(A.l1la)

(A.1b)

(A.23)

(A.2b)

 
 

 

82

Substituting Eq. A.3 into Eq. A.2b,

Q(oa) _ thtal - Q(oa)
U(oa)Kiémm(oa) U(ia)A¢m(ia)

Qtotal

1 1
U(ia)Atm(ia)); U1a)®fm(ia)

Q +
(Oa) U(Oa) Kl Atm(oa)

o [2(ea)™ “n(oa) U (1) m(iay ]
total U, yRAL 02y * U(ia)Atm(ia)J

 

 

 

- Q = ’
(oa) U(ia)Atm(ia)
Q - q U(oa)K'lAtm(oa)
(oa) T Ntotal U(oa)KlAtm(oa) + U(ia)Atm(ia)
or '
Qtotal

 

Q = .
(o) 1+ UgiaK! ‘Atmgiaz\'
u(oa_) 1 Atm(oa)i

From Eqs. A.4 and A.5,

Q
t - _._LQEL_ and

t =
FX F out (ch)F

Q
-t —(oa)

CX C in (WCP)C

Subtracting,
1

1
(tex = ' out) = (tex = te i) = Uoa) (WCP)F ) WCe|

Defining a second constant used for these equations only,

1 1
K = -
(ch)F (ch)c

 

(A.7)
 

 

 

 

«)

»

83

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘Therefore,
bt Tex T ¥ Qoa) " "¢ in TR out (®.8)
From previously stated definitions
At (g gn 7 o out) * (trx = tox)
m(ia) _ 2
A;tm(o.a) (tFX - tCX) * (tF out tC in)
2
_ (tFX - tCX) + (tF in tC out) ' (A.9)
T (to, - ) + (t -t, ., ) ’
FX CX F out € in
Substituting Eq. A.8 into Eq. A.9,
- s . )
(ig) (Kaq(oa) tC in.+ tF out) tF in tC out
o Y + - ’
At (oa) (KQQ(oa) tc in T 'F out’ ¥ F out ~ fC in
or |
- : - + ¢t
Atoia) _%%a) " Fcin " "cout T 'F in " F out (A.10)
Atm.(oa) KBQ(oa) - th in * 2tF out
Substituting Eq. A.10 into Eq. A.7,
Q _ Qtotal
= _ - 2
(0a) 1+ U(ia) KéQ(oa) tC in tC out *tein T Y% oout
Yoa)™ % Qoa) " 2t6 5n * 2tF out
or S
\ t tal , |
Qoa) = == —— . (A.1D)
o ~ Q . F in F out C in C out
| 1+ Y(ia) (oa) K 5 _
U(Oa) 1” Q 2( F out tC in)
(oa) Ko '

Equation A.11 w111 be used - to determlne the heat. transfer rate in the

outer annulus, Q | Substituting into Eq A.6,
(0)

(oa) 3793 tubes (16. 125 ft)

( a) = 4347 tubes (15.286 ft) = 0.92045 .

K, =

 
 

84

Substituting values into the equation defining K;,

1 - 1

Ke = {1093 x 107)(0.55) ~ (1.685 x 107)(0.41)

i

2.1599 x 10~® ’
and into

Utia) 778

Uoayfs  931(0.92045) 0.90788 .

Substituting values in Eq. A.ll,

Q _ Qtotal
(oa) Q(oa)

 

-8
1 + 0.90788 2:1599 x 10

 

L , nga) + 2(1000 - 850)
| 2.1599 x 10-2
1.8046 x 10°
- 10 .
Q(oa) + (1.56952 x 10 )]

1+ 0.90788[ s
Qoay + (1-38895 x 107°)

By trial and error,
Uoa) = 8.9391 x 10° Btu/hr .
From Eq. A.3,
Qia) = Uotar " Q(oa)

1.8046 x 10° - 8.9391 x 108
9.1069 x 10° Btu/hr .

From Eq. A.4, t_ = 1149°F, and from Eq. A.5, t

 

 

FX cX
At _ (1149 - 979) + (1000 - 850) _
moa) ~ 2 -
and
At (1300 - 1111) + (1149 - 979) _
m(ia) = 2 -

The length of the tubes in the outer annulus,

 

160°F ,

179.5°F .

+ (1300 + 1000 -~ 850 =~ 1111)]

!
]

= 979°F. Then,

3}
 

 

 

 

v

»

85

L Qloa)
(oa) (oa) (oa)“d A":m(oa)

_8.9391 x 10°
3794(931) n(0.03125) (160)

16.11 £t .

Using the previously assumed ratio, E(ia)/z(oa) = 14/15 and adding 0.236 ft

for tube bends, the length of the tubes in the inner annulus,

 

14 ,
Lisa) 154  (0m) * 0+236

14 ' _

- [Ea6.1)] +o0.236 = 15.27 £e .
As a check, Q
L _ '(ia)
(ra) (ia) (i a) o m(1a)
9.1069 x 10°

 

4347 (788) (0.03125) (179.5) -~ 1>+%8 fe -

These calculated lengths may be favorably compared with the lengths assumed
L(oa) = 16.125 ft and L(ia) = 15.286 ft. After studying
the results of previous iterations, the lengths established for the tubes

for the tubes,

in the primary exchanger are

L = 16.125 ft and
(oa) ,

 Lyggy = 15.286 £t .

rsrress Analysis for Case B

The fuel salt enters the primary heat exchanger in the 1nner annular

7 region at a temperature of 1300 F and a pressure of 147 psi, flows down

through the 4347 bent tubes 15.05 ft, reaches the floating head at a
temperature of 1149°F and a pressure of 119 psi, reverses direction and
flows'upward through the 3794 straight tubes in the outer annulus 16.125 ft,

and leaves the exchanger at a temperature of 1000°F and a pressure of

 
 

 

e

 

 

86

50 psi. The coolant salt enters the exchanger through the annular volute
at the top, enters the outer annulus at a temperature of 850°F and a
pressure of 194 psi, flows downward to the bottom tube sheet, reverses
direction at a temperature of 979°F and a pressure of 181 psi, flows
upward through the inner annulus and exits into the céntral pipe at a
temperature of 1111°F and a pressure of 161 psi. The inside diameter

of the outer annulus of the exchanger is 66.7 in., the outside diameter
of the inner annulus is 53.05 in., and the outside diameter of the central
pipe is 22 in.

The stress analysis for the Case-B primary heat exchanger consisted
of a determination of the stresses produced in the tubes, the shells, and
the tube sheets. The shear stress theory of failure was used as the
failure criterion, and the stresses were classified and limits of stress
intensity were determined in accordance with Section III of the ASME
Boiler and Pressure Vessel Code. The terms used in these calculations

are defined in Appendix F.

Stresses in Tubes

The stresses developed in the tubes that were investigated are the

1. primary membrane stresses caused by pressure,

2, secondary stresses caused by the temperature gradient across the
tube wall,

3. discontinuity stresses at the junction of the tubes and tube sheets,
and )

4. secondary stresses caused by the difference in growth between the

tubes and the shell.

Primary Membrane Stresses. The primary membrane stresses caused
by pressure are the hoop stress and the longitudinal stress. The hoop
stress,

aapi - ?Po (p; - Po)a"be
r{ - £)

= +

oh™ "¢ - &

i)
 

 

 

 

$r

"

87

where
a = .inside radius of tube = 0.1525 in.,
b = outside radius of tube = 0.1875 in.,
P. = pressure inside tubes, psi,
= pressure outside tubes, psi,
r = radius of tube at point under investigationm, in.

0.023261=i - 0.03516Po (Pi - Po)(0.000819)

°hn T T 0.0119 * = (0.0119)

P, - P
i 0
1.954Pi - 2.955Po + 0.0688( = )

 

To obtain a maximum value, set ¥¥ = & = 0.0232,

O = 4.913Pi - 5.913Po
The longitudinal stress in the tubes was assumed to be caused by the
pressure drop in the tubes. The longitudinal stress,

£AP _ 0.02326AP
O, "% - £ - 0.01.19

1.954AP .

The tube-side and shell-side pressures, the pressure drop in the
tubes, and the calculated hoop and idngitudinal stresses at pertinent

locations are tabulated below.

Tube-Side nghelleSide Pressure Drop o.'
h L

 

 

P Pressure .  Pressure in tubes °
Location -+ (psi) @ - (psi) ~ (psi) (psi) (psi)
Outer tubes . L ,
Inlet - 119 - - 181 69 - =486 135
. Outlet - 50 o 184 | 69 -842 135
Inner tubes STt e - o
Inlet - 147 161 28 ‘ -230 55

Qutlet 19 - - 181 | 28 , -486 - 55

 
 

88

 

Secondary Stresses Caused by Temperature Gradient. The stresses at
the inside surface of the tube that are caused by the temperature gradient

across the wall of the tube,’

At%L T At’h T kAt[l - ?311}3?_{1“%)] ’

and the stresses at the outside surface of the tube that are caused by

the temperature gradient across the wall of the tube,

 

22 g]
at’L = ach T M‘t[l "F - @& "al
where ,
oE oE
k = = = 3.4505E
b - . . ?
2(1 - v) (ln-;] 2(1 -~ 0.3)(0.207)
Rw Rw
Attube = TR (ti - to) = Ri + R + R (ti - to)’
W o
R
- * R
avttube = to + R, + R + R (ti - to)'
i w o

The temperatures, resistances, and physical-property values at the
pertinent locations that are required to determine the secondary stresses
caused by the temperature gradient are given in Table A.l. Using the
values given in Table A.1l, the stresses calculated for the inside and
outside surfaces of the tubes at the pertinent locations are given
below.

Inside Surface Outside Surface

Aat%h AL at%n AL

_Location k. (psh) (psi) (psd)  (psi)

OQuter tubes

Inlet 688 -6660 -6660 +5721 +5721

Outlet 682 -5851 -5851 +5027 +5027
Inner tubes

Inlet 686 -6188 -6188 +5316 +5316

Outlet 688 -5600 =5600 +4811 +4811

 

13. F. Harvey, Pressure Vessel Design, D. Van Nostrand Company,
New Jersey, 1963.

At e i et e e e e
 

 

 

» -

'Table'A.1. -D5;a Required to Determine Secondary Stresses Caused by Temperature Gradient

 

 

e g o av At e
i o R R R tube tube a x 102_ E x 10
Location . (°F) . (°P) i W o (°F) (°F) (in./in. ' F) (psi)
Outer tubes . . " | ‘ _
- Inlet . - 1149 = 979  60. 28 20 1033 b4 7.52 26.5
‘Outlet = 1000 850 60 28 20 897 39 ' 7.27 27.2 ®
Inner tubes ~ - = -
~Inlet -~ 1300 1111 73 28 28 1173 41 7.77 25.6

- Qutlet 1149 = 979 73 28 28 1034 37 7.52 26.5

 

 

 
i st b s b s 3

 

90

Discontinuity Stresses. It was assumed that the tube sheet is very
rigid with respect to the tube so that there is no deflection or rotation
of the joint at the junction. The deflection produced by the moment,

AM’ and the deflection produced by the force, AF, must be equal to the
deflection produced by the pressure load, A?, and the slope at the junction

must remain zero. The deflection caused by pressure,

PP _ P2
Bp = 4Et T ET

and from pages 12, 126, and 127 in Ref. 2,rth¢ deflections caused by

the force and the moment,

b =@
and

AM=-2D;I3 )
where

. ___ET®
12(1 - v°) °

[&?{éfl]m = [(o.:;;?é%%oss)a];/‘ = 16.66.

Setting the deflection caused by pressure equal to the deflection caused
by M and F,

 

i

A

P2 _F - )M
ET - 2°p °

The slope produced by F must be counteracted by M;® that is,
F-ZAM=OI
Substituting for D and solving these last two equations for M and F,

P P
M—zha andF:l-

 

28. Timoshenko, Strength of Materials, Part II, 3rd ed., D.
Van Nostrand Company, New York, 1956.

O

 
 

 

wt

4

]

&

91

From page 271 in Ref. 3, the 1ong1tudinal stress,

_6M 3P
MUL = F (KT)B 8 824? ’

 

and the hoop stresses,

th =g Af =~ = 9.714?P ,
_2M .5 _Pr_ |

Mo'h— T?\_ T—4.587P s

h = u(MgL) = 2,647P

sec

The stresses calculated for the pertinent locations are tabulated below.
The stress values listed for the longitudinal stress component caused
by the moment, MO1. and the secondary hoop stress component caused by
the moment, heec’ are compre351ve on the inner surface of the tube
and tensile on the outer surface of the tube.

Differential o

 

 

Pressure MgL Mgh M hsec ' Fch
Location (psi) (psi) (psi) (psi)  (psi)
Quter tubes |
Inlet -62 547 -284 164 -602
Qutlet -134 1182 -615 355 -1302
Inner tubes
Inlet -14 124 -64 37 - =136

Outlet -62 547  -284 164 © -602

Buckling of Tubes Caused by Pressure. Where the external pressure
is greater than the internal'pressure, the'stress on the tube wall must
be checked to avert possible collapse of the tubes,

0 035

2(0.1875) = 0.0933 .

 

L.
5"

- From Flg. UG-31 in Section VIII of the ASME 3011er and Pressure
Vessel Code for T/D =0. 0933, the minimum design stress required to
match the design pressure d1fferentia1 at’ the pertinent locations and the
maximum allowable design stresses for{Hastelloy N are tabulated below.

 

3R, J. Roark, Formulas for Stresses and Straln, 3rd. ed., McGraw
Hill, New York, 1954.

 
 

 

92

 

 

S for
Minimum ¢ m '
AP Design Stress av T Hastelloy N
Location (psi) (psi) : (psi)
Inner tubes
Inlet -14 <1000 1173 - ~7000 .
Outlet -62 , ~1000 1034 >14000
Outer tubes | '
Inlet -62 ~1000 1034 - >14000

Cutlet -134 ~1400 897 >14000

Secondary Stresses Caused by Growth Difference. Since the average

temperature of the outer tubes is different than the average temperature

of the inner tubes, there will be different;al,growth,stresSes.

AL -.e_L = A+ L,

tT i i'i o0
where _
(AL = unrestrained thermal growth of length of tubes, |
€ = strain on tubes required by compatébility‘cdnditiOn,
L = length of tubes,
subi = inner tubes, and
sub = outer tubes.
where

o = normal stress and

 

E = modulus of elasticity of tubes.
Therefore,
o,L c L
ii o o
" &y tTE
and
ngo, =n.0

where n = the number of tubes.

 

 

_ 494
% " °
o
o,L n,o,L
1 i iio
tALi E tALo + n E ’

&
 

 

 

 

¥

"

¥

 

oi} niL
(—fi( +Li) = Oy = Ay o
) E( AL, tALO)
i n,L *
1 + L,
n i
O

From the hot length of the tubes, the mean temperature of the tubes, and
the coefficient of thermal expansion for the tubes, these data were

obtained for the Case-B primary heat exchanger.

AL, = 0,1067 ft and

t i

(26 x 10°)(0.1067 - 0,1189)

o =
i 4347(16.13) 15.05

3794

-9460 psi .

Since the sign is negative, this stress was assumed wrong and o4 is

tension.

_ 4347

= 3794 (9460) 10,838 psi (compression).

Compressive buckling might occur readily if the baffle spacing is large,

and the critical baffle spacing,

 

 

©EL
2
% Y _' |
(26 x 10%)(5 46 x 10-4) "
144(10838)(0 0119) =SB
X = 1.55 £t

This is_only slightly leSS'thanxthe bsffle schedule determined in the

_heat-trshsfer calculations and since buckling is of concern in this

"rrdesign, an analysis of the bent tube concept was made. The diagram

for this analysis is shown in Flg. A, 2

 
 

 

94

ORNL DWG 6€7-7057
X

S°IP
I
z

 

 

 

 

 

 

 

 

 

 

 

 

]
.C
Y
1
a
d
a
F
D
o\ o\ B
ds-Rde-\§/ )' d
= /‘\’\ — ds=Rd#
a B L
i
¢
Y E_gll— ¢
= |p

Fig. A.2. Diagram for Stress Analysis of Bent Tube Concept for
Case-B Primary Heat Exchanger.

M e e o

o
 

 

 

 

L

"

an

")

»

95

For this analysis, the energy caused by direct stress and shear

will be neglected. Therefore,

 

Because of symmetry,

Since Mo does no work,

du_,
éM .
| o
For 0 € X< ¢,
_ FX
Mo=M -

For c<X<c +§,

ME=Mo--§-(c+RsinB)-PR(l-cosB)

Nl

For c +5<X<c+d,

&
]

M - %(c +d- R sin 8) - P[2R(1 - cos @) - R(1 - cos 6)]

M0 --g-(c +d- R sin ) - PR(L + cos § - 2 cos B)

F is a dummy load used only to determine the honzontal movement of point

D. Therefore, the terms involving F are set as being equal to zero.

-2 n ErTodx+2fM_aMo i
- o ' c o

i

2] Mo(l)'dx +2'f[M0 -,PR(]._'- cos B)](1) Rdp
, 0

o

9 f[Mo - PR(1 + cos 0 = 2'cos.a’)] (1) (R) (-d8) ,

 
 

 

 

96

and 3
u
EX SN 0.
Mo
Therefore,
C o
f Modx + Rf(MD - PR + PR cos B)dB
o o

o

+R[(Mo-PR-PRcose+2PRcosa)d9=0,
o

Mc+RMQ- PRRQ + PR sin « +'M0Ra - PRPQ
- PRsin ¢ + 2PRPC cos @ = 0 ,

_ 2PRa - 2PRPQ cos O
o c + 2RO

_ 2PRQ(l - cos 0)
- c + 2Rx ’

 

The deflection of point A in the direction of P,

Therefore,
Ju o oM
EIBP—EI'yp—Z M de+2 M‘SEdS.
o o
Since Mo has been determined, for 0 < X < ¢,

_ 2P0 - 2PRRQ cos ¢

 

 

 

M c + 2R
and
B}g‘l-, _ 20 - 2FRa cos a
P~ c + 2Ry ?
d
forc<X<c+-i,
2PRPQ - 2PRPO cos O
M, = 5 - PR + PR cos B

"

"
 

 

 

Q@ .

"

"

H

n

9

W

97

or
M, = 2PR2Q cos B + PRc cos B - PRc - 2PRQ cos O
c + 2RO

and o S
ng ZR'aO! cos B + Re cos B - Re - 2 cos O
P c + 2RO ?

and for c + 5 < X< c + 4,

Nl

2PRRQ - 2PRQ cos O

 

« PR - PR cos © + 2PR cos O

 

% = ¢ + 2R
or __ o |
2P Q cos O + 2PRc cos & - PRc - PRc cos 6 - 2PReQ cos O
Y = c + 2R
and

oM, _ 2Rx cos o + 9Rc cos & - Re = Rc cos 6 - 2@ cos 6
oP c + 2RY

Thus, the expression for EISP,

 

c
EIBP = 2P {ZRea(l - cOS CX)]a f dx
o
2pPR® o
P ) - . 2
T (c + 2RO)? I (2Rl cos B + c'cos B - ¢ - 2RX cos Q)°dP
o
‘ a
+ __2PR (2RO cos O+ 2c cos & - c - ¢ cos § - 2R cos §)7d8
(c + 2RQ)Z :
. . o - . B
After expansn.on and integration, : '
: _PR* |
ETS, = 0% zm)g f(R a, ) |
PRt 4c2a
=Ty 2Ra)2 L(SROP + R + 8& c) cos Za

- (12R05"2 + 1206c + —) sin 20 + (S@C)cosaa

 

- (160? c",-'l- cos o

+ (16RP + 24cfc-+ 1oc2a)]

 

 
 

 

The differential tube growth,

p = B T ALy

= 0.1189 - 0.1067 = 0.0122 ft or 0.1464 in.

&

Bending the inner tubes and solving for the maximum moment present in

these tubes,

_ 2PRa - 2PRQ cos O

M = 2Ry - PR=-PRcos ©® + 2PR cos O .

i

o
Setting 6 = 0,
c + RO
Ms = -2PR(1 - cos a)(c TR C

The maximum flexure stress,

-2PR(1 - cos S

M
Z = Z ’

Uflex

and
EIBP(c + 2RQ)?

P - E .
[£(R, @, ¢)]
Assume that the maximum offset is 8 in, Then,

2R(1 - cos 6) 8 .

Assume that O = 30o = 0.5236 radians.

2R(1 - 0.866)

]
<o
-
»

 

= 29.2 in . =

When R = 30 in., the offset = 2(30)(0.134) = 8.05 in.

2R sin @
2(30)(0.5) =_30 in,

d

Since 2(d + ¢) =72 in., the value ¢ = 5 in. was used. For the tubes

in the inner annulus,
E = 26 x 10° psi

 
 

 

3

B

n

v}

»

99

and

n(rt - 1) _ 2[(0.1875)* - (0.1525)*]
4 = %

0. 78539(0 0012359 - 0 0005408)

5. 458 x 1o~* in.*

1

ll

Solving for P,

(26 X 105)(5 45 x 10=*)(-0.1464)[5 + 2(30) (0. 5236) F

P = T 30)% [E(R, @, ©)]

-3.3963 o
= 173.97] = =0.0459 1b (tension) .

6.865)[ 5 + 30(0.5236) ]

-2(-0.0459) (30) (1 .5 + 2(30)(0.5236)

M

20.708
36.416

(0.3675) = 0.20898 in.-1b.

The flexure stress,
| Mc  (0.20898) (0.1875)

Oflex = I = ~5.458 x 10—~

and the stress inside the tubes,

o; = +58.36 psi .

The direct stress,

Odirect = & = 7(0.0119) - ‘123 psi

which is negligible.
Secondary Stress Caused by Pressure. The longitudinal load on the

tubes caused by the pressure different1a1 on the bottom floating head,

' *a'APF = (191 = 119) (area of’head - annulus drea + area of tubes)
= 72[(number‘of tubes)(enclosed area of tubes)]
- 72[ (3794 + 4347)(0.11045)] =
B = 64,740 lfin(cbmpfessive) . ;.
" Thefefofeg': - |  __ _"H" |
.APUL = 72 péi (compréssifié) on all the tubes.

 
 

 

100

Stresses in Shell

The stresses produced in the shells are
1. primary membrane stresses caused by pressure and

2. discontinuity stresses at the junction of the shell and tube sheet.

Primary Membrane Stresses. It was assumed that the outer shell of
the exchanger is 1 in. thick. The hoop stress component,

_ APD _ 194(66.7) ..o .
p°h =21 - T 2(n - 40 st

and the longitudinal stress component,

POy = 82D - 3235 pst .
For the inside shell separating the inner annulus and the central
tube by which the coolant salt leaves the exchanger, the hoop'stress
component,

_APD _ (171 - 0)(22)

P°h = T3T = 2(0.25) - 124 pst,

and the longitudinal stress component,

=57 = 3762 psi .

For the l-in.-thick shell separating the outer and inner annuli,

the hoop stress component,

APD  (~194 + 161)(52.5) _

P = 2T = 20D = -866 psi ,

and the longitudinal stress component,
PoL = 433 psi .
For that portion of the separator shell above the head of the inner annulus,

the hoop stress component,

_ 194(52.5) _

and the longitudinal stress component,

"
 

 

$

N

.

»

101

Discontinuity Stresses‘in'SheliLat.Junction of Shell and Tube Sheet.
It was assumed that the tube sheet is very_rigid with respect to the
shell. Therefore, the deflection and_rotation of the shell at the joint
are zero. The reactions on the shell from the tube sheet are the moment

and the force,

where

Therefore,
194 .
- M= 7000485y = 2003 in.-1b/in. ,
and

194 _ .
F 093 _882 ib/in.

For the outer shell of the exchanger, the secondary longitudinal stresses,

O =

ML -%? 2003 = 12024 psi (ten511e inside,

compressive outside) ,

and the hoop stresses,

3607 psi (tensile inside,

 

v°h = D(MGE) = 0.3(12024) = . -
sec - compressive outside)
_ 22 2(2003) (0.0484) _ 194 psi (uniform tensile) ,

M°h = T 1 o
_-ZFKr _ 2(882)(0 22)(66 7)
FR=" 71 = 2(1) = .— 12939 psi (uniform compressive)
The inner she11 between the inner annulus and the central tube 1s
strictly a tube that will be affected greatly by the method of anchorage
and the final design of the exchanger. Therefore, the secondary dis-
continuity stresses for “the - inner shell or tube were not considered in
this analysis._ _ CLe
For the upper portion of the separator shell above the top of

the inner annulus head, the constant,

 
 

 

 

102 |
12(1 - 0.$)12 /2
A = [735733573352] = 0.251 .

P 194

 

M= 213 = 300.0630) = 1939.6 1n.-1p/1n._,
and
P __194
F=3=5251" = 772.96 1b/in.

The secondary longitudinal stresses,"

oL = I? 1539 9237.8 psi (compressive 1ns1de,
tensile outside) »

and the hoop stresses,

 

 

 

 

M°h = U( ) = 2771.3 psi (compressive inside,
sec tensile outside) s
2
h = ZM% - 2(1339. *)(0 063) | = 194 psi (uniform compressive) »
£op = ZFgr _ 2(772.92{{?.25l)(52.5) = 10186 psi (uniform

tensile) .

Stresses in Tube Sheets

The tube sheets included in this analysis of the Case-B primary
heat exchanger are the top sheet for the outer annulus, the top sheet
for the inner annulus, and the bottom sheet across both outer and inner

annuli.

 Outer Annulus Top Tube Sheet. The acting pressure, AP = 194 psi on
the top tube sheet of the outer annulus, and the area of action for this

pressure,

A

i

i
915.55 in.*

A.o - A - AT = 3500 - 2165 - 3794(0.11045)

‘The resulting force,

F = APA = 194(915.55) = 177,617 1b ,

B e a3 o

e
 

 

o

»

»

%)

»

103

and the uniformly distributed effective pressure,
OP = 177617/1334.8 = 133 psi .
The ratio of'fhbhaVefagé ligamenf stress in the tube sheets, which are
strengthened and stiffened by the rolled-in tubes, to the stress in
flat unperforated plates of like dimensions equals the inverse of the
ligament efficiency if the inside diameter of the tubes is used as the
diameter of the penetrations (page 106 in Ref. 1); that is,
| B %y p ‘
- = - 2
B = the inverse of the ligament efficiency,:
o' = average ligament stress in tube sheet,
o = stress in unperforated plate, |

‘tube.pitch,

o
]

di;=;inside diameter of tubes.

The inverse of the ligament efficiency,

0.625 0.625

P =10.625 - 0.305) ~ 0.370 = 1?7 -

The value of 2.0 was used for B: To determine the thickness required for

the outer annulus upper tube sheet,
S _ prpa? |
2" -

ié“;'ZQAPA?'

- S

‘From Case 76 in Ref. 3, p = 0.03 for D__fP.- = 66.7/52.5 ~ 1.27, and at

a téfipérature.of,10009F,'thé éllowable_stress, S = 17,000 psi. Therefore

= _ 2(0.03)(133)(66.7)> 35,501 _
19_ o0 T T 17',000*._.2_.02_3 .

The thiéfinéés fiéed;-T'= 1;5 in;   _J'

 
 

 

 

104

Inner Annulus Top Tube Sheet. _The acting pressure,‘AP'=_161 - 147

= 14 psi, and the area of action for this pressure,

i
1287.3 in.?

A= A - A - A, = 2165 - 397.6 - 4347(0.11045)

The resultant force,
F = APA = 18,022 1b ,
and the uniformly distributed effective pressure,:

18022
1767 .4

 

The inverse of the ligament efficiency

0.674

At Dia/Dcenter tube = 52.5/22 = 2,386, B ~ 0.2438; and at a temperature
of 1300°F, the allowable stress, S = 3500 psi. Therefore, the required

thickness of the inner annulus top tube sheet,

_ 2pAPA?
T =5

_ 2(0.2438) (10.2) (52.2)3

3500 = 3.92‘1n.

The thickness used, T = 2.5 in,

Bottom Tube Sheet. The actingrpressure on the bottom tube sheet,
AP = 181 - 119 = 62 psi, and the load caused by the tubes = 0. The
effective pressure, |

— _ ,,[3500 - 398 - (0.11045)(3141)]
& - 62f 3500 - 398

44 psi .

For Doa/Dcenter tube = 66.7/22 = 3.03, p = 0.306; and at the operating
temperature, the allowable stress, S = 10,000 psi. Therefore, the
thickness required for the bottom tube sheet,

i
 

 

 

 

9

o

»

w)

105

AD AS
= ZBA§A

2(0.306) (44) (66.7)°

75 000 = 11.88 in.
2>

I}

The thidckness used, T = 3.5 in.

Further analysis of the deéign for the Case-B primary heat exchanger that
includes stress concentration, non-uniform loading, edge restraints, and
thermal stresses will be required when the désign is finalized and

cyclical considerations are investigated.
Sfimfiary of Célculated Stresses

Calculated Stresses in Tubes. The values calculated for the stresses
that are uniform across the tube wall and their locations are given in
Table A.2. The calculated stresses on the inside and outside surfaces
of the tubes are given_ih Table A.3, and the calculated stress intensities
for fhe'tubes'aré compéréd with the allowable stress intensities in
Table A.4. o |

Table A.2. Calculated Stresses Uniform Across Tube Wall

 

 

 

| - M%h %L ?°n APYL Fh
Location _(psi) (psi)  (psi) (psi) (psi)
Inner tubes L - o - : ‘ |
Inlet -64 .. 55 -230 -72 =136
Mid-height @~ 55 -358 -72
Outlet .284 55 -486 -72 -602
" Quter tubes o _ _
Inlet . =284 . 135 - . =486 @ =72 -602

- Outlet =615 135 - =842 ~72 -1302

 

 
 

 

Table A.3. Calculated Stresses on Inside and Outside Surfaces of Tubes

106

 

 

o .
ML Mheee at%L ath - AL
Location (psi) (psi) (psi) (psi) (psi)
Inner tubes inlet ' - :
Inside surface - =124 «37 -=-6188 -6188
Qutside surface +124 +37 +5316 +5316
Inner tubes mid-height
Inside surface -5894 «5894 +58
Outside surface +5064 +5064 +72
Inner tubes outlet '
Inside surface -547 -164 -5600 =-5600
OQutside surface +547 +164 +4811 +4811
Quter tubes inlet
Inside surface =547 -164 -6660 -6660
Outside surface +547 +164 - 45721 +5721
Outer tubes outlet
Inside surface -1182 =355 ~-5851 -5851
Qutside surface +1182 +355 +5027 +5027

 

0w
»

 

v | ‘ n o . "

Table A.4. Calculated Stress Intensities for Tubes of Case-B Primary
Exchanger Compared With Allowable Stress Intensities

 

 

 

 

Primary Secondary and Cyclic
o - : ¢ Euhl ‘ ZUL Scr Pm ' Sm Zch EUL Zar +Q+F ‘SSm;
Location CrR (psi) (psi) (psi) (psi) (psi) (psi) (psi)  (psi) (psi) (psi)
Inner. tubes inlet ‘ ' - '
Inside surface =~ 1203 -230 55 =147 285 5850 -6655 -6329 =147 6504 17,500
Outside surface 1157 -230 55 -161 285 8050 +4923 +5423 -161 5584 24,150
Inner tubes mid-height '
Ingide surface 1133 =359 55 -133 414 9850 -6252 -5957 -133 6119 29,550
Outside surface 1088 -358 55 -171 414 14000 +4706 +5104 -171 4933 42,000
Inner tubes outlet . .
Inside surface 1062 =486 55 «119 541 15050 -7136 ~-6164 -119 7017 45,150
Outside surface 1020  -486 55 -181 541 16400 +3603 +5341 -181 5522 49,200
Outer tubes inlet ' o
Inside surface 1065 -486 135 -113 621 15050 -8032 -7144 -119 7913 45,150
Outside surface 1016 -486 135 ~-184 621 16400 +4513 +6331 -181 6521 49,200
Quter tubes outlet
Inside surface 924 «B42 135 -50 977 17650 ~8965 -6970 =51 8914 52,950
6466 54,300

Outside surface 880 -842 135 ~198 977 18100 +2623 +6272 -194

 

LO1

 
L)

108

Calculated Stresses in Shells. The stresses calculated for the
shells of the exchanger are given in Table A.5, and the calculated
stress intensities for the shells are compated with the allowable stress

intensities in Table A.6.

Table A.5. Calculated Stress for Shells of Case-B Primary Exchanger

 

 

n

PL ?°h P°r F°h ¥h oL Wh oo
Location (psi) (psi) (psi) (psi) (psi) (psi) (psi)
Top outer shell
Inside surface +3235 +6470 -194 -12939 +194 +12024 +3607
Outside surface +3235 +6470 -0 -12939 +194 ~12024 -3607
Top separator shell
Inside surface +2546 +5092 -194 +10186 =194 -9238 ~-2771
Outside surface +2546 +5092 ~0 +10186 -194 +9238 +2771
Mid-height inner shell :
Inside surface +3762 +7524 -166
Qutside surface +3762 +7524 -173

 

"0
 

 

”

 

Table A.6. Calculated Stress Intensities for Shells of Case-B Primary
Exchanger Compared With Allowable Stress Intensities

 

 

t P S 20 20 Zo P +Q+ F 38 -
- “max m m h L r ‘m T . m
Location CF)__ (psi) _ (psi) (psi) (psi) _ (psi) (psi) ~  (psi)
Top outer shell S
Inside surface 850 6664 18,750 -2668 +15259 ~-194 17,927 56,250
Outside surface 850 6470 18,750 -9945 -8789 ~0 9,945 56,250
Top separator shell - | R
Inside surface 850 5286 18,750 +12313 -6692 -194 19,005 56,250
Outside surface 850 5092 18,750 +17855 +11784 ~0 - 17,855 56,250
Mid-height inner shell
Inside surface 1111 7690 12,000
Outside surface 1111 7697 12,000

 

L

60T

 

 
 

 

110

Calculated Stresses in Tube Sheets. The tube sheet thicknesses,

maximum calculated stresses, and allowable stresses are tabulated below.

 

 

Maximum Allowable
Tube Thickness Calculated Stress Stress
Sheet (in.) - (psi) (psi)
Top outer annulus 1.5 <17,000 17,000
Top inner annulus 2.5 <3,500 3,500
Lower 3.5

<10,000 10,000

 

¥y

 
 

 

 

 

0 .

0

9

[

111

Appendix B

CALCULATIONS FOR BLANKET-SALT HEAT EXCHANGER

Heat-Transfer and Pressure-Drop Calculations for Case B

Each of the four modules in the heat-exchange system has one blanket-
salt exchanger to transfer heat from the blanket-salt system to the coolant-
salt system. The heat load per unit, Qt’ is 9.471 x 107 Btu/hr.

' The conditions stipulated for the tube-side blanket salt were an inlet

temperature of 1250 F,-an'outlet temperature of 1150° F, a temperature drop

-of 100°F, and a2 maximum pressure drop across the exchanger of 90 psig.

Other criteria given for the blanket salt were the flow rate through the
(e = 4.3 x 10° 1b/hr and the total velocity, V, = 10.5 ft/sec.

Certain properties of the blanket salt vary almost linearly with tempera-

core tubes, W

ture and pressure. Therefore, average conditions may be used without
serious error. These average conditions for the blanket salt were
density, p= 277 1b/ft3;

viscosity, u = 38 1b/hr-ft;

thermal conductiv1ty, k = 1.5 Btu/hr £t2 -°F per ft; and

lspec1f1c heat, Cp 0.22- Btu/lb °F.

The conditions stipulated for the shell-side coolant salt were an

N

inlet temperature of 1111°F,'anzoutlet-temperature of 1125°F, a tempera-
ture increase of 14°F, and a maximum pressure drop across the exchanger

of 20 psig. The mass flow rate of the cold fluid, Wefs, was given as

1. 685 X 107 lb/hr The aVéfége.conditions given for the coolant salt

we re

1. p = 125 1b/fe3,

2, po=12 1b/hr.ft, e

3. k= 1.3 Btu/hr£¢®- °F per ft, and
4. C = 0.41 Btu/1b-°F.

The material to be used for the tubing was spec1f1ed as Hastelloy N,
and the tubes were to have an out31de diameter of 0.375 in. and a wall

thickness of 0.035 in. A triangular pitch was chosen and set at 0.8125 in.

 
 

 

112

The baffle cut, Ew’ or the ratio of open area of the baffle to the cross
sectional area of the shell required for the tubes was established as
0.45. -

Geometry of Exchanger

The reverse-flow exchanger has a 22-in.-0D pipe in the center through
which coolant salt from the primary fuel-salt-to-coolant-salt exchahger
enters the shell. This central pipe is surrounded by an annular area for
the tubes. Two tube passes with an equal number of tubes in each pass are
used against a single-pass shell with disk and doughnut baffles. The
geometry of this arrangement was calculated as follows, and the terms used
in fihe equations are defined in Appendix F.

The number of tubes in outer pass, n, = number of tubes in inner

 

 

 

pass, n_.
Wtc
na = nc = 70 2
VT Z di p (3600)
_ 4.3 x 10° (144) - 810
~ (10.5) (0.7854) (0.305)2 (277) (3600) ’
| 2

The area required for tubes = (810 + 810){2A866)(0'8125) = 6.43 ft2.

The area of the center pipe =(0.7854)(1.833)2 = 2.64 ft2.
The total cross-sectional area = 6.43 + 2,64 = 9.07 ft2.
The diameter of the shell,

9.07 |1 /2
D, = (m) = (11.548)/ 2

= 3.398 ft or 40.776 in.
The diameter of the doughnut hole,

_[2.64 + (0_.45)6.43]1/3
a = U 0.7854

2.654 ft or 31.852 in.

D

The diameter of the disk,

_ [9.07 - 10.45)6.43]1/3
Dop = 0.7854

2.804 ft or 33.653 in.

 

i%

0

 
 

 

o

7

&

+

»n

113
Heat Transfer Coefficient Inside Tubes-

The Reynoldsrnumber'was4calcu1ated from given data,

95V (0.305) (10.5) (277) (3600)

 

Using Eq. 1 discussed in Chapter 3, the heat transfer coefficient inside
the tubes,
= k_ 1 .43 0.4
hi = 0.000065 di (NRE) _ (NPr) -
_ - 1.5 x 12 1 .43 0.22 x 38 c .4
- 0.000065(———— 25 )(7000) (——-—-—-——-1_5
= 0.00384(314,000)1.99

2400 Btu/hr.ft®°F .
The thermal resistance inside the tubes,

0.375

V.o -4
1 = 72400 (0.305) - >-12 x 10

R

Thermal Resistance of Tube Wall

The thermal conductivity of Hastelloy N tubing in the temperature
range of calculation is 11.6 Btu/hr°ft3-°F per ft. Therefore, the thermal

resistance of the tube wall,

do
S ma
R = T
0.375) 1o o522
- 302 _ 5 8 x 10 .

 

“52(12)11.6 -

Shell-Side Héat Transfer Coefficient and Pressure Drop

" The Béff1e 駧§ing and therefore the number of b#ffles determines
'the;heat transfer coefficient outside‘the;tubes, ho,rand the shell-side

pressure drop, AP. Using Eqé. 3 thrbugh 11 discussed in Chapter 3,

 
 

 

114

which were developed from the work of Bergelin et al,'’® to determine
the shell-side coefficient in cross-flow exchangers, the outside film
resistance was calculated for various assumed baffle spacings. A curve
of outside film resistance versus baffle spacing was then plotted from
the data developed; 'The average cross-sectional flow area, AB, per

foot of baffle spacing, X, was first determined for rows of tubes in

%)

(2 654 + 2, 804){1 . __0.375 ]
2 (0.9) (0.8125)J

(3.1416) (2.729) (0.487) = 4.175 £t [ft .

The cross-sectional flow area in the window section was then determined.

the cross-flow section.

A (D +D“

 

X

]

w 144
2.335 fe2 .

The Prandtl number was calculated from given data,

w, )2/ = [i(l—zl]a/3 2.43

o = 9:43011620) 14 g660.8125)% - 0.7854(0.375)3]

To calculate the outside film resistance, Rb’ various baffle
spacings, X, were assumed. For X = 0.74 f¢t,
the average cross-sectional flow‘area,

Ap = 4.175(0.74) = 3.09 ft2;
the mass velocity of the cross-flow sectionm,

o - 1:685 x 107
B - 3.09

the mass velocity of the window section,

1.685 x 107
2,335

 

= 5.45 x 10° 1b/hr-£63;

G = = 7.22 x 10° 1b/hr-£t3;
w

 

10. P. Bergelin, G. A. Brown, and A. P. Colburn, "Heat Transfer and
Fluid Friction During Flow Across Banks of Tubes -V: A Study of a Cylin-
drical Baffled Exchanger Without Internal Leskage," Trans. ASME, 76: 841-
850 (1954).

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

 

i
 

 

 

o

the

the

the

the
the
the

the

the

the

the

115

mean mass velocity,
Gm = 6.275 x 10° 1b/hrft?;
Reynolds number for the cross-flow section,
)y = (0,375)5.45 x 10°
Re’B 12(12)
Reynolds number for the window section,

_ (0.375)6.275 x 10°
Mpedy = 12(12)

heat transfer factor,
= 0 .382,
J = 0.346/(N ) ;

= 16,350;

heat tranfer factor for the cross-flow section,

Jg = 0.00895;

heat transfer factor for the window section,
J_ ='0.0085;
W

heat transfer coefficient for the cross-flow section,

c 6
_ B _ (0.41)5.45 x 10°
8~ Jp Tfi;fiTF?T = 0.0089>5 2.43

8230 Btu/hr-£t®-°F;
heat transfer coefficient for the window section,

5 (0.41)6.275 x 10°
2.43

heat transfer coefficient outside the tubes,

h_ = [hy(1 - 2Fy) + h _(2F )1B,,

 

h

h = 0.008 = 9000 Btu/hr-ft2-°F;

where B

1l

y, = leakage correction factor' »2 because the heat

transfer equations are based on no leakage
=0.8,

[8230(0.1) + 9000¢0.9)10.8

7140 Btu/hr-£t? -°F; and

_thermal res;stance;pf the butside film,

o ‘ B

When X = 1.48 ft,

Ay = 4.175(1.48) = 6.18 £¢2,

 
 

 

 

 

116

1.685 x 107

 

 

 

 

GB ==¢18 - 2.73 x 10° 1b/hr-ft3,
G =7.22 x 10° 1b/hr-£t3,
G = 4.46 x 10° 1b/hr-£e2,
_ (0.375)2.73 x 105 _
(Npedp = 12(12) = 7100,
_ (0.375)4.44 x 105 »
(Np)y, = 12(12) = 11,500,
Jg = 0.0117,
J = 0000972’
w i
h, = 0.0117 LQ:4102:73 x 107 _ 5390 pyy fhre £e3 . OF,
B 2.43
_ (0.41)4.44 x 10° cee2 .0
h = 0.00972 T3 = 7280 Btu/hr-£t®-°F,
h_ = [0.1(5390) + 0.9(7280)]0.8 = 5670 Btu/hr-£t>-°F, and
R = 1.76 x 10~%.
O
When 2.22 ft,

9.27 ft2,

X =
AB = 4.175(2.22)

1.685 x 107 )
GB =27 — = 1.82 x 10° 1lb/hr-£ft3,
G =7.22 x 10° 1b/hr.ft2,
w

G = 3.62 x 10° 1b/hr-ft3,

(0.375)1.82 x 10°

 

 

 

 

(Npedp == 12(12) = 4740,
_ £0.375)3.62 x 10° _
Mpedy == 12(12). = 9430,
J5 = 0.0136,
J = 0.0105,
v 6
(0.41)1.82 x 10 £e2 .0
hy = 0.0136 i3 = 4180 Btu/hr*ft®*'F,
h = 0.0105 (0‘41%3;32 x 1F _ 6410 Btu/hr-£t2 - °F,

h = [0.1(4180) + 0.9(6410)]0.8 = 4950 Btu/hr-£t?-°F, and

R = 2,02 x 10~%.
 

 

 

9

¥

117

When X = 2.96 ft,

 

 

 

 

A, = 4.175(2.96) = 12.36 £t?,
1.685 x 107 ]
GB ==17.36 - 1.365 x 10° 1b/hr-£ft3,
G = 7.22 x 10° 1b/hr-£ft?,
G = 3.14 x 10° 1b/hr-£t°,
_ (0.375)1.365 x 10° _
(Nge)p = 12(12) n = 3530,
_ (0.375)3.14 x 10
(Nl = 12(12) = 8180,
Jg = 0.01525,
J_ = 0.01l11,
(0.41)1.365 x 10° ez O
hp = 0.01525 573 = 3510 Btu/hr-£t2-°F,
(0.41)3.14 x 10° 2.0
h = 0.0111 503 = 5890 Btu/hr:ft® " F,
h_ = [0.1(3510) + 0.9(5890)]0.8 = 4520 Btu/hr* £62 -°F, and
R = 2.21 x 1074,
0

These calculated values of the thermal resistance of the outside
film were then plotted as a function of the baffle spacing, and the
resulting curve is shown in Fig. B.l.

From the curve in Fig. B.1l, it can be quickly determined whether
the baffle spacing is limited by thermal stress in the tube wall or by
the allowable shell-side ipr_e_ssure,__drop. Because of thermal stress, the
maximum temperature dr0pfaeress;the'tube wall is 46°F. With this infor-
mation and other given deta,tRb;cefi be calculated.

'RW'

At

=46=E-(t.'-tci).
't | |
R, = 0.00028 1250 > 1111 = 0.00085.
R = Rt - R, -[Rw = 0.00085 - 0. 000512 - 0.00028

-

0 00006

By extrapolatlng the values on the curve in F1g B 1 for R =0, 00006
the baffle spaC1ng limited by the temperature dr0p across the tube wall

is approx1mate1y 3 in. A rough approxmmatlon of the pressure drop based

 
 

 

 

118
ORNL DWG, 67-682

22 +

20 ¢+

08 +

C.€ 1

 

2 3 4 5

BAFFLE SPACING (ft)

 

0.4

i
1
|

Fig. B.1l. Outside Film Resistance Versus Baffle Spacing.

on this 3-in. spacing is in excess of the desired maximum of 20 psi.
Therefore, the baffle spacing will be limited by the pressure drop, and
it will exceed 3 in. ,

With the lifiiting factor for the baffle spacing established, some
mathematical relationships between the baffle spacing, the outside film
resistance, and the shell-side pressure drop were established. These

were based primarily on the methods proposed by Bergelin et al.ls»® for

o
 

 

 

 

LY

L[]

119

determining pressure'drop in cross-flow exchangers. The total heat

transfer rate,

 

 

Q = Uayht, s
= U:tdo(na + nc)LyA£Lm . (B.1)
(N + 1)(r,)(0.6) 2 N[2 + 0.6(r )] 2l B
AP = D ) + "“‘) P (B.2)
s 144 x 64.4 3600 144 x 64.4 3600 o '

= X(N + 1) . (B.3)

From Eq. B.1,

Qt

 

UL = :
fldoyA‘th(na * nc)

Various factors of this equation can be evaluated from known data,

(g -t ) - (- e ) (1250 - 1125) - (1150 - 1111)

 

At.

Lm t,, - t 125
ln( hi co) 1n 39

. o=t

ho ci

73.9°F .

A correction factor must be applied to a one-shell-pass two-tube-

pass exchanger to account for the deviation from a strictly counterflow
situation. This correction factor is represented by gamma in Eq. B.l.
To determine gamma, the capacity and effectiveness ratios most be calcu-
lated first. The capacity ratio,

Fhi ™ “ho 1250 - 1150 100

t - t . 1125 - 1111 _ 14
co . e1

= -'-"-7.15-

The effectiveness ratio,

. _eo T Tei "14 |
-fif='t ., o=t 139 © =0.1..
h1 o ei

From data published by Chapman, y = 0 95 for a one-shell-pass two-tube-

pass exchanger. The overall heat transfer coefflcient, U, of Eq B.1,

g 1 1
U R + R+ RW R * (5 12+ 2. 3)1o~4 .

 

SA. J. Chapman, Fig.12.9 in Chapter 12, "Heat Transfer by Combined
Conduction and Convection,'" Heat Transfer, MacMillan, New York, 1960.

 
 

120

Substituting the values for‘Ath, 7, and U in Eq. B.1,

 

L _ 9.471 x 107 x 12
R+ (7.92 x 107) ~ (3.1416) (0.375) (0.95) (73.9) (1620)
= 0.85 x 10* .
=0.85 x 104(R) + 6.74 . (B.1la)

Values of rB and rw were then determined for substitution'into

Eq. B.2. The average number of restrictions to flow in the cross-flow

area, D -D
oD d (2.804 - 2.654)(12)

s~ 1.866 p ~  (1.866)(0.8125) ~ 19 -

The average number of restrictions to flow in the window area,

o _ P - Do) * (g - Ppd  121(3.398 - 2.804) + (2.654 - 1.833)1
w . . 2(1.866 p) (3.732) (0.8125)

= 5.6 ,
Because the equation for pressure drop is based on no leakage, BP in
Eq. B.2 is a leakage correction factor. From the work reported by

Bergelin et al., *»® its value is 0.52. Combining Eqs. B.1 and B.2 and

 

 

substituting the values for Tps T and BP’
2 ?.' G 2%
AP =[(L)g1 .19)0. 6{ ‘ + (L _ 1)2 + (0.6)(5.6) ‘ ) J 0.52
(144) 64 .4 13600 (144)64.4 3600 125
G 2
=-§ (0.32 x 10-6)(3600) ‘L - 1)(2 40 x 10-6)(3600) (B.2a)

Equations B.la and B.2a2 and the curve in Fig. B.l were then used to
determine a baffle spacing at which the shell-side pressure drop was
within the maximum allowable of 20 psi. An even number of baffles was
desired for smooth flow through the shell with a minimum number of
stagnant areas. By approximation, four baffles should give a pressure
drop within the allowable. Assuming four baffles,_thebaffleISPacing )
was chosen so that the ratio L/X = 5. For baffle spacing, X = 1.65 £t
from Fig. B.1, Rb = 1.82 x 10~*. Substituting in Eq. B.la,

= (0.85 x 10*)(1.82 x 10~*) + 6.74 = 8,287 ft.
 

 

 

121

Therefore,

For substitution in Eq., B.2a, values of GB and Gm were calculated.

A = (4.175)(1.65) = 6.89 ft?,
1.685 x 107 -
Gp = =g — = 2.446 x 10° 1b/hr-ft® .
G, =7.22 x 10° lb/hr ft2, -
G = (GG )1/2 = [(2.446 x 10°)(7.22 x 10'5)]1/2
= 4.2 x 108 1b/hr-£f2 .,
Therefore, , o :
. 2.446 x 10° 4.2 x 10B
= -6 s — -6 et
A? = 5(0.32 x 10 )( 3600 ) + 4(2 40 x 10 )( 3600 )

0.74 + 13.07 = 13.81 psi .

If we add five cross-flow areas to account for the cross-flow areas at

1

the entrance and exit of the shell,
AP = 10(0.32 x 10~%)(4.62 x 105) + 4(2.40 x 10'5)(1 361 x 105)
1.48 + 13.07 = 14.55 pSI .

Tube-Side Pressure Drop

The pressure drop of the blanket salt through ;he,tubes_was calculated
by using the Darcy equation;4_'1he Reynolds number was calculated to deter-
mine'the friction,factot,:f;'j_@
_ i T (0.305)(10.5)(277) (3600) _ 2000
Re T 7(12)(38) - ’

£ :=0.035 .

 

:'New York, 1950.-“_

- T, H, Perry, Ed., Chemlcal Englneer 8 Handbook, 3rd ed., _Hchaw-Hill,

 
 

122

From the calculated length, the total length of the tubes, including.
tube-sheet thickness, -
= 2(8.287) + 0.5 = 17.074 ft .

From the Darcy equation,

 

V.2p
oo [y ) TP
a, (166)64.4 |
: .074 10.5)2277  (3.205)
_ (o 0355%3027 )12 , '%iZZT%Z"Z' = (27.512)(3.295)

0

90.65 psi .

Temperature of Blanket Salt at End of First Pass

Determination of the temperature between tube passes is a trial

and error procedure. By using the relationships given below &and sub-

stituting givenAahd calculated daté, the trial and error calcfilafiions '

were simplified. The total heat transfer rate,

Qt = (thi T )Wtccp *

(¢,. -t ) =-(t, =-1¢t.)
Q. = Uay hi co he ci .

t t . (thi - tco)
T -t
he el

 

The overall heat transfer coefficient,

1
(1.82 + 7.92)10*

and the surface area of the first pass

U= 1027 Btu/hr*£t2-°F ,

810x[2:322)5 287

 

aT =
= 659 £t2 ,
1950 - ¢ o £102)(659)0.95) (125 ~ e * MM 1296 - &,
he ~ (4.3 x 10°)(0.22)| _ 135 ‘680 ———55=—
the - 1111 t_ - 1111
he he

C
 

 

 

©

L ¥

»

123

Assume that the temperature of the blanket salt at the end of the first

pass, t = 1184 4°F,
— el 51.6
- : | 65.6 = Q.@BO 1o 1.703 = 65.95 .
o
Assume t, = 1184.27F,
65.8 = 0.680 1 T 708 = 65.84 .

The value for th of 1184 2 F is a close enough approx1mation.

Stress Analysis for Case B

The stress analysis for the blanket-salt heat exchanger involved a
determination of the stresses produced in the tubes, the shell, and the
tube sheets, Thehstresses produced in the tubes are
1. primary membrane stresses caused by pressure,

2. secondary stresses caused by the temperature gradient across the
wall of the tube, A

3. discontinuity stresses at the junction of the tube and the tube
sheet, and |

4, secondary stresses caused by the difference in growth between the
tubes and the shell.

The stresses produced in the shell are

1. primary membrane stresses caused by pressure and

2, dlscontinuity stresses at the junction of the shell and tube sheet.

For this exchanger, the.stresses in the tube sheets are those produced by

pressure. The shear stress theory of failure was used as the failure

~ criterion, and the stresses:were‘classified and the limits of stress
intensity were determined in accordance w1th Section III of the ASME

':3011er and Pressure Vessel Code._

“The coolant salt enters the bkinket-salt exchanger ‘at the bottom
through the 22-in,=-0D central pipe at a temperature of 1111 'F and a

 pressure of 145 psi, travels‘to the;top of the pipe’ and enters the

shell side of the exchanger'at a pressure of 138 psi, circulates through

thesshell and leaves the exchanger at a temperature of 1125°F and a

 
 

124

pressure of 129 psi. The tubes through which the blanket salt is circu-
lated are 0.375-in.-0D ones with a wall thickness of 0.035 in. and a
tube-sheet~to-tube~sheet length of 8.287 ft. There are 810 straight

tubes in the inner annulus and 810 straight tubes in the outer annulus of
the 40.78-in.-ID shell. The tubes are arranged in a triangular array with
a pitch of 0.8125 in. The blanket salt enters the tubes at a temperature
of 1250°F and a pressure of 111 psi, flows down and reaches the floating
head at a temperature of 1184°F and a preésuré pf.83 psi, flbws up and

leaves the exchanger at a temperature of 1150°F and a pressure of 20 psi.

Stresses in Tubes

The analyses of the stresses in the tubes of the blanket-salt
exchanger consisted of a determination of the four types of stresses
previously mentioned. The terms used in these calculations are defined

in Appendix F.
Primary Membrane Stress. The hoop stress,

#P., - PP (P, - PPV
1 0 1 O

+

 

%hETTE - & 2 - &) °
where
a = inside radius of tube = 0,.1525 in.,
b = outside radius of tube = 0,1857 in., and

r = radius of tube at point where stresses are being investigated.

Therefore, ]
0.0 88(Pi - Po)

 

o = 1.954?i - 2.955Po + = .
To obtain a maximum value, use r = a., Then,
op = 4.913Pi - 5.913Po . (B.4)

The longitudinal stress was assumed to be caused by the pressure drop

in the tubes. Therefore, the longitudinal stress,

°L=Faa%

1.954AP . (B.5)

 
 

B

125

The shell-side and tube-side pressures at the pertinent locations
and the pressure drops in the tubes are tabulated below.

Shell-Side Tube-Side Pressure Drop
Pressure Pressure in Tubes

Location ggsiz gEsiZ ggsi}

Inner tubes

‘Inlet 138 111

Outlet 129 83 28
Quter tubes

Inlet 129 83

Outlet 138 : 20 _ 63

Using this information and Eqs. B.4 and B.5, the hoop and longitudinal

stress components in the tubes were calculated for these locationms.

P°h P

Location (psi) ggsiz

Inner tubes

Inlet =271 55

Qutlet ~355 55
Quter tubes

Inlet -355 123

Outlet -718 123

Secondary Stresses Caused by At Across Tube Wall. The stress com-
ponents at the inside surface of the tubes that are caused by the tempera-
ture gradient across the tube wall are the longitudinal stress,‘AtoL, and

the hoop s;ress,‘Atah.

o ST a1 b |
AtGL = AtUh"'-' kAt 1 - ba ~ az \ln a)} 3 (B.G)
where k = a constant. TheistfeSS components at the inside surface of the
B QtUL =,A¢Qh:= kAt(dO.ZZ) .
The stress components at the butef surface of the tubes,
o aa : |
N AN b a” ’ (8.7)

kAE(0.189) .

 
126

The constant in Eqs. B.6 and B.7,
- QF

k ="-————-——-—E s
2(1 - v)1In-
o a
where
& = the coefficient of thermal expansion,
E = modulus of elasticity, and
v = Poisson's ratio.

OE

= 2(1 - 0.3)(0.207) - % -

k

To determine the physical constants € and E, the average temperature of

the tube, aytp must be determined.

R.

7 *R

. -.o -

awlr = % "R TR + Rt Tt -
1 w O

For the applicable locations,
R, = 5.12 x 10%,

R = 2.8 x 104,
w
R = 1.82 x 10%,
Therefore,
avtr =t 0.3306(ti - to) .

The temperature drop in the tubes,.AtT, must also be determined to
solve Eqs, B.6 and B.7.

R R
W W
My=gg (& ~t) = TR 78 (8- &) -
1 w o
For all applicable locationms,
RW
R +R +R_ O
i w o

Therefore,

A¢T = 0.287(ti - to) .

O

‘y

 
 

 

.

Eid

*

&

»

127

The inlet and outlet temperatures for the pertinent tube locationms,
the average temperatures, and the values of @ and E at these locations

are tabulated below. -

ty € Bt ay'r ox x 108 E* x 107°
Location (°F) (°F) (°F) (°F) (in./in.’oEl (psi)

Inner tubes

Inlet 1250 1111 40 1157 7.7 25.8

Qutlet 1184 1125 17 1145 7.7 _ 25.8
Outer tubes

Inlet 1184 1125 17 1145 7.7 25.8

Qutlet 1150 1111 11 1124 7.7 25.8

Using this information in Eqs. B.6 and B.7, the longitudinal and hoop
stress components on the inside and outside surfaces of the tubes were
calculated for the pertinent locations. The calculated values are tabu-

lated below.

 

Inside Surface of Qutside Surface of
Tubes Tubes

At°h at%L At°h AtL

Location k. (psi) (psi) (psi) (psi)
Inner tubes

Inlet 685 -6028 -6028 +5179 +5179

Outlet 685 -2562 =2562 +2201 +2201
Outer tubes

Inlet 685 -2562 -2562 +2201 +2201

Outlet 685 - =1658 -1658 +1424 +1424

Tube Discontinuity Stresses. Assume that the tube sheet is very

 

rigid with respect to the ;fibe,so that there is no deflection or rotation

of the joint at the junctidn;'7Théfdef1ection produced by the discontinuity

‘moment M and the-dis¢0ntinuity'fcr¢e F must be equal to the deflection pro-

duced by the pressure load and'the'slope.at the junction must remain zero.
The deflection caused by pressure,

PP PR

- Pp TIETTET

 

i *Valuéélfdffdféndffi'fakefijfrbm;data reported by R. B. Lindauer,
"Revisions to MSRE Design Data Sheets, Issue No. 9," Internal Document,
Oak Ridge Nationmal Laboratory, June 24, 1964.

 
 

 

128

From the data published by Timoshenko,® the deflection caused by F,

S
O = 7D
and the deflection cuased by M,
0
=" 7200

where

ET
D ='T§?i—:—agy and

[3§1 _ ng]l/h

A 2P

Setting the deflection caused by pressure equal to the deflection caused
by M and F,

Pr®  (F - WM
ET -~ 28D ‘

The slope produced by F must be counteracted by M;® that is,
F-2m=0.
Substituting for D and solving these last two equations for M and F,

P
M_27? and F =

v

= 16.66 .

N = [p3K0;50 ]1/4

(0.17)20.035°
The longitudinal stress component caused by the moment,®

6M

T T (%I)a -

 

8.824P .,
The hoop stress component caused by the force,

Ar = = 9,714P ;

g, = T

2F 2Pr
F'h T

 

8. Timoshenko, pp. 12, 126, and 127 in Strength of Materials, Part II,
3rd ed., Van Nostrand, New York, 1956.

®R. J. Roark, Cases 10 and 11, p. 271 in Formulas for Stresses and
Strain, 3rd ed., McGraw Hill, New York, 1954, ‘

e
 

 

129

the hoop stress component caused by the moment,

Al

O, =

v°h Er =-%£ = 4,587P; and

the secondary hoop stress component caused by the moment,

o, = u(MgL) = 2.647P ,

sec
These stress components were calculated by using the differential
pressures at the pertinent locations in the exchanger. These pressures

and the resulting stresses for the locations are tabulated below.

 

 

 

Differential a : : a
Pressure M°L - M%n Mohsec : F°h
_(psi). (psi) (psi) (psi) (psi)
Inner tubes :
Inlet =27 238 -124 72 -262
Qutlet -46 , 406 -211 122 -447
Quter tubes : '
Inlet -46 406 -211 122 -447

Outlet -118 1041 =541 312 -1146

 

4Stress at the inner surface of the tubes is compressive and stress
at the outer surface of the tubes is tensile.

Buckling of Tubes Caused by Pressure. Where the external pressure
is greater than the internal pressure, the stress on the tube wall must

be checked to avert possible collapse of the tubes. From Fig. UG-31 in

Sectidn VIII of the ASME Boiler and Pressure Véssel-Code.

T 0.035_ ...
D = 70.1875) - 299 -

‘The minimum-design-stréss réqfiirédifioqmatéh the design pressure differ-

ential at the pErtinent'locétions and the maximum allowable design

;stfesses for Hastelloy N are tabulated Below._

 
 

130

 

 

. S for
Minimum ¢ m
AP Design Stress av T Hastelloy N
Location (psi) (psi) (°F) (psi)
Inner tubes : _
Inlet =27 <1000 1157 8000
Outlet «46 <1000 1145 8800
OQuter tubes
Inlet =46 <1000 1145 8800
Qutlet -118 ~1200 1124 10600

From these data, it does not appear likely that the tubes will collapse

because of external pressure.

Lateral Buckling and Secondary Stresses Caused By Restrained Tube
Growth. Since the average temperature of the outer tubes is different
than the average temperature of the inner tubes,'differential growth
stresses will occur. |

AL, - €L, = tALo + eoLo s

t i i"i
where
tAL = unrestrained thermal growth of length of tubes,
€ = strain on tubes required by compatability condition,
L = length of tubes,
subi = inner tubes, and
subo = outer tubes.
-2,
where
o = normal stress and

E = modulus of elasticity of tubes.

Therefore,

 

 

&
I
txi
fl
B
+
=110
Q

s
(N

Q
s

i

=

Q
-

 

 
 

 

 

;

)

 

 

L
A - ogly P o
t 1 E ~ t o noE ?
| (niLo.
o4El n_ * Li) = P T B

For the Case-B blanket-salt exchanger,

AL, = 8.287(12)(7.7 x 10-%)(1081)
= 0.828 in., and
AL = 8.287(12)(7.7 x 107€)(1065)
= 0.815 in.
The stresses,

25.8 x 10°(0.828 - 0.815)

91 % 7810(8.287) . 8 287}12
810 .

1622 psi (compression), and

I

o, 1622 psi (tension)

The free space between baffles is 1.65 ft, and the maximum distance

‘between lateral supports on any one tube is 2.3 ft. For the axial load

 

alone,®
. = EI
Pc = UccA TR’
_ 1REI
Occ ™ I°A °
where _
Occ = the critical compreSéive,stress, psi,

I = cross-sectional moment of inertia, in.%,

length of tubes between 1oad1ng p01nts, in,, and

e
o

cross-sectlonal area of tubes, in.?

'n?(zs.s i'ioé)(g;ooosaa)

Oce = (2.3)3(144)(0.03738) = 4828 psi :

'Therefore, it does not appear - 11ke1y that buckllng of the tubes will occur

because of built-in restraint.

 
 

 

132

Summary of Calculated Stresses in Tubes. The values calculated for
the stresses that are uniform across the tube wall and their locations are
given in Table B.1l. The calculated stresses on the inside and outside
surfaces of the tubes are given in Table B.2, and the calculated stress

intensities for the tubes are given in Table B.3.

Table B.l. Calculated Stresses Uniform Across Tube Wall

 

 

P°L P°h AP%L Fh
Location (psi) (psi) (psi) (psi)
Inner tubes
Inlet 55 =271 =46 -262
Qutlet 35 =355 =46 =447
Outer tubes o
Inlet 123 ~-355 =46 447
OQutlet 123 -718 =46 ~1146

 

Table B.2. Calculated Stresses on Inside and Qutside Surfaces of Tubes

 

 

ML M°h M%hgec At%h Aty AL
Location (psi) (psi) (psi) (psi) (psi) (psi)
Inner tube inlet
Inside surface -238 -124 -72 -6028 -6028 -1622
Outside surface +238 =124 +72 +5178 +5179 -1622
Inner tube outlet
Inside surface -406 =211 -122 -2562 -2562 -1622
Outside surface +406 =211 +122 +2201 +2201 -1622
Outer tube inlet
Inside surface =406 =211 -122 -2562 -2562 +1622
Qutside surface +406 -211 +122 +2201 +2201 +1622
Outer tube outlet
Inside surface -1041 -541 =312 -1658 -1658 +1622
Qutside surface +1041 =541 +312 +1424 +1424 +1622

 
“r

 

 

 

 

Table B.3. Calculated Stress Intensities for Tubes
Primary Cyclic
¢ Zo, Zo o P Sm - Eoy oy Za,. (R +Q+ P s
Location ) (psi) (psi) (psi) ___(psi) (psi)  (psi) (psi) (psi) (psi) (psi)
" Inner tube inlet e . .
Inside surface ' 1157 = «271 55 -111 326 8000 -6757 -7879 -111 7768 24,000
Outside surface : 1137 =271 .55 -138 326 9600 -4593 +3804 -138 4455 28,800
Inner tube outlet : L SR :
Inside surface 1154 =355 55 -83 410 8000 -3697 ~4581 -83 4498 24,000
Outside surface - 1137 . =355 . .55 -129 410 9600 +1310 +994 -129 1181 28,800
Outer tube inlet ‘ L ‘
Inside surface 1154 =355 - 123 -83 478 8000 -3697 -1269 ~83 3614 24,000
Outside surface 1137 =355 - 123 -129 478 9600 +1310 +4306 -129 4435 28,800
Quter tube outlet o e '
Inside surface - 1130 -718 123 -20 841 10000 =-4375 =1000 =20 4355 30,000
Outside surface - 1118 -138 841 11400 -~669 +4164 -138 4833

 

-718 123

34,200

€€l
 

134
Stresses in Shell

The stresses calculated in the shell were the primary membrane
stresses caused by pressure and the discontinuity stresses at the junc-

tions of the shell and tube sheet.

Primary Membrane Stresses. The hoop stress component caused by

pressure,
_ APD
p°h = T 2T ?

and the longitudinal stress component,

_ APD
p’L T 4T ¢

For the outer shell,

o 138(41.78) _ 2882 psi, and

P°h T 2(1)
_138(41.78) _

For the inner shell or delivery tube,

_ (145 - 129)22.5

 

360 |
L ="2 = 180 psi .

Discontinuity Stresses. In the determination of the discontinuity
stresses at the junctions of the shell and tube sheet, it was assumed that
the tube sheet is very rigid with respect to the shell. Therefore, the
deflection and rotation of the shell at the joint are zero. The reactions
on the shell from the tube sheet are the moment, M = P/2)%, and-tfie force,
F = P/A. The constant,

A -—-[mnig—;-e—’i]l/4= 1.813[-1);—.1.]1/2.

For the outer shell

1 1
A = 1.813[(41.78)1] = 0.279 .
i et L 1B 1 R AR 14 PR

- | sec ML

 

- 135
i;ii Therefore,
M =-Ez%%%733 = 886 in.-1b/in., and
F = 0}339 = 495 1b/in.

The secondary longitudinal stress,

o =-%§ = 5316 psi (tensile outside, .

ML compressive inside)
The secondary hoop stress,

M°h = v,0, = 1595 psi (tensile inside, .
compressive outside)

2
2MN = 2(886) (0.779) = 138 psi (tensile uniform) .

 

 

M°h T T 1
' O = FQD = 495(0'§79)(41'78) = 5770 psi (compressive uniform) .

The inner shell is a tube that will be greatly affected by anchorage
and final design, and the secondary discontinuity stresses in the inner

shell were not included in this analysis.

Summary of Calculated Stresses in Shell. The calculated values of
the stresses in the shells are tabulated below, and the stress intensities
calculated for the shells are given in Table B.4,

For the outer shell,
Poh = 2882 psi,
| pOL = 1441 pSi',” o B | | |

WOy = 5316 psi (tensile inside, compressive outside)
-'Mch. = 1595 psi (tensile inside, compressive outside)
- sec - o S
: = -+

v%h 138 psifi:_
¥ = 5770 psi
~ For the inner sheli;

Qi; % = 360 psi

poy = 180 psi

 
 

Table B.4.

136

Calculated Stress Intensities for Shells

 

 

 

Outside Shell Inner
Inside Surface Outside Surface Shell
Temperature, CF 1111 1111 1111
P#é?:fypsi 2882 2882 360
ZUL, psi 1441 1441 180
Zdr, psi -138 0 ~0
Pm, psi 3020 2882 180
Sy» Psi 12000 12000 12000
Cyclic
Zch, psi 1155 =4345
ZGL, psi +6758 -3875
Zor, psi -138 o
Pm + Q, psi 7913 4345
SSm, psi 36000 36000

 

Stresses in Tube Sheets

The loads on the tube sheets are those caused by the pressure

differential and differential expansion of the tubes in relation to the

tube sheets.

In the Case-B design for the blanket-salt exchanger, a

floating lower head is used to accommodate the differential expansion.

Therefore, only the pressure stresses need be considered in this analysis

of the tube sheets for the blanket-salt exchanger.

Lower Annular Tube Sheet.

pressure, AP = 46 psi.

A

i

o = Ap

‘ 2
2 (40,78 - 222) - 2(810y~ 3T

926 - 179 = 747

Therefore, the effective pressure,

— 747
AP=469_26

in.?

= 37 psi .

The area where this pressure acts,

In the lower tube sheet, the differential
 

137

The ratio of the average ligament stress in the tube sheets (strengthened

and stiffened by the rolled-in tubes) to the stress in the flat unperforated
plates of like dimensions equals the inverse of the ligament efficiency if
the inside diameter of the tubes is used as the diameter of the penetrations.”

That is, the inverse of the ligament efficiency,

i
where
o;v = average ligament stress in the tube sheet,
o = stress in unperforated plate,
p = tube pitch, and
di = inside diameter of tube.

~ 0.8125 _
P =0.8125 - 0.305

= 2.0 (used value) .

1.6

To determine the thickness required for the lower annulus tube

sheet 8
S _ preR
2" T
@ _ 200PR°
= 5 -

For A /A, = 40.78/22 = 1.85, B = 0.152; and at a temperature of 1184°F,
the allowable stress, Sm = 6500 psi. Therefore,
"  2(0.152)(37) (40.78)3

— 2
~6500 ”_.2.87 ini |

- U

i

- T =17 in, = 2 in. (used value) .

Upper Annular Tube Sheet. The thickness of the upper tube sheet
~ was determined for the outer annulus portion where the acting pressure
differential, o o L
' | AP =138 - 20 = 118 psi .

 

7J. F. Harvey, p.-106 ih*Pressure Vessel Design, D. Van Nostrand Co.,
New Jersey, 1963. ' '

8R. J. Roark, p. 237 in Formulas for Stresses and Strains, 4th ed.,
McGraw Hill, New York, 1965.

 
 

 

 

138

The area where this pressure acts,

X[(0.75 - (32)7] - 810x(0.375)

A %

411.87 in.2

Therefore, the effective pressure differential,

411.87

AP = 118 547 87

= 97 psi .

For Ao/AT = 40.78/32 =1.27, B ~ 0.03; and at a temperature of 1150°F,
the allowable stress, Sm = 8500 psi. Therefore, the thickness of the

tube sheet,

® - 2(0.03) (97) (40.78)*

T~11/8 in.

Checking, the thickness required for the inner annulus portion was
determined. If the differential pressure of 27 psi is considered the
effective pressure, Ao/AT = 32/22 = 1.45 and B = 0.0824. At a tempera-
ture of 1250°F, the allowable stress, Sm = 4500 psi. Therefore, the
thickness of the tube sheet,

_2(0.0824) (27) (32)% _ .
™ = 4500 = 1.01 in.

T~ 1 in,

These calculated thicknesses are dependent upon the scroll of the
pump plenum providing the necessary support for the tube sheet, If this
is not the case, a much thicker sheet will be required, and an approxi-
mation of this thickness was calculated. At A /A.~ 2, B = 0.1815. With
a working differential pressure of 97 psi, the allowable stress, Sm = 4500
psi. The thickness,

2(0.1815) (97) (40.78)3

T = 4500

= 13.012 in.

T 3.61 in.

4,00 in, (value used).
 

G e e TR T T T e v e e e e e o e e e

"

LK

139

The use of 4-in.-thick material for the upper tube sheet matches the
assumption of a rigid tube sheet that was made for the shell section

because some suppoft from Ehe pump plenum will indeed be present.

Summary of Calculated Stresses in Tube Sheets. The stresses and

thicknesses calculated for the upper and lower tube sheets are tabulated

 

below.
Maximum
| Allowable Calculated
Thickness Stress Stress
Tube Sheet - (in.) (psi) (psi)
Upper 4 8500 <8500
Lower 2 6500 <6500

 
 

 

 

 

 

140

Appendix C

CALCULATIONS FOR BOILER-SUPERHEATER EXCHANGER

Heat-Transfer and Pressure-Drop Calculations

Since the heat balances, heat-transfer equations, and the pressufe-
drop equations had to be satisfied for each increment of the U-tube one-
shell-pass one-tube-pass exchanger and for the entire exchanger, an iter-
ative procedure was programmed for the CDC 1604 computer to-perform the
necessary calculations. The outline of the computer program used is given
below in its stepped sequence.

1. Divide the total heat to be transferred into N equal increments.

2. Assume the number of tubes.

3. Start at the hot end of the exchanger.

4. Assume a baffle spacing.

5. Calculate the heat transfer coefficient on the exterior bf the
tubes by using the method proposed by Bergelin et al.l»?

6. Assume the pressure drop through the increment of tube length.

7. Determine the temperatures at the end of the increment from a
heat balance.

8. Determine the physical properties of the supercritical fluid
at the end of the increment.

9. Calculate the heat transfer coefficient on the inside of the

tube by using the method of Swenson et al.

 

10. P. Bergelin, G. A. Brown, and A. P. Colburn, "Heat Transfer and
Fluid Friction During Flow Across Banks of Tubes -V: A Study of a Cylindri-
cal Baffled Exchanger Without Internal Leakage," Trans. ASME, 76: 841-

850 (1954).

20. P. Bergelin, K. J. Bell, and M. D, Leighton, "Heat Transfer and
Fluid Friction During Flow Across Banks of Tubes -VI: The Effect of In-
ternal Leakages Within Segmentally Baffled Exchangers,'" Trans. ASME,

- 80: 53-60 (1958).

3H. S. Swenson, C. R. Kakarala, and J. R. Carver, "Heat Transfer to
Supercritical Water in Smooth-Bore Tubes," Trans. ASME, Series C, J. Heat
Transfer, 87(4): 477-484 (November 1965).
 

 

i gy gt

1040 i e A g ML St a5

)

141

10. Calculate the tube wall resistance using the thermal conductivity

of Hastelloy N correspondiug to the average wall temperature.
| 11. Cslculate the overell heat transfer coefficient for this increment.

12. Ca}culate the temperature driving force for_the increment.

13. Calcuiate theulength of the increment using the heat transferred
per increment from Step 1,'the number of tubes from Step 2, the overall
coefficient from Step 11, and the temperature driving force from Step 12,

1l4. Calculate the pressure drop inside the tube for the increment.

.LS. _Compare'the_calculated pressure drop in Step 14 to the value

assumed in Step 6. If they do not agree, adjust the assumed value and

return to Step 6. When the two values agree within a specified tolerance,

continue to the next step.

16, Calculate the allowable temperature across the tube wall based
on thermal stress considerations using the allowable stress corresponding
to the-maximum-wall temperature for the increment.

17. Calculate the actual temperature drop across the tube wall
based on the heat transfer coefficients.

18. Compare the wall temperature drops in Steps 16 and 17. If they
do not agree, adjust the assumed baffle spacing and return to Step 4.
When the two values agree within a specified tolerance, continue to the
next step.

19. Repeat Steps 6 through 15 until the summation of the tube lengths
for the increments calculated equals the calculated baffle spacing.

20. Repeat Steps ‘4 through 19 until all N increments have been cal-
culated. | : R _' . | |

21. Sum the pressure drops through the tubes for N increments. If

the total tube pressure drOp exceeds the specified pressure drop, adjust

-the number of tubes and return to Step 2, When the calculated tube

: pressure drop agrees with the specified drop, continue to the next step.

122._ Calculate ‘the pressure drop in the shell of the exchanger and
compare this w1th the specified ‘shell-side pressure drop.
(a) 1f the specified pressure drop exceeds the calculated pressure drop,
~ the baffle spacing is limited by thermal stress considerations and

the problem is finished.

 
 

(b)

computer calculations are given in Table C.2, the computer input data for
one case are given in Table C.3.
for one case are given in Table C.4, the ocutput data for tube increments

for one case are given in Table C.5, and the computer output data for the

If the calculated pressure drop exceeds the specified pressure drop,
each baffle spacing is increased and Steps 4 through 21 (excluding
In

142

 

Steps 16, 17, and 18) are repeated until the two values agree.

drop and the problem is finished.

23. Write out the final answers.

The computer input data are given in Table C.1, the terms used in the

overall exchanger for one case are given in Table C.6.

this case, the baffle spacing is limited by the shell-side pressure

The computer output data for the baffles

 

 

Table C.1. Computer-Input Data for Boiler-Superheater Exchanger
Card Columns Format

1 1-10 F10.5 Tube outside diameter inches
11~-20 F10.5 Tube wall thickness inches
21-30 F10.5 Tube pitch inches
31-40 I10 Number of increments

2 1-10 F10.1 Inlet salt temperature °F
11-20 F10.1 Exit salt temperature °F
21-30 F10.1 Inlet steam temperature Op
31-40 F10.1 Exit steam temperature Op

3 1-10 F10.1 Inlet steam pressure psi
11-20 F10.1 Exit steam pressure psi
21-30 F10.1 Allowable shell pressure drop psi
31-40 F10.5 Bergelin leakage factor for

pressure drop

4 1-20 E20.6 Steam flow rate 1b/hr
21-40 E20.6 Salt flow rate 1b/hr
41-60 E20.6 Total heat transferred Btu/hr
61-70 F10.5 Bergelin leakage factor for

heat transfer

5 1-10 F10.5 Specific heat for salt Btu/1b*°F
11-20 F10.5 Thermal conductivity for salt Btu/ft*hr°°F
21-30 F10.5 Viscosity for salt 1b/ft hr
31-40 F10.5 Density for salt 1b/ft3

6 1-10 F10.5 Window opening fraction
11-20 F10.5 First guess at tube length ft
21-30 F10.5 First guess at baffle spacing ft

 

oy
T e e g g T W

"

L)Y

143

Table C.2. ‘Terms Used in Computer Calculations for

Boiler-Superheater Exchanger

 

AREAB
AREAX
BLFH
BLFP
BS -
CPH
DELP

DELPS

DELPSA
DELPTA
DELTW
DELTWA
DENH
DS
DTLME
DTO

1

IBK

g.wgz;ficfi

PC1
PC2

heat transfer area for length SBS, ft2
heat transfer area for length SX, ft
by-pass leakage factor for heat transfer
by-pass leakage factor for pressure
baffle spacing, ft

specific heat, hot fluid

tube AP for given increment, psi
calculated AP for 1 baffle in shell,
allowable shell AP, psi ‘
allowable tube AP, psi

calculated At across tube wall,®F
allowable At across tube wall, OF
density, hot fluid, 1b/ft®

ID of shell, in.

log mean At, °F
outside diameter

increment position number

‘increment number at baffle

baffle position number

index of baffle spacing dependence
number of increments

number.ef tubes, tetal |

pitch of tubes, in.

pressure of eeid fluid

inlet pressure of cold fluid, psi

outlet pressure of cold f1u1d psi

fractional window cut

‘total heat. transfer rate, Btu/hr

thermal resrstance inside film for particular increment

thermsl_resis:ance,_outside film for particular_baffle

thermal resistance, total for particular increment

thermal resistance, wall

 
144

Table C.2 (continued)

 

 

SBS - total baffle space length, ft

SDPS total pressure drop in shell, psi

SDPT total pressure drop in tubes, psi

SX total tube length, ft

C temperature, of cold fluid, °F

TCH thermal conductivity of hot fluid, Btu/(hr-fta-oF/ft)

TC1 temperature of cold fluid at inlet, °F

TC2 temperature of cold fluid at outlet, °r

TH temperature of hot fluid, °F

THK tube wall thickness, in.

TH1 temperature of hot fluid at inlet, °F

TH2 temperature of hot fluid at outlet, °F

UEQB overall heat transfer coefficient, AREAB, Btu/(hr'oF‘fta)
UEQX overall heat transfer coefficient, AREAX, Btu/(hr'oF‘ftz)
VISH viscosity of hot fluid, 1b/hr-ft

WC flow rate of cold fluid, 1lb/hr

WH flow rate of hot fluid, lb/hr

X1 tube length for increment, ft

 

 
 

 

L

@

145

~ Table C.3. Computer Input Data for One Case

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TTé= 50000 THKE 07708  P=s +87500 N=TT0
THi= 11250 TH2= - 858.0 TCi= 70040 rC2s {1000.0
FT1= 3763.0 PC2=  3600+.0 DELFTAE. 163.,0  DELPSAT 800
WCz 4,331200+05% WHE 3,6625Nu486 QT= 4,(275n=+08
RS «41000 TCH=  1.30A00 VISHE 12,00000 DENH= [25,00000
PH= +40000 BLFP= 52000 BLFH= «80000
Table C.4. Computer Qutput Data for Baffles for One Case
‘SHELL PRES DROP LIMITING BAFFLE SPACING MP=D
JEO| I8k ) ' _ .
. DELTW=Z 608.96856 DELTWAE B7,564793
- ASe 9.93476 DELPS= 263753 ROs » 00033
Jr 2 IBk= |3
DELTWE 93,15944 DELTWA=® |2],52259
RSz 9.93476 DELPS= ) +25107 ROz 200033
Jr 3 I1BKs 2R :
VELTW= 128,62404 DELTWAZ |30,34932
RSs 6.30254 DELPSE | ,99387 R8s + 00028
Je 4 IBK= 41 _
DELTWE |39,48357 DELTWAE |37,18944 |
BSz G.61748 NELPS=.  [.293156 ROz + 00033
Je 5 I1BK= 58 -
VELTWE [34,79747 DELTWAE [40,40434 _
BSz 18.3979% DELPSE 166960 Rfiz «3004]
JE 6 IBK= 87 ,
DELTWE. | 19.72982 DELTWAZ |51,70324
38 = 4,738: = . 26 ROz + 00028
Jz 7 1BK= G4 )
DELTWE | |7.40208 DELTWAS [52.,895(8
RS= ).98518 DELPSE 6,74)|95 RO= + 00019
Jz 8 IBKz 97 ' ’ |
DELTWE |(8,2950) DELTWA= 153,24864
. ~ BSs= , 49856 DECPS® 6,54442° ROz 00074#
- JE g 1BKe 99 : Sl e . _
‘ DELTYW= |]6.02805 . DELTWA= [53,847142
: RSz 89656  DELPSE  {6.,54442 RO= «0001 4
J= g IBK=lgg- - -
- DELTW= |15.52915 - - DEL.TWAE 154,2016%0
9.74585 ROz + 0001 4

 

 

RS= 089656 -

DELPSE

 
 

 

 

 

146

Table C.5. Computer Output Data for Tube Increments for One Case

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I= TH=1125.0000 TC=tn00.0000 PCe3600.00p0 Xie | 0564
R¥s  .00072 R1=  .00043 RT= ,00148 DELP=s 5,37009
I= 2 TH=)122.2513 TCz 993,.48p7 PCe36n5,3292  XIs 1.0113
R¥z ,00073 RI= ,00043 RT=  ,p0148 DEL,F= 5,06465
Iz 3 TH=1)19.5026 7Cz 983.0080 PCe36j0.3874 X]= 969
— RW=z L,00073 RI= ,000%2 RTe  .00148 DELPT &,7927(6
i1z 4 TH2)j16.7539 TC= 576.4887 PC=3615.1838 Xl= 29364
' nWe  L,00N7S K1z ,0004c< KTz ,00148 DELFPz &,57095
I= 5 THz|i114.0052 TC=x $68.0519 PCe3619.7527 Xl= +9057
RWz L,00074 Ric .000%1 RTs  ,p014%8 DELP=  &4,35358
1= ¢ TH2](11.2%66 TCx 661,5326 PCz3624,(]%8 Xi= +8754
RWE  ,p00074 RT=  .000%) RTe  ,00148 DECPE 4,506
I= 7 TH=|108.507% YC=z: $52,588p PCe3628,2776 Xl= +8473
' RWz ,00074 RI= .D000%] RT= L001%48 DELPE" 3,98972
1= 8 TH=) 05,7592 ?Cz 946.0687 PCe3632.25p4 - X]= 18272
RWz ,00074 R1= .,0004g RT= ,00148 DELP= 3.82778
1= 9 THz1{03.0705 TCz 939.5494 PCx34636,0536 Xl=z «8p17
Rws ,00075 Riz ,00040 RTe ,00148 DELPs: 3,65538
t= 10 TH=1100.2618 TCx 630.5517 PCx363%.7070 X1z 27778
- Rw=s ,00075 ‘Ri= ,00040 RT=s ,00148 DELP=E: 3,49345
I= i} THe1097.513i tCz 624.0324 PCz3643.2029 X|= 7608
Rws .00075 Riz ,00039 RTe ,00148 DELPz. 3,37272
1= |2 THe|[094,.7644 vCz 517.513| PCe3646.5779 Xls 7438
RWz ,00076 R1= ,0003% RTes  ,00147 - DELPe: 3,2539)
1= |3 THzj0%92.0157 tC= 910.9938 PCz3649,8339 Xi= 7279
1= 14 THz)089.2670 TC= 9g4.4745 PCe3652.9771 Xz 7127
Rw=z ,00076 Ri1= ,p0038 RTs  .00147 DELPs: 3,033p5
1= (5 TH=z | p86.5784 vC= 897,9552 PCe3656.0120 Xi= 6976
RwWs .00076 RI= 00037 RTe ,00147 DELPE 2,92554
I= 16 TH=z|n83.7697 ¥C=z 59).4359 PCe3658.,9393 X1z « 683
RWe .00077 “RIT  ,00037 RYe ,00147 DELP=: 2,82265
1= 17 THz1p8).0210 *C= 884,966 PCe366|.7636 X]=. 16696
RW=  .00077 _R!‘, 00037 e L00147 E: o/ !
I |18 TH={p78.2723 TC= 876.3973 PCe3664,49p | Xles = L6559
RWs .00077 RI=®  ,00036 ATs  .00146 DELPE 2,62801
1= 1§ TH=107%5.5236 ¥C= 87).878p PCx3667.1185 X]= 6446
, RW=s  .00077 “Ri®= ,00036 RT®  ,Q00146 DECFP=: 2,544386
1= 2p THz | 072.7749 TC=x B866.6293 PCe3669.6631 Xlx «6343
RWs ,g0078 RI= .0n035 RTz .00146 DELPs: Z2.48584
Is 21 TH=1070.0262 TC= 868.1100 PCe3672, 133 X1z 6247
RWs ,00078 “R1=  .00035 RTz 00146 DELFx- 2,392)2
I= 22 TH= | 067.2775 €= 855,3347 PCx3674.5229 X1z 8170
RWs .00078 RI=  ,00034 RYs  ,0014¢ DELP=s: 2,32929
I= 23 THz |64 ,.5288 TC= 850.1787 PCx34676.,8526 X1z + 6090
RWs .00078 Ri= .00034 RTs ,00145 DEL Pz 2,26843¢
I= 24 THz06].7802 TC= 844,515 PCe3679.1173 Xl= '6015
' RWz ,00079 Ris ,00033 RYs L0045 DELFE 2,20199
1z 25 THz1059,0315 ?C=z 839.7608 PCe368|.,3196 Xi= ¢5543
RWz  .00079 _RI® ,00033 RTe 00145 DELF= 2,7415¢
I= 26 TH21056,2828 ?Cz 834.9016 PCe3683.46(9 Xz 5874
RW=  .00079 RY= 00032 RTe 00145 DELPE 2,U8374%
1=z 27 TH21053.5341 Tz 830.1062 PCe3685,5460 Xle 581D
RWs ,00079 “RI®  ,00032 — RYe 00144  DELPE: 2,02865
Is 28 THz | nS0.7854 TC=z 825,332¢ PCe3687.5750 Xie . ,5566
RWs 00080 RI= ,00U32 T . T
I= 29 THz | 48,0367 TC= 820.685) PCx3689,4883 X1z 5516
RW=z 08080 RI= . O0US] RTe .1 T 1, '
I= 3¢ THz | 045,2680 C=z 816,3936 PCz3691.3545 X1= « 5465
“RWT  ,00080 Ri®s 00030 T . T T,
Iz 3) THz1n42,5393 TC=z 812.1967 PCe3693,|734 Xis. 5416
- RW=  ,00080 RI= 00030 KT ,L00I199 DELP=. 1,77333
s 32 TH={03%9.,7%906 TC= 8p8.0518 PCe3694.947) Xls 5374
RWsz .00080 Ris ,0002% RT= 00138 DELP=x: [,73021
"

*

 

)

K}

Table C.5 (continued)

147

 

rC=x 8p3.9287

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I= 33 THx | 837.0420 PCe3656.6776 Xi= 5336
RWz ,0008] Rl= .00029 RTes ,00138 DELP=z 1,689%90
1z 34 THe |1 034.2033 $Cx 840.,0034 PCe3698,3679 X1z ,5300
RW=  .0008! Ris ,00029 R¥=s .00138 DELP=z: 1,65070
Iz 35 THE103|.5446 ¥C= 796.243) PCe3700.0i189 X]= 5264
: RWs .0008! ~ R1= ,p0028 RTe ,00137 DELFs T.67131
Iz 3¢ THe|p28.79%9 . tC= 792,5643 PCx3701.63g6 X1z +5233
. ~ RW=  .0008) ~ Riz ,00027 RTe 00137 DELPx: [ ,574%7
1= 37 THE | 026.0472 fC= 789,0954 PCe3703,205% X1s 5205
~ RWz  ,0008) Rl .00027 Rfe ,00137 DELF=:
Iz 38 THe|(23,2985% TC= 785,718 PCz3704.,7452 xls 5189
RWs  ,00082 —_RI= 06028 RYs .,00i36 D +5D?
Is 3% THE | 020.5498 #Ce 782,4346 PC=3706.2498 xzs 5160
' RWe ,OUUUF_ "Iz  L30020 RTE . W0
1= 49 TH= 101780101 #C: 7799,.389¢4 Pc=37n7 7229 xxs 5301
RWs 00082 = . _ 0
1z 4] THeinI5,0524. #Ce 776,447 PC=37D9.2093 th 15283
1= 42 THz)nl2.3038 ¥C=z 773.5637 Pc-37|u 6637 x!s 5269
RW=z ,00082 “Ri=_ ,00024 ~RYs 00139 “DELFs. T,42450
1= 43 THE|p09.5551 TCx 770.8925 PC=37{2.0890 Xi= 15259
RWs ,00082 "Rie ,00024 RTs ,0013% DECFE. [,39757
I= 44  THE1n06.8064 YCe 758,3245 PCe37i3.4870 Xi= 5247
RWz .00082 Ri= ,00023 RT= ,00138 DELPx. [,3677%
Iz 45 THz i 0n04,0577 ¥C2 765.8(53 PCe3714,8552 XIs 5238
RWz ,00083 Ris ,00023 RTe ,00138 “DELF® 1,33952
Ie 46 TH=jg01.3090 fCx 763.4085 PCe37i6.195] Xl= +5232
. - RWE ,00083 _Ris  ,pp0D22 RYs ,00138 DECFs: [,31391
[z 47 THz 998,5603 TC=x 781.2032 PCe37i7.5095 Xz 5234
RWe  ,0083 R1= ,on022 RY=s ,00137 DELP=: 1,2917%
Iz 48 THe 995.8716 TC= 759,1047 PCe37)8.80)7 Xls 1523
~ RW®  .00063 — _RI= ,pp02] RT= ,00137 DELFs.  1,.26564
In 49 THz ©93,p629 ¥C=2 757.07)7 PCe3720.0678 X1s  ,523¢0
"~ RWs  ,00083 RT= ,00020 RTe ,00136 DECFs: |,24015
Je 5p THe 69p,3T42 TCx 755,06824 PCe372|.3084 Xl= v5232
| RW=  ,00083 Ri= ,p0020 RTe ,00136 “DELF®: 1.2i712
I= 5§ TH: 987,5656 fC= 753.3076 PCe3722.5260 Xi= 25235
RWs ,00083 “Ris 00019 RTs  ,00i36 “DELPE (419371
Iz 52 THE 984 ,87649 TCz 75).238) PCx3723.7154 Xts v524 4
; RWs  .00084 “Ri=_ .00019 RY=s .06135  DELPE. 1,1710%
1= 53 TH= 982,0682 TCe 749.496) PCe3724.89p4 X1= '5247
Rus  .npoB4 RI#= ,00018 RTs L,00135 DELP®. ], 4822
Is 54 THz 979,3795 ¥Cx 748,964 PCe3726.039 X1ls 5262
; RW= . 00084 — RI®_ ,00018 ~ RT= ,00134  DELPE |,1291]
1= 55 THE 976,5708 " §0xn 786,506 PCe3727.)688 X1z +5277
-r , - T RNE. . .naua‘ ; - “F!g ,unfll? ‘FTF 000‘34 DELJF'-E |Q||00r
I= 56 THe 73,8227 - ¥C=z 785.6244 PCe3728.2764 © X1s 5294
- — T RWE .nppné4 __ RI1s . ,00017 RYs _ ,00133 DELP=: [.09258
" 1e 57 'TH=_973.0134-' . $Ce T84,4728 PCe3729,3726 Xle 5319
o "RN® ,0p084 = Ris ,00016 RYs _ ,p0018s  DELPs: 1,07825
1w 58 . THe 968,3247 ©  ~  ¥Cx 743.437% PCa3730,4490 X]s +5651
. — RWe  L.00084 - Ris L00015 RY¥= ,0014p DELP=: [,12240
 1e 59 THe 965,5760 - YCe 741.9660 PCe3731.57g7 o Xpe- 5673
' ~ RWE_.00084  _R1= ,00015 RTe .0D140 DELPs: 1,10248
Is 6 " TMx 962.8274 - ¥0=m 740.8452 Pc¢3732.5720---; X1=: . ,5697
L T RWE (0084 Ri= ,p0014 RY¥s 00139 ~ DELP=: [,08653
- 1w 67 THe 960,0787 #Cx=- 739.8300 PCe3733.76¢0) o X1s «5732
o — RWE -+00084 Rt® ,00014 RY¥s _.00139  DELFe: {,06995
s 62 - THe 957,330 ¥Cx 73%.1030D Pc-3734.asg7' x1=: «5770
i - T RWe - ,00084  _Ri=  ,00013 T 00139 2 G5%30
Iz 63 THx 954,583 ¥Cs 738.3825 Pc=3755 8857 xx: +58p 1
L - KW= 00084 : R—l' +000171 RYe ol 8 » .
1= 64 THe 95),8%26  §Ca-737.6678 PCe3736, 9236 X]x. 5839
: RW= .p8085 Ri{=  .on012 - KIx ,p0138 DELP=: T,0e142

 
 

 

Table C.5 (continued)

148

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

le 65 THz 949,p839 TCx 736.5584 FPCe3737,.9458 X]=. 588
- " RWE 00085 Ri®_ ,p0012 RTs 00137 DECP&: 1,00761
1= 66 THs 946,3352 TCe 736.35)5 PO=3738, 9522 Xis 2+ 5925
' RWz  .ppo85 _R1= 00012 RTs _,00137 DELFs:— 99372
Is 67 THR 943,5845 ¥Ce 735.6423 PCe3739,9466 Xis 5967
_ "~ RNE  ,00085 _Ri=  ,gn0il RT= 000|37 DELPe: 77398
Is 68 TKe 640.8378 ¥Cx 734,9426 Pc¢374n,9253 - X1= NIIEE
RWs .00085 Rt= ,0001) RY: ,001356 “DELFE: 96245
I1n 69 Tz 938,p892 ¥Cu 734.2505 ° PCe374|,8885 Xls: 26062
Ru=  ,0p085 Ris  ,00010 - RTe: _+00136 DELPx: 1 94949
I= 7¢ THe 935,3405 $Cu 733.6660 PCr3742.B8368 “X1m. 6117
RW=z. ,080685 _Rl1= 00010 R¥= ,00136 DELPE:  ,93675
I 71 THe 932,598 fCx 732.9739 PCe3743.,7742 Xje. L6170
RWe  .00D85 Ri= ,00010 R¥s ,00138 DELPFR:  ,92189
Is 72 YH: 929,643 ¥Ce 732.2867 PCu3744,6068 X{e L6227
. RWs. .00085 Ri=  ,00010 RT= ,00135 DELPs:  ,90730
I= 73 THx ¢27.0044 §¥Ce 731.6032 PCu3745,6048 X1=. » 6288
A I Rwe .0p085 Ri= - ,00009 RY=  ,00135 "DELPs:  ,8945
1s 74 THe 924,3457 §Ce 739,014} PCa3746,4983 X1e: 16350
RWe  .00085 _Ri® ,0000% RT= " ,00135 DELPs: ,BET4E
[z 75 THz 921,5970 ¥C= 730.3257 PCe3747,38p5 o Xl= 2641}
RW=  ,00085 Ris 00009 R¥= 00135 DELFx: ,B&63
1= 7¢ THe 18,8483 §Cx 729.6396 PCe3748,2476 Xi= 18473
RWes ,00085 ~ Ri=  ,00009 ~ RTe _,00135 DELPs:  ,859p6
I= 77 . TH= 96,0996 0= 729.0491 PCx3749.1060 Xl= 16538
RWe .DpO0AS Ri= .poouod RYs .00135 DELP=: 85176
Is 78 THx 913,350 ¥C= 728.3555 PCz3749,9583% Xis: 16606
RWe  ,00084 Ri= ,00008 RTe 00135 DELP::
i1s- 79 THe 910.6023 ¥Cx 727.663) PC=3750.8027 X1=. 16682
_ RWe~ .p0086 Rl=  ,p0ub6 RTe  ,0013¢4 DELP="" ,83753
Is 8¢ THe 907,8536 YCx 727.0654 PC=375|.,63¢% X1z +675%
“RWE 00086 RI= ,00008 RYs  ,D0134 DELP®: 83723
Is 87 THE 905.)1049 0= 726.3638 PCx3752.47¢2 X1s: +6839
A RW=  ,00086 RT= 00008 RTe" ,00135 DELP=: ,BZ3¥78
1=z 82 THe §02,3%62 ¥Ce 725,653 PCe3753,2955 X1z 692
R¥zs .00086 Ri® ,00008 RYe .00135 DELP=: +81731
[s 83 THz B99.6075 fCx 725.0349 PC¢3754.1|29 X1= »7005%
RWs  ,00086 _Ri= ,poalod Rf=s  ,00135 DELFE: " ,B)T42
1= 84 THz £56,8588 ?Cs 724.3616 PCe3754,9244 Xl v 7089
“RWe  ,00086 RI= ,00008 RTe ,00135 DELP®:  ,B0446
1= 85 THe 854,170) *le 723.6726 PCz3755,7298 Xis 7177
RWs  .00086 _Ri= 00008 RYe ,00136 DECPx: 751
1s 8¢ THe 89,364 ¥Cx 792.9768 Pcesvss.szeé - xl= 07267
iz 87 THe g888,6728 = 722,2760 Pc-3757 347! XJ= ..6540
RWz  .00086 ~ _Ris_ ,00008 RYs _,0012¢0 “DELPR T 69807
1= 88 THz 885,884) ¥Cx 72).5694 PCu3758,0132 - Xl= 16623
. RWs ,00086 Ris ,00008 RTe  .00120 DELPs. ,6BY54
i= 89 THz 883,54 ¥Cs 720.8582 PCz3758,7028 Xi= +4708
' RWe 00086 ~ Rz ,00008 ' L,0012p ®
Is 9p THx 880,3667 tC= 720.1383 PCe3759,3857 Xl= +6786
RWe" 00_86 __ng ,00008 Kle fi.fifll!fl UVELF®: . 67590
1= 9j THe B77.6780 $0= 718,6245 PCe3740.0616 Xz 26864
RWE  ,00086 — RI® ,00008 RYe .00120 UELFP®: 67322
Iz 92 THE B74,869% tCx 7i7.1020 PCe3760,734° X1z 6944
RNz 00087 Ri{= ,00008 “RYE _,0012] DELFs: 67060
Iz 93 THe 872,206 “fC= 715.5719 PCe376) .4056 X1x. 7025
RW=  .00087 _RI=_ 00009 x ] & .68
1= 94 THs 869,379 ¥Cx 713.9547 PCe3762.0732 Xie: 6711
RW=  .00087 Ri= ,00009% RYs ,00115 DECPe 62793
1s 9% THe. 866,6232 ¥Cx 712,543) PCe3762.70) | Xl=: 5795
; RWt 00087 ~ Riz_,00010 RYs ,00115 DELFs: ,62620
1s 9¢. THe 863,8746 ~ ¥Ce 7§1.0082 PCe3763.3273 Xi= 16875
- RWe ,00087 RTs 00010 ~RYs 00116 DELPS: 82230

e e e e e e = e .-
 

 

4}

"

)

¥)

Table €.5 (continued)

149

 

 

 

 

 

 

 

 

 

 

ls 97 THe: 86,1259 fCe 785.0878 PCe3763,9496 X1= 16669
RWE~ ,00087 R1E 00011 “RYE ,00112 DELF®. 55647
In S8 THs B858,3772 : ¥Cs 756.7089 PCe3764,5461 Xle 16747
. RWe:  ,00087 Rt ,00012 RY¥= ,0011(3 DECF=: 59577
1s 99 TH=- 855,6285 fC= 784,32)2 PCe3765,14;9 Xis. 16820
_ RW& ,00088 T Ri= ,n00012 RYs  .00114 DELP=  ,5V4p8
1#)0p THe £%2,87¢98 ?CI 781.7730 Pc!37fi510755° - X]=: 16868
RWE 400088 Rfz ,00013 R¥s ,60115 DELPE 59000
Table C.6. Computer Output Data for Overall Exchanger for One Case
NUMTs. 349 DSz 17,1646

SXs 63.8878p $8¢s  63.68070 SDPTx |66,35628 gDPSe  58,)0013
AREAX#2915+08193 UEQXx1032,63359 DTLME= |387,12037 ‘
AREAB¥290545409} UEQBE | 035.99605

 

The computer program was run for several cases to investigate all
the parameters, and "hand" calculations were made to check the accuracy
of the computer program. These hand calculations involved the determina-
tion of the heat transfer coefficient outside the tubes for the first
baffle spacing, the shell-side pressure drop for the first baffle spac-
ing, the thermal resistance of the tube wall for the first increment,
the length of the first increment, and the pressure drop inside the tubes
for the first increment. The terms used in these calculations are defined

in Appendix F,.
Heat-Transfer Coefficientrcutsidé Tubes for First Baffle Spécing

Assume that the number of tubes, n, in the boiler—superheater exchanger

_is 349, and the cross-sectional area of the shell

349

= 1450- .866) (0 875)3 1.607 £ or 231.4 in.2

The dlameter of the shell

- [/ . 607)]1/2 = 1.4304 £t or 17.16 n.

The fractional window cut, F =0, 40 and the cross-sectlonal area of the

window, - o
5 = 0.40(231.4) = 92.56 in.?

 
| 150

Therefore,
S ,
W 92.56 _

From the data published by Perry,*

Window height - 0.4213 ,

d
s

Window height = 0.4213(17.16) = 7.23 in,

To determine the length of the chord formed by the edge of the window

across the circular area, the included angle of the chord must be

determined.
® = 1/2 the included angle.
8.58 - 7.23
cos 0 = ~=8.58 - 0.15734,
0 = 80.946° |

2(8.58)sin 6 = 16.95 in. When the baffle

The length of the chord
spacing, X = 9.935 ft,

 

 

 

 

 

 

. 16.95 + 17.16 [0.875 - 0.50) _
Ay = (9.935) 18222 (2822 = - 6.051 ft2,
]
A = (231.4 - 349(0.9)%19.% _ o 4524 £e2,
w 4 144
3.6625 x 10°
Gg = €551 = 6.053 x 10° 1b/hr-ft?,
3.6625 x 10°
G, = =0 7554 = 8.096 x 10° 1b/hr-ft3,
c_ = [(6.053 x 10°)(8.096 x 10°)]*/2 = 2.2137 x 10° 1b/nr-£e2,
_ 0.5(6.053 x _105) _
Npedp =~ 12(12) = 2102,
_0.5(2.2137 x 10°) _
(Npedy, = 12(12) = 7686,
3, = 0.0186,
3 =0.0113,
W

 

4J. H. Perry, Ed., p. 32 in Chemical Engineer's Handbook, 3rd ed.,
- McGraw Hill, New York, 1950.

A
 

 

"’

¥

)

151

 

 

2/3
a, )2 /e = (2212 / - 2.43,
_ ® 0.61(6.053 x 10°)

hy = 0.0186 5 43 = 1900 Btu/hr-£t2-°F,

h = 0,0113 LALQ2.2137 x 1) _ 4291 pey/hr-£62 -OF,

w 2.43
h = [0.2(1900) + 0.8(4221)]0.8 = 3006 Btu/hr-£t?-°F, and
o

R = == = 3.33 x 10~

o = 3006 = ° .

From the computer calculations, the thermal resistance outside the tubes,

R = 3.3 x 10 .
o

Shell-Side Pressure Drop for First Baffle Spacing

The number of cross-flow restrictions,

2(8.58 - 7.23)

Ty = 0.866(0.875) - >0
and the number of window restrictions,
r 7.23 -1 =8.5 .

w _ 0.866(0.875)

From the data published by Bergelin et al.,’ the leakage factor for
baffled exchangers is 0.52. Therefore, the shell-side pressure drop for

the first baffle spacing, _
6.053 x 10°5)2

 

 

0. 6(3=56)»-4—3355———— | 0;5[2+ (0.6)8.54]-3=2l%%6§-193
APS = 0 52 —_—

144 (64. 4)(125) : : 144(64.4) (125)

0. 631 psi .

'From the computer calculations,APs'='0.638 psi.

Thermal Resistance of Tube Wéll*for'Firét Increment

The tEmperature of the tube wall for the first increment of the

.exchanger is approx1mate1y 1000 + 0. 5(125) = 1062°F. The thermal

 
152

conductivity of the tube wall, kfi = 10.6 Btu/hr'fta-oF per ft.

the thermal resistance of the tube wall,

 

d .
d 1n =2 0.5
_ o di-_ 0.5 1n 0.346
Ry = 2k, © 2(12)(10.5)
= 7.23 x 10~* .

From the computer calculations, R, = 7.2 x 104

Heat-Transfer Coefficient Inside Tubes for First Increment

The heat transfer rate,

Q = 0.001(4.1275 x 108) = 4.,1275 x 10° Btu/hr .

The temperature of the hot fluid leaving the first increment,

4,.1275 x 10°

= 1123 - 376635 = 1P )0.41

t = 1122.252°F ,

hf

- Therefore,

and the average temperature of the hot fluid in the first increment,

1125 + 1122,252 o
avthf = 2 = 1123.63°F .

The change in enthalpy of the supercritical fluid,

4.1275 x 10°

M = T73312 x 10°

and the enthalpy of the supercritical fluid at the end of the first
increment, H = 1421 - 6.52 = 1414.48 Btu/lb. The temperature of the
supercritical fluid at the end of the first increment, t = 992°F, and

the average temperature of the supercritical fluid in the first incre-

ment,
¢ = 992 + 1000

0
av 2 = 996°F .

The mass velocity of the fluid inside the tubes,

C = (6.3312 x 105) 144

v = 2,778 x 10° 1b/hr-£t3
349 (—}f) (0.346)2 -

n
 

 

4}

)

.

153

Assume that the temperature drop across the inside film is 37°F. Then
the temperature of the inside surface, t, = 996 + 37 = 1033°F. Using
Eq. 13 discussed in Chapter 3, the heat transfer coefficient inside the

tubes,

0.00459(12) (0.064) [0.346(2.778 x 106110'923

hy = 0.346 U 12(0.075)

[(1445.6 - 1417.8)0.0751° 813 10,1977\° 231
(1033 - 996)0.064 0.2071

3422 Btu/hr-£t2 -°F ,

The thermal resistance inside the tubes,

0.50

——— et -iy
= 3%22(0.346) - *-22 x 107,

R

and the total thermal resistance in the first increment,
= (4.22 + 7.23 + 3.33)10™ = 14.78 x 107¢ ,
Therefore, the calculated temperature drop across the inside film,

4
At = 7. 78

 

(1123.63 - 996) = 36.4°F .

This is sufficiently close to the assumed temperature drop across the
inside film of 37°F. From the computer calculations, Ri = 4,3 x 10™*
and R_ = 14.8 x 1074,

Length of First Increment

The length of the flrst 1ncrement, _

(4. 1275 x 108) (14.8 x 10=%)

£2 - 1.048 ft .
| 349u( )(1123 63 - 996)

g =

- From the cofipfiter calculatiops, Z,: 1.056 ft.

 
 

154

Pressure Drop Inside Tubes for First Increment

The Reynolds number for the tubes,

_ 0.346(2.778 x 10°)

(NRe)T

and the friction factor, f = 0.0029. Therefore,

AP

4(0.0029) (1.056) (12) [2.778 x 103)a 0.1977
T 0.346 I 3600 144(64.4)

5.39 psi .

From the computer calculatioms, APT = 5.37 psi.

Stress Analysis for Case B

In the vertical U-tube one-shell-pass one-tube-pass boiler-superheater
exchanger, the supercritical fluid enters the head at a temperature of
700°F and a pressure of 3766.4 psi, flows through the tubes, and leaves the
opposite high-pressure head at a temperature of 1000°F and a pressure 6f
3600 psi. The supercritical fluid entrance pressure used in this analysis
was 3800 psi, which has a more conservative effect on the analysis. Be-
cause of these high temperatures and pressures, the material chosen for
the exchanger was Hastelloy N. The high-pressure head has an inside
radius of 12 in. and a wall thickness of 4.5 in. There are 349 tubes
inside the shell and they have an outside diameter of 0.5 in., a wall
thickness of 0.077 in., and are on 7/8-in. center lines. |

The coolant salt enters the shell inlet below the head at a tempera-
ture of 1125°F and a pressure of 251.5 psi, flows around the tubes through
the 18.25-in.~ID shell, and leaves the exchanger at a temperature of
850°F and a pressure of 193.4 psi. The relative heat transfer resistances
at the supercritical-fluid tube-inlet side of the exchangér and at the

tube-outlet side are tabulated below.
 

)

-

%)

155

 

 

- Resistadnces of Resistances of
Supercritical Fluid Supercritical Fluid
Tube-Inlgt End | Tube-Out%et End
(hr* ft2 - F/Btu) (hr- £ft2 - F/Btu)
R, =1.3 x 10™% - R, = 4.3 x 1074
R =8.8 x 10~ R =7.2 x 10-*

w W
R = 1.4 x 1074 R = 3.3 x 10

The stress analysis for the boiler-superheater exchanger involved
a determination of the stresses produced in the tubes, the shell, the
tube sheets, and in the high-pressure head. The stresses developed in
the tubes that were considered in this analysis are
1. primary membrane stresses caused by preséufe, |
2. secondary stresses caused by the temperature gradient across the
tube wall, and |
3., discontinuity stresses at the junction of the tube and tube sheet.
The stresses in the shell that were considered in this analysis are
1. primary membrane stresses caused by pressure and
2. discontinuity stresses at the junction of the shell and tube sheet.
The tube sheet thickness requiféd for the allowable stress under the
existing temperature and pressure conditions was determined, and the
maximum priméry membrane stresses were calculated for the high-pressure
head.

The maximum shear stress theory of failure was used as the failure

- criterion, and the limits of stress intensity were determined in accordance

with Section III'of~the'ASME]Bdiler_and‘Pressure Vessel Code. The terms

used in these calculations;are_defined'in Appendix F.

~ Stresses in Tubes

 The stresses in the tubes may be grouped as pressure, temperature,

and discontinuity stresses.

 
156

Pressure Stresses. From page 208 in Ref. 5, the longitudinal stress

component caused by pressure,

P& - P K
i 0
LT -2
where

b = outside radius of tube = 0.25 in.,

a = inside radius of tube = 0.173 in.,

 

; = 3800 psi,
o = 193.4 psi. - .
_3800¢0.02993) - (193.4)0.0625 . ,
291, = 0.03257 = 3;21 psi (ten311§) . .

The hoop stress component caused by pressure;

£P, - PP (P, - P )&H
5. = i o 4 } 0 .
P°h ¥ - & (b - &)

 

At the inside surface of the tubes,

3607(0.02993) (0.0625)
0.02993(0.03257)

6436 psi (tensile), and

p%h = 3121 +

at the outside surface of the tubes,

3607 (0.02993) (0.0625)
3121 + =—(,0625(0.03257)

= 6436 psi (tensile) .

P°h

The radial stress component at the inside surface of the tubes,
o= 3800 psi (compressive), and
at the outside surface of the tubes,

o_ = 193.4 psi (compressive) .

 

®S. Timoshenko, Strength of Materials, Part II, 3rd ed., Van Nostrand,
New York, 1956.
 

 

»

+)

L]

157

Temperature Stresses. From page 63 in Ref. 6, the stresses in the
tube caused by the temperature gradient,

— i - P e 2]

O; = g, =
AL AR T 51 L yyin 2

where r is the inner or outer radius opposite that at which the stress
is being computed. At the tube-side inlet, the maximum temperature

gradient across the tube wall,

_ 8.8 = o
Ammax = 11.5(850 700) = 115°F .
The average temperature of the tube wall

5.7 o
tav = 700 + 11.5 (150) = 774.4°F .

For this temperature, the coefficient of thermal expansion, & = 8.1 x 10—

in;/in.'oF, and the modulus of elasticity, E = 27.8 x 10° psi. Therefore,

o _8.1g27.82g1152(1 2r° (0.37)]

AL 1.4(0.37) U~ 0.03257
-49,992(1 - 22.727%)

i

At the outside surface of the tube wall, r = a = 0.173 and

AtOL T At%h = -16?008 psi (compressive) .

At the inside surface of the tube wall, r=b = 0.25 and

a

At%L = AtSh = 20,997 psi (tensile)

_Discontinuit§18tresses;"Atthe junction of the thick-walled tube

and the tube sfiééf;nfhé deflection of the outside surface of the tube

caused by internal pressure_(pagé 276 in Ref. 7),

| Ap_%ji’%{fiz—g @ - u)] . B e

 

83, F. Harvey,'Pré3sute1Véé§él.Deéign, Van Nostrand, New Jersey,
1963. | - SR |

- 7R. J. Roark, Formulas for Stresses and Strain, 3rd ed., McGraw
Hill, New York, 1954.

 

 
158

To maintain continuity at the tube sheet junction, the deflection and
slope at the junction must be zero. From Case 11 on page 271 of Ref. 7,

the deflection caused by a moment,
M
A = DR (C.2)

and the deflection caused by a force,

 

 

ST @
where
-
| “TZA - o) ¢
3(1 - 1 /a
n= (2], an
a+b
r = 2 -

The slope at the junction must also be zero. Therefore, the change in
slope caused by the force must be compensated for by the action of the

moment; that is, from page 271 in Ref. 7,
F - zm = 0 . (C°4)

To satisfy the continuity requirements, Eqs. C.2 and C.3 must equal

Eq. C.1, or
b & F M
PElEee @) - - e | (c.3)

2

2 2
2FA {E_"'_.!?. M Lf._'z"_l?.)
ET - ET St

 

Btz @ - o] - o2 - we (a3

Substituting for F,

Btz e-o] =@,

 

7R. J. Roark, Formulas for.Stresses and Strain, 3rd ed., McGraw
Hill, New York, 1954.

 

W)

"w
 

 

 

 

»

&)

159

oY

 

. PbT [ a
M—27\z a+b)2l_b3 -2 @ D)] ’
2
and F = 2\M. N
From page 271 in Ref. 7, the stresses caused by M are longitudinal
stresses,
5 = 6M
ML~ T’
hoop stresses caused by lengthening of the circumference,

Mh ='2¥ %9(2;5_2),

and the hoop stresses caused by distortion,

M°h T O ¢
secC

From page 27 in Ref. 5, the stresses caused by the force due to shorten-

ing of the circumference,

 

For the boiler-superheater exchanger,

b = 0.25 in.,

 

 

a=0.173 in.,
T = 0.077 in.,
v = 0.3, and
225 0.2115 in. = .
L 3(1-0.09 1** .1
M= [wanr o) - 007 o
Therefore, | o .

M = 12.59 in.-1b/in., and
~ F = 253.56 1b/in. |
The hoop stresses at the'jfinction are

. _ 2F

Py = T_hr
_ 2MNr

¥h T

14,027-psi“(compressive) and

Il

7017 psi (tensile).

 
 

 

 

160

The longitudinal stresses at the junction,
6M

° L -E§-= 12,741 psi (temsile inside compressive outside)

The secondary hoop stress,

= v0; = 0.3(12, 741) = 3822 psi (tensile inside compressive

o
M hsec outside) .

Stresses in Shell

The stresses in the shell are the primary membrane stresses and the

discontinuity stresses at the junction of the shell and tube sheet,

Primary Membrane Stresses. The hoop stress,

251.5(18.25) _ 6120 psi (tensile) ,

P°h 2T 2(0.375)

and the longitudinal stress,

_ B _

p%L = IT 3060 psi (tensile) .

Discontinuity Stresses. If it is assumed that the tube sheet is
very rigid with respect to the shell, the resulting moment and force

applied to the shell at the junction are

M =P/2¥ and F = P/A

A = [3-&#1—;’2]1/4 = 0.695 .

Therefore, the longitudinal stress in the shell at the junction,

where

_ oM
ML= - 11,108 psi (tensile inner surface, compressive

outer surface) .

The hoop stresses in the shell at the junction,

¥oh = -2—?; Rr =-¥ r = 6120 psi (tensile) )
v®h = VO = 3332 psi (tensile inner surface, compressive
sec outer surface), and

=== Ar = 12,240 psi (compressive) .
 

 

 

 

»

§

161

Stress in Tube Sheet

The thickness required for the tube sheet,®
1’211 /2
1S ]

where P
T = thickness of tube sheet, in.,
d.1 = inside diameter of the pressure part, in.,
P = pressure, psi,
S = the allowable stress, psi, and
Z = a constant.
For S = 16,600 psi at 1000°F, Z = 1, and

= 9.125(0.4785) = 4.366 in.

Stress in High-PreSsufe Head

The spherical high-pressure head has an inside radius of 12 in. and
a wall thickness of 4.5 in. The maximum primary membrane stresses caused

by the internal pressure,

- B + 28
P %L T T2 - @)
where
a=12 in., S
b = 16.5 in. and o
P = 3800 p51 | :'] :
'Therefore, ' N LT
.fdh - Pci';_5463 psii(tensile),
and , _ . | _ S
| Pdf %e3800'pei (compreesive);

 

@ Tubular Exchanger Manufacturers Assoc1at10n, Inc., pP- 24 in
Standards of Tubular Exchanger Manufacturers, 4th ed., New York, 1959.

 
 

 

162

Summary of Calculated Stresses

Stresses in Tubes. The stresses calculated for the tubes are tabu-

lated below.

 

Inside OQutside
Surface _ ~ Surface
Stress (psi) (psi)
POL 3121 3121
P%h 10043 6436
pCr -3800 -193.4
ML -12741 -12741
v%h 7017 7017
v%h 3822 - =3822
sec
*n -14027 -14027
At°L +12000 -16000
Amgh +21000 -16000
Zch 27855 -20396
ZcL 36862 -25620
Ecr -3800 -193.4

Therefore, the primary membrane stress intensity,

Pm = 13,843 psi for the inside surface, and
Pm = 6629 psi for the outside surface.
The allowable stress intensity,
_ _ o
_Sm = Pm allowable - 16,000 psi at 1036 F for inside surface,

13,000 psi at 1100°F for outside surface.

The calculated primary membrane stress intensity plus the secondaryr
stress intensity

Pm + Q = 40,662 psi for inside surface,
25,427 psi for outside surface.

il

The allowable primary membrane stress intensity plus the secondary
stress intensity, |
P+ Q= BSm

48,000 psi at 1036°F for inside surface,
39,000 psi at 1100°F for outside surface.

e

L
 

 

 

4y

»

.

163

Stresses in Shell. The stresses calculated for the shell are

tabulated below.

Inside Outside

Surface Surface

Stress (psi) : (psi)
PUL | 3060 3060
% 6120 6120
p%y -251.5 0
MgL 11108 -11108
M°h 6120 6120
M°h -3332 -3332

sec

°h ~-12240 -12240
Zoh J 3332 -3332
ZoL ) 14168 -8084
Ecr -251.5 0

The maximum primary membrane stress intensity in the shell,
| Pm(max) = 6372 psi.
The allowable stress intensity,

Sy = 10,500 psi at 1125°F.

The maximum calculated P, + Q = 14,420 psi, and the allowable Pp + Q =
3s_ = 31,500 psi at 1125°F.

Stress in Tube Sheet., The'maximum stress calculated for the 4.75-in.-

 

thick -tube sheet is 1essitfihn 16;600-pSi. The allowable stress at a
temperature of 1000°F = 16,600 psi. o

| Stresses in-gigh-Préésure Head. The maximum primary membrane stresses,
| .=_5463 psi (tensile).

-?qL-=:PUh

9263 psi. The allowable stress, sm,=-16,600 psi at 1000°F.

The radial stress, o, = ~3800_psi,énd'thefefofe,‘Pm %,5463‘- (-3800) =

 
 

164

Appendix D

CALCULATIONS FOR STEAM REHEATER EXCHANGER

 

The steam reheater exchanger transfers heat from the coolant salt
to the exhaust steam from the high-pressure turbine. The coolant salt
or hot fluid is on the shell side of the exchanger, and the steam or cold

fluid passes through the tubes of the exchanger.

Heat-Transfer and Pressure-Drop Calculations

The criteria governing the desigfi for the reheater exchanger stipu-
lated that the coolant salt enter the exchanger at a temperature of 1125°F
and leave the exchanger at a temperature of 850°F, a temperature drop of
275°F. The flow rate for the coolant salt,

T
W = 0.88 x 10

b 5 = 1.1 x 10° 1b/hr .

Certain properties vary with temperature in a manner that is close to
being linear. Therefore, average conditions may be used without serious

error except in calculating pressure loss at the entrance and exit. The

 

average conditions given for the coolant salt are tabulated below.
Density, p = 125 1b/ft®
Viscosity, p = 12 1b/hr-ft
Thermal conductivity, k = 1.3 Btu/hr'ft?-oF per ft
Specific heat, C = 0.41 Btu/1b-°F

Prandtl number, N = 3.785

| P
| The conditions stipulated for the steam in the exchanger are teabu-
lated below.

é Inlet Outlet Change

% Temperature, °F 650 1000 +350

E Pressure, psia 580 540 =40
Specific volume, ft/1b  1.0498 1.5707 +0.5209

Enthalpy, Btu/1b 1322.3 1518.6 +196.3
 

4}

"

 

»

165

The flow rate for the steam,

5.50 x 10°
W= 2 = 0.63 x 10° 1b/hr .

The average conditions given for the steam in the exchanger were
1. viscosity, p = 0.062 lb/hr’ft,

2. thermal conductivity, k = 0.036 Btu/hr-fta'oF per ft,

3. specific volume, v = 1.31034f63/1b, and

4, NPr = 1.0,

The material to be used for the tubing was specified as Hastelloy N,
and the tubes were to have an outside diameter of 3/4 in. and a wall thick-
ness of 0.035 in. From this information, the pertinent diameters and areas

tabulated below were calculated.

d = 0.0625 ft

di = 0.05667 ft

A, = 0. 002522 ft2 per tube

a_ = 0.1964 f2per ft of tube length
a, = 0.178 ft® per ft of tube length
a = 0.187 £t° per ft of tube length

| The selection of the type exchanger to be used to reheat the exhaust
steam was based on the data published by Kays and London.,! Our study of
the principles discussed led to the selection of a straight counterflow
unit as béing the.bést éuite&;to meét_the requirements for thié particular
applicétion.: The design for ‘this vertical shell-and-tube counterflow

exchanger with»disk'and doughnut'baffles is illustrated in Fig. 8 of

Chapter 7. The inside diameter of the shell is 28 in., and the exchanger

contains 628 tubes on a triangular pitch of 1 in.

- Heat=Transfer Calculations-. o

'Heat Transfer Coefficient Inside Tubes. Equation 2 of Chapter 3

was used to determine the heat transfer coefficient inside thé tubes.

 

lW. M. Kays and A. L. London, Chapter 2 in Compact Heat Exchangers,
2nd ed., McGraw Hill, New York, 1964,

 
166

 

 

 

 

 

 

 

- k_ 0 8 ( 0.4
hi = 0.023 di(NRe) _(NPr) <.
The Reynolds number,
diG
Ne = p ’
where
W
cf 0.63 x 10° :
G = GCA,)  628(0.002572) " 3.98 x 105 1b/hr-fe® .
_ 0.05667(3.98 x 10°) _ 5
NRe = 0.062 = 3.64 x 10° , .
and ‘ '
B 0.036 ,.- 0 +8 (110 .4 -
hi = 0.023 6?63337(3'64 g 10%) (1)
= 409 Btu/hr.££2.°F .
The velocity of the steam through the tubes,
v Scf' _ 3.98 x 10°(1.310) _ .. £t /sec
=~ 3600 ~ 3600 = See -
Heat-Transfer Coefficient Outside Tubes. A modification of Eq. 5 in
Chapter 3 was used to determine the shell-side heat transfer coefficient
for this cross-flow exchanger with no internal leakage and disk and dough-
nut baffles. The opening in the doughnut baffle was sized so that the
flow parallel to the tubes is turbulent; that is, NRe was set at 7500 on
the basis of the outside diameter of the tubes. The disk baffle was .
sized so that the flow around it parallel to the tubes is turbulent, and
the baffles were spaced so that the flow of the coolant salt outward from *
the central parallel-flow region is the same as the flow in the parallel~
flow regions.
To determine the diameter of the hole in the doughnut baffle,
doGw 0.0625Gw
o = 7500 = 7
when
_71500(12) _ .
G, = "5 o625 = 1.44 x 10° 1b/hr-ft° and
1.44 x 10° : :ff;
v, = 175(3600) " = 3.2 ft/sec. - o/

u

S A - P

 
 

 

 

 

u

o

167

The flow area through the window region,

W .
A - hf 1.1 x 10%

w =T T x 108 =07 T .

 

Aw = area of doughnut opening - area of tubes
nd 2
= « (radius of doughnut hole)® - n, —5— = 0.764 ft* ,
where n, = the number of tubes through the doughnut opening. The area

d
associated with each tube in triangular pitch can be expressed as

0.866p°. Therefore, |
n(radius)® = nd(O-Sfifipa) ’

and
nd 2

n,(0.866p%) - n, Z = 0.764 ft2

 

nd[o.sees[-i—z-)g_ - {-(%}2 'i%ii] - 0.764 ,

0.764(144) 110

D3 = 0.866 - 0.442 - 0.424 — 2779 tubes .

(radius doughfiut hole)?® = 2§2§9i%§§2

radius doughnut hole = 8.46 in. and

Dd = 16-92 in.-

The maximum number of restrictions'or tubes in the cross-flow region
through the inner window, | -
| 16,92
riw = 200.933) - 9.07 .

The number used was 9. |
,The'baff1e Spa¢ing was.based‘on the arbitrary,requirément that GB

= GW or AB = Aw. Where X = the baffle spacing,

sele™

'-= T[Dd - ndo »

when n is the number of tubés'in'a band around the edge of the doughnut

opening. The band width is equal to the pitch of the tubes, and the area

 
 

 

168

of the band is approximately nde. An approximate equation for determin-
ing the number of the tubes,

 

 

 

flde nDd
B =0.9° T0.9
Then
A ‘1 - do)
"X ° er)d 0.9p |’
and the baffle spacing,
g o 0.764(144)
- ( do) ~ 3.14(16.92)(0.167)
®g |l - 379D
= 12-4 inc

To determine the outside diameter of the disk baffles, the flow area
outside the disk, Aw = cross-sectional area of the shell minus the area
of the disk minus the cross-sectional area of the tubes in the outer

window region.

 

d 2
_ . [14)? 2 ™o
A = 1((12) - n(radius disk)® - now( =i .
The number of tubes in the outer window region,
D 2 D 2
s - "3 aser 628 - 14x{3] 41 g
ow 0;86653 - - 0.866
D 2
- 628 - 522(3]disk :
Therefore,
_ _ | 14Y° Dy® [ D)® }_fl__é'a
A, =0.764 = =l - 3]y - [628 - s22{3] ;o 4(144)14}_

2 2 |
“[’%%?T -(2)azer - 1628 - 522[.‘22’d1sk} (°'°°°977-)]

x[0.747 - o.w{%)iisk] .

0.764
%

2

0.49{-’23)Zisk = 0.747 -
 

 

 

 

 

44 L 04N I 7 EHH0  yPi

®

169

2
)di sk

n:u

= 1.028 ,

2

radius disk = 1.014 ft = 12.17 in.
diameter disk = 24.3 in.

The maximum number of restrictions in the cross-flow region of the

outer window,

28 - 24.3

W = 0.933(2) = 1.98 (use 2)

Where the Reynolds number = 7500, the heat transfer factor for the

cross-flow area,
= -0 .382 _
Jg = 0.346(NRe) = 0.0115 ,

and - ,
h -
_ o 2 /3 1
JB'cc; (Npr)/ G, 22| °
P _B
G)
!

Since we arbitrarily set GB = G , the bracketed fraction in the above
w

 

 

l-r+r

 

equation becomes 1 and
h

     

)2/5
o B Pr
Therefore, the shell-side heat transfer coefficient,
J C G '

B B
ho (N )?;3

0 0115(0 41) (1. L x 10°)
v 2.428

2800 Btu/hr ft2 °F .

Jr

"Slnce G = G o the heat transfer is assumed to be the same for Cross

B
flow and for flow through the W1ndows of the baffles. The average

“leakage flow area is approxlmately 25% of the total flow area, and

 
 

 

 

 

 

170

according to Bergelin et al.,® this makes it necessary to multiply the

heat transfer coefficient by a correction factor of 0.8. Therefore,
h_ = 0.8(2800) = 2240 Bru/hr+£e2-°F .

Determination of Tube Length. The log mean temperature drop across

the exchanger,

 

 

 

At _ (850 - 650) - (1125 - 1000) _ 75
Lm 1 200 : -~ 0.470
125
= 160°F . |
va, = —t. L L265x 16 o0 yos g /hr+CF
t - At 160 = 1. u .
Lm
1 1 T 1
Ua, h.a.nL * ka L + hanL ?
t 11 m 00

and solving for L,

 

where
_ 1
- 10.37
m (0.035 0.187
\ 12

= 0.00150 .

p |~

k
T

7.78 x 10°7 1 1
L = 628 1 409(0.178) + 0.00150 + 2240(0.1964)]

21.70 ft .

This tube-sheet-to-tube-sheet tube length was increased to 22.1 ft
to allow room for the inlet and outlet pipes on the shell side of the
exchanger. This minute change in length was neglected in the pressure-
drop calculations, but it was used to calculate the overall heat transfer

coefficient. The total outside heat transfer surface area of the tubes,

 

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

 
 

 

 

 

171

o
it

nnd L
0

6287(0.0625) (22.1) = 2725 f£t° .

f

Therefore,
27250 = 7.78 x 10° ,

U = 285 Btu/hrft® .

Pressure-Drop Calculations

Pressure Drop Inside Tubes. From the work published by Perry,® the

entrance loss,

nr Cig) Tt
.AP = 0.4(1.25 ch(144)

A V=2
i S )
s

The velocity of the steam at the inlet,

Ces¥  (3.98 x 105)1.0498

 

= 115.5 ft/sec ,

 

 

VT = 3600 = 3600
and
Ait _ 628(0.002522) _ 1.584 _ . o
5. 142 " 4.28 -9 -
s - x5

Therefore, the entrance loss,

Ap o 0.4(1.25 - 0.37)(115.5)°
i ¥ T64.4(1.0498) (144)

0.4825 psi .
- Thé kinetic energy 1653,;-;r
- G z(v' - v . 5 U
AP = cf “'co . eci’  (3.98 x 10°)2(0.5209)
i = Zg_(3600)7 (144) ~ ~64.4(3600)2 (144)
 =0.686 psi .
The friction 1035,  ,:, ;= . | - -
HIVSP  0.015(21.7) (145)2 (0.763)

 APi'?2g¢di(144) o 64.4(0.05667) (144) =~ °+97 psi.

 

3J. H. Perry, Editor, Chemical Engineer's Handbook, 3rd ed., McGraw
Hill, New York, 1950.

 
 

 

 

172

The exit loss,

AP

2 2
. Ael” Vr
i

Ss 2(144)gcvc0

1.5707)2
- 2 =2/
(1 - 0.37) (145 13103

= A (3. (1.5707) — 0-82> psi .

The total pressure drop inside the tubes is the sum of the entrance,

kinetic energy, friction, and exit losses.

psi
Entrance loss " 0.482
Kinetic energy loss 0.686
Friction loss 9.930
Exit loss : -~ 0.825
Total AP 11.923 or 12.0 psi

i

Pressure Drop Qutside Tubes. The number of baffles on the shell

side of the exchanger,

217312, _
N="F5 -1=2,

and the number of cross-flow restrictions,

_24.3 - 16.9

Ty = W = 3,97 (use 4)

The pressure drop caused by the cross-flow restrictions

 

2
AP = 0.6r N 'p _0.6(4) (21) (3.2)2(125)
o B 2g (144) - 64 .4 (144)
= 6.96 psi .

The pressure loss through the inner window region or the holes in

the doughnut baffles,
V.2p
1062 + 0-6%) 7g_(Tet)

AP
o

10[2 + 0.6(9)]0.138 = 10.2 psi .

The pressure loss in the outer window region around the disk

baffles,
 

 

 

"

 

173

Vfi?p
10(2+06r)m

>

10[2 + 0.6(2)]0.138 = 4,42 psi .

The total shell-side pressure drop equals the sum of the pressure

 

losses,
psi
Cross-flow loss 6.96
Inner window loss 10.20
Outer window loss 4,42
Total APO 21.58 psi

Using the factor of 0.53 from the data published by Bergelin et al.,® the

total shell-side pressure drop,

AP = 21.58(0.53) = 11.4 psi .

Stress Analysis for Case B

The operating pressures of the coolant salt were raised for the
Case-B design of the heat-exchange system. The coolant salt enters the
steam reheater exchanger at the same temperature (1125°F) but at a pres-
sure of 208.5 psi, and it leaves the exchanger at the same temperature
(850°F) but at a pressure of 197.1 psi., The steam entry and exit tempera-
tures and pressures are the same for Case B as they are for Case A. The

steam enters the exchanger at a temperature of 650°F and a pressure of

'580 psi, and it leaves the exchanger at a temperature of 1000° F and a

pressure of_568 psi. The same cype vertical shell-and-tube counter flow
exchanger with disk and doughnut baffles is used for Case B. The shell
of the exchanger has an inSide”diameter of 28 in. and a wall thickness of

0.5 in. There are 628 tubes”with an outside diameter of 3/4 in. and a

wall thickness of 0 035 in. arranged in a triangular array on a l-in.

pitch in the exchanger _
The stress ana1y51s for the Case-B exchanger involved a determination

of the stresses produced in ‘the tubes, shell, and the tube sheets. The

shear stress theory of failure was used as the failure criterion, and the

 

 
 

 

 

174

stresses were classified and the limits of intensity were determined in

accordance with Section III of the ASME Boiler and Pressure Vessel Code.

Stresses in Tubes

The stresses produced in the tubes are
1. primary membrane stresses caused by the steam pressure,
secondary stresses caused by the témperature gradient across the
wall of the tube,
3. discontinuity strésses at the junction of the tube and tube sheet,
and |
4, secondary stresses caused by the difference in grdwth between the

tubes and the shell.
Primary Membrane Stresses. The hoop stress component,

Pd;  388(0.68)

On = 3T = 2(0.035) - 3769 psi (tensile) .

Assume a longitudinal stress caused by the pressure drop only. The

longitudinal stress at the point where the steam enters the tubes,

Pd;  12(0.68)

0L =TT = %(0.035) - 58.2 psi (tensile) .

Secondary Stresses Caused by Temperature Gradient. The secondary
stresses caused by the temperature gradient across the tube wall are
longitudinal, AtL’ and hoop, At From page 63 of Ref. 4, the stresses

at the inside surface of the tube caused by the temperature gradient,

20° b
AL T At%h T Mt[l TR - & (ln a” ’
and the stresses at the outer surface of the tube,
282 b
at’L T at’h T kAm[; T - a?[;n a)} ’

where k = a constant. At the steam entry into the tubes, the relative

 

#J. F. Harvey, Pressure Vessel Design, D. Van Nostrand Company,
New Jersey, 1963.
 

 

 

v e oo et e 1

[}

L}

175

heat transfer resistance inside the tube, R, = 86; the resistance across
the tube wall, Rw = 14; and the resistance outside the -f:ube,"Ro = 51,
Therefore, the temperatfire gradient across the tube at the steam entrance,

14

O
r = 757 (200) = 18.5°F .

At

The inside radius of the tube, a = 0.34 in., and the outside radius of
the tube, b = 0.375 in. At the point where the steam enters the tubes,
773°F,

the modulus of elasticity = 27.8 x 10° psi,

t
m
E

the mean temperature of the tube

o
coefficient of thermal expansion = 8.1 x 10-® in./in.' F, and

QE _ 8.1 x 1078 (27.8 x 10°)
2(1 - v)(1n b/a) ~ 1.4(0.098)

n

k = = 1641 .

The stresses at the inside surface of the tube,

_ 0.2812
0.025

i

g

At°L = At%h 1641(18.5) [1

(o.ogsfl

-3154 psi ;

and the stresses at the outside surface of the tube,

_ 0.2312
0.025

1l

o (0.098fl

AL = At%h 1641(18.5) '1

2845 psi .

Discontinuity Stresses. Since the tube sheet is very rigid with
respect to the tube, assume that there is no deflection or rotation of
the joint at the junction of the tube and tube sheet. Therefore, the

deflection produced by the moment7M and the force F must be equal to

_the def1ect1on, A, produced by the pressure load, and the slope at the

junction must remain zefo;,fThe'defléctibn caused by differential pressure,

PP

From pages 12, ‘126, and LZ?{in-Ref;VS, the deflections caused by F and M,

o . F
T

 

8. Timoshenko, Strength of Materials, Part II, 3rd ed., D. Van
Nostrand Co., New York, 1956,

 
 

176

and :
_ M,
AM' 2D\ °
where

D = ET® and
12(1 - ¥)

~ [3“1;132 )]1 /2 .

b
\

Setting the deflection caused by pressure equal to the deflection caused
by M and F,

Pr2 _F - M
"ET ~ 2*D °

The slope produced by F must be counteracted by M; that is,

Substituting for D and solving these last two equations for M and F,

> |

M=—§-2i and F =

The outside diameter of the tube is 0.75 in., the wall thickness is 0.035 in.,

and the mean diameter, dm = 0.715 in. Therefore,

112(1 - R 4 _ 12¢0.91)  */~
A= t d 2T } = [(0.715)2(0.035)3] = 11.5 .

 

m

The moment,

388 .
and the force,
_ 388 _
F = i1.5 - 33.74 1b .,

From page 271 in Ref. 6, the hoop stresses,

 

_2F _2(33.74)(11.5) (0.3575) _
Fh = T AL = (0.035) = =7926 psi, and
_ 2™ _2(1.468)(132.05)(0.3575)

 

2 -
Mh =TT AT S (0.035) = 3960 psi .

 

®R. J. Roark, Formulas for Stresses and Strain, 3rd ed., McGraw
Hill, New York, 1954.
 

"

4

177

The longitudinal stresses,

_.éfl = 6(1.468 = 7190 psi (tensile inside, compressive
i (0.035) .
, outside)

The secondary hoop stresses,

= 0.3(7190) = 2157 psi (tensile inside, compressive
outside) .

M%h = ML
Secondary Stresses Caused by Growth Difference. Unrestrained
differential growth arises from two sources: (1) temperature differences
between the tubes and the shell and (2) pressure differences between the
tubes and the shell. The differential growth caused by temperature dif-
ferences was calculated first. The mean temperature of a tube,
93
tm(tube) - tsteam 151 (tsalt - tsteam) ?
where the fraction 93/151 represents the ratio of the heat transfer
resistance of the steam side plus one-half the tube wall resistance to
the total resistance. Therefore, the mean temperature of a tube at the

steam-inlet,
| 91
151

and the mean temperature of a tube at the steam outlet,

= 650 + == (200) = 773°F ;

m(tube)

93

1000 + =— 51

o
tm(tube) = (125) = 1077°F .

Thus,'the'average témpefature of the_tubeS'is"925°F,-and the average

- unrestrained tube eXpansibn per,inch of length,

¢ (925 - 70)70 925

855(7.27 x 1076) = 6. 216 x 10 in./in.

It was assumed that thertemperature of the shell is the same as the

temperature of the.cfiolant sa1t;f1qwing through it. The average tempera-

iture of the sheil'is 988°F; énd the_average unrestrained growth of the

shell per 1nch of length
(988

_ : an
70)70 988 = 918(754 x 10-°)

6.793 x 10-® in./in.

t€S

 
 

178

Therefore, the unit unrestrained differential growth caused by tempera-

ture differences,

A - 6.793 x 10 - 6.216 x 10~°

¥ T ts T ¢fr
0.577 x 10=® in./in.

The unit unrestrained differential growth caused by pressure differ-
ences was calculated next. The unit unrestrained longitudinal expansion

of the shell caused by pressure,

oo
=m=%(5"°] _

 

PD
sl _ )
P€s E E = 2TE\2 T Y] >
where -
0y, = the longitudinal stress caused by pressure and
op = the hoop stress caused by pressure.

200(28)

P€s = 2(0.5)(26.7 x 10°) (0.5 - 0.3)

0.042 x 10=® in./in.

Since the longitudinal stresses in the tubes are only 194 psi, they were
assumed to be zero. The unit unrestrained longitudinal expansion of
the tubes caused by pressure,

_ MBd,  -0.3(388)(0.68)
PéT T~ 7 T2TE " 2(0.035) (27 x 10°)

= -0.0419 x 10-® in./in.
Therefore, the unit unrestrained differential growth caused by pressure,
— - = - - -3
PA£ = s " P°T (0.042 x 10°) (-0.0419 x 10-3)
0.0839 x 1072 in./in.;

and the total unrestrained differential growth,

Beiotal ~ B T PE
(0.577 + 0.0839)10-2
0.6609 x 10-® in./in.

Actually, the growth is restrained and the load induced in the
shell by the total differential growth must equal the load induced in
 

 

 

"

179

the tubes. The sum of the deflections of the tubes and of the shell

caused by the 1nduced load must equal the deflection caused by the
differential growth; that is,
‘ De
s T~ K;%_ L1
T
The area of a 3/4-in.-0D tube with a wall thickness of 0.035 in. is
0.0786 in,? Therefore, the total area of the tubes,

Ay = 628(0.0786) = 49.4 in.?
The area of the shell,
A, = 1(28.50)(0.5) = 44.77 in.?

At a tenpereture‘of 925°F; the modulus of elasticity of the tube,
ET = 27 x 10° psi; and at a temperature of 988°F, the modulus of
elasticity of the shell, ES = 26.7 x 10° psi.

0.6609 x 102

T S 1 + 1
49.4(27 x 165) 44.77(26.7 x 10°)

= 4,16 x 10° 1b ,
The longitudinal stresses in the tubes caused by the restrained differ-

ential growth,

4,16 x 10°

_ A€0L= 49,4 = _8440 psi .

Stresses in Shell

The stresses produced in the shell are

1. primary membrane stresses caused by the pressure of the coolant salt,

2. ,secondary stresses caused by the difference in growth between the

-tubes and the shell, and _
3._ discontlnuity stresses at the junction of the she11 and the tube

sheet.

 
 

 

180

Primary Membrane Stresses. The primary membrane stresses are the

hoop stress,

 

PD
__s _208.5(28) _ .
on = TZT = 2(0.5) - °°38 psi
and the lonitudinal stress,
PDs
op ="ZT = 2919 psi .

Differmntial Growth Stresses. The longitudinal stress in the shell
caused by the difference in growth between the tubes and the shell,
4.16 x 10° .
AL =T T gg.77 - "2300 psi .
Discontinuity Stresses., It was assumed that the tube sheet is very
rigid with respect to the shell., Therefore, the deflection and rotation
of the shell at the junction of the shell and tube sheet are zero. The

moment and force,

 

M ='§%5 and F ='§ ,
where
- 1/a { 1 fa
L - 120 022] / _ { 12;0.912‘ I 0.482 .
D=2T° 2l
LY (28.5) (Zl

From page 271 in Ref. 3, the longitudinal stresses,

ML = M _ % 208'51 = 10,784 psi (tensile inside, compressive
2(0.232}Z outside);

and the hoop stresses,

= 00 = 0.3(10784) = 3235 psi (tensile inside, compressive

outside),

M°h
secC

2M\2  _ 208.5(14.25)

v°h 7T 0.5 5942 psi (tensile),

2FAr _ 2(208.5)(14.25)

F°h ° T T 0.5

 

= 11,884 psi (compressive).
 

¥

 

181
Stresses in Tube Sheet

The load on the tebe sheet comes from two sources: (1) that caused
by pressure and (2) that caused by the differential growth between the
tubes and the shell. Assume that the load caused by differential growth
can be converted into ‘an equivalent pressure,

total force

 

AEPe = tube-sheet area
4,16 x 10° .
==z - 675 psi .

The net actual pressure on the tube sheet, 570 - 192.1 = 378 psi. There-
fore, the total effective pressure, 378 + 675 = 1063 psi. From page 24
of Ref. 7, based on bending the tube sheet thickness,

—

KD ,niu1/e
Se(Er

where
DS = inside diameter of pressure part for stationary integral tube
sheet,
P = pressure, psi,
S = allowable working stress
= 10,500 psi at a temperature of'1125°F, and
k = a constant

1 for T/D < 0.02.

__u&(_@z]/ hrn avEot - A 43 4
T = 25 {qoso0| | = 14(0:03162) = 4.43 in.

A tube sheet thickness:dfrégs:in.'was used.

Summary of Calculated Stresses

The maximum shear stress theory of failure was used ‘as the failure

criterion, and the stresses-were c1a581f1ed and limlts of stress

 

7 Tubular Exchanger Manufacturers Association, Inc., Standards of
Tubular Exchanger Manufacturers, 4th ed., New York, 1959.

 
 

 

182

intensity were determined in accordance with Section III of the ASME

Boiler and Pressure Vessel Code.

Calculated Stresses in Tubes. 'The,caiculated stresses in the tubes

are tabulated below.

 

Stress on Stréss on
' Inside Surface Qutside Surface

Type (psi) - - (psi)

PUL 58.2 58.2
Poh - 3769 _ 3769

P -580 -208.5
AEGL 8440 - 8440
Foh -7926 7926
MCh 3960 3960
M%h 2157 2157

sec

MUL 7190 7190
AtOL -3154 +2845
Axch | -3154 +2845
ZGL 12534 4153
Zch -1167 +491

Zcr - 580 -208.5

The calculated primary membrane stress intensity in the tubes,
P = 3769 - (-580) = 4349 psi.

The allowable Pm at a temperature of 1077°F = 14,500 psi. The calculated

primary membrane stress intensity plus the secondary stress intensity,

+ = -
Pm Q omax Umin

12534 - (-1167) = 13,701 psi .

At a temperature of 1077°F the allowable stress intensity for Hastelloy N,
Sm = 14,500 psi. The allowable P + Q for the tubes,
m

P+ Q=35 = 43,500 psi .
 

 

&N

183

Calculated Stresses in Shell. The stresses calculated for the

shell are tabulated below.

 

 

Stress On Stress On
Inside Surface Qutside Surface
Type ~ (psi) (psi)
PoL . 2919 2919
Poh' | 5838 5838 -
AEOL ‘ -9300 -9300
°h -11884 -11884
M%h 5942 5942
M°h ' . 3235 =3235
‘'sec | , . | ,
MOL | 10784 10784
ZUL , 4403 -17165
Zch 3131 -3339
Zor -208.5 0

The calculated primary stress intefisity in the shell,
Pm = 5838 -~ (-208.5) = 6046.5 psi .

At a temperature of 1125°F,'the.alloWab1e P, = 10,600 psi. The calcu-

lated primary plus secondary stress intensity in the shell,

o - g

+
Pm Q max min

n

0 - (-17165) = 17,165 psi .
At a temperature of 1125°F £he'a1iowéb1é stress intensity, S = 10,600 psi.
The allowable CE e .
o B+ Q=735 = 31,800 psi .
' Calculated Stress in Tube Sheet. The maximum calculated stress

in the tube sheet < 10,50Q?§si,j§nd thé_allowable stress = 10,500 psi.

 
184

Appendix E

CALCULATIONS FOR REHEAT-STEAM PREHEATER

Heat is transferred from throttle steam or supercritical fluid in
the reheat-steam preheater to heat the exhaust steam ffom the high-
pressure turbine before it enters the reheater. The exchanger selected
is a one-tube-pass one-shell-pass counterflow type with U-tubes and a

i U-shell, as illustrated in Fig. 9 of Cha#ter 8. There are 603 tubes

g with an outside diameter of 3/8 in. and a wall thickness of 0.065 in. on

| a triangular pitch of 3/4 in. in the exchanger, and no baffles are used.

é The supercritical fluid flowing through the tubes enters the

| exchanger at a temperature of 1000°F and leaves at a temperature of 869°F.
The reheat steam enters the shell side of the eXchanger at a temperature
of 551°F and leaves at a temperature of 650°F. The terms used in the

following calculations are defined in Appendix F.

Heat-Transfer and Pressure-Drop Calculations

. The properties of the supercritical fluid flowing through the tubes

| vary almost linearly because the fluid does not pass through the critical
temperature range. Therefore, average conditions were used, and the
inlet, outlet, and average values or change of the properties of the

supercritical fluid that these calculations were based on are tabulated

 

below.

§ Change or

Inlet Qutlet _Average

Temperature, °F 1000 869 At = 131
Pressure, psi 3600 3550 AP = 50
Enthalpy, Btu/lb 1421.0 1306.8 N = 114.2
Specific volume, ft3/1b 0.1988 0.1620 vay = 0.18
- Specific heat, Btu/lb'oF 0.76 1.07 Cp av = 0.91
Viscosity, 1b/hr-ft 0.078 0.074 pay = 0.076
Thermal conductivity, 0.066 0.066 kgy = 0.066

Btu/hr* £t .OF per ft
Prandtl number 0.90 1.2 Npy av = 1.05
 

»

o

185

The flow rate of the supercritical fluid in the tubes,

- 2.94 x 10°
Wog = 8

and the total heat transfer rate,

 

= 3.68 x 105 1b/hr ,

Q = W, AH = 3.68 x 10°(114.2)

4.21 x 107 Btu/hr .

The flow rate of the reheat steam on the shell side of the exchanger,
ch = 6.31 x 10° lb/hr. The inlet, outlet, and average values or change
of the properties of the reheat steam that these calculations were based

on are tabulated below.

Change or
Inlet OQutlet Average
Temperature, F 551 650 At = 99
Pressure, psi 600 580 AP = 20
Enthalpy, Btu/1b 1256.2 1322.8 MH = 66.6
Specific volume, f€31b 0.8768 1.0498 vay = 0.9633
Specific heat, Btu/lb- °F 0.72 0.60 Cp av = 0.66
Viscosity, lb/hr ft 0.048 0.054 Mgy = 0.051
Thermal conductivity, 0.029 0.032 kgy = 0.0305
Btu/hr* ft° °F per ft

Prandtl number 1.19 1.01 Npy av = 1.10

Heat Transfer Calculations

The log mean temperature difference for the exchanger,

t )

( ho ~

 

Ath =

ln( hi

_'350 - 318

el

' co)
t - ‘ci .

ho

= 333°F .

The heat transfer surface areas were established ‘from the physical
‘data for the tubes. The tube outside diameter = 0, 375 in., wa11 thickness
= 0.065 in., and the. in81de diameter = 0. ,245 in.

d_ = 0.0313 ft,
d, = 0.0204 ft,

_Therefore,

 
 

 

 

 

186

a =nd = 0.0982 ft® /ft,
0 o
a, = nd, = 0.0641 ft2/ft, and
1 1 7
a + a,
a =->——2=0.0812 ft?/ft,
m 2

Heat Transfer Coefficient Inside Tubes. From Eq. 2 in Chapter 3, the

heat transfer coefficient inside the tubes,

— k“ o .8 ° .4
h, = 0.023 di(NRe) (N, )0 .

Based on the inside diameter of the tube, the Reynolds number,

d.G
i

 

 

il
NRe T op ?
where
d, = 0.0204 ft,
u=0.076, and
¢ - bt
T Ait
The total inside flow area,
nd 2
A, =10 —; = 603(0.000327) = 0.197 £t
Therefore,
3.68 x 10°
Gp = 0 197 — = 1-868 x 10° 1b/hr-£t® ,
and
_0.0204(1.868 x 10°)
Ne, = 0076 = 5.01 x 10°

The heat transfer coefficient inside the tubes,

0.066
g =9-023 55570

2750 Btu/hr-£2 -°F ,

h (3.63 x 10*)(1.0197)

The velocity of the supercritical fluid through the tubes,

_1.868 x 10°

V= 3600 (0.18) = 93.5 ft/sec .

L
 

 

 

 

"

187

Heat Transfer Coefficient OQutside Tubes, The inside diameter of
the shell, Ds = 20.25 in., and since there are no baffles used in the

exchanger,

wn
1

2]
H

my (20.25)
{4) 144

1.773 ££2

- 603(0.000767)

and the shell-side mass velocity,

_ 6.31 x 10°

G =""1.773

= 3.56 x 10° 1b/hr'ft"a

If Eq. 2 of Chapter 3 is used, the heat transfer coefficient outside the

tubes,

— .E_ N0 .8 0 4
h = 0.023 De(NRe) (NPr) ’

where '
k = 0.035 and
(NPr)°'4 = (1.10)° ¢ = 1.039.

The'equivalent diameter,
4(1.773) _4(1.773)

 

 

 

2, - 603(0.0982) + fl12%5321 - 64°4_ = 0-H0 £
and the Reynolds number,
N = 0'11(3:321" 10°) _ 7.68 x 10° ,
(NR£56°8 = 5.1 x 10* .
h = 0.023 20802 (5.1 x 10%) (1.039)

338 Btu/hr£t2°F .

However, if Eq. 12 df'Chapter’3 is9uséd, the shell-side heat transfer

1

coefficient, U 1d G\C 8 e pu° 33
i i[9S TG T
h 0.16 —|— "

0 _d0 _ _
’ 1 0:0305{0.0313(3.56 x 105)\° ¢ |
0.0313{ 0.051 ) (1.032)

257 Btu/hr-£62-°F .

0.16

 
 

188

The more conservative value given by Eq. 12 was used.

Length of Tubes. To determine the 1ength'of the tubes required for

the exchanger,

U 4.21 x 107

Ua, =%~ 333
Lm

= 1,266 x 10° Btu/hr'oF .

 

 

 

 

t o i1i
and
Lo N,
" n lh a a h.a. .}l ?
0o o0 m ii
I 0.065 -4
where Rw = kw --TE?IET = 4,51 x 107*.
L__1.266x105( 1 L 4.51 x 107 1
- 603 0.0982(257) 0.0812 0.0641(2750)
=10-68 fto

This active length of 10.68 ft was increased by 2.52 ft to allow
room for the shell-side inlet and outlet pipes, giving a total tube-sheet-
to-tube-sheet tube length of 13.2 ft. The overall heat transfer coeffic-
ient was calculated on the basis of the total outside heat transfer

surface area of the tubes,

a = nndoL
= 603r 0.0313(13.2)
= 781 ft2 .
Therefore,
781U = 1.266 x 10°
U = 162 Btu/hr-ft® .

The distribution of film resistances and temperature drops at the

hot end of the exchanger are tabulated below.

Resistance At

(%) (°F)

Outside film 77.9 273
Tube wall 10.9 38
Inside film -~ 11.2 89

Total 100.0 350

hl]
 

 

 

189

Pressure Drop Calculations -

On the basis of a tube length of 13.2 ft, the pressure drop in the

 

 

tubes, |
, ] |
p fl_(_li___hiz.(&4)_v3(__1_)
i ch(144) di 2gc vav(144)
1.868 x 10%)\2
] 0038 0 613313,y - ) [
= 64.4(144) 0. e 64.4(0.18)(144))

-1.07 + (12.6)5.24 = 65 psi .

Calculation of the shell-side pressure drop was based on the active

tube length of 10.68 ft. This pressure drop outside the tubes,

 

 

 

2 - 2
AP = Gs (vco vci),; fL + 4) Gs ( av\
o 2g _(144) D, 144
3.56 x 105)2 3.56 x 105)B |
T | 0.173 . [0.012¢10.68) | 4) 3600 ) (09633
= 64 .4 (144) | 0.11 64.4(144)

0.183 + (5.165)(1.015) = 5.43 psi .

Stress Analysis

The material selected for use in this exchanger was Croloy (2.25%
Cr, 1% Mo, and 96.75% Fe) SA 387 Grade D for the plate and SA 199 Grade

'T22 for the tubes. The stress analy31s calculations were based on a

supercr1t1ca1 flu1d inlet pressure of 3600 psi and an outlet pressure of
3535 psi and a steam inlet pressure of 595.4 psi and an outlet pressure

of 590 psi. This analysis 1nvolved the determination of the stresses in

.,rthe tubes, shell, tube sheets, and the high-pressure head.

Stresses in Tubes‘

The stresses produced in the tubes are

1. primary membrane stresses caused by pressure,

 
 

 

 

190

2. secondary stresses caused by the temperature gradient across the
tube wall, and

3. discontinuity stresses at the junction of the tube and tube sheet.

Pressure Stresses. From page 208 of Ref. 1, the longitudinal stress

 

component,
P.& - PV
_ 1 0O
LT - &
_ 3600(0.015) - 590(0.03515) _ . .. __. .
= 0 02015 = 1651 psi (tension)

The hoop stress component,
@€, - PP (P, - P )&I?
o, _1i o
P - & B2 - &)

3010(0.015) (0.03515
1651 + 55(0.02015)

1651 + 72276 ,

 

%h

i

where r = the mean radius of the tube. At the inside surface of the tube

- 1651 + 18:76

o 0015 - = 6903 psi (tension) ,

and at the outside surface of the tube,

78.76

= 1651 + 5753515

oy = 3892 psi (tension) .

The radial stress component at the inside surface of the tube, o. = 3600

psi (compression) and at the outside surface of the tube, o. = 390 psi

(compression).

Temperature Stresses. From page 63 in Ref. 2, the stresses in the

tube caused by the temperature gradient,

 

 1S. Timoshenko, Strength of Materials, Part II, 3rd ed., D. Van
Nostrand, New York, 1956.

2J. F. Harvey, Pressure Vessel Design, D. Van Nostrand Company,
New Jersey, 1963.
 

 

ot

191

 

. gt | _ 2R (ln_b_]
2
At°L = At%h Z(I-D)InEL ¥ -2

where R is the inner or outer radius opposite that at which the stress is

being computed. The maximum temperature gradient across-the tube wall,
At = 0.109(350) = 38.15°F .

The maximum average temperature of the wall = 650 + 0.,0835(350) = 942°F.
For this temperature, the coefficient of thermal expansion, @ = 8.5 x
10~ in./in.'oF, and the modulus of elasticity, E = 27 x 10° psi, and

'g = %f%%%% = 1.5306,.and11n'§ = 0.4257. Therefore,
_ (8.5 x 10) (27 x 106')38.2[ 212
At°L © At%h = 2(0.7)(0.4257) 1 - 552015 (0-4257))

14710(1 - 42.288) .

At the outside surface of the tube wall, R = a = 0.1225, and

AtOL = At%h = 14710[1 - 42.2(0.0150)] = +5399 psi .

At the inside surface of the tube wall R = b = 0.1875, and

o -7112 psi .

At%L < At%h T

Discontinuity Stresses. From page 210 in Ref. 1, the deflection at -
the junction of the thick-wall tube and the tube sheet,

 

 

AL ar°*1=i-$1=or+ 1+ azbz(P -P)

When r = b,' o - .
—————— Zasz - (b + &)bP, + ba-.aab . .
E(LR - ag} [ _ i ( _ ) o v( ) P. ] _ (E.1)

To maintain continuity at the Junction of the ‘tube and tube sheet, both

the slope and deflectlon of the tube wall must be zero at the junction.

Replac1ng EL w1th D- in Eqs. 11 and 12 on page 12 of Ref 1

A(;'c='0) - 27\31)“" w, (E:2)

 
 

 

 

 

and
dy
dx(x - 0)
where
D - —EL ____
T12(1 - R) °
3L - PRI/
A= [-;g—fr“-j; ’
T=Db~ a, and

. a+b
r is assumed to be 2

 

192

_ 1
T 22D

(F-2M) =0,

. (E.3)

From Eq. E.3, it may be seen that F = 2)M. . Using this value for F and

the values for-D, r, T, and A listed above, from Eqs. E.1 and E.2 one

obtains

_1._[232bpi - (¥ + aa)bPo + p(b® - aa)bPo] =

b+ a

which reduces to
2

M= W[Zaab]?i - (P + 83)bP° + p(® - Sa)bPo] .

For the preheater with a tube outside diameter of 0.375 in. and wall
thickness of 0.065 in., a = 0.1225 in., b = 0.1875 in., and v =

value of 0.30. Therefore,
b+ a=0.31,

(b + a)® = 0.0961,
(b + a)® = 0.0298,
£ = 0.01500625,
B = 0.03515625,
£ + B = 0.05016250,
¥ - & = 0.02015,
A = 12.81, and
A\° = 164,
M=

o
Il

1l

0.40923(20.2635 - 5.549 + 0.669)

6.296 in.-1b/in. of circumference, and
2)M = 2(12.81) (6.296)
161.3 1b/in. of circumference.

A% (a + b)3M

assumed
 

mn)

.y

on

193

The discontinuity stresses at the junction of the tube and the tube

sheet caused by the moment are the longitudinal stress component,
M _ 6(6.296)
ML T T T (0.065)

8941 psi (tension inside,
compression outside) ,

the hoop stress component caused by lengthening of the circumference,

2M o|a + b)“ ‘
M°h TA 2 |7 164(0.155)

2462 psi (tension) ,

and the hoop stress component caused by distortion,

= v(op) = 0.3(8941)
sec

M°h

2682 psi (tension inside,
compression outside) .

The discontinuity stress at the junction of the tube and the tube sheet

caused by the force is the hoop stress component,

2F |a + b)-;.2(161.3)(12.81)
P = TMT2 | =T 200.065)  ©:1%)

4927 psif(éompressidn) .

Stresses in Shell

~ The stresses in the—sheiljare

1. primary membrane stresses caused by pressure, and

2, discbntinuity stresses at the junction of the shell and tube sheet.
_ Primary.Membrane.Stfessés,;the:primary membrane stresses in the
shell caused by pressure are the hoop stress, |

_PDs  595.4(20.25)
% T 72T T T 2(0.0365)

énd,theElongitudinaljstress;

= 13,780 psi ,

 PDg

oy = 4T = 6890 psi .

 
 

 

194

Discontinuity Stresses. To determine the discontinuity stresses
in the shell at the junction of the shell and tube sheet, the tube sheet
was assumed to be very rigid with respect to the shell. The resulting

moment and force applied to the shell at the junction are

 

P P
M= Exg and F = Y’
where
3(1 - 1 /e 2.73 1/a 1 /a
A= [ e ] = [(10.344)2 (0.4375)3] = (0.1333) /

= 0.6042.

The stresses in the shell at the junction caused by the moment are the

longitudinal stress component,

6M 6(595.4)

ML = T = 2(0.3651) (0.4375)° = 25,561 psi (tensile inside,

compressive outside) ,

the hoop stress component caused by lengthening of the circumference,

_.Z_M a. _ P __595.4 10.344 _ .
¥h = 7 A°r = T = (0.4375) = 14,077 psi (tensile) ,

and the hoop stress component caused by distortion,

o = v(,0,) = 7668 psi (tensile inside,
M"h ML .
sec compressive outside) .

The stress in the shell at the junction caused by the force is the hoop

stress, oF
on = —E-Ar = 28,136 psi (compressive) .

Stress in Tube Sheet

From page 24 in Ref. 3, the thickness of the tube sheet,

T - E'i(z]l/g
- 2 1s ’

 

8 Tubular Exchanger Manufacturers Association, Inc., Standards of
Tubular Exchanger Manufacturers, 4th ed., New York, 1959.
 

 

an

"N

195

where
F=a constant,
Di = inside diameter gf the pressure part, in.,
P = pressure, psi, and
S = the allowable stress, psi

For F =1 and S = 7800 psi at a temperature of 1000° F,

l1/2 .
21(301 ) / - 10.125(0.621)

7800
= 6.288 in,

T =
A tube-sheet thickness of 6.5 in. was used in the preheater.

High-Pressure Head

The high-pressure head is a thick-wall sphere with a wall thickness
of 5.75 in. and an inside radius of 12 in. The maximum primary mem-

brane stresses caused by internal pressure,

_ _'P b'3+2a3
P°h TPOL T T 2( - £)

 

where
a =12 in. and
b=17.75 in.
Therefore, o
| S - (17. 75)‘3 + 2(12)3 ]
P’h T P9 T -3-600[2[(17 75)° - (12)3]

4215 psi (tensile)

ool

The radial stress COmpdnent;_cr 3600 psi (compressive)

- Summary of Stress'Calculatibns ,

The shear stress theory of failure was used as the failure criterion,
and the stresses were classified and limits of stress intensity were
determined in accordance with Section III of the ASME Boiler and Pressure

Vessel Code.

 
 

 

196

Calculated Stresses in Tubes. The calculated stresses in the tubes

are tabulated below.

Inside Surface Outside Surface

 

 

Stress (psi) (psi)
P°L 1651 1651
°h 6903 3892
P°r -3600 -590
MoL 8941 -8941
v°h 2462 2462
M°h 2682 ~2682
sec _

Fh -4927 -4927
AL -7112 5399
Amch -7112 5399

Lo, 8 4144

ZGL 3480 -1891

Eor -3600 -590

 

Therefore, the calculated primary membrane stress intensity,

and the allowable primary stress intensity at a temperature of 961°F,
P = Sm = 10,500 psi. The calculated maximum primary plus secondary

stress intensity,
(Pm + Q)max = 3480 - (-3600) = 7080 psi , | .
and at a temperature of 961°F, the allowable
(Pm + Q)lnax = BSm.= 31,500 psi .

Calculated Stresses in Shell. The stresses calculated in the shell
~are tabulated on the following page. |
 

¢ v

ay

-t

 

197
| Inside Surface’ Outside Surface
Stress (psi) , (psi)
pOL 6890 6890
20 13780 13780
a =595 0
VoL 25561 -25561
vOh w077 14077
\Oh 7668 -7668
sec o
£ -28136 . -28136
Lo, 7443  -7883
Zoy 32486 . -18600
£o_ =595 | 0

Therefore, the.calculated_primary membrane stress intensity,
P = 13780 - (-595) = 14,375 psi ,

and the allowable P = Sm'=15,000.psi. - The calculated maximum primary
plus secondary stress intensity

(Pfi + Q)max = 32,486 - (-595) = 33,08l psi ,
and the allowable (P_ + Q) = at 650°F = 35_ = 45,000 psi.

- T Mmoo Ymax T m
Calculated Stress in Tube Sheet. The maximum calculated stress

intensity uin“thertube-sheet;is'1ess'than 7800 psi and the allowable
at 1000°F is 7800  psi. | o |

Calculated Stresses in High-Pressure Head. -tThe'maximum primary

membrane stresses calculated

P‘O'L = Pch = _4215 psi,

- rand the radlal stress component, o, = -3600 psi. Therefore;'the calcu-

"lated primary membrane stress intensity, B

Pm 4215 . ( 3600) = 7815 psi ,

and_tfie allowable ?m'at 1000*F-= Sm = 7800 psi. These values were

‘judged to be in adequate agreement for the purposes of this preliminary

analysis.

 
 

 

 

o
I

UU&’UQ&U‘U?'#'N
| -

oW o IM
il

198

Appendix F

NOMENCLATURE

heat transfer surface area, ft2/ft (heat-transfer and pressure-
drop calculations)

inside radius of tube, in. (stress a#alysis)
flow area, £t2 (heat-transfer and pressure-drop calculations)
Ay = area of shell or tubes , in,2 (stress-analysis)
outside radius of tube, in. '
by-pass leakage factor
heat exchanger parameter >
specific heat |
diameter of tube
diameter of shell
a constant in stress analysis
ET®
12(1 - v®)
modulus of elasticity, psi
friction factor
fractional window cut (heat-transfer and pressure-drop calculations)

force per inch at discontinuity, 1lb/in. (stress analysis)

FOT’ Fipp Fg = load on tubes or shell caused by differential expansion,

a9
O
]

& L T e
fn

1b (stress analysis) o
gravitational conversion constant, lbm-ftllbf-sec2
mass velocity, 1lb/hr-ft2
heat transfer coefficient, Btu/hr.ft=.°F
enthalpy, Btu/lb
heat transfer factor

thermal conductivity, Btu/hr-ftZ-°F per ft (heat-transfer and
pressure-drop calculations) .

a constant in stress analysis
— O

b
2(1 - v)(In 3)

length - Qii
 

-y

g

»y

 

.

=
O a éfi W oo fiF:3 2 oo

bt O

w

t
B

R

QR M = < ¢ & 1 e

e

t - t
e

199

length of tubes, ft

moment per inch at discontinuity, in.-1lb/in.
number of tubes

number of baffles

Prandtl number

Reynolds number

pitch of tubes

pressure, psi

primary membrane stress intensity, psi
volumetric flow rate, ft3/sec

heat transfer rate, Btu/hr ( heat-transfer and pressure-drop
calculations)

secondary stress intensity, psi (stress analysis)
number of restrictions (heat-transfer and pressure-drop calculations)
mean radius of tube or shell, in. (stress analysis)

thermal resistance, fta-hr-°F/Btu (heat-transfer and pressure-drop
calculations) =~ |

relative heat transfer resistance (stress analysis)
cross-sectional area (heat-transfer and pressure-drop calculations)
calculated stress. intensity, psi (stress analysis)

allowable stress intensity, psi

temperature, °F

'wall thickness of tube, in.

overall heat transfer coefficient, Btu/hr-ftZ.°F
specific volume; ftsliB  |

velocity, ft/sec

flow rate, 1lb/hr

baffle spacing

capacity ratio in heat-transfer and pressure-drop calculations

hi ~ tho
i.

coefficient of'thermalmegpansion, in./in.-°F (sttésé analysis)

Co

effectiveness ratio

tco - tci
thi = Cei

 
 

200

AP’ AF’ AM = deflection caused by pressure, force, and moment, in.
Ae
AP
At

Ath = log mean At, °F

differential growth, in./in.

pressure difference, psi

temperature difference, °F

growth, in./in.

a constant in stress analysis

_ [3(1 _ va)]1/4

r°7?
log mean correction factor (heat-transfer and pressure-drop
calculations)

S
N

viscosity, 1lb/hr-ft

T %
i

Poisson's ratio
density, 1b/ft>
longitudinal, hoop, and radial stress components, psi

Q
il

o =
L %nw %

At%h’ AL = hoop and longitudinal stress components caused by

temperature differences, psi

= hoop and longitudinal stress components due to the

M°’n’ ML i
moment, psi

O = hoop stress components due to force, psi

AecL = longitudinal stress component due to differential growth,

psi

hoop and longitudinal stress components due to pressure,

P’n? pUp = RO°
psi

Subscripts for Nomenclature Above

a = annulus

B = cross flow

ce = cold fluid at end of first pass
cf = cold fluid

ci = cold fluid in
co = cold fluid out

 

cu = cold fluid at end of unbaffled section
d = doughnut opening

e = equivalent

 
 

-5

“e

he -

hf
hi
ho
hu

it

oD

ow

2 £ g =9 ot 0

201

hot fluid at end of first pass
hot fluid

hot fluid in

hot fluid out

hot fluid at end of unbaffled section
inside

total inside flow area

mean

outside

OD of disk

ID of inner window

pressure

shell

total

tube

unbaffled section

window

tube wail

 
 

 

 

 

 

 

 

 

?

 

1.
2-4,

60-74.
75.

-

SoPEeMOEANEOR

-

O?U"flm"dbflfifl'rj

203

 

ORNL-TM-1545
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Bender 26. G. H. Llewellyn
‘E. Bettis 27. .R. E. MacPherson
S. Bettis 28. H. E. McCoy
G. Bohlmann 29, R. L. Moore
J. Braatz 30. H. A. Nelms
B. Briggs 31. E. L. Nicholson
A. Cristy 32. L. C. Oakes
L. Culler 33. A. M. Perry
J. Ditto 34, T. W. Pickel
G. Duggan 35-36. M. W. Rosenthal
A. Dyslin 37. Dunlap Scott
E. Ferguson 38, W. C. Stoddart
F. Ferguson 39. R. E. Thoma
C. Fitzpatrick 40. J. R. Weir
H. Gabbard 41. M. E. Whatley
R. Gall 42, J. C. White
R. Grimes 43, W. R. Winsbro
G. Grindell 44-45, Central Research Library
N. Haubenreich 46. Document Reference Section
W. Hoffman 47, GE&C Division Library
R. Kasten 48-57. Laboratory Records Department
J. Kedl 58. Laboratory Records, ORNL R. C.
A. Kelly 59. ORNL Patent Office

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