ORNL-TM-2952.txt

 

 

 

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ORNL-TM-2952

Contract No.' W-'-7403-eng-26l
REACTOR DIVISION
PARAMETRIC SURVEY OF THE EFFECTS OF MAJOR PARAMETERS

ON THE DESIGN OF FUEL~TO-INERT-SALT HEAT
EXCHANGERS FOR THE MSBR

A, P, Fraas and M, E, LaVérne

NOVEMBER 1971

 

P . N O TI C E : :
-‘-'l'his rcport was prepared as an account of work’
-‘]. sponsored by -the United States Government, Neither
.| the United States nor the United States Atomic Energy
.| Commission, nor-any of their. employees, nor any of | -
* { their- contractors, subcontractors, or their employees, |
7'} makes sny warranty, express or implied, or assumes any
-} legal Hability “or responsibility for the accuracy, com-
’ ‘pléteness or: usefulness of any information, apparatus, | .
| product 6r process disclosed, or represents that its nse -
P wonld not infrlnge private!y owned rights '

 

 

 

 

 

 

OAK RIDGE NATIONAL LABORATORY
' Oak Ridge, Tetinessee 37830
- operated by _
UNION CARBIDE CORPORATION “x\'
~ for the o ‘
U S ATOMIC ENERGY COMMISSION

BISTRIBUTION OF THIS DOCUMENT g UNUWZM .
 

 

  
 
 
 
 
 
 
 
 
 
 

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ABSTRACT .

iii

CONTENTS

® 9 & 0 0 0 8 9 800w e 4 % 29 80 88" s & 8 0 8 & 80 68 8 ¢ 8B s & & o & 8 9 00 0 & 9 4 e ey

INTRODUCTION ¢ & & 00 & 90 4 9 b A s e S " " e 0N * & & 5 &6 8 0 & 80 e s B E 90 .......'.V'....l

SUMMARY ..

ANATLYSIE seveeeteacancanncans Ceteiescicatt et aes st eas a0 nsasun veeess
Design Bases and Criteria ....ccveienecanass teees st rasnsessn s
Derivation of Heat Exchanger Equations ....iooeeevennns ceteaseans

Heat BalalnCeS ..e.eeeeenseenss seassan tesesesasetaresbanaan
Convective Heat Transfer .....veeees. T

Temperature Difference Between Fluids ............... veasse

Pressure Drops ¢ PS8 dE S PSS SrERe NSNS e Y.

Shell Side Eq_uivalent Diameter | 8 9 8 2 6 00 8P 80000 e 6088 0.

Solution of the Equations .....ccvesceses eeeraeeeeeaans teesnens

Reduction to a Single Equation ettt tesas e tena et aaann

Computer SOlution lll...‘.!.'...l-...OVOOVCI'.l..l... ..... T8 8 0 0 s

Extensions of the Analysis ....... tesacsscacesvtercenssesentasona
Other Fluids ........'.I-. ..... ........‘.....7 ................

Tube Pa‘tterns ....... ‘..............'l.. .............. e 20 2 e

Other Conditions ....ceeeveeeenececccceansns teesseesvesanaves
PARADdETRIC STUDY 8 S g 00 09040 P E RO tET SIS ST EEERTSTTRETDS 4 808 8000080 08080 e
CHOICE OF INERT SALT .ccceeeceescssnscsascsessns IEEEEEY R EERR R

Materials Compatibility Considerations e..eeeeseeecesscenceseen.

Melting POint ..... _'.."."-.’..“.l...'.‘I...C....‘...I..."......O..

Leaka-ge PrOblemS cru'.oro'roi;_o .orovo-t:oooo.oucco ooooooooooo Vol_.oaroooc ooooooo

Off-GaS PrOblemS l.‘..’.'.._...f‘l....I....‘....'.......v. .......... - &

Heat TransferPerformnce ...C..'.'.'...............l‘...'.l...‘

{REFERENCES
~ APPENDIX A.
- APPENDIX B.

APPENDIX C.

......l'...._."i_'"'_"...I...."........' ......... . 8 809 &0 0

Solution of the Heat Exchanger Equations ..............

FORTRAN Program.for Computer Solution of the Heat
Exchanger Equations trtessarsecss sttt rrarrcessaanatace

Sa.mple Program Input and Qutput evvvenvnenrennnconnans

Page

 

O O 39 2N & &= MnM H -

W W W Wwwwh N H H 2 e e
O U1 W Ww RO 0V VYV WU & W WwH RO

= =
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PARAMETRIC SURVEY OF THE EFFECTS OF MAJOR PARAMETERS
| ON THE DESIGN OF FUEL-TO-INERT-SALT HEAT
EXCHANGERS FOR MOLTEN SALT REACTORS

A. P. Fraas and M. E. LaVerne
ABSTRACT

The design of heat exchangers for molten salt reactors
involves so many parameters and their interrelationships are
so complex that it is difficult to envision the effects of
the various trade-offs that can be made in attempts to opti-
mize the system. This report presents a procedure for
carrying out such analyses together with the results of a
parametric study showing the effects of tube diameter, fuel
pressure drop, inert salt pressure drop, and the temperature
difference between the fuel and the inert salt with either
NaBF, or Flinak as the fluid in the intermediate heat trans-
port system An unusual design for a 2200 Mw(t), 100 Mw(e)
power plant? was used as the reference design for the de-
tailed calculations of the parametric study presented in
thls report.

INTRODUCTION

In response to & request from.R.'B.'Briggs of this Laboratory,
A. P. Fraas worked out a conceptual design for a molten-salt breeder
reactor in which the heat exchangers and the pumps were‘enclosed with
the reactor in a single pressure vessel.® This design'approach was
taken in part to minimize the fuel inventory in the system and in part
to avoid difficulties with'thermal stresses and possible thermal stress
cracking that might be. caused by differential expansion in connectlng
plplng Extremely dlfflcult problems arise in plplng systems in whlch the
pipe length-diameter ratlo is too low to give good flex1bility for accom-

modation of the dlfferentlal thermal expansion between the hot and cold

'portlons of the system ThlS 1s partlcularly 80 because the system must

also be de31gned to w1thstand a severe earthquake.

'When the report descrlblng the 1ntegrated reactor-heat exchanger de-

's1gn was 01rculated 1n rough draft form, quite a number of people raised

questlons with regard to ‘the effects on fuel inventory of changes in the

major des1gn parameters. The analys1s presented in the following section

- was therefore carrled out to answer these questions. Inasmuch as the
 

2

calculational technique and computer program have general application, it

seemed desirable to present the study in this report.
SUMMARY

An anaslysis has been made of the performance of fuel-to-inert-salt
heat exchangers for the MSER. - Employing this analysis, a parametric study
has been made of the effects on the heat exchanger design of changes in the
input parameters of major interest. The result is to clarify the effects
of the various trade-offs that can be médé in attempts to optimize the sys-
tem design. Table 1 is a concise summary of the principal results of the

parametric study.

Table 1. -Summary.of:Effects of Changes in Major
Parameters on Number of Tubes, Tube Length,
and Heet Exchanger Fuel Inventory

 

Approximate Percentage Effect

 

Parameter and Change

 

Number of Tube ;Fuel
Tubes Length Inventory
Tube OD ‘ , +40 =20 -25
3/8 to 5/16 in.
Fuel ap(ap,_) -5 -10 -30
100 to 280 psi
Salt 4p(ap,) -25 +25 © 420
100 to 250 psi
Salt - . =10 : -10 ~20
 NaBF, to Flinak
Temperature difference (AT)
100 to 125°F -10 -15 -25
100 to 150°F ~-15 =30 -40

 

Minimization of the heat exchanger fuel inventory is highly desirable.
As can be seen from Table 1, the fuel inventory can be reduced by decreas-
ing the tube size, increasing the.fuel pressure drop, changing the inert
salt from NaEF, to Flinak, and by increasing the temperature difference
between the fuel and inert salt. Note that, in contrast with thé effect

of the fuel pressure drop, the fuel inventory is increased by an increase

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in the inert salt pressure drop. From the table, one can deduce that, if
all the parameter changes producing reductions were employed, a reduction
in heat exchanger fuel inventory of as much as 62% could be obtained over
the reference design conditions. For the full-scale 1000 Mw(e) reactor
system described in Ref, 1, this would mean a reduction in total system
fuel inventory from approximately 1185 ft3 to approximately 871 ft3 for
NaBF; and from about 1095 ft> to about 825 ft for Flinak.

Fabrication costs for a tube bundle will depend primarily on the num-

ber of tubes in the bundle;'because this determines the number of header

- welds required. Material costs will vary with tube length and the total

tube cross~sectionallarear For the same set of parameter changes employed
above with respect to fuel inventory, one finds virtually no change in

the number of tubes and, thus, essentially an unchanged fabrication cost.
Tube'length,'from Table 1, is,reduced‘by a factor of approximately O.45.
The smaller tube'cross-sectional area contributes a further factor of 0.68,
for an overall reduction_factor of about 0.3, that is, a reduction in mate-
rial weight of nearly 70%. | -

A substantial fraction of the above savings is predicated on the
ability to increase the temperature difference between the fuel and inert
salt from 100 to 150°F; Experience gained in the ANP Program with thermal
stresses indicated that it is not difficult to assure a high degree of
reliability and freedom from difficulties with thermal stresses if the
temperature difference between the two fluid circuits does not exceed 100°F.
However, with careful design it seems likely thet the temperature differ-

‘ence might be increased to]asrmuch as 150°F without deleterious effects

provided that both”sfthorough"analysis_and near full-scsle'tests could be

~carried out.

As can be shown from the equatlons in the analysis of this report for

8 given system and fluid temperature rise, the pumping power in either

fluid circuit depends only on the salt properties and the pressure drop in

dthat circuit being linear in the pressure drop. Thus, for a given fuel
and inert salt combination, the pumping power can be reduced only by reduc-

" ing the pressure drop For a given fuel and set of specified operating

conditions, the pumping power can be reduced 10 to 20% by using Flinak in
 

 

place of NaBF, in the secondary circuit. The savings in total heat ex-
changer pumping power range from 10 to 20%, depending only on the ratio

of the inert salt pressure drop to the fuel pressure drop.
ANALYSIS

The analysis presented in this section is predicated on the use of
smooth, round tubes on an equilateral triangular pitch with axial fluid
flow outside the tubes. Conventional, well-established relationships
were used for the various heat balance, convective heat transfer, and
pressfire drop equations employed. (Recent experiments with molten salt
favor reducing the heat transfer coefficients about 15% from the values

used here.)

Design Bases and Criteria

 

The analysis and parametric study presented in this report were
carried out on the basis of a U-tube heet exchanger tube bundle having
the tubes in an equilateral triangular pattern with the fuel salt flowing
axially on the shell side and the inert salt (in the secondary circuit)
in counterflow on the tube side as described in Ref. 1. A cross section
of the exchanger configuration envisaged is shown in Fig. 1. However, as
will be seen subsequently, the analysis is by no means limited to the
particular configuration and conditions treated here but is applicablé to
a much wider range of problems. | |

The tubes were placed on an equilateral triangular pitch, rather
than a square pitch, in order to increase the thickness of the fluid
stream in the region between adjacent tubes because data from ANP heat
exchanger tests had indicated that thin fluid ligaments between tubes
'lead to flow stratification and a loss in heat transfer performance. This
effect was deduced from the curves in'Figs. 2 and 3, which were obtained
with ANP heat exchangers.®

‘The tube spacers, consisting of "oombs" of flattened wire, employed
in the ANP heat exchangers could be used with the equilateral triangular
spacing considered hefe. That approach would yield &n increase in pres-
sure drop by a factor of about 1.5 over that for the ideal case with no

spacers. It seems likely that spiral wire spacers would lead to an

‘R
 

 

 

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RNL DWG T1-9163
) i ’

 

 

 

 

 

 

 

" Fig. 1. Tube Bundle for One of the Six Fuel-to-Inert Salt Heat Ex-
changers Employed in Pa.ra.llel in the Conceptual Design of Ref. 1 for a
2200 Mw(t) Reactor. |
 

 

ORNL-LR-DWG 42878
100 ,

4 MIXTUR

 

Npgy WNpr) 420,023 (Nge)

 

Nwu/(Npr)®4

TA EXTERNAL

 

10,000

Fig. 2. The Heat-Transfer Characteristics of a Molten Sa.lt When
Flowing Inside Round Tubes (Yarosh, Ref. 2).

ORNL—LR-DWG 42860
100
ORNL 1 = { IHE-8
ORNL { SHE-2 B2 IHE-8
OPE{ SHE 2
APE {1 SHE 7
APE 2 SHE7T
OORNL{ TYPE
e ORNL { IHE-3

o ORNL 2 IHE-3
10

B4 (LEG 1) IHE-3
B2 2) IHE-3

(Nnu/Npr)OA

 

100 » 1000
Nre

0,000

Fig. 3. The Heat-Transfer Characteristies of a Molten Salt Flowing

on the Shell Side of Twelve Different Z-Tube Heat Excha.ngers Tested in
Six Different Systems (Yarosh, Ref. 2).
 

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increase in pressure dfbp Somewhat less than this and they might also have
a somewhat more favorable effect on the heat transfer coefficient, but no
clear-cut data are available, A definitive ansfier to these guestions would
require testing of the exact geometry of the heat exchanger matrix contem-
plated. | | |

Similarly, the effects of varlous types of surface roughness designed
to increase the heat transfer coefficiEnt,.in.fabt, aréfvery-difficult to
predict and will also require tests of the éXact geometry contemplated in
order to determine the extént to which the heat trahsfer coefficient is
improved at the expense of an increase in préssure drop. Because it ap-
pears that surface roughness frequently has not paid important dividends
for cases of the type of interest here, and because of the uncertainties
involved, it was decided to conduct the analysis assufiing bare, smooth

tubes with no allowances for spacers, Incluéion'of:the latter would in-

_créase the fuel pressure drop by around 30 to 50%, but should also in-

crease the heat transfer coefficient somewhat so that, with an equilateral

triangular tube pattern, the_éhélléside.heat transfer coefficient might

- well be higher than for-the.corfesponding circular passages inside the

round tubes.
Derivatioh bf fieat Exchanger Equations

We assume that the heat exchanger tube bundle is composed of round,
smooth tubes with axial flgid flow outside the tubes. We neglect entrance
effects and the shell-Side?firessure drop associated with the,tube spacers.

Nomenclature for the analyéis[is given'in Table 2.

,Heat Balanfies

 The axial heat transport is given in terms of thé)maés flows, fluid

temperature changes,'and'exéhangér geometry by

g_é-GSAscpsaTS | | - (1)

| and
Table 2. Nomenclature

 

 

R Q H o

 

P

Symbol Meaning Units
A Axial flow area ft2 |
Cp Specific heat | ' Btu/lbm'F
Diameter . _ ft
Blasius friction factor o )
Mass velocity | lb:m/hr'ft2
o Dimensional conversion constant .lbmft/lbf'hr2
| (4.170 x 108)
h  Heat transfer coefficient _Btu/hr-ftz-F
k Thermal conductivity Btu/hr- £t.F
L Tube length £t
N Number of tubes
AP Pressure difference l'bf/ft2
Q Heat transfer rate 7 Btu/hr
Sy — S5 Shell-side coefficients and exponents -
Ti - Ts Tube -side coefficients‘and'exponents
AT | Film temperaturé difference ' F degrees
&T Fluid axial temperature difference F degrees
t Thickness ft
i Viscosity lbm/hr- ft
Density lbm/ft3
Subscripts |
m Mean
o Outside
8 Shell side
t Tube side
W Tube wall

 
 

 

 

2
Q= GMDtNC 0Ty - (2)

The radial heat transport by convection and conduction through the

)

two fluid films and the tube wall, respectively, is given by

Q = n 0 e | e
Q = b wD LNAT, , | (4)
and
C - = kwTrDmen/tu : (5)

Convective Heat Transfer -

 

The convective heat transfer relations employed here are those of
Sieder and Tate? for laminar flow, and Colburn“ for turbulent flow. Both
relations may be expressed in the form given by Eqs. 6 and 7, where the

several coefficients and exponents are determined from Table 3 according

-

to the flow regime,

3
2ol o (s (e} o

-}

 

B

i
s

B Tlc_vz EreE” o

Temperature Difference BetWeen Fluids'

~ The overall temperature difference, AT between the two fluids is
~glven by the summation of the temperature differences through the two
fluid films and the tube wall

“

AT--_-.ATS "'_ATW +ATt . | (8)

a)
 

10

Table 3. Coefficients and Exponents Used in Convective
Heat Transfer and Friction Factor Equations

 

 

 

Sy S Ss S, S5
Qutside tubes
(shell side)
Laminar flow 4/2/10 1/3 1/3 64 1
Purbulent flow 0.032 0 4[5 0.256 1/5
Ty Ts Ty T, Ts
Inside tubes
(tube side)
Laminar flow 4/3/10 1/3 1/3 64 1
Turbulent flow 0.023 0 4[5 0.18  1/5

 

Note: The coefficient Sy for turbulent flow is obtained from
Ref., 5,

Pressure Drops
The pressure drop on the shell side is given by the Blasius relation,

L @2

P = f e —— (9a)
s sDS 2gcos

where the friction factor is defined, in terms of the shell-side Reynolds

(%Ds)fss
£ = S, o . | - (9b)

Similerly, the tube-side pressure drop is determined from

number, by

 

L Gi
AP, = f o= =2 (10a)
t tD, 2g o,

and
 

 

ot

s

"}

-

11

D, -T5
£, m(fl t b | (10b)
™ |

The coefficients and exponents appearing in the expressions for the fric-

tion factors also are determined from Table 2 according to the flow regime,

Shell -Side Equivalent Diameter

The equivalent diameter of the shell-side flow passage is determined
from the definition, |
D = —= S (11)
 Solution of the Equations

Let us take as input parameters (independent variables) the total heat

. transport ‘the pressure drops on the ‘shell and tube-sides, the tube size,

the temperature phanges\in the,two fluid streams, and the overall_tempera-
ture difference between_the'fiuids.- Then5,the foregoing set of 11 equa-
tions is just sufficient to determine the two mass flows, the equivalent
diameter and flow area on the .shell side, the overall length and number of

tubes in the bundle, the three transverse temperature differences, and the

‘two heat transfer eoefficients,_ll dependent variables in all.

' _Reduction to a Single Equation'

| Let us now eliminate the friction factors between Eqs. 9a and 9b and

_,Vbetween Eqs. 10a and lOb Rewriting the remaining equstions with only
known quantities on thelr right hand sides then ylelds

 

S Q
Ghy = O =57 - (12)

ps 8
L e Q : S ( )
GN=Cp = — (3

t In2c_, st

4t pt Tt
 

 

12

 

_ Q
hSLNATS =C3 = ?fi; » (14)
Q
h, INAT, = C, =~;fi; ’ (15)
Qt |
me=cs=ka, ,, - (16)
mw .
n pt-52-83182-53 ¢ (c k2)1/3 1/3- G 1)
578 s 6 ps s ?
h L7263 = Cq = T{(C kz)l/ 3,1/3-T3-14T5+T; (18)
£ pt t % t I
ATS+ATW+ATt=o_3=AT, (19)
o 1o 2g p AP
6> Ssp7 1S5y, o g = —SE & (20)
s ' S5 :
S4b
2-T 28 0, AP D2
Gy °L=Cyo = ) (21)
t | -
4ty
and
-1.-1 _ T | L |
AN D~ =Ca=7D . (22)

The coefficients C; through C;; are defined by the groupings of input
parameters appearing on the extreme right of each multiple equation.
We now reduce the above set of 1] equations to the following single
equation in tube-side mass flow,
E

E E
th + C20Gt2 + CZlG‘bB —Co=0. _ (23)
 

 

 

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13

- The coefficients and exponents appearing in Eq. 23 are, in general, rather

complex combinations of the coefficients Cy through Cy; and the various
coefficients and eprnegts obtained from Table 3, Details of the elimina-
tion process will not bérpresented'here but are availgble in Appendix A.

Equation 23 may be solved for the tube-side mass flow rate by an
iterative process,ffollowing-which the remaining dependent variables may
be determined by a series of back-substitutions. | 7 B

In any iterative prdcess, the speed 6f‘convergence, in fact, perhaps
convergence at all, dependS'on_having a good firét estimate of the value
of the variable being soUght. Empifically;'the-followingrequation,was
found to give a good initial estimate for the yalue’of_the tube-side mass

flow rate.

1/E,

o= odemrem] -

Equation 24 fias'tested on a wide variety of-input parameters and, in most

. cases, gave an initial value_for_the tubefside flowAwithin-2% of the final

'iterated value.

Computer Solution

Because of the obvious tedium, and the attendant error-proneness,

~involved in any sort of desk calculator solution of the above equations,

a FORTRAN program was prepared for use on the Call-A-Computer (CAC) time-

. sharing syStem.__Details_ofgthe program operation may be found in the

appendices. In,particfilar,_a,chPUter-prepared printout of the complete

program is presented in Appendix B, Appendix C contains samples of pro-

gram input'and output,'togefihgrrwith instructions for uSé'Of the programQ

o  Exte£§ions of the.Analysié_

'-'Although the parametfic;étudy:presentedjlater'in this-repbrt aSéumes

© an equilateral triangular tube pattern and fused salts in counterflow with

equal temperature changes in the two streams, the basic analysis is not,
in fact, so limited, as will be shown below.
 

14

6ther Fluids

Equations 6 and 7 for the convective heat transfer.coefficients,
although applied in the parametric study only to fused salts, are actually
applicable to any fluid having a relatively high Prandtl number, For
liquids of very low Prandtl number, such as liquid metals, Eqs. 6 and 7
must be modified, For example, one could employ the Lubarsky-Kaufman re-
lation® for the Nusselt number in turbulent flow and the theoretical value
of 4.36 in laminar flow.  These changes involve only redefining the expo-

nent on the Prandtl number in Egs. 6 and 7 to be a variasble rather than
the present constant and extending Table 3.

‘Tube Patterns

The basic equations, 1 though 11, contain no reference to tube pat-
tern, per se. The implication is that, for a given set of input parameters,
- the same solution set of dependent variables would be obtained for an
equilateral triangular pattern as for, say, a square pattern. This, of
course, involves the implicit assumption that the latter spacing is not
such as to result in the performance deterioration dbserved in Figs. 1
and 2. S

In order to determine tube spacing, one must employ an auxiliary rela-
tion such as Eq. 25,

A, = N(/352/2 — 1D2/4) - (25)

which defines the tube spacing in terms of the shell-side flow area, the
number of tubes, and the tube OD for an equilateral triangular pattern.

Other Conditions

Although applied in the parametric study only to a counterflow heat
exchanger with equal temperature -changes in the two streams,_the present

.analysis may be extended readily, both to parallel flow and to counterflow

 with unequal temperature changes, by the simple device of properly defin-

”ing the overall temperature difference. The appropriate quantity is the
log mean temperature difference (IMTD), defined by~
 

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GTD — LTD

IMTD = ——————— (26)
' log ——== GTD

eLTD

where GTD is the greater and LTD is the lesser of the two terminal tem-
perature differences between the two streams. When the two temperature
differences are equal, the IMTD becomes indeterminate and must be taken
as equal to either of the two temperature differences, The existing com~

puter program uses these definitions.

PARAMETRIC STUDY

In this study, the U-tube configuration of Fig. 1 was employed, with
the fuel salt flowing axially sround the tubes on the shell side and with
the inert salt in counterflow inside the tubes. The heat.load was kept
fixed and equal to that for one of the six heat exchangers for a 2200
Mw (t) reference design reactor.l The tube wall material was taken to be
INCO 800 and the fuelxemployed was the lithium-beryllium-thorium-uranium

- fuel salt in current use for reference design purposes at the time of

writing. Two different inert salts, NaBF, and Flinak, were used in the
secondary circuit. The. physical properties of the materials used were
taken from Refs. 7 and 8 as tabulated in Table 4 The temperature rise in
the inert salt and the temperature drop in the fuel in traversing the heat
exchanger were kept constant at 250°F

With a temperature difference between the two fluid streams of 100°F,
the heat exchanger characteristics were calculsted for each of the two

inert salts, using all combinations of three different shell side pressure

_drops three different tube side pressure drops, and two different tube

dismeters. The results are given in Table 5. For one of the tube sizes,

the effects of changing the temperature difference between the fluid

' streams to 125 and 150°F were then investigated for the same set of pres-
'sure drops and inert salts used previously. Table 6 summarizes the re-

sults from this set of calculations The input parameter variations used

in this study are summarized in Table 7.
 

16

Table 4. Reference Design Conditions and the Physical
Properties at Design Temperatures
for the Materials Used

 

‘Reference Design Condition

 

 

Fuel temperature in, °F | 1300
Fuel temperature out, °F | 1050
Inert salt in, °F : S 950
Inert salt out, °F 1200 -
Tube material L INCO 800
Tube thermal conductivity, Btu/hr<ft-F 11.5
Tube OD, in. 0.375
Tube ID,.in. ' .0.3190
Fuel pressure drop, psi 100
Inert salt pressure drop, psi | 100
Physical‘ a .. . b c
Property Fluoroborate Flinak Fuel
Cy» Btu/lb-F 0.36 0.437 0.325
b, lb/hr-ft 1.95 12.6 = 23.5
k, Btu/hr-ft-F - 0.266 2.66 0.58
0, 1b/ft® 119.0 132.0 208.0

 

%904 NaEF, + 8% NeF

bll.S% NaF + 46.5% LiF + 42% KF

°87% LizBeF, + 124 ThF, + 1% UF,
Teble 5. Effects of Choice of Inert Salt and Tube Diameter on the
. for a Full-Scale Molten Salt Breeder Resactor for a Tempe

 

Tibes

 

 

 

 

 

 

 

 

 

| Mibe - Tube Pressure Drops Fuel Side _ | Volumes Bundle
Inert op  ID . Equivalent o verline | | Weight
Salt (in. ) (1n. ) -Fuel Salt  Diameter Spact Number Iength ' Fuel Salt Tubes (1b)
L ’ ' (pst) (psi) = (in.,) (in ‘;—8 (££)  (£¢3)  (££3)  (£¢2) (20-6 .

RaBF, 0.3125  0,2665 100 100 0.2823 - 0,4106 4944 31.5 | 74.9 60.3° 22.6 - 34757
- - 150 10,3231 0.4244 4219 35.5 | 82.5 58.0 21.7 35598
- 200 - 0.3557 0.4352 374 38.7 ! 88.6 56.6 21.2 = 36420

150 100 0. 2466 10.3981 4806 29.9° | 60.4 55.7 20.9 30275

150 - 0,2823 0. 4106 4095 33.6 -1 66,3 53.3 20.0 - 30754

1200 0.3107 0.4203 3659 36.6 l 71.0. 51.9 19.5 31281

200 100 0.2241 0.3900 - 4716 28.9 .} 52.1 52.8 19.8 . 27634

- 150 - 0.2565 0.4016 4015 32.5  57.0 - 50.5 18,9 = 2711

__ 200 0.2823 0,4106 3586 35.3 4 60.9 49,0  18.4 28276

0.3750 0.3190 . 100 100 - 0.3374 - 0.4922 3498 40,0 | 96.6  77.7 2.7 - 45099

. ' 150 0.3862 -~ . 0.5088 2986 45,2 1106.5 7.8  28.6 46238
- 200  0.4251 . 0,526 . 2672 49,3 {114.5 73.1 27.9 47335 .

150 100 0.2947 0.4773 3403 38,1 - 78,2 72.0 27.5 . 39417

- 150 0.3374 0. 4922 2902 42,9 . 85,9 69.1  26.4 40091

200 0,374 0.5038 2594 46,7 - 92,1 67.3 25.7 . 40811

200 100 - 0.2678 0.4676 . 3343 36.9  67.5 68.4 26,1 . 36064

150 0.3065 0. 4814 2848 41.5 © 74.0 65.5 25.0 36478

‘ 200 ~ 0,3374 0. 4922 2544 45,1 - 79.2  63.7 24,3 36989

Flinak  0.3125 0.2665 100 100 0.2899 0.4132 bddid 28,1 . 61,7 - 48.4 18.2 28871
' ' : - 150 0.3318 - 0.4273 3820 321 | 69.4 47.5 17.8 30175
200 0.3652 10,4383 3434 35.4 | 75.6 47.0 17.6 31291

150 100 0,2532 - 0.4004 4299 26.5 | 49.2 @ 44,1 16.6 24842

150 ~ 0.2899 - 0.4132 3692 30,2 . 55.1 . 43,2  16.2 25770

‘ 200 0.3190 0.4231 3316 33,2  59.9 42.7 16.0 . 26584

200 100 0.2301 0.3921. 4206 25,5 1 42,0 - 41.5 15.6 22485

150 = 0,2634 0, 4040 3609 29.0  47.0 40.6 15,2 23204

. 200 0. 2899 0,4132 3240 31,9 51,0 40,0 15,0 23849

0.3750 0.3190 100 100 - 0.3464 0.4953 3153 35.9 . 80.3 62.9 24.0 37771

o ‘150 0. 3966 0.5123 - 2711 41.1  90.4 61.8 23.6 39493

- 200 0.4365 - 0.5253 2437 45.2 1 98.4 61.2 23.4 40962

150 © 100 0.3026 0. 4801 - 3055. 34,0 . 64.2 57.6 22.0 32647

150 - - 0,3464 0.4953 2624 38.8 72.1 56.4 1.6 33888

200 - 0.3813 - 0.5072 2358 42,6 - 78,4 55.8 21,3 34969

200 100 0.2750 ~ 0.4702 2992 32,7 . 55,1 54.3 20.8 29644

150 0.3148 0.4843 2569 37.3 61,6 53.1 20.3 30616

200 Q,3464 0, 4953 2307 41,0 66.9 52.4 20,0 31479
 

 

 

 

 

 

 

 

 

 

 

 

 

. Proportions of a Beries of Fuel-to~Inert-Salt Heat Exchangérs
rature. Change of 100°F in the Fuel and Salt Circuits
! .
‘ Mass Flows : Flow Velocities ' Pumping Power Temperature Drops
’ Reynolds Numbers -
: ettt Film Fim
Fuel Salt Ratio Fuel Salt Fuel Salt : Wall ,
< 1b/hr-£t2) (2076 x 1b/nr-f£t2)  Salt/Fuel  (ft/sec) |. (ft/sec) Fuel - Balt (hp)  (bp) F“ehfii)de (F°) Sa%;‘,,gide
6.497 7.263 1.1179 8.7 17.0 6504 82720 540 850 47.0 17.7 35,2
6.652 8,512 1.2797 8.9 19.9 7623 96947 540 1275 49.3 18.4 32.3
6.757 9.517 - 1.4084 9.0 . 22,2 852 108383 540 1700 50.9 18.9 30.3 -
7.652 7.473 ' 0.9766 10.2 17.4 6692 85109 811 850 43,5 19,2 37.3
7.845 8.770 1.1179 10.5 . 20.5 7853 99880 811 1275 45,17 20.0 34,3
7.976 9,813 1.2304 10.7 22.9 8788 111764 811 1700 47.2 20.6 32.2
8.582 7.615 | 0.8873 11.5 17.8. 6819 86722 1081 850 41.0 20,2 38.7
8.806 : 8.944 1.0157 1.8 20.9 8009 101866 1081 1275 43.2 21.2 35.6
8,959 10.015 1,1179 12.0 23.4 8968 114058 1081 1700 bt 7 2.8 33,5
6.403 7.166 1.1190 8.6 l6.7 766l 97683 540 850 45,7 20.0 34.3
6.553 8.394 . 1, 2809 8.8 19.6 8975 114428 540 1275 47,8 20,8 31.4
6.654 9,381 1,4099 8.9 21.9 10030 127886 540 1700 49.3 21.3 29.4
7.534 7.364 0.9775 10.1 17.2 7874 100396 811 850 42.1 21.6 36.2
7.719 8.638 1.1190 10.3 20.2 9235 117752 811 1275 44, 2 22.5 33.2
7.845 9.662 1.2316 10.5 22.6 10330 131713 811 1700 45.7 23.1 31.2
8.443 7.498 0. 8882 11.3 17.5 8017 102221 1081 850 39.7 22.7 37.6
8.658 8.802 1.0167 11.6 20.5 9411 119995 1081 1275 41,7 23,7 34.5
8, 804 9, 852 1,1190 11.8 23.0 10533 134301 1081 1700 43,2 24,4 32.4
7.040 6.658 . 0.9456 9.4 - 14.0 7237 11734 540 631 55.2 22.1 22.7
7.155 7. 745 1.0824 9.6 16.3 8419 13651 540 947 57.0 22.5 20.5
7.232 8.616 1,1914 9.7 18.1 9366 15186 540 1263 58.3 22,7 19,0
8.330 6. 881 0. 8261 11.1 14.5 7480 12128 811 631 51.5 24,2 24,3
8.474 8.014 0.9456 11.3 | 16.9 8711 14124 811 947 53.3 . 24.7 21,9
8.572 8.921 1.0408 11.4 | 18.8 9697 15724 8l1 1263 54.6 25.1 20.4
9,371 . 7.033 0. 7505 12,5 14.8 7645 12397 1081 631 48.9 25.7 25.3
9,541 8,197 0. 8591 12.7 17.2 8910 14448 1081 947 50,7 26,4 22.9
9,655 9.130 0. 9456 12,9 19,2 9924 16092 1081 1263 51,9 26.7 21.4
6.918 6,548 0. 9466 9.2 13.8 8499 13815 540 631 53.3 24,7 22.0
7.029 7.616 1.0835 9.4 16.0 9885 16068 540 947 55.0 25.2 15.8
7.103 - 8.471 1.1926 9.5 17.8 10994 17872 540 1263 56.2 25,4 18.4
8.173 6.758 ‘ 0. 8269 10.9 14.2 8771 14258 811 631 49,6 27.0 23.4
8.312 7. 868 : 0. 9466 11.1 16.6 10211 16599 - 811 947 51.3 27.6 21.1
8.405 8.757 1.0418 11.2 18.4 11365 18475 811 1263 52.5 27.9 19.6
9.184 6.900 0.7513 12.3 14.5 8956 14558 1081 631 47.0 28.6 24.4
9,347 8.039 0. 8600 12,5 16.9 10433 16960 1081 947 48.7 29.3 22.1
9.457 8.952 : 0, 9466 12.6 fif 18.8 11618 18886 1081 1263 49.8 29,7 20,5
|
|

 

 

 
Table 6. Effects of Choice of Temperature Change in the F
Intermediate Heat Exchangers for a Full-

 

 

 

 

 

 

 

 

Pressure Drops Fuel Side Tubes ; Volumes Sund’
_ : r undle
AT Inert .. Hauvalent . terline ' Weight
(°F) = salt Fuel  Salt Diameter Spaclin Number  Length  Fuel Salt Tubes (b) Fuel
- (pei)  (psi) (in.) I(’i‘g )g __  (£t) (££3)  (££3)  (£t3) (10~¢ x 1b/hr. ££2)
125 NaBF, 100 100 0. 2823 - 0. 4106 4456 26.1 56.0 45,1 16.9 25980 7. 209
: ' - 150 0.3231 0. 4244 3803 29.4 61.7 43.4 16.3 26630 7.379
200 0.3557 - 0,4352 3403 32.1 66.3 42,3 15.9 27258 7.494
150 100 - 0. 2466 0.3981 4334 24.8 45,2 41.7 15.6 22666 8. 486
150 0. 2823 0. 4106 3694 27.9 49.7 40,0 15.0 - 23046 8.697
' 200 0.3107 0. 4203 3302 30.4 53.2 38.9 14.6 - 23456 . 8. 840
200 - 100 0. 2241 - 0.3900 4255 24.0 39.0 39.6 14.8 20713 9.513
. A50 . 0.2565 . 0, 4016 3624 27.2 42,7 - 37.9 14.2 - 20942 9,758
i 200 0.2823 0.4106 - 3237 29, 45,7 36.8 13.8 21230 9,924
Flinak 100 100 0. 2899 0.4132 4012 23. 46. 4 36.4 13.6 21683 7. 798
150 0.3318 - 0.4273 3449 26, 52.1 35.7 13.4 22673 7.924
200 0.3652 0.4383 3101 29. 56.8 35.3 - 13.3 . 23517 8. 009
150 100 0. 2352 0.4004 3885 22.1 37.0 33.2 12.5 - 18700 9,219
150 0. 2899 0.4132 3336 25.2 41.5 32.5 12.2 19409 9.377 -
_ . 200 0. 3190 0.4231 2997 27.7 45,1 32.1 12.1 20028 9, 484
200 . 100 0.2301 0.3921 3803 | 2.2 31.7 31.3 11.7 16953 10, 366
150 0. 2634 0. 4040 3264 24,2 35.5 30.6 11.5 17506 10, 551
200 0. 2899 0.4132 2931 26. 6 38.5 30.2 11.3 17999 10, 676
150 © NaBF, 100 100 0. 2823 0.4106 4095 22,4 4, 2 35.6 13.3 20502 7. 845
: 150 0.3231 0. 4244 3496 25,3 48.7 34.3 12.8 21029 8.028
200 0.3557 0.4352 3128 27.6 52.4 33.5 12.5 21534 8,152
150 100 0. 2466 0.3981 3984 21. 35.7 32.9 12.4 17912 9,230
150 0.2823 0. 4106 3397 24.0 39.3 31.6 11l.9 18226 - 9. 457
‘ 200 0. 3107 0.4203 3037 26. 42.1 30.8 11.6 18559 . 9,611
200 100 o 0.2241 0. 3900 3913 20. 30.9 31.3 11,7 16384 10, 344
150 0. 2565 0. 4016 3334 23, 33.8 30.0 - 11.2 16579 10. 607
- . 200 0. 2823 - 0.4106 2978 25, 36,2 29,2 10.9 16816 10, 786
- Flinak 100 100 0, 2899 0. 4132 3692 20.1 36.7 28.8 10.8 17180 8. 474
150 0.3318 0. 4273 3174 23.0 41.3 28.3 10.6 17970 8.610
: 200 0.3652 0. 4383 2854 25,3 45.0 28.0 10.5 18644 8.701
150 . 100 0.2532 0. 4004 3577 19.0 29.4 26.4 9.9 14844 10.012
150 0. 2899 0.4132 3073 21.7 33.0 25.8 9.7 15414 10.182 -
200 0.3120 - 0.4231 2761 23.9 35.8 25.5 9.6 15910 10. 296
200 - 100 0.2301 0, 3921 3503 18.? 25.2 24.9 9.3 13476 11. 251
150 0. 2634 0. 4040 3007 20.9 28.2 24.3 9.1 13922 11. 450
200 0. 2899 0.4132 2701 22.9 30.6 24.0 9.0 14319

11.585 -

 

 
18

lel and Inert Salt on the Proportions of a Series of
icale Molten Salt Breeder Reactor '

 

 

 

 

 

ey

 

 

 

 

Mass Flows | Flow Velocities p 14 wumbers  PPLng Pover Temperature Drops

| | e ' Film - Film

Salt g Ratio Fuel Salt Fuel Salt ‘ Wall

(10°6 x 1b/hr-£t2)  Salt/Fuel  |(ft/sec)  (ft/sec) Fuel ~ Salt (bp)  (bp) F“e%,%de (°F) Sa%EFfiide

8.059 1.1179 9.6 18.8 7216 91781 540 850 57.9 23.7 43,4
9, 442 1. 2797 9.9 22.0 8455 107536 540 1275 60.6 24.6 . 39,7
- 10.554 1. 4084 10.0 24.6 9451 120200 540 1700 62.6 25.2 37.2
8,287 - 0,9766 1 11,3 19.3 7421 94377 - 811 850 53.5 25.6 45,9
9,722 1.1179 11.6 22.7 8706 110720 811 1275 56, 2 26.7 22.7
10,876 1. 2304 11.8 25.4 9739 123868 811 1700 58.0 27.5 39.5
8. 440 0.8873 12.7 19.7 7558 96127 1081 850 50.4 27.0 47.6
9,911 1,0157 -1 13.0 23.1 8875 112872 1081 1275 53.0 28.2 43.8
11,094 1.1179 13.3 25,9 9935 126352 1081 1700 54.9 29.0 41,1
7.37 ' 0.9456 10.4 15.5 8016 12998 540 631 67.7 29.4 27.9
8.578 1, 0824 10.6 18.1 9324 15118 540 947 69.9 29.9 25.1
9,541 1,1914 10. 7 20.1 10371 16817 540 1263 71.4 30.2 23.3
7.616 0.8261 12.3 le.0 8278 13423 811 631 63.1 32.2 29,7
8.867 0. 9456 12.5 18.7 19639 15629 - 811 947 65.3 32.8 26.9
9, 870 1.0408 12.7 20,8 10729 17397 8l1 1263 66.8 33,3 25.0
7.780 0. 7505 13.8 16.4 8457 13712 1081 631 59.8 34,1 31.0
9,065 0. 8591 14.1 19.1 9854 15977 1081 947 - 62.0 34.9 28.1
10,095 0.9456 ; 14.3 21,2 10974 17793 1081 1263 63.5 35.4 26.1
. 8.770 1.1179 10,5 20.5 7853 99880 540 850 68.6 30.1 51.4
10,273 1.2797 10.7 24,0 9199 116998 540 1275 71.8 31.2 47.0
11,481 1, 4084 10.9 26.8 10281 130756 540 1700 74.0 31,9 4, O
9,014 0.9766 12.3 21.0 8071 102655 811 850 63.3 32.4 54.3
10,572 1.1179 12.6 24,7 9467 120398 8l1 1275 66. 4 33.8 49.8
11, 825 1, 2305 12.8 27,6 10589 134671 811 1700 68.6 34.7 46,7
9,178 0.8873 13.8 21.4 8218 104523 1081 850 59.6 34.1 56.3
10.773 1.0157 14.2 25.1 9647 122693 1081 1275 62.7 35.6 51.7
12,057 1.1179 ;1.4 28.1 10797 137318 1081 1700 64.8 36.6 48,6
8.014 0.9456 P 11,3 16.9 8711 14124 540 631 80.0 37.1 32.9
9,320 : 1.0824 11.5 19.6 10131 16427 540 947 82.6 37.8 29,7
10. 366 1.1914 11.6 21.8 11268 18271 540 1263 84.3 38.1 27.5
8.270 0.8261 13.4 17.4 8990 14577 811 = 631 4.4 40,5 35.0
9.628 0.9456 13.6 20,3 10466 16970 811 947 77.0 4). 4 31.7
10.716 1.0408 13.8 22.6 11648 18888 811 1263 78.7 41.9 29.4
8. 444 0. 7505 15.0 17.8 9179 14884 1081 631 70.5 43,0 36.5
9,838 0. 8591 15.3 20,7 10693 17339 1081 947 73.0 43.9 33.1
10,954 0.9456 15.5 23.1 11908 19308 1081 1263 74,7 44,5 30.7

 

 

 
 

 

*

”

o

)

9

19

Table 7. Sunmar&:of Input'Parameter Variations
- Used in Parametric Study

 

Pressure Drops . : : Temperature
(psi) o T%g; gD Inert Salts Difference

(°F)

 

Shell Side Tube Side

 

100, 150, 200 100, 150, 200 5/16, 3/8 NaBF,, Flinak 100
100, 150, 200 100, 150, 200 5/16 NaBF,, Flinak 125, 150

 

The principal results of the parametric calculations are summarized
in the series of curVes_presented in Figs. 4 through 9. Figures 4 through
6 show the effects of pressure drop, tube size, and inert salt on the num-
ber of tubes, the'tuberlength, and the heat exchanger fuel inventory for
a temperature difference of 100°F between the'fuel and inert salt. Fig-

ures 7 through 9 show the;effects on the same dependent variables of

changes in pressure drop and temperature difference between the two fluids

for each of the two inert salts, with a tube OD of 5/16 in.

Examination of Fig. 4 reveals that, if one decreases tube OD from 3/8
to 5/16 in., the nuflber:orltubes in the bundle increases by approximately
40% for either inert salt"all other things beingrequsl' It can be seen

that changes in the tube side, or inert salt, pressure drop are much more

effective in reducing the number of tubes in the bundle than the corre-

sponding change in the shell 51de, or fuel pressure drop A change in

the salt pressure drop from 100 to 200 psi reduces the number of tubes by
mfapprox1mately 25%, whereas the seme change in the fuel pressure drop pro-
~duces a reduction of. only about 5% For a typical set of conditions,
r'changing the inert salt from NaBFz to Flinak produces a reduction in the
"upnuMber of tubes by approximately 10%. '

For the same set of changes, Fig. 5 shows the resulting effects on

“tube length. Reducing the;tube 0D to 5/16 in. yields, for elther inert

salt and for a'givenflsetflOffpréssure_drops,-a reduction in the tube length

of approximately 20%Q' As before, an increase in fuel pressure drop pro-

duces a reduction in the dependent variable, in this case, about 10% in
NUMBER OF TUEES

5000

kooo

3000

2000

ORNL DWG T1-916k4

AP =

 

Fig. h. Number of Tubes in a Bundle as a Function of Shell and Tube
Side Pressure Drops for Two Tube Sizes and Two Inert Salts. '

0c

 
 

» L ' L ” ) ‘ : o »

C _ - C

50 S L | o  ORNL.DWG T1-9165

TUBE IENGTH (£t)

 

Fig. 5. Tube Bundle Length as a Function of Shell and Tube Side Pres-
sure Drops for Two Tube Sizes and Two Inert Salts.

T2
 

- ORNL DWG T1-9166

120

100

cc

FUBEL SALT VOLUME (ft3)

Tube OD: O.. 5 in.

 

Fig. 6. ‘Fuel Salt Volume in Tube Bundle as a Function of Shell and Tube
Side Pressure Drops for Two Tube Sizes and Two Inert Salts.

 
¥)

5000

NUMBER OF TUEES

3000 -

2000

ORNL DWG 71-916

 

~ Fig. 7. Number of Tubes in a Bundle as a Function of Shell and Tube
Side Pressure Drops for Three Temperature Differences and Two Inert Salts.

C

¢z
TUEE IENGTH (ft)

45

 

- ORNL DWG T1-9168

 

Fig. 8. Tube Bundle Length as a Punction of Shell and Tube Size Pres-
sure Drops for Three Temperature Differences and Two Inert Salts.

42

 
L]

FUEL SALT VOLWE (fts)

 

Tube OD: O.

£ 5

Fig. 9. Fuel Salt Volume in Tube Bundle as alFunction of Shell and

' TUbe Side Pressure Drops for Three Temperature Differences and Two Inert
Salts.

»

Cah

 

1
 

26

the length. We note, however, that an increase in salt pressure drop has &hfij
the opposite effect, a doubling of the pressure’ drop yleldlng nearly 25%
increase in the tube length. Wlth all other condltions fixed, a change of
inert salt from NaBF, to Fllnak gives a reduction in tube length of about
104. | .
} The heat exchanger fuel inventory, a dependent variable of major in-
terest, is shown in Fig. 6. For a giveh set of conditions, the prescribed
reduction in tube OD yields a corresponding reduétion in fuel'volume of
about 25%. 'Ihcreasing the fuel pressure drop, as.before,iyields a substan-
: tial-savings in fuel invéntory of nearly 30%. ‘In cOntraét, hqfiever, in-
creasing the salt pressure:drop frdfi 100 fo 200 psi produces an increase
in fuel volume of about 20%. Replacing the inert salt in the secondary
circuit with Flinsk reduces the heat exchanger fuel inventory by about 20%.

Figures 7 through 9 are intended, primarily, to show the‘effects:of
increasing the température'difference between the two fluid streams, The
tube diameter used is the smaller one, 5/16 in. Figure 7 shows that in-
creasing the temperature difference from 100 to 125°F yields a decrease
~ in the number of tubes of approximately 10%. ;A further increase in the
temperature difference to 150°F yieldé only an additional 5%_reduction,
giving an overall reduction in the number of tubés of approximately 15%
from the 100°F temperature difference reference condition. For the same
changes in temperature difference between thé_two fluids, one observes
from Fig. 8 that the corresponding reductions in tube length are 15 and
30%, respectively. Finally, as can be seen'frdm‘Fig. 9, majorISavings
in fuel inventory can be effected if the temperature difference between
the salt étreams can be increased. Increasing the difference from 100 to
125°F results in a 25% reduction in fuel inventory éhd,a-l50°F_différénce
yields an overall reduction of 40% in the fuel salt volume. |

As discussed earlier, a temperature difference of 125°F would probably
pose'no problems with thermal stresées, but a temperature'difference 6f
150°F might give trouble and would require exténsire proof testing because
it is difficult to evaluate precisely socme of the modes of failure that
might prove important. | ,

Table 1 is a concise summary of the information contained in Figs. 4 ' Kfi';'
- through 9 as discussed in the preceding paragraphs This table can be
 

"

)

%)

27

used to make rough estimates of the effects on the number of tubes, the

tube length, and the foel volume of arbitrary combinations of changes in

. the listed parameters. For example, if we were, simultaneously, to re-

duce tube OD from 3/8 in., to 5/16 in. and raise the temperature dif-

ference from lOO°F to 150°F the relative number of tubes would be ap-
j prox1mated by

(1. ud)(o 85) = 1.19

the relatlve tube length would be
(o 80)(0 70) = 0.56

- and the relatlve fuel volume would be

(0.75)(0.60) = 0.45

Actually, some of the effects_are-interrelated in such a wey that taking

advantage of one effect may'redUCe'the effect of another, hence it is

" best to use the charts of Flgs. 4 to 9 when estimating the ‘combined

effects of several s1multaneous changes. If these are not applicable,

- new calculations can be made using the program appended at the end of

this report.

From the equatlone in the analy31s sectlon of this report it can

_be_Shown that the pumping power in either fluid circuit, for & given
" heat load and fluid tempereturerchange3 depends only on the salt pro-

perties, the temperaturejchange3 and the pressure drop in that circuit.
Then, for a given fuel salt-and ‘temperature change, the ratio of the
total heat exchanger pumplng powers for two dlfferent 1nert salts de-
pends only on the ratlo of the inert salt pressure drop to the fuel

“ ,pressure droP.‘ This relatlon 1s shown in Flg. lO for 8 change in inert
- 'salt from NaBE& to Flanak the total pumping power ratlo belng plotted
as a function of the pressure drop ratlo. Over the pressure drop ratio

- range of about 0.5 to 2.0,<the”oprrespond1ng'saVing in total heat ex-

| changer pumping power is from approximately lO_to'about5éO%. _
- TOTAL PUMPING POWER RATIO

 

ORNL DWG T1-
0.90 T1-9170

0.88

0.%

gc

0.84

0.82

0.80

 

0.5 1.0 1.5 2.0
RATIO OF INERT SALT TO FUEL SALT PRESSURE DROP - .

Fig. 10. Effect of Pressure Drop Ratio on the Reduction of Total Pump-
ing Power with a Change in Inert Salt from NaBF, to Flinek.

 
 

 

 

 

[

29

- CHOICE OF INERT SALT

In recent'years sodium fluoroborate has been the favored candidate
for use as the inert,salt in the intermediate heat transfer fluid system'
of the MSER. However, the writers felt that heat transfer considerations
make it worthwhile to review the possible advantages and disadvantages of
another candidate, Flinak, an inert salt that was employed in many tests
carried out under the ANP program .

Materialsrédmpatibility Considerations

The mass transfer and corrosion problems associated with the use of
both Flinek and fluorcborate salt were discussed at some length with
J. H. DeVan who kindly provided most of the material presented'here. The

:materials compatibility tests cited in this section are best understood if

considered in historical perspective It should be remembered that under

the ANP program some difficulties with corrosion and mass transfer were

. Observed in the Inconel loops operated_with fluoride salts, particularly

those containing UF;. As a consequence, a series of alloys was tested to
develop something having better corrosion resistance'than Incon€l, Around
40 individual thermal convection 1loops were built of di fferent nickel-

“molybdenum alloys containing various additions of titanium, aluninum,

chromium, niobium, vanadium, and iron. These loops were tested at 815°C
for periods of time ranging from 500 to 1000 hr. All of the loops except

" those containing large amounts of titanium and aluminum were essentially
unaffected by the fuel salt - The development of INOR-8 and ‘Hastelloy-N

was an outgrowth"of'this work, which is reported in Refs. 9 through 16.

_ Unfortunately, no recentftests'have been run with Flinsk in the latest

andamost_promising alloy,dHastelloyéN,_but it is belieVed'that the results

1of such tests would be'more'favorable than any of the earlier work because

of improved techniques for purifying the salt and loading it in the loop.
Note also that Hastelloy-N should be more corrosion resistant than the

thHastelloy-B and elimination of the UF, (added to the Flinak in the ther-
" mal convection loop tests) should reduce the tendency of the salt to at-

tack the structural material.
 

30

The results of tests with thermal convection and forced convection
loops both with Flinak and with fluoroborate salt are summarized in Table 8.
Note +that three of the Flinak foreed convection 1oops'were operated at
over 1700°F with a temperature drop in the salt circuit rangihg from 365
to 450°F, a very severe combination of conditions, While the first of
these showed some tendency to form subsurface voids as a result of solid
state diffusion and selective leaching of iron from the alloy, this effect
was not noticable in the other two loops.

The test experience with fluoroborate salt was discussed with
J. W. Koger who supplied the information summarized in the lower portion
of Table 8. The data fall into twormajor.éets. The«first-set was carried
out with the first fluoroborate salt to become availsble.l? This material
contained abeut 2000 ppm of oxygen because this was the highest purity
obtainable with the usual fluoride purification process; evolution of BF;
prevented a further reduction in impurities. (The vapor pressure of. BF,
at 1125°F ig 160 mm whereas the vapor pressure of the Flinak is less than
1 mm at the same temperature.) As a consequence of the high concentration
of impurities in the first batch of fluorcborate salt, the Croloy 9 Cr-l
Mo loop was attacked very rapidly so that operation had to be terminated
after about 1400 hr (Ref. 17). The Hastelloy-N loop, however, was only
lightly attacked — at a rate equivalent to about 2 mils/yr — but the cold
leg began to plug with Na3CeFg so that operation was“terminated at the.end
of 10,000 hr (Ref. 17). |

The second series of tests was run with a more highly purified fluoro-
borate salt having a nominal contamination level of 500 ppm of oxygen, 18
Three of these loops have been operated for over 20,000 hr with no apparent
signs of plug formation or other serious i1l effects.l?

Melting Poii.nfll:.f

In the design and operation of any high-temperature liquid system it
is always advantageous to reduce the melting point of the fluid employed
in order to ease the problems of preheatlng, filling, and draining the sys-
tem. Further, if the system is to include a steam generator, it would be
highly desirable to be able to make use of a molten salt whose melting
 

. able 8.

 

 

 

 

 

 

 

convection

_'Summary of Thermal and Forced Convection Loop Tests Carried Out with Flinak and with NaPBF,
P - : : Peak Metal Test
' Molten Salt.. e T Duructural Temperature (Qg) Duration - ‘Results
‘ . (°F) o (hr) : .
Flinak (46.5 LiF + 11 5 Na.F Thermal Inconel 1125 100 10008 Attack <1 mil
+ 42 KF) convection  Inconel 1050 100 43607 Attack €2 mils - ’
: Inconel 1250 - 100 43738 Attack to 13 mils in the form of
' ' : subsurface voids along grain
boundaries; after-test chemistry
indicated that initial salt lcad-
. ing wes contaminated w:lth moig=-
' -ture :
INOR-8 1125 100 1000° - - No attack
INOR-8 1250 - 100 13407 No attack -
e INOR-8 1250 100 876010 Attack <l mi1
Flinak + 258 UF;; .~  Forced Inconel 1200 100 8760 = System troubles led to three
YR .. .convection’ o ' ‘ S * changes of f£luld charge in course
e T _  of tests; maximum attack wvas 8
" SO : 'mils in hot zone
17 Mo, 6 Fe 1760 450 1000 Void formation to depth of ~é mils
Ba 1 Ni.
Hastelloy B 1767 410 1000 - - Pits present in ag-received tubing
L o ‘ ' were slightly accentuated; no '
o noticeable vold formation
Hastelloy B 1710 365 1000 Do sbove; a few metal crystals
A . ‘ : . noted at pump bowl exit
92 NaEF, + 8 NaF Thermal Croloy 9 1125 270 ~1400 Initial 0, 2000 ppm; severe attack
: convection . Cr=-1 Mo : :
Hastelloy N 1125 270 10,000 Initial 05 2000 ppm; attack ~2 mil;
. loop partially plugged by deposit
. . _ . _ of NasCrFg -
NaEF;-NaF (92-8) Thermal . Hastelloy N 607 260 20,380 Test continuing
-~ convection ' ' . ‘
Na.BF;,-NaF (92-8) " Thermal Hastelloy N 607 300 28,955  Test continuing
convection : _ ' .
LiF-Ber-ThF,; (73-2-25) Thermal Hastelloy N 677 130 17,880 Test continuing
- convection . : o '
mF-Ber-Un (65.5 -34, o-o.s) Thermal ~ Hastelloy N 704 340 22,240 Test continuing
© convection _ : ‘
Na.BF;,-NaF (92-8) plus steam . Thermal Hastelloy N 607 212 14,615 ‘Test continuing
additions : : convection , '
' 14 F-BeF,~ThF; ~UF Thermal ‘Hastelloy N 704 340 15,930 Test continuing
(68-20-11,7-0.3 convection _ '
' IiF-BeF,~ThF,;-UF; (68-20- Thermal ‘Hastelloy N 704 340 4660 Test continuing
11.7-0.3) plus biemuth in . convection
molybdenum hot finger ' :
NaBF;-NaF (92-8) Thermal Hastelloy N 687 480 10,515 Test continulng

 

T€
 

 

32

point is below the critical temperature for steam, that is, 706°F. One
of the outstanding advantages of the fluoroborate salt is that its melting
point is 725°F, only sbout 20°F above the critical temperature for water,
Flinak, on the other hand, has a melting point of 876°F, 170°F above the
critical temperature. The temperature difference is so largemfor the
latter that thermal stress problems under steam—generator.startup condi-

~ tions would be severe in heat,exchengers of conventionel‘design. Fertun-
‘ately, the reentry tube steam generator proposed in a cofipaniqn report2°
‘makes use of'a steam blanket between the boiling‘water‘and;the molten salt
sO that a large temperature difference between the two prdbably can be
accommodated without difficulties with salt freezing, heat transfer in-
stabilities associated with film boiling, or severe thermal stresses.

This favorable set of cosditiofis in the steam generator shOuldrhold over
the whole range of conditions from zero to full power including transients
and off-design operating conditions. As a conseguence, the difference in
melting point is not a controlling consideration in the use of fluoroborate

salt rather than Flinak from the steam generator standpoint.

Ieakage Problems

 

ORNL experience with high-temperature liquid systems has shown that,
while the probability of small leaks between systems can be kept very lofi,
'it is sot‘possible to assure that a small leak will never occur in a heat
exchanger. Thus it becomes important to cheose the fluids in systems
coupled by a heat exchanger so that a small leak from either system into
the other will not lead to a rapidly progressing failure or to a mess that
cannot be cleaned up readily. For example, in the ANP systems it was .
found that leakage of NaK into systems containing a fuel-bearing salt or
vice versa led to the formation of deposits that are highly 1nsoluble |
in either water or the molten salts, and hence could not be flushed from
the system in which they formed. Fortunately, it appears that either the
‘flfioroborate salt or the Flinak would beqcompatible with either the fuel
salt or the steam in this respect. Contamination of the erlrsalt by sub-
stantial quantities of either boron or natural lithium would pose problems,

the ©Li being much more seriocus. -
 

 

 

 

W)

-}

35

;Off—Gas Problems

 

In any pfactical system it is always necessary to have one or more
gas lines coupled to the gas space over the liquid in the expansion
tank., A variefiy of troubles has been experienced with material distil-~
ling off into these gas llnes, particularly in systems in which the
vapor pressure of the salt has been appreciable. The limited experlence
available to date with 92 NaRF, -8 NaF (which has a vapor pressure of
160 mm at 1125°F) indicates.that the problems posed by this material as
a consequence of the'evoiation of BFs are manageable, but_do require
care in the design and.operation of the system. The vapor pressure of

Flinak is so low that it has never given trouble of this sort.

Heat Transfer Performance

 'The physical propersies_of the molten salt used in the intermediate
fluid circuit affect not only the size and cost of the intermediate heat
exchanger‘and‘the boiler,,but they-also-affect the pumping power,_the
size of the piping, snd,'as'noted~above, the‘fuel inventory. The
physical properties of Flinek make it clearly superior to the fluoro- -
borate salt as a heat trensfer and heat transport fluid, the difference

running from 20 to 25% in favor of Flinak in ell of these items.

Tritium Leakage

Tritium generated 1n Fllnak by delayed neutrons released from the

’,fuel in the 1ntermed1ate heat exchanger would diffuse into the steam

system and thus would 1ntroduce hazards problems. The problems are

'essentlally s1milar to those posed by ‘tritium generatlon in the fuel
- salt, but it appears that they can be handled more readlly if fluoro-
L borate is employed rather than Fllnak.
 

 

 
 

v

10.

-1,

o

14,

35
.,REFERENCESf

A. P. Fraas, Conceptual Design of a Molten Salt Reactor with Its
Intermediate Heat Exchangers and Fuel Pumps Integrated in a Common
Pressure Vessel, internal ORNL memorandum, April 13, 1971.

M. M. Yarosh, Evaluation of the'Performance'of Liquid Metal and
Molten Salt Heat Exchangers, Nucl. Sci. and Eng., 8: 32 (1960).

E. N. Sieder and G. E. Tate, Heat Transfer and Pressure Drop of
Liquids in Tubes, Ind. Eng. Chem., 28: 1429-1435 (1936).

A, P. Colburn, A Method of Correlating Forced Convection Heat Trans-
fer Data and a Comparlson with Fluid Friction, Trans. AIChE, 29: 174—
209 (1933). |

P, Miller, Jd. dJ, Byrnes, and D. M. Benforado, Heat Transfer to Water
Flowing Parallel to a Rod Bundle, AIChE Jour., 2: 226235 (1956).

B. Lubarsky and S. J. Kaufman, Review of Experimental Investigations
of Liquid-Metal Heat Transfer, NACA TR 1270, 1956.

A. P. Fraas and M. N Ozisik, PP. 60—61 Heat Exchanger Design, John
Wiley & Sons, New York, 1965.

J. R. McWherter, MSER Mark I Primary and Secondary Salts and Their
Physical Properties, internal memorandum MSR 68-135, Sept. 27, 1968.

J. H. DeVan and R, B. Evans, III, Corrosion Behavior of Reactor Mate-
rials in Fluoride Salt Mixtures, USAEC Report ORNL-TM-328, Oak Ridge
National Laboratory, Sept. 19, 1962.

J. H. DeVan and R. S. Crouse, Examination of Nickel-Molybdenum Forced
Circulation Loop 7641-9, Oak Ridge National Laboratory, unpublished

internal document, Aug 13, 1957.

'J. H. DeVan and R. S.- Crouse, Examination of Hastelloy B Pump Loops

7641-1B and 7641-2B, Oak Ridge National Laboratory, unpublished in-

':ternal document, Jan 17, 1957

._MSRP Quarterly Progr. Rept July 31 1959 USAEC Report 0RNL-2799

Oak Ridge National Laboratory.,

MSRP Quarterly Progr Rept Jan 31, 1959 USAEC Report ORNL-2684
Oak Ridge National Laboratory :

MSRP Quarterly Progr. Rept. Oct. 31, 1958, USAEC Report 0RNL-2626

 Qak Ridge National Laboratory

 
 

 

 

 

15.

16.

17.

18,

19.

20.

36
MSRP Quarterly Progr. Rept. June 30, 1958, USAEC Report ORNL-2551,

Ozk Ridge National Laboratory.

MSRP Quarterly Progr. Rept. Jan. 31, 1958, USAEC Report ORNL-2474,
Oak Ridge National Laboratory.

J. W. Koger and A. P. Litman, Compatibility of Hastelloy N and Croloy
9M with NeBF,-NaF-KBF,; (90-4-6 mole %) Fluorcborate Salt, USAEC
Report -ORNL-TM-2490, . April 1969, '

MSRP Semiann. Progr. Rept. Feb. 29, 1968, pp. 218-225, USAEC Report
ORNL~-4254, Oak Ridge National Laboratory

MSRP Semiann. Progr. Rept. Avg. 31, 1970, pp. 166-i76,_USAEC Report

ORNL-4622, Ozk Ridge National Laboratory.

A. P, Fraas, A New Approach to the Design bf Steam Generators for
Molten Salt Reactor Power Plants, USAEC Report ORNL-TM-2953, Ozk

Ridge National Isboratory (to be published).
 

37

APPENDICES

 
 

 

i

39
APPENDIX A

Solution of the Heat Exchanger Equations

This appendix gives details of the elimination process involved in
going from the equation set, Eqs. 12 through 22, to the single equation in
tube-side mass flow, Eq. 23. We begin by using Egs. 12 and 22 of the text

to eliminate the shell-side flow area from the set, giving

C,
GND = o—m0 ., : (A-1)

We next eliminate the shell-side heat transfer coefficient between Eqs. 14
and 17 and the tube-side heat transfer coefficient between Egs. 15 and 18

to give
[1-S2y 524831 Ss o _ 2 | (ac2)
s B T8 Cg’ |
| o
1-T, T s | ]
L NDtBATt =5 (A-3)

By combining Eqs. 16 and 19 with Egs. A-2 and A-3 the three temperature
differences through the two fluid films and the tube wall may be eliminated

at one fell swoop to give

c .
- -S3pl- 52 "83752 40=T3 To | _ -
L]'N [Césns L™ + Cs + 56,7772 | = Cg . (A-4)

We now obtain an.expressibnifor the product LN from Eqs. 13 and 21,

G3-T5

LlN'

 

CZCIO ? o (8-5)

using it in Eq. A-4 to obtain
 

40

C .
3-T5 -S3.1-S5-S3. S, 3-7,
CaCeCiolt U Dy L2 CZCIOGt

c
4 3-T3-T5, T2 _ Ce

Y+ CCeCrot | (a-6)

The number of tubes, N, may be eliminated between Eqs. 13 and A-1 to give

_ Cc
-1 1
GSGt Ds = m . (A-'?)
A rewriting of Eq. 21 yields an expression for the tube length,_L,
L= oG5 2, ' , (A-8)

which may then be used to eliminate tube length from Eqs. 20 and A-6,

giving
2-S; Ts-2 -1-S5 _ C9
o5 e TRS L -
G, T°G.° "D 0o (4-9)

and

'_fifig_es-m5+sz(T5-2) “Sapl-S2-5s _5 3.,

0206010 t B CQCIQ t

C,0N2
10 M. _ -

02C7C10 t ’

From Eq. A-7, we obtain an expression for the shell side equivalent

diameter, Dé,

. Cl 1

%~ 501 % (h-11)

Then, using this expression in Egs. A-9 and A-10, we obtain Egs. A-12

- and A-13,
 

41

1455

C C
o~3-554T5 _ i
Gs t - C10lC2Cq1 | (3 )
. S, 1482-83 |
c5C53 [ Gy J - S3-T5+62(T5-3) Sp-1 , 0% 3-Ts
C2CeC10L.C2C11 . S Czclo t
To ' ' '
CaCi6 4 ’
3-T3-T5+T2(T5-2) _ - -
* TalrCro t =G | )

in which the only remaining unknowns are the two mass flows, Gs and Gt'
Finally, we eliminate the shell-side flow fram Eq. A-13 Dby using

Gg [010 <;2011

‘which is simply a rearréhgement of Eq. A-12, to give a single equation in

1465 1/3 | |
5:, G_t+(85—T5)/3 , | N (A-14)

 

which the only unknown is the tube-side mass flow, Gt'
3-Ts
Gt +
Sa_q. (82-1)/3 1-52-53+(S2-1)(1+85)/3 |
Eif__[c ] | [ o T | | G3-252'33+(52'1)(2T5+35)/3
C5C¢ LCir0 C2C1a | - t
C4C$o | ‘ C2CgCao
| 3-T3-T5+T3(T5-2) _ 10 -
+Wt c T - _—CS =0, _ (A-15)
Now, defining coefficients,clg, C20, 8nd Cpy by
e | 0203010 o .(A 16)

(8- l)/3 1-32-53+(sz-1)(1+sg)/3

c . 03010 Cl _ _ .
20 = T5Ce [Clo- RN 02011] , 7 (4-127)

 
 

 

42

 

C4C$§
- Cpy = CsCy (a-18)
and exponents Ei, E,, and E; by -
E, = 3-Ts , B ’ (A-19)
Ep = 3-285-83+(S2-1)(2T5455)/3 , (A-20)
E3 = 3-T3-T5+T2(T5-2) - (a-21)
fie reducg_Eq. A-ls fo |
Gfl + czoef2 + czlef-" - Cig =0, (23)

which is Eq. 23 of the text.
 

 

 

»

43

APPENDIX B, .FORTRAN :PROGRAM FOR COMPUTER:SOLUTION
OF THE HEAT EXCHANGER EQUATIONS

A brief description of the operation of a FORTRAN program written for
solving the heat exchanger equations presented in this report is given in
this Appendix. A computer-prepared printout of the program follows the

description. Instructions for program use will be found in Appendix C.

Program Line No. Operation

1 -3
100 — 110

115 — 125

130 — 135

140

145 =~ 185
190 — 215
220 — 335

340 ~ 370

375

380 — 430

435
440
445

450 — 455

460 — 650

655

Program identification.
Declaration statements.
Compute various constants needed later in the program.

Advance case number; note that this yields an initial
case number equal to one, if not specified. Read
and test "NIN"; stop if zero or negative.

Read NIN values into locations J in array DAT.
Set program variables from array; print case number,
Convert units; compute quantities needed later.

Campute coefficients C, through 021 and exponents
Ey through Es. Assume turbulent flow, both fluids.
-Compute estimate for G from Eq. 24.

Newton's Method 1teration for G,_; if converged, to
line 380,

If iteration fails to converge in 10 trials, print
Awarning message and continue,

Compute G corresponding to Gi; compute actual flow
regime and compare with assumed If in agreement,
to line 460; _otherW1se, to appropriate line, 435—
- 450. -

Assume leminar flow on tube. side. Repeat 280-430.
Assune laminar flow on shell side. Repeat 280-430.

Assume turbulent flow, tube side. Repeat 280~430.

Arrival here-means that no combination of assumed
flows ylelds a self-consistent result. Program .

- glves up, prints warning message, and reads in the

~data for the next case. (This has never happened
in any of the many calculations made to date. )

Compute- remaining dependent varlables, edit and
print.

Return to read in data for next case.
660

665 = 700

705

 

Program stop,

Subroutines for setting coefficients and exponents
according to flow regime. See Table 3,

Input data bank stored after this line.
 

&

™|

HEATX2
1% HEATX2. HEAT EXCHANGER DESIGN. M. LAVERNE. 9102 3=5702
o 19 MAR 1970

3% |

100  REAL MUSs MUT» KS» KT, KWALL, LTUBE»> NTUBE |

105 DIMENSI@N DAT(20) )

110 COMMON CLAM:CURT:SI152053054’55:Tl:T2:T3:T4:T5
115 PI = 3.1415926543 PI104 = Pl/4.

120 CURT = 147343 CLLAM = 44./10tCURT

125 TWOGC = 64.348%3600.123 C00 = 5*%PI/SQRT(3+)
130 | DAT(20) = DAT(20)+1.0

135 READ, NIN3 IFC(NIN)Y 21s21

140 READ» (JsDATCJY2I=1sNIN)

145 @ = DATCI1)

150 DPS = DAT(2)3 TSI = DAT(3)3 TSO = DAT(4)

135 CPS = DAT(S5)3 MUS = DAT(6)3 KS = DAT(7)3 RHOS = DAT(8)
160 DPT = DAT(9)3 TTI = DAT(10)3 TT® = DAT(11)

165 CPT = DAT(12)3 MUT = DAT(1335 KT = DAT(14)3 RHOT = DAT(15)

170 DO = DAT(16)3 TW = DATC17); KWALL = DAT(18)
175 RHOW = DAT(19)s ICASE = DAT(20)
180 PRINT 30, ICASE ,

185 30FBRMATC/“CASE "» 13)

190 DPS = 144.%DPS3 DPT = 144.%DPT
195 DO DO/12+3 TW = TW/12+3 DT = DO-2+%THW

200 A0 = PI@A*DO*DO3 AT "= PIfiA*DT*DT: AW = AO-AT

205 DTS = TSI-TSO3 DTT = TTO-TTI
210 DT1 = TSI-TTQs DT2 = TS@-TT1
215 DM = (DO-DT)/LO@GC(DO/DT)
220 €08 = DTi: IF(DTI-DT2) 2,3,2
225 2 CO08 = (DTI—DT2)ILGG(DT1/DT2)-
230 3 CO0S5 = Q/PI :
235 CO1 = Q/(CPS*DTS)3 coz = QI(AT*CPT*DTT)
240 C03 = COS/D0s3 .CO4 = COS/DT3 CO5 = COS*TwW/ (DM*KWALL)
245 co6A = (CPS*KS:Z*MUSTtCURT , ' '
250 CO7A = (CPT*KT?2*MUT)OCURT/DT
255 CO%9A = TW@GC*RHOS*DPS
260 C10A = TWGGC*RHGT*DPT*DT
265 Ci1t = PI@4xD03 C12 = CO1/C€CO02%C11%3 C13 = CO3/C05
270 C14 = C04/C053 C15- 602*008/005: N=0 R
275~ CALL STURB3 CALL TTURB; 1AS = IAT = -
"280 4 CO6 = CO6A%S1/MUS+S3 '
285 €07 = COTA*T!*DT?(TE+T3)IMUT?T3
290 €09 = CO%A/(S4*MUStSS) -
298 Cl0 = ClOA*(DT/MUT)fIS/T4
300 _Cté = C13/C063 c17 = 009/0103 018 = 0141007
©.- 305 €19 = C15%C10 ~
310  El = 3.-TS53 E4 = (S2- 1. )/3.; .
315 E2 = 3.-2.%52-S3+E4*(2.%T5+55)
- 320 E3 = E1-T3+4T2%(T5-24)
325 ES = 1.-S2- sa+aq*c1.+ss>h*

330 €20 = C16%C10152%C171EASCIZIES

 
 

 

L6

HEATX2 CONTINUED

335

340
345
350
355
360
365
370
375
380
385
390
395
400
405
410
415
420
425
430
435
440
445
450
455
460
465
470
475
480

485

490
495
500
505
510
515
520
525
530
535
540
545
550
555
S60
565
570
575
580

22FORMATC(//T7X"P DRGP T IN

C21 = C18%C10tT23 GT = 0.9%(C19/(C20+C21))t(1./E2)
DO S I =1, 10 »
GT! = GT*El13 GT2 = GTtE23 GT3 = GT*ES3
G6T20 = C20%GT23 GT21 = C21%GT3
FUN = GT1+GT20+GT21-C19 :
DER = (E1*GT1+E2*GT20+E3*GT213)/GT3 DGT = FUN/DER
GT = GT-DGT3 IFC(ABS(DGT/GTX-1.E-5) 6 :
5 CONTINUE ' ,
PRINT» tt"NOT CONVERGED. DGT/GT ='"» DGT/GT

6 GSAGT = (C17*C121C1.+SS)*GTt(S5~T5))*1CURT

GS = GT*GSOGTs DS = C12/GSOGT
RET = GT*DT/MUT3 RES = GS*DS/MUS
1CT = 03 IFCRET-1502.) 73 ICT = 1

7 NT = 03 IFCIAT-ICT) 9,859

8 NT = 1

9 ICS = 03 IF(RES-994.) 103 ICS = 1

10NS = 05 IFC(IAS-ICS) 12,11,12
1INS = 1 o
12IF(NT*#NS) 13,13,18

13N = N+13 GO TO (14,15,16,17) N

14CALL TLAM 3 IAT = 03 GO TO 4
1SCALL SLAM 3 IAS = 03 GO TO 4
16CALL TTURB3 IAT = 13 G@ TO 4

17PRINT, °*ASSUMED AND CALCULATED REGIMES DO NQT,AGREEQ“

Go TO 1 |

18LTUBE = C10#GTt+(TS-2.)3 NTUBE = C02/GT _
AS = CO1/GS3 HS = CO6%(DS*GS)1S3#(DS/LTUBE)*S2/DS
VS = GS/RH@S3 VT = GT/RHOT - -

HPS = DPS*AS#VS/1.98E63 HPT = DPT#AT*NTUBE#VT/1.98E6

HT = CO7*GT+T3/LTUBE*T23 DTW = COS5/ (LTUBE*NTUBE)
FDTT = Cl1A4%DTW/HTs FDTS = C13*DTW/HS

S = SQRTC(COO*DO*C(DS+D0))? ,

BUNWT = LTUBE*(NTUBE*(AT*RHOT+AWX*RHOW) +AS*RHOBS)
PRINT 205Q512.%D0s12¢%TWs12+%DT»KWALL»RHGW
PRINT 22,DPS/144.,TSI,TS0,CPS>MUS,»KS,RHBS,
+DPT/144¢>TTI>»TTO>CPT>MUT>KT»RHOT ‘

PRINT 24, NTUBESLTUBE,12.%S512.*DS>»

+AS*L.TUBE s AT*LTUBE*NTUBE » AW*LTUBE*NTUBE »BUNWT
PRINT 26,C08,DTWsFDTSsHSsFDTTHT

PRINT 285GT/GS»GSsVS/3600+sHPSsRESsGT»VT/3600+5HPTHRET

20FORMAT (/3X"HEAT"3XA4(4X"TUBE"Y7X"TUBE"/

+3X"LOAD" 7X"TeDeAX"WALL"AX" 1D 6 X"K"TX""DENSITY"/
+#2X"BTU/HR "3C(6X"IN")2X"BTU/HR FT F LB/FT*t3*"/
+1PE10:35s0P3F8¢4sF9:25F11+1)

+ LB/HR FT BTU/HR FT F LB/FT*3'/
+* FUEL:"F6¢05F8¢05FTe05F835sF10.25F11.25F12.1/

T QUT SP. HEAT VISCOS'Y
+ CONDUCTIV'Y DENSITY"/9X"“PSI"SX"F"6X"F"4X"BTU/LB F
 

 

»

 

“

 

u7
HEATX2 CONTINUED

585 +" SALT'"F6 OoFS 0:F7 OJFS 35F10+2,F11.2,F12.1)

- 590

595 24FORMATC(//™ NUMBER"4X2("TUBE"AX)"EQUIV "6 X"VOLUMES" 7X""BUNDLE"/

600 +"@F TUBES LENGTH SPACING DIAM'R FUEL SALT TUBE"2X"WEIGHT"/

605 412X"FT "2(5X“IN"2X)3(2X“FT*3")4X“LB"/F7-0:F8-l:2F9.4:3F6.1:F8 0)

" 610

615 26FGRMAT(//4X"LMTD WALL DT“IOX"FILM DT CIEFFICIENT"/

620 +SX"F"TX"F"16X"F"4X"BTU/HR FTt2 F"/2F841,3X" FUEL:",

625 4F8+41,F11.0/20X"SALT3"sF8¢15F11.0)

630 : ' L , : '

635 28F@RMAT(//"FLOW RATIG"11X"FLOWS"4X"VELOCITIES PUMPING

640 4 REYNPLDS"/3X"GT/GS*"11X"LB/HR FTt2 FT/SEC"6X"HP"

645 +5X“NUMBERS"/F8+4,4X"” FUEL:"1PE11+4,0PF8:1,F11.0,F10.0/

650 +!3X"SALT'"1PEllo4:0PF8 1,F11.0,F10.0/77) '

655 GO T@ 1

660 21STOP

665 SUBRGUTINE SLAM3 COMM@N CLAM:CURT:SI:S2:SS:S4:SS:T!:T23T3:T4:TS

670  S1=CLAM3 S2=S3=CURT3 S4=64.3 S5=1.3 RETURN

675 SUBRGUTINE TLAM;3 COMMON CLAM,CURT»51,52553554,55,T1,T2,T35T4,T5

680 T1=CLAM3 T2=T3=CURT3 T4=64.3 T5=1.3 RETURN

- 685 SUBROUT INE STURB3COMMON CLAM:CURT:SI:S2aS3:S4:SS:T!aT2:T3:T4:T5
- 690 S1=+0323 S2=0e3 S3=+83 S4=.2563 55=.23 RETURN

695 SUBRGUTINE TTURB3COMMON CLAM:CURT:SIoS2aSS:SA:SS:Tl:T2:T3oT4:T5
700 T1=.0233 T2=0.3 73=-Bi T4=.1843 TS=.23 RETURN

705 $DATA :

LENGTH
ABGUT 5800 CHARS.
 

L8

APPENDIX C

SAMPLE COMPUTER PROGRAM INPUT AND OUTPUT -

This Appendix contains information on the‘preparationVOf input for -
the computer program described in Appendix B. A suggested input form, com-
pleted, and the corresponding paper tapeiinformation are shown, followed
by a sample printout from a cdmputer run. B |

Table C-1 shows a suggested input form for HEATXE,with-data entered
for two sample cases. Note that the given units are ndt completely con~
sistent but are specified for convenience. Conversibn to a'éonsiStent
set is performed internally by the program. :

For each item specified in the column headed "DAT(I)", the correspond-
ing "I" must be given. Also, the pairsrof input'numbers specified must
agree with the corresponding number at the top of the form. Note that for
the first case a complete set of input (the first 19 items) must be given.
The initial case number need not be specified, in which case the program
will start with "one", incrémenting by unity for each sucéeeding'case.

For all cases after the first, only those items differing from the
immediately preceding case need'bé changed. Note that if item 20, "Case
Number", is specified, the normal sequence of consecutive case nunmbers
is interrupted, continuing with the new value.

A normal termination of the computer run is obtained by specifying
"NIN", the pairs of input numbers, to be zero or negative. If "NIN" is
omitted, inadvertently or otherwise, an abnormal termination will occur,
with an error message that may be disregarded. |

Table C-2 is a printout of a paper tape prepared from the specificé—
tions of Table C-1. The line numbers shown are not essehtial; the exist-
ing program ends at line T05, so that any greater line number will suffice
for starting the tape. It is suggested that an initial line number of
roughly 800 or greater be used for input to allow for possible program
eXpansion.

The input is free-form, i.e., the numbers fiay be typed in any con-
venient form (note the mixture of exponential, fixed-point, and integer

forms) with as many or as few numbers per line as convenient. It may be
 

 

 

 

v

49

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pairs of Input Numbers _ 19 5 0
" Quantity Units | I DAT(I) 1 DAT(I) DAT(1)
Beat Load Btu/hr 1 | 1.2 | |
Shell Side: -
Pressure Drop Psi 2 100
Inlet Temperature | OF 3 1500
Outlet Temperature. | °F | ¥ | 1050
Fluid Specific Heat | Btu/1b °F 5 .32k
" viscosity Ib/hr £t 6 23.5
| " Conductivity | Btu/br £t °F | 7 .58
" Density o/te° 1 8 | 208
Tube Side:
Pressure Drop Psi .9 100
Inlet -'I‘emperature Op 10 950
Outlet Temperature | °F 11 | 1200
Fluld Specific Heat | Btu/1b °F - | 12 . 12 437
" Viscosity Ib/hr £t | 13 1.95 13 12.6
"  Conductivity | Btu/hr £t OF | 1 " .266 1h 2,66
" Demsity w/ee> |15 | ng 15| 13
Tubes:
- 0. D. In s .3125
Wall Thickness In , _117'.- | 023
" Conductivity |Btu/br ££°F | 18.] 1.5
" Density /e’ g | sm
| Case Number .. el ; 20 | 19

 

© Teble C-1. Input Farm for EEATX2, Shoving Semple Input for Two Cases.
 

 

>0

800 19 .

801 1.25E9 '

802 2 100 3 1300 4 1050 S +324 6 23.5 7 «58 8 208

803 9 100 10 950 11 1200 12 «36 13 195 14 266 15 119
BO4 16 «3125 17 023 18 11.5 19 531

805 5 -

806 12 437 13 126 14 2.66 15 132

807 20 19 _

- 808 0

Teble C-2, Printout of Paper Tepe Prepasred from Data of Té,blé C-1.

-
 

 

 

uy

 

ol

seen by comparing Tables C-1 and C-2 that the partlcular grouping used

puts similar items on one line.
The results of a computer run; uSing the input tape of Table C-2,
are shown in Table C-3. The program spaces the printouts to give two

cases per page,

 
 

CASE 1
HEAT TUBE TUBE
LBAD QeDeo WALL
BTU/HR IN IN

1.252E+09 «3125  «0230

P DROP T IN T 2UT
PS1 F F

52

TUBE TUBE TUBE

IeDe K DENSITY
IN BTUWHR FT F LE/FTt3

2665 1150 531.0

SP. HEAT VISCOS'Y CONDUCTIV'Y
BTWLB F LB/HR FT BTU/HR FT F

FUEL: 100, 1300. 1050. 2324 23.50 58
SALT: 100. 950. 1200. «360 1.95 27
NUMBER TUBE TUBE EQUIV. VBLUMES BUNDLE

OF TUBES LENGTH SPACING DIAM'R FUEL SALT TUBE WEIGHT

FT IN
4944. 31.5- +4106

LMTD WALL DT

F F
100.0 177 FUEL?: -
SALT:
FLEW RATIO FLOWS
GT/GS LB/HR FTt2
11179 FUEL: 6+4973E+06

SALT: 7.2632E+06

CASE 19
REAT TUBE TUBE
LeAD BeDeo WALL
BTU/HR IN IN

1252E+09 «3125 « 0230

P DROP T IN T OUT
PS1 F F

IN FTt+3 FT*3 FT*3 LB

«2823 T4.9 603 2246 34757,

FILM DT C@EFFICIENT

F BTU/HR FTt2 F
47.0 2091.
35.2 3271.

VEL@CITIES PUMPING REYN@LDS

FT/SEC HP NUMBERS
8.7 S40. 6504.
17.0 E50. 82720,
TUBE TUBE TUBE
I.D. K DENSITY
IN BTU/HR FT F LB/FTt3
«2665 1150 531.0

SPe HEAT VISC@S'Y CONDUCTIV'Y
BTU/LB F LB/HR FT BTU/HR FT F

FUEL: 100. 1300. 1050. 0324 23.50 « 58
SALT: 100. 950. 1200. « 437 12.60 2566
NUMBER TUBE TUBE EOUIV. VOLUMES BUNDLE

OF TUBES LENGTH SPACING DI
FT IN
4444. 28.1 <4132

LMTD WALL DT

F F
"100.0 22.1 FUEL:
SALT:
FLEW RATI® FLOWS
GT/GS LB/HR FTt2
« 9456 FUEL: 7.0404E+06

SALT: 6«65TS5E+06

Table C-3. Computer Printout of Results for Input Data of Table C-1,

AM'R FUEL SALT TUBE WEIGHT
IN FTt+3 FT*+3 FTt3 LB

«2899 617 48.4 18B.2 28871,

FILM DT C@EFFICIENT

F BTU/HR FTt2 F
55.2 e2isg.

227 6324,

VEL@CITIES PUMPING REYNOLDS

FT/SEC HP NUMBERS
9.4 540. 7237
14.0 631e. 11734.

\

DENSITY .

LB/FTt3
208.0
119.0

DENSITY
LB/FT*3
208.0
132.0

ah
 

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- 100-101.

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53

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W. L. Smalley, AEC-CRO
Division of Technical Information Extension (DTIE)V

Laboratory and University Division, ORO

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I. Lundin ' - -

Director, Division of Reactor_Llcensing, AEC, Washington
Director, Division of Reactor Standards, AEC, Washington
Executive Secretary, Advisory Committee on Reactor Safeguards